Digital Control Techniques for Grid-Connected Inverters

AIN SHAMS UNIVERSITY FACULTY OF ENGINEERING Electronics and Communications Engineering Department

Digital Control Techniques for Grid-Connected Inverters A Thesis Submitted in partial fulfillment of the requirements of the degree of Master of Science in Electrical Engineering Submitted by Ahmed Abd Al-Rahman Ahmed B.Sc. of Electrical Engineering (Electronics and Communications Engineering) Thebes High Institute of Engineering, 2008 Supervisors: Prof. Dr. Abdel Haleem Zekry Dr. Ahmed Ali Al-Shazly Cairo, 2013

Judgment Committee Name: Ahmed Abd Alrahman Ahmed Abd Alrazek Thesis: Digital control techniques for grid-connected inverters Degree: Master of Science in Electrical Engineering

Title, Name and Affiliation

Signature

Prof. Dr. Mohamed Abd El-Monem Abou El-Ela (Professor in Faculty of Engineering, Future University)

.........................................

Prof. Dr. Wagdy Refaat Anis (Professor in Faculty of Engineering, Ain-shams University)

.........................................

Prof. Dr. Abdelhalim Abdelnaby Zekry (Professor in Faculty of Engineering, Ain-shams University)

Date: /

/

.........................................

STATEMENT This dissertation is submitted to Ain Shams University for the degree of Master of Science in Electrical Engineering (Electronics and Communications Engineering). The work included in this thesis was carried out by the author at the Electronics and Communications Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt. No part of this thesis was submitted for a degree or a qualification at any other university or institution. Name: Ahmed Abd Alrahman Ahmed Signature: Date:

Curriculum Vitae Name of Researcher

Ahmed Abd Alrahman Ahmed Abd Alrazek

Date of Birth

18/4/1986

Place of Birth

Egypt

First University Degree

B.Sc. in Electrical Engineering

Name of University

Thebes High Institute of Engineering

Date of Degree

June 2008

ABSTRACT Ahmed Abd Alrahman Ahmed, Digital control techniques for grid-connected inverters, Master of Science dissertation, Ain Shams University, 2013. This thesis demonstrates the design of a control algorithm for the grid-connected inverter, which is considered an important section in renewable-energy conversion systems. The thesis is arranged into four main parts: Firstly, the main hardware topologies of the renewable-energy conversion systems are presented. Then the block diagram of the grid-connected inverter and its control objectives are discussed. Secondly, this thesis introduces a comprehensive study of the three-phase grid-connected inverter with grid side controller. Initially, the stand-alone three-phase inverter is discussed. This is followed by a presentation of the mathematical model of the grid-connected inverter. After that, the possible current control strategies for the grid-connected inverter are studied. Then the PWM techniques of the three-phase inverter are addressed. After that, the synchronization algorithms for the grid-connected inverter are introduced. Finally, a discussion of grid filters topologies for interfacing the distributed generation with national electricity grid is provided. Thirdly, the stand-alone and the grid-connected inverter systems are modeled based on the theoretical basics presented in the previously. These systems are then simulated to verify the effectiveness of its control structure and to determine its performance parameters using PSIM simulation package. Finally, complete experimental versions for both the stand-alone and the grid-connected inverter are presented. The major differences between the simulation model and the experimental version are clarified.

Keywords: grid-connected inverter, synchronous PI controller, SVM, PLL.

SUMMARY Ahmed Abd Alrahman Ahmed, Digital control techniques for grid-connected inverters, Master of Science dissertation, Ain Shams University, 2013. This thesis demonstrates the different issues of implementing a control algorithm for the grid-connected inverter. The thesis is divided into four chapters organized as follows: Chapter One: is an introduction to renewable-energy and its applications. A brief review on the state of the contribution of renewable-energy sources like solar energy, wind energy, and biomass in the Egypt strategy of energy are presented. In addition, it discusses the structure of distributed generation systems. Moreover, the hardware topologies of PV systems and wind turbines systems for grid connection are presented. Finally, the block diagram of the grid-connected inverter, which is the goal of the thesis, is provided and its parts are showed. Chapter Two: presents a comprehensive study of the three-phase grid-connected inverters. Firstly, the basic construction of the three-phase inverter is introduced. Secondly, the mathematical model of the grid-connected inverter is presented. The closed loop current control techniques are studied, namely: hysteresis current controller, predictive controller, and linear PI controller. Then their performances are compared. It is found that the linear PI controller is more suitable for the grid-connected inverter application, since it offers an excellent steady-state response with zero steady-state error, low current ripple, and highly sinusoidal waveform to the grid-connected inverter. In addition, the controller is insensitive to system parameters since the algorithm does not need system models. Thirdly, the most common PWM techniques are addressed, and then the SPWM and SVM along with a comparison between them are discussed. The SVM is chosen for the gridconnected inverter application because SVM has many advantages such as constant switching frequency, well-defined output harmonic spectrum, optimum switching patterns, and excellent dc-link voltage utilization. Fourthly, the importance of the synchronization, for control purposes, of a grid-connected power generation system is presented. In addition, it is reported that several synchronization algorithms are capable of detecting the phase angle of the grid voltage, namely: zero crossing

detection, filtering of grid voltages, and PLL technique. It is concluded that the PLL is the best choice for the grid-connected inverter application. This is because the PLL can successfully detect the phase angle of the grid voltage even when noise or higher-order harmonics exist in the grid voltage. Finally, the grid filter that is used in the connection of an inverter to the utility grid is discussed. Three types of grid filter are addressed, namely: Lfilter, LC-filter, and LCL-filter. The LCL-filter is chosen for the grid-connected inverter application, since it is effective in the reduction of switching frequency harmonics of the power inverter. In addition, it reduces the dependence of the filter on the grid parameters. Chapter Three: in this chapter, the stand-alone and the grid-connected inverter systems are modeled based on the theoretical basics presented in the previous chapter. These systems are then simulated to verify the effectiveness of its control structure and to determine its performance parameters using PSIM simulation package. In the first part, a model for the stand-alone three-phase inverter is developed. The gating signals for 180º conduction are simulated, and the simulated output waveforms of the three-phase inverter are shown. In the second part, the SVM algorithm for three-phase inverter is simulated. The four steps that are used to implement the SVM algorithm are analyzed, and its results are given. In addition, the simulated output waveforms of the three-phase inverter with SVM are shown. In the final part, a model for the grid-connected three-phase inverter is constructed, and the parasitic elements of the constituting power components are taken into consideration. This simulation model includes the current controller, SVM, grid-filter, and PLL. All simulation results validate the theoretical studies performed in chapter 2. Chapter Four: presents complete experimental versions for both the stand-alone and the grid-connected inverter. The major differences between the simulation model and the experimental version are clarified. In the first place, the stand-alone inverter is implemented and tested. Then the experimental results are presented. All experimental results validate the theoretical and simulation studies that are done in chapter 2 and chapter 3, respectively. In the second place, a comprehensive implementation of the three-phase grid-connected inverter is introduced. The experimental results are shown after testing every part of this circuit. Additionally, the differences between the simulation and the experimental results are analyzed. Agreements are found between the simulation and experimental results when the

parasitic resistances of the power components of the inverter circuit are taken into consideration. Finally, the thesis ends by extracting conclusions and stating future work that might be done based on this work.

ACKNOWLEDGEMENT ‫ﺍﻟﺤﻤﺪ ﻟ ﺭﺏ ﺍﻟﻌﺎﻟﻤﻴﻦ‬ I would like to take the opportunity to acknowledge the direct and indirect help of many people who made this thesis possible. I would like to express my sincere appreciation to Prof. Dr. Abdel Haleem Zekry and Dr. Ahmed Al-shazly for their continuous support and valuable guidance. Prof. Dr. Abdel Haleem Zekry was always giving me valuable advices that help me not only in my thesis, but also in my life. I would like to thank my parents, Eng. Abd Al-Rahman and Eman, without their help, this degree would not have been possible. Moreover, I would like to thank my brothers, Eng. Mahmoud, Eng. Mohannad, and my little sister Mena Allah. I would like also to thank Dr. Ahmed Eldessouky for his support and encouragement. Additionally, I especially want to thank Dr. Noha Ghuneimi. Her assistance and advice was a tremendous help. Many thanks go to my colleagues and friends for their support and help during my thesis. Special thanks for Eng. Omar Abdal rehim, Eng. Ahmed Asmat, Eng. Mohamed Hawary, Eng. Allam Shehata, Eng. Mahmoud Alaa, and Eng. Amin Alsaied.

Ahmed Abd Alrahman November 2012

List of Contents LIST OF FIGURES.................................................................................................................................. IV LIST OF TABLES .................................................................................................................................. VII LIST OF SYMBOLS .............................................................................................................................. VIII LIST OF ABBREVIATIONS ..................................................................................................................... IX CHAPTER 1

RENEWABLE ENERGY AND ITS APPLICATIONS ................................................................. 1

1.1

INTRODUCTION ............................................................................................................................... 1

1.2

RENEWABLE ENERGY APPLICATIONS IN EGYPT ....................................................................................... 1

1.2.1

WIND ENERGY...................................................................................................................................... 2

1.2.2

SOLAR ENERGY ..................................................................................................................................... 2

1.2.2.1

Solar Thermal Technologies .......................................................................................................... 2

1.2.2.2

Photovoltaic (PV) Technology ....................................................................................................... 2

1.2.3 1.3

BIOMASS TECHNOLOGIES ....................................................................................................................... 3 RENEWABLE ENERGY GENERATION SYSTEMS ......................................................................................... 3

1.3.1

HARDWARE STRUCTURE FOR GRID-CONNECTED PV SYSTEMS ....................................................................... 4

1.3.2

HARDWARE STRUCTURE FOR GRID-CONNECTED WT SYSTEMS...................................................................... 6

1.4

GRID-CONNECTED INVERTER BLOCK DIAGRAM ..................................................................................... 10

1.5

SUMMARY ................................................................................................................................... 11

CHAPTER 2

THE THEORY OF THE GRID-CONNECTED THREE-PHASE INVERTER .................................. 13

2.1

INTRODUCTION ............................................................................................................................. 13

2.2

THE THREE-PHASE INVERTER............................................................................................................ 13

2.3

MATHEMATICAL MODEL OF THE GRID-CONNECTED INVERTER ................................................................. 17

2.4

THE CONTROL THEORY OF THE GRID-SIDE INVERTER ............................................................................. 19

2.4.1

HYSTERESIS CURRENT CONTROLLER ....................................................................................................... 22

2.4.2

PREDICTIVE CURRENT CONTROLLER ....................................................................................................... 23

2.4.3

LINEAR PI CURRENT CONTROLLER .......................................................................................................... 23

2.4.4

COMPARISON BETWEEN THE THREE CURRENT CONTROLLERS ..................................................................... 26

2.5

PULSE WIDTH MODULATION TECHNIQUES .......................................................................................... 28

I

2.5.1

SINUSOIDAL PWM .............................................................................................................................. 28

2.5.2

SPACE VECTOR MODULATION ............................................................................................................... 30

2.5.3

COMPARISON BETWEEN SPWM AND SVM............................................................................................. 33

2.6

GRID SYNCHRONIZATION ................................................................................................................. 34

2.6.1

ZERO CROSSING DETECTION .................................................................................................................. 35

2.6.2

FILTERING OF GRID VOLTAGES ............................................................................................................... 35

2.6.3

PHASE-LOCKED LOOP (PLL) .................................................................................................................. 36

2.7

GRID FILTER ................................................................................................................................. 37

2.7.1

L‐FILTER ............................................................................................................................................ 37

2.7.2

LC-FILTER .......................................................................................................................................... 38

2.7.3

LCL-FILTER ......................................................................................................................................... 38

2.8

SUMMARY ................................................................................................................................... 39

CHAPTER 3

SYSTEM SIMULATION .................................................................................................... 41

3.1

INTRODUCTION ............................................................................................................................. 41

3.2

SIMULATION OF THE STAND-ALONE THREE-PHASE INVERTER .................................................................. 41

3.3

SIMULATION OF SVM..................................................................................................................... 44

3.3.1

STEP 1, COMPUTATION OF UΑ, UΒ, UREF, AND ANGLE (Θ) ............................................................................ 45

3.3.2

STEP 2. SECTOR DETERMINATION .......................................................................................................... 47

3.3.3

STEP 3. CALCULATION OF TIME DURATION T1, T2, T0, AND T7..................................................................... 48

3.3.4

STEP 4. SWITCHING TIME DETERMINATION OF EACH TRANSISTOR (SW1 TO SW6). ......................................... 48

3.4

SIMULATION OF GRID-CONNECTED THREE-PHASE INVERTER ................................................................... 53

3.4.1

SIMULATION OF PLL SYNCHRONIZATION CIRCUIT ...................................................................................... 54

3.4.2

SIMULATION OF CURRENT CONTROL STRUCTURE FOR THE GRID-CONNECTED INVERTER .................................. 56

3.5

SUMMARY ................................................................................................................................... 61

CHAPTER 4

SYSTEM IMPLEMENTATION ........................................................................................... 63

4.1

INTRODUCTION ............................................................................................................................. 63

4.2

IMPLEMENTATION OF THE STAND-ALONE THREE-PHASE INVERTER ........................................................... 63

4.2.1

THREE-PHASE POWER INVERTER CIRCUIT ................................................................................................ 64

4.2.2

THE CONTROL CIRCUIT ......................................................................................................................... 68

4.2.3

EXPERIMENTAL DATA FOR THE STAND-ALONE THREE-PHASE INVERTER ........................................................ 71

II

4.3

IMPLEMENTATION OF THE GRID-CONNECTED THREE-PHASE INVERTER ...................................................... 75

4.3.1

THE POWER INVERTER CIRCUIT ............................................................................................................. 76

4.3.2

AUXILIARY POWER SUPPLIES ................................................................................................................. 76

4.3.3

EXTERNAL SENSORS BOARD .................................................................................................................. 76

4.3.3.1

Current Measurement Circuit ..................................................................................................... 77

4.3.3.2

Voltage Measurement Circuit ..................................................................................................... 78 THE INVERTER CONTROL DESIGN ........................................................................................................... 81

4.3.4 4.3.4.1

Hardware of Inverter Control Board ........................................................................................... 81

4.3.4.2

Firmware of dsPIC Microcontroller ............................................................................................. 83

4.3.4.3

PC Based Control Software.......................................................................................................... 89

4.3.5 4.4

EXPERIMENTAL DATA FOR THE GRID-CONNECTED THREE-PHASE INVERTER .................................................. 90 SUMMARY ................................................................................................................................... 96

CONCLUSIONS & FUTURE WORK ........................................................................................................ 98 BIBLIOGRAPHY................................................................................................................................. 101 EXTRACTED PAPER ........................................................................................................................... 106 APPENDIX A

COORDINATE TRANSFORMATION ............................................................................ 107

I.

CLARK TRANSFORMATION ................................................................................................................ 107

II.

PARK TRANSFORMATION ................................................................................................................ 108

APPENDIX B

SOFTWARE SOURCE CODE ........................................................................................ 110

I.

FIRMWARE FOR THE THREE-PHASE INVERTER ....................................................................................... 110

II.

FIRMWARE FOR THE GRID-CONNECTED INVERTER................................................................................. 116

III.

PC BASED CONTROL SOFTWARE SOURCE CODE .................................................................................. 128

III

List of Figures Fig. 1.1, Hardware structure for a PV system using a dc–dc stage to boost the input voltage. ...... 4 Fig. 1.2, Hardware structure for a PV system using step-up transformer. ...................................... 5 Fig. 1.3, Main components of the wind generation system ............................................................ 6 Fig. 1.4, WT systems using power electronic ................................................................................. 8 Fig. 1.5, Generalized power electronics converter for wind systems ............................................. 9 Fig. 1.6, Block diagram of grid-connected inverter ...................................................................... 10 Fig. 2.1, Three phase inverter circuit ............................................................................................ 14 Fig. 2.2, Gating signals and output line-to-line voltages of three-phase VSI ............................... 16 Fig. 2.3, output line-to-neutral voltages of three-phase VSI......................................................... 16 Fig. 2.4, Model of grid-connected inverter ................................................................................... 17 Fig. 2.5, Basic block diagram of current controlled PWM converter. .......................................... 20 Fig. 2.6, (a) Controller with open-loop PWM block. (b) On-off controller. ................................ 21 Fig. 2.7, Block diagram of HCC strategy for a three-phase grid-connected PWM VSI. ............. 22 Fig. 2.8, General structure for synchronous reference frame control structure [9]. ..................... 26 Fig. 2.9, Block scheme of carrier based sinusoidal PWM ............................................................ 29 Fig. 2.10, Basic waveforms of carrier based sinusoidal PWM ..................................................... 29 Fig. 2.11, Six active vectors and two null vectors in SVM. ......................................................... 30 Fig. 2.12, Block scheme of the space vector modulator ............................................................... 31 Fig. 2.13, Output pulses based on Symmetrical Sequence algorithm in sector ............................ 31 Fig. 2.14, Synchronization method using filtering on the synchronous frame. ............................ 35 Fig. 2.15, Synchronization method using filtering on the stationary frame. ................................ 36 Fig. 2.16, Basic structure of a PLL system for grid synchronization. .......................................... 36 Fig. 2.17, Filter configuration circuits .......................................................................................... 37 Fig. 3.1, Simulation circuit of stand-alone three phase inverter ................................................... 42 Fig. 3.2, Simulation of the gating signals of the stand-alone three-phase inverter ....................... 42 Fig. 3.3, Simulation waveforms of line-to-neutral voltage of the stand-alone three-phase inverter .......................................................................................................................................... 43 Fig. 3.4, Simulation waveforms of line-to-line voltage of the stand-alone three-phase inverter . 43 Fig. 3.5, Simulation circuit of the three-phase inverter with SVM............................................... 44 IV

Fig. 3.6, Simulation circuit for Determination Vα, Vβ, Vref, and angle (ϑ) ................................... 45 Fig. 3.7, (a) Simulation waveforms of input reference signals. (b) Simulation waveforms of the Uα and Uβ. .............................................................................................................................. 46 Fig. 3.8, Simulation waveform of angle (θ) .................................................................................. 46 Fig. 3.9, Simulation circuit of sector determination ..................................................................... 47 Fig. 3.10, Simulation waveform of sector allocation .................................................................... 47 Fig. 3.11, Simulation circuit of time interval calculation ............................................................. 48 Fig. 3.12, Simulation circuit for transistors switching time calculation ....................................... 49 Fig. 3.13, SVM switching patterns at each sector......................................................................... 50 Fig. 3.14, The overall simulation circuit of SVM algorithm ........................................................ 51 Fig. 3.15, The gating signals for sector 1...................................................................................... 52 Fig. 3.16, The simulation output phase-to-neutral voltage of three-phase inverter with SVM .... 52 Fig. 3.17, The simulation output of phase-to-phase voltages of three-phase inverter with SVM .............................................................................................................................................. 53 Fig. 3.18, Simulation model of the grid-connected inverter ......................................................... 54 Fig. 3.19, The grid phase angle and the output voltage on 50Hz grid .......................................... 55 Fig. 3.20, The grid phase angle and the output voltage on 40Hz grid .......................................... 55 Fig. 3.21, The grid phase angle and the output voltage on 60Hz grid .......................................... 56 Fig. 3.22, PI controller tuning with setting Ki to 0 and Kp=Kcr . .................................................. 57 Fig. 3.23, Id current reference and measured................................................................................ 58 Fig. 3.24, Iq current reference and measured................................................................................ 58 Fig. 3.25, Simulation result of phase grid current Ia. ................................................................... 59 Fig. 3.26, Simulation result of three-phase grid currents (ia, ib, ic). ............................................ 59 Fig. 3.27, Inverter phase voltage at the input of the filter............................................................. 60 Fig. 3.28, Inverter phase voltage considering ideal transistors. .................................................... 60 Fig. 3.29, Inverter phase voltage considering non-ideal transistors after step-up transformer ..... 61 Fig. 4.1, Circuit diagram of power circuit of the inverter ............................................................. 65 Fig. 4.2, IR2110 typical connection .............................................................................................. 66 Fig. 4.3, The PCB of the three-phase inverter power circuit ........................................................ 67 Fig. 4.4, The control circuit of three phase inverter...................................................................... 69 Fig. 4.5, Software flowchart of stand-alone three-phase inverter part-1 ...................................... 70 V

Fig. 4.6, Software flowchart of stand-alone three-phase inverter part-2 ...................................... 71 Fig. 4.7, The gating signal for sw1on CH1and the shifted by 60º signal for sw6 on CH2 ........... 72 Fig. 4.8, The gating signal for sw1on CH1and the shifted by 120º signal for sw2 on CH2 ........ 72 Fig. 4.9, The gating signal for sw1on CH1and the shifted by 180º signal for sw4 on CH2 ......... 73 Fig. 4.10, The gating signal for sw1on CH1and the shifted by 240º for sw3 on CH2 ................. 73 Fig. 4.11, The gating signal for sw1on CH1and the shifted by 300º signal for sw5 on CH2 ....... 74 Fig. 4.12, Snapshot of phase-to-neutral output voltage three-phase inverter ............................... 74 Fig. 4.13, Snapshot of phase-to-phase output voltage three-phase inverter. ................................ 75 Fig. 4.14, Schematic diagram of grid-connected inverter ............................................................. 75 Fig. 4.15, current sensors circuit ................................................................................................... 77 Fig. 4.16, oscilloscope screenshot of current measurement circuit output for two phases. .......... 78 Fig. 4.17, Voltage measurement circuit ........................................................................................ 79 Fig. 4.18, Oscilloscope screenshot of voltage measurement circuit output for two phases. ........ 80 Fig. 4.19, Output of voltage sensor on CH1 and grid voltage on CH2......................................... 80 Fig. 4.20, Circuit diagram of grid connected inverter control board ............................................ 82 Fig. 4.21, dsPIC software flow chart (The main routine) ............................................................. 86 Fig. 4.22, dsPIC software flow chart (The SVM routine) ............................................................ 87 Fig. 4.23, dsPIC software flow chart ( PWM interrupt service routine) ....................................... 88 Fig. 4.24, dsPIC software flow chart ( ADC interrupt service routine) ........................................ 89 Fig. 4.25, Screenshot of PC software for inverter control ............................................................ 90 Fig. 4.26, The output pulses for two transistors S1 and S3 .......................................................... 92 Fig. 4.27, The measured voltage signal on CH1 and the generated pulses on CH2. .................... 92 Fig. 4.28, The generated pulses from microcontroller on CH1 and pulses after driver IC on CH2 ............................................................................................................................................... 93 Fig. 4.29, The output pulses for two complementary transistors S1 and S4................................. 93 Fig. 4.30, The dead time that inserted between two complementary transistors S1 and S4 ......... 94 Fig. 4.31, Experiment waveform of the phase-to-neutral voltage of grid-connected inverter...... 94 Fig. 4.32, Experiment waveform of the phase-to-phase voltage of grid-connected inverter........ 95 Fig. 4.33, Experimental waveform of the output phase voltage and the grid voltage .................. 95 Fig. A.1, Clark Transform for current......................................................................................... 107 Fig. A.2, Park transform for current ........................................................................................... 109 VI

List of Tables Table 2.1, switches states of three-phase VSI............................................................................... 15 Table 2.3, Comparison between the three current controllers ...................................................... 27 Table 2.2, Comparison between SPWM and SVM ...................................................................... 34 Table 3.1, Switching Time Calculation at Each Sector ................................................................ 49 Table 4.1, dsPIC30F peripheral usage .......................................................................................... 84 Table 4.2, Source code files .......................................................................................................... 85

VII

List of Symbols E

The peak value of the grid voltage

ea,b,c

Phase Voltages of the grid

Ɛa,b,c

The three-phase error signals in current controller

ed,q

Phase Voltages of the grid in synchronous dq reference frame

eα,β

Phase Voltages of the grid in stationary αβ reference frame

f

Grid frequency

Fs

The sampling frequency

Fsn

The number of samples

ia,b,c

The output phase currents of the inverter

L

The inductance between the inverter and grid

R

The resistance between the inverter and grid

SA,B,C

The switching signals for the three-phase inverter

T0,1,2,7

Time-shares of voltage vectors in SVM

Ts

Sampling time

U0→7

Voltage Space Vectors

ua,b,c

The output phase voltages of the inverter

ud,q

The output phase voltage of the inverter in synchronous dq reference frame

Udc

Input DC voltage to the inverter

Uref

Reference Space vectors

Ut

Triangular Carrier Signal

uα,β

The output phase voltage of the inverter in stationary αβ reference frame

θ

The grid angle

ω

The angular frequency of the grid

ωff

The utility nominal frequency

VIII

List of Abbreviations AC

Alternate Current

ADC

Analog-to-Digital Converter

CC

Current Controlled

CPU

Center Processing Unit

DC

Direct Current

DPGS

Distributed Power Generation System

DSC

Digital Signal Controller

DSP

Digital Signal Processor

HCC

Hysteresis Current Control

I2C

Inter-Integrated Circuit

LED

Light Emitted Diode

MIPS

Mega Instruction Per Second

MOSFET

Metal Oxide Semiconductor Field Effect Transistor

MPPT

Maximum Power Point Tracking

MW

Mega watt

PC

Personal Computer

PCB

Printed Circuit Board

PI

Proportional Integral

PLL

Phase Locked Loop

PV

Photovoltaic

PWM

Pulse Width Modulation

SCIG

Squirrel-Cage Induction Generator

SPI

Serial Peripheral Interface

SPWM

Sinusoidal Pulse Width Modulation

SVM

Space Vector Modulation

THD

Total Harmonic Distortion

TWh

Terawatt Hour

UART

Universal Asynchronous Receiver/Transmitter

VCO

Voltage Controlled Oscillator IX

VSI

Voltage Source Inverters

WT

Wind Turbines

X

Chapter 1

Renewable Energy and its Applications

Chapter 1 Renewable Energy and its Applications 1.1 Introduction Fossil fuels and hydropower along with non-commercial fuels such as firewood are considered the main energy resources in Egypt. Nowadays, oil and natural gas are the most significant Fossil fuel energy sources in Egypt and will be for several years in the future. The Nile's hydropower is considered the third major supplier of energy, but most of its hydropower potential has already been used to generate about 13 TWh of electricity per annum [1]. Because of the growing demand in fossil fuel resources and the resulting environmental effects, Egypt’s energy strategy aims to increase the reliance on renewable energy sources, particularly wind and solar power. Consequently, the national energy plan aims to achieve 20% of total generated electricity from renewable energy sources by the year 2020 including 12% from wind energy. This expected to be achieved through establishing grid-connected wind farms and solar photovoltaic (PV) systems. This chapter begins with a brief review of the commercially exploited renewableenergy applications in Egypt. Then, the renewable-energy generation systems for both PV systems and wind turbines (WT) systems are presented. Finally, the block diagram of the grid side converter and its control is introduced.

1.2 Renewable Energy Applications in Egypt Egypt is endowed with different renewable-energy resources, especially wind and solar energies. This section presents the renewable-energy resources potential in Egypt, their status, and government policies to developing renewable-energy technology [1].

1

Chapter 1


1.2.1 Wind Energy Wind turbines convert kinetic energy in the wind into mechanical power that can be converted into electrical energy using a generator. Wind Atlas of Egypt concluded that there are many promising areas with high wind speeds in the Gulf of Suez, some areas located on both sides of the Nile River, and some areas in Sinai. These areas are qualified for the establishment of large-scale wind energy projects. At the end of 2010, some of wind energy projects have been established like Zafarana 545 MW Wind Farm, and 5 MW Wind Farms in Hurghada. Moreover, it is planned to implement wind energy projects with total capacities of 2370 MW as part of the national strategy to promote wind energy. 1.2.2

Solar Energy Solar technologies use the energy of the sun directly, and then it produces heat, light,

and power. Egypt is considered one of the countries that located in “sunbelt” area and most suitable for solar-energy applications. The solar Atlas of Egypt shows that the average direct normal solar radiation is 2000 – 3200 kWh/m2/year. In addition, the sunshine duration ranges between 9 – 11 h/day, which means that Egypt is suitable for solar-energy applications. 1.2.2.1 Solar Thermal Technologies Solar Thermal technologies are identified to be among the main renewable-energy technology options that can make an impact in achieving the strategy targets. Intensive efforts are directed mainly at three options: •

Solar thermal water heating that is used for domestic and commercial sectors.

•

Solar thermal systems that is used in industrial process heat.

•

Solar thermal systems that is used for electricity generation.

1.2.2.2 Photovoltaic (PV) Technology Photovoltaic (PV) technology involves converting solar energy directly into electrical energy by a solar cell. A solar cell is typically made of semiconductor materials such as 2

Chapter 1


crystalline silicon that absorbs sunlight and produces electricity through a process called the photovoltaic effect. In spite of being an expensive technology, Photovoltaic systems are considered the most appropriate energy application for rural and remote areas of small-scattered loads, which are far away from the national grid. The cost of PV systems maintenance is limited while the PV life span is about 25 years. At the end of 2010, the total capacity of PV systems in Egypt is around 10 MW, for lighting, water pumping, wireless communications, cooling and commercial advertisements on highways. Solar projects are considered one of the main aspects to increase the contribution of the renewable-energy the national energy plan. Consequently, the five-year plan (2012 2017) includes: •

Solar thermal plants of electricity generation provide total capacity of 100 MW.

•

Photovoltaic plants provide total capacity of 20 MW.

1.2.3

Biomass Technologies Biomass, as a renewable-energy source, is a biological material from living or

recently living organisms such as dead trees and agricultural wastes. As an energy source, biomass can either be used directly or converted into other energy products such as bio-fuel. In Egypt, the total biomass resources potential reach 40 million Ton / year. Therefore, many small-scale research projects are implemented to use this technology.

1.3 Renewable Energy Generation Systems The power-generation systems that based on renewable-energy sources like photovoltaic, and wind turbines can be either in centralized systems or in distributed power generation systems (DPGSs). In the centralized power plants, the electricity is generated at a remotely located, large-scale power plant, and then it transmitted to the consumer through the power lines. On the other hand, the DPGSs are small-scale power generation technologies (typically in the range of 3 kW to 10,000 kW), which is used to provide an alternative or an enhancement to the traditional centralized power generation system. The DPGS provides

3

Chapter 1


electric power at a site closer to the customer, eliminating the unnecessary transmission and distribution costs. In addition, it is quieter and less polluting than large power plants. The DPGS can be designed either as standalone systems or as grid-connected systems. The stand-alone systems are used in off-grid applications that meet the local demands from electricity in the remote locations [2], [3]. On the other hand, the grid-connected systems are the systems that integrated with the mains power grid, and it can feed the surplus power generated at the utility grid. In this case, the system output voltage and frequency should be the same as that of grid voltage and frequency [4]. Consequently, the control of the gridconnected systems should be improved to meet the requirements for grid interconnection. In [5], it is stated that the control tasks of the grid-connected systems can be divided into two parts: input-side controller and grid-side controller. The control objective on the input-side controller is to capture maximum power from the input source. However, the control objectives on the grid-side controller are to control the power delivered to the grid, ensure high quality of the injected power and grid synchronization. The integration of the renewable-energy sources to the utility grid can be done with the aid of the power electronics converters. These power conversion units have different hardware structures, which are closely related to the input power nature. The following subsections presents an overview on the technologies mostly used today in PV systems and wind turbines systems. 1.3.1

Hardware Structure for Grid-connected PV Systems

Fig. 1.1, Hardware structure for a PV system using a dc–dc stage to boost the input voltage.

4

Chapter 1


In PV system, the output voltage is a constant DC whose magnitude depends on the configuration in which the solar cells/modules are connected. On the other hand, the current output from the PV system primarily depends on the available solar irradiance. Although PV systems have a low-voltage input provided by the PV panels, more such units can be connected together to obtain the required voltage and power level. In this case, it called PV arrays. The main requirements of power electronic interface units for the PV systems are to convert the generated DC voltage into a suitable AC for utility connection. As shown in Fig. 1.1, the DC voltage magnitude of the PV array is required to be boosted to a higher value by using DC-DC converters before converting them to the utility compatible AC. The DC-AC inverters are then utilized to convert the output voltage from the DC-DC converter into AC voltage. To meet the requirements for grid interconnection, the inverter output voltage and frequency should be the same as that of grid voltage and frequency. The process of controlling the voltage and current output of the array must be optimized based on the weather conditions. Specialized control algorithm has been developed called maximum power point tracking (MPPT) used to extract the maximum amount of power from the array under varying conditions. The control objective in the DC-DC converter is to perform the MPPT algorithm and the voltage boosting. However, the control objective in the DC-AC inverter is to control the injected power into the grid and grid synchronization. Nevertheless, this configuration does not have a galvanic isolation between input and output [6], [7].

Fig. 1.2, Hardware structure for a PV system using step-up transformer.

5

Chapter 1


Another configuration is used is shown in Fig 1.2. In this configuration DC-AC inverter and a transformer operated at grid-frequency are used. The transformer is used to boost the voltage magnitude to a higher level, and provide isolation. Moreover, the DC-AC inverter controls the injected power into the grid and performs grid synchronization. The presence of a transformer also leads to a reduction of leakage currents. However, this design has its disadvantages in the form of losses and increased weight and size of the inverter [8]. 1.3.2

Hardware Structure for Grid-connected WT Systems

Fig. 1.3, Main components of the wind generation system

Wind turbines (WT) convert kinetic energy in the wind into mechanical power that can be converted into electrical energy using a generator. As illustrated in Fig 1.3, the main components of the wind-turbine system are the turbine blades, gearbox, generator, transformer, and potential power electronics [6]. In this section, a classification of WT systems in those using and those not using power electronics as an interface to the utility grid is given. Hardware structures in each case will be illustrated to distinguish the systems [5]. [1] WT Systems without Power Electronics: Most of these topologies are based on squirrel-cage induction generator (SCIG), which is directly connected to the grid. A soft starter is usually used to reduce the inrush currents during start up. Moreover, a capacitor bank is necessary to compensate for the reactive power of the machine, as shown in Fig. 1.4(a). [2] WT Systems with Power Electronics: By adding power electronics units into the WT systems, the complexity of the system is increased. In addition, the solution becomes more expensive. Nevertheless, better control of the input power and grid 6

Chapter 1


interaction is obtained. For example, maximum power for a large interval of wind speeds can be extracted while control of both active and reactive powers into the grid is achieved by power electronics. The usage of power electronics into WT systems can be further divided into two categories, namely: 1) system using partial-scale power electronics units and 2) systems using full-scale power electronics units. A particular structure is to use an induction generator with a wounded rotor. An extra resistance controlled by power electronics is added in the rotor, which gives a variable-speed range of 2% to 4%. The power converter for the rotor resistance control is for low voltage but high currents. In any case, this solution also needs a soft starter and a reactive power compensator. Additionally, another solution is to use a medium-scale power converter with a wounded rotor induction generator, as shown in Fig. 1.4(b). In this case, a power converter connected to the rotor through slip rings controls the rotor currents. If the generator is running super-synchronously, the electric power is delivered through both the rotor and stator. If the generator is running sub-synchronously, the electric power is only delivered into the rotor from the grid. A speed variation of 60% around synchronous speed may be obtained using a power converter of 30% of nominal power. By implementing a full-scale power converter between the generator and the utility grid, additional technical performances of the WT system can be achieved, with the payback in losses in the power conversion stage. Normally, as shown in Fig.1.4(c), SCIG is used in this configuration, but an advantage to eliminate the gearbox can be obtained by using multipole wound-rotor synchronous generator or permanent-magnet synchronous generator, as depicted in Fig. 1.4(d).

7

Chapter 1


Fig. 1.4, WT systems using power electronic (a) Minimum electronics unit. (b) Partial power converter. (c) Full-scale power converter structure with gearbox. (d) Full-scale power converter structure without gearbox and using Multi-pole synchronous generator.

8

Chapter 1


The most generalized form of power electronics topology for the wind-energy application is the back-to-back rectifier/inverter connection, which provides the improved power flow control as well as increased efficiency. The voltage-fed converter scheme used in such systems is shown in Fig 1.5. A PWM-based bridge rectifies the variable-frequency variable-voltage power from the wind generator. The rectifier also supplies the excitation needs for the induction generator. The inverter topology is identical to that of the rectifier, and it supplies the generated power at 50 Hz to the utility grid.

Fig. 1.5, Generalized power electronics converter for wind systems

It could be noticed that for interacting with the utility grid, all the structures presented above use two-level pulse-width-modulation (PWM) voltage-source inverters (VSI). This technology is the state-of-the-art that used today by all manufacturers of WT systems and PV systems. The possibility of high switching frequencies combined with a proper control makes these converters suitable for grid interface in the case of distributed generation, which has a large contribution to the improvement of generated power quality. Therefore, the next section presents a discussion on the block diagram of the control structures applied to two-level VSI PWM driven converters, focusing in this thesis on the grid-side inverter control.

9

Chapter 1


1.4 Grid-connected Inverter Block Diagram

Fig. 1.6, Block diagram of grid-connected inverter

As mentioned previously, this thesis demonstrates the different issues of implementing a control algorithm for the grid-connected inverter. The block diagram of the grid-connected inverter system is shown in Fig. 1.6. The main components of this system are: •

Three-phase PWM inverter, which is used to convert the DC–to-AC.

•

Grid Filter, which is used to attenuate the harmonic in the output voltage of inverter.

•

The three phase transformer, which is used to boost the voltage magnitude to a higher level, provide isolation, and prevent DC-current from entering the connected grid.

•

Grid side controller, which is used to control the power delivered to the grid, ensure high quality of the injected power and grid synchronization. A number of papers, such as [9], [10], [11], are dealing with control of the grid side

inverter, which use a current control loop to regulate the grid current. In other works, the control of the grid-connected inverter is based on two cascaded loops: an internal current loop, which regulates the grid current, and an external voltage loop, which is designed for balancing the power flow in the system [5]. Moreover, control strategies employing an outer power controller and an inner current control loop are also reported [12]. The next chapter presents a comprehensive study of the three-phase grid-connected inverter with grid side controller.

10

Chapter 1


1.5 Summary The national energy plan aims to reach 20% of total generated electricity through renewable energy by the year 2020 including 12% from wind energy, in addition to other renewable-energy applications such as solar energy and hydro power. In this chapter, a brief review on the state of the contribution of renewable-energy sources like solar energy, wind energy, and biomass in the Egypt strategy of energy is presented. In addition, the hardware topologies of PV systems and wind turbines systems for grid connection are presented. Finally, the block diagram of the grid-connected inverter, which is the goal of the thesis, is discussed.

11

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter

Chapter 2 The Theory of the Grid-Connected ThreePhase Inverter 2.1 Introduction As explained in the last chapter, most of renewable-energy technology produces a DC power output. An inverter is needed to convert the generated DC power from the renewableenergy source into useful power that can be directly interconnected with the utility grid, and can be used for consumer applications. The control of this inverter should be improved in order to increase the power quality and meet the requirements of grid integration. This chapter presents a comprehensive study of the three-phase grid-connected inverter with grid side controller. Initially, the three-phase inverter is discussed. This is followed by a presentation of the mathematical model for the grid-connected inverter. After that, the possible current control strategies for the grid-connected inverter are introduced. Then the PWM techniques for the three-phase inverter are presented. Additionally, the synchronization algorithms for the grid-connected inverters are addressed. Finally, a discussion of grid filters topologies for interfacing the inverter with national electricity grid is provided.

2.2 The Three-Phase Inverter The inverter is a power electronic-based device that converts the DC input voltage into a symmetric AC output voltage of desired magnitude and frequency [13]. Inverters can be broadly classified into two types: single-phase inverters, and three-phase inverters. Singlephase voltage source inverters (VSIs) cover low-range power applications. This inverter is out of scope in this thesis. On the other hand, the three-phase VSIs cover medium- to highpower applications. The main purpose of three-phase inverter is to provide a three-phase balanced (fundamental) voltage source. As shown in Fig. 2.1, the standard three-phase VSI topology is a configuration of six transistors and six freewheeling diodes [7]. 13

Chapter 2


Fig. 2.1, Three phase inverter circuit

The switches of any leg of the inverter (S1 and S4, S3 and S6, or S5 and S2) cannot be switched ON simultaneously because this will cause a short circuit across the DC link voltage supply. Similarly, in order to avoid undefined states in the VSI, and thus undefined AC output line voltages, the switches of any leg of the inverter cannot be switched OFF simultaneously. Two types of control signals can be applied to the transistors: 180º conduction or 120º conduction. The 180º conduction is preferred method, since it offers better utilization to the transistors. On the other hand, the 120º conduction is out of scope in this thesis, since the transistors are less utilized as compared with those of 180º conduction for the same load condition. In 180 º conduction, each transistor is conduct for 180º. Three transistors remain ON at any instant of time. The gating signals are shifted from each other by 60º to obtain three-phase balanced (fundamental) voltages, as shown in Fig. 2.2. The standard three-phase VSI topology has eight valid switch states are given in Table 2.1. Of the eight valid states, two of them (states 7 and 8 in Table 2.1) produce zero AC line voltages. In this case, the AC line currents freewheel through either the upper or the lower freewheeling diodes. The remaining states (states 1 to 6 in Table 2.1) are producing the non-zero AC output voltages. In order to generate a given voltage waveform, the inverter moves from one state to another. Thus, the resulting AC output line voltages consist of discrete values of voltages those are Udc, 0, and − Udc for the topology shown in Fig. 2.1. The selection of the states in order to generate the given waveform is done by the modulating technique that should ensure the use of only the valid states. The gating signals and the

14

Chapter 2


instantaneous line-to-line voltages are shown in Fig.2.2. Moreover, the line-to-neutral voltages are shown in Fig 2.3. State

State#

S1, S2, and S6 are on and S4, S5, and S3 are off S2, S3, and S1 are on and S5, S6, and S4 are off S3, S4, and S2 are on and S6, S1, and S5 are off S4, S5, and S3 are on and S1, S2, and S6 are off S5, S6, and S4 are on and S2, S3, and S1 are off S6, S1, and S5 are on and S3, S4, and S2 are off S1, S3, and S5 are on and S4, S6, and S2 are off S4, S6, and S2 are on and S1, S3, and S5 are off

uab

ubc

uca

1

Udc

0

- Udc

2

0

Udc

3

4

Udc Udc

Udc

Space vector U1 = 1+j0.577

U2 = j1.155

Udc

0

U3 = -1+j0.577

0

Udc

U4 = -1-j0.577

Udc

U5 = -j1.155

0

U6 = 1-j0.577

-

5

0

6

Udc

7

0

0

0

U7 =0

8

0

0

0

U8 =0

Udc Udc

Table 2.1, switches states of three-phase VSI

15

Chapter 2


Fig. 2.2, Gating signals and output line-to-line voltages of three-phase VSI

Fig. 2.3, output line-to-neutral voltages of three-phase VSI

16

Chapter 2


2.3 Mathematical Model of the Grid-Connected Inverter

Fig. 2.4, Model of grid-connected inverter

In this section, the mathematical model for the grid-connected inverter is presented [11]. As shown in Fig. 2.4, the three-phase grid voltages are represented as follows: 𝑒𝐴 = 𝐸 cos 𝜔𝑡

𝑒𝐵 = 𝐸 cos �𝜔𝑡 −

𝑒𝐶 = 𝐸 cos �𝜔𝑡 +

2𝜋 3

�

Equation 2.1

2𝜋 � 3

where E and ω are the maximum phase voltage and angular frequency of the power source respectively. The system equation in the stationary (ABC) frame can be represented as follows: 𝑑𝑖𝐴

⎡ 𝑑𝑡 ⎤ 1 ⎢𝑑𝑖𝐵⎥ −R = � 0 ⎢ 𝑑𝑡 ⎥ L 0 ⎢𝑑𝑖𝐶 ⎥ ⎣ 𝑑𝑡 ⎦

𝑢𝐴 − 𝑒𝐴 0 0 𝑖𝐴 1 𝑢 1 0� �𝑖𝐵 � + 𝐿 � 𝐵 − 𝑒𝐵 � 𝑢𝐶 − 𝑒𝐶 0 1 𝑖𝐶

Equation 2.2

where iA, iB and iC are the output currents and uA, uB and uC are the output voltages of the grid-connected inverter, L is the inductance between the grid-connected inverter and the grid, R is the resistance between the grid-connected inverter and the grid. As discussed in Appendix A, Clark transformation can be used to convert the three phase stationary (ABC) frame into two-phase stationary (αβ) frame as given in Equation 2.3.

17

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter 1 𝑒𝛼 �𝑒 � = � 𝛽 0

1� 2 √3� 2

−1� 2 𝑒𝐴 −√3� � �𝑒𝐵 � 2 𝑒𝐶

Equation 2.3

According to Equation 2.2 and 2.3, the following equation is obtained:

1 1�2 𝑒𝛼 �𝑒 � = � 𝛽 0 √3�2 =�

𝑑𝑖𝐴 ⎡ 𝑢𝐴 − 𝐿 − 𝑅𝑖𝐴 ⎤ −1� ⎢ 𝑑𝑡 ⎥ 2 𝑑𝑖𝐵 ⎢ − 𝑅𝑖𝐵 ⎥ −√3� � 𝑢𝐵 − 𝐿 𝑑𝑡 ⎢ ⎥ 2 𝑑𝑖𝐶 ⎢ ⎥ 𝑢 − 𝐿 − 𝑅𝑖 𝐶 𝐶 ⎣ ⎦ 𝑑𝑡

𝑢𝛼 − 𝐿 𝑢𝛽 − 𝐿

𝑑𝑖𝛼

𝑑𝑡 𝑑𝑖𝛽 𝑑𝑡

− 𝑅𝑖𝛼 − 𝑅𝑖𝛽

�

Equation 2.4

Moreover, as discussed in Appendix A, Park transformation can be used to transform the stationary (αβ) into the synchronous (dq) frame as given in Equation 2.5. 𝑒𝑑 cos 𝜔𝑡 �𝑒 � = � 𝑞 − sin 𝜔𝑡

sin 𝜔𝑡 𝑒𝛼 �� cos 𝜔𝑡 𝑒𝛽

Equation 2.5

Using Equation 2.4 and 2.5, the following equation is obtained: 𝑒𝑑 cos 𝜔𝑡 �𝑒 � = � 𝑞 − sin 𝜔𝑡

sin 𝜔𝑡 𝑢𝛼 cos 𝜔𝑡 � �𝑢 � − � 𝛽 cos 𝜔𝑡 − sin 𝜔𝑡

𝑢𝑑 cos 𝜔𝑡 = �𝑢 � − � 𝑞 − sin 𝜔𝑡

𝑑𝑖𝛼 𝐿 sin 𝜔𝑡 cos 𝜔𝑡 � � 𝑑𝑡 � − � 𝑑𝑖 cos 𝜔𝑡 − sin 𝜔𝑡 𝛽 𝐿 𝑑𝑡

𝑑 sin 𝜔𝑡 cos 𝜔𝑡 � . 𝐿 �� cos 𝜔𝑡 𝑑𝑡 − sin 𝜔𝑡

𝑢𝑑 = �𝑢 � − 𝐿 𝑞

𝑖𝑑 sin 𝜔𝑡 −1 𝑖𝑑 � �𝑖 �� − 𝑅 �𝑖 � cos 𝜔𝑡 𝑞 𝑞

𝑖𝑑 𝑖𝑑 𝑖𝑞 �𝑖 � − 𝑅 �𝑖 � + 𝜔𝐿 � � 𝑑𝑡 𝑞 −𝑖𝑑 𝑞 𝑑

sin 𝜔𝑡 𝑅𝑖𝛼 �� cos 𝜔𝑡 𝑅𝑖𝛽

Equation 2.6

where ed and eq are park transformation of the grid voltage. ud and uq are the park transformation of the inverter output. From Equation 2.6, it can be concluded that Equation 2.7 gives the output voltages of the grid-connected inverter in the synchronous (dq) frame.

18

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter 𝑢𝑑 �𝑢 � = 𝐿 𝑞

𝑒𝑑 𝑖𝑑 𝑖𝑑 −𝑖𝑞 �𝑖 � + 𝑅 �𝑖 � + 𝜔𝐿 � � + �𝑒 � 𝑑𝑡 𝑞 𝑞 𝑖𝑑 𝑞 𝑑

Equation 2.7

2.4 The Control Theory of the Grid-Side Inverter

In order to control three-phase VSI, there are two control strategies: current control and voltage control. The voltage-controlled VSI use the phase angle between the inverter output voltage and the grid voltage to control the power flow. In the current controlled VSI, the active and reactive components of the current injected into the grid are controlled using pulse width modulation (PWM) techniques. A current controller is less sensitive to voltage phase shifts and to distortion in the grid voltage. Moreover, it is faster in response. On the other hand, the voltage control is sensitive to small phase errors, and large harmonic currents may occur if the grid voltage is distorted. Consequently, the current control is recommended in the control of the grid-connected inverter [14]. The current controller of three-phase VSI is an essential part in controlling the gridconnected inverters. Consequently, the quality of the applied current controller largely influences the performance of the inverter system. The current controlled PWM (CC-PWM) converters have the following advantages [15]: •

Control of instantaneous current waveform, high accuracy

•

Peak current protection

•

Overload rejection

•

Extremely good dynamics

•

Compensation of effects due to load parameter changes (resistance and reactance)

•

Compensation of the semiconductor voltage drop and dead times of the converter

•

Compensation of the DC link and AC side voltage changes

The main task of the control scheme in a CC-PWM converter as shown in Fig. 2.5 is to force the currents in a three-phase AC load to follow the reference signals. By comparing the command iAc (iBc, iCc) and measured iA (iB, iC) instantaneous values of the phase currents, the CC generates the switching states SA (SB, SC) for the converter power devices which decrease the current errors ƐA (ƐB, ƐC). Hence, the current controller implements two tasks:

19

Chapter 2


error compensation (decreasing ƐA, Ɛ

ƐC). Moreover, pulse width modulation

B,

(determination of switching states SA, SB, SC).

Fig. 2.5, Basic block diagram of current controlled PWM converter.

The basic requirements and performance criteria of the current controller are [16]: • No phase and amplitude errors (ideal tracking) over a wide output frequency range • High dynamic response of the system • Limited or constant switching frequency to guarantee safe operation of converter semiconductor power devices • Low harmonic content • Good DC-link voltage utilization Many control mechanisms have been proposed to regulate the inverter output current that injected into the utility grid. The current control techniques are divided into two main groups: Controllers with open loop PWM block as shown in Fig. 2.6a and On-off controllers as shown in Fig. 2.6b [15]. In contrast to the on-off controllers (Fig. 2.6b), schemes with open-loop PWM block (Fig. 2.6a) have clearly separated current error compensation and voltage modulation parts. This concept allows us to exploit the advantages of open-loop modulators (sinusoidal PWM, space vector modulator) such as constant switching frequency, well-defined harmonic spectrum, optimum switch pattern, and good DC link utilization. In addition, full independent design of the overall control structure as well as open loop testing of the converter and load can be easily performed. 20

Chapter 2


Fig. 2.6, (a) Controller with open-loop PWM block. (b) On-off controller.

As an example of the On-off controllers, the hysteresis current control (HCC) is widely employed for three-phase PWM VSIs [10]. With HCC, current errors are directly used to determine the next PWM state of the VSI. The current error compensation and PWM generation are carried out in the same control unit at the same time, rendering the controller a good dynamic response, and an inherent current protection. However, HCC has some disadvantages such as high-current ripples and variable switching frequency, which usually cause a reduction in current quality and introduces difficulties in output filter design. Among the previously developed controllers with open loop PWM block, proportional-integral (PI) regulation and predictive control are two dominant algorithms for current error compensation. Current control strategies based on PWM are widely employed. A PWM-based current controller separates current error compensation and PWM functions, making it possible to exploit the advantages of PWM as well as design the overall control structure independently. The PWM algorithms are discussed in details in section 2.5. However, with the development of faster and more powerful microprocessors, the implementation of new and more complex control schemes is possible. Some of these new control schemes for power inverters include fuzzy logic and sliding mode control [15]. Fuzzy logic is suitable for applications where the controlled system or some of its parameters are unknown. Sliding mode present robustness and takes into account the switching nature of the power converters. Other control schemes found in the literature include neural networks, 21

Chapter 2


neuro–fuzzy and other advanced control techniques. However, these control algorithms is out of scope in these thesis. In following sections, three current control strategies, namely: hysteresis current controller, predictive current controller, and linear proportional-integral (PI) controller are studied for the application of the three-phase grid-connected PWM VSI. 2.4.1

Hysteresis Current Controller A basic hysteresis current control is developed and implemented for the application of

the grid-connected inverter, as shown in Fig. 2.7. Three-phase output currents of the inverter are detected and compared with the corresponding phase current references individually. The resulting three current errors are used directly to generate the PWM signals for the power switches through hysteresis comparators. HCC generates the desired PWM signals for the next control cycle to maintain the current trajectories within the hysteresis bands [10], [16].

Fig. 2.7, Block diagram of HCC strategy for a three-phase grid-connected PWM VSI.

Clearly, HCC is simple for implementation and insensitive to system parameters. Moreover, its dynamic response is extremely fast; actually, it is the fastest possible for any VSI with given dc link voltage and output inductance. The basic reason for this is that the hysteresis controller does not require any modulator. The state of the converter switches is determined directly by comparing the instantaneous converter current with its reference.

22

Chapter 2


However, the HCC has some drawbacks such as variable switching frequency and high current ripples. This causes a poor current quality and introduces difficulties in the output filter design. Moreover, in the VSI applications like grid connection, the injection of a variable frequency noise into the utility grid is not recommended, because unpredictable resonances with other connected loads could be triggered [17]. 2.4.2

Predictive Current Controller The main characteristic of predictive control is the use of the model of the system for

the prediction of the future behavior of the controlled variables. The controller uses this information in order to obtain the optimal actuation, according to a predefined optimization criterion [18]. A well-known type of predictive controller is the deadbeat controller. This approach uses the model of the system to calculate, once every sampling period, the required reference voltage in order to reach the reference value in the next sampling instant. That means the optimal actuation is the one that makes the error equal to zero in the next sampling instant. Then, this voltage is applied using a modulator. The predictive controller is capable of achieving a very fast dynamic response, the best among digital current controllers and clearly superior to that achievable by any other linear controller. However, the stability and robustness of the predictive current control are mainly affected by parameter variation. The current delivered by grid-connected inverters passes through a filter inductor and possibly a coupling transformer. Interfacing parameters, such as the equivalent inductance and resistance of the coupling transformer, filter inductors, and connection cables, are frequency dependent. Moreover, these parameters vary with temperature, core saturation, cables overload, and other environmental conditions. This leads to parameter sensitivity problems. 2.4.3

Linear PI Current Controller Proportional-integral (PI) controller is the most common control algorithm used for

current error compensation. A PI controller calculates an error value as the difference between a measured inverter output current and a desired injected current to the grid, then the controller attempts to minimize the error between them. The PI controller calculation

23

Chapter 2


algorithm involves two separate constant parameters, the proportional, the integral values, denoted Kp and Ki. The proportional term Kp (sometimes called gain) of the controller is formed by multiplying the error signal by a Kp gain. This will cause the PI controller to produce a control response that is a function of the error magnitude. As the error signal becomes larger, the Kp term of the controller becomes larger to provide more correction. The effect of the Kp term will tend to reduce the overall error with time. However, the effect of the Kp term will reduce as the error approaches zero. In most systems, the error of the controlled parameter will get very close to zero, but will not converge. The result is a small remaining steady-state error. The Integral term of the controller is used to fix small steady-state errors. The Integral term integrates the error. Therefore, a small steady-state error will accumulate into a large error value over time. This accumulated error signal (integrating the error) is multiplied by a Ki gain factor and becomes the integral output term of the PI controller. The integral term (when added to the proportional term) accelerates the movement of the process towards set point and eliminates the residual steady-state error that occurs with a proportional only controller. The PI current control offers an excellent steady-state response, low current ripple, constant switching frequency, and well-defined harmonic content. Moreover, the controller is insensitive to system parameters since the algorithm does not need system models [10]. PI controllers can be applied either in the stationary (αβ) or in the synchronous (dq) reference frame. When the synchronous PI controller is used, the control variables become DC, and the PI compensators are able to reduce the stationary error of the fundamental component to zero. This is not the case with PI controllers working in the stationary system, where there is an inherent tracking error of phase and amplitude. Therefore, current control in a synchronous (rotating) reference frame, using PI controllers is the typical solution in the three‐phase grid connected inverters [16]. According to the mathematical model of the grid-connected inverter section 2.3, the output voltages of the inverter in the synchronous (dq) frame are given by Equation 2.7.

24

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter 𝑢𝑑 𝑒𝑑 𝑑 𝑖𝑑 𝑖𝑑 −𝑖𝑞 �𝑢 � = 𝐿 �𝑖 � + 𝑅 �𝑖 � + 𝜔𝐿 � � + �𝑒 � 𝑞 𝑞 𝑖𝑑 𝑑𝑡 𝑞 𝑞

Where ed and eq is park transformation of the grid voltage. ud and uq is the park transformation of the inverter output. ω is the angular frequency of the grid. L is the inductance between the grid-connected inverter and the grid. R is the resistance between the grid-connected inverter and the grid. By rearrange the equation, it can be found that: 𝐿

Assuming

�

𝐿

𝑑𝑖𝑑

𝑑𝑡 𝑑𝑖𝑞 𝑑𝑡

+ 𝑅𝑖𝑑 = 𝑢𝑑 − 𝑒𝑑 + 𝜔𝐿𝑖𝑞 + 𝑅𝑖𝑞 = 𝑢𝑞 − 𝑒𝑞 − 𝜔𝐿𝑖𝑑

𝑢�𝑑 = 𝑢𝑑 − 𝑒𝑑 + 𝜔𝐿𝑖𝑞 � 𝑢�𝑞 = 𝑢𝑞 − 𝑒𝑞 − 𝜔𝐿𝑖𝑑

Equation 2.8

Equation 2.9

Using Equation 2.8 and 2.9, we obtain

𝑢�𝑑 = 𝐿

�

𝑢�𝑞 = 𝐿

𝑑𝑖𝑑 𝑑𝑡 𝑑𝑖𝑞 𝑑𝑡

+ 𝑅𝑖𝑑

Equation 2.10

+ 𝑅𝑖𝑞

In order to make the output currents track the reference current, the PI-type current controllers can be utilized. In this case, the output voltages of the current controllers are as follows: �

𝑢�𝑑 = 𝑘𝑝 (𝑖𝑑∗ − 𝑖𝑑 ) + 𝑘𝑖 ∫(𝑖𝑑∗ − 𝑖𝑑 ) 𝑑𝑡 𝑢�𝑞 =

𝑘𝑝 �𝑖𝑞∗

− 𝑖𝑞 � +

𝑘𝑖 ∫�𝑖𝑞∗

Equation 2.11

− 𝑖𝑞 � 𝑑𝑡

The d-axis reference voltage and q-axis reference voltage are expressed as follows: �

𝑢𝑑∗ = 𝑒𝑑 − 𝜔𝐿𝑖𝑞 + 𝑢�𝑑 𝑢𝑞∗ = 𝑒𝑞 + 𝜔𝐿𝑖𝑑 + 𝑢�𝑞

25

Equation 2.12

Chapter 2


Fig. 2.8, General structure for synchronous reference frame control structure [9].

According to Equation 2.12, the block diagram of the synchronous controller for the grid-connected inverter can be represented as shown in Fig.2.8. The figure shows that the inverter has two PI controllers to compensate the current vector components that defined in the synchronous reference frame (dq). Because of coordinate transformations, iq and id are DC components and therefore, PI compensators reduce the error(s) between the desired current I*d (I*q) and the actual current Id (Iq) to zero. The output energy and power factor can be controlled via changing d-axis current and q-axis current. For improving the performance of PI controller in such a structure, cross-coupling terms and voltage feed forward are usually used [11], [9]. 2.4.4

Comparison Between the Three Current Controllers The explanation of the three most common current control strategies namely:

hysteresis current controller, predictive controller, and linear PI controller have been presented in the last subsections. In this subsection, the advantages and disadvantages of each

26

Chapter 2


current control strategy are presented in the application of grid-connected inverters. Moreover, a comparison between the three current controllers has been provided. The hysteresis current controller is attractive for its highly simplicity, robustness, extremely fast dynamic response, and inherent over-current protection. However, highcurrent ripple and variable switching frequency are the drawbacks of the hysteresis current controller, which limit its applications in grid-connected VSIs. The predictive current controller has a very good steady-state performance, and it provides a good dynamic performance. However, its performance is sensitive to system parameters, especially to the output filter inductance L that may vary due to its nonlinearity. The linear PI current control offers an excellent steady-state response with zero steady-state error, low current ripple, and highly sinusoidal waveform. Moreover, the controller is insensitive to system parameters since the algorithm does not need system models. Its dynamic response is inferior to those of the hysteresis current controller. As shown in Table 2.3, the advantages and disadvantages of the three current controllers are summarized. Consequently, according to the advantages of the linear PI control algorithm, it concluded that this control algorithm is the best choice to implement the grid-connected inverter. Parameter

Hysteresis current

Predictive current

Linear PI current

controller

controller

controller

High THD Steady State

high current ripple and

response

variable switching

Very low THD Low THD

Even with high distorted grid

frequency Sensitivity to system

None

Sensitive to system

parameters Dynamic response

None

parameters

Very fast

Very fast

Slightly inferior than

Table 2.2, Comparison between the three current controllers

27

others

Chapter 2


2.5 Pulse Width Modulation Techniques After calculating the reference voltages U*a, U*b and U*c by the current regulation algorithm, the gating pulses for individual inverter switches is generated using the PWM algorithm. Then the desired inverter voltage is generated. PWM techniques have been the subject of intensive research during the last few decades. A large variety of methods, different in concept and performance, have been newly developed and described. Their implementation is depended on the machine type, the power level, and the semiconductor devices used in the power converter. It is lastly performance and the cost, which determine the choice of a PWM method in a specific application. Historically, the best-known PWM technique is triangular carrier-based sinusoidal PWM. However, with microprocessor development, the space vector modulation (SVM) becomes a basic power processing technique in three-phase PWM converters [13]. In the following two subsections, the sinusoidal PWM and SVM are discussed in details. Then, a comparison between them is presented. 2.5.1

Sinusoidal PWM The sinusoidal pulse width modulation (SPWM) is the most widely used method of

pulse width modulation. As shown in Fig. 2.9, the SPWM algorithm is consisted of three sinusoidal reference signals UAc, UBc, UCc each shifted by 120◦ from each other. The three reference signals are compared with high frequency triangular carrier signal Ut, which is common to all three phases. In this way, the logical signals SA, SB, and SC are generated, which define the switching instants of the power transistors [7], [13]. The generation of gating signals, line-to-line output voltages, and line-to-neutral output voltages are shown in Fig. 2.10. The control parameter that used to control the amplitude of the output voltage is the modulation index (m). The modulation index is defined as the ratio between the peak magnitudes of the modulating waveform and the carrier waveform. The modulation index m can be varied between 0 and 1 to give a linear relation between the reference and output wave. The maximum amplitude of the fundamental ac output line voltage is one can write 28

√3𝑈𝐷𝐶 . 2

Therefore,

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter 𝑢 � 𝑎𝑏1 =

√3 2

𝑚𝑈𝑑𝑐 ; 0 < 𝑚 ≤ 1

Fig. 2.9, Block scheme of carrier based sinusoidal PWM

Fig. 2.10, Basic waveforms of carrier based sinusoidal PWM

29

Equation 2.13

Chapter 2 2.5.2


Space Vector Modulation As mentioned in last subsection, conventional sinusoidal PWM essentially compares

low-frequency three sinusoidal reference signals with high frequency triangular or saw-tooth carrier to generate firing pulses for turning controlled switches ON and OFF. However, with microprocessor development, the space vector modulation (SVM) becomes popular and possibly the best PWM technique in three-phase PWM inverter. SVM has many advantages such as constant switching frequency, well-defined output harmonic spectrum, optimum switching patterns, and excellent dc-link voltage utilization [11], [19], [20]. SVM treats the three-phase inverter as a single unit. Specifically, in case of the twolevel inverter as shown in Fig.2.1, there are eight possible unique states, each of which determines a voltage space vector. As shown in Fig.2.11, six voltage space vectors shape the axis of hexagonal and divide the whole space into six sectors from 1 to 6. Moreover, there are two zero vectors, U0 and U7 lies at the origin. The angle between any two adjacent nonzero vectors is 60°. Space vectors and voltages corresponding to each state are shown in Table 2.1. Therefore, SVM is a digital modulating technique where the objective is to find an appropriate combination of active and zero vectors to approximate a given reference voltage.

Fig. 2.11, Six active vectors and two null vectors in SVM.

30

Chapter 2


In SVM, the three phase reference frame voltages U*a, U*b, and U*c are mapped to the complex two-phase orthogonal α-β plane. This is known as the Clark’s transformation and explained in details in Appendix A. 1 𝑈𝛼 �𝑈 � = � 0 𝛽

− 1�2 √3� 2

− 1�2

Ua∗ � �Ub∗ � − √3�2 Uc∗

Equation 2.14

The signal flow in space vector modulator is shown in Fig. 2.12.

Fig. 2.12, Block scheme of the space vector modulator

Fig. 2.13, Output pulses based on Symmetrical Sequence algorithm in sector

The construction of any space vector Uref lie in the hexagon can be done by time averaging the adjacent two active space vectors and any zero vectors, as follows. 31

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter 𝑈𝑟𝑒𝑓 =

𝑢𝑛 ∗𝑇1 +𝑢𝑛+1 ∗𝑇2 +𝑢0 ∗𝑇0 +𝑢7 ∗𝑇7

Equation 2.15

𝑇𝑠

Where Un and Un+1 are the non-zero adjacent active vectors. U0 and U7 are the zero vectors. T1, T2, T0, and T7 are time-shares of respective voltage vectors. Ts is the sampling period. SVM can be implemented through the following steps [21]: 1. The computation of reference voltage and angle (𝛉) Uref = �Uα2 + Uβ2 θ = tan−1

𝑈𝛽 𝑈𝛼

Equation 2.16

Equation 2.17

2. Identification of the sector number that is done by taking the angle computed from the last step, and then comparing it with angles range of each sector 3. Calculate the modulation index (𝑚) and the time duration T1, T2, T0, T7

𝑇1 =

√3 2

𝑇2 =

𝑚=

𝑈𝑟𝑒𝑓 𝑈𝐷𝐶� 2

𝑇𝑠 𝑚 sin(𝜋�3 − θ) ; √3 2

𝑇𝑠 𝑚 sin(θ) ;

𝑇0 + 𝑇7 = 𝑇𝑠 − 𝑇1 − 𝑇2

Equation 2.18

Equation 2.19

Equation 2.21 Equation 2.20

4. After T1, T2, T7, and T0 are calculated; the SVM pulses can be generated. The arrangement of switching sequence must ensure minimum transition between one vector and the next. This method reduces the switching frequency and has fewer harmonic. For the first sector, one can use 01277210 for symmetry reasons as shown in Fig.2.13 To maintain three-phase and half-wave symmetry output voltage, the samples should be evenly distributed in each sector. Furthermore, the sequences used for each sample should be identical with corresponding positions within each sector. The number of samples used in each sector should be an integer number. Defining Fsn as 32

Chapter 2

The Theory of the Grid-Connected Three-Phase Inverter 𝐹𝑠𝑛 =

𝐹𝑠 𝑓

𝐹𝑠 = 6𝑁

Equation 2.23 Equation 2.22

Fs is the sampling frequency and f is fundamental frequency of the waveform to be reconstructed (or equivalently Uref), it should be an integer multiple of six. N is the number of samples in a sector [20]. In SVM, the maximum fundamental line-voltage amplitude is unity as 0 ≤ θ ≤ π/3. This is an advantage over the SPWM technique, which achieves a √3/2 maximum fundamental line-voltage amplitude in the linear operating region [7]. 2.5.3

Comparison Between SPWM and SVM As mentioned previously, in the SPWM method, three reference signals are compared

with triangular carrier signal, then gate signals are generated. In the SVM, time duration of active (T1, T2) and zero (T0, T7) vectors are calculated, and from these times switching signals are obtained. The SPWM can be implemented by hardware or software methods [22]. In the hardware method, a simple comparator between reference signals and triangular carrier signal is used. Then gate pulses are generated. In the software method, a programmable device like microprocessor/controller is usually used to perform SPWM algorithm. The SPWM implementation is considered easy for either hardware or software implementation methods. Nevertheless, this algorithm has the following drawbacks: •

The Sine PWM algorithm is unable to utilize the available DC bus supply voltage (UDC) to the VSI. The generated line-to-line voltage is less than 90% of UDC in the linear operating region

•

This algorithm gives more Total Harmonic Distortion (THD)

•

Often, to reduce run-time processing load for slow controllers, three 120° phaseshifted sine tables are created in the controller memory. This is an inefficient usage of the controller memory

•

There is no degree of freedom in implementation

33

Chapter 2


On the other hand, SVM is more sophisticated, and it offers more voltage output (approximately 15% more) if compared to SPWM, and thus DC voltage utilization is increased by using SVM. In terms of THD, losses such as switching, and commutation losses, SVM has an advantage over SPWM as SVM minimizes both aspects that tend to haunt the SPWM technique. Advantages and strength of SVM over SPWM are paving the way towards wider usage of SVM in AC motor control and AC power generation [20]. Table 2.2 compares both SVM and SPWM techniques in a simple manner. SPWM

SVM

Comparing high frequency triangular

The duration of each switch state is

carrier signal with three sinusoidal explicitly calculated (as can be seen in reference signals (treated as separate computations involved for determination identity).

of ON times of space vectors).

SPWM is unable to utilize the available Increase utilization of DC supply voltage, DC supply voltage.

15% more than SPWM.

SPWM causes more Total Harmonic SVM Distortion.

causes

less

Total

Harmonic

Distortion.

SPWM does not facilitate more advanced SVM enable more advanced vector vector control implementation.

control implementation.

Table 2.3, Comparison between SPWM and SVM

2.6 Grid Synchronization The inverter output current that injected into the utility network must be synchronized with the grid voltage. The synchronization algorithm objective is to extract the phase angle of the grid voltage. The feedback variables can be converted into a suitable reference frame using the extracted grid angle. Hence, the detection of the grid angle has an essential role in control of the grid-connected inverter [5], [9]. The synchronization algorithms should respond quickly to changes in the utility grid. Moreover, it should have the ability to reject noise and the higher-order harmonics.

34

Chapter 2


Many synchronization algorithms have been proposed to extract the phase angle of the grid voltage such as the zero crossing detection, the Filtering of grid voltages, and phaselocked loop (PLL) technique [23]. 2.6.1

Zero Crossing Detection The simplest synchronization algorithm is the zero crossing detection. Owing to the

fact that grid voltage is sinusoidal, the maximum number of zero crossings in a period is three. By detecting the zero crossing points, the phase and frequency information of the grid voltage can be obtained. However, this method has many disadvantages such as low dynamics, since the phase tracking action is impossible between the detecting points. In addition, it is affected by noise and higher-order harmonics in the utility grid. Therefore, this method is unsuitable for applications that required continuous accurate phase angle detection. 2.6.2

Filtering of Grid Voltages Filtering of grid voltages is another solution for detecting the phase angle of grid

voltage. In this method, the grid voltage is transformed into a Cartesian coordinate system such as stationary αβ or synchronous rotating dq system as shown in Fig. 2.14 and Fig. 2.15 respectively. Then the arctangent function is used to obtain the phase angle of the utility voltage. This method has been used in drive applications, for transforming feedback variables to a reference frame suitable for control purposes. However, when used in conjunction with grid-connected power converters, additional filtering is necessary in order to obtain a clean synchronization signal in situation when distortions are present in the voltage waveform.

Fig. 2.14, Synchronization method using filtering on the synchronous frame.

35

Chapter 2


Fig. 2.15, Synchronization method using filtering on the stationary frame.

However, this method has the drawback that requires additional filtering in order to obtain an accurate detection of the phase angle and frequency in the case of a distorted grid voltage. Nevertheless, the usage of filters introduces a delay in the phase angle calculation. Therefore, this technique is not suitable for grid-connected inverter applications. 2.6.3

Phase-Locked Loop (PLL) Phase-locked loop (PLL) is a phase tracking algorithm widely applied in

communication technology, being able to provide an output signal synchronized with its reference input in both frequency and phase. Nowadays, the most common synchronization algorithm for extracting the phase angle of the grid voltages is the PLL. The PLL can successfully detect the phase angle of the grid voltage even when the noise or higher-order harmonics in the grid voltage exist. PLL schematic is illustrated in Fig. 2.16.

Fig. 2.16, Basic structure of a PLL system for grid synchronization.

36

Chapter 2


As shown in Fig.2.16, the PLL is implemented in synchronous (dq) reference frame. eabc is the sensed grid voltage which is then transformed into DC components using park transformation abc-dq. The PLL is locked by setting e*d to zero, which acts as a phase detector. A controller, usually PI, is used to control this variable, which brings the phase error to zero and acts as a loop filter. The ωff represents the utility nominal frequency that is added to the output of the regulator then outputted as the grid frequency. After the loop filter, whose output is the grid frequency, a voltage-controlled oscillator (VCO) is applied. This is usually an integrator, which gives the phase locked angle of the grid θ as output. This algorithm has a better rejection of grid harmonics, notches, and any other kind of disturbances [24].

2.7 Grid Filter The connection of an inverter to the utility grid is typically done using a filter [25]. Harmonics in the output voltage of the inverter are usually attenuated by connecting a filter between the VSI and the grid in order to cope with the power quality requirements of the utility. The most common filters used for this purpose are reviewed in this section. Three types of grid filter are addressed namely L-filter, LC-filter and LCL-filter [26].

Fig. 2.17, Filter configuration circuits

2.7.1

L‐Filter The degree of which the harmonic content is attenuated depends on the filter used. A

first-order filter consisting of one inductor in series with the mains is the most commonly 37

Chapter 2


used filter as shown in fig. 2.17(a). This is because the filter is easy to make, and it has no resonance problems as higher-order filters may have. Attenuation of the basic inductor filter is –20 dB/decade over the whole frequency range. Using this filter, the inverter switching frequency has to be high in order to attenuate the inverter harmonics sufficiently. The major drawback of this filter is the size of the inductor needed to achieve a reasonable attenuation of the current harmonics. Consequently, in order to obtain a good damping, a large filter (that can be bulky and expensive) is needed. 2.7.2

LC-Filter Higher order filters consisting of combinations of inductors and capacitors, can give a

better attenuation of the harmonics, but they also make the design more complex. The LCfilter in Fig 2.17 (b) is a second-order filter giving –40 dB/decade attenuation. Since the previous L-filter achieves low attenuation of the inverter switching components, a shunt element is needed to further attenuate the switching frequency components. In gridconnected systems, the LC filter is seldom used, since the resonance frequency of the filter will vary with the inductance value of the grid. 2.7.3

LCL-Filter The third filter common in the literature is the LCL filter configuration shown in Fig.

2.17 (c). It produces better attenuation of inverter switching harmonics than the L and LC filters. The key advantages of the LCL-filters are [27]: •

Low grid current distortion and reactive power production

•

Attenuation of -60 dB/decade for frequencies in excess of the resonance frequency

•

Possibility of using a relatively low switching frequency for a given harmonic attenuation

•

The resonance frequency is mostly depending on the filter components The LCL filter provides good performances with a lower costs. This is the main

reason why this filter is chosen for this application.

38

Chapter 2


2.8 Summary This chapter presents a comprehensive study of the three-phase grid-connected inverters. Initially, the basic construction of the three-phase inverter is introduced in section 2.2. After that, the mathematical model of the grid-connected inverter is presented in Section 2.3. The closed loop current control techniques are studied in section 2.4, namely: hysteresis current controller, predictive controller, and linear PI controller. Then their performances are compared. It is found that the linear PI controller is more suitable for the grid-connected inverter application, since it offers an excellent steady-state response with zero steady-state error, low current ripple, and highly sinusoidal waveform to the grid-connected inverter. In addition, the controller is insensitive to system parameters since the algorithm does not need system models. After that, the most common PWM techniques have been addressed, and then the SPWM and SVM along with a comparison between them are discussed in section 2.5. The SVM is chosen for the grid-connected inverter application because SVM has many advantages such as constant switching frequency, well-defined output harmonic spectrum, optimum switching patterns, and excellent dc-link voltage utilization. In section 2.6, the importance of the synchronization, for control purposes, for the grid-connected inverter is presented. In addition, it is reported that several synchronization algorithms are capable of detecting the phase angle of the grid voltage, namely: zero crossing detection, filtering of grid voltages, and PLL technique. It is concluded that the PLL is the best choice for the grid-connected inverter application. This is because the PLL can successfully detect the phase angle of the grid voltage even when noise or higher-order harmonics exist in the grid voltage. Finally, the grid filter that used in the connection of an inverter to the utility grid is introduced in section 2.7. Three types of grid filter are addressed, namely: L-filter, LC-filter, and LCL-filter. The LCL-filter is chosen for the grid-connected inverter application, since it is effective in the reduction of switching frequency harmonics of the power inverter. In addition, it reduces the dependence of the filter on the grid parameters.

39

Chapter 3

System Simulation

Chapter 3 System Simulation 3.1 Introduction In this chapter, the stand-alone and the grid-connected inverter system are modeled based on the theoretical basics presented in the previous chapter. The system is then simulated to verify the effectiveness of its control structure and to determine its performance parameters using PSIM 1 simulation package. PSIM is simulation software specifically designed for power electronics and motor drives. With fast simulation and friendly user interface, PSIM provides a powerful simulation environment for power electronics, analog and digital control, magnetic, renewable-energy, and motor drive system studies [28]. This chapter is divided into three major parts: Firstly, the stand-alone three-phase inverter is modeled and simulated. Secondly, the SVM algorithm for three-phase inverter is developed. Finally, a model for the grid-connected three-phase inverter is constructed, and the parasitic elements of the constituting power components are taken into consideration. This simulation model includes the current controller, SVM, grid-filter, and PLL.

3.2 Simulation of the Stand-Alone Three-Phase Inverter The simulation model of the stand-alone three-phase inverter is shown in Fig. 3.1. This simulation model consists of six MOSFET transistors and six freewheeling diodes. Additionally, three 1KΩ load resistors are connected in the star form, and the inverter input is 12V DC source that represents the output power from the renewable-energy source. In case of 180º conduction, each transistor conducts for 180º. Three transistors remain ON at any instant of time as described previously in chapter 2. In order to obtain three-phase balanced (fundamental) voltages, six gating pulses that are shifted from each other by 60º must be used, as shown in Fig. 3.2. The gating signals are generated by three- square wave

1

PSIM is a registered trademark of, and is copyrighted by, Powersim Inc., 2001-2010

41

Chapter 3

System Simulation

voltage sources with Vpeak-peak=1V and frequency= 50HZ. A 60º phase delay is inserted between them to provide the required phase shift.

Fig. 3.1, Simulation circuit of stand-alone three phase inverter

Fig. 3.2, Simulation of the gating signals of the stand-alone three-phase inverter

42

Chapter 3

System Simulation

The line-to-neutral voltages are shown in Fig 3.3. Moreover, the line-to-line voltages are shown in Fig.3.3. Consequently, the simulation results validate the theoretical studies that have been done in chapter 2.

Fig. 3.3, Simulation waveforms of line-to-neutral voltage of the stand-alone three-phase inverter

Fig. 3.4, Simulation waveforms of line-to-line voltage of the stand-alone three-phase inverter

43

Chapter 3

System Simulation

3.3 Simulation of SVM As described in chapter 2, the space vector PWM (SVM) is an alternative method used to control three-phase inverters. In this method, the PWM duty cycles are computed rather than derived through hardware comparison like SPWM. The SVM has many advantages such as constant switching frequency, well-defined output harmonic spectrum, optimum switching patterns, and excellent dc-link voltage utilization.

Fig. 3.5, Simulation circuit of the three-phase inverter with SVM.

As shown in Fig. 3.5, the model contains a three-phase sinusoidal voltages source work as reference signal and SVM sub-circuit which contain the SVM algorithm. Moreover, it consists of three-phase inverter with six MOSFET transistors and six freewheeling diodes. In addition to three 1KΩ load resistors are connected in the star form, and the inverter input is 12V DC source that represents the output power from the renewable-energy source. The SVM sub-circuit can be implemented through the following steps:  Step 1, Computation of Uα, Uβ, Uref, and angle (θ)  Step 2, Determine the sector of reference signal  Step 3, Determine time duration T1, T2, T0, and T7  Step 4, Determine the switching time of each transistor (sw1 to sw6)

44

Chapter 3

System Simulation

Each one of these steps is explained and its corresponding output waveforms are showed in the following subsections. 3.3.1

Step 1, Computation of Uα, Uβ, Uref, and angle (θ) The first step in SVM algorithm is to compute Uα and Uβ. That done with simple

Clark's transformation as explained in appendix A. Then the Uref is calculated by a square root of the sum of (Uα)2 and (Uβ)2. The angle (θ) is computed by use of arctangent function. The simulation circuit that doing this calculation is shown in Fig 3.6. Moreover, the waveforms of the input reference signals are shown in Fig. 3.7(a). In addition, the simulation waveforms of the Uα and Uβ are shown in Fig 3.7(b). Additionally, the waveform of the angle (θ) is shown in Fig 3.8.

Fig. 3.6, Simulation circuit for Determination Vα, Vβ, Vref, and angle (ϑ)

45

Chapter 3

System Simulation

Fig. 3.7, (a) Simulation waveforms of input reference signals. (b) Simulation waveforms of the Uα and Uβ.

Fig. 3.8, Simulation waveform of angle (θ)

46

Chapter 3 3.3.2

System Simulation

Step 2. Sector Determination The second step in SVM algorithm is to determine the sector of reference signal. That

is done by take the angles computed from last step, and then compare it with angles range of each sector by using six comparators. The output of each comparator is high (value= 1) when the non-inverting input is higher than the inverting input. When the positive input is lower, the output is zero. The circuit of simulation is shown in Fig. 3.9. Moreover, the output of this circuit is shown in Fig 3.10.

Fig. 3.9, Simulation circuit of sector determination

Fig. 3.10, Simulation waveform of sector allocation

47

Chapter 3 3.3.3

System Simulation

Step 3. Calculation of Time Duration T1, T2, T0, and T7 The third step in SVM algorithm is to calculate the time duration T1, T2, T0, and T7.

As explained in chapter 2 the time duration is calculated by a set of equations that are a function of sampling Time (Ts), modulation index (𝑚) and angle (θ). The simulation circuit of time interval calculation is shown in Fig.3.11.

Fig. 3.11, Simulation circuit of time interval calculation

3.3.4

Step 4. Switching Time Determination of Each Transistor (sw1 to sw6). The fourth and final step is to determine the switching time for each transistor (sw1 to

sw6). The switching state of each transistor is shown in table 3.1. The simulation circuit that performs this function is shown in Fig. 3.12. The circuit contains six monostable multivibrator with adjustable width allows the pulse width to be specified externally. Each pulse with specified width that calculated from previous step is marked by unique amplitude. Then six two-dimensional lookup tables used to output the switching pulse for each transistor. The SVM switching patterns at each sector is shown in Fig. 3.13.

48

Chapter 3

System Simulation

Sector

1

2

3

4

5

6

Upper switches

Lower switches

(Sw1, Sw3, Sw5)

(Sw4, Sw6, Sw2)

Sw1=T1+T2+T0/2 Sw3=T2+T0/2 Sw5=T0/2 Sw1=T1+T0/2 Sw3=T1+T2+T0/2 Sw5=T0/2 Sw1=T0/2 Sw3=T1+T2+T0/2 Sw5=T2+T0/2 Sw1 =T0/2 Sw3=T1+T0/2 Sw5=T1+T2+T0/2 Sw1=T2+T0/2 Sw3=T0/2 Sw5=T1+T2+T0/2 Sw1=T1+T2+T0/2 Sw3=T0/2 Sw5=T1+T0/2

Sw4 =T0/2 Sw6=T1+T0/2 Sw2=T1+T2+T0/2 Sw4 =T2+T0/2 Sw6=T0/2 Sw2=T1+T2+T0/2 Sw4 =T1+T2+T0/2 Sw6=T0/2 Sw2=T1+T0/2 Sw4 =T1+T2+T0/2 Sw6=T2+T0/2 Sw2=T0/2 Sw4 =T1+T0/2 Sw6=T1+T2+T0/2 Sw2=T0/2 Sw4 =T0/2 Sw6=T1+T2+T0/2 Sw2=T2+T0/2

Table 3.1, Switching Time Calculation at Each Sector

Fig. 3.12, Simulation circuit for transistors switching time calculation

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System Simulation

Fig. 3.13, SVM switching patterns at each sector.

50

Fig. 3.14, The overall simulation circuit of SVM algorithm

Chapter 3 System Simulation

51

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System Simulation

At the end, the overall simulation circuit of SVM algorithm is shown in Fig 3.14. The gating signals for sector 1 on the upper switches sw1, sw3, and sw5 are shown in Fig. 3.15. The simulation output phase-to-neutral voltages of the three-phase inverter are shown in Fig 3.16. In addition, the simulation output of phase-to-phase voltages are shown in Fig 3.17.

Fig. 3.15, The gating signals for sector 1.

Fig. 3.16, The simulation output phase-to-neutral voltage of three-phase inverter with SVM

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System Simulation

Fig. 3.17, The simulation output of phase-to-phase voltages of three-phase inverter with SVM

3.4 Simulation of Grid-Connected Three-Phase Inverter In this section, the grid-connected inverter system is modeled based on the theoretical basics presented in chapter 2. The system is then simulated to verify the effectiveness of its control structure and to determine its performance parameters. As shown in Fig. 3.18, the inverter input is 24V DC source that represents the output power from renewable-energy source. In addition, there is a Three-phase inverter with six MOSFET transistors and six freewheeling diodes. Every transistor has an on-resistance of 0.55-Ohm. The connection of an inverter to the utility grid is typically done using a grid filter. The objective of the grid filter is to attenuate harmonics in the output voltage of the inverter. In the simulation model, an LC-filter is utilized as that used in the practical circuit to be able to compare the simulation results with the experimental ones. So, 5mH inductors with an internal resistance of 0.172-Ohm resistance and 10uF capacitors are used as an LC-filter in order to achieve the desired voltage and current ripple characteristics. A three-phase step-up transformer is used to achieve isolation, DC decoupling and step-up voltage to 220V phase-to-neutral for grid connection. Moreover, three current sensors and three voltage sensors are used to sense the injected current to the grid and grid

53

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System Simulation

voltage respectively. Finally, to emulate the utility grid a three-phase 220V, 50Hz AC source is used.

Fig. 3.18, Simulation model of the grid-connected inverter

3.4.1

Simulation of PLL Synchronization Circuit As described in chapter 2, the PLL circuit is the best-known synchronization algorithm.

The PLL simulation model is shown in Fig.3.18 as a part of the simulation model of the gridconnected inverter. The simulation results of PLL as shown in Fig. 3.19 through Fig. 3.21 show that the PLL can successfully extract, without errors, the phase angle of the grid voltages, which allows for synchronization with the grid. The extracted phase angle is used to convert the feedback variables into the (dq) reference. Consequently, synchronization between output of inverter phase and grid phase angle is achieved by locking PLL for every instant of time between 0 to 2π.

Fig.3.19 represents the grid phase angle and the output voltage on the 50Hz grid. Furthermore, if grid frequency is shifted into 40Hz or 60Hz, the PLL can successfully track the variation in grid frequency and extracts the phase angle as shown in Fig. 3.20 and Fig.3.21 for 40Hz or 60Hz respectively. 54

Chapter 3

System Simulation

Fig. 3.19, The grid phase angle and the output voltage on 50Hz grid


55

Chapter 3

System Simulation


3.4.2

Simulation of Current Control Structure for the Grid-Connected Inverter In the grid-connected inverter, the inverter operates as a current-controlled source to

generate an output current based on a reference current signal. The amount of desired output power delivered to the utility is controlled through the current regulation algorithm. The accuracy of the current regulation algorithm is important for effective maximum power processing. The quality of the current regulation algorithm is also important to meet the total harmonic distortion restrictions imposed by the applicable standards. As described before in chapter 2, there are many control algorithms have been proposed to control inverter output current for utility interactive operations such as hysteresis controller, predictive controller, and linear proportional-integral (PI) controller. It is found that the linear PI controller is more suitable for the grid-connected inverter application, since it offers an excellent steady-state response with zero steady-state error, low current ripple, and highly sinusoidal waveform to the grid-connected inverter. In addition, the controller is insensitive to system parameters since the algorithm does not need system models. 56

Chapter 3

System Simulation

In order to obtain a synchronous control, the feedback variables are converted into the (dq) reference frame, which is obtained by using the Park transformations. The three-phase currents and voltages from (abc) frame are transformed into (dq) frame currents and voltages. For a high-performance application with accurate current tracking capability at a dynamic state, the decoupled controller diagram for the grid-connected three-phase inverter should be applied, as described previously in chapter 2 in Fig. 2.8. The output signals from PI controllers after dq/abc transformations are used as input to a space vector modulator (SVM) block in order to generate gating pulses. As shown in Fig. 3.18, two identical conventional PI controllers are used. Each of them contains the basic proportional (Kp) component and the integral (Ki) component. The process of setting the optimal gains for Kp, and Ki to get an ideal response from a control system is called tuning. There are different methods used for tuning the PI. In this application, Ziegler-Nichols tuning rules is used to give an educated guess for the parameter values and provide a starting point for fine tuning [29]. In this method, the Ki terms are set to zero first. Then, increase Kp from 0 to some critical value Kp=Kcr at which sustained oscillations occur as shown in Fig. 3.22. Once oscillation starts, the critical gain Kcr and the period of oscillations Pcr are noted. The Kp is set to 0.45Kcr, and the Ki is set to 1.2Kp/Pcr. The optimum parameters for PI controller are chosen to be Kp=0.1 and Ki=0.001.

Fig. 3.22, PI controller tuning with setting Ki to 0 and Kp=Kcr .

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System Simulation

To simulate the operation of the current control, a step reference input active current Id whose amplitude is 5A at time t = 0.05 s is applied. Then followed at t = 0.1 s by a reactive current reference component step Iq whose amplitude also is 5A. The input current waveforms are depicted in Fig 3.23 and Fig. 3.24. The simulated output inverter current Ia is shown in Fig 3.25. Additionally, the simulation result of three-phase grid currents (Ia, Ib, Ic) are shown in Fig.3.26. Those figures show that after a small transient time, the output inverter current reaches its steady-state value of 5A, which is exactly equal to the reference value. On the application of the reactive current step, the output inverter current changed accordingly. This proves that the current loop controller is effective such that measured currents track their references. In addition, its dynamic behavior is satisfactory.

Fig. 3.23, Id current reference and measured

Fig. 3.24, Iq current reference and measured

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System Simulation

Fig. 3.25, Simulation result of phase grid current Ia.

Fig. 3.26, Simulation result of three-phase grid currents (ia, ib, ic).

Assuming ideal transistor switches with zero on resistance, the simulated output phase-to-neutral voltage of the grid-connected inverter before LC-filter is shown in Fig. 3.27. This waveform is typical for such an inverter. To demonstrate the effect of the filter, the output voltage waveform of the inverter after the LC-filter is shown in Fig. 3.28. This figure shows that the waveform is a nearly pure sinusoidal waveform with small ripples.

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System Simulation

Fig. 3.27, Inverter phase voltage at the input of the filter.

Fig. 3.28, Inverter phase voltage considering ideal transistors.

Then, in order to take into consideration the non-ideal effects of the model component, especially the on-resistances of the transistors, the simulation is repeated with an on-resistance of 0.55 Ohm. The simulated waveform of the output phase voltage is shown in Fig. 3.29. It is clear from the figure that the presence of an appreciable on resistance in the power switches causes noticeable distortion of the output voltage waveform.

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System Simulation

Fig. 3.29, Inverter phase voltage considering non-ideal transistors after step-up transformer

3.5 Summary In this chapter, the stand-alone and the grid-connected inverter systems are modeled based on the theoretical basics presented in the previous chapter. The systems are then simulated to verify the effectiveness of its control structure and to determine its performance parameters using PSIM simulation package. This chapter is divided into three parts: In the first part, a model for the stand-alone three-phase inverter is developed. The gating signals for 180º conduction are simulated, and the simulated output waveforms of the three-phase inverter are shown. In the second part, the SVM algorithm for three-phase inverter is simulated. The four steps that are used to implement the SVM algorithm are analyzed, and its results are given. In addition, the simulated output waveforms of the three-phase inverter with SVM are shown. In the final part, a model for the grid-connected three-phase inverter is constructed, and the parasitic elements of the constituting power components are taken into consideration. This simulation model includes the current controller, SVM, grid-filter, and PLL. All simulation results prove that the control structure is effective, and validate the theoretical studies performed in chapter 2.

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Chapter 4 System Implementation 4.1 Introduction In this chapter, complete experimental versions for both the stand-alone and the gridconnected inverter are constructed. The major differences between the simulation model and the experimental version are clarified. Additionally, this chapter explains the theory that must be considered along with the approach that has allowed for the successful implementation of the power inverter system. It is worth mentioning that power inverter design requires knowledge of various areas in electrical and computer engineering, including circuit analysis, power electronics, signals and systems, microcontrollers, software programming, and feedback controls. A general knowledge of these areas is critical for understanding the physical behavior of each circuit component, as well as the interaction with other components. This chapter is divided into two major parts: Firstly, the stand-alone inverter is implemented and tested. Then the experimental results are presented. Additionally, a general overview of the technology considered in this project for both hardware and software by the implementation is presented in this section. Secondly, a comprehensive implementation of the three-phase grid-connected inverter is introduced. The experimental results are shown after testing every part of this circuit. Additionally, the differences between the simulation and the experimental results are analyzed.

4.2 Implementation of the Stand-Alone Three-Phase Inverter The stand-alone inverter is a power electronic-based device that converts DC power output from the solar arrays or wind turbine into clean AC electricity for AC appliances without connecting to the grid. According to the theoretical bases that are described in chapter 2, and the circuit simulation that has been done in chapter 3, the stand-alone threephase inverter topology is a configuration of six MOSFET transistors and six freewheeling diodes. Additionally, three 1KΩ load resistors are connected in the star form, and the inverter 63

Chapter 4


input is 12V DC source that represents the output power from the renewable-energy source. The gating signals are six pulses shifted from each other by 60º to obtain three-phase balanced (fundamental) voltages. In order to implement the three-phase inverter an extensive research has been done to find the suitable circuit components. Some of the major factors that determined the circuit components for this project include power capabilities, efficiency, size, and cost. The hardware design of the three-phase inverter platform will consist of two sections, the power circuit, and the control circuit. The power circuit consists of the power switches and their drivers. On the other hand, the control circuit consists of the dsPIC microcontroller with the software of operation. The following two sections provide a detailed description of each part: 4.2.1

Three-Phase Power Inverter Circuit The hardware implementation of the three-phase power inverter circuit is shown in

Fig. 4.1. It consists of six IRF740 N-channel power MOSFET 2 transistors with 0.55-Ohm drain to source on resistance and can handle up to 400V and 10A. When utilizing N-Channel MOSFETs to switch a DC voltage across a load, the drain terminals of the high side MOSFETs are often connected to the highest voltage in the system. This creates a difficulty, as the gate terminal must be approximately 10V higher than the drain terminal for the MOSFET to conduct. Often, integrated circuit devices known as MOSFET drivers are utilized to achieve this difference through charge pumps or bootstrapping techniques. These chips are capable of quickly charging the input capacitance of the MOSFET quickly before the potential difference is reached, causing the gate to source voltage to be the highest system voltage plus the capacitor voltage, allowing it to conduct. Consequently, in order to utilize the MOSFETs transistors, an integrated circuit device known as MOSFET driver is needed. Additionally, the circuit contains six freewheeling diodes. The freewheeling diodes are used to protect the switching device from being damaged by the reverse current of an inductive load.

2

International Rectifier Co.

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Fig. 4.1, Circuit diagram of power circuit of the inverter

There are many MOSFET drivers available to power N-Channel MOSFETs through level translation of low voltage control signals into voltages capable of supplying sufficient gate voltage. The IR2110 high and low side driver 3 is chosen in this circuit [30], since it exceeds all requirements for driving the MOSFETs in the three-phase power inverter circuit. The IR2110 high and low side drivers are used to convert the 5 V logic level signals from the dsPIC microcontroller to the power MOSFETs level of operation. The operation of the IR2110 device will be controlled through generated gating signals. The gating signal will be fed to the HIN and LIN pins simultaneously. The gating signal on HIN pin will control the high side output (HO) and the gating signal on LIN pin will control the low side output (LO). The SD pin controls shut down of the device and will be tied to the dsPIC microcontroller. The VDD that will be tied to 5V, this pin is the supply voltage providing biasing to the input side circuit of the IC (such as the HIN, LIN, and SD signals). Additional pins are required external connections such as the Vss pin, which will be tied to the ground, and the Vcc pin, which will be tied to 15V. Moreover, the device contains some pins requiring connections to bootstrapping components. With the three-phase configuration, three of these devices are utilized, as shown in Fig. 4.1. A typical connection of a single IR2110 device is shown in Fig. 4.2.

3

International Rectifier Co.

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Fig. 4.2, IR2110 typical connection

As shown in Fig. 4.2, the bootstrap diode and capacitor are the only external components strictly required for operation of the IR2110. The bootstrap capacitor provides gate charge to the high side MOSFET. As the switch begins to conduct, the capacitor maintains a potential difference, rapidly causing the MOSFET to further conduct, until it is fully on. The values for these components are calculated from [31]. The formula for minimum bootstrap capacitor value obtained from this document is shown below.

𝐶≥

𝐼𝑞𝑝𝑠(𝑚𝑎𝑥) 𝐼𝑐𝑝𝑠(𝑙𝑒𝑎𝑘) + 𝑄𝑙𝑠 + � 𝑓 𝑓 𝑉𝑐𝑐 − 𝑉𝑓 − 𝑉𝑙𝑠 − 𝑉Min

2 �2𝑄𝑔 +

The elements of the equation above can be found in datasheets as follows: 

Qg = gate charge of high side MOSFET = 41nC



Iqbs = Quiescent current for high side driver circuitry = 230uA



Qls = Level shift charge required per cycle = 5nC (given in application note)



Icbs(leak) = Bootstrap capacitor leakage current = 250uA



f = Frequency = 50Hz



Vcc = Supply Voltage = 15V



Vf = Forward voltage drop across bootstrap diode = 1V



Vls = Voltage drop across low side FET = 1.5V

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According to the calculation above, the bootstrap capacitor is chosen to be 10µF. The bootstrap diode should be able to block the full-power rail voltage, which is seen when the high side MOSFET is switched on. The bootstrap diode should also be a fast recovery diode to minimize the amount of charge fed back from the bootstrap capacitor into the Vcc supply. In this design, the bootstrap diode is chosen to be 1N4001. The printed circuit board (PCB) is designed by using Proteus Design Suite 4 . As shown in Fig.4.3, a double layer PCB is implemented for the power circuit. It should note that the tracks had to set and positioned in a certain way to minimize the interferences between the high tension and digital controller circuits. Moreover, the high-tension track width is set to 3.8 mm to be able to carry high current. Additionally, a heat sink along with thermal compound is used for every transistor in order to cool the devices by dissipating heat into the surrounding air.

Fig. 4.3, The PCB of the three-phase inverter power circuit

4

Labcenter Electronics Ltd.

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Chapter 4 4.2.2


The Control Circuit The purpose of the control circuit is to provide six-pulse gating signals that shifted

from each other by 60º. Moreover, it observes the power circuit then shut down the power circuit when detected an abnormal condition. Additionally, it provides an indication LEDs to show the status of system operation. The main component in the control circuit is the microcontroller, which is chosen to be dsPIC30F3010 5. The 16-bit dsPIC30F Digital Signal Controller (DSC) is the newest and advanced processor family from Microchip [32]. The dsPIC30F is an advanced 16-bit processor, which offers true DSP capability with the fundamental real-time control capabilities of a microcontroller and speed up to 30 MIPS (Mega instruction per second). In addition, the chosen microcontroller is from Motor Control and Power Conversion Family, which is specially designed to support motor control applications. They are also suited for Uninterruptible Power Supplies, inverters, switched mode power supplies, and related equipment. This variant family has: •

10-bit, 500-ksps ADC Converter

•

Motor Control PWM

•

Timers, Input Capture, Output Compare

• UART, SPI, I2C. As shown in Fig. 4.4, the control circuit of the three-phase inverter is consisting of dsPIC30F3010 microcontroller, 5MHZ crystal oscillator and two indication LEDs. PORTE is used to generate output pulses to the three-phase power circuit. The software is written to run at a CPU speed of 20 MIPS. This operating speed can be achieved by using the 16X PLL on the dsPIC device and using the 5 MHz crystal.

5

Microchip Technology Inc.

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Fig. 4.4, The control circuit of three phase inverter

The basic idea of software implementation for gating signals generation is to divide every 50HZ cycle into six-divisions. The duration of each is 0.0033 second. That can be done by implementing a timer that interrupts every 0.0033 second. After the timer interrupt, a variable called INDEX.X is incremented, then the pulses is outputted via PORTE. A dead time of 4µsec is inserted to the pulses. The dead time is the period of time that must be inserted between the turn-off event of one transistor in a complementary pair and the turn-on event of the other transistor. This is a precaution to avoid short circuits across the DC source of the inverter. Moreover, an external interrupt is used to supervise the abnormal condition detections of the power circuit. In the case of abnormal condition detection, the gating signals are stopped to prevent the damage of the power circuit. The software flowchart of three-phase inverter is shown in Fig.4.5 and 4.6. MPLAB® (v8.63) is used for the development environment and the Microchip C30 optimizing compiler (v3.01) is used for compilation [33] [34]. The source code is written in C programming language and included in Appendix B.

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Fig. 4.5, Software flowchart of stand-alone three-phase inverter part-1

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Fig. 4.6, Software flowchart of stand-alone three-phase inverter part-2

4.2.3

Experimental Data for the Stand-Alone Three-Phase Inverter The experimental results for the three-phase inverter are shown in the following

figures. Snapshots of the generated pulses from dsPIC microcontroller are shown in Fig 4.74.11. From these figures, it has shown that the generated pulses from dsPIC microcontroller are shifted from each other by exactly 60º. These figures are the same as the simulation results shown in Fig. 3.2. Additionally, the phase-to-neutral voltage of the three-phase inverter is shown in Fig.4.12. This experimental waveform is very similar to the corresponding simulated waveforms shown in Fig. 3.3. Moreover, the phase-to-phase voltage is shown in Fig.4.13. This is the same as the simulation result shown in Fig. 3.4. Consequently, the results validate the theoretical and simulation studies that done in chapter 2 and chapter 3 respectively.

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Fig. 4.7, The gating signal for sw1on CH1and the shifted by 60º signal for sw6 on CH2


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Fig. 4.10, The gating signal for sw1on CH1and the shifted by 240º for sw3 on CH2

73

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Fig. 4.12, Snapshot of phase-to-neutral output voltage three-phase inverter

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Fig. 4.13, Snapshot of phase-to-phase output voltage three-phase inverter.

4.3 Implementation of the Grid-Connected Three-Phase Inverter

Fig. 4.14, Schematic diagram of grid-connected inverter

Now a complete experimental version of the grid-connected inverter is presented. The major differences between the simulation model and the experimental version are intended to clarify. Due to the limitation of facilities available in the laboratory, the experimental model is modified down to a lower level but still achieve the same goal. The hardware design is 75

Chapter 4


verified by testing of different components of the project, which included the power circuit, the control board, and measurement board. After the individual components are tested for proper functionality, an experimental data for the grid integration is presented at the end of this section. As shown in Fig.4.14, the schematic diagram the grid side converter feed by the DC voltage source that represent the renewable energy source. The three-phase inverter performs the DC-to-AC conversion. The connection to the grid is done by means of a passive LC-filter and transformer. A measurement board is needed to measure the three-phase grid-voltage and the injected current to the grid to achieve control. A control circuit performs the control algorithm of the overall system. The reference active and reactive current is changed via computer. All communications between the computer and the control board is done through the RS-232 interfaces [35], [36]. 4.3.1

The Power Inverter Circuit The power circuit of the inverter platform is the same of the power circuit of the

three-phase inverter explained previously in section 4.2.1. This circuit consists of six IRF740 MOSFET transistors with 0.55-Ohm drain to source on resistance and can handle up to 400V and 10A; along with three IR2110 high and low side drivers that convert the 5 V logic level signals from the dsPIC microcontroller to the power MOSFETs level of operation. Additionally, it contains six freewheeling diodes as shown in Fig. 4.1. 4.3.2

Auxiliary Power Supplies Different DC voltage levels are necessary for the operation of different parts of the

hardware. The power circuit requires 15 V DC power supply. The control board requires 5V, and additional +12V is required for the measurement board. 4.3.3

External Sensors Board A measurement board is needed to measure the three-phase grid-voltage and the

injected current to the grid to achieve control [37]. The following subsections describe the current sensing circuit and voltage sensing circuit separately.

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4.3.3.1 Current Measurement Circuit This circuit measures the inverter output current flowing into the grid. In this circuit, the current transformer is connected between the inverter output and the grid. The idea of the current transformer is that the current carrying conductor threads through a toroidal core, forming the primary of a transformer. A secondary winding on the same core provides an output voltage. The current transformer is designed to produce a linear voltage output, which accurately tracks the AC component of the current in the primary. In practice, the sum of the three-phase current values is zero in a three-phase system. This advantage can be used to measure only two components of the three-phase current, and the third component will be known through calculation. Consequently, the cost of the hardware will be reduced because only two current sensors are required.

Fig. 4.15, current sensors circuit

As shown in Fig.4.15, the current sensor circuit contains a current transformer (5A/5mA) is connected to 0.5KΩ resistor and the output of the current sensor is fed to the inverting pin of the Op-amp (LM158). The voltage of the analog input of dsPIC microcontroller must be between 0V and 5V. Therefore, an offset of 1.25V is supplied to the non-inverting input, which amplified to provide an offset of 2.5V. The output of Op-amp, 77

Chapter 4


which is the 2.5V offset voltage in addition to the output of the current transformer, is provided directly to the ADC pin of dsPIC. By this method, the sensed current delivered to the dsPIC microcontroller with the right voltage level. The output waveforms of the current measurement circuit are shown in Fig.4.16. It is noted that output of the circuit is out of phase with actual output of current transformer due to the inverting amplifier. However, this problem can be solved in the software, by multiplying the ADC result by negative one.

Fig. 4.16, oscilloscope screenshot of current measurement circuit output for two phases.

4.3.3.2 Voltage Measurement Circuit The circuit adjective is to measure the three-phase grid voltages. The inverter output voltage and grid voltage are AC in nature. Therefore, it cannot be sensed through a resistive divider network, because the voltage of the analog input of dsPIC microcontroller must be between 0V and 5V. Therefore, the high-voltage AC signals must be stepped down firstly. Then a 2.5V-offset voltage is added to the output using the LM158 operational amplifier as shown in Fig. 4.17.

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Since, the voltage of the analog input of dsPIC microcontroller must be between 0V and 5V. Therefore, an offset of 2.5 V is supplied to the non-inverting input. The 2.5V-offset voltage allows the bidirectional AC sense voltage centered around this DC offset voltage. The step-down transformer makes sure that the sense signal voltage varies from 0V to 5V with an offset of 2.5V at the analog pin of the dsPIC DSC, to utilize the available voltage range of the ADC effectively. As described before, the sum of the three-phase voltage values is zero in a three-phase system. This advantage can be used to measure only two components of the three-phase voltage and the third component will known through calculation. Consequently, the cost of the hardware will be reduced because only two voltage sensors are required. The circuit diagram of the voltage measurement circuit is shown in Fig.4.17. The output waveforms of the voltage measurement circuit are shown in Fig.4.18. It is noted that the output is out of phase with actual output of the step-down transformer due to the inverting amplifier. However, this problem can be solved in the software, by multiplying the ADC result by negative one. As shown in Fig. 4.19, the output of the voltage sensor has the same frequency and phase as the grid voltage.

Fig. 4.17, Voltage measurement circuit

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Fig. 4.18, Oscilloscope screenshot of voltage measurement circuit output for two phases.

Fig. 4.19, Output of voltage sensor on CH1 and grid voltage on CH2

80

Chapter 4 4.3.4


The Inverter Control Design The purpose of the control circuit is to perform the control loop. The control strategy

that used in developing the grid-connected inverter is described before in chapter 2. Moreover, a simulation of the overall grid-connected system that included SVM based PI controller, PLL and grid-filter is presented in chapter 3. The control structure of the gridconnected inverter is shown in Fig. 2.8. As shown in this figure the grid voltage and the injected current to the grid are sensed firstly. Then, the grid angle is extracted by PLL algorithm. After that, the PI controller is executed for the current control loop. Finally, SVM is executed then the gating signals to the power circuit are generated. There are two significant parts in the inverter control design: the hardware and the software. The hardware design revolves around the control board, which includes the dsPIC microcontroller. In addition, an interface that required for communication between the control board, and the higher level CPU based controller. In The software part, the software codes for both the local dsPIC microcontroller and for the PC based controller are implemented. 4.3.4.1 Hardware of Inverter Control Board As shown in Fig.4.20, the control circuit contains the dsPIC30F3010 microcontroller along MAX232 that is RS232 transceiver (transceiver means transmitter and receiver). The software is written to run at a CPU speed of 20 MIPS. This operating speed can be achieved by using the 8X PLL on the dsPIC device and using the 10 MHz crystal oscillator. The output of the measurement board is inserted to the dsPIC 10-bit high-speed analog-to-digital converter (ADC) directly. That allows conversion of an analog input signal to a 10-bit digital number. This module is based on successive approximation register architecture, and provides a maximum sampling rate of 500 Ksps. Four analog input pins (AN2-to-AN5) are simultaneously sampled to perform the ADC of the grid voltage and the injected current to the grid respectively. The Simultaneous sampling of multiple signals ensures that the snapshot of the analog inputs occur at precisely the same time for all inputs. Therefore, the accuracy of the control loop increases.

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Fig. 4.20, Circuit diagram of grid connected inverter control board

The dsPIC motor control PWM module simplifies the task of generating multiple synchronized pulse width modulated outputs. The module has six PWM output pins, numbered PWM1H/PWM1L through PWM3H/PWM3L. The six I/O pins are grouped into high/low numbered pairs, denoted by the suffix H or L, respectively. The complementary mode is operated. In this mode, the low PWM pins are always the complement of the corresponding high I/O pin. A hardware dead time generator for complementary mode is programmed to generate 4µsec dead time between high/low pairs. There are fault pins, FLTA associated with the PWM module. When the power circuit sends an alarm-signal, these pin can optionally drive each of the PWM I/O pins to a defined state that is zeros. This action takes place without software intervention so fault events can be managed quickly. By this technique, the power circuit is protected against any up normal condition. 82

Chapter 4


The PWM module has a special event trigger that allows A/D conversions to be synchronized to the PWM time base. The ADC sampling and conversion time is programmed to occur at the end of PWM period. The special event trigger allows the user to minimize the delay between the time when ADC conversion results are acquired and the time when the duty cycle value is updated. The main outputs of the control board are the gate drive PWM signals to the power circuit. Additionally, a D-type RS232 connector is used to interface the circuit to the computer via RS232-to-USB cable adaptor. Since, the hardware serial ports with their 9-pin D connectors have disappeared from laptop and desktop computers. The input of the circuit is output of voltage and current measurement signals from the external sensors and the alarm signal from the power circuit. LED1 emitted when the alarm signal detected. LED2 emitted to indicate that the process is functional well. 4.3.4.2 Firmware of dsPIC Microcontroller MPLAB® (v8.63) is used as the development environment and the Microchip C30 optimizing compiler (v3.01) is used as compilation [33], [34], [38]. The source code is written in C programming language and included in Appendix B. Generally, microcontrollers can be programmed in two modes: free-run and multitasking. In free-run mode, the processor executes the one program loop continuously. On the other hand, Multitasking takes place when two or more programs on one microcontroller at precise, calculated moments, to execute the firmware routines. Therefore, the multitasking goal is to run several tasks together. Multitasking requires the code to be structured and broken into small fragments [39]. The first mode of operation is appropriate for applications that implement only few functions, one or two, which require maximum controller speed. In this application, the free-run mode will be a good choice because it executes very fast. Moreover, in order to control the program all events need to be interrupt driven. Although the source code is thoroughly commented, the major routines specific to grid-connected inverter control are explained in the flow charts contained in Fig.4.21 through Fig 4.24. Table 4.1 explains which of the dsPIC30F peripherals are used and for what 83

Chapter 4


purpose. Table 4.2 describes the content and function of the 14 individual source code files. The source code is written in C programming language and included in Appendix B.

dsPIC30F Peripheral

Function and Configuration

PWM Module

The PWM module is used in order to drive the three-phase modulation.

inverter

with

Outputs

are

3.6

kHz

PWM

configured

in

complementary mode, center aligned PWM signals, 4µsec dead time generated, and the special event trigger is used to initiate ADC conversions just before switches turn off. PWM interrupt is enabled with priority 4. FLTA interrupt is enabled with priority 7. High Speed 10-bit ADC

The ADC is used in order to take four simultaneous samples per PWM cycle of injected current and grid voltage. CH0 to CH3 are enabled. The samples are synchronized to the PWM module. Auto sampling selected. ADC interrupt is enabled with priority 5. The UART is used in order to interface with

UART

computer. Full-duplex 8- data transmission through the U1TX and U1RX pins enabled. No Parity, one stop bit and 9600-baud rate selected. Receive Interrupt is enabled with priority 3. External Interrupt 1

The external interrupt is used in order to stop the system operation when needed. INT1 interrupted on falling edge with priority 6.

Table 4.1, dsPIC30F peripheral usage

84

Chapter 4


Filename p30f3010.h math.h

Purpose of File This file is MPLAB-C30 dsPIC30F3010 processor header. The header file math.h consists of a macro and various functions that calculate common mathematical operations.

ports.h

Header for I/O ports module library functions.

dsp.h

Interface to the DSP Library for the dsPIC30F.

adc10.h

Header for 10-bit ADC module library functions.

pwm.h

Header for PWM module library functions.

UART.h

Header for UART module library functions.

GENRAL.c mainControl.c DATA.c

Store constant names and macros used all over the program. This file is for Initialization and background code. This file holds Application global data and performs variables declaration.

initiate

Initiate all dsPIC30F peripherals.

peripheral.c ClarkPark.c SVM.c interrupts.c

This file controls Clark and Park transformation. This file controls PWM calculations. This file handles Interrupt Service Routines. Table 4.2, Source code files

85

Chapter 4


Fig. 4.21, dsPIC software flow chart (The main routine)

86

Chapter 4


Fig. 4.22, dsPIC software flow chart (The SVM routine)

87

Chapter 4


Fig. 4.23, dsPIC software flow chart ( PWM interrupt service routine)

88

Chapter 4


Fig. 4.24, dsPIC software flow chart ( ADC interrupt service routine) 4.3.4.3

PC Based Control Software The PC software is needed in order to provide a mean to change the reference active

and reactive current. Moreover, change the Kp and Ki parameters of the PI controller. Visual Studio 2010 is used to implement such software. Visual Studio 2010 is an integrated environment for building, testing, debugging, and deploying a variety of applications: windows applications, web applications, classes and custom controls, and even console 89

Chapter 4


applications. Visual Basic 2010 is the languages that used to build this application within Visual Studio 2010.

Fig. 4.25, Screenshot of PC software for inverter control

As shown in Fig.4.25, the PC software of inverter control is used to change the reference active and reactive current, the Kp and Ki parameters of PI controller in the current control loop. Moreover, the Kp and Ki parameters of PI controller in PLL loop. In order to use the software, RS232 cable must connect from PC to inverter control circuit and establish a connection between them by chose the COM port from radio button and press connect button. The start button used to switch ON and OFF the inverter. In order to change any parameter, the value is chosen from the track bar, and then presses the send button. The source code for PC based control software is included in Appendix B. 4.3.5

Experimental Data for the Grid-Connected Three-Phase Inverter The experimental results for the grid-connected three-phase inverter are shown in the

following figures. A typical oscilloscope snapshot of the control voltage pulses for the two transistors S1 and S3 are shown in Fig. 4.26. This is the same as the simulation result shown in Fig. 3.15. Moreover, a typical oscilloscope snapshot for the measured voltage and the 90

Chapter 4


gating pulses for S1 are shown in Fig. 4.27. This figure shows that the pulse widths of the generated gating pulses are varied as a function of the control loop as described before in chapter 2. Additionally, a typical oscilloscope snapshot for the generated pulses from the dsPIC microcontroller and the generated pulses after the IR2110 driver IC are shown in Fig. 4.28. This figure shows that the generated pulses from the IR2110 driver IC are the same as the generated pulses from dsPIC microcontroller. However, it is larger in amplitude. A typical oscilloscope snapshot of the control voltage pulses for the two transistors in a complementary pair S1 and S4 are shown in Fig. 4.29. A dead time of 4µsec is inserted between the gating pulses of any two transistors in a complementary pair as shown in Fig. 4.30. As described previously, the dead time is the period of time that must be inserted between the turn-off event of one transistor in a complementary pair and the turn-on event of the other transistor. This is a precaution to avoid short circuits across the DC source of the inverter. Fig. 4.31 shows a typical oscilloscope snapshot of the phase-to-neutral voltage of our experimental grid-connected inverter taken directly before the filter. Moreover, a typical oscilloscope snapshot of the phase-to-phase voltage taken directly before filter is shown in Fig. 4.32. The experimental waveforms are very similar to the corresponding simulated waveforms as shown in Fig. 3.16 and Fig. 3.17 respectively. A typical output voltage of the grid-connected inverter taken after the transformer, and the grid voltage are shown in Fig.4.33. As it is clear from the figure, the inverter output voltage and the grid voltage are the same in amplitude, frequency, and phase except that the waveform shape of the inverter is distorted. This waveform is to be compared with that simulated in Fig.3.29. It is apparent that the two waveforms are identical to a large extent. Consequently, it can be concluded that the major waveform distortion of the output inverter voltage is caused basically by the internal resistances of the power supply and the power transistors. The presence of these parasitic resistances not only dissipates power but also distorts the voltage waveform. Therefore, one must design the inverter with the smallest possible parasitic resistances such that the total voltage drop across them is much smaller than the power-supply voltage at the peak current of the circuit.

91

Chapter 4


Fig. 4.26, The output pulses for two transistors S1 and S3

Fig. 4.27, The measured voltage signal on CH1 and the generated pulses on CH2.

92

Chapter 4


Fig. 4.28, The generated pulses from microcontroller on CH1 and pulses after driver IC on CH2

Fig. 4.29, The output pulses for two complementary transistors S1 and S4

93

Chapter 4


Fig. 4.30, The dead time that inserted between two complementary transistors S1 and S4

Fig. 4.31, Experiment waveform of the phase-to-neutral voltage of grid-connected inverter

94

Chapter 4


Fig. 4.32, Experiment waveform of the phase-to-phase voltage of grid-connected inverter

Fig. 4.33, Experimental waveform of the output phase voltage and the grid voltage

95

Chapter 4


4.4 Summary In this chapter, complete experimental versions for both the stand-alone and the gridconnected inverter are presented. The major differences between the simulation model and the experimental version are clarified. This chapter is divided into two main sections: In the first section, the stand-alone three-phase inverter is implemented and tested. Then the experimental results are presented. All experimental results validate the theoretical and simulation studies that are done in chapter 2 and chapter 3, respectively. In the second section, a comprehensive implementation of the grid-connected threephase inverter is introduced. The experimental results are shown after testing every part of this circuit. Additionally, the differences between the simulation and the experimental results are analyzed. Agreements are found between the simulation and experimental results when the parasitic resistances of the power components of the inverter circuit are taken into consideration. An important conclusion is that such parasitic resistance causes not only power losses but also a distortion in the output voltage waveform.

96

Conclusions & Future Work

Conclusions & Future Work With the development of the control structures of the grid-connected inverter, the efficiency and the performance of renewable-energy sources can be increased. This thesis demonstrates the design of a control algorithm for the grid-connected inverter. In this thesis, the theory of the three-phase grid-connected inverter is outlined. The closed loop current control techniques are discussed. Then it is found that the linear PI control is more suitable for this grid-connected inverter application, since it offers an excellent steady-state response with zero steady-state error, low current ripple, and highly sinusoidal waveform to the grid-connected inverter. In addition, the controller is insensitive to system parameters since the algorithm does not need system models. The most common PWM techniques are addressed. The SVM is chosen for the gridconnected inverter application because the SVM has many advantages such as constant switching frequency, well-defined output harmonic spectrum, optimum switching patterns, and excellent dc-link voltage utilization. The importance of the synchronization for control purposes of a grid-connected power generation system is presented. In addition, it is reported that several synchronization algorithms are capable of detecting the phase angle of the grid voltage. Then it concludes that the PLL is the best choice for the grid-connected inverter application. This is because the PLL can successfully detect the phase angle of the grid voltage even when the noise or higher-order harmonics exist in the grid voltage. The stand-alone and the grid-connected inverter systems are modeled based on the theoretical basics presented in the previously. These systems are then simulated to verify the effectiveness of its control structure and to determine its performance parameters using PSIM simulation package. Finally, complete experimental versions for both the stand-alone and the gridconnected inverter are presented. The major differences between the simulation model and the experimental version are clarified. Agreements have been found between the simulation and experimental results when the parasitic resistances of the power components of the 98

Conclusions & Future Work inverter circuit are taken into consideration. An important conclusion is that such parasitic resistance causes not only power losses but also a distortion in the output voltage waveform. Future research can be done based on this work, as summarized in the following points: •

Design and implementation of other control strategies for the grid-connected inverter in order to do a comparison between methods of control.

•

This work has been focused and implemented only on the grid side converter. A complete implementation of the control strategy for the generator side together with the control for the grid side convertor could be built.

99

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Extracted Paper

Extracted Paper Ahmed Abdalrahman, Abdalhalim Zekry and Ahmed Alshazly. Article: Simulation and Implementation of Grid-connected Inverters. International Journal of Computer Applications 60(4):41-49, December 2012. Published by Foundation of Computer Science, New York, USA.

106

Appendix A

Coordinate Transformation

Appendix A Coordinate Transformation The objective of this section is to give the basic knowledge needed to describe the control principles for three-phase grid-connected inverter. Two fundamental tools are required to design an efficient three-phase current controller: Clark transformation and Park transformation.

I.

Clark Transformation Clark transformation (αβ transformation) represents a very useful tool for the analysis

and modeling of three-phase electrical systems. Clark transforms maps three-phase a, b, c components which are equally shifted by 120° into a two-phase system. The new rotating vector is represented by two orthogonal components α and β. The space vector consists of a real (α) and imaginary (β) part, which represents two sinusoids shifted by 90° in time [17], [37].

Fig. A.1, Clark Transform for current

As illustrated in Fig. A.1, the αβ transformation can be defined as follows: 1 𝑋𝛼 2 �X � = � � 3 0 𝛽

− 1�2 √3� 2 107

− 1�2

X𝑎 � �𝑋𝑏 � − √3�2 𝑋 𝑐

Equation A.1

Appendix A


In the balanced three-phase system, the instantaneous sum of the three-phase current values will be zero. This advantage can be used to measure only two components of the three-phase currents. Then the third component can be known through calculation. In this case, the cost of the hardware is reduced because only two current sensors are required [40]. Moreover, this technique can be applied for the three-phase voltage system. �

II.

Park Transformation

𝑋𝛽 =

𝑋𝛼 = 𝑋𝑎 1

√3

𝑋𝑎 +

2

√3

𝑋𝑏

Equation A.2

Park Transformation converts the stationary system into a rotating system, which is called synchronous coordinate, or dq coordinates. Space vector which rotates in one direction converted by Park transformation will be visible as a (not rotating, similar to the standard) complex phases. The instantaneous angle of the space vector will be referenced to the θ angle. This transform make the rotating vectors look like DC quantities, thus simplifying analysis and control [17], [37]. The reference angle θ for synchronous frame is usually synchronized with some other rotating quantity, e.g. voltage. It is important that the reference angle θ rotates smoothly; therefore, a PLL is often used. The idea behind Park’s transformation is quite simple. Instead of mapping the three-phase inverter and its load onto a fixed two-axis reference frame, this transformation maps it onto a two-axis synchronous rotating reference frame. This practically means moving from a static coordinate transformation to a dynamic one, i.e., to a linear transformation whose matrix has time varying coefficients.

108

Appendix A


Fig. A.2, Park transform for current Park transformation defines a new set of reference axes, called d and q, which rotate around the static αβ reference frame at a constant angular frequency ω. This means that θ = ωt. The new system quantities are d (direct) and q (quadrate). The conversion from stationary system (α, β) to the synchronous (rotating) system is defined as: �

𝑋𝑑 cos 𝜃 �=� 𝑋𝑞 − sin 𝜃

sin 𝜃 𝑋𝛼 �� cos 𝜃 𝑋𝛽

Equation A.3

In case of direct transformation from the three-phase system (abc) to the synchronous system (dq) the equations are given by: 2𝜋

cos �𝜃 + � 𝑋𝑑 2 𝑐𝑜𝑠(𝜃) 3 � �= � 2𝜋 3 𝑋𝑞 −𝑠𝑖𝑛(𝜃) −sin (𝜃 + ) 3

2𝜋

𝑋𝑎 � �𝑋𝑏 � −sin (𝜃 − ) 𝑋𝑐 3 cos �𝜃 −

�

3 2𝜋

Equation A.4

In the digital signal processing theory, Park transformation is known as a shift in the frequency domain. Park transformation causes all frequency components to be shifted by a specified frequency. This is why 50 Hz signal shifted with -50Hz become a DC signal; analogously, the 250 Hz signal becomes a 200 Hz.

109

Appendix B

Software Source Code

Appendix B Software Source Code The objective of this section is to list the source code of programs that is created for both the stand-alone and the grid-connected inverter. Firstly, the microcontroller firmware for the stand-alone three-phase inverter is presented. Secondly, the microcontroller firmware for the grid-connected inverter is introduced. All dsPIC microcontroller programs in this thesis have been written in C programming language, and uses the MPLAB® (v8.63) as a development environment and the Microchip C30 optimizing compiler (v3.01) is used as compilation [33], [34]. Finally, the source code of PC control software is provided. This program uses the Visual Basic 2010 as a programming language, and uses Visual Studio 2010 to build this application.

I.

Firmware for the Three-Phase Inverter

/* ============================================================= Project/File: digital control/general.c Processor: 30F3010 Frequency: XT w/PLL*8; 80MHz; 20MIPS Copyrights: Eng. Ahmed Date 1-st built: 22/6/2011 ============================================================== == Description: This file contains useful macros =========================================================== */ // general constants #define FCY 20000000 // xtal = 10Mhz; PLLx8 #define MILLISEC FCY/1000 //20000*50nsec= 1 mSec delay #define FPWM 3600 // PWM freq. Fsn= Fs/f &Fsn=6N where N is odd in SVM #define TPWM 0.0033 #define VDC 40 // dc voltage #define #define #define #define

Outmax 346 Outmin 0 kp 1 Ki 0.1 110

Appendix B


//generic constants definitions #define ON 1 //generic ON value #define OFF 0 //generic OFF value #define TRUE 1 //generic TRUE value #define FALSE 0 //generic FALSE value #define LOW 0 //generic logic low #define HIGH 1 //generic logic high #define RISINGEDGE 0 //pulse rising edge value #define FALLINGEDGE 1 //pulse falling edge value #define OK 1 //OK value #define NOTOK 0 //Not OK value #define ACTIVE 1 //active state of UART/SPI #define PASSIVE 0 //passive state of UART/SPI #define INTMAX 65535 //maximum unsigned integer limit #define CHARMAX 255 //maximum unsigned char limit

// MASK #define #define #define #define #define #define #define #define #define #define #define #define #define #define #define #define

difination MASK0 0X0001 MASK1 0X0002 MASK2 0X0004 MASK3 0X0008 MASK4 0X0010 MASK5 0X0020 MASK6 0X0040 MASK7 0X0080 MASK8 0X0100 MASK9 0X0200 MASK10 0X0400 MASK11 0X0800 MASK12 0X1000 MASK13 0X2000 MASK14 0X4000 MASK15 0X8000

// // // // // // // // // // // // // // // //

BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT BIT

0000000000000001 0000000000000010 0000000000000100 0000000000001000 0000000000010000 0000000000100000 0000000001000000 0000000010000000 0000000100000000 0000001000000000 0000010000000000 0000100000000000 0001000000000000 0010000000000000 0100000000000000 1000000000000000

// general MACRO definition #define nop() {Nop();} p30f4011.h #define nop2() {nop();nop();} instructions #define nop3() {nop2();nop();} instructions #define nop4() {nop2();nop2();} instructions

111

IS IS IS IS IS IS IS IS IS IS IS IS IS IS IS IS

SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET SET

//Nop() defined in //2 "no operation" //3 "no operation" //4 "no operation"

Appendix B


#define nop5() {nop2();nop3();} //5 "no operation" instructions #define nop10() {nop5();nop5();} //10 "no operation" instructions #define nop20() {nop10();nop10();} //20 "no operation" instructions #define nop40() {nop20();nop20();} //40 "no operation" instructions #define toggle(a) {a=a^1;} //toggle bit a ON and OFF; a must be one bit XOR //glue macros #define glue2(a,b) a##b //the arguments a and b are read as ab #define glue3(a,b,c) a##b##c //the arguments a, b, c are read as abc #define xglue2(a,b) (glue2(a,b)) //used to force the glue2() #define xglue3(a,b,c) (glue3(a,b,c))//used to force glue3() //bit macros //general bit macros #define setbit(bit,a) {a=a|(xglue2(MASK,bit));} //sets bit in variable a #define clearbit(bit,a) {a=a&(~(xglue2(MASK,bit)));} //clears bit from variable a #define isbit(bit,a) ((a&(xglue2(MASK,bit)))==(xglue2(MASK,bit))) //true if bit is set in a //bit shift macros #define lshift1(a) #define lshift2(a) #define lshift3(a) #define lshift4(a)

{a=a4;}

//a //a //a //a

is is is is

shifted shifted shifted shifted

right right right right

rshift1(a) rshift2(a) rshift3(a) rshift4(a)

1 2 3 4

bit (*2) bits (*4) bits (*8) bits (*16) 1 2 3 4

bit (/2) bits (/4) bits (/8) bits (/16)

//delay macros unsigned int x; //local variable #define delay10() {for(x=0;x> ialpha, ibeta { sample.Ic = -(sample.Ia + sample.Ib); T.Ialpha= 0.6667*sample.Ia- 0.3333*(sample.Ic+ sample.Ib); T.Ibeta= 0.577*(sample.Ib-sample.Ic); } void Parki() //convert ialpha, ibeta =>> id, iq { T.Id= T.Ialpha*cosf(angle)+T.Ibeta*sinf(angle); T.Iq= -T.Ialpha*sinf(angle)+T.Ibeta*cosf(angle); } void InvParki() //convert id,iq => ialpha,ibeta { Inv.Ialpha=(outId*cosf(angle) - outIq*sinf(angle)); Inv.Ibeta= (outId*sinf(angle) + outIq*cosf(angle)); 120

Appendix B


} void Clarkv() //convert va, vb, vc =>> valpha, vbeta { sample.Vc = -(sample.Va + sample.Vb); T.Valpha= 0.6667*sample.Va- 0.3333*(sample.Vc+ sample.Vb); T.Vbeta= 0.577*(sample.Vb - sample.Vc); } void Parkv() //convert Valpha, Vbeta =>> Vd, Vq { T.Vd= T.Valpha*cosf(angle)+T.Vbeta*sinf(angle); T.Vq= -T.Valpha*sinf(angle)+T.Vbeta*cosf(angle); } /*============================================================ Project/File: TEST/data.c Processor: 30F3010 Frequency: XT w/PLL*8; 80MHz; 20MIPS Copyrights: Eng. Ahmed Date 1-st built: 17/8/2011 ============================================================== Description: This file holds App. global data ============================================================== */ #include "math.h" // This sine-wave lookup table const int sinetable[] ={ 0,3425,6812,10125,13327,16384,19260,21926,24351,26509,28377}; /* variables declaration*/ struct //allows for bit-fields declaration { unsigned i :1; // interrupt flag unsigned ref :2; } obs; float desIdf,desIqf,outputId,outputIq; unsigned int outId, outIq, desId, desIq; //makes variables static and global struct { float Id; // The reference parameter float Iq; unsigned int P; unsigned int Q; float outputIq; 121

Appendix B


float outputId; unsigned int k; } ref; struct{ float PIout; float sum; float intg; float angle; float freq; }PLL; /*============================================================ Project/File: digital control/initiate peripheral .c Processor: 30F2010 Frequency: XT w/PLL*8; 80MHz; 20MIPS Copyrights: ENG. Ahmed Date 1-st built: 16/8/2011 ============================================================== Description: This file initiates the peripherals ============================================================ */ void iniADC() { unsigned int PinConfig ,Scanselect, Adcon3_reg , Adcon2_reg ,Adcon1_reg ; ADCON1bits.ADON = 0; /* turn off ADC */ /*configures the ADC interrupt*/ ConfigIntADC10(ADC_INT_ENABLE & ADC_INT_PRI_6 ); /*configures the ADCHS register*/ // Connect AN3,AN4,AN5=>CH0, AN0=>CH1, AN1=>CH2, AN2=>CH3, ADCHS=0x0004; /*configures the ADC*/ //configure AN0>>AN5 to analog input PinConfig = ENABLE_ALL_ANA; // //skip input scan Scanselect = SKIP_SCAN_AN0 & SKIP_SCAN_AN1 & SKIP_SCAN_AN2 ; //configure the ADCON3 register Adcon3_reg = ADC_SAMPLE_TIME_1 & ADC_CONV_CLK_SYSTEM & ADC_CONV_CLK_6Tcy; //Tconv=12*((1+6)/2)*50nsec=3usec //configure the ADCON2 register Adcon2_reg = ADC_VREF_AVDD_AVSS & ADC_SCAN_ON & ADC_ALT_BUF_OFF & ADC_ALT_INPUT_OFF & ADC_CONVERT_CH_0ABC & ADC_SAMPLES_PER_INT_4; //configure the ADCON1 register 122

Appendix B


Adcon1_reg = ADC_MODULE_ON & ADC_IDLE_CONTINUE & ADC_FORMAT_SIGN_INT& ADC_CLK_MPWM & ADC_SAMPLE_SIMULTANEOUS & ADC_AUTO_SAMPLING_ON; OpenADC10(Adcon1_reg,Adcon2_reg,Adcon3_reg,PinConfig,Scanselec t); } /*-----------------------------------------------------------*/ void initPWM() { unsigned int config; /* Holds the PWM interrupt configuration value*/ unsigned int period; /* Holds the value to be loaded into dutycycle register */ unsigned int sptime; /* Holds the value to be loaded into special event compare register */ unsigned int config1; /* Holds PWM configuration value */ unsigned int config2; /* Holds the value be loaded into PWMCON1 register */ unsigned int config3; /* Holds the value to configure the special event trigger post-scale and duty-cycle */ /* Configure PWM interrupt enable/disable and set interrupt priorities */ config = (PWM_INT_EN & PWM_INT_PR4 & PWM_FLTA_EN_INT & PWM_FLTA_INT_PR7); ConfigIntMCPWM( config ); /*configures dead time values and clock prescalers */ SetMCPWMDeadTimeGeneration(PWM_DTAPS2 & PWM_DTA35); // Tcy =50nsec dead time = 2*40*Tcy =4 usec /*configures Fault A Override bits*/ SetMCPWMFaultA(PWM_OVA3H_INACTIVE & PWM_OVA2H_INACTIVE & PWM_OVA1H_INACTIVE & PWM_OVA3L_INACTIVE & PWM_OVA2L_INACTIVE & PWM_OVA1L_INACTIVE & PWM_FLTA_MODE_LATCH & PWM_FLTA3_EN & PWM_FLTA2_EN & PWM_FLTA1_EN); /* configure the motor control PWM module */ //PWM Time Base Period= 10KHZs period = (FCY/FPWM - 1)>>3; //contains the special event compare value to be stored in SEVTCMP register. sptime =2 ; // Cannot be 0 -> turns off trigger (Missing from doc) 123

Appendix B


//A special event trigger will occur when the PWM time base is counting downwards. SEVTCMPbits.SEVTDIR=0; //configure the PTCON register config1 = (PWM_EN & PWM_IDLE_CON & PWM_OP_SCALE1 & PWM_IPCLK_SCALE4 &PWM_MOD_UPDN); //configure the PWMCON1 register config2 = (PWM_MOD3_COMP &PWM_MOD2_COMP &PWM_MOD1_COMP & PWM_PEN3H & PWM_PEN2H & PWM_PEN1H & PWM_PEN3L & PWM_PEN2L & PWM_PEN1L);//configure the PWMCON2 register config3 = (PWM_SEVOPS1 & PWM_OSYNC_PWM & PWM_UEN); OpenMCPWM(period,sptime,config1,config2,config3); } /*-----------------------------------------------------------*/ void initint1() { ConfigINT1(FALLING_EDGE_INT & EXT_INT_PRI_5 &EXT_INT_ENABLE); } /* ============================================================ Project/File: FD2/interrupts.c Processor: 30F3010 Frequency: XT w/PLL*8; 80 MHz; 20 MIPS Copyrights: ENG. Ahmed Date 1-st built: 20/8/2011 ============================================================== Description: This file handles Interrupt Service Routines =============================================================* / //ISR ADC ----------------------------------------------------void __attribute__((interrupt, auto_psv)) _ADCInterrupt() { if (obs.ref == 0) { sample.Ia=ADCBUF0; //read converted data sample.Va=ADCBUF1; sample.Vb=ADCBUF2; desId =ADCBUF3+512; obs.ref++; toggle(_LATF2); IFS0bits.ADIF=0; //clear ADC interrupt flag } else if (obs.ref == 1) { sample.Ib=ADCBUF0; //read converted data 124

Appendix B


sample.Va=ADCBUF1; sample.Vb=ADCBUF2; desId =ADCBUF3+512; obs.ref++; toggle(_LATF2); IFS0bits.ADIF=0;

//clear ADC interrupt flag

} else if (obs.ref == 2) { desIq =ADCBUF0+512; sample.Va=ADCBUF1; sample.Vb=ADCBUF2; desId =ADCBUF3+512; obs.ref=0; toggle(_LATF2); IFS0bits.ADIF=0;

//read converted data

//clear ADC interrupt flag } } //ISR PWM ----------------------------------------------------void __attribute__((interrupt, auto_psv))_PWMInterrupt() // PWM interrupt { if (SV.sector==1) { PDC1 =(SV.T1+SV.T2+SV.T0); // PWM 1, 2 and 3 duty cycles PDC2 =(SV.T2+SV.T0); PDC3 =(SV.T0); } else if (SV.sector==2) { PDC1 =(SV.T1+SV.T0); PDC2 =(SV.T1+SV.T2+SV.T0); PDC3 =(SV.T0); } else if (SV.sector==3) { PDC1 =(SV.T0); PDC2 =(SV.T1+SV.T2+SV.T0); PDC3 =(SV.T2+SV.T0); } else if (SV.sector==4) { PDC1 =(SV.T0); PDC2 =(SV.T1+SV.T0); PDC3 =(SV.T1+SV.T2+SV.T0); } 125

Appendix B


else if (SV.sector==5) { PDC1 =(SV.T2+SV.T0); PDC2 =(SV.T0); PDC3 =(SV.T1+SV.T2+SV.T0); } else if (SV.sector==6) { PDC1 =(SV.T1+SV.T2+SV.T0); PDC2 =(SV.T0); PDC3 =(SV.T1+SV.T0); } IFS2bits.PWMIF=0; //clear RX Interrupt flag } //ISR int1 --------------------------------------------------void __attribute__((interrupt, auto_psv)) _INT1Interrupt() //will come here whenever INT1 interrupts { LATE=0x00; obs.i=1; CloseMCPWM(); IFS1bits.INT1IF=0; //clear timer1 interrupt flag } //ISR FlTA --------------------------------------------------void __attribute__((interrupt, auto_psv)) _FLTAInterrupt() //will come here whenever FLTA interrupts { LATE=0x00; obs.i=1; CloseMCPWM(); IFS2bits.FLTAIF=0; //clear timer1 interrupt flag } /*============================================================ Project/File: digital control/SVM.c Processor: 30F3010 Frequency: XT w/PLL*8; 80MHz; 20MIPS Copyrights: ENG. Ahmed Date 1-st built: 20/8/2011 ============================================================== Description: This file controls PWM ============================================================ */ //variables declaration struct { 126

Appendix B


long x; unsigned int vref; unsigned int m; unsigned int sector; double a2; float th; float th2; float th3; unsigned int thno; unsigned int thno2; unsigned int T0; unsigned int T1; unsigned int T2; } SV; unsigned int tpwm; void SVM() { /*************** angle cal.****************************/ SV.a2=57.2958*angle; //*180/pi if (SV.a2>=0) SV.th=SV.a2; else if (SV.a2 15; SV.T2 = ((long)SV.T2*(long)tpwm) >> 15; SV.T0 = (tpwm - SV.T1 - SV.T2) >> 1; }

III.

PC Based Control Software Source Code

Public Class Form1 Dim P As String Dim Kp1 As String Dim x As String Private Sub connbtn_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles connbtn.Click If connbtn.Text = "Connect" Then ToolStripStatusLabel2.Text = "connecting to inverter" 'SerialPort1.PortName = ComboBox1.SelectedItem If RadioButton1.Checked Then SerialPort1.PortName = "COM1" ElseIf RadioButton2.Checked Then SerialPort1.PortName = "COM2" ElseIf RadioButton3.Checked Then SerialPort1.PortName = "COM3" End If Try SerialPort1.Open() Catch ex As Exception MsgBox(Err.Description) Finally If SerialPort1.IsOpen = True Then ToolStripStatusLabel2.Text = "Connected to inverter" connbtn.Text = "Disconnect" Else ToolStripStatusLabel2.Text = "Can not connect to Inverter" End If End Try ElseIf connbtn.Text = "Disconnect" Then ToolStripStatusLabel2.Text = "Disconnecting from inverter" Try SerialPort1.Close() Catch ex As Exception MsgBox(Err.Description) Finally If SerialPort1.IsOpen = False Then

128

Appendix B


ToolStripStatusLabel2.Text = "Disconnected from inverter" connbtn.Text = "Connect" Else ToolStripStatusLabel2.Text = "Can not disconnect from Inverter" End If End Try End If End Sub Private Sub TrackBar1_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar1.Scroll TextBox1.Text = TrackBar1.Value * 10 End Sub Private Sub TrackBar2_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar2.Scroll TextBox2.Text = TrackBar2.Value * 10 End Sub Private Sub TrackBar3_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar3.Scroll TextBox3.Text = TrackBar3.Value / 10 'string => hex 'TextBox4.Text = Hex(TrackBar3.Value) ' TextBox2.Text = CStr(TextBox4.Text) End Sub Private Sub TrackBar4_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar4.Scroll TextBox4.Text = TrackBar4.Value / 1000 End Sub Private Sub TrackBar5_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar5.Scroll TextBox5.Text = TrackBar5.Value / 10 End Sub Private Sub TrackBar6_Scroll(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles TrackBar6.Scroll TextBox6.Text = TrackBar6.Value / 1000 End Sub Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click If Button2.Text = "Start" Then If SerialPort1.IsOpen = True Then SerialPort1.Write("o") ToolStripStatusLabel1.Text = "Inverter ON" Button2.Text = "Stop" ElseIf SerialPort1.IsOpen = False Then MsgBox(" Connect to the inverter first") End If ElseIf Button2.Text = "Stop" Then If SerialPort1.IsOpen = True Then SerialPort1.Write("f") ToolStripStatusLabel1.Text = "Inverter OFF" Button2.Text = "Start" ElseIf SerialPort1.IsOpen = False Then MsgBox(" Connect to the inverter first")

129

Appendix B


End If End If End Sub Private Sub Button1_Click_1(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click If SerialPort1.IsOpen = True Then SerialPort1.Write("00A") If TrackBar1.Value < 10 Then SerialPort1.Write(0) SerialPort1.Write(0) SerialPort1.Write(TrackBar1.Value) ElseIf TrackBar1.Value >= 10 And TrackBar1.Value < 100 Then SerialPort1.Write(0) SerialPort1.Write(TrackBar1.Value) ElseIf TrackBar1.Value >= 100 Then SerialPort1.Write(TrackBar1.Value) End If SerialPort1.Write("A") If TrackBar2.Value < 10 Then SerialPort1.Write(0) SerialPort1.Write(0) SerialPort1.Write(TrackBar2.Value) ElseIf TrackBar2.Value >= 10 And TrackBar2.Value < 100 Then SerialPort1.Write(0) SerialPort1.Write(TrackBar2.Value) ElseIf TrackBar2.Value >= 100 Then SerialPort1.Write(TrackBar2.Value) End If ElseIf SerialPort1.IsOpen = False Then MsgBox(" Connect to the inverter first") End If End Sub Private Sub Button3_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button3.Click If SerialPort1.IsOpen = True Then SerialPort1.Write("00B") If TrackBar3.Value < 10 Then SerialPort1.Write(0) SerialPort1.Write(0) SerialPort1.Write(TrackBar3.Value) ElseIf TrackBar3.Value >= 10 And TrackBar3.Value < 100 Then SerialPort1.Write(0) SerialPort1.Write(TrackBar3.Value) ElseIf TrackBar3.Value >= 100 Then SerialPort1.Write(TrackBar3.Value) End If SerialPort1.Write("B") If TrackBar4.Value < 10 Then SerialPort1.Write(0)

130

Appendix B

Software Source Code SerialPort1.Write(0) SerialPort1.Write(TrackBar4.Value) ElseIf TrackBar4.Value >= 10 And TrackBar4.Value < 100

Then SerialPort1.Write(0) SerialPort1.Write(TrackBar4.Value) ElseIf TrackBar4.Value >= 100 Then SerialPort1.Write(TrackBar4.Value) End If ElseIf SerialPort1.IsOpen = False Then MsgBox(" Connect to the inverter first") End If End Sub Private Sub Button4_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button4.Click If SerialPort1.IsOpen = True Then SerialPort1.Write("00C") If TrackBar5.Value < 10 Then SerialPort1.Write(0) SerialPort1.Write(0) SerialPort1.Write(TrackBar5.Value) ElseIf TrackBar5.Value >= 10 And TrackBar5.Value < 100 Then SerialPort1.Write(0) SerialPort1.Write(TrackBar5.Value) ElseIf TrackBar5.Value >= 100 Then SerialPort1.Write(TrackBar5.Value) End If SerialPort1.Write("C") If TrackBar6.Value < 10 Then SerialPort1.Write(0) SerialPort1.Write(0) SerialPort1.Write(TrackBar6.Value) ElseIf TrackBar6.Value >= 10 And TrackBar6.Value < 100 Then SerialPort1.Write(0) SerialPort1.Write(TrackBar6.Value) ElseIf TrackBar6.Value >= 100 Then SerialPort1.Write(TrackBar6.Value) End If ElseIf SerialPort1.IsOpen = False Then MsgBox(" Connect to the inverter first") End If End Sub Private Sub Button10_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button10.Click Me.Close() End Sub End Class

131

Digital Control Techniques for Grid-Connected Inverters

Digital Control Techniques for Grid-Connected Inverters

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