Multiphase Wind Energy Generation with Direct Matrix ...

2014 IEEE International Conference on Industrial Technology (ICIT), Feb. 26 - Mar. 1, 2014, Busan, Korea

Multiphase Wind Energy Generation with Direct Matrix Converter Omar Abdel-Rahim 1,2, IEEE Student Member, Hirohito Funato 2, Haitham Abu-Rub 3, IEEE Senior Member and Omar Ellabban 3,4, IEEE Senior Member 1

2

Electrical Engineering Department, Aswan Faculty of Engineering, Aswan University, Aswan, Egypt, 81542. Electrical and Electronic Engineering Department, Utsunomiya University, Utsunomiya, Tochigi, 321-8585 Japan. 3 Electrical and Computer Engineering Department, Texas A&M University at Qatar, Doha, Qatar. 4 Electrical Machines and Power Engineering Department, Helwan University, Cairo, Egypt. [email protected]

Abstract— This paper proposes a multiphase power generation with matrix converter for Wind Energy Conversion System (WECS). The proposed system consists of five-phase Permanent Magnet Synchronous Generator (PMSG), to generate five-phase voltage with variable amplitude and frequency. The grid is a threephase system and hence deployment of multiphase generator needs some sort of phase conversion system. Therefore, a five-to-three phase Direct Matrix Converter (DMC) is used to interface the fivephase PMSG with the grid. The choice of multiphase machine comes from the inherent advantages of multiphase machine such as higher output power, reduced phase’s losses, reduced sized for the same amount of output power compared to three phase generator. The proposed control strategy for the converter is Model Predictive Control (MPC). The proposed algorithm does the following functions: extract maximum power from the WECS, and ensures unity power factor at the grid terminal and machine terminal. Keywords— Wind Energy Conversion System, Permanent Magnet Synchronous Generator; Direct Matrix Converter; Model Predictive Control.

I.

INTRODUCTION

Wind energy conversion system is one of most important sources of renewable energy. The new trend in all over the world is to use renewable energy in power generation instead of fossil fuel [1]-[4]. Due to the importance of wind power generation, different types of electric generators are used for the generating of electric energy from the wind. These include the squirrel cage induction generator (SCIG), the doubly fed induction generator (DFIG), and the synchronous generator (SG) [5]. This paper proposes another electric generator for wind generation, a fivephase PMSG to generate electric energy from the wind integrated with matrix converter [6-8]. The grid is a three-phase system and hence deployment of multiphase generator needs some sort of phase conversion system. Matrix converter can be broadly classified into direct and indirect types. Direct matrix converter (DMC) is able to convert ac voltage into ac voltage with different amplitude, frequency and different number of phases. It is considered as a powerful topology for AC to AC power conversions, so that it receive considerable attentions in recent times. It offer inherent advantages such as bi-directional power flow, which is very important in regeneration process, nearly sinusoidal input and output waveform, controlled input power factor, output current

amplitude and frequency are also controllable, compact design and lack of dc-link capacitors for energy storage. There are many configurations that have been developed for matrix converter in the literature [9]-[13]. Five-to-three matrix converter is able to convert five-phase input into three-phase output. It has fifteen switches as each output phase is connected to all the input phases through a bidirectional semiconductor switches, and hence, there are in total 215 expected switching states. But with taking into account the two important constraints: input phases should not be short circuited together (to protect the input phases) and output phases should not interrupt under any condition, due to the presence of inductive loads, the switching states are limited to 125. To control those fifteen switches and select the appropriate switching states MPC is used in this paper. Model predictive control is considered one of the most interesting controllers [14]-[17] due to their simple implementation and competitive results. The basic idea of the MPC is to perform a model for the controlled system to enable prediction of the system state and simplify the control operation and selection of optimum operation according to the specified cost function. Cost function determines the required control criteria. DMC provides a control of output voltage amplitude and frequency and also enables controlling input current displacement. Therefore, it is an excellent combination to combine the DMC with MPC for multiphase system. II.

PROPOSED WIND ENERGY CONVERSION SYSTEM

The proposed multiphase WECS is depicted in Fig.1. The proposed system consists of a five-phase PMSG used to convert the mechanical power obtained from the wind turbine into electrical power in forms of five-phase voltages, with variable amplitude and variable frequency. As the grid is a three-phase system so that five-to-three phase DMC is used to convert fivephase input into three-phase output and at the same time control the amplitude and frequency of the output current, that will be injected into the grid. The proposed control, shown in Fig. 1, should satisfy the following criteria: ensures the operation of the wind turbine at the maximum power point, injects a sinusoidal current into the grid, and keeps input current in phase with input voltage. The proposed control principles of operation is as follows: maximum power point tracking algorithm [18], changes the reference current for the MPC until the wind reached to MPP, then MPC controls the switches according to

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the reference current provided by the MPPT controller to control the switches of the DMC. Five Phase PMSG

Five to three Matrix Converter

FIlter

Three-phase laod

To Switches

A. Matrix Converter Model Matrix Converter depicted in Fig. 2 uses a set of bidirectional switches to connect Five-phase input supply with three-phase load and enables bidirectional power flow. The relation between input and output voltage of the five-to-three phase matrix converter is as follow: 𝑣𝑎𝑢 𝑣𝐴 (𝑡) 𝑆𝐴𝑎 𝑆𝐴𝑏 𝑆𝐴𝑐 𝑆𝐴𝑑 𝑆𝐴𝑒 𝑣𝑏𝑢 [𝑣𝐵 (𝑡)] = [𝑆𝐵𝑎 𝑆𝐵𝑏 𝑆𝐵𝑐 𝑆𝐵𝑑 𝑆𝐵𝑒 ] . 𝑣𝑐𝑢 (6) 𝑆𝐶𝑎 𝑆𝐶𝑏 𝑆𝐶𝑐 𝑆𝐶𝑑 𝑆𝐶𝑒 𝑣𝑑𝑢 𝑣𝐶 (𝑡) [ 𝑣𝑒𝑢 ]

MPC

V, I MPPT COntroller

Unity Amplitude

Fig. 1: Schematic of the proposed multiphase WECS.

III.

WIND TURBINE MODEL

The wind turbine output power depends on wind speed, rotor power coefficient, air density, and rotor swept area, and as given by (1), [1]-[3]. The relationships between rotor power coefficient as a function of tip-speed ratio and pitch-angle are given in (2) and (3). 𝑃𝑅 = 0.5 ∗ 𝜌 ∗ 𝐴 ∗ 𝑣𝑤3 ∗ 𝐶𝑝 (𝜆, 𝛽) 𝐶

𝐶𝑝 (𝜆, 𝛽) = 𝐶1 { 2 − 𝐶3 𝛽 − 𝐶4 } 𝑒 𝛾𝑖

1 λi

=

𝜆=

1 λ+.08β

−

.035 1+β3

wr

(1) (

−𝐶5 ) λ𝑖

+ 𝐶6

(2) (3) (4)

vw

Where: 𝑣𝑤 is the wind speed in (m/s), A is the rotor swept area, 𝐶𝑝 is the rotor power coefficient, 𝜌 is the air density (kg/𝑚3 ), 𝑃𝑅 wind power (W), 𝜆 tip-speed ratio, 𝛽 and is the pitch angle. C1, C2, C3, C4, C5 and C6 are constants. IV.

FIVE-TO-THREE DIRECT MATRIX CONVERTER

Five-to-three phase direct matrix converter is able to convert five-phase input into three-phase output with required voltage amplitude and frequency. General topology of the five-to-three matrix converter is depicted in Fig. 2. There are fifteen bidirectional power switches, five switches for every output phase. The Switching pattern is defined as follow:Sij= 1 for closed switch and 0 for open switch, with 𝑖 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒} and 𝑗 = {𝐴, 𝐵, 𝐶}. The switching constrains is defined as follows: 𝑆𝑎𝑗 + 𝑆𝑏𝑗 + 𝑆𝑐𝑗 + 𝑆𝑑𝑗 + 𝑆𝑒𝑗 = 1

A prediction for the input and output current is performed and their values are calculated, after that the cost function is calculated and an optimization process is performed to enable the choice of the best switching state that gives the value for the predicted currents. For the predicted current calculation, a model for input filter, matrix converter and load have to be performed. In the following sections those models are developed for the proposed system.

B. Load Model Load model is very important in MPC as it’s used to enable the prediction of the load current in the next sample interval. Figure 4 shows the model of the inductive load. Load current could be obtained from Fig. 4 by applying Kirchhoff’s voltage law as follow: 𝐿

𝑑𝑖𝑜 (𝑡)

= 𝑣𝑜 (𝑡) − 𝑅 ∗ 𝑖𝑜 (𝑡)

𝑑𝑡

Where L and R are the inductance and resistance of the load. Using the discrete form of the current equation is as follows: 𝑑𝑖𝑜 𝑑𝑡

=

𝑖𝑜 (𝑘+1)−𝑖𝑜 (𝑘)

(8)

𝑇𝑠

Where 𝑇𝑠 is the sampling period, the equation for predicting the load current is obtained from substituting (8) into (7), and the resulting equation is as follows: 𝑖𝑜 (𝑘 + 1) = (1 −

𝑅∗𝑇𝑠 𝐿

) ∗ 𝑖𝑜 (𝑘) +

MODEL PREDICTIVE CONTROL ALGORITHM

Due to the inherent advantages of the MPC algorithm, it is used to control the operation of the matrix converter. As shown in the flowchart, Fig. 3. Input current, source voltage, and voltage after the input filter are sensed to control input current. Actual output current and reference value also are measured and used to control output current.

𝐿

∗ 𝑣𝑜 (𝑘)

(9)

SaA SbA ia

L

Sc A

a

iA A

C SdA b

ib

L

SeA

C

c

ic

L

SaB C SbB id ScB

d C

e

iB

B

SdB ie

V.

𝑇𝑠

Where 𝑖𝑜 (𝑘 + 1) is the predicted value of the current for sampling interval (k+1).

L

(5)

(7)

SeB

C

SaC SbC ScC iC SdC

C

SeC

Fig. 2: Five-to-three direct matrix converter.

520

D. Cost Function The key parameter of the MPC is the cost function as it determines the required control functions. In the proposed system, the required control function is to control output current amplitude and frequency and also to control the input current to be in-phase with supply voltage. For the required control criteria for the proposed system the cost function is given as:

Measure Vs, Ve, Is, Io Prediction os source and load current Eqs. (9) and (5) Gopt=inf.

𝑝

𝑝

𝑝

𝑝

∗ ∗ ∗ ∗ 𝑔 = |𝑖𝑜𝛼 − 𝑖𝑜𝛼 | + |𝑖𝑜𝛽 − 𝑖𝑜𝛽 | + |𝑖𝑠𝛼 − 𝑖𝑠𝛼 | + |𝑖𝑠𝛽 − 𝑖𝑠𝛽 |(14) For i=1...125

∗ ∗ Where ioα currents and ioβ are the real and imaginary parts of 𝑝 𝑝 the reference output current vector. Currents 𝑖𝑜𝛼 and 𝑖𝑜𝛽 are the real and imaginary parts of the predicted output current vector ∗ ∗ calculated in equation (9). Currents 𝑖𝑠𝛼 and 𝑖𝑠𝛽 are the real and imaginary parts of the reference source current vector. Currents 𝑝 𝑝 𝑖𝑠𝛼 and 𝑖𝑠𝛽 are the real and imaginary parts of the predicted source current vector calculated in equation (13). The reference source current could be calculated as follows [17]:

Cost Function Eq. (10)

i>=125

Applying optimum switching state

𝑖𝑠∗ = 𝐺 ∗ 𝑉𝑠

(15)

Where 𝐺 is the instantaneous conductance calculated as follow:

Figure 3: MPC flowchart.

𝑃

𝐺 = ‖𝑉 𝑠‖2

R

Io(t)

(16)

𝑠

Vo(t)

Where 𝑃𝑠 the average source power and || || is the 2-norm of vector 𝑉𝑠 . This cost function doesn’t need for weighting factor. Elimination the weighting factor from cost function make it simpler and more reliable, as the process of choosing the weighting factor not a straight way and it requires to try many times before reaching to the best value.

L

Figure 4: Inductive load modeling.

C. Filter Model The input filter model, based on the circuit shown in Fig. 5, can be described by the following continuous-time equations: 𝑣𝑠 (𝑡) = 𝑅𝑓 ∗ 𝑖𝑠 (𝑡) + 𝐿𝑓 𝑖𝑠 (𝑡) = 𝑖𝑢 (𝑡) + 𝐶𝑓

𝑑𝑖𝑠 (𝑡)

𝑑𝑣𝑖 (𝑡)

𝑑𝑡

+ 𝑣𝑢 (𝑡)

(10) (11)

𝑑𝑡

Where 𝐿𝑓 and 𝑅𝑓 are the inductance and resistance of the input filter, while 𝐶𝑓 is the capacitance of the input filter. Considering the approximation for the derivative of the input current 𝑑𝑖𝑠 𝑑𝑡

=

𝑖𝑜 (𝑘+1)−𝑖𝑜 (𝑘)

(12)

𝑇𝑠

The equation for predicting the source current is obtained from substituting (12) into (11), gives: 𝑖𝑠 (𝑘 + 1) = (1 −

𝑅𝑓 ∗𝑇𝑠 𝐿𝑓

) ∗ 𝑖𝑠 (𝑘) +

𝑇𝑠 𝐿

∗ (𝑣𝑠 (𝑘) − 𝑣𝑢 (𝑘)) (13)

VI.

RESULTS AND DISCUSSIONS

The whole system, comprising of the wind turbine, PMSG, and a five-to-three DMC is simulated using the MATLAB software environment. Special computations and algorithms, such as the MPPT algorithm and the MPC, are written as MATLAB functions. Each wind velocity has its own maximum power point, and this cause the output frequency of the PMSG to vary according to the speed that gives the maximum power. To interface the variable frequency terminals of the PMSG to the fix frequency grid, a DMC is connected between the PMSG and the grid. The results obtained from the simulation, illustrates the proper operation of the proposed control algorithm. The functions of the proposed system are as follows: extract maximum power from wind turbine, inject sinusoidal current into the grid and keep input current in phase with input voltages. Figure 6 depicts the relation between input and output currents, and Fig.7 illustrates grid voltage and current injected into the grid. The current injected into the grid is sinusoidal and in phase with the grid voltage. During the simulation a step change in the wind speed done to check the ability of the proposed system to track maximum power and, as shown in Figs. 8 and 9, when a step change occur at the wind speed, maximum power coefficient 𝐶𝑝 remains at the same maximum value.

Figure 5: L-C input filter modeling.

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VII. CONCLUSION

Figure 6: input voltage (V) and input current (A) multiplied by 20.

Multiphase wind generation system has been proposed in this paper. The proposed system consists of five-phase PMSG and five-to-three DMC controlled with MPC algorithm. The PMSG has a variable output frequency and voltage. A five-tothree DMC was used to interface the WECS with the three phase grid. Using MPC facilitates the change of frequency and voltage at the generator terminals and is able to maintain unity power factor at the grid terminals and also satisfies the reactive power requirement of the PMSG. The proposed algorithm satisfies the required control functions such as extract maximum power from WECS, maintain unity power factor at the grid terminal and ensures the reactive power requirement of the PMSG. The proposed system has some inherent advantages such as: enable using multiphase generation due to its inherent advantage, compact size and robust control. ACKNOWLEDGMENT This paper was supported by NPRP grant No. [4-077-2-028] from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. REFERENCES M Meisam Shirazi, Abbas Hooshmand Viki, Omid Babayi, “A comparative study of maximum power extraction strategies in PMSG wind turbine system”, Proc 2009 IEEE electrical power & energy conference (EPEC), 22–23 October, 2009, Montreal, QC. p. 1–6. [2] Eftichios Koutroulis and Kostas Kalaitzakis “Design of a Maximum Power Tracking System for Wind-Energy-Conversion Applications “IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 2, APRIL 2006. [3] Aryuanto Soetedjo, Abraham Lomi, Widodo Puji Mulayanto, “Modeling of Wind Energy System with MPPT Control”, 2011 International Conference on Electrical Engineering and Informatics 17-19 July 2011, Bandung, Indonesia. [4] Hamdy Radwan, Omar Abdel-Rahim, Mahrous Ahmed, Mohamed Orabi, and Ahmed Alaa El-Koussi, “Two Stages Maximum Power Point Tracking Algorithm for PV Systems Operating under Partially Shaded Conditions”, Power System Conference, MEPCON 2010. [5] Vivek Agarwal, Senior Member, IEEE, Rakesh K. Aggarwal, Pravin Patidar, and Chetan Patki “A Novel Scheme for Rapid Tracking of Maximum Power Point in Wind Energy Generation Systems”, IEEE Transactions on Energy Conversion, Vol. 25, No. 1, March 2010. [6] S. Ayman, A. Khalik, and K. H. Ahmed, “Performance Evaluation of Grid Connected Wind Energy Conversion Systems with Five phase Modular Permanent Magnet Synchronous Generators having Different Slot and Pole Number Combinations” Proc. IEEE International Electric Machines and Drives conference, IEMDC-2011, 15-18 May, Niagara Falls, Canada, pp. 1135-1140, 2011. [7] O. Ojo and IE. Davidson, “PWM-VSI inverter-assisted stand-alone dual stator winding induction generator”, IEEE Trans Energy Conversion, vol. 36, 2000, pp. 1604–1611. [8] D. Levy, “Analysis of a double-stator induction machine used for a variable-speed /constant-frequency small-scale hydro /wind electric power generator”, Electric Power Systems Research, vol. 11, pp. 205-223, 1986. [9] P. Wheeler, J. Rodríguez, J. Clare, L. Empringham and A. Weinstein “Matrix converters: a technology review”, IEEE Trans. On Ind. Elect., vol. 49, no. 2, April 2002. [10] Omar Abdel-Rahim, Haitham Abu-Rub and Sk. Moin, “Space vector PWM or five to three phase matrix converter”, Applied Power Electronics Conference and Exposition (APEC), 2013. [1]

Figure 7: Grid voltage (V) and grid current (A) multiplied by 10.

Figure 8: Rotor power coefficient Cp

Figure 9: wind speed (m/s) during step change

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