Chapter 1: Background, objective, and structure of

Faculty of Engineering Department of Electrical and Computer Engineering

Grid-connected Photovoltaic Systems

A thesis submitted in partial fulfillment of the requirements for the degree of Master in Electric Power and Machines

By Alaa-eldine Abdallah

Supervised by: Dr. Ahmed Mordi Assistant professor

Dr. Mohamed Tarnini Assistant professor

2015

Faculty of Engineering Department of Electrical and Computer Engineering

Grid-connected Photovoltaic Systems

A thesis submitted in partial fulfillment of the requirements for the degree of Master in Electric Power and Machines

By Alaa-eldine Abdallah

Supervised by: Dr. Ahmed Mordi Assistant professor

Dr. Mohamed Tarnini Assistant professor

Examining committee

Signature

Prof. Mohamad Oeidat Dr. Ahmed Mordi Dr. Mohamad Tarnini Dr. Nabil Abdel Karim

2015

Abstract The photovoltaic energy as one type of renewable energy has attracted in the past decade a great interest due to its free availability, to its ease of use relatively to other electricity resources, and its “green” operation on the entire earth planet. So it is necessary to highlight its operation, its use, its evolution, its advantages, and furthermore its capability to solve several problems on the electric grid. The advances in this field of electrical engineering are great till now and keep discovering new contributions which are illuminating the future plan of this industry. On the other hand, the photovoltaic energy as an additional source on the grid requires studying its behavior under specific circumstances like electric faults, islanding operation, and so on. In this thesis, the above ideas are studied, simulated in Matlab/Simulink, and the results are analyzed to end up with a conclusion. They are described with explanatory schematics and their results are exhibited using Matlab model screenshots to demonstrate the concept. In the end of this thesis, a future work plan is presented to implement more advances in this field of electrical engineering.

i

Acknowledgement I would like to use this opportunity to express all my thanks and full gratitude to my supervisors Dr. “Ahmed Mordi” and Dr. “Mohamed Tarnini” who didn’t miss any support or guidance that can give me advances. I am thankful a lot for their supportive criticism which illuminated for me technical views on a number of issues related to the thesis. I am sincerely grateful for them and for their advices which has really improved my educational level and technical knowledge especially in my thesis subject.

ii

Contents Chapter 1: Background, objective, and structure of thesis 1.1- Photovoltaic energy 1.2- Photovoltaic cell equivalent circuit and equations 1.3- Representation of photovoltaic energy 1.4- Photovoltaic inverters 1.5- Topologies of photovoltaic inverters 1.6- Objective 1.7- Structure of thesis

1 1 2 5 5 5 6 7

Chapter 2: Building photovoltaics using Matlab/Simulink

9

Chapter 3: Maximum power point tracking 3.1- Why maximum power point tracking 3.2- MPPT as function of the load 3.3- Methods of MPPT 3.4- Simulation by Matlab 3.5- MPPT in our grid-connected PV systems 3.6- Power loss caused by weak MPPT

14 14 14 15 18 20 20

Chapter 4: Grid-connected PV system driven by load 4.1- Operating principle 4.2- Simulation by Matlab 4.3- Preliminary conclusion 4.4- Elimination of harmonics

22 22 23 27 27

Chapter 5: The recent evolution in grid-connected PV system 5.1- Introduction 5.2- Structure of grid-connected PV system independent from load 5.2.1- DC-DC boost converter control 5.2.2- Voltage source inverter control 5.2.3- Current control in the rotating reference frame 5.3Simulation by Matlab 5.4- Grid energy storage 5.4.1- Compressed-air energy storage 5.4.2- Pumped hydroelectric storage 5.4.3- HVDC capacitors 5.5- Conclusion

32 32 32 33 34 34 36 41 41 41 41 42

Chapter 6: Grid-connected PV system for grid support 6.1- Introduction 6.2- Control method solving voltage disturbances

43 43 43

iii

6.36.46.5-

Grid under-voltage Grid overvoltage Conclusion

43 46 49

Chapter 7: Grid-connected PV system under faults conditions 7.1- Introduction 7.2- Case of infinite bus 7.3- Case of non-zero impedance grid with 3-phases to earth fault 7.4- Case of non-zero impedance grid with 2-phases to earth fault 7.5- Case of non-zero impedance grid with one phase to earth fault 7.6- Conclusion

50 50 50 52 55 56 58

Chapter 8: Islanding problem and mitigation 8.1- Definition 8.2- Simulation by Matlab 8.2.1- Case of pure resistive grid impedance 8.2.2- Case of inductive grid impedance 8.2.3- Case of capacitive grid impedance 8.3- Mitigation techniques

59 59 59 59 62 63 65

Chapter 9: Conclusion and future work 9.1- Conclusion 9.2- Future work

66 66 66

iv

List of symbols A AC DC Dq0 Eg0 I IGBT I0 IMPP Iph Ipv Irs ISC ISCr K Ki Kp MPP MPPT Np Ns P PI PL PV PWM Q QL Rs T THD Tr VMPP Vg* Voc Vpv VSI

Ideality factor of the photovoltaic diode Alternative current Direct Current direct quadrature zero (transformation) Band gap of silicon Current injected by the photovoltaic system into the grid Insulated-Gate Bipolar Transistor Photovoltaic module saturation current Photovoltaic module current at maximum power point operation Light generated current in a photovoltaic module output current of a photovoltaic module Reverse Saturation Current Photovoltaic module short circuit current at operating temperature Photovoltaic module short circuit current at 298 K Boltzman constant Integral controller constant Proportional controller constant Maximum Power Point Maximum Power Point Tracking Number of photovoltaic cells connected in parallel Number of photovoltaic cells connected in series Active power injected by the photovoltaic system into the grid Proportional Integral Active power of the connected load Photovoltaic Pulse Width Modulation Electron charge reactive power of the connected load Series resistance of a photovoltaic cell Operating temperature Total Harmonic Distortion Reference temperature = 298 K Voltage across photovoltaic module at maximum power point operation RMS phase-to-neutral reference grid voltage Open Circuit Voltage of a photovoltaic module Output voltage of a PV module Voltage Source Inverter

v

List of figures

Figure 1.1: Process resulting from conjunction of P and N type semiconductors Figure 1.2: A photovoltaic cell operating principle Figure 1.3: Equivalent circuit of photovoltaic cell Figure 1.4: I-V characteristic of photovoltaic cell Figure 1.5: P-V characteristic of photovoltaic cell in function of irradiances Figure 1.6: P-V characteristic of photovoltaic cell in function of temperature Figure 1.7: Topologies of photovoltaic inverters Figure 2.1: Sub-model 1 of photovoltaic module Figure 2.2: Sub-model 2 of photovoltaic module Figure 2.3: Sub-model 3 of photovoltaic module Figure 2.4: Sub-model 4 of photovoltaic module Figure 2.5: Sub-model 5 of photovoltaic module Figure 2.6: Sub-model 6 of photovoltaic module Figure 2.7: The whole model of photovoltaic module Figure 2.8: I-V and P-V characteristics of photovoltaic module Figure 3.1: Determination of maximum power point Figure 3.2: IMPP VS ISC from to 1000W/m2 for “Sanyo hit 215W” Figure 3.3: VOC VS Irradiance for “Sanyo hit 215W” Figure 3.4: Maximum power point Figure 3.5: Algorithm for P&O method Figure 3.6: Maximum power point tracking simulation Figure 3.7: Maximum power point tracking results Figure 3.8: Conceptual maximum power point tracking in grid connected photovoltaic systems Figure 3.9: ripples in voltage and power during MPPT Figure 4.1: Operating principle of grid-connected PV system driven by load Figure 4.2: Control schematic per phase for grid-connected PV system driven by load Figure 4.3: Matlab model Figure 4.4: PWM technique Figure 4.5: voltage on one phase at the output of the inverter Figure 4.6: Waveforms of various currents Figure 4.7: THD of conventional source delivered current Figure 4.8: circuit schematic with LC filter Figure 4.9: Matlab model Figure 4.10: Waveforms of the currents with LC filter Figure 4.11: THD of conventional source delivered current using LC filter Figure 5.1: Structure of grid-connected PV system independent from load Figure 5.2: Boost converter Figure 5.3: Voltage source inverter vi

1 2 2 4 4 5 7 9 10 10 11 11 12 12 13 15 16 17 18 19 19 20 20 21 22 23 24 25 26 26 27 28 29 30 30 33 33 34

Figure 5.4: Matlab model Figure 5.5: Behavior of the photovoltaic source Figure 5.6: DC link voltage Figure 5.7: Voltage applied at the output of the photovoltaic inverter

37 38 38 39

Figure 5.8: Waveforms of various currents Figure 5.9: Synchronization with grid voltage Figure 5.10: Values of Id and Iq Figure 5.11: Waveforms of various currents in case of excess in power Figure 6.1: Control method of voltage disturbance Figure 6.2: Waveforms of voltages during under-voltage Figure 6.3: Values of injected currents in dq domain at the time of undervoltage Figure 6.4: Waveforms of the injected three currents during the undervoltage Figure 6.5: DC link voltage during conventional source undervoltage Figure 6.6: Waveforms of voltages during overvoltage Figure 6.7: Values of injected currents in dq domain at the time of overvoltage Figure 6.8: Waveforms of the injected three currents during the overvoltage Figure 6.9: DC link voltage during conventional source overvoltage Figure 7.1: Matlab model Figure 7.2: Injected currents during fault in case of zero impedance grid Figure 7.3: Voltage on one phase during the fault Figure 7.4: Grid voltage Vgd and Vgq in dq domain during the fault Figure 7.5: Injected currents in the three phases at the starting of the fault Figure 7.6: Value of power delivered to grid from the photovoltaic source Figure 7.7: DC link voltage during fault Figure 7.8: grid voltage during 2-phase to earth fault in dq domain Figure 7.9: three injected currents at the beginning of the 2-phase to earth fault Figure 7.10: grid voltage during one phase to earth fault in dq domain Figure 7.11: three injected currents at the beginning of the one phase to earth fault Figure 8.1: Matlab model Figure 8.2: Grid voltage on one phase in case 8.2.1.a at the end of islanding period Figure 8.3: Grid voltage on one phase in case 8.2.1.b at the end of islanding period Figure 8.4: Grid voltage on one phase in case 8.2.1.c at the end of islanding period Figure 8.5: Grid voltage on one phase in case 8.2.2 at the end of islanding period Figure 8.6: Grid frequency in case 8.2.2 before and during islanding period Figure 8.7: Grid voltage on one phase in case 8.2.3 at the end of islanding period Figure 8.8: Grid frequency in case 8.2.3 before and during islanding period

39 40 40 41 43 44 45

vii

45 46 47 47 48 48 51 52 53 53 54 54 55 56 56 57 57 60 61 61 62 62 63 64 64

Figure 9.1: Conceptual schematic of the future work

viii

67

Chapter 1: Background, objective, and structure of thesis

Chapter 1: Background, objective, and structure of thesis 1.1- Photovoltaic energy: A photovoltaic cell is constituted by a junction of two semi-conductors, one is dopped P-type, and the other is dopped N-type. When these two semi-conductors are put in conjunction, a diffusion process takes place between the electrons of Ntype and the holes of P-type, which results to a depletion zone and an electric field across this zone as shown in figure 1.1.

N-type

P-type

Depletion region

Figure 1.1: Process resulting from conjunction of P and N type semi-conductors When the photovoltaic cell absorbs solar irradiations, these irradiations provide the electrons of P-type semi-conductor and the holes of N-type semi-conductor with more energy via the photons that hit them frequently. These particles, when charged with energy exceeding the band gap, can overcome the electric field of the depletion zone and can move each to the other side [7]. Finally, the positive charges are accumulated in the P-type semi-conductor and the negative charges are accumulated in the N-type semi-conductor, the fact that -1-


creates a difference of potential at the ends of the photovoltaic cell as shown in figure 1.2 [7].

Figure 1.2: A photovoltaic cell operating principle It is worth to say that some of the radiations spread by the sun are reflected by the surface of the PV cell. These reflected radiations are not converted to electric energy and we are concerned only about the radiations absorbed by the photovoltaic cells.

1.2- Photovoltaic cell equivalent circuit and equations: The equivalent circuit of a photovoltaic cell is exhibited in figure 1.3:

Figure 1.3: Equivalent circuit of photovoltaic cell From figure 1.3, we can conclude the following equation: I  I I I L D SH

(1.1)

And V j  V  IRS

(1.2)

Where: I = Output current IL = Photo generated current

-2-


ID = Diode current ISH = Shunt current Vj = Voltage across both diode and resistor RSH V = Voltage across the output terminals RSH = Shunt resistance RS = Series resistance The Shockley diode equation gives the current flowing through the diode [14]:

  qV j I D  I 0 exp    nkT  

    1    

(1.3)

Where: I0 = Reverse saturation current n = Diode ideality factor (1 for an ideal diode) q = Elementary charge k = Boltzmann's constant T = Absolute temperature Substituting in the first equation, we conclude the characteristic equation of a photovoltaic cell



    q V  IR S I  I L  I 0 exp    nkT  



 

 

R SH

(1.4)

When the photovoltaic cell is operating with open circuit, we shall have I = 0. Assuming the shunt resistance of the photovoltaic cell is very high as it is usually, we get the open circuit voltage [14]: Voc 

nkT q



   1  V  IRS

I  ln  L  1  I0   

(1.5)

When the photovoltaic cell is operating with short circuit, we shall have V = 0. For high quality solar cell, RS and I0 are low, and RSH is high. We get the short circuit current [14]: -3-

Chapter 1: Background, objective, and structure of thesis I SC  I L

(1.6)

Noting that the photovoltaic array short-circuit current is directly proportional to changes in solar irradiation whereas the open-circuit voltage does not change notably. On the other hand, the open-circuit voltage descends as the cell temperature rises.

Current Density (mA/cm2)

The I-V characteristic of a photovoltaic cell is shown in figure 1.4:

Voltage (V)

Figure 1.4: I-V characteristic of photovoltaic cell The P-V characteristics of a photovoltaic module are shown in figures 1.5 and 1.6 [15]:

Figure: 1.5: P-V characteristic of photovoltaic module in function of irradiances

-4-


Figure: 1.6: P-V characteristic of photovoltaic module in function of temperature The voltage at the output of a photovoltaic module decreases with the increase of the temperature. The current generated by the photovoltaic module increases with the increase of irradiations falling on the photovoltaic module [14]. In addition, the values of current, voltage, and then power, depends also of the combination of number of cells in series and in parallel.

1.3- Representation of photovoltaic energy: According to the characteristics of photovoltaic source, a photovoltaic energy can be considered as a current source when operating at the left of the maximum power point, and a voltage source when operating at the right of the maximum power point. But for more accuracy, a photovoltaic energy in our following simulations will be considered as a controlled current source whose current value is a function of the voltage across it as the above equations imply.

1.4- Photovoltaic inverters: An inverter is necessary to convert the DC voltage of photovoltaic modules to AC voltage synchronized with the voltage of the grid. This involves two major tasks. One is to insure that the photovoltaic module is operated at the maximum power point, and the other is to inject a sinusoidal current into the grid or at least, to minimize the harmonic distortion factor of the current injected as much as possible.

1.5- Topologies of photovoltaic inverters: We distinguish three main topologies [1]: a. Centralized inverters: This technology illustrated in figure 1.7.a, was based on centralized inverters that interface a large number of photovoltaic modules to the grid. The photovoltaic modules were divided into series -5-


connections (called strings), each generating a sufficiently high voltage to avoid further amplification. These series connections were then connected in parallel, through string diodes in order to reach high power levels. This centralized inverter includes some severe limitations, such as high voltage DC cables between the photovoltaic modules and the inverter, power losses due to a centralized maximum power point tracking, mismatch losses between the photovoltaic modules, and losses in the string diodes. b. String inverters: The string inverter shown in figure 1.7.b is a reduced version of the centralized inverter, where a single string of photovoltaic modules is connected to the inverter. The input voltage may be high enough to avoid voltage amplification. In this technology, there are no losses associated with string diodes and separate maximum power point tracking can be applied to each string. This increases the overall efficiency compared to the centralized inverter. c. Multi-string inverters: The multi-string inverter is shown in figure 1.7.c and is the further development of the string inverter, where several strings are interfaced with their own DC-DC converter to a common DC-AC inverter. This is beneficial since every string can be controlled individually compared to centralized system. Thus, the operator may start his own photovoltaic power plant with a few modules.

1.6- Objective: The researches for solutions to overcome the booming in energy demand, the recently-introduced economical constraints, the limitations in the construction of additional transmission lines which deliver the electrical power to the consumers, the conditions set by many standards regarding the environmental pollution of conventional power plants, In addition to the declining cost and prices of solar modules, an increasing efficiency of solar cells, manufacturing technology improvements, are the main causes behind the world’s attitude toward renewable energies, where they are being used to compensate for the power drawn by various loads –whatever are their types- either totally or partially, as an effort to minimize the energy bills and diminish the stress on generation units, without neglecting the power quality requirements. Moreover, the recent evolutions of grid-connected photovoltaic systems have confirmed more advances and more capabilities to control the grid behavior by these systems in addition to the power compensation.

-6-


DC/ AC

DC/ AC

DC/ AC

DC/ DC

DC/ DC DC/ AC

a)

b)

c)

Figure 1.7: Topologies of photovoltaic inverters

1.7- Structure of thesis: This thesis is organized as follows:

-

Chapter 2 describes a step-by-step procedure of how to build a photovoltaic cell in Simulink/Matlab from the photovoltaic equations.

-

Chapter 3 describes what is and why “maximum power point tracking”, and its electrical interpretation, in addition to the most popular methods to maximize extracted power.

-

Chapter 4 describes the grid-connected photovoltaic system driven by load: operating principle, simulation by Matlab showing the behavior of all parts of the circuit.

-7-


-

Chapter 5 describes the recent evolution of grid-connected photovoltaic system operating in a new principle, satisfying great advances and more control capability. The simulation by Matlab verifies the expectations.

-

Chapter 6 shows how the grid-connected photovoltaic system is used to support the electric grid in case of voltage disturbances.

-

Chapter 7 presents the study of the grid-connected photovoltaic system under faults conditions.

-

Chapter 8 presents the islanding problem and its mitigation.

- Chapter 9 provides a quick survey on the future work, as an effort to implement more advances in this field of electrical engineering.

-8-

Chapter 2: Building Photovoltaics using Matlab/Simulink

Chapter 2: Building Photovoltaics using Matlab/Simulink A step-by-step procedure is presented in order to build a mathematical model on Matlab/Simulink representing a photovoltaic module constituted of 36 cells. The mathematical model is built from the equations concluded from the schematic of a photovoltaic cell shown in figure 1.3. A. The model in figure 2.1 converts the temperature given in degrees Celsius to Kelvin:

Figure 2.1: Sub-model 1 of photovoltaic module According to the following equations:

Trk  273  25 (Reference temperature)

(2.1)

Tak  273  Top (Operating temperature)

(2.2)

B. The model in figure 2.2 calculates the short circuit current at given operating temperature:

-9-


Figure 2.2: Sub-model 2 of photovoltaic module According to the following equation [2]: I ph  I sc  K i Tak  Trk X

(2.3)

Where X = Irradiations C. The reverse saturation current of the diode is calculated in the model shown in figure 2.3:

Figure 2.3: Sub-model 3 of photovoltaic module According to the following equation [2]: I rs 

I sc

 qV OC exp   N s kATak 

(2.4)

  1  

D. The model in figure 2.4 calculates the module saturation current from reverse saturation current and module operating temperature:

- 10 -


Figure 2.4: Sub-model 4 of photovoltaic module According to the following equation [2]:

T I 0  I rs  Tr 

3  qE    1 g0 1   exp      Ak  T r T     

(2.5)

E. The model in figure 2.5 calculates the product NsAKT:

Figure 2.5: Sub-model 5 of photovoltaic module

F. The following equation [2]:       q V PV  I PV R s   I PV  N p I ph  N p I 0 exp    1 N AkT s        





Is modeled by the function shown in figure 2.6: - 11 -

(2.6)


Figure 2.6: Sub-model 6 of photovoltaic module G. The above 6 models are interconnected as shown in figure 2.7:

Figure 2.7: The whole model of photovoltaic module Simulating the above model using Matlab/Simulink, and setting the parameters in accordance to SOLKAR module 36W (for example) having the specifications as per Table 2.1 [2]: Table 2.1: Specifications of SOLKAR module 36W Rated power Voltage at maximum power point (Vmpp) Current at maximum power point (Impp) Open circuit voltage (VOC) Short circuit current (ISCr) Number of cells in series (Ns) Number of cells in parallel (Np)

37.08 W 16.56 V 2.25 A 21.24 V 2.55 A 36 1 - 12 -

Chapter 2: Building Photovoltaics using Matlab/Simulink We get the I-V and P-V characteristic curves in function of the voltage across the photovoltaic module as shown in figures 2.8:

PV module current (A)

3 2.5 2 1.5 1 0.5 0

0

2

4

6

8

10

12

14

16

18

20

14

16

18

20

PV module voltage (V)

PV module power (W)

40 30 20 10 0

0

2

4

6

8

10

12

PV module voltage (V)

Figure 2.8: I-V and P-V characteristics of photovoltaic module

- 13 -

Chapter 3: Maximum power point tracking

Chapter 3: Maximum power point tracking 3.1- Why maximum power point tracking (MPPT): In the photovoltaic applications, all available photovoltaic power is delivered to the electric grid and the system should operate in order to improve its energy conversion. Therefore it is necessary that a control system detects variations in the photovoltaic array conditions and lead the system to a new operating point where the maximum power can be extracted, especially that it is not possible to predict offline the maximum power point, and it is only possible online and should be determined by a control system. In addition, while the cost of installation of photovoltaic array is high relatively compared to its operation cost, it is strongly recommended that the photovoltaic array generates its maximum power to benefit from this available energy as much as possible, especially that, the photovoltaic array once installed, it will generate the electric energy approximately for free. Furthermore, it may happen that efficiency of the photovoltaic plant is acceptable in the morning, diminishes at midday, and then augments afternoon, due to the fact that extracted power depends on several factors including but not limited to temperature which is high at midday, so it is also recommended to accommodate again.

3.2- MPPT as function of the load: The power at maximum power point is not always additive with the increase of load neither subtractive, there is an optimum impedance of the network (seen from the photovoltaic plant) where the power is maximal, so it is necessary to accommodate for the continuous change of loads. To determine the optimum load extracting the maximum power, this can be done by looking in figure 3.1 for the intersection of the I-V characteristic of the photovoltaic source and that of the load seen from the photovoltaic plant (a straight line in case of a linear load).

- 14 -


40

P-V characteristic I-V characteristic

35

Current (A) and power (W)

30

25

20

15

I-V characteristic of load

10

5

0

0

2

4

6

8

10

12

14

16

18

20

Voltage (V)

Figure 3.1: Determination of maximum power point For example, for a photovoltaic source having as I-V characteristic the above (environmental factors are considered constant in this stage), the optimum load seen from the photovoltaic plant is R = 16.5/2.5 = 6.6 ohms.

3.3- Methods of MPPT: As mentioned in previous chapter and concluded from the P-V curve of the photovoltaic module, the power extracted from the photovoltaic module is not linear with the variations of voltage. From the equation which relates the output current to the output voltage of the photovoltaic module, we can conclude the value of the output current once the voltage is determined, therefore, as a first tip, for a maximum power extraction, we have to regulate the output voltage of the photovoltaic module to a value where the power is maximal. Generally, the photovoltaic modules are equipped with capacitors in parallel with them to minimize the fluctuations of the voltage. The greater is the capacitance, the slower is the maximum power point tracking, and vice versa. There are many methods of maximum power point tracking, each of them depends on the topology of connection between the photovoltaic array and the grid, but the most known methods [6 & 11] are: 3.3.1- Open circuit voltage method: This method is simple and consists of measuring the open-circuit voltage of the photovoltaic array Voc. The maximum power point voltage is generally Vmpp = 0.75 X Voc. However, care must be taken for any variations in the environmental parameters because this method works correctly only at fixed environmental parameters.

3.3.2- Short circuit current method: This method is also simple and consists of measuring the short-circuit current of the photovoltaic array Isc. The maximum power point current is generally Impp = 0.94 X Isc. - 15 -

Chapter 3: Maximum power point tracking In this method also, care must be taken for any variations in the environmental parameters because this method works correctly only at fixed environmental parameters.

Figure 3.2: IMPP VS ISC from to 1000W/m2 for “Sanyo hit 215W” 3.3.3- Temperature methods: The open circuit voltage VOC of the solar cell varies mainly with the cell temperature, whereas the short circuit current is directly proportional to the irradiances level and is relatively steady over cell temperature changes. The open circuit voltage VOC doesn’t change with the variations of irradiances as shown on figure 3.3, and can be described through the following equation:



dV VOC  VOCSTC  OC T  TSTC dT



(3.1)

Where: VOCSTC is the open circuit voltage under Standard Test Conditions (STC) dV OC dT

= 0.08 V/K

TSTC is the cell temperature under Standard Test Conditions On the other hand, the maximum power point voltage VMPP can be described through the following equation: V MPP  u  S .v   T w  S . y  .V MPPSTC (3.2)   Where VMPPSTC is the maximum power point voltage under STC.

- 16 -


Figure 3.3: VOC VS Irradiance for “Sanyo hit 215W” The following table 3.1 shows the values of u, v, w, and y of the optimal voltage equation (3.2) in relation to the irradiance level S. Table 3.1: S(kW/m2) 0.1÷0.2 0.2÷0.3 0.3÷0.4 0.4÷0.5 0.5÷0.6 0.6÷0.7 0.7÷0.8 0.8÷0.9 0.9÷1.0

u(S) 0.43404 0.45404 0.46604 0.46964 0.47969 0.48563 0.49270 0.49190 0.49073

v(S) 0.1621 0.0621 0.0221 0.0131 -0.0070 -0.0169 -0.0270 -0.0260 -0.0247

w(S) 0.00235 0.00237 0.00228 0.00224 0.00224 0.00218 0.00239 0.00223 0.00205

y(S) -6e-4 -7e-4 -4e-4 -3e-4 -3e-4 -2e-4 -5e-4 -3e-4 -1e-4

3.3.4- Incremental conductance: In this method, the slope of power versus voltage characteristic is used to define the direction of the perturbation. The slope (dP /dV) is zero at the maximum power point, positive on the left of the maximum power point, and negative on the right of the maximum power point. Since: dPpv





d I pv V pv

dV pv

I

dV pv

pv V pv

dI pv

(3.1)

dV pv

It can be rewritten as: 1

dPpv

V pv dV pv



I pv V pv



dI pv

(3.2)

dV pv

- 17 -

Chapter 3: Maximum power point tracking The signal of the slope is the same as the second term of the above equality because the voltage Vpv is always positive. So, by measuring the components of the second term of the equality (usually by a microcontroller) we can get the signal of the slope and control the circuit in a way to reach the maximum power point. Whatever is the method of maximum power point tracking, its control is a continuous process of varying the parameters of the circuit around their maximum power point, without this process maximum power point tracking cannot be achieved.

Power (W)

3.3.5- Perturbation and observation: The Perturbation and Observation method compares the power of the previous step with the power of the new step in such a way that the next action can increase or decrease the array voltage. This method changes the reference value by a constant factor of voltage. It moves the operating point toward the maximum power point by periodically increasing or decreasing the array voltage. From figure 3.4, it can be seen that incrementing (decrementing) the voltage increases (decreases) the power when operating on the left of the maximum power point, and decreases (increases) the power when on the right of the maximum power point. Therefore, if there is an increase in power, the subsequent perturbation should be kept the same to reach the maximum power point and if there is a decrease in power, the perturbation should be reversed.

Voltage (V)

Figure 3.4: Maximum power point

3.4- Simulation by Matlab: The Perturbation and observation method is expressed in algorithm (figure 3.5) and has been selected to be simulated by Simulink/Matlab because it is the most popular method. The model is shown in figure 3.6. Maximum power point tracking is achieved successfully as shown in figure 3.7 where the power and the current are stabilized with small oscillations around the maximum power point:

- 18 -


Figure 3.5: Algorithm for P&O method

Figure 3.6: Maximum power point tracking simulation

- 19 -


45 Power Current

PV module current (A) and power (W)

40

35

30

25

20

15

10

5

0

0

1

2

3

4

5

6

7

8

9

10

Time (s)

Figure 3.7: Maximum power point tracking results

3.5- MPPT in our grid-connected PV system: Vi and Ii in figure 3.8 are not constants, they vary with the parameters of the network which affect the power delivered by the photovoltaic source. Among these parameters is the duty ratio of the converter which, when varies, it changes the value of the current Ii and the voltage Vi. As a result, Ri = Vi/Ii changes with the variation of the duty cycle of the converter. This phenomenon is used to vary the voltage at the output of the photovoltaic source in order to implement the maximum power point tracking process.

Figure 3.8: Conceptual maximum power point tracking in grid connected photovoltaic systems

3.6- Power loss caused by weak MPPT: Power losses are not caused only by devices such as resistors and switching transistors, we have a power loss at each time there is a deviation from the maximum power point. As shown in figure 3.9, a voltage ripple across the photovoltaic module causes a ripple in the extracted power under the maximum power point, the greater is the voltage ripple, and the greater is the power loss. - 20 -


Ppv

MPP

Pmpp

Vpv Vmpp Figure 3.9: ripples in voltage and power during MPPT To avoid the voltage ripple across the photovoltaic module, we can increase the capacity of the capacitor installed across the photovoltaic module, as an effort to reduce power losses. However, this solution is not suitable for the case of frequent variations in the load or in the irradiations, where the maximum power point tracking becomes slower at each variation.

- 21 -

Chapter 4: Grid-connected photovoltaic system driven by load

Chapter 4: Grid-connected photovoltaic system driven by load 4.1- Operating principle:

Figure 4.1: Operating principle of grid-connected PV system driven by load Figure 4.1 describes a common schematic principle for a single stage grid-connected photovoltaic system: where a photovoltaic plant provides a DC voltage, the DC voltage is then transferred to AC voltage by a 3-phase inverter controlled by a PWM technique, the inductor is then used to provide a suitable coupling with the grid and minimize the currents fluctuations in the lines. A conventional plant is coupled to the network to feed the load in parallel with the photovoltaic plant. The PWM technique which controls the switching of IGBTs in the inverter shall operate in a way that track the current of the load sensed by a current sensor and inject it into the grid as shown in figure 4.2.

- 22 -


Figure 4.2: Control schematic per phase for grid-connected PV system driven by load As figure 4.2 shows, the current flowing to the load side is sensed and then injected by the photovoltaic source to compensate for the power drawn from the conventional plant. Proportional Integral controllers with feedbacks are used in the simulation to fasten the compensation process and decrease the oscillations In this type, the DC voltage bus at the input of the inverter must be higher than the grid voltage, and this is very obvious and natural because we know that the current flows inside conductors and semi-conductors from the higher voltage to the lower voltage. So we need to arrange the photovoltaic modules of the photovoltaic plant in a way to have a big number of them in series in each string to reach higher voltages.

4.2- Simulation by Matlab: The above system has been modeled using Simulink/Matlab (figure 4.3), where 20kW of load and 65X100 photovoltaic modules are used. The figures below illustrate the results:

- 23 -

In

Discre te , Ts = 5e -005 s. powe rgui

+

Me an Scope6

i -

C urrent Measurement

Scope2

Mean Value (linear) + v -

g

m

C

E

m

C

E

IGBT/Diode2

g

m

C

E

IGBT/Diode4

+

IGBT/Diode

g

Constant

+

+

-

Product

+ v -

i -

+

NOT

g

m

Logical Operator

C

E

IGBT/Diode1

NOT Logical Operator1

g

m

g

m

C

E

C

E

IGBT/Diode3

IGBT/Diode5

i -

27

100 Constant1

Temp Divide

i + -

Series RLC Branch9

C urrent Measurement7

B C

i + -

i + -


C urrent Measurement9 A

Logical Operator2

N

B

PI(s) +

SubtractPID Controller

i -

C urrent Measurement8 Scope7 Three-Phase Source

Temp Vout

PI(s) Subtract1 PID Controller1

Vin Irrad

1

Three-Phase Series RLC Load A

i


Series RLC Branch8

C

Scope1

Scope4 +

-

NOT

Voltage Measurement

i -

Scope3

Voltage Measurement2

C urrent Measurement2 i + C urrent Measurement1

Series RLC Branch7


10

+ v -

Scope8


Series RLC Branch s

C ontrolled C urrent Source

Scope


+ v -

Ipv

PI(s)


PV module

Subtract2 PID Controller2

Irradiance Scope10

Signal Generator

Figure 4.3: Matlab model

- 24 -

>=

signal

THD

In

Me an Scope11

Total Harmonic Distortion

Relational Operator1 >= Relational Operator2

Scope5 Product1

>= Relational Operator

Scope9

Mean Value

Chapter 4: Grid-connected photovoltaic system driven by load Figure 4.4 shows the process of PWM technique in one lag which switches the upper IGBT:

Figure 4.4: PWM technique In the above figures, the difference between the load current (considered as reference current) and the inverter current for one phase is compared to a saw tooth signal to control the upper IGBT switch correspondent to the same phase, the below IGBT switch has just the opposite state of the upper switch. When the difference is above the saw tooth, a positive voltage (which is the voltage of the photovoltaic source) is applied to the output of the inverter for the correspondent phase to inject a positive current into the grid and compensate for the load current, and vice versa. Figure 4.5 shows the voltage on one phase applied at the output of the inverter by controlling the inverter switches as described above.

- 25 -


Figure 4.5: voltage on one phase at the output of the inverter Figure 4.6 shows simultaneously the waveforms of the current pulled by the load, the current delivered by the conventional source, and the current delivered by the photovoltaic source.

Current of load Current injected by PV source

Current of conventional source

Figure 4.6: Waveforms of various currents Figure 4.7 shows the value of total harmonic distortion (THD) of the current delivered by the conventional source resulting from switching in the photovoltaic inverter and equal to THD = 32%. - 26 -


Figure 4.7: THD of conventional source delivered current

4.3- Preliminary conclusion: According to the above simulation, we noticed the following: 1. The power drawn from the conventional source is partially compensated. So, the conventional source and the photovoltaic source are sharing the power consumption of the load. 2. The current of the conventional source is encountering some harmonics which have several side effects on the generation units. These harmonics are due to frequent switching of inverter IGBTs at a frequency 5 KHz.

4.4- Elimination of harmonics: As an effort to remove the harmonics from the currents waveforms, an LC filter is inserted in each phase between the inverter and the coupling inductor as shown in figure 4.8 and figure 4.9 (Matlab model).

- 27 -


Figure 4.8: circuit schematic with LC filter

- 28 -

In

Discre te , Ts = 5e -005 s. powe rgui

+

Me an Scope6

i -


Scope2

Series Series RLC Series RLC Branch4 RLC Branch5 Branch6

Mean Value (linear) + - v

g

m

C

E

m

C

E

IGBT/Diode2

g

m

C

E

IGBT/Diode4

+

IGBT/Diode

g

Series RLC Branch

Constant

+

+

10 Product

+ v -

NOT

g

m

Logical Operator

C

E

IGBT/Diode1


g

m

g

m

C

E

C

E

IGBT/Diode3

IGBT/Diode5

i -

+

i -

-

Series RLC Branch8

C urrent Measurement7 Series RLC Branch3

Series RLC Branch9

i + -

N

B C

27 Scope1

100 Constant1

Temp Divide

i + -

+ i -


C urrent Measurement9 PI(s) +

Subtract PID Controller

i -


Temp Vout

PI(s) Subtract1 PID Controller1

Vin Irrad

1


A

Logical Operator2

+ - v

Ipv

PI(s)


PV module


Irradiance Scope10

Signal Generator

Product1


>= Relational Operator >= Relational Operator1 >= Relational Operator2

Scope5

- 29 -

i -

Scope9

Scope3

Voltage Measurement2 Scope4 +

i

C urrent Measurement2 i + C urrent Measurement1

Series RLC Branch7


NOT

Voltage Measurement

+ v -

Scope8


-

s

C ontrolled C urrent Source

Scope


Three-Phase Series RLC Load A B C

Chapter 4: Grid-connected photovoltaic system driven by load This simulation shows us the improvement in the tracking of the load current and in the filtration of harmonics as in figure 4.10. The new THD value of the conventional source delivered current is shown in figure 4.11 where it has decreased from 32% to 20%.

Current of load Current injected by PV source


Figure 4.10: Waveforms of the currents with LC filter

Figure 4.11: THD of conventional source delivered current using LC filter However, the LC filter causes phase shifting of the current in reference with the grid voltage, which worsen also the power factor at the conventional source unit. But this - 30 -

Chapter 4: Grid-connected photovoltaic system driven by load issue can be ignored due to the small value of the current drawn from the conventional source.

- 31 -

Chapter 5: The recent evolution in grid-connected photovoltaic systems

Chapter 5: The recent evolution in gridconnected photovoltaic system 5.1- Introduction: It is seen in chapter 4 that the current of the load can be sensed and injected even partially into the grid to compensate for the load power. In this chapter, the gridconnected photovoltaic system independent from load made by some researchers [5] is presented, where the current injected into the grid is independent from the connected load. It really depends on the available power generated by the photovoltaic source in a way that all available extracted power is injected into the grid even though the injected power may exceed the power demanded by the loads. In this case, the surplus of power can be stored on the grid for future use when the photovoltaic source is weak. In this chapter, the point of common coupling between the photovoltaic system and the grid is considered as infinite-bus.

5.2- Structure of grid-connected PV system independent from load: Figure 5.1 shows the structure of a grid-connected photovoltaic system independent from loads [5]. It is composed of a photovoltaic array connected to a DC-DC boost converter. A DC link capacitor was connected to the converter and served as a relatively constant voltage DC bus for the three-phase voltage source inverter (VSI). The current controlled voltage source inverter was used to convert the DC power stored in the DC link capacitor and to inject sinusoidal currents into the grid. The system had multiple control blocks that worked together to ensure that maximum power was extracted from the photovoltaic array and then converted to AC power to be injected into the grid. The details of each control block in the system are discussed in the next few subsections.

- 32 -


Figure 5.1: Structure of grid-connected PV system independent from load 5.2.1- DC-DC boost converter control: The DC-DC boost converter was used to extract maximum power output from the photovoltaic array and also increase the terminal voltage to a level suitable for interfacing with the grid. A schematic diagram of the converter is shown in figure 5.2.

Figure 5.2: Boost converter The photovoltaic array was connected at the input side of the converter while the DC link capacitor was connected at the output. The switching control law, u, applied at the gate of transistor Q is defined as [5]:

1...if …Vpv >V MPP u  0…if…Vpv = Relational Operator3

i -

Subtract2

Scope15

vq*

abc

PI(s)

dq0

Iq* PID Controller2

sin_cos

abc_to_dq0 Transformation

>= 0 v0*

Relational Operator1

dq0 abc sin_cos

dq0_to_abc Transformation

Signal Generator2

>= Relational Operator2



- 37 -

Scope17

Three-Phase Series RLC Load A B

+

N

Product1

16.5

+


Series RLC Branch7 C urrent Measurement9

i -

Scope19

3.14

Signal Generator1

i -

Scope4

i + -


PV module

Irradiance

PI(s)

Voltage Measurement7 +

Scope3


+ v -


i -

+ v -

Voltage Measurement6 Scope11

i -


IGBT/Diode5

+ v -

Sin_C os

PI(s) Scope12

Vin

Constant2

3-phase PLL

Scope14


NOT

Temp Vout

Irrad

+

Logical Operator2


Scope1

Divide3

C urrent Measurement6 g

+ v -

Voltage Measurement

Vabc (pu) wt


Series RLC Branch

IGBT/Diode6

Divide2 Scope


-

s

C ontrolled C urrent Source Series RLC Branch5

+ v -

Scope8 Fre q

Scope6

+

Series RLC Branch4

Me an

Scope16


Power of one module

Current in one module

Figure 5.5: Behavior of the photovoltaic source

Figure 5.6: DC link voltage

- 38 -


Figure 5.7: Voltage applied at the output of the photovoltaic inverter

Current injected by PV source Current of load


Figure 5.8: Waveforms of various currents

- 39 -


Voltage on one phase

Current in the same phase

Figure 5.9: Synchronization with grid voltage

Id

Iq

Figure 5.10: Values of Id and Iq Now the electric load on the grid is decreased in order to have an excess of electric power on the grid. Figure 5.11 shows the waveforms of the load current, the current delivered by the photovoltaic source, and the current of the conventional source during this excess of power.

- 40 -


Current injected by PV source

Current of load


Figure 5.11: Waveforms of various currents in case of excess in power As shown in figure 5.11, the conventional source absorbs the excess of the electric power on the grid to verify the current kirchoff’s law.

5.4- Grid energy storage: It may happen that there is a surplus of electric energy on the grid due to a sharp decrease in the connected loads, the fact which causes an overvoltage on the grid due to its impedance. Accordingly, energy storage system is surely needed. There are many methods for electric energy storage; among them the following is summarized: 5.4.1- Compressed-air energy storage: Ambient air is compressed by the excess of energy and stored under pressure in an underground cavern. When electricity is required, the pressurized air is heated and expanded in an expansion turbine driving a generator for power production 5.4.2- Pumped hydroelectric storage: These facilities store energy in the form of water in an upper reservoir, pumped from another reservoir at a lower elevation. During periods of high electricity demand, power is generated by releasing the stored water through turbines in the same manner as a conventional hydropower station. During periods of excess of power, the upper reservoir is recharged by using this excess in power to pump the water back to the upper reservoir. 5.4.3- HVDC capacitors: In this type of storage, the excess of power is transmitted to the high voltage direct current capacitors via AC/DC reversible converters. When electricity is needed, these converters act as inverters to - 41 -

Chapter 5: The recent evolution in grid-connected photovoltaic systems transform the direct current electricity to alternative current electricity. The purpose of using high voltage levels is that when the energy is boosted to higher levels, less value of capacities are needed.

5.5- Conclusion: By simulation of the grid-connected photovoltaic systems independent from load described in this chapter, we conclude the following:    

The current injected into the grid is independent from the connected load. It depends on the available power generated by the photovoltaic source. All available extracted power is injected into the grid even though the injected power may exceed the power demanded by the loads. Surplus of power can be stored on the grid by energy storage devices for future use when the photovoltaic source is weak.

- 42 -

Chapter 6: Grid-connected PV systems for grid support

Chapter 6: Grid-connected PV system for grid support 6.1- Introduction: In the previous chapter, the recent evolution of grid-connected photovoltaic system and how the process of current injection into grid takes place, are discussed. In this chapter, what will be discussed is the process of how the grid-connected photovoltaic system can support the grid especially during grid voltage disturbances. In this chapter, the grid is considered as non-zero impedance grid since otherwise no need to support the grid.

6.2- Control method solving voltage disturbances: The method to compensate for the grid voltage disturbances is based on the fact that the greater Id* is, the more the photovoltaic energy is supplied to the grid, and the lower Id* is, the less the photovoltaic energy is supplied to the grid. So, when there is an under voltage in the grid, it is needed to supply to the grid more energy to boost up the grid voltage to the nominal level, i.e. it is needed to boost Id*, and vice-versa. The grid voltage Vgd in dq domain is controlled in a way to follow Vgd* = 326.6, which corresponds to a grid nominal voltage 400 V phase-to-phase.

Figure 6.1: Control method of voltage disturbance

6.3- Grid undervoltage: In this case, the conventional source was supposed to facing an undervoltage by a step down of 30% of its nominal amplitude. The model was simulated and the photovoltaic source could successfully compensate for this undervoltage to lead the

- 43 -

Chapter 6: Grid-connected PV systems for grid support grid to the correct voltage by injecting more energy to the grid. The results are as follows: Figure 6.2 shows simultaneously the voltage of the conventional source and the voltage of the grid. It is shown clearly that the undervoltage has been compensated.

New actual grid voltage

Old grid voltage

Figure 6.2: Waveforms of voltages during undervoltage Figure 6.3 shows the values of the injected currents in dq domain at the time of undervoltage. It verifies that the implementation of the presented control concept is achieved. Figure 6.4 shows the three currents injected by the photovoltaic system during the undervoltage where the photovoltaic system is injecting more energy into the grid to compensate for the undervoltage. Figure 6.5 shows the DC link voltage and how this voltage drops during the undervoltage because the stored energy is being transferred to the grid progressively.

- 44 -


Id Iq

Figure 6.3: Values of injected currents in dq domain at the time of undervoltage

Figure 6.4: Waveforms of the injected three currents during the undervoltage

- 45 -


Figure 6.5: DC link voltage during conventional source undervoltage

6.4- Grid overvoltage: In this case, the conventional source was supposed to facing an overvoltage by a step up of 30% of its nominal amplitude. The model was simulated and the photovoltaic source could successfully compensate for this overvoltage to lead the grid to the correct voltage by injecting less energy to the grid. The results are as follows: Figure 6.6 shows simultaneously the voltage of the conventional source and the voltage of the grid. It is shown clearly that the overvoltage has been compensated. Figure 6.7 shows the values of the injected currents in dq domain at the time of overvoltage. It verifies that the implementation of the presented control concept is achieved. Figure 6.8 shows the three currents injected by the photovoltaic system during the overvoltage where the photovoltaic system is injecting less energy into the grid to compensate for the overvoltage.

- 46 -


New actual grid voltage Old grid voltage

Figure 6.6: Waveforms of voltages during overvoltage

Id Iq

Figure 6.7: Values of injected currents in dq domain at the time of overvoltage Figure 6.9 shows the DC link voltage and how this voltage raises during the overvoltage because the excess of energy is being accumulated in the DC link progressively.

- 47 -


Figure 6.8: Waveforms of the injected three currents during the overvoltage

Figure 6.9: DC link voltage during conventional source overvoltage

- 48 -


6.5- Conclusion: In this chapter, we found that either there is an under-voltage or overvoltage on the grid, the job of grid-connected photovoltaic system is not limited to injecting current into the grid and compensate for the power consumption of the loads, its job consists also of solving the grid problems specifically the amplitude of the voltage at the point of common coupling, and compensate for these disturbances.

- 49 -

Chapter 7: Grid-connected PV systems under faults conditions

Chapter 7: Grid-connected PV systems under faults conditions 7.1- Introduction: Any electrical grid is vulnerable to electrical faults. In this chapter, an analysis of the impact of these faults on the photovoltaic systems connected to the electric grid is presented. In fact, two major different cases are distinguished: a. The grid is considered as infinite bus and thus, the grid voltage will remain constant (strong voltage) at the point of common coupling between the grid and the photovoltaic system. b. The grid owns some small impedance, the fact which affects the grid voltage and accordingly the behavior of the photovoltaic system.

7.2- Case of infinite bus: This case was simulated in Matlab/Simulink and the model is shown in figure 7.1 where the fault is occurred from time 5 seconds till time 5.5 seconds. In this case, and due to the fact that the fault can be considered as very huge load and that the injected current in this type of grid-connected photovoltaic system is independent from the load connected to the grid, in addition to that the grid voltage is maintained constant, the behavior of the photovoltaic system will not change before and after the fault regarding the control of boost converter, the control of DC/AC inverter, and the injected current. This result can be verified by figure 7.2 where the injected currents sustain their values without any change before, after, and during the fault.

- 50 -

PI(s) Discre te , Ts = 5e -005 s.

600

powe rgui

Vmin

Subtract

In

PID Controller Scope18 i + -

C urrent Measurement a

m k

+

i -

DiodeC urrent Measurement2

Divide1

Mean Value (linear)

Scope2

+ v g

m

g

m

g

m

C

E

C

E

C

E

150 Constant

g

m

IGBT/Diode

IGBT/Diode2

+

IGBT/Diode4

C

E

+ NOT

Product

Logical Operator

+ v -

m

C

E

IGBT/Diode1


g

m

g

m

C

E

C

E

IGBT/Diode3

27

100 Constant1

Temp Divide

1

Subtract1

Ipv

+

Scope5


i -

C Scope9


A +

i -

B Scope13

A

B C

i + -

+ v -


dq0 sin_cos

vd*

Scope10

abc_to_dq0 Transformation1 Product19

Subtract2

Scope15

vq*

abc

PI(s) Product2

Iq* PID Controller2

dq0

Scope20 sin_cos


>= 0 v0*


dq0 abc sin_cos


Signal Generator2




- 51 -

Scope17

C Three-Phase Fault


Product18

Three-Phase Series RLC Load A B

+

abc

wLf

0

i -

PID Controller1


+



i -

N

Product1 Signal Generator1

i -

Scope4

i + -

Scope19

3.14

PI(s)



Scope3


+ v -

Scope11

i i -

+ v -



PV module

Irradiance

16.5

Sin_C os


IGBT/Diode5

+ v -

PI(s) Scope12

Vin

Constant2

+

Logical Operator2

Temp Vout

Irrad

3-phase PLL

Scope14


NOT


Scope1

Divide3


+ v -

Voltage Measurement

Vabc (pu) wt


Series RLC Branch

IGBT/Diode6

Divide2 Scope


-

s


+ v -

Scope8 Fre q

Scope6

+

Series RLC Branch4

Me an

Scope16


Figure 7.2: Injected currents during fault in case of zero impedance grid

7.3- Case of non-zero impedance grid with 3-phase to earth fault: In this case, the behavior of the photovoltaic system will change in every transition in fault condition as we will describe progressively, because the injected current depends on the grid voltage which will decrease in case of fault. Figure 7.3 shows the voltage on one phase before the fault, during the fault, and after the fault. It is noticed that a sharp decrease in the voltage amplitude occurs during the fault, and this is consistent also with figure 7.4 which shows the behavior of the voltage in dq domain, where Vgd decreases sharply during the fault. It is also noticed that after the fault is removed, there are transient harmonics components on the grid voltage which are caused by the sudden decrease in the connected load on the grid at the instant of fault removal. These harmonics are great especially if the connected load is much reactive.

- 52 -


Figure 7.3: Voltage on one phase during the fault

Vgd Vgq

Figure 7.4: Grid voltage Vgd and Vgq in dq domain during the fault When the fault occurs, Vd decreases, vd* decreases refer to equation (5.8), the duty ratio of IGBTs decreases, the injected power drops, the electric energy accumulates in the DC link capacitor. However, the injected current increases at the point of common coupling to unsuccessfully compensate for the sharp decrease in the grid voltage as shown in figure 7.5. - 53 -


Figure 7.5: Injected currents in the three phases at the starting of the fault As it is mentioned, the delivered power which is P = IdXVd is also decreasing sharply as verified by the screenshot of figure 7.6. The voltage of the DC link is also consistent with the above where it increases as long as the fault is not cleared because the power generated by the photovoltaic source is being accumulated in the DC link capacitor, as shown in figure 7.7.

Figure 7.6: Value of power delivered to grid from the photovoltaic source

- 54 -


Figure 7.7: DC link voltage during fault

7.4- Case of non-zero grid impedance with 2-phase to earth fault: In this case, two of the three phases are faulted to earth and one phase remain without fault. Figure 7.8 shows the values of grid voltage in dq domain. There will be a loose in synchronization because the grid voltage becomes no longer balanced during the fault. Figure 7.9 shows the waveforms of the three injected currents at the beginning of the 2-phase to earth fault. In this screenshot, it is demonstrated that the photovoltaic system continues to inject three currents in the three phases but with greater amplitude. This fact is justified by the unification of control regarding the injection of the currents in the three phases.

- 55 -


Vgd Vgq

Figure 7.8: grid voltage during 2-phase to earth fault in dq domain

Figure 7.9: three injected currents at the beginning of the 2-phase to earth fault

7.5- Case of non-zero impedance grid with one phase to earth fault: In this case, one of the three phases are faulted to earth and the remaining two phases remain without fault. Figure 7.10 shows the values of grid voltage in dq domain. In this case, the grid voltage is also unbalanced during the fault. However, this type of fault has light - 56 -

Chapter 7: Grid-connected PV systems under faults conditions influence on the values of grid voltage in dq domain because this type of fault is the less dangerous among the various types of faults. This scene is clearly illustrated by the small ripples in the “d” and “q” values. Figure 7.11 shows the waveforms of the three injected currents at the beginning of the one phase to earth fault.

Vgd

Vgq

Figure 7.10: grid voltage during one phase to earth fault in dq domain

Figure 7.11: three injected currents at the beginning of the one phase to earth fault

- 57 -


Conclusion: It is concluded from this chapter that the 3-phase to earth is the most dangerous type of faults in meaning of amplitude for the fault currents and the injected currents. The 2-phase to earth fault is also dangerous especially for the control process because the values of Vgd and Vgq are varying violently during this type of fault. The one-phase to earth fault is less dangerous from the first mentioned two types of faults. In all above cases of faults, and whenever there is a fault on the grid, the fault shall be sensed and the electric sources should be disconnected from the part of faulted grid. Usually, the circuit breakers will change states to “open circuit” in case of fault. However, if, for any reason, any circuit breaker didn’t operate, the photovoltaic system shall stop injecting current into the grid. The fault can be sensed by measuring the inrush current of the faulted feeder and the photovoltaic source can go out of network by turning “OFF” all IGBTs in the inverter.

- 58 -

Chapter 8: Islanding problem and mitigation

Chapter 8 Islanding problem and mitigation 8.1- Definition: Islanding is occurred when the main electric source in the grid (the conventional generator) is going out of network and leaves the load and the photovoltaic plant alone to form an “island”.

8.2- Simulation by Matlab: Simulation of islanding is done by opening for several seconds the normally closed 3phase circuit breaker installed at the outgoing of the conventional source as per figure 8.1, and then the circuit breaker is reclosed. Three different major cases are considered during the islanding period, the behavior of the network is illustrated in the next sections. However, it is noted that, whatever is the case, the photovoltaic system continues to inject three-phases AC currents into the grid. 8.2.1- Case of pure resistive grid impedance: In this case, the variations in the network behavior can be regrouped in three subsections: a. The power of the connected load is approximately equal to the power generated by the photovoltaic source: in this case, negligible variations occur in the amplitude and the frequency of the grid voltage [3] as shown in figure 8.2. b. The power of the connected load is much greater than the power generated by the photovoltaic source: which result in a negligible variation in the frequency but an under-voltage on the grid as shown in figure 8.3, because the generated power is not sufficient to feed the connected load [3]. c. The power of the connected load is much less than the power generated by the photovoltaic source: which result in a negligible variation in the frequency but an overvoltage on the grid as shown in figure 8.4, because the generated power exceeds the need of the connected load [3].

- 59 -

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- 60 -

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Figure 8.2: Grid voltage on one phase in case 8.2.1.a at the end of islanding period

Figure 8.3: Grid voltage on one phase in case 8.2.1.b at the end of islanding period

- 61 -


Figure 8.4: Grid voltage on one phase in case 8.2.1.c at the end of islanding period 8.2.2- Case of inductive grid impedance: In this case, the amplitude of the grid voltage can be interpreted in relation to the comparison between the power of the load and the power generated by the photovoltaic source, as in 8.2.1.

Figure 8.5: Grid voltage on one phase in case 8.2.2 at the end of islanding period However, the frequency in the grid faces an escape from the nominal value, and increases as long as the impedance of the grid is more inductive [3], as shown in

- 62 -

Chapter 8: Islanding problem and mitigation figures 8.5 and 8.6. For example, with a load of (PL = 1000KW, QL = 300Kvar), the frequency reaches 63.4 Hz in 4 seconds of islanding.

Figure 8.6: Grid frequency in case 8.2.2 before and during islanding period 8.2.3- Case of capacitive grid impedance: In this case, the amplitude of the grid voltage can be interpreted in relation to the comparison between the power of the load and the power generated by the photovoltaic source, as in 8.2.1. However, the frequency in the grid faces an escape from the nominal value, and decreases as long as the impedance of the grid is more capacitive [3], as shown in figures 8.7 and 8.8. For example, with a load of (PL = 1000KW, QL = -300Kvar), the frequency reaches 27.5 Hz in 4 seconds of islanding.

- 63 -


Figure 8.7: Grid voltage on one phase in case 8.2.3 at the end of islanding period

Figure 8.8: Grid frequency in case 8.2.3 before and during islanding period

- 64 -


8.3- Mitigation techniques: During islanding, the variations of network behavior take place in the AC side of the grid-connected photovoltaic system. So, it is obvious to monitor the AC parameters in order to detect an islanding status. Since the amplitude of the grid voltage during islanding depends on the ratio between the power of the load and the power generated by the photovoltaic system, it is recommended to detect an islanding status by a frequency relay which gives prompt notice in case of any over-frequency or under-frequency detection. An islanding status, once detected, should give order to the photovoltaic inverter to switch “OFF” all IGBTs in order to isolate the photovoltaic system from the grid.

- 65 -

Chapter 9: Future work

Chapter 9: Conclusion and future work 9.1- Conclusion: In this thesis, the operating principle of photovoltaic energy extraction is introduced, it is presented how to build a mathematical model in Matlab of the photovoltaic module starting from its characteristic equations, the most important methods of maximum power point tracking are also presented with an emphasis on the “Perturbation and Observation” method, the concept of grid-connected photovoltaic system is presented with an emphasis on the recent evolution whose control is based on the dq0 transformation, where the current injected into the grid is designed to follow a specified reference Id* + jIq*, where Id* is positive as long as there is an available power in the DC link, and Iq* = 0 for synchronization purposes. The results provide us with an injection of power from the photovoltaic source into the grid independently from the loads connected on the grid. In this thesis also, the behavior of the system is studied and analyzed under various circumstances like faults conditions and islanding operation which lead us to a necessary monitoring and control of the photovoltaic system in such cases and it is concluded that the photovoltaic system should be isolated from the grid in these circumstances by switching OFF all its inverter IGBTs.

9.2- Future work: Some researchers proposed to inject a current following a specified reference where Iq* ≠ 0, as an effort to compensate for the under-voltage and over-voltage of the grid. Some other researchers studied the behavior of the electric network in case of poor photovoltaic energy. The future work consists of using a fuzzy logic controller which takes into consideration the variation of irradiances, the variation in the ambient temperature, and the variation of the connected loads over the day, to generate the reference signals Id* and Iq* as shown in figure 9.1. The variations in the temperature and the irradiances will affect the electric power generated by the photovoltaic system, whereas the variations in the connected loads will affect the power consumption, the overall power factor on the grid, and the grid voltage. So the job of the fuzzy logic controller is to determine the reference signals Id* and Iq* to regulate and make a compromise between these variations, to sustain a correct voltage on the grid and to ensure a unity power factor in the generation units.

- 66 -

Chapter 9: Future work

Figure 9.1: Conceptual schematic of the future work

- 67 -

Appendix: DQ0 transformation In electrical engineering, direct–quadrature–zero (or dq0) transformation is a mathematical transformation that rotates the reference frame of three-phase systems in an effort to simplify the analysis of three-phase circuits. In the case of balanced three-phase circuits, application of the dq0 transform reduces the three AC quantities to two DC quantities. Simplified calculations can then be carried out on these DC quantities before performing the inverse transform to recover the actual three-phase AC results.

Definition: DQ0 transformation applied to any three-phase quantities is shown below in matrix form:

x dq 0

xd   xq x  0

    Tx abc  

  cos   2    sin  3  2   2

2  2     cos     cos     3  3    xa  2  2        sin      sin     xb 3  3      x  c  2 2  2 2 

The inverse transform is:

x abc

xa      x b   T 1x dq 0 x   c

 cos    2 2    cos    3 3    cos    2  3  

 sin  2      sin     3    2      sin     3   

2  2  xd 2   xq 2   x0 2  2 

    

Geometric interpretation: The dq0 transformation is two sets of axis rotations in sequence. We can begin with a 3D space where a, b, and c are orthogonal axes.

If we rotate about the a axis by -45 degrees, we get the following rotation matrix

   1   0 0 0   1  1        0 cos    sin       0 2  4  4      1       0 sin    cos      0  2  4  4   

 0   1    2 1   2 

Then we can rotate about the new b axis by about 35.26 degrees which is

  cos 1

2 , we get the second rotation: 3    cos  0  sin      1 0   0  sin  0 cos        

2 3 0 1 3

0  1 0

1   3 0   2   3 

When these two matrices are multiplied, we get the Clarke transformation matrix C:

   2 3    

1 0 1 2

1 2 3 2 1 2



1  2   3  2   1  2  

This is the first of the two sets of axis rotations. At this point, we can re-label the rotated a, b, and c axes as α, β, and z. This first set of rotations places the z axis an equal distance away from all three of the original a, b, and c axes. In a balanced system, the values on these three axes would always balance each other in such a way that the z axis value would be zero. The second set of axis rotations is very simple. In electric systems, very often the a, b, and c values are oscillating in such a way that the net vector is spinning. In a balanced system, the vector is spinning about the z axis. Very often, it is helpful to rotate the reference frame such that the majority of the changes in the abc values, due to this spinning, are canceled out and any finer variations become more obvious. So, in addition to the Clarke transform, the following axis rotation is applied about the z axis:

 cos     sin   0 

sin  cos  0

0  0 1 

To get the dq0 transformation by multiplication of the matrices of the 2 sets.

References 1. S. B. Kjaer and J. K. Pedersen, “A Review of Single-Phase Grid-Connected Inverters for Photovoltaic Modules”, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005. 2. N. Pandiarajan and R. Muthu, “Mathematical Modeling of Photovoltaic Module with Simulink”, ICEES 2011, 3-5 Jan 2011. 3. T. Tran-Quoc, C. Kieny and S. Bacha, “Behaviour of Grid-Connected Photovoltaic Inverters in Islanding Operation”, 2011 IEEE Trondheim PowerTech. 4. N. Kroutikova, C.A. Hernandez-Aramburo and T.C. Green, “State-space model of grid-connected inverters under current control mode”, IET Electr. Power Appl., 2007, 1, (3), pp. 329–338. 5. A. S. Khalifa and E. F. El-Saadany, “Control of Three Phase Grid Connected Photovoltaic Power Systems”, IEEE pp. 1–7, September 2010. 6. G. M. S. Azevedo, M. C. Cavalcanti, K. C. Oliveira, F. A. S. Neves and Z. D. Lins, “Evaluation of Maximum Power Point Tracking Methods for Grid Connected Photovoltaic Systems”, IEEE 2008. 7. S. Li and H. Zheng, “Energy Extraction Characteristic Study of Solar Photovoltaic Cells and Modules”, IEEE 2011. 8. D. Freeman, “Introduction to photovoltaic systems maximum power point tracking”, Texas Instruments, Application report, November 2010. 9. Z. Ahmad and S.N. Singh, “Modeling and control of grid connected photovoltaic system”, International Journal of Emerging Technology and Advanced Engineering, Volume 3, Issue 3, March 2013. 10. H.S. Seo, C.H. Kim, Y.M. Yoon, and C.S. Jung, “Dynamics of Grid-Connected Photovoltaic system at Fault Conditions”, IEEE T&D Asia 2009. 11. R. Faranda and S. Leva, “Energy Comparison of MPPT Techniques for PV Systems”, WSEAS transactions on power systems, Issue 6, Volume 3, June 2008. 12. Dash and Yazdani, “Model and Performance of a Grid-Connected Photovoltaic system”, Berkeley Electronic Press, 2008.

13. A. F. Sherwani, J. A. Usmani, Varun, and Siddhartha, “Life cycle assessment of 50kW Grid Connected Solar Photovoltaic System in India”, International journal of energy and environment, Volume 2, Issue 1, 2011. 14. www.wikipedia.com. 15. www.emrwebsite.org.

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