MODELLING, SIMULATION AND PERFORMANCE

MODELLING, SIMULATION AND PERFORMANCE ANALYSIS OF A PV ARRAY IN AN EMBEDDED ENVIRONMENT S.Chowdhury(1,2), G.A.Taylor(1), S.P.Chowdhury(3), A.K.Saha(3) and Y.H.Song(1) (1) Brunel University, UK, (2) Women’s Polytechnic, India, (3) Jadavpur University, India

ABSTRACT Photovoltaic (PV) generation involves the direct conversion of sunlight into electrical energy. In recent years it has proved to be a cost-effective method for generating electricity with minimum environmental impact. Due to the environmental and economic benefits, PV generation is now being deployed worldwide as an embedded renewable energy source and extensive research is being performed in order to study and assess the effectiveness of PV arrays in Distributed Generation (DG) systems either as a potential energy source or as energy reserve in combination with other types of distributed energy resources. This paper presents the modeling and MATLAB simulation of a stand-alone polycrystalline PV Array system and investigates load following performance efficiency under various loading and weather conditions as well as suitability with regard to enhancing power supply reliability to critical loads. The modeling of the PV array that has been performed in this research using MATLAB Simulink is based on the calculation of parameters for the Thevenin’s equivalent circuit of each cell of the array. The standard double exponential polycrystalline cell model has been adopted for this research with solar irradiance E and ambient temperature T as the input and Thevenin’s voltage Vthar and Thevenin’s resistance Rthar as the output. Keywords : PV Generation, Embedded Power Systems, converter system, irradiance, double exponential model

1 INTRODUCTION Due to the environmental and economic benefits obtained from PV generation, PV systems are being widely deployed as small-scale, on-site DG in embedded power systems. PV cells generate electric power by directly converting solar energy to electrical energy. Since the voltage and current output of a single PV cell is too small for practical usage, PV generation systems usually consist of series-parallel combinations of PV cells in order to obtain the required voltage and current output. These combinations, known as PV panels and arrays, generate DC power that has to be converted to AC at standard power frequency in order to feed the loads. Therefore PV systems are provided with sophisticated converter systems for performing the DCAC conversion. The function of the converter system is to keep the AC output voltage at the specified level in spite of the variation of the DC voltage with variation of solar irradiance E (W/m2) and ambient temperature T (°K).

critical loads, but whenever grid power is lost, the PV system is automatically connected to the 415V, 50Hz distribution grid. The entire modeling and simulation has been done in MATLAB Simulink. The schematic diagram of the stand-alone PV system is shown in Fig.1 and that operating as a backup supply is shown in Fig.-2.

In this paper, the authors report on the development of the model for a stand-alone embedded system consisting of a polycrystalline PV array connected to the 415V distribution grid. The PV system is designed to work as a back up power supply to provide power to the critical loads during unavailability of grid power supply because of any fault or routine shutdown. Under normal operating conditions, when grid power is available, the PV system is disconnected from supplying the local and

Figure 1 Stand-alone PV System

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In the above equation, V and I are the terminal voltage and current respectively, k is Boltzmann’s constant, T is the absolute temperature and e the electronic charge. The parameters Iph, Isl, Is2, Rs and Rp of the double diode model are the photocurrent, the saturation currents of the two diode terms, the series resistance and the parallel resistance, respectively. The diode parameter A is usually set to 2 for approximating the Shockley-Read-Hall recombination in the space-charge layer in the photo-diode. The remaining parameters are calculated from the values of irradiance E (W/m2) and ambient temperature T (°K) using the following empirical relationships obtained from experimental polycrystalline cell characterization as reported in earlier works [1]:

Figure 2 PV System as Backup Power Supply The entire PV array has been modeled as a Thevenin’s equivalent consisting of a Thevenin’s voltage source Vthar with a Thevenin’s resistance Rthar in series. The PV array consists of series-parallel combination of PV cells with Ns cells in series and Np cells in parallel in order to achieve the required power capacity. For a single cell, Thevenin’s voltage Vth and resistance Rth have been calculated using the standard double exponential cell model from the values of irradiance E and temperature T. Vthar and Rthar have been calculated from the values of Vth, Rth, Ns and Np. The DC output of the PV array has been converted to 50Hz AC through a PWM inverter system that maintains a constant AC voltage at its output terminals irrespective of the fluctuations in DC voltage caused by variations in irradiance and temperature.

Iph = K 0 E (1 + K 1T ) IS1 = K 2T 3 .e

(

K3 ) T

IS = K 4T 1.5 .e 2

……Eq.(3) ……Eq.(4)

K5 ( ) T

……Eq.(5)

A = K 6 + k 7T K9 RS = K 8 + + K 10T E K 12T Rp = K 11.e

……Eq.(6) ....…Eq.(7) ……Eq.(8)

Vth has been calculated from Eq.(1) by putting V=Vth and I=0 and rearranging the terms as follows:

Vth = Rp.[ Iph − Is1[e

 Vth     vt 

− 1] − Is 2[e

 Vth     Avt 

]]

……Eq.(9) The authors have used this model to study the load following performance of the PV system under varying conditions of solar irradiance and ambient temperature and its efficiency as a back up power supply in case of loss of grid power due to scheduled maintenance and sudden faults.

Isc =

2 MODELING OF PV ARRAY Each cell of the PV array has been modeled as a Thevenin’s equivalent circuit comprising the Thevenin’s voltage source (Vth) with the Thevenin’s resistance (Rth) in series. The values for Vth and Rth have been calculated from the double diode model of a typical polycrystalline PV cell that expresses the V-I characteristic of a PV cell by the equation as given below:  V + IRs   vt 

I = Iph − Is1[e

where, vt = kT/e

 V + IRs   Avt 

− 1] − Is 2[e

]−

V + IRs Rp

Similarly, the short circuit current Isc has been calculated from Eq.(1) by putting V=0 and I=Isc and rearranging the terms as shown in Eq.(10):

Rp[ Iph − Is1{e

 IscRs     vt 

− 1} − Is 2{e

 IscRs     Avt 

}]

Rp + R s ……Eq.(10)

Rth has been calculated from the relation Rth = Vth/Isc. The overall model of the PV array calculates Vth and Rth for each cell from the values of irradiance and ambient temperature and then computes the DC voltage and current output at the PV terminal from the values of Vth, Rth, number of cells in series and number of cells in parallel. The DC voltage is then fed to a standard PWM converter model with voltage feedback for conversion to AC at the specified magnitude and frequency at the customer load terminals.

……Eq.(1) ……Eq.(2)

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For each cell, Rth has been calculated as

Rth =

Vth Isc

……Eq.(11)

For the entire array,

Vthar = Vth.Ns

……Eq.(12)

and

Rthar =

Rth.Ns Np

……Eq.(13)

where, Np = no. of cells in parallel and Ns = no. of cells in series. All the calculations are done iteratively by solving Equations (3-12). In the calculation, the values of the K coefficients used are as per earlier works [1]. The values of K coefficients and those of E, T, Ns and Np are listed below in Table-1.

Figure 3 Variation of Solar Irradiance

Table-1: Values of Input Coefficients and Parameters Input Coefficients/Parameters K0 K1 K2 K3 K4 K5 K6 K7 K8 K9 K10 K11 K12 E T Ns Np

Value -5.729e-7 -0.1098 44.5355 -1.2640e4 11.8003 -7.3174e3 2 0 1.47 1.6126e-3 -4.47e-3 2.3034e6 -2.8122e-2 1000 W/m2 300 °K 1600 1600

Figure 4 Variation of DC Voltage at PV Array Terminals It is seen from the plots of Fig.-3 and 4 that the DC output voltage of the PV Array increases with irradiance. 3.2 Case 2: Load following performance with varying temperature at constant irradiance E=1000 W/m2

3 CASE STUDIES AND RESULTS The model for the stand-alone PV system has been used for the following four case studies and has been found to work efficiently and smoothly both as stand-alone system as well as a backup power supply. 3.1 Case 1: Load following performance with varying solar irradiance at constant temperature T=300°°K The power output and bus voltage profiles for the standalone PV system has been studied for switching variable loads and the relevant plots are given below.

Figure 5 Variation of Ambient Temperature

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In Cases 3 and 4, the PV system is configured to operate as a back up power supply for providing uninterrupted power to critical loads of the main utility grid system. It is connected to the 415V distribution bus of the main distribution grid and automatically reconnects whenever there is a loss of grid power supply either due to scheduled shutdown or due to an unscheduled fault. In these cases, the authors have studied that how efficiently and rapidly the PV system can take up the critical loads, in case of scheduled shutdown and faults in the main grid.

Figure 6

3.3 Case 3: Scheduled Shutdown of Main Utility Grid

Variation of DC Voltage at PV Array Terminals

The authors have studied the load following performance for both Case-1 and Case-2 with the loads of 6kW from t=0 to 0.2s, 9kW from t=0.2 to 0.3s, 12kW from t=0.3 to 0.4s and again 9kW from t=0.4 to 0.5s. It is seen from the plots of Figs.-7 and 8 that for both Cases 1 and 2, the PWM inverter system maintains a constant voltage of 415V at load terminals and the PV is also able to cater to the load variation smoothly, in spite of the switching transients for about 0.15 secs from the switching instant t=0.

Figure 9 Grid Power Output (Grid delivering 22kW load of which 6kW is critical load. Grid shutdown at t=0.2s)

Figure 7 AC Output Voltage at Load Terminals

Figure 10

Figure 8

6kW Backup Power Supply from PV System from t=0.2s

Power Output from PV Array

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preferable source for alternative power in the field of embedded generation. The authors are at present developing a model for a PV-based microgrid where several PV arrays will be operating in parallel. The arrays will augment power supply to the distribution grid at LV level during peak load periods and will supply a back-up storage facility during off-peak load periods.

Case 4: Fault at main utility grid

5 ACKNOWLEDGEMENTS The authors would like to thank the India Incoming Fellowship Scheme, Royal Society, UK for providing funds and Brunel Institute of Power Systems, School of Engineering and Design, Brunel University, UK for providing necessary infrastructure and facilities for undertaking this research work. 6 REFERENCES Figure 11

Figure 12

Grid Power Output (Grid delivering 6kW load. Grid fault at t=0.2s, cleared at t=0.25s. Grid shuts off from t=0.25s to 0.8s. Grid power is restored at t-0.8s)

6kW Backup Power Supply from PV (Supplies load from t-0.25s to 0.8s and then turns off as grid power is restored)

The Figures 9-12 show that the PV system works efficiently as a backup power supply in catering to critical loads in case of unavailability of main grid power. 4 CONCLUSION AND FURTHER WORK From the results the authors conclude that the standalone PV system with polycrystalline arrays can be successfully deployed in an embedded environment in order to provide readily available on-site power to the customers as well as to enhance service reliability to critical loads that are normally supplied by the main distribution grid. The performance efficiency of PV arrays along with their ability to provide eco-friendly power and almost nil fuel cost definitely makes them a

1. Gow J.A., Manning C.D, “Development of a model for photovoltaic arrays suitable for use in simulation studies of solar energy conversion systems”, Power Electronics and Variable Speed Drives, 23-25 September 1996, Conference Publication No.429, @IEE, 1996. 2. Marion B., et al., “Performance Parameters for GridConnected PV Systems,” 31st IEEE PVSC, Lake Buena Vista, FL, January 2005. 3. Sukamongkol, Chungpaibulpatana, Ongsakul, "A Simulation Model For Predicting The Performance of a Solar Photovoltaic System With Alternating Current Loads", Renewable Energy, Vol.27, 2002, pp.237- 258. 4. King D., Boyson W., Kratochvil J., “Analysis of Factors Influencing the Annual Energy Production of PV Systems,” 29th IEEE PVSC, New Orleans, May 2002. 5. Tian Feng, Al-Atrash H., Kersten R, Scholl C., Siri K., Batarseh I., “A single-staged PV array-based high-frequency link inverter design with grid connection”, Applied Power Electronics Conference and Exposition, 2006. APEC '06. Twenty-First Annual IEEE, 19-23 March 2006 6. A.Kovach A.,”Effects of inhomogeneous irradiation distribution on a PV array in an urban environment”, Photovoltaic Energy Conversion, 5-9 Dec. 1994. 7. T.Markvart, L.Castaner, “Practical Handbook of Photovoltaics: Fundamentals and Applications”, Elsevier AUTHOR'S ADDRESS The first author can be contacted at Brunel Institute of Power Systems School of Engineering and Design Brunel University, Uxbridge, UB8 3PH, UK email [email protected]

[email protected]

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