As Conventional sources of energy are rapidly depleting and

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1 15 CHAPTER-2 MATHEMATICAL MODELING OF PHOTOVOLTAIC SYSTEM 2.1 INTRODUCTION As Conventional sources of energy are rapidly depleting and the cost of energy is rising, photovoltaic energy becomes a promising alternative source. Recently Govt. of India has started focusing more on renewable energy source addition into the distribution network.in India there is enormous shortage of power and at the same time, there are ample possibilities of PV solar application, grid connected and off-grid both. Many research papers have been published on this technology considering various environmental conditions. Amongst others, Villalva, etal. have proposed a comprehensive approach for the design of photovoltaic arrays. Author proposed a method to determine the parameters of the non uniform V-I equation by aligning the curve at three points: open circuit, short circuit and maximum power. These three points are taken from commercial array datasheets are used for finding V-I equation for the solar (PV) model by adjusting the parameters of V-I equation, the PV model can be built by using basic math blocks [1].A novel approach for solar module temperature estimation using a simple diode model has been described by Farivar, et al. [2].Heat and light directly comes from the power of the sun that is solar energy, then electricity is produced. Different technologies are used to produce solar-electric power, which converts solar irradiance directly to electrical energy using solar cells. A photovoltaic system is a system which

2 uses one or more solar panels to convert solar energy into electricity. An easy and accurate method of modeling photovoltaic arrays is presented by Villalva, etal. [3].As PV system produces less voltage and current, so this can only be used for low power applications like feeding of small loads such as lighting systems and DC motors. For high power applications power electronic converters are required to process the electricity from the PV device. The details of modeling of photovoltaic arrays in MATLAB/Simulink environment and the use of power converter in photovoltaic application is reported in the papers[5]-[10].tracking of maximum power point and the regulation of output voltage, output current, the power flow in grid-connected PV systems is done by using the power converters. First of all proper mathematical modeling of photovoltaic system is needed, before connecting this with the converter. PV devices present a nonlinear I V characteristic as the characteristic depends on the temperature and solar irradiance. The equations of photovoltaic system are presented in details and the validation of the models against experimental data has been discussed in ref. [11]-[12]. The mathematical model of the photovoltaic system is simulated in MATLAB/Simulink environment which is required in the study of the dynamic analysis of converters, in the study of MPP tracking (MPPT) algorithms. So this chapter focuses on the understanding of behavior and functioning of a PV device and writes its basic equations. A photovoltaic system directly converts solar irradiance into electrical energy. The fundamental part of a photovoltaic system is the PV cell. A solar cell is a small device in terms of area, and the electricity a single solar cell can 16

3 generate is also small as compared to the electricity needs. For example, a single solar cell can generate daily electricity in rage of 6 Wh to 10 Wh while our daily requirement is much higher. Therefore in order to generate more electricity, many solar cells are connected together in the form of PV module. The number of solar cells to be connected together and the way they are connected together determine current and voltage that can be obtained from the modules, and the average energy it can produce every day. The cells are interconnected to form panel, then series and parallel combination of panel forms array. The figure 2.1 shows the basic physical structure of a single PV cell. Fig. 2.1 Physical structure of a PV cell. 2.2 WORKING PRINCIPLE OF A PV CELL Solar cells are the basic constituents of photovoltaic panels. Maximum solar cells are manufactured using silicon also other materials are employed. Solar cells have property of photoelectric effect: where some semiconductors have capability of changing electromagnetic radiation precisely to electrical current. The charged particles produced using incident radiation is distinguished smoothly to develop an electrical current by using 17

4 suitable layout of the solar cell. A solar cell is essentially a p-n junction formed using two distinct strata of silicon are doped using small amount of impurity atoms. So, when the two strata are combines, close to the junction, the free electrons of the n-layer are dispersed in the p-side, leaving behind an area positively charged created by the donors. Likewise, the free holes in the p-layer are dispersed in the n side, leaving behind a region negatively charged created by the acceptors. This generates an electrical field between two sides to permit potential barrier to encourage flow. When the electrons and holes cannot overcome the potential barrier the equilibrium in the junction is reached and consequently they cannot move. The current can flow in one way only since electric field drags the holes and electrons in opposite directions is shown in Figure 2.2. Fig 2.2 Effect of combination of photon and electron Under the conditions of non uniform irradiance the behavior of PV module model is discussed by author K. Ding et al.[13]. 18

5 2.3 TYPES OF PV CELL Monocrystalline Solar Cell They also known as "single crystalline" cells are readily known by their coloring. These cells are believed to be singular due to it is assumed constituted of very pure type of silicon. In the silicon world, efficiency of material depends on the purity of aligned molecules, so as to convert sunlight into electricity. Its efficiency around 20%.They are constituted of what are called "silicon ingots," which is of a cylindrical pattern that aids in optimizing execution. In this way, panels are made up of monocrystalline cells with rounded edges instead being square, like other types of solar cells. This is due to the fact fewer cells per unit of electrical output. Another advantage of these cells is that they also have highest longevity Polycrystalline Solar Cell These cells do not require the cutting process as in the case of monocrystalline cells. Here, the silicon is of square shaped as silicon is disintegrated and poured into a square mould. In this way, these cells are very much economical as hardly any silicon is wasted during the manufacturing process. Generally, efficiency of this system is around 13-16% efficiency - main reason is due to lower purity of material Amorphous Solar Cell This cell is made up of thin films. This thin films consist of amorphous silicon are generally employed for low power applications. A new method known as "stacking" is used for developing multiple layers of 19

6 amorphous silicon cells which leads to higher rates of efficiency (up to 8%) for these technologies; even though it is quite costly. 2.4 TYPES OF SOLAR PV SYSTEM From application point of view, photovoltaic power systems are categorized into two types grid connected as well as off grid. They can be designed to produce DC and/or AC voltage, can function independent of grid or with grid Grid connected PV system: For grid-connected PV systems inverter, or power conditioning unit (PCU) is the primary component.the PV system produces very less DC power. Then this less DC power must be converted to AC power up to the level or the need of grid by means of inverter. So PV inverter plays very important role in grid connected PV system. In a grid-interactive system, all excess power is fed to grid. Also, during absence or inadequate sunshine, supply of power is maintained from the grid and thus battery is eliminated. As PV produce DC power is first converted to AC power by inverter, harmonics are filtered and then only AC power is fed into grid after adjusting the voltage level. Figure 2.3 describes about the block diagram of a grid connected PV system. 20

7 Figure 2.3 Grid connected PV system Stand-Alone Photovoltaic Systems: Off-grid solar PV system can be used without power grid. Presently, such solar PV systems are usually set up at isolated sites where the power grid is far away, such as off-shore islands or rural areas. They can also be set up within the city when it is inconvenient or very expensive to tap electricity from the power grid. An off-grid solar PV system employs deep cycle rechargeable batteries such as nickel-cadmium, lead-acid or lithium-ion batteries used for accumulating electricity for use under various circumstances when there is no or little output from the solar PV system, essentially when it is dark. For low power applications, stand-alone PV systems are generally used to supply certain DC and/or AC electrical loads. In order to operate the load during sunlight hours as well as night hours fed by PV power, electrical energy storing devices (batteries) are required, which makes the system costlier. Figure 2.4 depicts about the block diagram of standalone PV system where PV array is connected to DC and AC load through charge controller. 21

8 Fig 2.4 Standalone PV system 2.6 ADVANTAGE AND DISADVANTAGE OF SOLAR PV SYSTEM Advantage PV panels produce neat green energy. Cost of solar panels has fallen considerably in recent years thereupon future of solar PV panels is indeed bright for environmental sustainability and economical viability. Photovoltaic panels, generates using photoelectric phenomenon electricity. Maintenance and operating costs are considered to be less, nearly negligible, as compared to other sources. It requires less conservation in comparison to other renewable energy systems. PV panels are totally soundless Since solar energy concurs with energy used in cooling PV panels so it can furnish an efficient remedy for energy demand peaks mostly 22

9 during scorching summer months where energy requirement is eminent. Residential solar panels are can be simply set up on the ground or on rooftops without any interference to residential lifestyle Disadvantage As in the case of all renewable energy sources, solar energy has regularity problem; They need extra devices for converting DC to alternating electricity AC so that it can be used on the distribution system. To get an uninterrupted provision of electric power, for some applications storage batteries are also required; that increases the cost. Efficiency levels of solar panels are relatively low (between 14%- 25%) in comparison to the efficiency levels of other renewable energy systems. Although they have no significant operating costs or maintenance costs, they are delicate and can be tampered relatively easily; eventually it is important to have extra insurance cost to safeguard a PV investment. 2.7 BASIC CIRCUIT CONFIGURATION OF PHOTOVOLTAIC SYSTEM A basic circuit configuration of photovoltaic system is shown below in Fig.2.5. This model represents the equivalent circuit diagram of PV system and is called four parameters model which consist of a current 23

10 source, a diode, a series resistance and a parallel resistance. The current source represents the light generated current of the solar cell, a diode represents the nonlinear impedance of the p-n junction, series resistance represents the internal electrical losses and shunt resistance corresponds to the leakage current to the ground.the diode is connected in anti parallel with the light generated current source represents the theoretical model of ideal solar cell. When solar radiation falls on cell, the direct current generated that varies linearly with solar radiation. Fig 2.5 Basic circuit diagram of Photovoltaic module The characteristic equation is developed, based on the circuit diagram of a photovoltaic panel which is shown in figure 2.5 Applying KCL, the output current of the cell is: (2.1) The light generated current or photo current varies with irradiance and temperature is given by these mathematical equations (2.1 to 2.7) ( V IRs) q V IRs I Iph Is 1] aktns Rsh [exp (2.2) I ph = I r I sc I r0 24 (2.3)

11 Voc I s I sc /[exp( ) 1] (2.4) av t V IRs I d I s[exp( ) 1] (2.5) av t I sh = (V + IR S )/R sh (2.6) V ktn q s t (2.7) These expressions depict the relation between voltage and current of a photovoltaic module. The mathematical equation (2.2) is a nonlinear equation whose parameters are N s represent series connected cells I ph is the light generated current I S is the reverse saturation current R S and R sh represent the series and parallel inherent resistances of the cell. q is the electron charge C k Boltzmann s constant J/K and a the ideality factor Modified Photovoltaic Panel Modeled The mathematical model is developed by using the above equations given. Here, for mathematical analysis KC200GT PV array has been chosen. The key specifications are shown in Table

12 Table 2.1 Key specification of KC200GT PV array Model Cell type KC200GT Polycrystalline silicon(156mm 156mm) Maximum Power[W] Open circuit voltage V oc [V] 32.9 Short circuit current I sc [A] 8.21 Voltage, maximum power V mpp [V] 26.3 Current, maximum power I mpp [A] 7.61 K V [V/K] K I [A/K] a 1.3 R sh [Ω] R s [Ω] N s 54 The evaluation of performance of solar cell is normally done under the standard test condition (STC), for solar spectrum at AM 1.5 is used, irradiance 1000W/m 2, and temperature 25 ºC Parameters of Solar cell A Solar cell converts the sunlight into electricity. Conversion of sunlight to electricity is determined by the parameter of solar cell. There are several parameters of solar cells that determine the effectiveness of sunlight to electricity conversion. They are: 26

13 Short Circuit current (I SC ): Short Circuit Current is calculated by considering voltage equals to zero. I (at V=0) = I sc Open circuit voltage (V OC ): Open Circuit voltage is calculated by considering current equals to zero. V (at I=0) = V oc Maximum power point (Pm): P m = V m I m Where, V m is the maximum voltage and I m is the maximum current. Fill Factor (FF):It is the ratio of maximum power to the theoretical power available at it s output terminal. Efficiency (η): It is the ratio of maximum power to the incident light power IV & PV Curves of Solar cell The dependence of the I-V and P-V characteristics on temperature and irradiance are shown in Fig

14 Fig 2.6 I-V and P-V characteristics curve The output voltage reduces acutely with the raise in temperature whereas the current at the output terminal rises slightly; overall there is a net devaluation in power. With increase in irradiance, increase in the output current occurs greatly, subsequently results in increase in the output power. From fig. 2.6 it can be consummate that the output current of PV array is greatly depended on solar irradiation, while the output voltage PV array depends on temperature. 2.8 RESULT ANALYSIS Photovoltaic circuit model built with MATLAB/SIMULINK Figure 2.7 represents the photovoltaic circuit model with current controlled source where temperature and irradiance are considered as inputs. 28

15 Fig 2.7 Photovoltaic circuit model in simulink Figure 2.8 shows calculation of different parameters of photovoltaic circuit model by using MATLAB/Simulink Calculation of V t V t ktn q s 29

16 Calculation of I ph Ir Constant1 Isc Constant3 Divide2 Iph Goto Ir0 Constant2 Scope Isc Iph Ir Ir Calculation of I s Voc Divide e u Math Function Isc a 1 Add Divide2 Is Product k Scope T Product1 Divide1 Ns q Voc Is Isc /[exp( ) 1] avt 30

17 Calculation of I sh V Scope From Add [I] From1 Divide Ish Goto Product Rsh Rs Constant1 Constant I sh =(V+IR s )/R sh Calculation of I d Isc Voc e u Constant7 Constant Divide Math Function Add Divide2 a 1 Constant1 Product1 Constant2 Display1 k V Constant3 T Constant4 Product From Add1 Divide3 e u Math Function1 Ns Constant14 q Constant6 Divide1 I From1 Rs Product2 a Constant5 Product5 1 Add2 Product3 Id Goto Constant8 k Constant9 Constant10 Display3 T Product4 Constant11 Ns Constant12 q Constant13 Divide4 I d I s V IR [exp( av t s ) 1] Fig 2.8 Simulink model with tags 31

18 2.8.2 Electrical characteristic of PV module at different cell temperature V-I & P-V curve of the KC200GT PV array are plotted by designing this mathematical model in MATLAB for various values of temperature but at constant solar irradiance given in fig.2.9. Figure 2.9 and 2.10 depict about the behavior of PV module at different temperature keeping irradiance constant. Figure 2.9:I-V Characteristic curve at different cell temperatures With increase in temperature, excessive decrease in the output voltage occurs whereas the current at the output terminal increases to some extent. Figure 2.10: P-V Characteristic curve at different cell temperature 32

19 With increase in cell temperature, excessive decrease in the output voltage occurs whereas the current at the output terminal increases to some extent; henceforth output power reduces clearly Electrical characteristic of PV module at different irradiance Figure 2.11 and 2.12 depict about the behavior of PV module at different irradiance keeping temperature constant. Figure 2.11: I-V Characteristic curve at different irradiations With increase in irradiance, increase in the output current occurs significantly, while voltage at the output terminal increases marginally. Figure 2.12: P-V Characteristic curve at different irradiations 33

20 With increase in irradiance, increase in the output current occurs significantly; consequently increase in output power takes place Electrical characteristic of PV module at different ideality factor Figure 2.13 and 2.14 depict about the behavior of PV module at different diode ideality factor variation between 0.8 to 1.6 keeping other parameter constant. Figure 2.13: V-I Characteristic curve at different ideality factor The impact of variation of ideality factor can be seen in the KC200GT model, Fig higher values soften the knee of the curve. Figure 2.14: P-V Characteristic curve at different ideality factor 34

21 For regular action of a PV cell, a value of 1.3 is recommended as typical ideality factor and used at the beginning, prior to the estimation of a more correct value. 2.9 CONCLUSION This section describes the detailed study of photovoltaic system which includes standalone and grid connected system. This chapter also includes model description of PV system, PV data sheet, simulation diagram, different characteristic equations depending upon which I-V and P-V curves were obtained. This chapter deals with modeling and simulation of standalone photovoltaic system. With consideration of impacts of solar irradiance and temperature, the model is developed depending on the basic circuit equations of a solar PV cell. The proposed model takes sunlight irradiance and cell temperature as input parameters and different electrical characteristics are obtained under different circumstances. It is clearly visible from the result that the output voltage of PV mainly supervised by temperature while output current of PV directed by solar irradiances. Hence, a significant objective in a PV system is to establish the generation of maximum energy from the PV array with association of a flexible load. This dilemma is solved by inclusion of a power converter in the middle of the PV array and load, such that by employing a control technique, the impedance of the circuit can be varied dynamically. This chapter is the early footstep to design a detailed solar photovoltaic power electronic conversion system in simulation. ===###=== 35