Proceedings of the World Congress on Engineering and Computer Science 2008WCECS 2008, October 22 - 24, 2008, San Francisco, USA Development of Generalized Photovoltaic Model Using MATLAB/SIMULINK Huan-Liang Tsai, Ci-Siang Tu, and Yi-Jie Su, Member, IAENG temperature and output voltage of PV module. Since PV Abstract—This paper presents the implementation of a module has nonlinear characteristics, it is necessary to model generalized photovoltaic model using Matlab/Simulink it for the design and simulation of maximum power point software package, which can be representative of PV cell, tracking (MPPT) for PV system applications. The module, and array for easy use on simulation platform. The proposed model is designed with a user-friendly icon and a mathematical PV models used in computer simulation have dialog box like Simulink block libraries. This makes the been built for over the pass four decades [1]-[3]. Almost all generalized PV model easily simulated and analyzed in well-developed PV models describe the output conjunction with power electronics for a maximum power point characteristics mainly affected by the solar insolation, cell tracker. Taking the effect of sunlight irradiance and cell temperature, and load voltage. However, the equivalent temperature into consideration, the output current and power circuit models are implemented on simulation platforms of characteristics of PV model are simulated and optimized using the proposed model. This enables the dynamics of PV power power electronics, such as SPICE. Recently, a number of system to be easily simulated, analyzed, and optimized. powerful component-based electronics simulation software package have become popular in the design and development Index Terms—Generalized model, photovoltaic module, of power electronics applications. However, the Matlab/Simulink. SimPowerSystem tool in Matlab/Simulink package offers wind turbine models but no PV model to integrate with current electronics simulation technology. Thus, it is difficult I. INTRODUCTION to simulate and analyze in the generic modeling of PV power With increasing concerns about fossil fuel deficit, system. This motivates me to develop a generalized model skyrocketing oil prices, global warming, and damage to for PV cell, module, and array using Matlab/Simulink. environment and ecosystem, the promising incentives to The main contribution of this paper is the implementation develop alternative energy resources with high efficiency and of a generalized PV model in the form of masked block, low emission are of great importance. Among the renewable which has a user-friendly icon and dialog in the same way of energy resources, the energy through the photovoltaic (PV) Matlab/Simulink block libraries or other component-based effect can be considered the most essential and prerequisite electronics simulation software packages, such as Caspoc. sustainable resource because of the ubiquity, abundance, and The remainder of this paper is organized as follows. For easy sustainability of solar radiant energy. Regardless of the presentation, the traditional PV models are addressed in intermittency of sunlight, solar energy is widely available and Section II. And the nonlinearity of PV current versus voltage completely free of cost. Recently, photovoltaic array system (I-V) and power versus voltage (P-V) characteristics are is likely recognized and widely utilized to the forefront in shown as well. Section III demonstrates the implementation electric power applications. It can generate direct current and simulation results for the proposed model using electricity without environmental impact and contamination Matlab/Simulink software package. A different MPPT when is exposed to solar radiation. Being a semiconductor strategy is found and some interested issues are also device, the PV system is static, quite, and free of moving discussed. Finally, brief conclusions are drawn in Section IV. parts, and these make it have little operation and maintenance costs. Even though the PV system is posed to its high capital fabrication cost and low conversion efficiency, the II. PHOTOVOLTAIC MODELS skyrocketing oil prices make solar energy naturally viable Solar cell is basically a p-n junction fabricated in a thin energy supply with potentially long-term benefits. wafer or layer of semiconductor. The electromagnetic PV module represents the fundamental power conversion radiation of solar energy can be directly converted electricity unit of a PV generator system. The output characteristics of through photovoltaic effect. Being exposed to the sunlight, PV module depends on the solar insolation, the cell photons with energy greater then the band-gap energy of the semiconductor are absorbed and create some electron-hole pairs proportional to the incident irradiation. Under the Manuscript received July 24, 2008. This work was supported by the National Science Council of the Republic of China under Grant influence of the internal electric fields of the p-n junction, NSC97-2815-C-212-006-E. these carriers are swept apart and create a photocurrent which H. L Tsai is with the Electrical Engineering Department, Da-Yeh is directly proportional to solar insolation. PV system University, Chang-Hua, 51505, Taiwan, R.O.C. (phone: 886-4-8511888 ext2204; fax: 886-4-8511245; e-mail:
[email protected]). naturally exhibits a nonlinear I-V and P-V characteristics Ci-Siang Tu and Yi-Jie Su are with the Graduate School of Electrical which vary with the radiant intensity and cell temperature. Engineering, Da-Yeh University, Chang-Hua, 51505,Taiwan, R.O.C. ISBN: 978-988-98671-0-2 WCECS 2008 An appropriate equivalent is the solar insolation in kW/m2.5V flow. USA A. the PV efficiency is ground-leakage currents under zero-terminal voltage. 2(b). The above equivalent A general mathematical description of I-V output circuit of PV solar cell can be simplified as shown in Fig. San Francisco.Proceedings of the World Congress on Engineering and Computer Science 2008 WCECS 2008. k ( = 1. The photocurrent mainly depends on the solar RS but insensitive to variation in RSH . K I is the cell’s short-circuit current temperature PV module in order to obtain adequate working voltage. The (1) can be rewritten to be four decades [1]-[3]. therefore.e. October 22 . which is called the double exponential model as shown I = N P I PH − N P I S [exp(qV/N S kTC A) − 1] (8) in Fig. Equation (1) can be assuming the output current is zero. two diodes. a parallel resistor expressing a leakage current. N P = 1 and N S : series number of cells for a PV I S = I RS (TC / TRef )3 exp[qEG (1 / TRef − 1 / TC ) / kA] (3) module. EG is the be described as bang-gap energy of the semiconductor used in the cell. 2(a). RS = 0 and RSH = ∞ . and array is generalized and saturation current varies with the cell temperature. there is no series loss and no leakage ISBN: 978-988-98671-0-2 WCECS 2008 . [12] of generalized PV in Table I. there are The most important parameters widely used for describing some limitations to develop expressions for the V-I curve the cell electrical performance is the open-circuit voltage parameters subject to the implicit and nonlinear nature of the VOC and the short-circuit current I SC . 1(a). The equivalent where I PH is a light-generated current or photocurrent. PV where I SC is the cell’s short-circuit current at a 25°C and cells are generally connected in series configuration to form a 1kW/m2. TRef is the cell’s reference temperature. On the other hand.e. Therefore. PV modules are then arranged in series-parallel structure to coefficient. leakage current to ground. and λ achieve desired power output. the cells must be connected in series-parallel equation of a solar cell is given as configuration on a module to produce enough high power. the series resistance becomes apparently important and as the shunt down resistance approaches infinity which is I PH = [ I SC + K I (TC − TRef )]λ (2) assumed to be open. The I = N P I PH − N P I S [exp(q(V / N S + IRS / N P ) / kTC A) − 1] (7) ideal factor A is dependent on PV technology [4] and is listed The most simplified model [6]. this model is rarely used in the subsequent literatures and is not taken into consideration for the equations are implicit and nonlinear. the insensitive to variation in RSH and the shunt-leakage short-circuit current I SC is approximately equal to the resistance can be assumed to approach infinity without photocurrent I PH . module.38 × 10−23 J/K) is a Boltzmann’s I = N P I PH − N P I S [exp(q(V / N S + IRS / N P ) / kTC A) − 1] constant. The terminal equation for the current and voltage of the array becomes as follows [8]-[11]. is shown in Fig. Solar Module and Array Model series resistor describing an internal resistance to the current Since a typical PV cell produces less than 2W at 0. In most commercial PV products. Given the PV rewritten to be open-circuit voltage VOC at reference temperature and I = I PH − I S [exp(q(V + IRS ) / kTC A) − 1] (4) ignoring the shunt-leakage current. The voltage-current characteristic approximately.. which is expressed in Fig. 1(d) characteristics for a PV cell has been studied for over the pass [1]. For a PV module or insolation and cell’s working temperature. I S circuit for the solar module arranged in NP parallel and NS is the cell saturation of dark current. Determination of Model Parameters cell constructed from polycrystalline silicon. a All of the model parameters can be determined by examining the manufacturer’s specifications of PV products. A is an ideal − ( N PV / N S + IRS )/RSH (6) factor. 1(b) [5]. 2008. it is difficult to arrive at an analytical solution for a set of model generalized PV model. 2(c). parameters at a specific temperature and irradiance. the reverse saturation For an ideal PV cell. and N S and N P : series-parallel number for a PV where I RS is the cell’s reverse saturation current at a array. It can be shown that N S = N P = 1 for described as a PV cell.[ 6]-[7]. a diode. the VOC parameter is obtained by The appropriate model of PV solar cell with suitable complexity is shown in Fig. The aforementioned model. Such an equivalent circuit-based model I = I PH − I S [exp(qV / kTC A) − 1] (5) is mainly used for the MPPT technologies. and a B. RSH is a shunt resistance. On the other hand. i. a small I PH = I SC (9) variation in RS will significantly affect the PV output power. and RS is a series In fact. The equivalent circuit of the general model which consists of a photo current. is derived from the physical behavior of solar C. 1(c) [4]. TC is the cell’s working temperature. i. module is depicted in Fig. The equivalent circuit is An even more exact mathematical description of a solar described on the following equation cell. Since The shunt resistance RSH is inversely related with shunt normally I PH >> I S and ignoring the small diode and leakage current to the ground.. However. The mathematical equation of generalized model can reference temperature and a solar radiation. the PV efficiency is sensitive to small change in resistance.6 × 10−19 C) is an series is shown in Fig. the cell’s circuit for all PV cell. Solar Cell Model to ground.24. q ( = 1. which is described array. A I = I PH − I S [exp(q (V + IRS ) / kTC A) − 1] − (V + IRS ) / RSH PV array is a group of several PV modules which are electrically connected in series and parallel circuits to (1) generate the required current and voltage. In general. This model is composed of a light-generated current source. electron charge. series resistance and a parallel resistance. On the other hand. the saturation current of the diode. The resistance is considered based on the Shockley diode reason is the open-circuit voltage is logarithmically equation. Given sunlight irradiance for a sample day.S. Statistical Simulation of the photovoltaic potential directly into electricity with both For easy simulation. October 22 . in which the parameters of PV module the conditions: λmax = 1kW/m 2 . the net power decreases at high temperatures. which is used to is directly proportional to the radiant intensity. 7(a) and 7(b) that with increase of γ is the cell fill factor which is a measure of cell quality. CONCLUSIONS increase of solar insolation. 2008. and a series PV module increase as shown in Figs. the includes the temperature independence of the photocurrent short-circuit current and the maximum power output of the source. Both I-V and P-V where Vmax and I max are terminal voltage and output output characteristics of PV module at various insolation and temperatures are carried out and the results are shown in Figs. Without taking cell temperature variations into consideration. GENERALIZED PV MODEL BUILDING AND SIMULATION less than the decrease in the open-circuit voltage. The proposed model takes sunlight short-circuit current is directly proportional to the radiant irradiance and cell temperature as input parameters and intensity. For shown in the figures.Proceedings of the World Congress on Engineering and Computer Science 2008 WCECS 2008. short-circuit current of the PV cell increases. we observe from Figs. Simulation Results of PV Cell and Module temperature of NOCT by ignoring the effect of the solar For a PV cell with an ideal I-V characteristic. the root mean square (R. A generalized PV model sample day is assumed to be a function of Gaussian function is built using Matlab/Simulink [13] to illustrate and verify the which is defined as nonlinear I-V and P-V output characteristics of PV module. PV cell converts part C. 4(a). determined by the ensuing load. irradiation. and 3(b).8kW/m2 and a I RS = I SC /[exp(qVOC /N S kATC ) − 1] (10) wind speed less than 1 m/s. On the other hand. USA current at reference temperature can be approximately operated at open circuit in an ambient temperature of 20°C obtained as under AM 1.. we also A model of PV module with moderate complexity which observe that with increase of solar insolation. and the effect makes maximum power decreasing by about 0.24. current of PV module at maximum power point (MPP). and σ = 0. temperature for a sample day is assumed to be at a fixed B. It is important to build a generalized model suitable dependent on the solar irradiance. the circuit voltage and short-circuit current are given as output current is governed by its output voltage which is VOC = 0. module. We find from Figs.0A . This model has also been designed in the form of taken for example. In addition. outputs the I-V and P-V characteristics under various By the same token. whereas the power during the course of a sample day occurs with the maximum power output decreases. For different output voltage.e. 9 shows a plot of the Gaussian addition. The electrical characteristics of In addition. The reason is the open-circuit voltage is Matlab/Simulink and been verified with a PV cell and a logarithmically dependent on the solar irradiance. respectively.5 . Inasmuch as the increase output voltage in the range of 15-16V. yet the commercial module. In order to make the generalized model easier to use and understand. the solar radiation intensity for a I-V and P-V output characteristics. the calculated an depicted in Fig. in the output current is much less than the decrease in the voltage. from. On the other hand. In Gaussian function. San Francisco. the short-circuit current of the A generalized PV model which is representative of the all PV module increases. We also see from Figs. and the maximum power output PV cell. The nonlinear nature of PV cell is apparent as power are shown in Figs.S. the Solarex MSX 60 PV module is conditions. the masked model is designed to have a dialog box function for the solar radiation intensity for a sample day with as shown in Fig. and solar insolation as well. Bing illuminated with radiation of sunlight. the output current and in Figs. 4(b). 5(a) and 5(b) that with increase of working temperature. 3(a) [ ] λ (t ) = λmax exp − (t − tC ) 2 / 2σ 2 (12) where λmax is the maximal radiation intensity at a given time. the output current and power of PV easy comparisons. 8(a) and 8(b). The key specifications are listed in Table Simulink block libraries. The can be configured in the same way for the Simulink block peak of sunlight intensity occurs at noon. the short-circuit current of the PV module increases. The increase in the short-circuit current is much III. The cell libraries. The user-friendly icon is shown in Fig. The maximum R. whereas the maximum power output decreases. 11. the maximum N S = N P = 1 for a PV cell. Fig. and σ is the standard deviation of masking icon. design and analyze a maximum power point tracker. and array. its open. and array has been developed with increases as well. tC = 12 .5 irradiance conditions with λ=0. working temperature. 6(a) and 6(b) that with IV.596V and I SC = 2. yet the short-circuit current for all of the PV cell. the maximum power can be expressed as PV module are generally represented by the current versus Pmax = Vmax I max = γVOC I SC (11) voltage and power versus voltage curves. The proposed model is implemented and shown in Figs. Both I-V and P-V output power is determined by both radiation intensity and output characteristics of generalized PV model for a cell are shown voltage. i.) values of cell depend on the cell’s terminal operating voltage and output power for various output voltage for a sample day are temperature. Building of Generalized PV Model at high temperatures. and 7-8. 10(a) and (b) for a sample day.M. module.M. 5-6. we used an image file of PV icon as a tC is the center time.45%/°C A. The masked icon makes the block II in which the nominal operating cell temperature (NOCT) is model more user-friendly and a dialog box lets the users the temperature that the cells will reach when they are ISBN: 978-988-98671-0-2 WCECS 2008 . vol. Chan. 1 Equivalent circuit models of PV cell. I. pp. 2005. 2000. 1998. V Voltage (c) Appropriate model (d) Simplified model Scope1 Insolation Fig. 86-93. H.406-408. 2005. Muta. pp. ISBN: 978-988-98671-0-2 WCECS 2008 . Hua and C. Kim. M. vol. [8] M. [12] K. W. C. in the context 8 6444474444 of the SimPowerSystem tool. D. Shinoy. and K. pp. pp.” IEEE Transaction Generalized PV Module on Industrial Electronics. 4. 953-959. and J. 4. vol. PAS-102. Veerachary and K. “Modeling and dynamic performance of a line. Such a generalized PV model N NS RS 47P444 NP is easy to be used for the implementation on Matlab/Simulink 644 8 modeling and simulation platform. “Voltage-based maximum (c) Appropriate model power point tracking control of PV system. A. “V2-based power tracking for nonlinear PV sources. vol. “Maximum 1 photovoltaic power tracking: an algorithm for rapidly changing Coltage Input atmospheric conditions. 2006. B. Youn. Pearson Input Education. T. 1982. pp. pp. 142.” Proceedings of 29th annual IEEE Power Electronics Specialists Conference.” IEEE Transactions on Energy Conversion. Kim and M. V Coltage Input vol. pp. 1984. J. 3031-3037.” IEE 6444474444 Proceedings. H. 1999. 38. no. S.” Electronics Letters. J. “Accurate analytical method for the extraction of solar cell model parameters. Wasynczuk. vol. pp. “Study of maximum power tracking techniques and control of dc-dc converters for photovoltaic power (b) Generalized model system. Solar irradiance 953-959.” IEE Proceedings-Electric Power Applications. Uezato. “Variable-structure observer for solar array Voltage Scope1 current estimation in a photovoltaic power-generation system. Mastering Simulink . D. 152. Wasynczuk. (a) General model REFERENCES NS RS [1] S. 177-227. Solar irradiance Tc TC Scope Cell Temperature Generalized PV Module Fig. CRC Press. and M. Veerachary. C.Inc. 4th N 47P444 644 8 NP edition. “Dynamic behavior of a class of photovoltaic power systems. pp. 1 Power Power Transmission and Distribution. 2002. 262-270. no. Angrist. 1. 5. no. 8 6444474444 [2] O.” IEE Insolation Insolation Input Proceedings-Electric Power Applications. [7] R. Ventre. no. Philips. pp.” IEEE Transactions on Power Apparatus and Systems. Dabney and T. Especially. pp. Fig. Osakada. 2005. B. no.41-51. vol. 3 Ki Iph Cell Product Temperature Short-Circuit Current f(u) I 2 Input Temperature Coefficient Current Current Output Output Is Isc Short-Circuit Current f(u) Irs f(u) Reverse Tref Saturation Current Saturation Current (a) General model (b)Double exponential model Reference Temperature Fig. N 47P444 644 8 [5] J. “Development of a photovoltaic array 8 model for use in power-electronics simulation studies. NS [3] J. no.” IEEE Transactions on Aerospace and Electronic Systems.Electric Power Applications. S. 10.. October 22 . Kim. no. Phang. [6] O. 2008. Fig. NS commutated photovoltaic inverter system. Inc. vol. pp. M. Current Output [11] I. 2. Senjyu.S. 4(a) Masked implementation of generalized PV model. H. 146. 193-199. 1.24. T.” IEE Proceedings of Generation. USA easily configure the PV model. 4. “New maximum power point Tc TC Cell Temperature Input tracker using sliding-mode observer for estimation of solar array Scope Cell Temperature current in the grid-connected photovoltaic system. 53. 1263-1270. Youn. 337-343. Hussein. 1027-1035.. no. 2004. Shen. 1983. 2 Output ® Insolation [13] J. 3. Photovoltaic Systems Engineering. Power Output [10] I. vol. Allyn and Bacon. L.Proceedings of the World Congress on Engineering and Computer Science 2008 WCECS 2008. Hoshino. and M. 9. S. . 3(a) Generalized PV model. [4] C. San Francisco. 3(b) Subsystem implementation of generalized PV model. 1. there is now a generalized PV NS model which can be used for the model and analysis in the NS NP RSH filed of solar PV power conversion system. Gow and C. [9] M. 2 Equivalent circuit models of generalized PV. vol. Messenger and J. 20. R. 152. Direct Energy Conversion. no. Harman. Manning. 1989. Fig. 5(a) I-V output characteristics with different Tc. October 22 .24. Fig. San Francisco. Fig. ISBN: 978-988-98671-0-2 WCECS 2008 . USA Fig. 7(a) I-V output characteristics with different Tc. 7(b) P-V output characteristics with different Tc. Fig. 6(b) P-V output characteristics with different λ. 6(a) I-V output characteristics with different λ. Fig. Fig. 2008. 5(b) P-V output characteristics with different Tc.Proceedings of the World Congress on Engineering and Computer Science 2008 WCECS 2008. 4(b) Dialog box of generalized PV model. 8(b) P-V output characteristics with different λ. Voltage at peak power (Vpp) 17. 25°C) Characteristics SPEC. October 22 . values of output power for various output voltage. ISBN: 978-988-98671-0-2 WCECS 2008 . 2008.1V Current at peak power (Ipp) 3.S.Proceedings of the World Congress on Engineering and Computer Science 2008 WCECS 2008.24. 10(a) Current characteristics during a sample day for different voltage.38W/ C Nominal operating cell temperature (NOCT) 49 C Fig. Typical peak power (Pp) 60W Fig.5A : V = 14 Short-circuit current (ISC) 3. San Francisco. 11 R. USA : V = 14 : V = 15 : V = 16 : V = 17 : V = 18 Fig. 10(b) Power characteristics during a sample day for different voltage. Fig. Table I Factor A dependence on PV technology Table II Solarex MSX 60 Specifications (1kW/m2.M. Fig.8A : V = 15 Open-circuit voltage (VOC) 21. 8(a) I-V output characteristics with different λ.1V : V = 16 : V = 17 Temperature coefficient of open-circuit voltage -73mV/ C : V = 18 Temperature coefficient of short-circuit current (KI) 3mA/ C Approximate effect of temperature on power -0. 9 Solar radiation intensity for a sample day in the form of Gaussian function. Fig.