This may be the author’s version of a work that was submitted/accepted for publication in the following source: Walker, Geoffrey R. (2000) Evaluating MPPT converter topologies using a MATLAB PV model. In Australasian Universities Power Engineering Conference, AUPEC’00, 2000-09-24 - 2000-09-27. This file was downloaded from: https://eprints.qut.edu.au/63586/ c Copyright 2000 Please consult the author This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the docu- ment is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recog- nise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to [email protected] Notice: Please note that this document may not be the Version of Record (i.e. published version) of the work. Author manuscript versions (as Sub- mitted for peer review or as Accepted for publication after peer review) can be identified by an absence of publisher branding and/or typeset appear- ance. If there is any doubt, please refer to the published source. EVALUATING MPPT CONVERTER TOPOLOGIES USING A MATLAB PV MODEL Geoff Walker Dept of Computer Science and Electrical Engineering, University of Queensland, Australia. email: [email protected] Abstract An accurate PV module electrical model is presented based on the Shockley diode equation. The simple model has a photo-current current source, a single diode junction and a series resistance, and includes temperature dependences. The method of parameter extraction and model evaluation in Matlab is demonstrated for a typical 60W solar panel. This model is used to investigate the variation of maximum power point with temperature and inso- lation levels. A comparison of buck versus boost maximum power point tracker (MPPT) topologies is made, and compared with a direct connection to a constant voltage (battery) load. The boost con- verter is shown to have a slight advantage over the buck, since it can always track the maximum power point. 1 PHOTOVOLTAIC MODULES IIL RS Solar cells consist of a p-n junction fabricated in a thin wafer or layer of semiconductor. In the dark, the I-V G output characteristic of a solar cell has an exponential V characteristic similar to that of a diode. When exposed to light, photons with energy greater than the bandgap energy of the semiconductor are ab- T sorbed and create an electron-hole pair. These carri- Figure 1: The circuit diagram of the PV model. ers are swept apart under the influence of the internal electric fields of the p-n junction and create a current I proportional to the incident radiation. When the cell is Temperature dependence of the photo current L . short circuited, this current flows in the external circuit; R Series resistance S , which gives a more accurate when open circuited, this current is shunted internally shape between the maximum power point and the by the intrinsic p-n junction diode. The characteristics open circuit voltage. of this diode therefore sets the open circuit voltage char- R acteristics of the cell. Shunt resistance P in parallel with the diode. n 1.1 Modelling the Solar Cell Either allowing the diode quality factor to be- come a variable parameter (instead of being fixed Thus the simplest equivalent circuit of a solar cell is a at either 1 or 2) or introducing two parallel diodes =1 A =2 current source in parallel with a diode. The output of (one with A , one with ) with indepen- the current source is directly proportional to the light dently set saturation currents. falling on the cell. The diode determines the I-V char- acteristics of the cell. For this research work, a model of moderate complexity was used. The model included temperature dependence Increasing sophistication, accuracy and complexity can I of the photo-current L and the saturation current of the be introduced to the model by adding in turn I R S diode 0 . A series resistance was included, but not a shunt resistance. A single shunt diode was used with Temperature dependence of the diode saturation the diode quality factor set to achieve the best curve I current 0 . match. This model is a simplified version of the two msx60 model, 1Sun, 25C, 1.0 < A < 2.0 diode model presented by Gow and Manning [1]. The 4 circuit diagram for the solar cell is shown in Figure 1. A = 1.0 3.5 The equations which describe the I-V characteristics of A = 2.0 the cell are 3 2.5 q V +IR =nk T S I = I I e 1 0 L (1) 2 Module Current (A) 1.5 I = I 1 + K T T L 0 1 T L (2) 1 = G I =G I 1 T SC T ;nom nom L (3) 1 1 K = I I =T T 0 2 1 T SC T SC (4) 1 2 0.5 0 0 5 10 15 20 25 =n 3 Module Voltage (V) I = I T=T 0 1 0T 1 Figure 2: The Matlab model VI curves for various diode qV =nk 1=T 1=T g 1 e (5) quality factors. qV =nk T 1 OC T 1 I = I =e 1 T SC T 0 (6) 1 1 msx60 model, 1Sun, 25C, Rs = 0, 8, 16 mOhm per cell 4 Rs = 0 R = dV =dI 1=X S V V (7) OC 3.5 qV =nk T 1 T OC Rs = 16mOhm 1 X = I q =nk T e V 1 T 0 (8) 1 3 All of the constants in the above equations can be de- 2.5 termined by examining the manufacturers ratings of 2 the PV array, and then the published or measured I-V curves of the array. As a typical example, the Solarex Module Current (A) 1.5 MSX60 60W array will be used to illustrate and verify 1 the model. 0.5 I The photo-current L (A) is directly proportional to ir- 2 0 Wm radiance G ( ). When the cell is short circuited, 0 5 10 15 20 25 Module Voltage (V) negligible current flows in the diode. Hence the propor- Figure 3: The Matlab model VI curves for various tionality constant in equation 3 is set so the rated short model series Resistances. I circuit current SC at is delivered under rated irradia- 2 tion (usually 1 Sun = 1000Wm ). For the MSX60, I = 3:8A T = 25 1 SC at 1 Sun at C (298K), so until a more accurate value is estimated later through I =3:8A=S un: T L curve fitting. The effect of varying the ideality factor 1 can be seen in the MSX60 model, figure 2 – higher val- The relationship between the photo-current and temper- ues soften the knee of the curve. ature is linear (eqn. 2) and is deduced by noting the I change of photo-current with the change of tempera- The relationship of 0 to temperature is complex, but I ture (eqn. 4). For the MSX60, L changes from 3.80 to fortunately contains no variables requiring evaluation 3.92A (3%) as T changes from 25 to 75 C. (eqn 5) [1]. When the cell is not illuminated, the relationship be- The series resistance of the panel has a large impact V = V tween the cell’s terminal voltage and current is given on the slope of the I-V curve at OC , as seen in by the Shockley equation. When the cell is open cir- figure 3. Equations 7 and 8 are found by differentiating V = V cuited and illuminated, the photo-current flows entirely equation 1, evaluating at OC , and rearranging R in the diode. The I-V curve is offset from the origin by in terms of S [1]. Using the values obtained from I the the photo generated current L (eqn 1). the MSX60 manufactures’ curves, a value of total panel R =8m series resistance S was calculated. I 25 The value of the saturation current 0 at C is cal- culated using the open circuit voltage and short circuit 1.2 Matlab model of the PV module current at this temperature (eqn 6). The Solarex MSX60, a typical 60W PV module, was An estimate must be made of the unknown “ideality chosen for modelling. The module has 36 series con- factor” n. Green [3] states that it takes a value between nected polycrystalline cells. The key specifications are 1 and 2, being near one at high currents, rising towards shown in table 1. two at low currents. A value of 1.3 is suggested as typical in normal operation, and may be used initially, The model was evaluated using Matlab. The model pa- At Temperature T 25 C V function Ia = msx60i(Va,Suns,TaC) Open Cct Voltage OC 21.0 V % msx60.m model for the MSX-60 solar array I % current given voltage, illumination and temperature Short Cct Current SC 3.74 A % Ia = msx60(Va,G,T) = array voltage V % Ia,Va = array current,voltage Voltage, max power m 17.1 V % G = num of Suns (1 Sun = 1000 W/mˆ2) I % T = Temp in Deg C Current, max power m 3.5 A P k = 1.38e-23; % Boltzman’s const Maximum Power m 59.9 W q = 1.60e-19; % charge on an electron % enter the following constants here, and the model will be Table 1: The key specifications of the Solarex MSX60 % calculated based on these.