Explicit Expressions for Solar Panel Equivalent Circuit Parameters

Transcription

1 Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-Function Javier Cubas Santiago Pindado Carlos de Manuel 1

2 I Introduction Modeling photovoltaic systems To obtain better performance is necessary to optimize electric systems. Modeling a system to reproduce different situations is a useful tool for optimization. Photovoltaic systems are a very variable energy source (Temperature, irradiance,...). Most common way of modeling of solar cells/panels is to calculate equivalent circuit. 2

3 II Solar Cell Modeling Easy and realistic way of simulate the solar cell behavior I (A) Current source V (V) One diode One series resistance 3 One shunt resistance

4 One diode model Equation I, current V, voltage n, number of cells V T, termal voltage I pv, constant current I 0, sat. current of diode a, ideality factor of diode R s, series resistance R sh, shunt resistance 4

5 I-V Curve and characteristic points Example of the current-voltage curve of a typical solar panel. I (A) I sc I mp ; V mp Solar cell IV behaviour Short circuit point I = I sc ; V = 0 Open circuit point V oc I = 0; V = V oc Maximum power point V (V) 5 I = I mp ; V = V mp

6 Exampe of Data included in manufacturer datasheet Manufacturer information (AM1.5g; 25ºC) MSP290AS-36.EU (multicrystalline) MSMD290AS-36.EU (monocrystaline) n 72 T r (ºC) 25 n 72 T r (ºC) 25 P mp (W) 290 γ (%/ºC) P mp (W) 290 γ (%/ºC) I mp (A) 7.82 αi mp (%/ºC) - I mp (A) 7.70 αi mp (%/ºC) - V mp (V) βv mp (%/ºC) V mp (V) βv mp (%/ºC) I sc (A) 8.37 αi sc (%/ºC) I sc (A) 8.24 αi sc (%/ºC) V oc (V) βv oc (mv/ºc) V oc (V) βv oc (mv/ºc) Objetive: Design an equivalent circuit that meets all that specification 6

7 III Parameter Calculation I pv, constant current I 0, sat. current of diode a, ideality factor of diode R s, series resistance R sh, shunt resistance 7 Main disadvantage of equivalent circuit models is the determination of the parameters Dependent of external conditions Temperature Illumination Available information Experimental data Many I-V curve points Manufacturer data Characteristic points Numerical Analytical

8 Manufacturer data 4 Equations from boundary conditions Short circuit Open circuit I R I R Isc Ipv I0 exp 1 avt Rsh Maximum power point [I mp ; V mp ] Maximum power at [I mp ; V mp ] sc s sc s V oc V 0 Ipv I0 exp 1 avt R V I R V I R Imp Ipv I0 exp 1 avt Rsh mp mp s mp mp s P V 8 oc sh I V I 0 V 5 param. One has to be estimated, a is the most delimited a 1, 1.5 a = 1.1 R s R sh I 0 I pv

9 New analytical method The use of a new analytical method is proposed. New methodology, first analytical model that only uses manufacturer data. Using Lambert-W function explicit ecuations for the parameters of the equivalent circuit are achieved. The method calculates parameters analytically only from manufacturer data. Non-iterative Accurate Straight forward 9

10 Solving sequence 1 Estimate a a 2 R s av Vmp 2Imp I sc 2 VmpIsc VocImp 2 VmpIsc V T mp oc mp oc mp oc oci V V V V V V mp W 1 exp Imp VmpIsc Voc Imp Isc avt VmpIsc Voc Imp Isc avt avt VmpIsc Voc Imp Isc 3 R sh V I R V R I I av mp mp s mp s sc mp T V I R I I av I mp mp s sc mp T mp a, R s 4 I 0 R R I V sh s sc oc R sh V exp av oc T a, R s, R sh Parameters 5 I pv R R R sh sh s I sc 10 a, R s, R sh, I 0, I pv

11 MSP290AS-36.EU (multicrystalline) MSP290AS-36.EU (multicrystalline) n 72 P mp (W) 290 I mp (A) 7.82 V mp (V) I sc (A) 8.37 PM EQUIVALENT CIRCUIT PARAMETERS a 1.10 I pv.tr R s,tr R sh,tr I 0,Tr 8.37 A Ω 331 Ω A V oc (V) solar panels equivalent circuits at STC (1000W/m² irradiance, 25 C cell temperature, AM1.5g spectrum

12 MSMD290AS-36.EU (monocrystaline) MSMD290AS-36.EU (monocrystaline) n 72 P mp (W) 290 I mp (A) 7.70 V mp (V) I sc (A) 8.24 PM EQUIVALENT CIRCUIT PARAMETERS a 1.10 I pv.tr R s,tr R sh,tr I 0,Tr 8.24 A Ω 316 Ω A V oc (V) solar panels equivalent circuits at STC (1000W/m² irradiance, 25 C cell temperature, AM1.5g spectrum

13 IV Dependence on temperature I-V behaviour of the solar cell depends on temperature. Thus parameters of equivalent circuit depends on temperature. There are methods that relates parameters with temperature, but 13 We are going to take advantage of the ease of the method to directly calculate the variation of the parameters from manufacturer datasheet

14 Characteristic points T dependence Recalculate characteristic points for temperature T according to manufacturer data. I I I sc, T sc, T I mp, T mp, T r I sc ( T Tr ) Imp ( T Tr ) 1 r 100 oc, T oc, T mp, T mp, T Voc ( T Tr ) Vmp ( T Tr ) For the new characteristic points repeat solving sequence. V V V V r r Do for the entire interval of T. 14

15 Characteristic points T dependence R s R sh MSP290AS-36.EU (multycrystaline) I T T T T pv ( ) , R T T T T R T T T T I T ) s ( ) , sh( ) 1/ ( ), ( ) exp( T 4.8 T T I 0 I pv MSMD290AS-36.EU (monocrystaline) I T T T T pv ( ) , R T T T T R ( T) 1/ ( T T T ), I T ) s ( ) , sh ( ) exp( T 4.69 T T 15

16 V Dependence on irradiation I-V behaviour of the solar cell depends on irradiation Manufacturer data for this solar cell is referred to AM1,5g (G r = 1000 W/m 2 ) Experimental behaviour with irradiation G I sc varies lineally with G V oc varies logarithmic with G R s is constant with G Parameter behaviour I pv,g = I pv,gr G/G r I 0, R s, R sh and a non dependent of G 16

17 Summarizing MSP290AS-36.EU a: R s : R sh : I 0 : I pv : MSP290AS-36.EU n 72 T r (ºC) 25 P mp (W) 290 γ (%/ºC) I mp (A) 7.82 αi mp (%/ºC) - V mp (V) βv mp (%/ºC) I sc (A) 8.37 αi sc (%/ºC) V oc (V) βv oc (mv/ºc) a 1.1 Eq. circuit parameters expresions have been calculated taking in account I pv T T T T 17 G r Manufacturer experimental data for temperature dependance Dependance with irradiation G R T T T T s ( ) , R T T T T sh ( ) 1/ ( ), I T T T T ( ) exp( ), G ( )

18 Summarizing MSMD290AS-36.EU a: R s : R sh : I 0 : I pv : MSMD290AS-36.EU n 72 T r (ºC) 25 P mp (W) 290 γ (%/ºC) I mp (A) 7.70 αi mp (%/ºC) - V mp (V) βv mp (%/ºC) I sc (A) 8.24 αi sc (%/ºC) V oc (V) βv oc (mv/ºc) a 1.1 Eq. circuit parameters expresions have been calculated taking in account I pv T T T T 18 G r Manufacturer experimental data for temperature dependance Dependance with irradiation G R T T T T s ( ) , R T T T T sh ( ) 1/ ( ), I T T T T ( ) exp( ), G ( )

19 LTSpice Examples LTSpice model. MSP290AS-36.EU Temperature variation (15:5:70) : 19

20 LTSpice Examples LTSpice model. MSP290AS-36.EU Irradiance variation (200:100:1000) : 20

21 LTSpice Examples LTSpice model. MSMD290AS-36.EU Temperature variation (15:5:85) : 21

22 LTSpice Examples LTSpice model. MSMD290AS-36 Irradiance variation (200:100:1000) : 22

23 Accuracy The results of the simulations performed reproduce with high accuracy the experimental results for the characteristic points, regarding the temperature variations, included in the datasheet.

24 VIII Conclusions New analytical methodology Explicit Non-Iterative Straight forward Parameter identification of the equivalent circuit for a solar cell/panel. Meeting manufacturer datasheet for any Temperature Illumination 24

25 VIII Conclusions Possible applications: End users with little calculation and testing resources Analysis that imply profuse calculations. Determination of initial values for numerical methods Construct realistic models of solar panels that can be used in simulations of MPPT algorithms 25

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27 Any questions? Javier Cubas 27