Explicit Expressions for Solar Panel Equivalent Circuit Parameters - PowerPoint PPT Presentation

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

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

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

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

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

Exampe of Data included in manufacturer datasheet  Manufacturer information (AM1.5g; 25ºC) MSP290AS-36.EU MSMD290AS-36.EU (monocrystaline) (multicrystalline) 72 25 72 25 n n T r (ºC) T r (ºC) 290 -0.45 -0.44 P mp (W) P mp (W) γ (%/ºC) 290 γ (%/ºC) 7.82 - - I mp (A) I mp (A) α I mp (%/ºC) 7.70 α I mp (%/ºC) 37.08 -0.35 -0.35 V mp (V) V mp (V) β V mp (%/ºC) 37.66 β V mp (%/ºC) 8.37 +0.04 +0.04 I sc (A) I sc (A) α I sc (%/ºC) 8.24 α I sc (%/ºC) 44.32 -0.33 -0.31 V V β V 44.68 β V oc (V) oc (V) oc (mV/ºC) oc (mV/ºC)  Objetive:  Design an equivalent circuit that meets all that specification 6

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

Manufacturer data  4 Equations from  5 param. boundary conditions One has to be  Short circuit estimated, a is the     I R I R     0 exp 1    sc s  sc s I I I most delimited sc pv    aV  R T sh  a ∈ 1, 1.5  Open circuit     V V     0 exp 1  a = 1.1    oc  oc I I 0 pv    aV  R T sh  R s  Maximum power point [ I mp ; V mp ]        R sh V I R V I R     0 exp mp mp s 1 mp mp s     I I I mp pv    aV  R T sh  I 0  Maximum power at [ I mp ; V mp ]    I pv P I    0 V I   V V 8

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

Solving sequence a 1 Estimate a                   2    2 2 V I I V I V I V I V I V V V V V V aV         2   mp mp sc   mp sc oc mp    mp sc oc mp  exp mp oc mp oc mp oc T R W                  1     s         I aV aV aV V I V I I V I V I I V I V I I         mp T T T mp sc oc mp sc mp sc oc mp sc mp sc oc mp sc a, R s           V I R V R I I aV mp mp s mp s sc mp T   3 R    sh    V I R I I aV I mp mp s sc mp T mp a, R s , R sh     R R I V 4   sh s sc oc I 0   V exp  oc  Parameters R sh   aV T a, R s , R sh , I 0 , I pv  R R  5  sh s I I pv sc R sh 10

MSP290AS-36.EU (multicrystalline) MSP290AS-36.EU EQUIVALENT CIRCUIT (multicrystalline) PARAMETERS 1.10 a n 72 8.37 A I pv.Tr P mp (W) 290 PM 0.162 Ω R s,Tr I mp (A) 7.82 331 Ω R sh,Tr V mp (V) 37.08 2.86 × 10 -9 A I sc (A) 8.37 I 0, Tr V 44.32 oc (V) solar panels equivalent circuits at STC (1000W/m² irradiance, 25˚C cell temperature, AM1.5g spectrum 11

MSMD290AS-36.EU (monocrystaline) MSMD290AS-36.EU EQUIVALENT CIRCUIT (monocrystaline) PARAMETERS 1.10 a n 72 8.24 A I pv.Tr P mp (W) 290 PM 0.130 Ω R s,Tr I mp (A) 7.70 316 Ω R sh,Tr V mp (V) 37.66 2.36 × 10 -9 A I sc (A) 8.24 I 0, Tr V 44.68 oc (V) solar panels equivalent circuits at STC (1000W/m² irradiance, 25˚C cell temperature, AM1.5g spectrum 12

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

Characteristic points T dependence  Recalculate characteristic points for temperature T according to manufacturer data.       ( )  ( )  I T T V T T     1 1 sc r oc r I I     V V , , , , sc T sc T  100  oc T oc T 100   r r      ( )   ( )  I T T V T T     1 m p r 1 m p r     I I V V , , , , m p T m p T 100 m p T m p T 100     r r  For the new characteristic points repeat solving sequence.  Do for the entire interval of T . 14

Characteristic points T dependence MSP290AS-36.EU  R s (multycrystaline)              3 6 2 8 3 ( ) 8.37 3.62 10 3.38 10 7.58 10 , I T T T T pv                1 3 7 2 8 3 ( ) 1.62 10 3.21 10 7.05 10 3.01 10 , R T T T T s       3   4    6  2   8  3 ( ) 1/ (3.03 10 2.65 10 1.50 10 1.56 10 ), R T T T T sh  R sh       1   1    4  2   6  3 ( ) exp( 1.97 10 1.44 10 4.8 0 10 1.15 10 ). I T T T T 0 MSMD290AS-36.EU (monocrystaline)  I 0              3 6 2 8 3 ( ) 8.24 3.49 10 1.68 10 2.41 10 , I T T T T pv                1 3 6 2 8 3 ( ) 1.30 10 1.97 10 2.53 10 1.07 10 , R T T T T s       3   4    6  2   8  3 ( ) 1/ (3.18 10 2.33 10 1.27 10 1.33 10 ), R T T T T sh       1   1    4  2   6  3 ( ) exp( 1.98 10 1.41 10 4.69 10 1.13 10 ). I T T T T  I pv 0 15

 I-V behaviour of the solar V cell depends on irradiation Dependence  Manufacturer data for this solar cell is referred to on AM1,5g ( G r = 1000 W/m 2 ) irradiation  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

Summarizing MSP290AS-36.EU  Eq. circuit parameters MSP290AS-36.EU n expresions have been 72 T r (ºC) 25 calculated taking in account P mp (W) 290 γ (%/ºC) -0.45  Manufacturer experimental I mp (A) 7.82 α I mp (%/ºC) - data for temperature V mp (V) 37.08 β V mp (%/ºC) -0.35 dependance I sc (A) 8.37 α I sc (%/ºC) +0.04  Dependance with irradiation V 44.32 β V -0.33 oc (V) oc (mV/ºC) G  a: a  1.1  R s :                1 3 7 2 8 3 ( ) 1.62 10 3.21 10 7.05 10 3.01 10 , R T T T T s  R sh :                3 4 6 2 8 3 ( ) 1/ (3.03 10 2.65 10 1.50 10 1.56 10 ), R T T T T sh                1 1 4 2 6 3  I 0 : 0 ( ) exp( 1.97 10 1.44 10 4.80 10 1.15 10 ), I T T T T   G               I pv : 3 6 2 8 3 ( ) 8.37 3.62 10 3.38 10 7.58 10 . I T T T T pv G 17 r