UNIVERSITATEA POLITEHNICA DIN BUCURETI

FACULTATEA DE ENERGETIC

Laboratoare

Profesor:

Conf. dr. ing. Tiberiu Tudorache

Masterand:

Ciobanu Mihai2015Determinarea experimental a caracteristicilor de funcionare a panourilor fotovoltaice

1. Scopul lucrrii

Scopul acestei lucrri de laborator const n nsuirea abilitilor practice necesare caracterizrii panourilor fotovoltaice i a determinrii experimentale a caracteristicilor specifice de funcionare.

2. Chestiuni de studiat

2.1. Introducere

2.2. Datele principale ale panoului fotovoltaic

2.3. Caracteristicile de funcionare ale panourilor fotovoltaice

2.4. Determinarea experimental a caracterisiticilor de funcionare

2.5. Interpretarea rezultatelor. Observaii i concluzii

3. Elemente teoretice

3.1. Introducere

Principiul conversiei fotovoltaice are la baz fenomenul de conducie electric n materiale semiconductoare. Semiconductorul poate deveni bun conductor de electricitate atunci cnd i se transfer o anumit cantitate de energie din exterior, numit i energie de activare. Energia de activare poate proveni din nclzirea materialului sau din iluminarea sa.

Efectul fotovoltaic const n apariia unui cmp electric (imprimat) ntr-un semiconductor omogen sub influena luminii (de regul lumina solar), Fig. 1.1. Celula elementar ce asigur conversia luminii n electricitate se numete celul solar sau celul fotovoltaic. Mai multe celule fotovoltaice conectate n serie i/sau n paralel constituie un panou fotovoltaic utilizat n mod uzual la captarea energiei solare i la conversia ei n electricitate.

Fig. 1.1. Seciune printr-un panou fotovoltaic.

Principiul conversiei fotovoltaice

3.2. Datele principale ale panoului fotovoltaic

Datele principale ale panourilor fotovoltaice studiate, de tip Suntech 175 S 24 Ac sunt:

- Putere nominal Pn = 175 [Wp]

- Tensiunea n punctul de putere maxim UMPP = 35.8 [V];

- Curentul n punctul de putere maxim IMPP = 4.9 [A];

- Tensiunea de mers n gol U0 = 44.7 [V];

- Curentul de scurtcircuit ISC = 5.23 [A];

- Numr de celule nseriate Ns = 72;

- Coeficientul de modificare cu temperatura a tensiunii de mers n gol U0 Kv = -0.155

- Coeficientul de modificare cu temperatura a curentului de scc ISC Ki = 0.06.

3.3. Caracteristicile de funcionare ale panourilor fotovoltaice

3.3.1. Caracteristica extern a unui panou fotovoltaic. Aceast caracteristic reprezint dependena dintre curentul I de sarcin debitat de panou i tensiunea U de la bornele acestuia, I = f(U).

Se observ c aceast caracteristic depinde de intensitatea radiaiei luminoase i de temperatura panoului.

3.3.2. Caracteristica puterii unui panou fotovoltaic. Aceast caracteristic reprezint dependena dintre puterea P debitat de panou i tensiunea U de la bornele acestuia, P = f(U).

n punctul optim de funcionare al panoului acesta livreaz putere maxim Pmax.

3.4. Determinarea experimental a caracteristicilor de funcionare

Pentru a determina caracteristicile de funcionare ale unui panou fotovoltaic este necesar realizarea unei scheme electrice de montaj ca cea prezentat n Fig. 1.4.

Aparatele de msur din schem trebuiesc corelate cu datele nominale ale panoului (sau a grupului de panouri) studiate.

Fig. 1.4. Schema electric de montaj

utilizat pentru determinarea

caracteristicilor panourilor Elaborarea modelului Matlab al panourilor fotovoltaice pe baza datelor nominale. Validri experimentale

1. Scopul lucrrii

Scopul acestei lucrri de laborator const n nsuirea cunotinelor teoretice i abilitilor practice necesare implementrii n mediul Matlab a modelului numeric al unui panou fotovoltaic calibrat pe baza datelor nominale furnizate de productor. n finalul lucrrii rezultatele numerice vor fi validate prin rezultate msurate experimental. 2. Chestiuni de studiat

2.1.Modelul celulei fotovoltaice ideale

2.2.Modelul celulei fotovoltaice reale implementat n Matlab

2.3.Programul de calcul Matlab utilizat pentru determinarea caracteristicilor panourilor fotovoltaice

2.4.Rezultate numerice. Observaii i concluzii

3. Elemente teoretice

3.1. Modelul celulei fotovoltaice ideale

n Fig. 2.1 este prezentat modelul de circuit echivalent al celulei fotovoltaice ideale.

Fig. 2.1. Modelul celulei fotovoltaice cu o singur diod.

Fig. 2.2. Caracteristica celulei fotovoltaice ideale.

Datele tehnice ale panoului Suntech 175S-24Ac, n condiii standard de temperatur i radiaie solar (Tn = 25 C i Gn = 1000 W/m2):

- Putere nominal Pn = 175 [Wp]

- Tensiunea n punctul de putere maxim UMPP = 35.8 [V];

- Curentul n punctul de putere maxim IMPP = 4.9 [A];

- Tensiunea de mers n gol U0 = 44.7 [V];

- Curentul de scurtcircuit ISC = 5.23 [A];

- Numr de celule nseriate Ns = 72;

- Coeficientul de modificare cu temperatura a tensiunii de mers n gol U0 Kv = -0.155

- Coeficientul de modificare cu temperatura a curentului de scc ISC Ki = 0.06. 3.2. Modelul celulei fotovoltaice reale

Modelul celulei PV cu o singur diod este util pentru ajustarea parametrilor i corelarea lor cu datele de catalog. Productorii de panouri fotovoltaice furnizeaz n mod uzual n cataloage un set limitat de date tehnice ale produsului, insuficiente pentru determinarea caracteristicilor I = f(U). Printre mrimile utile care influeneaz semnificativ caracteristica I = f(U) a unui panou fotovoltaic i care n general rmn inaccesibile sunt rezistenele serie Rs i paralel Rp.Ecuaia (1) a celulei fotovoltaice elementare nu reprezint caracteristica I = f(U) a unui panoul fotovoltaic real. Panourile fotovoltaice reale sunt compuse din mai multe celule fotovoltaice conectate ntre ele, descrierea ansamblului de celule necesitnd includerea unor parametrii adiionali.

REZLOVARE

Model 1

% Matlab script for evaluating the photovoltaic array model% Tested with MATLAB Version 7.10 (R2010a)%% Information from the Suntech solar array datasheet% You may change these parameters to fit the I-V model% to other kinds of solar arrays.Iscn = 5.23; %Curent nominal de scurt-circuit [A] Vocn = 44.7; %Tensiunea nominala de mers in gol [V] Imp = 4.9; %curent nominal al panoului @ punctul de putere maxima [A] Vmp = 35.8; %Tensiunea nominala a panoului @ punctul de putere maxima [V] Pmax_e = Vmp*Imp; %Putere maxima de vrf a panoului [W] Kv = -0.155; %Coeficient tensiune/temperatura [V/K] Ki = 3.138e-3; %Coeficient curent/temperatura [A/K] Ns = 72; %Numar de celule in serieRs = 0.00001; Rp = 10000000;%% Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]a = 1.3; %Diode constant%% Evaluates the model %Temperatures [K] T = 20 + 273.15; %Evaluates the model for three inputsG = 1000; %Irradiance [W/m^2] %Choose G=1000,800,600,400,200 to compare the model %with experimental data from datasheetIon = 0; % Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]% Nominal values Gn = 1000; % Nominal irradiance [W/m^2] @ 25oCTn = 25 + 273.15; % Nominal operating temperature [K]% Thermal voltages Vtn = k * Tn / q; %Thermal junction voltage (nominal) Vt = k * T / q; %Thermal junction voltage (actual temperature)%Calculation of Io (method 1) %This is the original Io equation generally found in the literature.%This requires finding the optimal value of Eg.%See details in: %"Modeling and circuit-based simulation of photovoltaica arrays" %Calculation of Eg Tmax = 75 + 273.15; dT_ = Tmax - Tn; Isc_ = ( Iscn + Ki*dT_ ); Voc_ = ( Vocn + Kv*dT_ ); Vt_ = k * Tmax / q; Eg = log(Isc_*Tn^3/Io/Tmax^3/(exp(Voc_/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(Tmax-Tn); %or: Eg = -log((Iscn+Ki*(Tmax-Tn))*Tn^3/Ion/Tmax^3/(exp((Vocn+Kv*(Tmax-Tn))/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(-Tmax+Tn);%Uncomment this line if you wish to use this equation:%Io = Ion *(T/Tn)^(3) * exp( q * Eg/a/ k * (1/Tn-1/T) ); %Calculation of Io (method 2) %This is the alternative Io equation suggested in:%"Comprehensive approach to modeling and simulation of photovoltaic arrays"dT = T - Tn;Isc_ = ( Iscn + Ki*dT );Voc_ = ( Vocn + Kv*dT );%Comment this line if you wish to use the original Io equation:Io = Isc_/(exp(Voc_/a/Ns/Vt)-1);% Temperature and irradiation effect on the currentdT = T-Tn;Ipvn = (Rs+Rp)/Rp * Iscn; % Nominal light-generated currentIpv = (Ipvn + Ki*dT) *G/Gn; % Actual light-generated current Isc = (Iscn + Ki*dT) *G/Gn; % Actual short-circuit current% Solving the I-V equation for several (V,I) pairs clear Vclear IV = 0:.1:45; % Voltage vectorI = zeros(1,size(V,2)); % Current vectorfor j = 1 : size(V,2) %Calculates for all voltage values % Solves g = I - f(I,V) = 0 with Newntonn-Raphson g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); while (abs(g(j)) > 0.001) g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); glin(j) = -Io*Rs/Vt/Ns/a*exp((V(j)+I(j)*Rs)/Vt/Ns/a)-Rs/Rp-1; I_(j) = I(j) - g(j)/glin(j); I(j) = I_(j); end end%% Final adjusted I-V and P-V curves % I-V curve figure(3) grid on title('Adjusted I-V curves'); xlabel('V [V]'); ylabel('I [A]'); Vsp = [0 35.8 44.7]; Isp = [5.23 4.9 0]; plot(V, I, 'm', Vsp, Isp, 'ro' ) %axis([0 50 0 6]);grid on; %plot([0 Vmp Vocn ],[Iscn Imp 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') % P-V curve figure(4) grid on hold on title('Adjusted P-V curves'); xlabel('V [V]'); ylabel('P [W]'); axis([0 50 0 200]); plot(V,V.*I, Vsp, Vsp.*Isp, 'bo') % %plot([0 Vmp Vocn ],[0 Pmax_e 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k')

Modelul 2% Matlab script pentru modelarea unei panou fotovoltaic%% Testat cu MATLAB versiunea 7.7 (R2008b) clear allclc%% Informatiile din fisa tehnica a panoului solar Suntech % Se poate modifica acesti parametri pentru a se potrivi modelului I-V % pentru alte tipuri de panouri solare.Iscn = 5.23; %Curent nominal de scurt-circuit [A] Vocn = 44.7; %Tensiunea nominala de mers in gol [V] Imp = 4.9; %curent nominal al panoului @ punctul de putere maxima [A] Vmp = 35.8; %Tensiunea nominala a panoului @ punctul de putere maxima [V] Pmax_e = Vmp*Imp; %Putere maxima de vrf a panoului [W] Kv = -0.155; %Coeficient tensiune/temperatura [V/K] Ki = 3.138e-3; %Coeficient curent/temperatura [A/K] Ns = 72; %Numar de celule in serie% Panoul cu Nss x module Npp Nss = 2;Npp = 2;%% Constantek = 1.3806503e-23; %constanta Boltzmann [J/K]q = 1.60217646e-19; %Sarcina electronului [C]a = 1.3; %Constanta diodei%% Valori nominaleGn = 1000; % Radiatia nominala [W/m^2] @ 25oCTn = 25+273.15; % Temperatura nominala operativa [C]%% Ajustarea algoritmului% Modelul este adaptat la starea nominala T = Tn;G = Gn; Vtn = k * Tn / q; %Tensiunea jonctiunii termice (nominala) Vt = k * T / q; %Tensiunea jonctiunii termice (la temperaturile actuale)Ion = Iscn/(exp(Vocn/a/Ns/Vtn)-1); % Curentul nominal de saturatie al diodeiIo = Ion;% Valorile de referinta pentru Rs si Rp Rs_max = (Vocn - Vmp)/ Imp;Rp_min = Vmp/(Iscn-Imp) - Rs_max;%Incercarea initiala pentru Rp si RsRp = Rp_min;Rs = 0;tol = 0.05; % Toleranta P=[0];error = Inf; %valoare falsa% Proces iterativ pentru Rs si Rp pna la Pmax,model = Pmax,experimental while (error>tol) %Efectul temperaturi si radiatiei asupra curentului dT = T-Tn;Ipvn = (Rs+Rp)/Rp * Iscn; % Curentul fotovoltaic nominal Ipv = (Ipvn + Ki*dT) *G/Gn; % Curentul fotovoltaic actual Isc = (Iscn + Ki*dT) *G/Gn; % Curentul de scurt-circuit actual % Incrementare Rs Rs = Rs + .01; % Rezistenta paralelaRp = Vmp*(Vmp+Imp*Rs)/(Vmp*Ipv-Vmp*Io*exp((Vmp+Imp*Rs)/Vt/Ns/a)+Vmp*Io-Pmax_e); % Rezolvare ecuatii I-V pentru mai multe perechi (V,I) clear Vclear IV = 0:.1:44.7; % Vectorul tensiuneI = zeros(1,size(V,2)); % Vectorul curent for j = 1 : size(V,2) %Calculeaza pentru toate valorile tensiunii % Calculeaza g = I - f(I,V) = 0 cu Newntonn-Raphson g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j);while (abs(g(j)) > 0.001) g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j);glin(j) = -Io*Rs/Vt/Ns/a*exp((V(j)+I(j)*Rs)/Vt/Ns/a)-Rs/Rp-1;I_(j) = I(j) - g(j)/glin(j);I(j) = I_(j); end end % for j = 1 : size(V,2)plott = 1; %Permite plotarea curbelor n timpul executarii algoritmului if (plott) %Plotarea curbelor I-V si P-V %Curent x Tensiune figure(1) grid on hold on title('Curbele I-V - Ajustarea Rs si Rp'); xlabel('V [V]'); ylabel('I [A]'); xlim([0 Vocn+1]); ylim([0 Iscn+1]); %Plotarea curbei I x V plot(V,I,'LineWidth',2,'Color','k') %Ploteaza punctelor remarcabile de pe curba I x V plot([0 Vmp Vocn],[Iscn Imp 0],'o','LineWidth',2,'MarkerSize',5,'Color','k') %Putere x Tensiune figure(2) grid on hold on title('Curbele P-V - Ajustarea puteri de vrf'); xlabel('V [V]'); ylabel('P [W]'); xlim([0 Vocn+10]) ylim([0 Vmp*Imp+10]);end % if(plott) % Calculeaza puterea folosind ecuatia I-V P = (Ipv-Io*(exp((V+I.*Rs)/Vt/Ns/a)-1)-(V+I.*Rs)/Rp).*V; Pmax_m = max(P); error = (Pmax_m-Pmax_e); if (plott) %Ploteaza curba P x V plot(V,P,'LineWidth',2,'Color','k') %Ploteaza punctelor remarcabile de pe curba puteri plot([0 Vmp Vocn],[0 Vmp*Imp 0],'o','LineWidth',2,'MarkerSize',5,'Color','k') end % if (plott) end % while (error>tol) %% Iesiri % I-V curve figure(3) grid on hold on title('Ajustarea Curbei I-V'); xlabel('V [V]'); ylabel('I [A]'); xlim([0 Vocn+1]); ylim([0 Iscn+1]); plot(V,I,'LineWidth',2,'Color','k') % plot([0 Vmp Vocn ],[Iscn Imp 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') % Curba P-V figure(4) grid on hold on title('Ajustarea curbei P-V'); xlabel('V [V]'); ylabel('P [W]'); xlim([0 Vocn+10]); ylim([0 Vmp*Imp+10]); plot(V,P,'LineWidth',2,'Color','k') plot([0 Vmp Vocn ],[0 Pmax_e 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') disp(sprintf('Model info:\n'));disp(sprintf(' Rp_min = %f',Rp_min));disp(sprintf(' Rp = %f',Rp));disp(sprintf(' Rs_max = %f',Rs_max));disp(sprintf(' Rs = %f',Rs));disp(sprintf(' a = %f',a));disp(sprintf(' T = %f',T-273.15));disp(sprintf(' G = %f',G));disp(sprintf(' Pmax,m = %f (model)',Pmax_m));disp(sprintf(' Pmax,e = %f (experimental)',Pmax_e));disp(sprintf(' tol = %f',tol));disp(sprintf('P_error = %f',error));disp(sprintf(' Ipv = %f',Ipv));disp(sprintf(' Isc = %f',Isc));disp(sprintf(' Ion = %f',Ion));disp(sprintf('\n\n'));

Model 3

% Matlab script for evaluating the photovoltaic array model% Tested with MATLAB Version 7.10 (R2010a)%% Information from the Suntech solar array datasheet% You may change these parameters to fit the I-V model% to other kinds of solar arrays. Iscn = 5.23; %Curent nominal de scurt-circuit [A] Vocn = 44.7; %Tensiunea nominala de mers in gol [V] Imp = 4.9; %curent nominal al panoului @ punctul de putere maxima [A] Vmp = 35.8; %Tensiunea nominala a panoului @ punctul de putere maxima [V] Pmax_e = Vmp*Imp; %Putere maxima de vrf a panoului [W] Kv = -0.155; %Coeficient tensiune/temperatura [V/K] Ki = 3.138e-3; %Coeficient curent/temperatura [A/K] Ns = 72; %Numar de celule in serie% Panoul cu Nss x module Npp Nss = 2;Npp = 2;%% Constants k = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]a = 1.3; %Diode constant%% Evaluates the model for jj = 1:3 %Temperatures [K] if (jj==1) T = 25 + 273.15; end %Evaluates the model for three if (jj==2) T = 50 + 273.15; end %different temperatures if (jj==3) T = 75 + 273.15; end% InputsG = 1000; %Irradiance [W/m^2] %Choose G=1000,800,600,400,200 to compare the model %with experimental data from datasheet % Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]% Nominal values Gn = 1000; % Nominal irradiance [W/m^2] @ 25oCTn = 25 + 273.15; % Nominal operating temperature [K]% Thermal voltages Vtn = k * Tn / q; %Thermal junction voltage (nominal) Vt = k * T / q; %Thermal junction voltage (actual temperature) %Calculation of Io (method 1) %This is the original Io equation generally found in the literature.%This requires finding the optimal value of Eg.%See details in: %"Modeling and circuit-based simulation of photovoltaica arrays" %Calculation of Eg Tmax = 75 + 273.15; dT_ = Tmax - Tn; Isc_ = ( Iscn + Ki*dT_ ); Voc_ = ( Vocn + Kv*dT_ ); Vt_ = k * Tmax / q; Eg = log(Isc_*Tn^3/Ion/Tmax^3/(exp(Voc_/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(Tmax-Tn); %or: Eg = -log((Iscn+Ki*(Tmax-Tn))*Tn^3/Ion/Tmax^3/(exp((Vocn+Kv*(Tmax-Tn))/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(-Tmax+Tn);%Uncomment this line if you wish to use this equation:%Io = Ion *(T/Tn)^(3) * exp( q * Eg/a/ k * (1/Tn-1/T) ); %Calculation of Io (method 2) %This is the alternative Io equation suggested in:%"Comprehensive approach to modeling and simulation of photovoltaic arrays"dT = T - Tn;Isc_ = ( Iscn + Ki*dT );Voc_ = ( Vocn + Kv*dT );%Comment this line if you wish to use the original Io equation:Io = Isc_/(exp(Voc_/a/Ns/Vt)-1);% Temperature and irradiation effect on the currentdT = T-Tn;Ipvn = (Rs+Rp)/Rp * Iscn; % Nominal light-generated currentIpv = (Ipvn + Ki*dT) *G/Gn; % Actual light-generated current Isc = (Iscn + Ki*dT) *G/Gn; % Actual short-circuit current % Solving the I-V equation for several (V,I) pairs clear Vclear IV = 0:.1:45; % Voltage vectorI = zeros(1,size(V,2)); % Current vectorfor j = 1 : size(V,2) %Calculates for all voltage values % Solves g = I - f(I,V) = 0 with Newntonn-Raphson g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); while (abs(g(j)) > 0.001) g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); glin(j) = -Io*Rs/Vt/Ns/a*exp((V(j)+I(j)*Rs)/Vt/Ns/a)-Rs/Rp-1; I_(j) = I(j) - g(j)/glin(j); I(j) = I_(j); end end%% Final adjusted I-V and P-V curves % I-V curve figure(3) grid on hold on title('Caracteristici I-U'); xlabel('V [V]'); ylabel('I [A]'); xlim([0 Vocn+1]); ylim([0 Iscn+2]); plot(V,I,'LineWidth',2,'Color','k') % %plot([0 Vmp Vocn ],[Iscn Imp 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') % P-V curve figure(4) grid on hold on title('Adjusted P-V curves'); xlabel('V [V]'); ylabel('P [W]'); xlim([0 Vocn+1]); ylim([0 200]); plot(V,V.*I,'LineWidth',2,'Color','k') % %plot([0 Vmp Vocn ],[0 Pmax_e 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') End

Model 4

% Matlab script for evaluating the photovoltaic array model% Tested with MATLAB Version 7.10 (R2010a) %% Information from the Suntech solar array datasheet% You may change these parameters to fit the I-V model% to other kinds of solar arrays.Iscn = 5.23; %Curent nominal de scurt-circuit [A] Vocn = 44.7; %Tensiunea nominala de mers in gol [V] Imp = 4.9; %curent nominal al panoului @ punctul de putere maxima [A] Vmp = 35.8; %Tensiunea nominala a panoului @ punctul de putere maxima [V] Pmax_e = Vmp*Imp; %Putere maxima de vrf a panoului [W] Kv = -0.155; %Coeficient tensiune/temperatura [V/K] Ki = 3.138e-3; %Coeficient curent/temperatura [A/K] Ns = 72; %Numar de celule in serie%% Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]a = 1.3; %Diode constant%% Evaluates the model for jj = 1:3 % Inputs %Temperatures [K]T = 25 + 273.15 ; %Evaluates the model for three %different temperatures %Irradiance [W/m^2] if (jj==1) G = 400; end %Choose G=1000,700,400 to compare the model if (jj==2) G = 700; end %with experimental data from datasheet if (jj==3) G = 1000; end % Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]% Nominal values Gn = 1000; % Nominal irradiance [W/m^2] @ 25oCTn = 25 + 273.15; % Nominal operating temperature [K] % Thermal voltages Vtn = k * Tn / q; %Thermal junction voltage (nominal) %Calculation of Io (method 2) %This is the alternative Io equation suggested in:%"Comprehensive approach to modeling and simulation of photovoltaic arrays"dT = T - Tn;Isc_ = ( Iscn + Ki*dT );Voc_ = ( Vocn + Kv*dT );%Comment this line if you wish to use the original Io equation:Io = Isc_/(exp(Voc_/a/Ns/Vt)-1);% Temperature and irradiation effect on the currentdT = T-Tn;Ipvn = (Rs+Rp)/Rp * Iscn; % Nominal light-generated currentIpv = (Ipvn + Ki*dT) *G/Gn; % Actual light-generated current Isc = (Iscn + Ki*dT) *G/Gn; % Actual short-circuit current% Solving the I-V equation for several (V,I) pairs clear Vclear IV = 0:.1:100; % Voltage vectorI = zeros(1,size(V,2)); % Current vectorfor j = 1 : size(V,2) %Calculates for all voltage values % Solves g = I - f(I,V) = 0 with Newntonn-Raphson g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); while (abs(g(j)) > 0.001) g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); glin(j) = -Io*Rs/Vt/Ns/a*exp((V(j)+I(j)*Rs)/Vt/Ns/a)-Rs/Rp-1; I_(j) = I(j) - g(j)/glin(j); I(j) = I_(j); end end%% Final adjusted I-V and P-V curves % I-V curve figure(3) grid on hold on title('Adjusted I-V curves'); xlabel('V [V]'); ylabel('I [A]'); xlim([0 Vocn+1]); ylim([0 Iscn+2]); plot(V,I,'LineWidth',2,'Color','k') % %plot([0 Vmp Vocn ],[Iscn Imp 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') % P-V curve figure(4) grid on hold on title('Adjusted P-V curves'); xlabel('V [V]'); ylabel('P [W]'); xlim([0 Vocn+1]); ylim([0 Vmp*Imp+10]); plot(V,V.*I,'LineWidth',2,'Color','k') % %plot([0 Vmp Vocn ],[0 Pmax_e 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') End

Model 5 cer innorat% Matlab script for evaluating the photovoltaic array model% Tested with MATLAB Version 7.10 (R2010a)%% Information from the Suntech solar array datasheet% You may change these parameters to fit the I-V model% to other kinds of solar arrays.Iscn = 5.23; %Curent nominal de scurt-circuit [A] Vocn = 44.7; %Tensiunea nominala de mers in gol [V] Imp = 4.9; %curent nominal al panoului @ punctul de putere maxima [A] Vmp = 35.8; %Tensiunea nominala a panoului @ punctul de putere maxima [V] Pmax_e = Vmp*Imp; %Putere maxima de vrf a panoului [W] Kv = -0.155; %Coeficient tensiune/temperatura [V/K] Ki = 3.138e-3; %Coeficient curent/temperatura [A/K] Ns = 72; %Numar de celule in serie% Panoul cu Nss x module Npp Nss = 2;Npp = 2;%% Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]a = 1.3; %Diode constant%% Evaluates the model for jj = 1:1 IEX = [0.01.751.482.233.063.974.514.554.584.614.634.634.604.60];UEX = [82.6679.3179.8178.0475.5070.6355.7638.6522.337.704.2642.221.980]; PEX = IEX.*UEX; %Temperatures [K]T = 35 + 273.15;G = 445; %Irradiance [W/m^2] %Choose G=1000,800,600,400,200 to compare the model %with experimental data from datasheet % Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]% Nominal values Gn = 1000; % Nominal irradiance [W/m^2] @ 25oCTn = 25 + 273.15; % Nominal operating temperature [K]% Thermal voltages Vtn = k * Tn / q; %Thermal junction voltage (nominal) Vt = k * T / q; %Thermal junction voltage (actual temperature)%Calculation of Io (method 1) %This is the original Io equation generally found in the literature.%This requires finding the optimal value of Eg.%See details in: %"Modeling and circuit-based simulation of photovoltaica arrays" %Calculation of Eg Tmax = 75 + 273.15; dT_ = Tmax - Tn; Isc_ = ( Iscn + Ki*dT_ ); Voc_ = ( Vocn + Kv*dT_ ); Vt_ = k * Tmax / q; Eg = log(Isc_*Tn^3/Ion/Tmax^3/(exp(Voc_/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(Tmax-Tn); %or: Eg = -log((Iscn+Ki*(Tmax-Tn))*Tn^3/Ion/Tmax^3/(exp((Vocn+Kv*(Tmax-Tn))/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(-Tmax+Tn);%Uncomment this line if you wish to use this equation:%Io = Ion *(T/Tn)^(3) * exp( q * Eg/a/ k * (1/Tn-1/T) ); %Calculation of Io (method 2) %This is the alternative Io equation suggested in:%"Comprehensive approach to modeling and simulation of photovoltaic arrays"dT = T - Tn;Isc_ = ( Iscn + Ki*dT );Voc_ = ( Vocn + Kv*dT );%Comment this line if you wish to use the original Io equation:Io = Isc_/(exp(Voc_/a/Ns/Vt)-1);% Temperature and irradiation effect on the currentdT = T-Tn;Ipvn = (Rs+Rp)/Rp * Iscn; % Nominal light-generated currentIpv = (Ipvn + Ki*dT) *G/Gn; % Actual light-generated current Isc = (Iscn + Ki*dT) *G/Gn; % Actual short-circuit current% Solving the I-V equation for several (V,I) pairs clear Vclear I V = 0:.1:45; % Voltage vectorI = zeros(1,size(V,2)); % Current vectorfor j = 1 : size(V,2) %Calculates for all voltage values % Solves g = I - f(I,V) = 0 with Newntonn-Raphson g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); while (abs(g(j)) > 0.001) g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); glin(j) = -Io*Rs/Vt/Ns/a*exp((V(j)+I(j)*Rs)/Vt/Ns/a)-Rs/Rp-1; I_(j) = I(j) - g(j)/glin(j); I(j) = I_(j); end end %% Final adjusted I-V and P-V curves % I-V curve figure(3) grid on hold on title('Adjusted I-V curves'); xlabel('V [V]'); ylabel('I [A]');axis([0 100 0 15]) UEX = UEX IEX = IEX plot(UEX, IEX, 'ro', V*2,I*2, 'b') % %plot([0 Vmp Vocn ],[Iscn Imp 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') % P-V curve figure(4) grid on hold on title('Adjusted P-V curves'); xlabel('V [V]'); ylabel('P [W]');axis([0 100 0 800]) plot(UEX, PEX, 'ro', V*2,V.*I*4,'LineWidth',2) % %plot([0 Vmp Vocn ],[0 Pmax_e 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') End

Model 5 cer senin

% Matlab script for evaluating the photovoltaic array model% Tested with MATLAB Version 7.10 (R2010a) %% Information from the Suntech solar array datasheet% You may change these parameters to fit the I-V model% to other kinds of solar arrays.Iscn = 5.23; %Curent nominal de scurt-circuit [A] Vocn = 44.7; %Tensiunea nominala de mers in gol [V] Imp = 4.9; %curent nominal al panoului @ punctul de putere maxima [A] Vmp = 35.8; %Tensiunea nominala a panoului @ punctul de putere maxima [V] Pmax_e = Vmp*Imp; %Putere maxima de vrf a panoului [W] Kv = -0.155; %Coeficient tensiune/temperatura [V/K] Ki = 3.138e-3; %Coeficient curent/temperatura [A/K] Ns = 72; %Numar de celule in serie% Panoul cu Nss x module Npp Nss = 2;Npp = 2; %% Constants k = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]a = 1.3; %Diode constant%% Evaluates the model for jj = 1:1IEX = [0.01.692.032.543.24.095.286.096.397.178.388.979.8610.1510.3110.31];UEX = [80.678.3377.9177.2776.3875.0573.1171.7371.0269.5566.4664.3558.9254.1140.010]; PEX = IEX.*UEX; %Temperatures [K]T = 57 + 273.15;G = 980; %Irradiance [W/m^2] %Choose G=1000,800,600,400,200 to compare the model %with experimental data from datasheet % Constantsk = 1.3806503e-23; %Boltzmann [J/K]q = 1.60217646e-19; %Electron charge [C]% Nominal values Gn = 1000; % Nominal irradiance [W/m^2] @ 25oCTn = 25 + 273.15; % Nominal operating temperature [K]% Thermal voltages Vtn = k * Tn / q; %Thermal junction voltage (nominal) Vt = k * T / q; %Thermal junction voltage (actual temperature)%Calculation of Io (method 1) %This is the original Io equation generally found in the literature.%This requires finding the optimal value of Eg.%See details in: %"Modeling and circuit-based simulation of photovoltaica arrays" %Calculation of Eg Tmax = 75 + 273.15; dT_ = Tmax - Tn; Isc_ = ( Iscn + Ki*dT_ ); Voc_ = ( Vocn + Kv*dT_ ); Vt_ = k * Tmax / q; Eg = log(Isc_*Tn^3/Ion/Tmax^3/(exp(Voc_/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(Tmax-Tn); %or: Eg = -log((Iscn+Ki*(Tmax-Tn))*Tn^3/Ion/Tmax^3/(exp((Vocn+Kv*(Tmax-Tn))/a/Ns/k/Tmax*q)-1))*a*k*Tn*Tmax/q/(-Tmax+Tn);%Uncomment this line if you wish to use this equation:%Io = Ion *(T/Tn)^(3) * exp( q * Eg/a/ k * (1/Tn-1/T) ); %Calculation of Io (method 2) %This is the alternative Io equation suggested in:%"Comprehensive approach to modeling and simulation of photovoltaic arrays"dT = T - Tn;Isc_ = ( Iscn + Ki*dT );Voc_ = ( Vocn + Kv*dT );%Comment this line if you wish to use the original Io equation:Io = Isc_/(exp(Voc_/a/Ns/Vt)-1);% Temperature and irradiation effect on the currentdT = T-Tn;Ipvn = (Rs+Rp)/Rp * Iscn; % Nominal light-generated currentIpv = (Ipvn + Ki*dT) *G/Gn; % Actual light-generated current Isc = (Iscn + Ki*dT) *G/Gn; % Actual short-circuit current% Solving the I-V equation for several (V,I) pairs clear Vclear IV = 0:.1:45; % Voltage vectorI = zeros(1,size(V,2)); % Current vector for j = 1 : size(V,2) %Calculates for all voltage values % Solves g = I - f(I,V) = 0 with Newntonn-Raphson g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); while (abs(g(j)) > 0.001) g(j) = Ipv-Io*(exp((V(j)+I(j)*Rs)/Vt/Ns/a)-1)-(V(j)+I(j)*Rs)/Rp-I(j); glin(j) = -Io*Rs/Vt/Ns/a*exp((V(j)+I(j)*Rs)/Vt/Ns/a)-Rs/Rp-1; I_(j) = I(j) - g(j)/glin(j); I(j) = I_(j); end end%% Final adjusted I-V and P-V curves % I-V curve figure(3) grid on hold on title('Adjusted I-V curves'); xlabel('V [V]'); ylabel('I [A]');axis([0 100 0 15]) UEX = UEX IEX = IEX plot(UEX, IEX, 'ro', V*2,I*2, 'b') % %plot([0 Vmp Vocn ],[Iscn Imp 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') % P-V curve figure(4) grid on hold on title('Adjusted P-V curves'); xlabel('V [V]'); ylabel('P [W]');axis([0 100 0 800]) plot(UEX, PEX, 'ro', V*2,V.*I*4,'LineWidth',2) % %plot([0 Vmp Vocn ],[0 Pmax_e 0 ],'o','LineWidth',2,'MarkerSize',5,'Color','k') end

Concluzii

Comparnd rezultatele i graficele obinute n urma ajustrii modelului cu cele din modelul ideal se pot observa diferene mari ntre caracteristicile I=f(U) i P=f(U).

n cazul modelului ideal, pentru curba I=f(U) are un punct de maxim pentru un curent I5 A i o tensiune U35 V, dup acest punct curba ncepnd s descreasc, avnd un curent de mers n gol I=0 A i o tensiune U45 V.

De asemenea, n cazul modelului ideal, n urma reprezentrii caracteristicii P=f(U) punctul maxim se obine pentru valoarea puterii P190 W i a tensiunii U35 V.

Pentru cazurile studiate, cer senin i cer nnorat, se remarc diferene ale valorilor tensiunii, curentului, respectiv puterii.

Pentru cer senin, curba I=f(U) nregistreaz valori maxime la I10 A i U65 V, iar curba P=f(U) la P580 W i U65 V.

Pentru cer nnorat, curba I=f(U) nregistreaz valori maxime la I5 A i U65 V, iar curba P=f(U) la P300 W i U70 V.

Aceste valori au rezultat n urma unor ajustri ale temperaturii i iradianei, mrimi care influeneaz caracteristicile descrise. Aceste mrimi au valori mari n cazul unei zi nsorite (T = 55+ 273.15 [K]; G =935 [W/m2K]) i mai sczute pentru o zi nnorat (T = 35+ 273.15 [K]; G =451 [W/m2K]). Se observ o proporionalitate direct ntre mrimile studiate- curent debitat de panou, tensiunea la borne i putere i cele ajustate temperatur i iradian