Simulation Programming Design. PV Model, MPPT, and Simulation

Transcription

1 Simulation Programming Design (L3) PV Model, MPPT, and Simulation Woei-Luen Chen Simulation Programming Design PV System (L3) - 1 Outline Types of Photovoltaic Cells PV Model Simulation-1: Curve Fitting Technique Simulation-2: Find PV Parameters by Curve Fitting Simulation-3: Build a PV Model under specific irradiation Simulation-4: Build a PV Model under various irradiations Algorithms to Track Maximum Power Point (MPP) Simulation-5: Track MPP by P&O under specific irradiation Simulation-6: Track MPP by P&O under various irradiations Simulation-7: Track MPP by IncCond under specific irradiation Simulation-8: Track MPP by IncCond under various irradiations Woei-Luen Chen Simulation Programming Design PV System (L3) - 2

2 Types of Photovoltaic Cells 1. mono crystalline : efficiency % rejected by the electronic industry for reasons of impurity 2. multi-crystalline: efficiency %. the step is skipped in which a mono crystal is slowly grown from a small seed to a large ingot. This makes these cells less expensive Disadvantages : cannot easily be produced in larger sizes and they require enormous investments in clean-room factories. The energy payback time is also quite long due to the power consuming processes required for refining silicone. mono crystalline photovoltaic cell of silicon Woei-Luen Chen Simulation Programming Design PV System (L3) - 3 Woei-Luen Chen Simulation Programming Design PV System (L3) - 4

3 3. Dye Sensitised Solar Cell (DYSC), or Grätzel-cell as it is often referred to, after its inventor Michael Grätzel, Switzerland. Instead of two solid-state semiconductors, a dye solution and a solid state semiconductor (TiO2) are employed. Advantage -relatively low cost. No clean room is needed, which makes them attractive for developing countries. -At low light irradiation, such as in indoor applications, these cells are more favourable as the efficiencies of the other types decrease and become of the same order as the dye-sensitised cell. disadvantages -lower efficiency (5-8%) and that they are not yet stable. 4. Multijunction cell (or tandem cell in case of two layers): A type of PV-cell that at present has the highest value of efficiency (officially 32.6%). It consists of two or more PV-cells stacked with different band gaps so each cell utilizes different regions of the irradiated spectrum. Woei-Luen Chen Simulation Programming Design PV System (L3) - 5 PV Model: Fill Factor (FF) of the cell The departure of the I-V characteristic of a real cell from that of a perfect cell is measured by the fill factor (FF) of the cell. The assumption is that a perfect cell would have a rectangular characteristic, with constant current up to the maximum cell voltage, and then constant voltage. The constant current would be the shortcircuit current and the constant voltage would be the open-circuit voltage. Woei-Luen Chen Simulation Programming Design PV System (L3) - 6

4 Effect of irradiation and temperature on the i-v characteristic Woei-Luen Chen Simulation Programming Design PV System (L3) - 7 Effect of temperature Woei-Luen Chen Simulation Programming Design PV System (L3) - 8

5 PV Model: Equivalent Electrical Circuit The diode-saturation current can be determined experimentally by applying voltage Voc in the dark and measuring the current going into the cell. This current is often called the dark current or the reverse diode-saturation current. Woei-Luen Chen Simulation Programming Design PV System (L3) - 9 PV Model: Equivalent Electrical Circuit In a typical high quality one square inch silicon cell, R s = 0.05 to 0.10 ohm R sh = 200 to 300 ohms. The pv conversion efficiency is sensitive to small variations in Rs, but is insensitive to variations in Rsh. A small increase in Rs can decrease the pv output significantly. Woei-Luen Chen Simulation Programming Design PV System (L3) - 10

6 Simulation-1: Curve Fitting Technique Example 1: Linear Regression 1600 x=10:10:80; y=[25, 70, 380, 550, 610, 1220, 830, 1450]; plot(x,y) data 1 linear quadratic y = 19*x - 2.3e+002 y = 0.037*x *x - 1.8e Woei-Luen Chen Simulation Programming Design PV System (L3) - 11 Simulation-1: Curve Fitting Technique Example 2: Nonlinear Regression Given depent force data F for indepent velocity data v, determine the coefficients for the fit: F av 1 a 2 First - write a function called fssr.m containing the following: Then, use fminsearch in the command window to obtain the values of a that minimize fssr: where [1, 1] is an initial guess for the [a1, a2] vector, [] is a placeholder for the options Woei-Luen Chen Simulation Programming Design PV System (L3) - 12

7 Simulation-1: Curve Fitting Technique nonlinear regression y = 0.037*x *x - 1.8e Woei-Luen Chen Simulation Programming Design PV System (L3) - 13 Simulation-2: Find PV Parameters by Curve Fitting Use the nonlinear least squares to fit the PV cell model (find optimum I o and R sh ) qv V I Vo 3.5 Io exp kt R o o, T=300, q= , k= to the following data: where the initial guesses are I o = and R sh =1.0. I V o sh Woei-Luen Chen Simulation Programming Design PV System (L3) - 14

8 Simulation-2: Find PV Parameters by Curve Fitting PV_fSSR.m function f = PV_fSSR(a, xm, ym) yp =3.5-a(1)*(exp(((1.6e-19)*xm)/(1.92*1.38e-23*300))-1)-xm/a(2); f = sum((ym-yp).^2); PV_fSSR_main.m clear all clc Im=[ ]; Vm=[ ]; q=1.6e-19; k=1.38e-23; T=300; m=q/1.92/k/t; a=fminsearch(@pv_fssr, [0 0],[], Vm, Im) Io=a(1); Rsh=a(2); Vd=0.3:0.01:0.6; Id=3.5-Io*(exp(Vd*m)-1)-Vd/Rsh; plot(vd,id,vm,im,'*') Woei-Luen Chen Simulation Programming Design PV System (L3) - 15 Simulation-2: Find PV Parameters by Curve Fitting I (A) V o (V) Woei-Luen Chen Simulation Programming Design PV System (L3) - 16

9 Simulation-3: Build a PV Model under specific irradiation PVmodel_VSI_1D.mdl P (W) V o (V) Woei-Luen Chen Simulation Programming Design PV System (L3) - 17 Simulation-4: Build a PV Model under various irradiations Add the following codes to PV_fSSR_main.m irradiation=0.5:0.001:3.55; for kc=1:length(irradiation) Id2(kc,:)=irradiation(kc)-Io*(exp(Vd*m)-1)-Vd/Rsh; Id2=Id2'; P (W) PVmodel_VSI_nD.mdl V o (V) Woei-Luen Chen Simulation Programming Design PV System (L3) - 18

10 Algorithms to Track Maximum Power Point (MPP) Woei-Luen Chen Simulation Programming Design PV System (L3) - 19 Algorithm 1: Perturb & Observe (P&O): The operating voltage is increased as long as dp/dv is positive. That is, the voltage is increased as long as we get more power. If dp/dv is sensed negative, the operating voltage is decreased. The voltage is kept put if the dp/dv is near zero within a preset dead band. Woei-Luen Chen Simulation Programming Design PV System (L3) - 20

11 Simulation-5: Track MPP by P&O under specific irradiation mppt_po.m PVmodel_VSI_1D.mdl function Vin=mppt_PO(u) dp=u(1)-u(2); %Pn-Pn_1; dv=u(3)-u(4); %Vn-Vn_1; if (dp<0) if (dv>0) Vin=u(3)-0.01; else Vin=u(3)+0.01; elseif (dp>0) if (dv>0) Vin=u(3)+0.01; else Vin=u(3)-0.01; else Vin=u(3); Woei-Luen Chen Simulation Programming Design PV System (L3) - 21 Simulation Results Woei-Luen Chen Simulation Programming Design PV System (L3) - 22

12 Simulation-6: Track MPP by P&O under various irradiations PVmodel_VSI_nD.mdl Woei-Luen Chen Simulation Programming Design PV System (L3) - 23 Simulation Results Woei-Luen Chen Simulation Programming Design PV System (L3) - 24

13 Algorithm 2: Ignoring a small term, simplifies to the following: The P should be zero at peak power point, which necessarily lies on a locally flat neighborhood. Therefore, at max power point, the above expression in the limit becomes as follows: Note that dv/di is the dynamic impedance of the source, and V/I is the static impedance. Woei-Luen Chen Simulation Programming Design PV System (L3) - 25 Algorithm 2: Incremental Conductance (IncCond): A small signal current is periodically injected into the array bus and the dynamic bus impedance Z d = dv/di and the static bus impedance Z s = V/I are measured. The operating voltage is then increased or decreased until Z d = Z s. At this point, the maximum power is extracted from the source. C 1 : the chosen perturbation step size Woei-Luen Chen Simulation Programming Design PV System (L3) - 26

14 Simulation-7: Track MPP by IncCond under specific irradiation mppt_inc.m function Vin=mppt_INC(u) e1=0.001; e2=0.001; e3=0.001; di=u(1)-u(2); %In-In_1; dv=u(3)-u(4); %Vn-Vn_1; dyn_imp=di/dv; sta_imp=u(1)/u(3); if (abs(dv)<e1) if (abs(di)>=e3) if (di>e3) Vin=u(3)+0.01; else Vin=u(3)-0.01; else Vin=u(3); else if (abs(dyn_imp+sta_imp)>=e2) if ((dyn_imp+sta_imp)>=e2) Vin=u(3)+0.01; else Vin=u(3)-0.01; else Vin=u(3); PVmodel_VSI_1D.mdl Woei-Luen Chen Simulation Programming Design PV System (L3) - 27 Simulation-8: Track MPP by IncCond under various irradiations PVmodel_VSI_nD.mdl Woei-Luen Chen Simulation Programming Design PV System (L3) - 28

15 Simulation Results Woei-Luen Chen Simulation Programming Design PV System (L3) - 29 Algorithm 3: The third method makes use of the fact that for most pv cells, the ratio of the voltage at the maximum power point to the open circuit voltage (i.e., Vmp/Voc) is approximately constant, say K v. (K v = 0.72~0.78) The operating voltage of the power-producing array is then set at K v V oc, which will produce the maximum power. The 4th method also makes use of the fact that for most pv cells, the ratio of the current at the maximum power point to the short circuit current (i.e., I mp /I sc ) is approximately constant, say K i. (K i = 0.85~0.95) The operating current of the power-producing array is then set at K i I sc, which will produce the maximum power. Woei-Luen Chen Simulation Programming Design PV System (L3) - 30