Contents1. Introduction.............................................................................................................................................2

Conditions of most efficient operation of MPPTs:...................................................................................2

2. Theory.....................................................................................................................................................2

Perturbation and Observe Method:........................................................................................................3

Incremental Conductance method:.........................................................................................................4

3. Results.....................................................................................................................................................7

4. Discussion..............................................................................................................................................13

6. Conclusion.............................................................................................................................................14

7. References.............................................................................................................................................15

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1. Introduction

Maximum Power point Tracking (MPPT) is an electronic system which is design to on photovoltaic (PV) model in a way that allows the module to produce the maximum power that they possibly can. A Maximum Power Point Tracker operates by comparing the output of solar panels to the battery voltage. It then uses an algorithm to calculate the best power that can be outputted by the module. It uses this power to obtain the best voltage which will supply the maximum current to the battery. Most of the MPPT’s are 92% to 97% efficient.

Conditions of most efficient operation of MPPTs:

Winter or cloudy days: when there is a greater demand for the extra power.

Cold Weather: this result better operation of solar cells, thus a MPPT is used to take advantage of this fact.

Low battery Charge: the lower that state of charge on the battery the more current the MPPT is able put into them.

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2. Theory

Perturbation and Observe Method:

It is an iterative method used for obtaining the maximum power point (MPP). It measures the PV array characteristics, and then it perturbs the operating point of the PV generator to observe the change direction. The maximum point will be reach when the dPPV/dVPV = 0. There are many adaptations of this method, varying from simple to complex, an algorithm flowchart for a basic form is shown in Figure 1, below.

Figure 1: Perturbation and Observe Algorithm Flowchart[3]

From the above flowchart is can be noted that the operating voltage of the PV module is perturb by a small incremental voltage (ΔVPV), thereby enabling measure of resulting change in power

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(ΔPPV). If the ΔPPV is positive the perturbation of the operating voltage is in the same direction of the increment, but if it’s negative the system operating point moves away from the MPPT and therefore the operating voltage should be in the opposite direction of the increment. Hence if the power is increased so shall the operating point.

The disadvantage of this type of method is seen in the sudden increase in irradiance, as shown in Figure 2, where the reacts as if the increase had occurred as a result of previous perturbation.

Figure 2: Deviation of the Perturbation and Observe Method Algorithm under increasing Irradiance. [2]

The advantages of this type of algorithm are; no previous knowledge of the PV module is required, therefore it relatively simply. Even though it is an unsuitable method in rapidly changing atmospheric conditions its reaction can be improved by increasing the speed of execution of the algorithm or by introducing optimisation.

Incremental Conductance method:

This method is an alternative to the perturbation and observe method, and is based on equation (1) below, where the derivative of the PV power with respect to voltage is obtained and then equated to zero, as shown in Figure 3.

dPPVdV PV

=I PVdV PV

dV PV

+V PVdIPVdV PV

=I PV+V PVdIPVdV PV

=0(1)

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−IPVV PV

=dI PVdV PV

(2)

The left hand side of Equation 2 represents the opposite of the instantaneous conductance (G = IPV/VPV), whereas the right hand side represents the incremental conductance. The incremental variations, dVPV and dIPV, can be approximated by increments of both parameters, ΔVPV and ΔIPV, with the intent on measuring the actual value of VPV and IPV with values measured from the previous instant.

dV PV (t 2)≈ ∆V PV (t2)=V PV (t 2)−V PV (t 1)(3)

dI PV (t2)≈∆ IPV (t2)=I PV (t2 )−IPV ( t1)(4)

Figure 3: P-V Characteristic Curve of a PV Module. [2]

Therefore analysis of the derivative can determine whether the PV module is operating at its maximum power point or far from it, Equations (5), (6) and (7) illustrates this. A flowchart implementation of this algorithm is shown in Figure 4.

dPPVdV PV

>0 for V PV<V PMP(5)

dPPVdV PV

=0 for V PV=V PMP(6)

dPPVdV PV

<0 for V PV>V PMP(7)

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Figure 4: Incremental Conductance Algorithm Flowchart. [3]

The main advantage of this algorithm is that it offers a good resulting method under rapidly changing atmospheric conditions. It also achieves a decrease in oscillation at the maximum power point then the Perturbation and observe method.

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3. Results

The two methods were simulated under the conditions and result obtained from Matlab computer program is shown below, as well as the simulation code.

Figure 5: Results obtained for Perturbation and Observe Method

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Figure 6: Graph of Output Power vs Voltage for Incremental Conductance Algorithm

Matlab Function Code for the BP SX 150S PV Module: [4]

function Ia = bp_sx150s(Va, G, TaC) % function bp_sx150s.m models the BP SX 150S PV module% calculates module current under given voltage, irradiance and temperature% Ia = bp_sx150s(Va,G,T)%% Out: Ia = Module operating current (A), vector or scalar% In: Va = Module operating voltage (V), vector or scalar% G = Irradiance (1G = 1000 W/m^2), scalar% TaC = Module temperature in deg C, scalar %////////////////////////////////////////////////////////////////////////// % Define constantsk = 1.381e-23; % Boltzmann¡¦s constantq = 1.602e-19; % Electron charge% Following constants are taken from the datasheet of PV module and% curve fitting of I-V character (Use data for 1000W/m^2)n = 1.62; % Diode ideality factor (n),% 1 (ideal diode) < n < 2Eg = 1.12; % Band gap energy; 1.12eV (Si), 1.42 (GaAs),% 1.5 (CdTe), 1.75 (amorphous Si)Ns = 72; % # of series connected cells (BP SX150s, 72 cells)TrK = 298; % Reference temperature (25C) in KelvinVoc_TrK = 43.5 /Ns; % Voc (open circuit voltage per cell) @ temp TrKIsc_TrK = 4.75; % Isc (short circuit current per cell) @ temp TrKa = 0.65e-3; % Temperature coefficient of Isc (0.065%/C)

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% Define variablesTaK = 273 + TaC; % Module temperature in KelvinVc = Va / Ns; % Cell voltage% Calculate short-circuit current for TaKIsc = Isc_TrK * (1 + (a * (TaK - TrK)));% Calculate photon generated current @ given irradianceIph = G * Isc;% Define thermal potential (Vt) at temp TrKVt_TrK = n * k * TrK / q;% Define b = Eg * q/(n*k);b = Eg * q /(n * k);% Calculate reverse saturation current for given temperatureIr_TrK = Isc_TrK / (exp(Voc_TrK / Vt_TrK) -1);Ir = Ir_TrK * (TaK / TrK)^(3/n) * exp(-b * (1 / TaK -1 / TrK));% Calculate series resistance per cell (Rs = 5.1mOhm)dVdI_Voc = -1.0/Ns; % Take dV/dI @ Voc from I-V curve of datasheetXv = Ir_TrK / Vt_TrK * exp(Voc_TrK / Vt_TrK);Rs = - dVdI_Voc - 1/Xv;% Define thermal potential (Vt) at temp TaVt_Ta = n * k * TaK / q;% Ia = Iph - Ir * (exp((Vc + Ia * Rs) / Vt_Ta) -1)% f(Ia) = Iph - Ia - Ir * ( exp((Vc + Ia * Rs) / Vt_Ta) -1) = 0% Solve for Ia by Newton's method: Ia2 = Ia1 - f(Ia1)/f'(Ia1)Ia=zeros(size(Vc)); % Initialize Ia with zeros% Perform 5 iterationsfor j=1:5Ia = Ia - (Iph - Ia - Ir .* ( exp((Vc + Ia .* Rs) ./ Vt_Ta) -1))..../ (-1 - Ir * (Rs ./ Vt_Ta) .* exp((Vc + Ia .* Rs) ./ Vt_Ta));end

Matlab Function Code for finding the Maximum Power Point [4]

function [Pa_max, Imp, Vmp] = find_mpp(G, TaC)% find_mpp: function to find a maximum power point of pv module% [Pa_max, Imp, Vmp] = find_mpp(G, TaC)% in: G (irradiance, KW/m^2), TaC (temp, deg C)% out: Pa_max (maximum power), Imp, Vmp %////////////////////////////////////////////////////////////////% Define variables and initializeVa = 12;Pa_max = 0;% Start processwhile Va < 48-TaC/8Ia = bp_sx150s(Va,G,TaC);Pa_new = Ia * Va;if Pa_new > Pa_maxPa_max = Pa_new;Imp = Ia;Vmp = Va;endVa = Va + .005;end

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Matlab Code for Incremental Conductance Method [4]

% incCondTest1: Script file to test incCond MPPT Algorithm% Testing with rapidly changing insolation %///////////////////////////////////////////////////////////////////////clear;% Define constantsTaC = 25; % Cell temperature (deg C)C = 0.5; % Step size for ref voltage change (V)E = 0.002; % Maximum dI/dV error% Define variables with initial conditionsG = 0.045; % Irradiance (1G = 1000W/m^2)Va = 31; % PV voltageIa = bp_sx150s(Va,G,TaC); % PV currentPa = Va * Ia; % PV output powerVref_new = Va + C; % New reference voltage% Set up arrays storing data for plotsVa_array = [];Pa_array = [];Pmax_array =[];% Load irradiance data%load irrad7d; % Irradiance data of a cloudy dayirrad7d = [0 0.1; 1 0.2; 2 0.3; 3 0.4; 4 0.5; 5 0.6; 6 0.7; 7 0.8; 8 0.9;... 9 1.0; 10 1.1; 11 1.2; 12 1.3; 13 1.4;]x = irrad7d(:,1)'; % Read time data (second)y = irrad7d(:,2)'; % Read irradiance dataxi = 1:200; % Set points for interpolationyi = interp1(x,y,xi,'cubic'); % Do cubic interpolation% Take 43200 samples (12 hours)for Sample = 1:14% Read irrad valueG = yi(Sample);% Take new measurementsVa_new = Vref_new;Ia_new = bp_sx150s(Vref_new,G,TaC);% Calculate incremental voltage and currentdeltaVa = Va_new - Va;deltaIa = Ia_new - Ia;% incCond Algorithm starts hereif deltaVa == 0if deltaIa == 0Vref_new = Va_new; % No changeelseif deltaIa > 0Vref_new = Va_new + C; % Increase VrefelseVref_new = Va_new - C; % Decrease Vrefendelseif abs(deltaIa/deltaVa + Ia_new/Va_new) <= EVref_new = Va_new; % No changeelseif deltaIa/deltaVa > -Ia_new/Va_new + EVref_new = Va_new + C; % Increase VrefelseVref_new = Va_new - C; % Decrease Vref

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endendend% Calculate theoretical max[Pa_max, Imp, Vmp] = find_mpp(G, TaC);% Update historyVa = Va_new;Ia = Ia_new;Pa = Va_new * Ia_new;% Store data in arrays for plotVa_array = [Va_array Va];Pa_array = [Pa_array Pa];Pmax_array = [Pmax_array Pa_max];end% Total electric energy: theoretical and actualPth = sum(Pmax_array)/3600;Pact = sum(Pa_array)/3600;% Plot resultfigureplot (Va_array, Pa_array, 'g')%plot(Va, Ia);% Overlay with P-V curves and MPPVa = linspace (0, 45, 200);hold onfor G=.2:.2:1Ia = bp_sx150s(Va, G, TaC);Pa = Ia.*Va;plot(Va, Pa)[Pa_max, Imp, Vmp] = find_mpp(G, TaC);plot(Vmp, Pa_max, 'r*')endtitle('Graph of Output Power vs Voltage for Incremental Conductance Method')xlabel('Voltage(V)')ylabel('Output Power (Watts)')axis([0 50 0 160])hold off

Matlab Code for Perturbation and Observe Method [4]

clear;% Define constantsTaC = 25; % Cell temperature (deg C)C = 0.5; % Step size for ref voltage change (V)% Define variables with initial conditionsG = 0.028; % Irradiance (1G = 1000W/m^2)Va = 31.0; % PV voltageIa = bp_sx150s(Va,G,TaC); % PV currentPa = Va * Ia; % PV output powerVref_new = Va + C; % New reference voltage% Set up arrays storing data for plotsVa_array = [];Pa_array = [];% Load irradiance data%load irrad; % Irradiance data of a sunny dayirrad7d = [0 0.1; 1 0.2; 2 0.3; 3 0.4; 4 0.5; 5 0.6; 6 0.7; 7 0.8; 8 0.9;...

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9 1.0; 10 1.1; 11 1.2; 12 1.3; 13 1.4;];x = irrad7d(:,1)'; % Read time data (second)y = irrad7d(:,2)'; % Read irradiance dataxi = 1: 200; % Set points for interpolationyi = interp1(x,y,xi,'cubic'); % Do cubic interpolation for i = 1:14% Read irradiance valueG = yi(i);% Take new measurementsVa_new = Vref_new;Ia_new = bp_sx150s(Vref_new,G,TaC);% Calculate new PaPa_new = Va_new * Ia_new;deltaPa = Pa_new - Pa;% P&O Algorithm starts hereif deltaPa > 0if Va_new > VaVref_new = Va_new + C; % Increase VrefelseVref_new = Va_new - C; % Decrease Vrefendelseif deltaPa < 0if Va_new > VaVref_new = Va_new - C; % Decrease VrefelseVref_new = Va_new + C; %Increase VrefendelseVref_new = Va_new; % No changeend% Update historyVa = Va_new;Pa = Pa_new;% Store data in arrays for plotVa_array = [Va_array Va];Pa_array = [Pa_array Pa];end% Plot resultfigureplot (Va_array, Pa_array, 'g')% Overlay with P-I curves and MPPVa = linspace (0, 45, 200);hold onfor G=.2:.2:1Ia = bp_sx150s(Va, G, TaC);Pa = Ia.*Va;plot(Va, Pa)[Pa_max, Imp, Vmp] = find_mpp(G, TaC);plot(Vmp, Pa_max, 'r*')endtitle('Graph of Output Power vs Voltage for Perturbation and Observe Method')xlabel('Voltage (V)')ylabel('Output Power (Watts)')axis([0 50 0 160])hold off

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4. Discussion

The two maximum power point tracking methods discussed previous were simulated. Since a comparison needed to be drawn between the two methods, the both algorithms were simulated by modelling the same PV module under the same conditions, to isolate the system from other influences such as load resistance. From the graphs obtained it can be note that the both algorithms operate close to the maximum tracking points with little deviation in their performances. The data used in the simulation may not truly represent a rapidly changing condition therefore resulting in the graph being similar. Further optimization of the algorithm procedures may provide for better results. The different in performance between the two algorithms would not be relatively large. The results show that the two methods operate at similar efficiencies, however in practise it can be noted that the Perturbation and Observe method produces more oscillations near the maximum power point as compared to the Incremental Conductance method. It can also be note that the simulation could provide better understanding of the algorithms by simulating the procedure under different environmental conditions.

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6. Conclusion

The perturbation and observe and increment conductance algorithms were compared to observe the advantages and disadvantages between these two. The two methods were simulated under the same conditions, so that an accurate analysis of the results can obtained. It can be noted that the Incremental Conductance algorithm proved to operate with a greater efficiency then the Perturbation and observe method.

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7. References

1. G.M. Hans, Solar cell and test circuit, Patent US3, 350, 635, 1967.

2. M.A. Hamdy, A new model for the current-voltage output characteristics of photovoltaic modules, J. Power

3. W.J.A. Teulings, J.C. Marpinard, A. Capel, A maximum power point tracker for a regulated power bus, in:Proceedings of the European Space Conference, 1993.

4. Akihiro Oi, Design and Simulation of Photovoltaic Water Pumping System, California Polytechnic State University, 2005

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