Assume a wind unit with the following parameters: NumberofPoles=4,Ng =15,Rt =35m

Question

Assume a wind unit with the following parameters: NumberofPoles=4,Ng =15,Rt =35m,=1.225kg/m3.

a) If Cp = 0.48( 0.018 5.8)e0.16 then find opt and Cp.max.

answer: lambda=12.05 & Cp=0.4363

syms Lambda Betta

cp1(Lambda,Betta) = 0.48*(Lambda-0.018*Betta^2-5.8).*exp(-0.16*Lambda);

cp2(Lambda) = cp1(Lambda,0);

g = diff(cp2,Lambda);

la = solve(g==0,Lambda);

la = double(la);

cp = double(cp2(la));

fprintf('Lambda = %f ',la);

fprintf('Cp = %f ',cp);

b) Assuming cut-in, nominal and cut-off wind speeds are 2, 14, and 20 m/s, respectively, plot Pm (MW) vs.

Vw (m/s) showing all three modes of operation.

c) Plot Cp vs. for mode II operation.

My question is for part b and c. I need “script” matlab code.

Subject Year Month Date Nate e Vm is maxim am f rhoset t(al voltage. Vu (RNS line, to line altoge) is given Wind Units Power IN wind can be calculated as N Pwer of the wind Air densi A Area of the blades (m) Wind veted do mechanical eneaa The feNet twiLine A CP lower coeficient Ce is not anstant The mouimim value f cp is (Dun o.S. ce depends on tw variables Tie speed ratio CA Radius of twib blaues Line an la s

Explanation / Answer

clc;
close all;
clear all;

%QUESTION b

Vw_cutin = 2;
Vw_nom = 14;
Vw_cutoff = 20;

Vw = 0:0.01:Vw_cutoff ;

rho = 1.225;
A = 1;
Cp = 0.4363;

k = (rho*A*Cp/2);

%P = (0<Vw<Vw_cutin)*0 + (Vw_cutin<=Vw<Vw_nom )*k.Vw.^3 + (Vw_nom <=Vw<=Vw_cutoff)*k*Vw_nom.^3;
%P = (Vw>=0).*1 + (Vw>=Vw_cutin).*k*pow(Vw,3));
%(Vw>=0).*0 + (Vw>=Vw_nom).*k*Vw.^3;
%+ (Vw_cutin<=Vw<Vw_nom )*k.Vw.^3;
P = [];
for i = 1:1:length(Vw);
    if Vw(i) <Vw_cutin
        P(i)=0;
    elseif Vw(i) < Vw_nom
        P(i) = k*Vw(i).^3;
    else
        P(i) = k*Vw_nom.^3;
    end
end

figure
plot(Vw,P);
title('P vs Vw');
xlabel('SPeed Vw');
ylabel('Power P');

%QUESTION c
Beta = 0;
Rt = 35;
wt = 5;

Vw = Vw_cutin:0.01:Vw_nom;

Lambda = Rt*wt./Vw;

Cp = 0.5*(Lambda-0.022*Beta.^2-5.6).*exp(-0.17*Lambda);

figure
plot(Lambda,Cp);
title('Cp vs Lambda');
xlabel('TIp speed ratio lambda');
ylabel('Cp');

%UPDATE

%QUESTION b

Vw_cutin = 2;
Vw_nom = 14;
Vw_cutoff = 20;
%QUESTION c
Beta = 0;
Rt = 35;
wt = 5;

Vw = 0.9:0.01:Vw_cutoff;

Lambda = Rt*wt./Vw;

Cp = 0.5*(Lambda-0.022*Beta.^2-5.6).*exp(-0.17*Lambda);

figure
plot(Lambda,Cp);
title('Cp vs Lambda');
xlabel('TIp speed ratio lambda');
ylabel('Cp');

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