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test.m
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test.m
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clear; clc;
close all;
cmap = get(groot,'defaultAxesColorOrder');
%# common variables
w0 = 2*pi*50;
s = sym('s');
I = eye(2);
w = logspace(-2,3,1e5)*2*pi;
wd = [-flip(w),w];
%%
%# default parameters
para1.J = 3.5*2/w0^2;
para1.D = 1/w0^2;
para1.L = 0.02/w0;
para1.R = 0.01;
para2.V_dc = 2.5;
para2.C_dc = 2*0.1*para2.V_dc^2;
para2.kp_v_dc = para2.V_dc*para2.C_dc*(10*2*pi);
para2.ki_v_dc = para2.kp_v_dc*(10*2*pi)/4;
para2.kp_pll = 2*2*pi;
para2.ki_pll = para2.kp_pll * (2*2*pi)/4;
para2.tau_pll = 1/(2*pi*200);
para2.k_pf = 0;
para2.L = 0.03/(w0);
para2.R = 0.01;
para2.kp_i_dq = para2.L * (500*2*pi);
para2.ki_i_dq = para2.kp_i_dq *(500*2*pi)/4;
%%
%# Test: low inertia interact with pll
layout = 4;
sweep = 2;
if layout == 1
%2 buses : test the match between symbolic and tf models
%-----------------------------------------------------------
% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |
Bus = [ 1 1 1.0 0 1.0 0 0.0 0 -1 1;
2 3 1.0 0 1.0 -0.2 0.0 0 -1 1];
%-----------------------------------------------------------
% | From | To | R | L | C | G |
% | Bus | Bus | | | | |
Line = [ 1 2 0.00 0.3 0.00 inf;
1 1 0 0 1e-1 2.0;
2 2 0 0 1e-1 0.0];
elseif layout == 2
%3 buses : test generator interaction
%-----------------------------------------------------------
% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |
Bus = [ 1 1 1.0 0 0.5 0 0.0 0 -1 1;
2 2 1.0 0 0.5 0 0.0 0 -1 1;
3 2 1.0 0 1.0 0 0.0 0 -1 1];
%-----------------------------------------------------------
% | From | To | R | L | C | G |
% | Bus | Bus | | | | |
Line = [ 1 2 0.01 0.3 0 inf;
2 3 0.01 0.3 0 inf;
3 1 0.01 0.3 0 inf;
1 1 0 0 2e-2 1.0;
2 2 0 0 2e-2 1.0;
3 3 0 0 2e-2 0.0];
elseif layout == 3
%4 buses : test generator converter interaction
%-----------------------------------------------------------
% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |
Bus = [ 1 2 1.0 0 0.5 0 0.0 0 -1 1;
2 2 1.0 0 0.5 0 0.0 0 -1 1;
3 1 1.0 0 0.5 0 0.0 0 -1 1;
4 3 1.0 0 0.5 -0.2 0.0 0 -1 1];
%-----------------------------------------------------------
% | From | To | R | wL | wC | G |
% | Bus | Bus | | | | |
Line = [ 1 2 0.01 0.3 0 inf;
2 3 0.01 0.3 0 inf;
3 1 0.01 0.3 0 inf;
3 4 0.01 0.3 0 inf;
1 1 0 0 1e-5 0.6;
2 2 0 0 1e-5 0.6;
3 3 0 0 1e-5 0.8;
4 4 0 0 1e-5 0];
elseif layout == 4
%5 buses : test generator converter interaction in more meshed grid
%-----------------------------------------------------------
% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |
Bus = [ 1 2 1.0 0 0.5 0 0.0 0 -1 1;
2 2 1.0 0 0.5 0 0.0 0 -1 1;
3 1 1.0 0 0.5 0 0.0 0 -1 1;
4 3 1.0 0 0.4 -0.2 0.0 0 -1 1;
5 3 1.0 0 0.1 0.0 0.0 0 -1 1];
%-----------------------------------------------------------
% | From | To | R | wL | wC | G |
% | Bus | Bus | | | | |
Line = [ 1 2 0.01 0.3 0 inf;
2 3 0.01 0.3 0 inf;
3 1 0.01 0.3 0 inf;
3 4 0.01 0.3 0 inf;
3 5 0.01 0.3 0 inf;
1 4 0.10 1.0 0 inf;
2 5 0.10 1.0 0 inf;
1 1 0 0 1e-5 0.6;
2 2 0 0 1e-5 0.6;
3 3 0 0 1e-5 0.8;
4 4 0 0 1e-5 0.0;
5 5 0 0 1e-5 0.0];
end
[~,~,Ang0,P0,Q0,V0]=PowerFlow(Bus,Line);
nbus = max(Bus(:,1));
[Ytf1,Yb1] = YbusCalcTF(Line(1:(end-nbus),:),w0);
[Ytf2,Yb2] = YbusCalcTF(Line((end-nbus+1):end,:),w0);
Yb1 = minreal(Yb1);
Zb2 = inv(Yb2);
Zb2 = minreal(Zb2);
Zb = feedback(Zb2,Yb1);
if layout == 1
bandwidth_sweep = linspace(1,10,10);
elseif layout == 2
bandwidth_sweep = linspace(1,10,10);
elseif layout == 3
%bandwidth_sweep = linspace(5,20,10);
bandwidth_sweep = 20;
elseif layout == 4
bandwidth_sweep = 20;
end
%bandwidth_sweep = 20;%debug
cpoint = 1; %colormap pointer
for bandwidth = bandwidth_sweep
% reduce generator inertia
para1_ = para1;
para1_.J = para1_.J/10;
para1__= para1;
para1__.J = para1__.J/2;
% change converter control gain
para2_ = para2;
if sweep == 1 %sweep pll gain
para2_.kp_pll = bandwidth*2*pi;
para2_.ki_pll = para2_.kp_pll * (5*2*pi)/4;
para2_.kp_v_dc = para2_.V_dc*para2_.C_dc * (10*2*pi);
para2_.ki_v_dc = para2_.kp_v_dc * (10*2*pi)/4;
elseif sweep == 2 %sweep pll and dc-link gain
para2_.kp_pll = bandwidth*2*pi;
para2_.ki_pll = para2_.kp_pll * (bandwidth*2*pi)/4;
para2_.kp_v_dc = para2_.V_dc*para2_.C_dc * (bandwidth*2*pi);
para2_.ki_v_dc = para2_.kp_v_dc * (bandwidth*2*pi)/4;
end
% parameters
if layout == 1
type = {0,10};
para = {para1_,para2_};
elseif layout == 2
% three generators
type = {0,0,0};
para = {para1,para1,para1};
elseif layout == 3
% four generators
%type = {0,0,0,0};
%para = {para1,para1,para1_,para1};
% three generators and one wind farm
type = {0,0,0,10};
para = {para1,para1,para1_,para2_};
elseif layout == 4
type = {0,0,0,10,10};
para = {para1,para1__,para1_,para2_,para2};
end
% model and link
Gm = cell(1,nbus);
Gc = cell(1,nbus);
for n = 1:nbus
[~,Gm{n},Gc{n},~] = MdlCreate('type', type{n} ,'flow',[-P0(n) -Q0(n) V0(n) Ang0(n) w0],'para',para{n});
end
Gm = MdlLink(Gm);
dimu = length(Gm.B(1,:));
Gsys = feedback(Gm,Zb,(dimu-2*nbus+1):dimu,(dimu-2*nbus+1):dimu);
% manual link for two-node system
if (layout == 1) && 1
Ys1 = Gc{1}((end-1):end,(end-1):end);
Ys2 = Gc{2}((end-1):end,(end-1):end);
Ys1 = Ys1 + eye(2)*Line(2,6);
Ys1 = Ys1 + [(1j + 1/w0*s) 0;0 (-1j + 1/w0*s)]*Line(2,5);
Ys2 = Ys2 + [(1j + 1/w0*s) 0;0 (-1j + 1/w0*s)]*Line(3,5);
Zs1 = Ys1^(-1);
Zs1 = Zs1 + [(1j + 1/w0*s) 0;0 (-1j + 1/w0*s)]*Line(1,4);
Ys1 = Zs1^(-1);
Y = Ys1 + Ys2;
Z = Y^(-1);
pc = vpasolve(1/Z(1,1))/2/pi;
end
if 1 % pole plots
psys = pole(Gsys)/2/pi;
figure(layout);
scatter(real(psys),imag(psys),'x','LineWidth',1.5);
hold on; grid on;
if (layout == 1) && 1
scatter(real(pc),imag(pc),'o','LineWidth',1.5);
end
xlabel('Real Part (Hz)');
ylabel('Imaginary Part (Hz)');
axis([-25,5,-80,80]);
end
if 1 % torque coefficient bode plots
for n = 1:length(type)
%Gtw{n} = -tf2sym(tf(Gsys(2*n-1,2*n-1))); %#ok<SAGROW>
Gtw{n} = -ss2sym(Gsys(2*n-1,2*n-1)); %#ok<SAGROW>
if type{n} < 10
Htw{n} = 1/(para{n}.J*s); %#ok<SAGROW>
elseif type{n} < 20
Htw{n} = 1/(1+para{n}.tau_pll*s)*(para{n}.kp_pll + para{n}.ki_pll/s); %#ok<SAGROW>
end
Kwt{n} = vpa(Gtw{n}^(-1) - Htw{n}^(-1)); %#ok<SAGROW>
Gtt{n} = Kwt{n}* vpa(Htw{n}); %#ok<SAGROW>
end
disp(['### test' num2str(cpoint) ': bandwidth=' num2str(bandwidth) ' ###']);
for nplot = 1:length(type)
figure(layout+10*nplot);
if layout <= 3
%isstable is very slow for layout >= 4, unsolved !!!
if ~isstable(Kwt{nplot})
disp(['K' num2str(nplot) ' is not stable']);
end
end
bodec(Gtt{nplot}*1j,1j*w,2*pi,'Color',cmap(mod(cpoint-1,length(cmap))+1,:));
hold on;
grid on;
end
end
if 1 %impedance bode plots
Tj = [1 1j;1 -1j]; % real to complex
for n = 1:length(type)
Ytr{n}(1,1) = ss2sym(Gsys(length(type)*2 +2*n-1 ,length(type)*2 +2*n-1)); %#ok<SAGROW>
Ytr{n}(1,2) = ss2sym(Gsys(length(type)*2 +2*n-1 ,length(type)*2 +2*n )); %#ok<SAGROW>
Ytr{n}(2,1) = ss2sym(Gsys(length(type)*2 +2*n ,length(type)*2 +2*n-1)); %#ok<SAGROW>
Ytr{n}(2,2) = ss2sym(Gsys(length(type)*2 +2*n ,length(type)*2 +2*n )); %#ok<SAGROW>
Ytc{n} = Tj*Ytr{n}*Tj^(-1); %#ok<SAGROW>
end
for nplot = 1:length(type)
figure(layout+100);
bodec(Ytc{nplot}(1,1),1j*wd,2*pi,'PhaseOn',0);
hold on;
grid on;
end
end
cpoint = cpoint+1;
end
if layout == 4
fig = figure(layout+100);
axis([1e0,1e3,1e-2,1e3]);
fig.Position = [185 148 720 310];
lgd = legend('Generator1','Generator2','Generator3','WindFarm1','WindFarm2');
lgd.FontSize = 10;
print(gcf,'Y.png','-dpng','-r600');
elseif layout == 1
fig = figure(layout+10);
fig.Position = [195 -28 560 590];
fig.Children(1).FontSize = 8;
fig.Children(2).FontSize = 8;
print(gcf,'K.png','-dpng','-r600');
end