Matrix converter demonstration

This is a demo of a dynamical model of the Matrix Converter presented in the reference below. A matrix converter converts n phases to m phases without a DC link. This simplifies the converter design.

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See also delta, ABC2SRF, MC33Switching, SRF2ABC
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Contents

Reference

Nikkhajoei et al "Dynamic Model of a Matrix Converter for Controller Design and System Studies", IEEE Transactions on Power Delivery, vol. 21, no. 2, April 2006, pp 744-754.

%--------------------------------------------------------------------------
%   Copyright (c) 2008 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------

Simulation parameters

%----------------------
d      = struct;
d.delT = 1e-4;
simlen = 2000;

Plotting arrays

%----------------
tP     = zeros(1,simlen+1);
xP     = zeros(6,simlen+1);
vabcsP = zeros(3,simlen+1);
vabciP = zeros(3,simlen+1);
vabcNP = zeros(3,simlen+1);
iabcsP = zeros(3,simlen+1);
iabcnP = zeros(3,simlen+1);
SwP    = zeros(3,simlen+1);

Circuit parameters

%-------------------
d.Rn = 0.0167;
d.Ln = 0.0628;
d.Rs = 0.0095;
d.Ls = 0.927;
d.CI = 0.755;

Define Grid/reference voltage

%------------------------------
vNMag   = 1;
omegaeN = 60*2*pi;
delta   = 0;
d.vref  = [vNMag;omegaeN;delta];

t       = 0;

Define generator frequency

%---------------------------
d.omegaGE = 600;

Initial Switching matrix

%-------------------------
d.S = [0 1 0;1 0 0;0 0 1];

Compute initial conditions

%----------------------------
iabcs        = [sin(d.omegaGE*t);sin(d.omegaGE*t+2*pi/3);sin(d.omegaGE*t+4*pi/3)]; % from generator
iabcsdot     = d.omegaGE*[cos(d.omegaGE*t);cos(d.omegaGE*t+2*pi/3);cos(d.omegaGE*t+4*pi/3)]; % from generator
isalbegas    = ABC2SRF(iabcs,d.S);
isalbegasdot = ABC2SRF(iabcsdot,d.S);

vsalbegas    = [0;sqrt(3)/2;-sqrt(3)/2];
vabcs        = SRF2ABC(vsalbegas,d.S);
d.vsalbega   = [0;0;0];

isalbegai    = [0;sqrt(3)/2;-sqrt(3)/2];
isalbegaidot = inv(d.S)*isalbegasdot; % only for initializing. In general the equlaity does not hold
isalbegaC    = isalbegas - isalbegai;

iabcn = isalbegai; % The output of MC to the grid
vabcN = [d.vref(1)*sin(d.vref(2)*t);d.vref(1)*sin(d.vref(2)*t+2*pi/3);d.vref(1)*sin(d.vref(2)*t+4*pi/3)];

vsalbegai = vsalbegas - d.Rs*isalbegas - d.Ls*d.S*iabcsdot;

x = [isalbegai;vsalbegai-d.vsalbega];
vabci = SRF2ABC(vsalbegai,d.S);

xP(:,1) = x;
vabcsP(:,1) = vabcs;
vabciP(:,1) = vabci;
iabcsP(:,1) = iabcs;
iabcnP(:,1) = iabcn;
vabcNP(:,1) = vabcN;
SwP(:,1) = d.S(1,:)';

h = waitbar(0,'Running Matrix Converter Demo...');

Simulation loop

%----------------
for i = 1:simlen
    waitbar(i/simlen)

    % Control Computation
    %--------------------
    Sm = d.S;
    d.Sm = Sm;
    d.S = MC33Switching(vabci,d.vref,t); % Switching Control
    Sp = d.S;
    d.Sp = Sp;
    d.ts = t;
    d.vsalbega = (Sp*inv(Sm)-eye(3))*vsalbegai;
    [ts,x] = ode45('MCDynamics',[t t+d.delT],x,[],d);
    t = ts(length(ts));
    x = x(length(ts),:)';
    tP(:,i+1) = t;
    xP(:,i+1) = x;
    vsalbegai = x(4:6) + d.vsalbega;
    vabci = SRF2ABC(vsalbegai,d.S);
    vabciP(:,i+1) = vabci;
    iabcs = [sin(d.omegaGE*t);sin(d.omegaGE*t+2*pi/3);sin(d.omegaGE*t+4*pi/3)];
    isalbegas = ABC2SRF(iabcs,d.S);
    isalbegai = x(1:3);
    isalbegaC = isalbegas - isalbegai;
    iabcsdot = d.omegaGE*[cos(d.omegaGE*t);cos(d.omegaGE*t+2*pi/3);cos(d.omegaGE*t+4*pi/3)];
    vsalbegas = vsalbegai + d.Rs*isalbegas + d.Ls*d.S*iabcsdot;
    vabcsP(:,i+1) = SRF2ABC(vsalbegas,d.S);
    iabcsP(:,i+1) = iabcs;
    iabcn = x(1:3);
    iabcnP(:,i+1) = iabcn;
    vabcN = [d.vref(1)*sin(d.vref(2)*t);d.vref(1)*sin(d.vref(2)*t+2*pi/3);d.vref(1)*sin(d.vref(2)*t+4*pi/3)];
    vabcNP(:,i+1) = vabcN;
    SwP(:,i+1) = d.S(1,:)';
end
close(h)

Plot results

Plot

%------
NewFig('MatConDemo')
plot(tP,vabcNP)
title('Grid voltage in ABC coordinates')

NewFig('MatConDemo')
subplot(2,1,1)
plot(tP,iabcsP)
title('Generator side currents in ABC frame')
grid on
subplot(2,1,2)
plot(tP,iabcnP)
title('Grid side currents in ABC frame')
grid on

NewFig('MatConDemo')
subplot(3,1,1),plot(tP,SwP(1,:))
title('Switching history')
subplot(3,1,2),plot(tP,SwP(2,:))
subplot(3,1,3),plot(tP,SwP(3,:))

NewFig('MatConDemo')
plot(tP,vabcsP),title('Source voltage in ABC coordinates')

NewFig('MatConDemo')
subplot(2,1,1)
plot(tP(2:simlen+1),iabcsP(:,2:simlen+1));
title('Generator side currents in ABC frame')
grid on
subplot(2,1,2)
plot(tP(2:simlen+1),iabcnP(:,2:simlen+1));
title('Grid side currents in ABC frame')
grid on


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Published with MATLAB® R2020a