Dear All,
I am working on Modal Analysis. I would like to show to my students, that in
the bifurcation point at least one of the reduced Jacobian eigenvalues is
zero. This is why I calculate these values once for the base case and then
for the nose point ( lambda max calculated by the CPF).
Unfortunately there is no change in the results. Could anyone help?
The results of the eigenvalues are as follows (for case14)
Eigb=
[
65,4207
39,9533
21,9939
18,9118
16,4492
11,3421
2,70658
5,56886
7,66373
]
And exactly the same ones in the nose points.
I would greatly appreciate any help from you as I got terribly stuck.
Best,
Mariusz Drabecki
Here is my code:
define_constants
mpc=loadcase(case14);
inc=2.5;
%% CPF options
mpopt = mpoption('out.all', 0, 'verbose', 2);
mpopt = mpoption(mpopt, 'cpf.stop_at', 'NOSE', 'cpf.step', 0.1);
mpopt = mpoption(mpopt, 'cpf.plot.level', 2);
%% Base case (base solution operating points)
%CPF
mpcb=mpc;
mpct = mpcb; % set up target case with
mpct.gen(:, [PG QG]) = mpcb.gen(:, [PG QG]) * inc; % increased generation
mpct.bus(:, [PD QD]) = mpcb.bus(:, [PD QD]) * inc; % and increased load
cpf1 = runcpf(mpcb, mpct, mpopt);
lambda_max=cpf1.cpf.max_lam;
%Modal Analysis for Base Case
[jb11,jb12,jb21,jb22,jacb,~,~,~] = makeJac(mpcb);
jb11=full(jb11);
jb12=full(jb12);
jb21=full(jb21);
jb22=full(jb22);
Hb=jb11;
Mb=jb12;
Nb=jb21;
Kb=jb22;
% The reduced Jacobian for the base case (Q-V sensitivities)
jacb_red=Kb-Nb*inv(Hb)*Mb;
% The eigenvalues of the reduced Jacobian (Q-V sensitivities)
[leftb eigb rightb]=(eig(jacb_red));
%% Target case (nose point)
mpct.gen(:, [PG QG]) = mpct.gen(:, [PG QG]) * lambda_max; % increased
generation
mpct.bus(:, [PD QD]) = mpct.bus(:, [PD QD])* lambda_max; % and increased
load
% The Jacobian for the target case
[jt11,jt12,jt21,jt22,jact,~,~,~] = makeJac(mpct);
jt11=full(jb11);
jt12=full(jb12);
jt21=full(jb21);
jt22=full(jb22);
njact=size(jact,1);
Ht=jt11;
Mt=jt12;
Nt=jt21;
Kt=jt22;
% The reduced Jacobian for the target case
jact_red=Kt-Nt*inv(Ht)*Mt;
% Eigenvalue decomposition of the reduced Jacobian for the target case
[leftt eigt rightt]=(eig(jact_red));
