// Calculate Vsh to match the tuned constant Q
private Complex solveConstQ(Complex vsh1, Complex vi, ConverterLF converter, double tunedValue) {
double qerr = 100.0;
Complex vsh = vsh1;
double vmsh = vsh.abs();
double thetash = Math.atan2(vsh.getImaginary(), vsh.getReal());
double vmi = vi.abs();
double thetai = Math.atan2(vi.getImaginary(), vi.getReal());
double gsh = converter.getYth().getReal();
double bsh = converter.getYth().getImaginary();
// Iteration by Newton method
while (qerr > 0.0001) {
// Active power balance equation Fp: active output of v source = 0
double fp =
vmsh * vmsh * gsh
- vmi * vmsh * (gsh * Math.cos(thetai - thetash) - bsh * Math.sin(thetai - thetash));
// Reactive power balance equation Fq: reactive injection at bus i = -Qsh ("-" means injecting
// other than absorbing)
double fq =
-tunedValue
+ vmi * vmi * bsh
+ vmi * vmsh * (gsh * Math.sin(thetai - thetash) - bsh * Math.cos(thetai - thetash));
// Update the mismatch
qerr = Math.max(Math.abs(fp), Math.abs(fq));
// Jacobian
double a =
2 * vmsh * gsh
- vmi
* (gsh * Math.cos(thetai - thetash)
- bsh * Math.sin(thetai - thetash)); // dFp/dVsh
double b =
-vmi
* vmsh
* (gsh * Math.sin(thetai - thetash)
+ bsh * Math.cos(thetai - thetash)); // dFp/dThetash
double c =
vmi * (gsh * Math.sin(thetai - thetash) - bsh * Math.cos(thetai - thetash)); // dFq/dVsh
double d =
-vmi
* vmsh
* (gsh * Math.cos(thetai - thetash)
+ bsh * Math.sin(thetai - thetash)); // dFq/dThetash
// Solve the mismatch equation
double det = a * d - b * c;
double dvmsh = (d * fp - b * fq) / det;
double dthetash = (-c * fp + a * fq) / det;
// Update Vsh and thetash
vmsh -= dvmsh;
thetash -= dthetash;
}
System.out.println("thetai=" + thetai + ", thetash=" + thetash);
return new Complex(vmsh * Math.cos(thetash), vmsh * Math.sin(thetash));
}
// Calculate Vsh to match the tuned constant B
private Complex solveConstB(Complex vsh1, Complex vi, ConverterLF converter, double tunedValue) {
double berr = 100.0;
Complex vsh = vsh1;
double vmsh = vsh.abs();
double thetash = Math.atan2(vsh.getImaginary(), vsh.getReal());
double vmi = vi.abs();
double thetai = Math.atan2(vi.getImaginary(), vi.getReal());
double gsh = converter.getYth().getReal();
double bsh = converter.getYth().getImaginary();
// Iteration by Newton method
while (berr > 0.00001) {
// Active power balance equation Fp: active output of v source = 0
double fp =
vmsh * vmsh * gsh
- vmi * vmsh * (gsh * Math.cos(thetai - thetash) - bsh * Math.sin(thetai - thetash));
// Shunt admittance equation Fb: shunt admittance at bus i = Vi / Ishunt
double fb =
vmsh * (gsh * Math.sin(thetash - thetai) + bsh * Math.cos(thetash - thetai))
+ vmi * (tunedValue - bsh);
// Update the mismatch
berr = Math.max(Math.abs(fp), Math.abs(fb));
// Jacobian
double a =
2 * vmsh * gsh
- vmi
* (gsh * Math.cos(thetai - thetash)
- bsh * Math.sin(thetai - thetash)); // dFp/dVsh
double b =
-vmi
* vmsh
* (gsh * Math.sin(thetai - thetash)
+ bsh * Math.cos(thetai - thetash)); // dFp/dThetash
double c = gsh * Math.sin(thetash - thetai) + bsh * Math.cos(thetash - thetai); // dFb/dVsh
double d =
vmsh
* (gsh * Math.cos(thetash - thetai)
- bsh * Math.sin(thetash - thetai)); // dFb/dThetash
// Solve the mismatch equation
double det = a * d - b * c;
double dvmsh = (d * fp - b * fb) / det;
double dthetash = (-c * fp + a * fb) / det;
// Update Vsh and thetash
vmsh -= dvmsh;
thetash -= dthetash;
}
return new Complex(vmsh * Math.cos(thetash), vmsh * Math.sin(thetash));
}