public static void Jacobian(List <int> BusNO, List <int> BusType, List <double> VolAng, List <double> VolMag, List <double> Pi, List <double> Qi, double[,] Gbus, double[,] Bbus, out double[,] Jacobian, out List <double> dPQ)
{
// return the Jacobian matrix from Gbus and Bbus matrix.
// find the bus type index.
List <int> PQ, PV, PVPQ, slack;
FindBusType(BusNO, BusType, out PQ, out PV, out PVPQ, out slack);
// initialize.
Jacobian = new double[PVPQ.Count + PQ.Count, PVPQ.Count + PQ.Count];
List <double> dP = new List <double>();
List <double> dQ = new List <double>();
dPQ = new List <double>();
double[,] J11 = new double[PVPQ.Count, PVPQ.Count];
double[,] J12 = new double[PVPQ.Count, PQ.Count];
double[,] J21 = new double[PQ.Count, PVPQ.Count];
double[,] J22 = new double[PQ.Count, PQ.Count];
// deltaP & Jacobian J11 i/i
foreach (int i in PVPQ)
{
double sigema = 0.0, sigemaJ = 0.0;
for (int j = 0; j < BusNO.Count; ++j)
{
sigema = sigema + VolMag[j] * (Gbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])) + Bbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])));
sigemaJ = sigemaJ + VolMag[j] * (Gbus[i, j] * ((-1) * Math.Sin(VolAng[i] - VolAng[j])) + Bbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])));
}
dP.Add(Pi[i] - VolMag[i] * sigema);
dPQ.Add(Pi[i] - VolMag[i] * sigema);
J11[i - 1, i - 1] = VolMag[i] * sigemaJ - VolMag[i] * VolMag[i] * Bbus[i, i];
Jacobian[i - 1, i - 1] = J11[i - 1, i - 1];
}
// Jacobian J11 i/j
foreach (int i in PVPQ)
{
foreach (int j in PVPQ)
{
if (i != j)
{
int indexi = PVPQ.FindIndex(x => x == i);
int indexj = PVPQ.FindIndex(x => x == j);
J11[indexi, indexj] = VolMag[i] * VolMag[j] * (Gbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])) - Bbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])));
Jacobian[indexi, indexj] = J11[indexi, indexj];
}
}
}
// Jacobian J12 i/i & J21 i/i
foreach (int i in PQ)
{
double sigemaJ = 0.0;
for (int j = 0; j < BusNO.Count; ++j)
{
sigemaJ = sigemaJ + VolMag[j] * (Gbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])) + Bbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])));
}
int indexi = PVPQ.FindIndex(x => x == i);
int indexj = PQ.FindIndex(x => x == i);
J12[indexi, indexj] = sigemaJ + VolMag[i] * Gbus[i, i];
J21[indexj, indexi] = VolMag[i] * sigemaJ - (VolMag[i] * VolMag[i]) * Gbus[i, i];
Jacobian[indexi, indexj + PVPQ.Count] = J12[indexi, indexj];
Jacobian[indexj + PVPQ.Count, indexi] = J21[indexj, indexi];
}
// Jacobian J12 i/j
foreach (int i in PVPQ)
{
foreach (int j in PQ)
{
if (i != j)
{
int indexi = PVPQ.FindIndex(x => x == i);
int indexj = PQ.FindIndex(x => x == j);
J12[indexi, indexj] = VolMag[i] * (Gbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])) + Bbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])));
Jacobian[indexi, indexj + PVPQ.Count] = J12[indexi, indexj];
}
}
}
// Jacobian J21 i/j
foreach (int i in PQ)
{
foreach (int j in PVPQ)
{
if (i != j)
{
int indexi = PQ.FindIndex(x => x == i);
int indexj = PVPQ.FindIndex(x => x == j);
J21[indexi, indexj] = VolMag[i] * VolMag[j] * (-Gbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])) - Bbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])));
Jacobian[indexi + PVPQ.Count, indexj] = J21[indexi, indexj];
}
}
}
// deltaQ & Jacobian J22 i/i
foreach (int i in PQ)
{
double sigema = 0.0;
for (int j = 0; j < BusNO.Count; ++j)
{
sigema = sigema + VolMag[j] * (Gbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])) - Bbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])));
}
dQ.Add(Qi[i] - VolMag[i] * sigema);
dPQ.Add(Qi[i] - VolMag[i] * sigema);
int indexi = PQ.FindIndex(x => x == i);
J22[indexi, indexi] = sigema - VolMag[i] * Bbus[i, i];
Jacobian[indexi + PVPQ.Count, indexi + PVPQ.Count] = J22[indexi, indexi];
}
// Jacobian J22 i/j
foreach (int i in PQ)
{
foreach (int j in PQ)
{
if (i != j)
{
int indexi = PQ.FindIndex(x => x == i);
int indexj = PQ.FindIndex(x => x == j);
J22[indexi, indexj] = VolMag[i] * (Gbus[i, j] * (Math.Sin(VolAng[i] - VolAng[j])) - Bbus[i, j] * (Math.Cos(VolAng[i] - VolAng[j])));
Jacobian[indexi + PVPQ.Count, indexj + PVPQ.Count] = J22[indexi, indexj];
}
}
}
}
private void NewtonRaphson_Click(object sender, EventArgs e)
{
// start Newton-Raphson power flow calculation when user clicks the button.
try
{
#region Useful infomation from bus and branch
List <int> BusNO = bus[0].ToList().Select(int.Parse).ToList();
List <int> BusType = bus[6].ToList().Select(int.Parse).ToList();
List <double> VolMag = bus[7].ToList().Select(double.Parse).ToList();
List <double> VolAng = bus[8].ToList().Select(double.Parse).ToList();
List <double> LoadMW = bus[9].ToList().Select(double.Parse).ToList();
List <double> LoadMVAR = bus[10].ToList().Select(double.Parse).ToList();
List <double> GenMW = bus[11].ToList().Select(double.Parse).ToList();
List <double> GenMVAR = bus[12].ToList().Select(double.Parse).ToList();
List <double> busG = bus[17].ToList().Select(double.Parse).ToList();
List <double> busB = bus[18].ToList().Select(double.Parse).ToList();
List <int> fromBus = branch[0].ToList().Select(int.Parse).ToList();
List <int> toBus = branch[1].ToList().Select(int.Parse).ToList();
List <double> LineR = branch[6].ToList().Select(double.Parse).ToList();
List <double> LineX = branch[7].ToList().Select(double.Parse).ToList();
List <double> LineB = branch[8].ToList().Select(double.Parse).ToList();
#endregion
// generate the Gbus and Bbus matrix.
double[,] Gbus, Bbus;
CommonFunctions.Ybus(bus, branch, out Gbus, out Bbus);
// find the PQ, PV, PVPQ, slack bus index.
List <int> PQ, PV, PVPQ, slack;
CommonFunctions.FindBusType(BusNO, BusType, out PQ, out PV, out PVPQ, out slack);
// initialize Pi, Qi, VolMag, VolAng according to bus type.
List <double> Pi = new List <double>();
List <double> Qi = new List <double>();
for (int i = 0; i < BusNO.Count; ++i)
{
if (BusType[i] == 3)
{
// slack bus, set GenMW = 0, GenMVAR = 0;
GenMW[i] = 0;
GenMVAR[i] = 0;
}
if (BusType[i] == 2)
{
// PV bus, set GenMVAR = 0, VolAng = 0;
GenMVAR[i] = 0;
VolAng[i] = 0;
}
if (BusType[i] == 1 || BusType[i] == 0)
{
// PQ bus, set VolMag = 1, VolAng = 0;
VolMag[i] = 1;
VolAng[i] = 0;
}
// Pinjection = Pgen - Pload, must convert to p.u.!
Pi.Add((GenMW[i] - LoadMW[i]) / 100);
Qi.Add((GenMVAR[i] - LoadMVAR[i]) / 100);
}
// initialize the iteration count and error.
int iter = 0;
double error = 1.0;
// Newton Raphson iteration.
while (error > stoppingError)
{
// generate Jacobian matrix and mismatch deltaP and deltaQ.
double[,] Jacobian;
List <double> dPQ;
CommonFunctions.Jacobian(BusNO, BusType, VolAng, VolMag, Pi, Qi, Gbus, Bbus, out Jacobian, out dPQ);
// compute [dVol] by inverse of Jacobian multiply [dPQ].
List <double> dVol;
CommonFunctions.LUFact(Jacobian, dPQ, out dVol);
// update the VolAng and VolMag,
// start another iteration until stopping error is satisfied.
foreach (int i in PVPQ)
{
int index = PVPQ.FindIndex(x => x == i);
VolAng[i] = VolAng[i] + dVol[index];
}
foreach (int i in PQ)
{
int index = PQ.FindIndex(x => x == i) + PVPQ.Count;
VolMag[i] = VolMag[i] + dVol[index];
}
iter++;
// update the error.
CommonFunctions.FindMaxAbs(dPQ, out error);
}
// display the power flow results.
UpdateResults(VolAng, VolMag, iter);
// results save to a txt file.
SaveResults(VolAng, VolMag);
}
catch (Exception ex)
{
MessageBox.Show("Please check data format! " + ex.Message);
}
}