/* Propagate the accuracy of the voltage measurements*/
public MathNetNumLin.Matrix <Complex> KVPropagation(List <int> inaccurate_line_set, int Accurate_line_num, int to_bus_number_int, Complex KV_accurate)
{
// Colloect accurate line V data
GetLineVI(Accurate_line_num.ToString(), to_bus_number_int);
Complex initial = 0;
DenseMatrix accurate_line_V = DenseMatrix.Create(m_V1.Count(), 1, initial);
//Matrix<Complex> accurate_line_V = null;
for (int idx2 = 0; idx2 < m_V1.Count(); idx2++)
{
accurate_line_V[idx2, 0] = m_V1[idx2] * KV_accurate;
}
// Colloect inaccurate lines V data
int inaccurate_line_num = 0;
for (int idx7 = 0; idx7 < inaccurate_line_set.Count(); idx7++)
{
if (inaccurate_line_set[idx7] == 0)
{
inaccurate_line_num = idx7;
break;
}
}
DenseMatrix inaccurate_line_V = DenseMatrix.Create(m_V1.Count(), inaccurate_line_num, initial);
//Matrix<Complex> inaccurate_line_V = null;
for (int idx3 = 0; idx3 < inaccurate_line_num; idx3++)
{
GetLineVI(inaccurate_line_set[idx3].ToString(), to_bus_number_int);
for (int idx4 = 0; idx4 < m_V1.Count(); idx4++)
{
inaccurate_line_V[idx4, idx3] = m_V1[idx4];
}
}
// Propagate voltage accuracy
MathNetNumLin.Matrix <Complex> KV_injection_set = MathNetNumLin.Matrix <Complex> .Build.Random(inaccurate_line_num, 1);
for (int idx5 = 0; idx5 < inaccurate_line_num; idx5++)
{
Complex[] temp_KV = new Complex[inaccurate_line_V.RowCount];
Complex temp_KV_sum = 0;
for (int idx6 = 0; idx6 < inaccurate_line_V.RowCount; idx6++)
{
temp_KV[idx6] = accurate_line_V[idx6, 0] / inaccurate_line_V[idx6, idx5];
temp_KV_sum = temp_KV_sum + temp_KV[idx6];
}
KV_injection_set[idx5, 0] = temp_KV_sum / inaccurate_line_V.RowCount;
}
return(KV_injection_set);
}
public MathNetNumLin.Matrix <Complex> LeastSquareEstimation(MathNetNumLin.Matrix <Complex> Y, MathNetNumLin.Matrix <Complex> X)
{
MathNetNumLin.Matrix <Complex> Beta;
MathNetNumLin.Matrix <Complex> A = X.ConjugateTranspose() * X;
MathNetNumLin.Matrix <Complex> B = A.Inverse();
Beta = (X.ConjugateTranspose() * X).Inverse() * X.ConjugateTranspose() * Y; // For complex LSE problems, note that there should be conjugate transpose
MathNetNumLin.Matrix <Complex> Error;
Error = Y - X.Multiply(Beta);
return(Beta);
}
/* Propagate the accuracy of the current measurements*/
public MathNetNumLin.Matrix <Complex> KIPropagation(List <int> inaccurate_line_set, int Accurate_line_num, int to_bus_number_int, Complex KI_accurate)
{
// Collect accurate line I data
GetLineVI(Accurate_line_num.ToString(), to_bus_number_int);
Complex initial = 0;
DenseMatrix accurate_line_I = DenseMatrix.Create(m_I1.Count(), 1, initial);
for (int idx2 = 0; idx2 < m_I1.Count(); idx2++)
{
accurate_line_I[idx2, 0] = m_I1[idx2] * KI_accurate;
}
// Collect inaccurate lines I data
int inaccurate_line_num = 0;
for (int idx7 = 0; idx7 < m_I1.Count(); idx7++)
{
if (inaccurate_line_set[idx7] == 0)
{
inaccurate_line_num = idx7;
break;
}
}
DenseMatrix inaccurate_line_I = DenseMatrix.Create(m_I1.Count(), inaccurate_line_num, initial);
for (int idx3 = 0; idx3 < inaccurate_line_num; idx3++)
{
GetLineVI(inaccurate_line_set[idx3].ToString(), to_bus_number_int);
for (int idx4 = 0; idx4 < m_V1.Count(); idx4++)
{
inaccurate_line_I[idx4, idx3] = m_I1[idx4];
}
}
// Propagate current accuracy
MathNetNumLin.Matrix <Complex> KI_injection_set = MathNetNumLin.Matrix <Complex> .Build.Random(inaccurate_line_num, 1);
MathNetNumLin.Matrix <Complex> accurate_line_I_matrix = accurate_line_I;
MathNetNumLin.Matrix <Complex> inaccurate_line_I_matrix = inaccurate_line_I;
MathNetNumLin.Matrix <Complex> I_right_side = accurate_line_I_matrix * (-1);
MathNetNumLin.Matrix <Complex> I_left_side = inaccurate_line_I_matrix;
KI_injection_set = LeastSquareEstimationInequalityConstrained(I_right_side, I_left_side);
return(KI_injection_set);
}
public LeastSquaresSolver(int Row_number, int Column_number)
{
m_A = MathNetNumLin.Matrix <double> .Build.Dense(Row_number, Column_number);
m_xInitial = MathNetNumLin.Vector <double> .Build.Dense(Column_number, 1);
m_xLowerBound = MathNetNumLin.Vector <double> .Build.Dense(Column_number, 1);
m_xUpperBound = MathNetNumLin.Vector <double> .Build.Dense(Column_number, 1);
m_b = MathNetNumLin.Vector <double> .Build.Dense(Row_number, 1);
m_results = MathNetNumLin.Vector <double> .Build.Dense(Column_number, 1);
RowNumber = m_A.RowCount;
ColumnNumber = m_A.ColumnCount;
}
/* Conduct PI section Impedance calibration of single line*/
public int SingleLineImpedanceEstimation(string LineID, int FromBusNumber, Complex KV1, Complex KI1, TextBox textBoxMessages) //ALso need Complex KV1, Complex[,] Z
{
int CurrentToBus = 0;
CurrentToBus = GetLineVI(LineID, FromBusNumber);
//if (LineID == "2")
//{ int a = 1; }
Complex KV2 = new Complex();
Complex KI2 = new Complex();
Complex Z = new Complex();
Complex y = new Complex();
//Find the sample sets 30 samples per second, 60 seconds in all => 30 sets of samples, 60 samples per set, rule out -9999
int i = 0; //set number
int feasible_flag = 0; //estimation feasible indicator, shows missing data quantity, if too large then the estimation is not feasible
Complex[] Zhat11 = new Complex[30];
Complex[] Zhat12 = new Complex[30];
Complex[] Zhat21 = new Complex[30];
Complex[] Zhat22 = new Complex[30];
int SecondsNumber = (int)Math.Floor((double)(m_V1.Count() / 30));
while (i < 30)
{
//get samples
Complex[,] V_sample_temp = new Complex[SecondsNumber, 2];
Complex[,] I_sample_temp = new Complex[SecondsNumber, 2];
int current_row = 0;
for (int j = 0; j < SecondsNumber; j++)
{
current_row = j * 30 + i;
if ((m_V1[current_row] != -9999) && (m_I1[current_row] != -9999) && (m_V2[current_row] != -9999) && (m_I2[current_row] != -9999))
{
V_sample_temp[j, 0] = m_V1[current_row];
I_sample_temp[j, 0] = m_I1[current_row];
V_sample_temp[j, 1] = m_V2[current_row];
I_sample_temp[j, 1] = m_I2[current_row];
}
else
{
V_sample_temp[j, 0] = -9999;
I_sample_temp[j, 0] = -9999;
V_sample_temp[j, 1] = -9999;
I_sample_temp[j, 1] = -9999;
}
}
//transfer into matrix mode
Complex initial = 0;
DenseMatrix Vhat = DenseMatrix.Create(2, 1, initial);
DenseMatrix Ihat = DenseMatrix.Create(2, 1, initial);
for (int k = 0; k < SecondsNumber; k++)
{
if ((V_sample_temp[k, 0] != -9999) && (V_sample_temp[k, 0] != null))
{
Complex[,] V_temp_array = new Complex[2, 1];
V_temp_array[0, 0] = V_sample_temp[k, 0];
V_temp_array[1, 0] = V_sample_temp[k, 1];
DenseMatrix V_temp = DenseMatrix.OfArray(V_temp_array);
if ((Vhat != null) && (V_temp != null))
{
if (Vhat[0, 0] == 0)
{
Vhat = V_temp;
}
else
{
Vhat = MatrixCalculationExtensions.HorizontallyConcatenate(Vhat, V_temp);
}
}
Complex[,] I_temp_array = new Complex[2, 1];
I_temp_array[0, 0] = I_sample_temp[k, 0];
I_temp_array[1, 0] = I_sample_temp[k, 1];
DenseMatrix I_temp = DenseMatrix.OfArray(I_temp_array);
if ((Ihat != null) && (I_temp != null))
{
if (Ihat[0, 0] == 0)
{
Ihat = I_temp;
}
else
{
Ihat = MatrixCalculationExtensions.HorizontallyConcatenate(Ihat, I_temp);
}
}
}
}
//check sample quantity, enough to do estimation or not
if (Vhat.ColumnCount < 20)
{
feasible_flag += 1;
i += 1;
continue;
}
else
{
MathNetNumLin.Matrix <Complex> Vhat_T = Vhat.Transpose();
MathNetNumLin.Matrix <Complex> Ihat_T = Ihat.Transpose();
//estimate Zhat
MathNetNumLin.Matrix <Complex> Zhat_temp = null;
Zhat_temp = LeastSquareEstimation(Vhat_T, Ihat_T);// Ihat_T.Transpose().Multiply(Ihat_T).Inverse().Multiply(Ihat_T.Transpose()).Multiply(Vhat_T);
Zhat11[i] = Zhat_temp[0, 0];
Zhat12[i] = Zhat_temp[0, 1];
Zhat21[i] = Zhat_temp[1, 0];
Zhat22[i] = Zhat_temp[1, 1];
//Zhat12[i] = Zhat_temp[1, 0];
//Zhat21[i] = Zhat_temp[0, 1];
}
i += 1;
}
// Take average of Zhat to eliminate PMU error, if there is enough estimation results
Complex from_bus_number = FromBusNumber;
Complex to_bus_number = CurrentToBus;
int from_bus_number_int = FromBusNumber;
int to_bus_number_int = CurrentToBus;
double BaseZ = m_currentSystem.Network.BaseKV * m_currentSystem.Network.BaseKV / m_currentSystem.Network.BaseMVA;
if (feasible_flag < 15)
{
Complex W = new Complex();
Complex[] KV2_hat = new Complex[30];
Complex[] KI2_hat = new Complex[30];
Complex[] Z_hat_pu = new Complex[30];
Complex[] y_hat_pu = new Complex[30];
Complex KV2_hat_sum = new Complex();
Complex KI2_hat_sum = new Complex();
Complex Z_hat_pu_sum = new Complex();
Complex y_hat_pu_sum = new Complex();
for (int l = 0; l < 30; l++)
{
if ((Zhat11[l] != null) || (Zhat12[l] != null) || (Zhat21[l] != null) || (Zhat22[l] != null))
{
Complex Zhat11_temp = Zhat11[l];
Complex Zhat12_temp = Zhat12[l];
Complex Zhat21_temp = Zhat21[l];
Complex Zhat22_temp = Zhat22[l];
W = (Zhat11_temp * Zhat22_temp) / (Zhat12_temp * Zhat21_temp);
W = Complex.Sqrt(W);
if (W.Imaginary < 0)
{
W = -1 * W;
}
KV2_hat[l] = 1 / W * Zhat11_temp / Zhat12_temp * KV1;
KI2_hat[l] = W * Zhat21_temp / Zhat11_temp * KI1;
if (KV2_hat[l].Real < 0)
{
KV2_hat[l] = KV2_hat[l] * (-1);
}
if (KI2_hat[l].Real < 0)
{
KI2_hat[l] = KI2_hat[l] * (-1);
}
y_hat_pu[l] = BaseZ * Complex.Sqrt((KI2_hat[l] * (W - 1)) / (KV2_hat[l] * (W + 1) * (Zhat11_temp * Zhat22_temp - Zhat12_temp * Zhat21_temp)) * KI1 / KV1);
//y_hat_pu[l] = Complex.Sqrt((KI2_hat[l] * (W - 1)) / (KV2_hat[l] * (W + 1) * (Zhat11_temp * Zhat22_temp - Zhat12_temp * Zhat21_temp)) * KI1 / KV1);
if (y_hat_pu[l].Imaginary < 0)
{
y_hat_pu[l] = Complex.Conjugate(y_hat_pu[l]);
}
Z_hat_pu[l] = (W - 1) / y_hat_pu[l];
if (Z_hat_pu[l].Real < 0)
{
Z_hat_pu[l] = Complex.Conjugate(-1 * Z_hat_pu[l]);
}
if (Z_hat_pu[l].Imaginary < 0)
{
Z_hat_pu[l] = Complex.Conjugate(Z_hat_pu[l]);
}
}
KV2_hat_sum = KV2_hat_sum + KV2_hat[l];
KI2_hat_sum = KI2_hat_sum + KI2_hat[l];
Z_hat_pu_sum = Z_hat_pu_sum + Z_hat_pu[l];
y_hat_pu_sum = y_hat_pu_sum + y_hat_pu[l];
}
KV2 = KV2_hat_sum / (30 - feasible_flag);
KI2 = KI2_hat_sum / (30 - feasible_flag);
Z = Z_hat_pu_sum / (30 - feasible_flag); // * BaseZ;
y = y_hat_pu_sum / (30 - feasible_flag); // / BaseZ;
//adding the computation results to K matrix and record KVs for both from_bus and to_bus for future calibrations
int m = 0;
while (m_K[m, 0] != 0)
{
m += 1;
}
int Line_ID_int = Convert.ToInt32(LineID);
m_K[m, 0] = Line_ID_int;
m_K[m, 1] = from_bus_number;
m_K[m, 2] = KV1;
m_K[m, 3] = KI1;
m_K[m, 4] = to_bus_number;
m_K[m, 5] = KV2;
m_K[m, 6] = KI2;
m_K[m, 7] = Z;
m_K[m, 8] = y.Imaginary;
//update the propagation references
int[] injections_set = FindInjections(to_bus_number_int);
List <int> inaccurate_line_set = new List <int>(); //List to save all inaccurate lines
for (int idx1 = 0; idx1 < injections_set.Count(); idx1++)
{
if (injections_set[idx1] != Line_ID_int)
{
inaccurate_line_set.Add(injections_set[idx1]);
}
}
//Accurate Voltage Propagation
MathNetNumLin.Matrix <Complex> KV_injections_set = KVPropagation(inaccurate_line_set, Line_ID_int, to_bus_number_int, KV2);
//Accurate Current Propagation
MathNetNumLin.Matrix <Complex> KI_injections_set = KIPropagation(inaccurate_line_set, Line_ID_int, to_bus_number_int, KI2);
int pointer = 0;
for (int idx1 = 0; idx1 < m_currentSystem.Network.LineNum; idx1++)
{
if (m_KVKILines[idx1].Line_ID == 0)
{
pointer = idx1;
break;
}
}
for (int idx2 = 0; idx2 < KV_injections_set.RowCount; idx2++)
{
if ((pointer + idx2) < m_currentSystem.Network.LineNum)
{
m_KVKILines[pointer + idx2].Line_ID = inaccurate_line_set[idx2];
m_KVKILines[pointer + idx2].From_bus_num = to_bus_number_int;
m_KVKILines[pointer + idx2].KV1 = KV_injections_set[idx2, 0];
m_KVKILines[pointer + idx2].KI1 = KI_injections_set[idx2, 0];
}
}
//Set visited line to be 1
for (int n = 0; n < m_currentSystem.Network.LineNum; n++)
{
if (Line_ID_int == m_lineVisited[n, 0])
{
m_lineVisited[n, 1] = 1;
break;
}
}
string msg0 = "### Line " + LineID.ToString() + " from bus " +
m_currentSystem.Network.BusOriginalLibrary[from_bus_number_int - 1].ToString() + " to bus " +
m_currentSystem.Network.BusOriginalLibrary[to_bus_number_int - 1].ToString() + " has been estimated.\n";
textBoxMessages.AppendLine(msg0);
}
else
{
string msg1 = "!!! Line " + LineID.ToString() + " from bus " +
m_currentSystem.Network.BusOriginalLibrary[from_bus_number_int - 1].ToString() + " to bus " +
m_currentSystem.Network.BusOriginalLibrary[to_bus_number_int - 1].ToString() + " can NOT be calibrated due to limited data.\n";
textBoxMessages.AppendLine(msg1);
}
return(0);
}
public MathNetNumLin.Matrix <Complex> LeastSquareEstimationInequalityConstrained(MathNetNumLin.Matrix <Complex> b, MathNetNumLin.Matrix <Complex> A)
{
int Row_number = A.RowCount;
int Column_number = A.ColumnCount;
MathNetNumLin.Matrix <double> A_realpart = MathNetNumLin.Matrix <double> .Build.Dense(Row_number, Column_number);
MathNetNumLin.Matrix <double> A_imagpart = MathNetNumLin.Matrix <double> .Build.Dense(Row_number, Column_number);
MathNetNumLin.Vector <double> b_realpart = MathNetNumLin.Vector <double> .Build.Dense(Row_number);
MathNetNumLin.Vector <double> b_imagpart = MathNetNumLin.Vector <double> .Build.Dense(Row_number);
for (int idx0 = 0; idx0 < Row_number; idx0++)
{
for (int idx1 = 0; idx1 < Column_number; idx1++)
{
A_realpart[idx0, idx1] = A[idx0, idx1].Real;
A_imagpart[idx0, idx1] = A[idx0, idx1].Imaginary;
}
b_realpart[idx0] = b[idx0, 0].Real;
b_imagpart[idx0] = b[idx0, 0].Imaginary;
}
MathNetNumLin.Vector <double> xInitial_realpart = MathNetNumLin.Vector <double> .Build.Dense(Column_number);
MathNetNumLin.Vector <double> xInitial_imagpart = MathNetNumLin.Vector <double> .Build.Dense(Column_number);
MathNetNumLin.Vector <double> xLowerBound_realpart = MathNetNumLin.Vector <double> .Build.Dense(Column_number);
MathNetNumLin.Vector <double> xLowerBound_imagpart = MathNetNumLin.Vector <double> .Build.Dense(Column_number);
MathNetNumLin.Vector <double> xUpperBound_realpart = MathNetNumLin.Vector <double> .Build.Dense(Column_number);
MathNetNumLin.Vector <double> xUpperBound_imagpart = MathNetNumLin.Vector <double> .Build.Dense(Column_number);
for (int idx2 = 0; idx2 < Column_number; idx2++)
{
xInitial_realpart[idx2] = 1;
xInitial_imagpart[idx2] = 0;
xLowerBound_realpart[idx2] = 0.9452;
xLowerBound_imagpart[idx2] = -0.1005;
xUpperBound_realpart[idx2] = 1.0526;
xUpperBound_imagpart[idx2] = 0.1005;
}
MathNetNumLin.Matrix <Complex> Beta = MathNetNumLin.Matrix <Complex> .Build.Random(Column_number, 1);
MathNetNumLin.Vector <double> RealBeta = MathNetNumLin.Vector <double> .Build.Random(Column_number);
LeastSquaresSolver RealPartSolver = new LeastSquaresSolver(Row_number, Column_number);
RealPartSolver.A = A_realpart;
RealPartSolver.b = b_realpart;
RealPartSolver.xInitial = xInitial_realpart;
RealPartSolver.xLowerBound = xLowerBound_realpart;
RealPartSolver.xUpperBound = xUpperBound_realpart;
RealPartSolver.LeastSqauresInequalityConstrainedEstimation();
for (int idx3 = 0; idx3 < RealPartSolver.Results.Count; idx3++)
{
RealBeta[idx3] = RealPartSolver.Results[idx3];
}
LeastSquaresSolver ImagPartSolver = new LeastSquaresSolver(Row_number, Column_number);
ImagPartSolver.A = A_imagpart;
ImagPartSolver.b = b_imagpart;
ImagPartSolver.xInitial = xInitial_imagpart;
ImagPartSolver.xLowerBound = xLowerBound_imagpart;
ImagPartSolver.xUpperBound = xUpperBound_imagpart;
ImagPartSolver.LeastSqauresInequalityConstrainedEstimation();
for (int idx4 = 0; idx4 < RealPartSolver.Results.Count; idx4++)
{
Beta[idx4, 0] = new Complex(RealBeta[idx4], ImagPartSolver.Results[idx4]);
}
return(Beta);
}