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AC equations simplification #559

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merged 2 commits into from
Jun 18, 2022
Merged

AC equations simplification #559

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0661144
AC equations optimization
geofjamg Jun 16, 2022
c682f72
Merge branch 'main' into ac_equations_optim
geofjamg Jun 18, 2022
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10 changes: 10 additions & 0 deletions ...in/java/com/powsybl/openloadflow/ac/equations/AbstractClosedBranchAcFlowEquationTerm.java
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Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,8 @@
import java.util.List;
import java.util.Objects;

import static com.powsybl.openloadflow.network.PiModel.A2;

/**
* @author Geoffroy Jamgotchian <geoffroy.jamgotchian at rte-france.com>
*/
Expand Down Expand Up @@ -83,6 +85,14 @@ protected double a1() {
return a1Var != null ? sv.get(a1Var.getRow()) : branch.getPiModel().getA1();
}

public static double theta1(double ksi, double ph1, double a1, double ph2) {
return ksi - a1 + A2 - ph1 + ph2;
}

public static double theta2(double ksi, double ph1, double a1, double ph2) {
return ksi + a1 - A2 + ph1 - ph2;
}

protected abstract double calculateSensi(double dph1, double dph2, double dv1, double dv2, double da1, double dr1);

@Override
Expand Down
62 changes: 29 additions & 33 deletions ...n/java/com/powsybl/openloadflow/ac/equations/ClosedBranchSide1ActiveFlowEquationTerm.java
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,6 @@

import java.util.Objects;

import static com.powsybl.openloadflow.network.PiModel.A2;
import static com.powsybl.openloadflow.network.PiModel.R2;

/**
Expand All @@ -30,69 +29,66 @@ public ClosedBranchSide1ActiveFlowEquationTerm(LfBranch branch, LfBus bus1, LfBu

protected double calculateSensi(double dph1, double dph2, double dv1, double dv2, double da1, double dr1) {
double v1 = v1();
double ph1 = ph1();
double r1 = r1();
double a1 = a1();
double v2 = v2();
double ph2 = ph2();
return dp1dph1(y, ksi, v1, ph1, r1, a1, v2, ph2) * dph1
+ dp1dph2(y, ksi, v1, ph1, r1, a1, v2, ph2) * dph2
+ dp1dv1(y, ksi, FastMath.sin(ksi), g1, v1, ph1, r1, a1, v2, ph2) * dv1
+ dp1dv2(y, ksi, v1, ph1, r1, a1, ph2) * dv2;
double theta = theta1(ksi, ph1(), a1(), ph2());
double cosTheta = FastMath.cos(theta);
double sinTheta = FastMath.sin(theta);
return dp1dph1(y, v1, r1, v2, cosTheta) * dph1
+ dp1dph2(y, v1, r1, v2, cosTheta) * dph2
+ dp1dv1(y, FastMath.sin(ksi), g1, v1, r1, v2, sinTheta) * dv1
+ dp1dv2(y, v1, r1, sinTheta) * dv2;
}

private static double theta(double ksi, double ph1, double a1, double ph2) {
return ksi - a1 + A2 - ph1 + ph2;
public static double p1(double y, double sinKsi, double g1, double v1, double r1, double v2, double sinTheta) {
return r1 * v1 * (g1 * r1 * v1 + y * r1 * v1 * sinKsi - y * R2 * v2 * sinTheta);
}

public static double p1(double y, double ksi, double sinKsi, double g1, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return r1 * v1 * (g1 * r1 * v1 + y * r1 * v1 * sinKsi - y * R2 * v2 * FastMath.sin(theta(ksi, ph1, a1, ph2)));
private static double dp1dv1(double y, double sinKsi, double g1, double v1, double r1, double v2, double sinTheta) {
return r1 * (2 * g1 * r1 * v1 + 2 * y * r1 * v1 * sinKsi - y * R2 * v2 * sinTheta);
}

private static double dp1dv1(double y, double ksi, double sinKsi, double g1, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return r1 * (2 * g1 * r1 * v1 + 2 * y * r1 * v1 * sinKsi - y * R2 * v2 * FastMath.sin(theta(ksi, ph1, a1, ph2)));
private static double dp1dv2(double y, double v1, double r1, double sinTheta) {
return -y * r1 * R2 * v1 * sinTheta;
}

private static double dp1dv2(double y, double ksi, double v1, double ph1, double r1, double a1, double ph2) {
return -y * r1 * R2 * v1 * FastMath.sin(theta(ksi, ph1, a1, ph2));
private static double dp1dph1(double y, double v1, double r1, double v2, double cosTheta) {
return y * r1 * R2 * v1 * v2 * cosTheta;
}

private static double dp1dph1(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return y * r1 * R2 * v1 * v2 * FastMath.cos(theta(ksi, ph1, a1, ph2));
private static double dp1dph2(double y, double v1, double r1, double v2, double cosTheta) {
return -dp1dph1(y, v1, r1, v2, cosTheta);
}

private static double dp1dph2(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return -dp1dph1(y, ksi, v1, ph1, r1, a1, v2, ph2);
private static double dp1da1(double y, double v1, double r1, double v2, double cosTheta) {
return dp1dph1(y, v1, r1, v2, cosTheta);
}

private static double dp1da1(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return dp1dph1(y, ksi, v1, ph1, r1, a1, v2, ph2);
}

private static double dp1dr1(double y, double ksi, double sinKsi, double g1, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return v1 * (2 * r1 * v1 * (g1 + y * sinKsi) - y * R2 * v2 * FastMath.sin(theta(ksi, ph1, a1, ph2)));
private static double dp1dr1(double y, double sinKsi, double g1, double v1, double r1, double v2, double sinTheta) {
return v1 * (2 * r1 * v1 * (g1 + y * sinKsi) - y * R2 * v2 * sinTheta);
}

@Override
public double eval() {
return p1(y, ksi, FastMath.sin(ksi), g1, v1(), ph1(), r1(), a1(), v2(), ph2());
return p1(y, FastMath.sin(ksi), g1, v1(), r1(), v2(), FastMath.sin(theta1(ksi, ph1(), a1(), ph2())));
}

@Override
public double der(Variable<AcVariableType> variable) {
Objects.requireNonNull(variable);
double theta = theta1(ksi, ph1(), a1(), ph2());
if (variable.equals(v1Var)) {
return dp1dv1(y, ksi, FastMath.sin(ksi), g1, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp1dv1(y, FastMath.sin(ksi), g1, v1(), r1(), v2(), FastMath.sin(theta));
} else if (variable.equals(v2Var)) {
return dp1dv2(y, ksi, v1(), ph1(), r1(), a1(), ph2());
return dp1dv2(y, v1(), r1(), FastMath.sin(theta));
} else if (variable.equals(ph1Var)) {
return dp1dph1(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp1dph1(y, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(ph2Var)) {
return dp1dph2(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp1dph2(y, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(a1Var)) {
return dp1da1(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp1da1(y, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(r1Var)) {
return dp1dr1(y, ksi, FastMath.sin(ksi), g1, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp1dr1(y, FastMath.sin(ksi), g1, v1(), r1(), v2(), FastMath.sin(theta));
} else {
throw new IllegalStateException("Unknown variable: " + variable);
}
Expand Down
62 changes: 29 additions & 33 deletions ...java/com/powsybl/openloadflow/ac/equations/ClosedBranchSide1ReactiveFlowEquationTerm.java
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,6 @@

import java.util.Objects;

import static com.powsybl.openloadflow.network.PiModel.A2;
import static com.powsybl.openloadflow.network.PiModel.R2;

/**
Expand All @@ -30,71 +29,68 @@ public ClosedBranchSide1ReactiveFlowEquationTerm(LfBranch branch, LfBus bus1, Lf

protected double calculateSensi(double dph1, double dph2, double dv1, double dv2, double da1, double dr1) {
double v1 = v1();
double ph1 = ph1();
double r1 = r1();
double a1 = a1();
double v2 = v2();
double ph2 = ph2();
return dq1dph1(y, ksi, v1, ph1, r1, a1, v2, ph2) * dph1
+ dq1dph2(y, ksi, v1, ph1, r1, a1, v2, ph2) * dph2
+ dq1dv1(y, ksi, FastMath.cos(ksi), b1, v1, ph1, r1, a1, v2, ph2) * dv1
+ dq1dv2(y, ksi, v1, ph1, r1, a1, ph2) * dv2;
double theta = theta1(ksi, ph1(), a1(), ph2());
double cosTheta = FastMath.cos(theta);
double sinTheta = FastMath.sin(theta);
return dq1dph1(y, v1, r1, v2, sinTheta) * dph1
+ dq1dph2(y, v1, r1, v2, sinTheta) * dph2
+ dq1dv1(y, FastMath.cos(ksi), b1, v1, r1, v2, cosTheta) * dv1
+ dq1dv2(y, v1, r1, cosTheta) * dv2;
}

private static double theta(double ksi, double ph1, double a1, double ph2) {
return ksi - a1 + A2 - ph1 + ph2;
}

public static double q1(double y, double ksi, double cosKsi, double b1, double v1, double ph1, double r1, double a1, double v2, double ph2) {
public static double q1(double y, double cosKsi, double b1, double v1, double r1, double v2, double cosTheta) {
return r1 * v1 * (-b1 * r1 * v1 + y * r1 * v1 * cosKsi
- y * R2 * v2 * FastMath.cos(theta(ksi, ph1, a1, ph2)));
- y * R2 * v2 * cosTheta);
}

private static double dq1dv1(double y, double ksi, double cosKsi, double b1, double v1, double ph1, double r1, double a1, double v2, double ph2) {
private static double dq1dv1(double y, double cosKsi, double b1, double v1, double r1, double v2, double cosTheta) {
return r1 * (-2 * b1 * r1 * v1 + 2 * y * r1 * v1 * cosKsi
- y * R2 * v2 * FastMath.cos(theta(ksi, ph1, a1, ph2)));
- y * R2 * v2 * cosTheta);
}

private static double dq1dv2(double y, double ksi, double v1, double ph1, double r1, double a1, double ph2) {
return -y * r1 * R2 * v1 * FastMath.cos(theta(ksi, ph1, a1, ph2));
private static double dq1dv2(double y, double v1, double r1, double cosTheta) {
return -y * r1 * R2 * v1 * cosTheta;
}

private static double dq1dph1(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return -y * r1 * R2 * v1 * v2 * FastMath.sin(theta(ksi, ph1, a1, ph2));
private static double dq1dph1(double y, double v1, double r1, double v2, double sinTheta) {
return -y * r1 * R2 * v1 * v2 * sinTheta;
}

private static double dq1dph2(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return -dq1dph1(y, ksi, v1, ph1, r1, a1, v2, ph2);
private static double dq1dph2(double y, double v1, double r1, double v2, double sinTheta) {
return -dq1dph1(y, v1, r1, v2, sinTheta);
}

private static double dq1da1(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return dq1dph1(y, ksi, v1, ph1, r1, a1, v2, ph2);
private static double dq1da1(double y, double v1, double r1, double v2, double sinTheta) {
return dq1dph1(y, v1, r1, v2, sinTheta);
}

private static double dq1dr1(double y, double ksi, double cosKsi, double b1, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return v1 * (2 * r1 * v1 * (-b1 + y * cosKsi) - y * R2 * v2 * FastMath.cos(theta(ksi, ph1, a1, ph2)));
private static double dq1dr1(double y, double cosKsi, double b1, double v1, double r1, double v2, double cosTheta) {
return v1 * (2 * r1 * v1 * (-b1 + y * cosKsi) - y * R2 * v2 * cosTheta);
}

@Override
public double eval() {
return q1(y, ksi, FastMath.cos(ksi), b1, v1(), ph1(), r1(), a1(), v2(), ph2());
return q1(y, FastMath.cos(ksi), b1, v1(), r1(), v2(), FastMath.cos(theta1(ksi, ph1(), a1(), ph2())));
}

@Override
public double der(Variable<AcVariableType> variable) {
Objects.requireNonNull(variable);
double theta = theta1(ksi, ph1(), a1(), ph2());
if (variable.equals(v1Var)) {
return dq1dv1(y, ksi, FastMath.cos(ksi), b1, v1(), ph1(), r1(), a1(), v2(), ph2());
return dq1dv1(y, FastMath.cos(ksi), b1, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(v2Var)) {
return dq1dv2(y, ksi, v1(), ph1(), r1(), a1(), ph2());
return dq1dv2(y, v1(), r1(), FastMath.cos(theta));
} else if (variable.equals(ph1Var)) {
return dq1dph1(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dq1dph1(y, v1(), r1(), v2(), FastMath.sin(theta));
} else if (variable.equals(ph2Var)) {
return dq1dph2(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dq1dph2(y, v1(), r1(), v2(), FastMath.sin(theta));
} else if (variable.equals(a1Var)) {
return dq1da1(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dq1da1(y, v1(), r1(), v2(), FastMath.sin(theta));
} else if (variable.equals(r1Var)) {
return dq1dr1(y, ksi, FastMath.cos(ksi), b1, v1(), ph1(), r1(), a1(), v2(), ph2());
return dq1dr1(y, FastMath.cos(ksi), b1, v1(), r1(), v2(), FastMath.cos(theta));
} else {
throw new IllegalStateException("Unknown variable: " + variable);
}
Expand Down
62 changes: 29 additions & 33 deletions ...n/java/com/powsybl/openloadflow/ac/equations/ClosedBranchSide2ActiveFlowEquationTerm.java
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,6 @@

import java.util.Objects;

import static com.powsybl.openloadflow.network.PiModel.A2;
import static com.powsybl.openloadflow.network.PiModel.R2;

/**
Expand All @@ -30,69 +29,66 @@ public ClosedBranchSide2ActiveFlowEquationTerm(LfBranch branch, LfBus bus1, LfBu

protected double calculateSensi(double dph1, double dph2, double dv1, double dv2, double da1, double dr1) {
double v1 = v1();
double ph1 = ph1();
double r1 = r1();
double a1 = a1();
double v2 = v2();
double ph2 = ph2();
return dp2dph1(y, ksi, v1, ph1, r1, a1, v2, ph2) * dph1
+ dp2dph2(y, ksi, v1, ph1, r1, a1, v2, ph2) * dph2
+ dp2dv1(y, ksi, ph1, r1, a1, v2, ph2) * dv1
+ dp2dv2(y, ksi, FastMath.sin(ksi), g2, v1, ph1, r1, a1, v2, ph2) * dv2;
double theta = theta2(ksi, ph1(), a1(), ph2());
double cosTheta = FastMath.cos(theta);
double sinTheta = FastMath.sin(theta);
return dp2dph1(y, v1, r1, v2, cosTheta) * dph1
+ dp2dph2(y, v1, r1, v2, cosTheta) * dph2
+ dp2dv1(y, r1, v2, sinTheta) * dv1
+ dp2dv2(y, FastMath.sin(ksi), g2, v1, r1, v2, sinTheta) * dv2;
}

private static double theta(double ksi, double ph1, double a1, double ph2) {
return ksi + a1 - A2 + ph1 - ph2;
public static double p2(double y, double sinKsi, double g2, double v1, double r1, double v2, double sinTheta) {
return R2 * v2 * (g2 * R2 * v2 - y * r1 * v1 * sinTheta + y * R2 * v2 * sinKsi);
}

public static double p2(double y, double ksi, double sinKsi, double g2, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return R2 * v2 * (g2 * R2 * v2 - y * r1 * v1 * FastMath.sin(theta(ksi, ph1, a1, ph2)) + y * R2 * v2 * sinKsi);
private static double dp2dv1(double y, double r1, double v2, double sinTheta) {
return -y * r1 * R2 * v2 * sinTheta;
}

private static double dp2dv1(double y, double ksi, double ph1, double r1, double a1, double v2, double ph2) {
return -y * r1 * R2 * v2 * FastMath.sin(theta(ksi, ph1, a1, ph2));
private static double dp2dv2(double y, double sinKsi, double g2, double v1, double r1, double v2, double sinTheta) {
return R2 * (2 * g2 * R2 * v2 - y * r1 * v1 * sinTheta + 2 * y * R2 * v2 * sinKsi);
}

private static double dp2dv2(double y, double ksi, double sinKsi, double g2, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return R2 * (2 * g2 * R2 * v2 - y * r1 * v1 * FastMath.sin(theta(ksi, ph1, a1, ph2)) + 2 * y * R2 * v2 * sinKsi);
private static double dp2dph1(double y, double v1, double r1, double v2, double cosTheta) {
return -y * r1 * R2 * v1 * v2 * cosTheta;
}

private static double dp2dph1(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return -y * r1 * R2 * v1 * v2 * FastMath.cos(theta(ksi, ph1, a1, ph2));
private static double dp2dph2(double y, double v1, double r1, double v2, double cosTheta) {
return -dp2dph1(y, v1, r1, v2, cosTheta);
}

private static double dp2dph2(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return -dp2dph1(y, ksi, v1, ph1, r1, a1, v2, ph2);
private static double dp2da1(double y, double v1, double r1, double v2, double cosTheta) {
return dp2dph1(y, v1, r1, v2, cosTheta);
}

private static double dp2da1(double y, double ksi, double v1, double ph1, double r1, double a1, double v2, double ph2) {
return dp2dph1(y, ksi, v1, ph1, r1, a1, v2, ph2);
}

private static double dp2dr1(double y, double ksi, double v1, double ph1, double a1, double v2, double ph2) {
return -y * R2 * v1 * v2 * FastMath.sin(theta(ksi, ph1, a1, ph2));
private static double dp2dr1(double y, double v1, double v2, double sinTheta) {
return -y * R2 * v1 * v2 * sinTheta;
}

@Override
public double eval() {
return p2(y, ksi, FastMath.sin(ksi), g2, v1(), ph1(), r1(), a1(), v2(), ph2());
return p2(y, FastMath.sin(ksi), g2, v1(), r1(), v2(), FastMath.sin(theta2(ksi, ph1(), a1(), ph2())));
}

@Override
public double der(Variable<AcVariableType> variable) {
Objects.requireNonNull(variable);
double theta = theta2(ksi, ph1(), a1(), ph2());
if (variable.equals(v1Var)) {
return dp2dv1(y, ksi, ph1(), r1(), a1(), v2(), ph2());
return dp2dv1(y, r1(), v2(), FastMath.sin(theta));
} else if (variable.equals(v2Var)) {
return dp2dv2(y, ksi, FastMath.sin(ksi), g2, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp2dv2(y, FastMath.sin(ksi), g2, v1(), r1(), v2(), FastMath.sin(theta));
} else if (variable.equals(ph1Var)) {
return dp2dph1(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp2dph1(y, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(ph2Var)) {
return dp2dph2(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp2dph2(y, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(a1Var)) {
return dp2da1(y, ksi, v1(), ph1(), r1(), a1(), v2(), ph2());
return dp2da1(y, v1(), r1(), v2(), FastMath.cos(theta));
} else if (variable.equals(r1Var)) {
return dp2dr1(y, ksi, v1(), ph1(), a1(), v2(), ph2());
return dp2dr1(y, v1(), v2(), FastMath.sin(theta));
} else {
throw new IllegalStateException("Unknown variable: " + variable);
}
Expand Down
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