[WIP] Avoid angle divergence with HVDC AC emulation and PMax

src/main/java/com/powsybl/openloadflow/ac/equations/AbstractHvdcAcEmulationFlowEquationTerm.java

@@ -37,6 +37,10 @@ public abstract class AbstractHvdcAcEmulationFlowEquationTerm extends AbstractEl
 
  protected final double pMaxFromCS2toCS1;
 
+ protected final double tetaMax;
+ protected final double tetaMin;
+ protected final double tetaZero;
+
  protected AbstractHvdcAcEmulationFlowEquationTerm(LfHvdc hvdc, LfBus bus1, LfBus bus2, VariableSet<AcVariableType> variableSet) {
  super(hvdc);
  ph1Var = variableSet.getVariable(bus1.getNum(), AcVariableType.BUS_PHI);
@@ -48,9 +52,12 @@ protected AbstractHvdcAcEmulationFlowEquationTerm(LfHvdc hvdc, LfBus bus1, LfBus
  lossFactor2 = hvdc.getConverterStation2().getLossFactor() / 100;
  pMaxFromCS1toCS2 = hvdc.getPMaxFromCS1toCS2();
  pMaxFromCS2toCS1 = hvdc.getPMaxFromCS2toCS1();
+ tetaMax = (pMaxFromCS1toCS2 - p0) / k;
+ tetaMin = (-pMaxFromCS2toCS1 - p0) / k;
+ tetaZero = -p0 / k;
  }
 
- protected double rawP(double p0, double k, double ph1, double ph2) {
+ protected double rawP(double ph1, double ph2) {
  return p0 + k * (ph1 - ph2);
  }
 
@@ -65,6 +72,28 @@ protected double boundedP(double rawP) {
  }
  }
 
+ /**
+ * Returns a "corrected value for k that is
+ * the droop factor between tetaMin and tetaMax
+ * 0 in a resonable range above tetaMin and tetaMax
+ * the slot between pMax and P0 for larger angle differences to help convergence
+ * @param ph1
+ * @param ph2
+ * @return
+ */
+ protected double dummySlope(double rawP, double ph1, double ph2) {
+ double boundedP = boundedP(rawP);
+ double factor = k;
+ double teta = ph1 - ph2;
+ // for large values of teta return a value that helps convergence
+ if (teta > tetaMax) {
+ factor = teta < tetaMax * 2 ? 0 : boundedP / (teta - tetaZero);
+ } else if (teta < tetaMin) {
+ factor = teta > tetaMin * 2 ? 0 : boundedP / (teta - tetaZero);
+ }
+ return factor;
+ }
+
  protected double ph1() {
  return sv.get(ph1Var.getRow());
  }

src/main/java/com/powsybl/openloadflow/ac/equations/HvdcAcEmulationSide1ActiveFlowEquationTerm.java

@@ -23,7 +23,7 @@ public HvdcAcEmulationSide1ActiveFlowEquationTerm(LfHvdc hvdc, LfBus bus1, LfBus
  }
 
  private double p1(double ph1, double ph2) {
- double rawP = rawP(p0, k, ph1, ph2);
+ double rawP = rawP(ph1, ph2);
  double boundedP = boundedP(rawP);
  return (isController(rawP) ? 1 : getVscLossMultiplier()) * boundedP;
  }
@@ -37,12 +37,12 @@ private boolean isInOperatingRange(double rawP) {
  }
 
  protected double dp1dph1(double ph1, double ph2) {
- double rawP = rawP(p0, k, ph1, ph2);
- if (isInOperatingRange(rawP)) {
-  return (isController(rawP) ? 1 : getVscLossMultiplier()) * k;
- } else {
-  return 0;
- }
+ // return the exact derivative unless ph1-oh2 us ti large (twice value of P limit)
+ // in this case returns a dummy slope to heo th NR convergence towards desired P
+ double rawP = rawP(ph1, ph2);
+ double factor = dummySlope(rawP, ph1, ph2);
+ return (isController(rawP) ? 1 : getVscLossMultiplier()) * factor;
+
  }
 
  protected double dp1dph2(double ph1, double ph2) {

src/main/java/com/powsybl/openloadflow/ac/equations/HvdcAcEmulationSide2ActiveFlowEquationTerm.java

@@ -23,7 +23,7 @@ public HvdcAcEmulationSide2ActiveFlowEquationTerm(LfHvdc hvdc, LfBus bus1, LfBus
  }
 
  private double p2(double ph1, double ph2) {
- double rawP = rawP(p0, k, ph1, ph2);
+ double rawP = rawP(ph1, ph2);
  double boundedP = boundedP(rawP);
  return -(isController(rawP) ? 1 : getVscLossMultiplier()) * boundedP;
  }
@@ -37,12 +37,11 @@ private boolean isInOperatingRange(double rawP) {
  }
 
  private double dp2dph1(double ph1, double ph2) {
- double rawP = rawP(p0, k, ph1, ph2);
- if (isInOperatingRange(rawP)) {
- return -(isController(rawP) ? 1 : getVscLossMultiplier()) * k;
- } else {
- return 0;
- }
+ // return the exact derivative unless ph1-oh2 us ti large (twice value of P limit)
+ // in this case returns a dummy slope to heo th NR convergence towards desired P
+ double rawP = rawP(ph1, ph2);
+ double factor = dummySlope(rawP, ph1, ph2);
+ return -(isController(rawP) ? 1 : getVscLossMultiplier()) * factor;
  }
 
  private double dp2dph2(double ph1, double ph2) {

src/test/java/com/powsybl/openloadflow/ac/AcLoadFlowVscTest.java

@@ -502,6 +502,44 @@ void testAcEmuWithOperationalLimits() {
  assertEquals(180, network.getHvdcConverterStation("cs3").getTerminal().getP(), DELTA_POWER);
  }
 
+ @Test
+ void testAcEmuWithOperationalLimitsWithDCInit() {
+ Network network = HvdcNetworkFactory.createHvdcLinkedByTwoLinesAndSwitch(HvdcConverterStation.HvdcType.VSC);
+ // without limit p=195
+ network.getHvdcLine("hvdc23")
+ .newExtension(HvdcOperatorActivePowerRangeAdder.class)
+ .withOprFromCS2toCS1(180)
+ .withOprFromCS1toCS2(170)
+ .add();
+
+ LoadFlow.Runner loadFlowRunner = new LoadFlow.Runner(new OpenLoadFlowProvider(new DenseMatrixFactory()));
+ LoadFlowParameters p = new LoadFlowParameters();
+ p.setHvdcAcEmulation(true);
+ p.setVoltageInitMode(LoadFlowParameters.VoltageInitMode.DC_VALUES);
+
+ // fool the DC initialization with large angle
+ network.getHvdcLine("hvdc23").setActivePowerSetpoint(0);
+ network.getLine("l14").setX(20);
+
+ LoadFlowResult result = loadFlowRunner.run(network, p);
+
+ assertTrue(result.isFullyConverged());
+
+ // Active flow capped at limit. Output has losses (due to VSC stations)
+ assertEquals(170, network.getHvdcConverterStation("cs2").getTerminal().getP(), DELTA_POWER);
+ assertEquals(-166.280, network.getHvdcConverterStation("cs3").getTerminal().getP(), DELTA_POWER);
+
+ // now invert the angle to test ill conditioned converence in the other direction
+ network.getLine("l14").setX(-20);
+ result = loadFlowRunner.run(network, p);
+ assertTrue(result.isFullyConverged());
+
+ // Active flow capped at other direction's limit. Output has losses (due to VSC stations)
+ assertEquals(-176.062, network.getHvdcConverterStation("cs2").getTerminal().getP(), DELTA_POWER);
+ assertEquals(180, network.getHvdcConverterStation("cs3").getTerminal().getP(), DELTA_POWER);
+
+ }
+
  @Test
  void testAcEmuAndPMax() {
  Network network = HvdcNetworkFactory.createHvdcLinkedByTwoLinesAndSwitch(HvdcConverterStation.HvdcType.VSC);