.PowerGrids.Electrical.Test.SynchronousMachine4Windings

Information

Test case for the conversion of external parameter to internal parameters taken from Kundur, Power System Stability and Control, example 4.1. Note that the system frequency for this example is 60 Hz.

The machine is directly connected to an ideal bus with UNom = 24 kV and phase = 0 and initialized in steady-state with PmPu = 0.9, ufPu = 0.000939, using the Kundur base excitation voltage.

ParameterMeaningValueUnit
SNomRated power550MVA
UNomRated phase-to-phase voltage24kV
xlPuStator Leakage0.15pu
xdPuDirect axis reactance1.81pu
xpdPuDirect axis transient reactance0.3pu
xppdPuDirect axis sub-transient reactance0.23pu
Tpd0Direct axis open circuit transient time constant8s
Tppd0Direct axis open circuit sub-transient time constant0.03s
xqPuQuadrature axis reactance1.76pu
xpqPuQuadrature axis transient reactance0.65pu
xppqPuQuadrature axis sub-transient reactance0.25pu
Tpq0Quadrature axis open circuit transient time constant1s
Tppq0Quadrature axis open circuit sub-transient time constant0.07s
raPuArmature resistance0.003pu
mrcPuCanay's mutual inductance0pu

The following internal parameter values are reported from Kundur and match the ones computed by the model with timeConstantApproximation=classicalDefinitions.

PowerGridsKundurMeaningValueUnit
LdPuLlDirect axis stator leakage0.15pu
MdPuLadDirect axis mutual inductance1.66pu
LDPuL1dDirect axis damper leakage0.1713pu
rDPuR1dDirect axis damper resistance0.0284pu
LfPuLfdExcitation winding leakage0.165pu
rfPuRfdExcitation windings resistance0.000605pu
LqPuLlQuadrature axis stator leakage 0.15pu
MqPuLaqQuadrature axis mutual inductance1.61pu
LQ1PuL1qQuadrature axis 1st damper leakage0.7252pu
rQ1PuR1qQuadrature axis 1st damper resistance0.0062pu
LQ2PuL2qQuadrature axis 2nd damper leakage0.125pu
rQ2PuR2qQuadrature axis 2nd damper resistance0.02368pu

The following table reports the steady-state solution computed by Kundur in Example 3.2 and by the PowerGrids model. Note that the Kundur example unfortunately includes a the effect of an 83.5% magnetic saturation, which is not accounted for in the PowerGrids model, so the two sets of values do not match exactly, particularly as regards the reactive power and the quadrature current. However, the difference is compatible with the effect of the reduced inductances. Also note that the sign convention for id, iq is opposite to Kundur's.

VariableNameValue KundurValue PowerGridsUnit
PGenPuGenerated active power0.90.89667pu
QGenPuGenerated reactive power0.4360.55206pu
thetaMachine angle39.138.61deg
udPuDirect axis voltage0.6310.6240pu
uqPuQuadrature axis voltage0.7760.7814pu
idPuDirect axis current0.906-0.9909pu
iqPuQuadrature axis current0.423-0.3562pu


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