SIMPLORER User Manual V6.0 - FER-a

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176 Modeling with Circuit Components
Component Nodes
Description Node Name Nature
Stator Node A A electrical
Stator Node B B electrical
Stator Node C C electrical
Excitation Circuit Node E1 E1 electrical
Excitation Circuit Node E2 E2 electrical
Synchronous Machine Permanent Excitation without Damper
>>Basics>Circuit>Electrical Machines
The model represents a synchronous machine with permanent magnet excitation and without
damper as a lumped circuit component. Depending on the parameter set, the machine can
be operate either as a salient or non-salient pole rotor. The circuit nodes A – B – C are the terminals
of star-connected stator winding. The component cannot be used with AC and DC
simulation.
If the line-to-line voltage vab , vbc , vac or the line currents ia , ib , ic of the synchronous machine
are of special interest, voltmeters or ammeters can be connected to the synchronous machine.
In the case of identical parameters for the inductances L1D and L1Q, a synchronous machine
with permanent magnet excitation and non-salient pole rotor is modeled. To model a permanent
magnet salient-pole machine, the parameters must be different for L1D and L1Q.See also
“Model Limits of Synchronous Machine Models” on page 170.
Equation System
The equation system is implemented in a rotor-fixed (rotor-fixed and also rotor flux-fixed) coordinate
system (d-q-coordinates). Index 1 represents the stator quantities. The phase quantities
of the real three-phase synchronous machine are indicated with a, b, c.
Voltage equations
dψ1d() t
v1d() t = i1d() t ⋅ R1 + ------------------ – p ⋅ ω() t ⋅ ψ1q() t
dt
dψ1q() t
v1q() t = i1q() t ⋅ R1 + ------------------ + p ⋅ ω() t ⋅ ψ1d() t
dt
Flux-linkage equations
ψ1d() t = i1d() t ⋅ L1d + ke ψ1q() t = i1q() t ⋅ L1q Torque equation (electromagnetic developed “internal” torque)
mi() t
=
3
--p ⋅ ( ψ
2 1d() t ⋅ i1q() t – ψ1q() t ⋅ i1d() t )
Motion equation
dω
-------------
() t
dt
=
1
-- ( m
J i() t – mw() t )