Three Phase Wound Rotor Synchronous Machine (Generic)
Description of the Three Phase Wound Rotor Synchronous Machine (Generic) component in Schematic Editor.
This simplified model of a three phase wound rotor synchronous machine allows simulation of machine dynamics in real time using only generic machine data such as power and voltage. It is built as an easy to use and implement, signalprocessingbased component.
component  component dialog window  component parameters 


A, B, and C are the stator winding terminals. The stator winding uses the voltage behind reactance interface. The stator winding arrangement (connection) is considered to be star connected with an accessible neutral point. The inputs to the system are the field winding voltage and mechanical source (which can be selected to be either mechanical torque or speed). Both inputs to the model are in the form of signals.
In the simplified model of the machine, the rotor is assumed to be round and the field winding is assumed to be decoupled and operating independently. Meanwhile, the machine has only one damper winding in the qaxis which is shortcircuited without accessible terminals.Electrical subsystem model
The electrical part of the machine is represented by the following system of equations, modeled in the rotating dq reference frame. The dq reference frame is attached to the rotor, and the direct axis is aligned with the field winding axis. The modeled dynamics can be represented with the following equations:
$\left[\begin{array}{c}{v}_{ds}\\ {v}_{qs}\\ {v}_{kq}\\ {v}_{fd}\end{array}\right]=\left[\begin{array}{cccc}{R}_{s}& 0& 0& 0\\ 0& {R}_{s}& 0& 0\\ 0& 0& {R}_{kq}& 0\\ 0& 0& 0& {R}_{fd}\end{array}\right]\left[\begin{array}{c}{i}_{ds}\\ {i}_{qs}\\ {i}_{kq}\\ {i}_{fd}\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\psi}_{ds}\\ {\psi}_{qs}\\ {\psi}_{kq}\\ {\psi}_{fd}\end{array}\right]+\left[\begin{array}{c}{\omega}_{r}{\psi}_{qs}\\ {\omega}_{r}{\psi}_{ds}\\ 0\\ 0\end{array}\right]$
$\left[\begin{array}{c}{\psi}_{ds}\\ {\psi}_{qs}\\ {\psi}_{kq}\\ {\psi}_{fd}\end{array}\right]=\left[\begin{array}{cccc}{L}_{ls}+{L}_{md}& 0& 0& {L}_{md}\\ 0& {L}_{ls}+{L}_{mq}& {L}_{mq}& 0\\ 0& {L}_{mq}& {L}_{lkq}+{L}_{mq}& 0\\ 0& 0& 0& {L}_{lfd}+{L}_{md}\end{array}\right]\left[\begin{array}{c}{i}_{ds}\\ {i}_{qs}\\ {i}_{kq}\\ {i}_{fd}\end{array}\right]$
${T}_{e}=\frac{3}{2}p({\psi}_{ds}{i}_{qs}{\psi}_{qs}{i}_{ds})$In this generic model of the synchronous machine, the machine electrical parameters are approximated based on the machine power, voltage, frequency, and speed to be as close to realistic values as possible.
Symbol  Description 

ψ_{ds}  Direct axis component of the stator flux [Wb] 
ψ_{qs}  Quadrature axis component of the stator flux [Wb] 
ψ_{kd}  Direct axis component of the damper winding flux, referred to the stator [Wb] 
ψ_{kq}  Quadrature axis component of the damper winding flux, referred to the stator [Wb] 
ψ_{fd}  Field winding flux, referred to the stator [Wb] 
i_{ds}  Direct axis component of the stator current [A] 
i_{qs}  Quadrature axis component of the stator current [A] 
i_{kd}  Direct axis component of the damper winding current, referred to the stator [A] 
i_{kq}  Quadrature axis component of the damper winding current, referred to the stator [A] 
i_{fd}  Field winding current, referred to the stator [A] 
v_{ds}  Direct axis component of the stator voltage [V] 
v_{qs}  Quadrature axis component of the stator voltage [V] 
v_{kd}  Direct axis component of the damper winding voltage, referred to the stator [V] 
v_{kq}  Quadrature axis component of the damper winding voltage, referred to the stator [V] 
v_{fd}  Field winding voltage, referred to the stator [V] 
R_{s}  Stator phase resistance [Ω] 
R_{kd}  Direct axis damper winding resistance, referred to the stator [Ω] 
R_{kq}  Quadrature axis damper winding resistance, referred to the stator [Ω] 
R_{fd}  Field winding resistance, referred to the stator [Ω] 
L_{ls}  Stator phase leakage inductance [H] 
L_{md}  Direct axis magnetizing (mutual, main) inductance [H] 
L_{mq}  Quadrature axis magnetizing (mutual, main) inductance [H] 
L_{lkd}  Direct axis damper winding leakage inductance, referred to the stator [H] 
L_{lkq}  Quadrature axis damper winding leakage inductance, referred to the stator [H] 
L_{lfd}  Direct axis field winding leakage inductance, referred to the stator [H] 
ω_{r}  Rotor electrical speed [rad/s] ( $=p{\omega}_{m}$ ) 
p  Machine number of pole pairs 
T_{e}  Machine developed electromagnetic torque [Nm] 
Mechanical subsystem model
Motion equation:
$\frac{{d\omega}_{m}}{dt}=\frac{1}{{J}_{m}}({T}_{e}{T}_{l})$ ${\theta}_{m}=\int {\omega}_{m}dt$Symbol  Description 

ω_{m}  Rotor mechanical speed [rad/s] 
J_{m}  Combined rotor and load moment of inertia [kgm2] 
T_{e}  Machine developed electromagnetic torque [Nm] 
T_{l}  Shaft mechanical load torque [Nm] 
θ_{m}  Rotor mechanical angle [rad] 
Electrical
Symbol  Description 

Nominal machine line to line voltage  Nominal line voltage at the machine stator terminals [V] 
Nominal apparent power  Nominal apparent power at the machine stator terminals [VA] 
Nominal active power  Nominal active power at the machine stator terminals [W] 
Nominal frequency  Nominal electrical frequency of the stator [Hz] 
Nominal revolutions per minute  Nominal mechanical speed of the rotor [RPM] 
Mechanical
Symbol  Description 

Inertia  Total rotational inertia attached to the machine rotor, including the rotor itself  additional load inertia should be included in this value [kgm2] 
Initial rotor angle  Initial mechanical angle of the rotor (ar axis with respect to as axis) [deg] 
Mechanical input  Type of mechanical input to the machine, consisting of mechanical torque [Nm] or mechanical speed [rad/s] 
Output
The output port is enabled when one or more signals are selected in the Output tab. The output is a vector signal of size 6. Signals that are not selected for monitoring in the Output tab will return zero on the output vector.
Symbol  Description 

i_{as}  Stator phase A current [A] 
i_{bs}  Stator phase B current [A] 
i_{cs}  Stator phase C current [A] 
T_{e}  Machine developed electromagnetic torque [Nm] 
ω_{m}  Rotor mechanical speed [rad/s] 
θ_{m}  Rotor mechanical angle [rad] 
Execution rate
The signal processing execution rate of the component is specified here. For more information on how execution rates are handled, please refer to our Execution rates documentation.
symbol  description 

Execution rate  Signal processing output execution rate [s] 