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, signal-processing-based component.

Table 1. Three Phase Wound Rotor Synchronous Machine (Generic) component in Typhoon HIL Schematic Editor
component	component dialog window	component parameters
		Property tabs: Electrical Mechanical Output Execution rate

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 q-axis which is short-circuited without accessible terminals.

Electrical sub-system 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:

$[\begin{matrix} v_{d s} \\ v_{q s} \\ v_{k q} \\ v_{f d} \end{matrix}] = [\begin{matrix} R_{s} & 0 & 0 & 0 \\ 0 & R_{s} & 0 & 0 \\ 0 & 0 & R_{k q} & 0 \\ 0 & 0 & 0 & R_{f d} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \\ i_{k q} \\ i_{f d} \end{matrix}] + \frac{d}{d t} [\begin{matrix} ψ_{d s} \\ ψ_{q s} \\ ψ_{k q} \\ ψ_{f d} \end{matrix}] + [\begin{matrix} {- ω}_{r} ψ_{q s} \\ ω_{r} ψ_{d s} \\ 0 \\ 0 \end{matrix}]$

$[\begin{matrix} ψ_{d s} \\ ψ_{q s} \\ ψ_{k q} \\ ψ_{f d} \end{matrix}] = [\begin{matrix} L_{l s} + L_{m d} & 0 & 0 & L_{m d} \\ 0 & L_{l s} + L_{m q} & L_{m q} & 0 \\ 0 & L_{m q} & L_{l k q} + L_{m q} & 0 \\ 0 & 0 & 0 & L_{l f d} + L_{m d} \end{matrix}] [\begin{matrix} i_{d s} \\ i_{q s} \\ i_{k q} \\ i_{f d} \end{matrix}]$

T_{e} = \frac{3}{2} p (ψ_{d s} i_{q s} - ψ_{q s} i_{d s})

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.

Table 2. Electrical sub-system model variables
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] ( $= p ω_{m}$ )
p	Machine number of pole pairs
T_e	Machine developed electromagnetic torque [Nm]

Mechanical sub-system model

Motion equation:

\frac{{d ω}_{m}}{d t} = \frac{1}{J_{m}} (T_{e} - T_{l})

θ_{m} = \int ω_{m} d t

Table 3. Mechanical sub-system model variables
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

Table 4. Electrical parameters
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

Table 5. Mechanical parameters
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.

Table 6. Output parameters
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.

Table 7. Execution rate parameters
symbol	description
Execution rate	Signal processing output execution rate [s]