Single Phase Induction Machine

Description of the Single Phase Induction Machine component in Schematic Editor.

Table 1. Single Phase Induction Machine component in Typhoon HIL Schematic Editor
component component dialog window component parameters

The component nodes m_pos and m_neg (shown in Table 1) are the main stator winding terminals. Three types of single phase induction machines are modeled —split-phase, capacitor-start and capacitor-start-run.Figure 1, Figure 2 and Figure 3 show the internal connections of the main and auxiliary windings for each of the machine types. The stator is represented by the single phase variant of the voltage behind reactance interface.

Figure 1. Diagram of a split-phase single phase induction machine
Figure 2. Diagram of a capacitor-start single phase induction machine

Figure 3. Diagram of a capacitor-start-run single phase induction machine

Electrical sub-system model

The electrical part of the machine is represented by the following system of equations, modeled in the stationary αβ reference frame. All rotor variables and parameters are referred to the stator.

v α s v β s v α r v β r = R s m 0 0 0 0 R s a 0 0 0 0 R r m 0 0 0 0 N 2 R r m i α s i β s i α r i β r + d d t ψ α s ψ β s ψ α r ψ β r + 0 0 1 N ω r ψ β r - N ω r ψ α r

ψ α s ψ β s ψ α r ψ β r = L l s m + L m m 0 L m m 0 0 L l s a + N 2 L m m 0 N 2 L m m L l r m + L m m 0 L m m 0 0 N 2 ( L l r m + L m m ) 0 N 2 L m m i α s i β s i α r i β r

T e = p ( N ψ α s i β s - 1 N ψ β s i α s )

In the above equations, currents are obtained from the main winding and auxiliary winding stator currents using the following transformation:

i α s i β s = 1 0 0 1 i m a i n i a u x
Table 2. Electrical sub-system model variables
symbol description
ψαs Alpha axis component of the stator flux [Wb]
ψβs Beta axis component of the stator flux [Wb]
ψαr Alpha axis component of the rotor flux, referred to the stator [Wb]
ψβr Beta axis component of the rotor flux, referred to the stator [Wb]
iαs Alpha axis component of the stator current [A]
iβs Beta axis component of the stator current [A]
iαr Alpha axis component of the rotor current, referred to the stator [A]
iβr Beta axis component of the rotor current, referred to the stator [A]
vαs Alpha axis component of the stator voltage [V]
vβs Beta axis component of the stator voltage [V]
vαr Alpha axis component of the rotor voltage, referred to the stator [V]
vβr Beta axis component of the rotor voltage, referred to the stator [V]
Rsm Stator main winding resistance [Ω]
Rsa Stator auxiliary winding resistance [Ω]
Rrm Rotor main winding resistance [Ω]
Llsm Stator main winding leakage inductance [H]
Lmm Main winding mutual inductance [H]
Llsa Stator auxiliary winding leakage inductance [H]
Llrm Rotor main winding leakage inductance [H]
ωr Rotor electrical speed [rad/s] ( = p ω m )
p Machine number of pole pairs
Te Machine developed electromagnetic torque [Nm]
N Auxiliary to main winding turns ratio (Na/Nm)

Mechanical sub-system model

Motion equation:

d ω m d t =   1 J m ( T e - T l - b ω m )

θ m =   ω m d t
Table 3. Mechanical sub-system model variables
symbol description
ωm Rotor mechanical speed [rad/s]
Jm Combined rotor and load moment of inertia [kgm2]
Te Machine developed electromagnetic torque [Nm]
Tl Shaft mechanical load torque [Nm]
b Machine viscous friction coefficient [Nms]
θm Rotor mechanical angle [rad]
Note: Motion equation is the same for all of the rotating machine models.

Electrical

Table 4. Electrical parameters
symbol description
Machine type Type of machine: split-phase, capacitor-start or capacitor-start-run
f Nominal frequency of the machine [Hz]
Rsm Stator main winding resistance [Ω]
Llsm Stator main winding leakage inductance [H]
Rsa Stator auxiliary winding resistance [Ω]
Llsa Stator auxiliary winding leakage inductance [H]
Lmm Main winding mutual inductance [H]
Rrm Rotor main winding resistance [Ω]
Llrm Rotor main winding leakage inductance [H]
Na/Nm Auxiliary to main winding turns ratio
Rst Capacitor-start resistance [Ω]
Cst Capacitor-start capacitance [F]
Rrun Capacitor-run resistance [Ω]
Crun Capacitor-run capacitance [F]

Mechanical

Table 5. Mechanical parameters
symbol description
pms Machine number of pole pairs
Jm Combined rotor and load moment of inertia [kgm2]
Friction coefficient Machine viscous friction coefficient [Nms]
Disconnection speed coefficient Rotor speed at which the auxiliary winding is disconnected (in % of synchronous speed)
Unconstrained mechanical angle Limiting mechanical angle between 0 and 2π

Load

Table 6. Load parameters
symbol description
Load source Load can be set from SCADA/external or from model (in model case, one signal processing input will appear)
External/Model load type External/Model load type: torque or speed
Load ai pin HIL analog input address for external torque command
Load ai offset Assigned offset value to the input signal representing external torque command
Load ai gain Assigned gain value to the input signal representing external torque command

External load enables you to use an analog input signal from a HIL analog channel with the load_ai_pin address as an external torque/speed load, and to assign offset (V) and gain (Nm/V) to the input signal, according to the formula:

T l = l o a d _ a i _ g a i n · ( A I ( l o a d _ a i _ p i n ) + l o a d _ a i _ o f f s e t)

Note: An analog input pin may be overwritten if another component uses the same analog input pin. If another property (from the same or a different component) uses the same analog input pin, the input signal value will be applied to only one of those properties. For instance, if both the load and the resolver carrier signal use the same analog input pin, the signal value will only be applied only to one of these.

Feedback

Table 7. Feedback parameters
symbol description
Encoder ppr Incremental encoder number of pulses per revolution
Encoder Z pulse length Z digital signal pulse length in periods. Can be Quarter length or Full period (default)
Resolver pole pairs Resolver number of pole pairs
Resolver carrier source Resolver carrier signal source selection (internal or external)
External resolver carrier source type External resolver carrier signal source type selection (single ended or differential); available only if the Resolver carrier source property is set to external
Resolver carrier frequency Resolver carrier signal frequency (internal carrier) [Hz]
Resolver ai pin 1 Resolver carrier input channel 1 address (external carrier)
Resolver ai pin 2 Resolver carrier input channel 2 address (external carrier); available only if the External resolver carrier source type property is set to differential
Resolver ai offset Resolver carrier input channel offset (external carrier)
Resolver ai gain Resolver carrier input channel gain (external carrier)
Absolute encoder protocol Standardized protocol providing the absolute machine encoder position

If an external resolver carrier source is selected, the source signal type can be set as either single ended or differential. The single ended external resolver carrier source type enables use of an analog input signal from the HIL analog channel with the res_ai_pin_1 address as the external carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal, according to the formula:

r e s _ c a r r _ s r c = r e s _ a i _ g a i n · ( A I ( r e s _ a i _ p i n _ 1 ) + r e s _ a i _ o f f s e t )

The differential external resolver carrier source type enables use of two analog input signals from the HIL analog channels with the res_ai_pin_1 and the res_ai_pin_2 addresses. Analog signals from these HIL analog inputs are subtracted, and the resulting signal is used as the external differential carrier source. Additionally, offset (V) and gain (V/V) values can be assigned to the input signal (similarly to the single ended case), according to the formula:

r e s _ c a r r _ s r c = r e s _ a i _ g a i n · ( ( A I ( r e s _ a i _ p i n _ 1 ) - A I ( r e s _ a i _ p i n _ 2 ) ) + r e s _ a i _ o f f s e t )
Note: Differential external resolver signal support is available from the 2023.1 software version. Only the single ended external resolver option was available in previous software versions.
Note: In order to get a resolver signal with an amplitude of 1 when using an external carrier signal, the offset and the gain should be chosen in such a way that the resolver carrier signal has an amplitude of 1 after the adjustment. As shown in Figure 1, the sinusoidal signal used to generate external resolver carrier source is fed to HIL analog input 1. The analog input signal is scaled in order to get the resolver signals with an amplitude of 1.
Figure 4. Machine resolver signals
Note: An analog input pin may be overwritten if another component uses the same analog input pin. If another property (from the same or a different component) uses the same analog input pin, the input signal value will be applied to only one of those properties. E.g. if both the load and the resolver carrier signal use the same analog input pin, the signal value will be applied only to one of these.

The following expression must hold in order to properly generate the encoder signals:

4 · e n c _ p p r · f m · T s 1
Table 8. Variables in the encoder limitation expression
symbol description
enc_ppr Encoder number of pulses per revolution
fm Rotor mechanical frequency [Hz]
Ts Simulation time step [s]
Figure 5. Machine encoder signals when Full period option is selected
Figure 6. Machine encoder signals when Quarter period option is selected
Note: While the machine speed is positive, the encoder channel B signal leads the encoder channel A signal.
Note: Absolute encoder protocol is not supported on HIL402 (configurations: 1, 2, 3, and 4).
Note: More information about absolute encoder protocol could be found here.

Output

This block tab enables a single, vectorized signal output from the machine. The output vector contains selected machine mechanical and/or electrical variables in the same order as listed in this tab.

Note: All machine components have the Execution rate, Electrical torque, Mechanical speed, and Mechanical angle, but the rest of the signals differ from component to component.
Table 9. Output parameters
symbol description
Execution rate Signal processing output execution rate [s]
Electrical torque Machine electrical torque [Nm]
Mechanical speed Machine mechanical angular speed [rad/s]
Mechanical angle Machine mechanical angle [rad]
Stator alpha axis emf Alpha axis component of the stator VBR equivalent back emf [V]
Stator beta axis emf Beta axis component of the stator VBR equivalent back emf [V]
Rotor alpha axis current Alpha axis component of the rotor current, referred to the stator [A]
Rotor beta axis current Beta axis component of the rotor current, referred to the stator [A]
Stator alpha axis flux Alpha axis component of the stator flux [Wb]
Stator beta axis flux Beta axis component of the stator flux [Wb]
Rotor alpha axis flux Alpha axis component of the rotor flux, referred to the stator [Wb]
Rotor beta axis flux Beta axis component of the rotor flux, referred to the stator [Wb]