Motor Models

Double Cage Flux Induction Motor

Figure 1: Double Cage Induction Motor Flux Model

Parameter

Units

Description

Rated HP

HP

 

Rated Eff

Percent

 

Rated Speed

RPM

 

Rated Voltage

Volts LL

 

Rated Current

Amps

 

Rated PF

 

 

Rated Slip

pu

Rated slip

Start Trq

pu

Starting torque

Start Crt

pu

Starting current

Start PF

 

Starting power factor

Pull-Out Trq

pu

Rated pull-out torque

Ra

pu

Stator winding resistance (armature resistance)

Xl

pu

Stator leakage reactance

X

pu

Unsaturated synchronous reactance

X’

pu

Unsaturated transient reactance

X’’

pu

Unsaturated sub-transient reactance

T’o

Seconds

Transient OC time constant

T’’o

Seconds

Sub-transient OC time constant

E1

pu

First voltage to define saturation

E2

pu

Second voltage to define saturation

S( E1 )

pu

Saturation at E1

S( E2 )

pu

Saturation at E2

H

kW-Sec / kVA

Combined machine and load inertia

Ld Tran Str

Seconds

Time at which load transfers – starting to running

Ld Tran Rmp

Seconds

Time it takes to transfer load – starting to running

SoftSt V1 (%)

Percent

Initial terminal voltage upon starting motor

SoftSt V2 (%)

Percent

Intermediate voltage for motor start after T12 seconds. This defines the first slope of ramp.

SoftSt V3 (%)

Percent

Final voltage for motor start at end of ramp after T23 seconds. This defines the final slope of ramp.

SoftSt T12 (sec)

seconds

Time elapsed between V1 and V2

SoftSt T23 (sec)

seconds

Time elapsed between V2 and V3

Note: OC = Open Circuit

Figure 2: Double Cage Induction Motor Impedance Model – Type 1 Form

Synchronous Motor

Figure 3: Synchronous Motor Model Block Diagram

Parameter

Units

Description

Rated HP

HP

 

Rated Eff

Percent

 

Rated Speed

RPM

 

Rated Voltage

Volts LL

 

Rated Current

Amps

 

Rated PF

 

 

Ra

pu

Stator winding resistance (armature resistance)

Xl

pu

Stator leakage reactance

Xd

pu

d-axis unsaturated synchronous reactance

Xq

pu

q-axis unsaturated synchronous reactance

X’d

pu

d-axis unsaturated transient reactance

X’’d = X’’q

pu

d & q-axis unsaturated sub-transient reactance

T’do

Seconds

d-axis transient OC time constant

T’’do

Seconds

d-axis sub-transient OC time constant

T’’qo

Seconds

q-axis sub-transient OC time constant

E1

pu

First voltage to define saturation

E2

pu

Second voltage to define saturation

S( E1 )

pu

Saturation at E1

S( E2 )

pu

Saturation at E2

H

kW-Sec / kVA

Combined machine and load inertia

Ld Tran Str

Seconds

Time at which load transfers – starting to running

Ld Tran Rmp

Seconds

Time it takes to transfer load – starting to running

EFD App Speed

Percent

Speed at which the field is applied during starting

EFD App Value

Percent

Value of field voltage to apply during starting

Rev Pwr Del

Seconds

Time it takes to trip the reverse power detection

SoftSt V1 (%)

Percent

Initial terminal voltage upon starting motor

SoftSt V2 (%)

Percent

Intermediate voltage for motor start after T12 seconds. This defines the first slope of ramp.

SoftSt V3 (%)

Percent

Final voltage for motor start at end of ramp after T23 seconds. This defines the final slope of ramp.

SoftSt T12 (sec)

seconds

Time elapsed between V1 and V2

SoftSt T23 (sec)

seconds

Time elapsed between V2 and V3

More Information

Dynamic Stability  
Stability Data Parameters