Table of Contents  


The asynchronous machine block can be squirrel cage (1rotor or 2rotor) or wound rotor machine. The model is a Norton equivalent that interfaces directly with network elements. The model allows to model the following phenomena:
 Independent d and q axes saturation
 The mutual inductance of d and q axes can be unequal
 The stator windings can be configured to be star connected with a common neutral or delta
 The coupling between the cages in the case of the double cage machine
 The transformation ratio between the stator and rotor coils is taken into account
The asynchronous machine participates in the loadflow as a constant positive impedance that is a function of the slip. Therefore, the user must provide the initial slip that corresponds to the steady state of the machine.
Mask and Parameters
The mask of the machine has three tabs:
 Electrical parameters: General parameters of the machine
 Mechanical data: Mechanical parameters of the machine
 Saturation: Parameters of the saturation curve
In the Saturation tab, the user must specify the points of the saturation curve if this is taken into account. In the case of the independent saturation of axes d and q, the two tables represent the positive part of the curve (the negative part is deduced by symmetry) and the number of points of these curves can be different. In the case of total saturation, only the d axis table is used.
Note: The first of each saturation curve must not be zero and corresponds to the linear inductance of the machine in the case of independent saturation.
Electrical Parameters Tab
Variable  Description  Unit  Variable = {Possible Values} 

Base power  Nominal power  kVA  
Base voltage  Nominal voltage (line to line)  kV  
Frequency  Nominal frequency  Hz  
Number of poles  Number of poles    
Rotor type  Wound rotor or cage rotor (single or double)    
DQ speed reference  dq axis reference frame of the machine    
Stator connection  Stator windings connection (wye or delta)    
Rs  Stator resistance  Ohm  
Lls  Stator leakage inductance  Henry  
Rr1  Cage 1 rotor resistance  Ohm  
Llr1  Cage 1 leakage inductance  Henry  
Rr2  Cage 2 rotor resistance  Ohm  
Llr2  Cage 2 leakage inductance  Henry  
Lmq  qaxis mutual inductance  Henry  
Lmd  daxis mutual inductance  Henry  
Lmr  d and q axes rotor cage mutual inductance  Henry  
Initial slip  Initial slip   
Mechanical Data Tab
Variable  Description  Unit  Variable = {Possible Values} 

Moment of Inertia J  Moment of Inertia  kgm^{2}  
Friction Kd  Friction coefficient  Nm.s  
Mechanical torque  User select if the mechanical torque characteristic is internal or external    
Tmec  Torque points of the mechanical torque versus speed  Nm  
Wmec  Speed points of the mechanical torque versus speed  rad/s 
Saturation Tab
Variable  Description  Unit  Variable = {Possible Values} 

Saturation Enable  User can disable or enable independent or total saturation    
daxis saturation curve points  Number of daxis saturation curve points    
Imd  daxis magnetizing current points of saturation curve.  A  
Fluxmd  daxis magnetizing flux points of saturation curve.  Wb  
qaxis saturation curve points  Number of qaxis saturation curve points    
Imq  qaxis magnetizing current points of saturation curve.  A  
Fluxmq  qaxis magnetizing flux points of saturation curve.  Wb 
Ports, Inputs, Outputs and Signals Available for Monitoring
Ports
Cage machine
Name  Description 

S  AC side stator connector (supports only 3phase connections) 
N  AC side neutral connector (supports only 1phase connections) 
Wound rotor machine
Name  Description 

S  AC side stator connector (supports only 3phase connections) 
R  AC side rotor connector (supports only 3phase connections) 
Ns  AC side network connector (stator neutral). It supports singlephase connection 
Nr  AC side network connector (rotor neutral). It supports singlephase connection 
Inputs
Name  Description  Unit 

Tmec_i  Load torque signal if load control is external 
Outputs
None
Sensors
Name  Description  Unit 

Flux0r1  Zero sequence rotor Flux of cage 1  V.s 
Flux0s  Zero sequence stator flux  V.s 
Fluxdr1  daxis rotor flux of cage 1  V.s 
Fluxdr2  daxis rotor flux of cage 2  V.s 
Fluxds  daxis stator flux  V.s 
Fluxm  Mutual magnetization flux  V.s 
Fluxmd  daxis mutual magnetization flux  V.s 
Fluxmq  qaxis mutual magnetization flux  V.s 
Fluxqr1  qaxis rotor flux of cage 1  V.s 
Fluxqr2  qaxis rotor flux of cage 2  V.s 
Fluxqs  daxis stator flux  V.s 
I0r1  Zero sequence rotor current of cage 1  A 
I0s  Zero sequence stator current  A 
Iar1  Phase A rotor current (cage 1)  A 
Iar2  Phase A rotor current (cage 2)  A 
Ias  Phase A stator current  A 
Ibr1  Phase B rotor current (cage 1)  A 
Ibr2  Phase B rotor current (cage 2)  A 
Ibs  Phase B stator current  A 
Icr1  Phase C rotor current (cage 1)  A 
Icr2  Phase C rotor current (cage 2)  A 
Ics  Phase C stator current  A 
Idr1  daxis rotor current of cage 1  A 
Idr2  daxis rotor current of cage 2  A 
Ids  daxis stator current  A 
Im  Magnetization current  A 
Imd  daxis magnetization current  A 
Imq  qaxis magnetization current  A 
Iqr1  qaxis rotor current of cage 1  A 
Iqr2  qaxis rotor current of cage 2  A 
Iqs  qaxis stator current  A 
Ps  Active power  W 
Qs  Reactive power  VAr 
Slip  slip  
Tmec  Mechanical torque  Nm 
Tmec_i  Load torque  Nm 
V0r1  Zero sequence rotor voltage of cage 1  V 
V0s  Zero sequence stator voltage  V 
Vdr1  daxis rotor voltage of cage 1 (Not used for squirrel cage machine but useful for future wound rotor machine)  V 
Vds  daxis stator voltage  V 
Vqr1  qaxis rotor voltage of cage 1 (Not used for squirrel cage machine but useful for future wound rotor machine)  V 
Vqs  qaxis stator voltage  V 
Wm  Mechanical speed  rad/s 
Wr  Electrical speed  rad/s 
Wrpm  Mechanical speed  rpm 
Additional Information & Model Equations
Model Equations
The equations below describe the double cage machine with mutual coupling between the two cages (due to leakage flux), in the arbitrary reference frame dq0 and where all parameters and variables are referred on the stator side.
The equations of the electrical system are given by:
Electrical Equations
Mathblock  

 
\begin{array}{1} v_{q s}=R_{s} i_{q s}+\omega \psi_{d s}+\frac{d \psi_{q s}}{d t} \\v_{d s}=R_{s} i_{d s}\omega \psi_{q s}+\frac{d \psi_{d s}}{d t} \\v_{0 s}=R_{s} i_{0 s}+\frac{d \psi_{0 s}}{d t} \end{array} 
Electrical Equations of the Rotor Cage
Mathblock  

 
\begin{array}{1} \\v_{d r1}=R_{r 1} i_{d r 1}\left(\omega\omega_{r}\right) \psi_{q r 1}+\frac{d \psi_{d r 1}}{d t} \\v_{d r2}=R_{r 2} i_{d r 2}\left(\omega\omega_{r}\right) \psi_{q r 2}+\frac{d \psi_{d r 2}}{d t} \\v_{q r1}=R_{1} i_{q r 1}+\left(\omega\omega_{r}\right) \psi_{d r 1}+\frac{d \psi_{q r 1}}{d t} \\v_{q r2}=R_{r 2} i_{q r 2}+\left(\omega\omega_{r}\right) \psi_{d r 2}+\frac{d \psi_{q r 2}}{d t} \end{array} 
Stator flux equations
Mathblock  

 
\begin{array}{l}{\psi_{q s}=L_{s q} i_{q s}+L_{m q} i_{q r 1}+L_{m q} i_{q r 2}} \\ {\psi_{d s}=L_{s d} i_{d s}+L_{m d} i_{d r 1}+L_{m d} i_{d r2}} \\ {\psi_{0 s}=l_{\sigma s} i_{0 s}} \end{array} 
Rotor flux equations
Mathblock  

 
\begin{array}{l}{\psi_{q r 1}=L_{r q 1} i_{q r 1}+L_{m q} i_{q r 2}+L_{m q} i_{q s}+L_{m r}\left(i_{q r 1}+i_{q r 2}\right)} \\ {\psi_{d r 1}=L_{r d 1} i_{d r 1}+L_{m d} i_{d r 2}+L_{m d} i_{d s}+L_{m r}\left(i_{d r 1}+i_{d r 2}\right)} \\ {\psi_{q r 2}=L_{r q 2} i_{q r 2}+L_{m q} i_{q r 1}+L_{m q} i_{q s}+L_{m r}\left(i_{q r 1}+i_{q r 2}\right)} \\ {\psi_{d r 2}=L_{r d 2} i_{d r 2}+L_{m d} i_{d r 1}+L_{m d} i_{d s}+L_{m r}\left(i_{d r 1}+i_{d r 2}\right)}\end{array} 
where
Mathblock  

 
\begin{array}{l} {L_{s q}=L_{m q}+l_{\sigma s}} \\ {L_{s d}=L_{m d}+l_{\sigma s}} \\ {L_{r q 1}=L_{m q}+l_{\sigma r 1}} \\ {L_{r d 1}=L_{m d}+l_{\sigma r 1}} \\ {L_{r q 2}=L_{m q}+l_{\sigma r 2}} \\ {L_{r d 2}=L_{m d}+l_{\sigma r 2}} \end{array} 
The electromagnetic torque and the mechanical equation are described as follows:
Mathblock  

 
\begin{array}{l}{T_{e m}=\frac{3}{2}\left(\frac{p}{2}\right)\left(\psi_{q r} i_{d r}\psi_{d r} i_{q r}\right)} \\ {J \frac{d \omega_{m}}{d t}=T_{e m}T_{l o a d}K_{D} \omega_{m}}\end{array} 
Note: In the case of a onecage or wound rotor machine the equations for the second cage are not used and the mutual induction between cages is zero. The d and q axis rotor voltages 1 are zero and not zero respectively for the onecage and wound rotor machine.
Limitations
This model does not account for iron losses.
References
Analysis of Electric Machinery and Drive Systems, 2nd edition, Paul C. Krause, Oleg Wasynczuk, Scott D. Sudhoff