SCIM/DFIM with saturation - Model Formulation

Induction Machine Electrical Model

Fig.1. Implementation block diagram (Squirrel-cage/Doubly-fed induction motor)

1. Motor modelling equations

The stator and rotor voltage equations of an induction motor in the stationary (stator reference frame) reference frame can be described by the equations (1)-(4).

Equations (1)-(4) can be represented in matrix form by the equation (5).

The stator and rotor flux linkages can be expressed as equation (6).

Note that the stator and rotor flux linkages are calculated by using the equation (5) and that the stator and rotor currents are calculated by using the equation (6).

2. Magnetizing flux linkage calculation

The magnetizing flux linkages ψ_m are calculated from the stator and rotor flux linkages by using equations (7) and (8).

where

ψ_mq & ψ_md = q & d-axis magnetizing flux linkages,
L_aq = q-axis inductance, such that L_aq= (L_m L_ls L_lr^‘)/(L_m L_ls + L_m L_lr^‘+L_lsL_lr^‘))
L_ad = d-axis inductance, such that L_ad= (L_m L_ls L_lr^‘)/(L_m L_ls + L_m L_lr^‘+L_lsL_lr^‘)) ,
L_ls = Stator leakage inductance,
L_lr^’ = Rotor leakage inductance (referred to stator side),
L_m = Magnetizing inductance.

Thermal modelling of stator and rotor resistances

where

is the temperature difference from the initial temperature of the stator and rotor windings ,
R_snom = stator resistance at initial temperature ,
R_rnom'  = rotor resistance at initial temperature ,
R_s      = stator resistance at temperature ,
R‘_r      = rotor resistance at temprature ,
α_cond   = temperature coefficient of resistance of the material.

Reference frame transformation

The transformations between the three-phase (abc) reference frame, the stationary dq0 (namely the αβ0 reference frame) and the dq0 rotating reference frame and their inverses can be represented by the following equations. The estimated flux angle can be calculated from the stator flux, the rotor flux, or the air-gap flux.

abc to dq0 (stator side)

abc to dq0, with a stationary reference frame

dq0 to abc (stator side)

dq0 to abc, with a stationary reference frame

abc to dq0 (rotor side)

abc to dq0, with a stationary reference frame

dq0 to abc (rotor side)

dq0 to abc, with a stationary reference frame

αβ to dq transformation, with or without an offset :

dq to αβ transformation, with or without an offset :