Tech:DeltaTPIM

=Three Phase Induction Motors=

Implement three phase induction motor dynamic phasor model into GridLAB-D.

Synopsis
This work will incorporate the ability to model three phase induction motor and other more advanced power flow capabilities into GridLAB-D.

Dynamic Phasor Equations
$$ V_{p} = [r_{s}+j.w_{s}.L_{s} +L_{s} \frac{\mathrm{d} }{\mathrm{d} t} ]I_{P}^{s}+ [j.w_{s}.L_{m} +L_{m} \frac{\mathrm{d} }{\mathrm{d} t}]I_{P}^{r} $$

$$0 = [r_{r}+j.w_{s}.L_{r} +L_{r} \frac{\mathrm{d} }{\mathrm{d} t} ]I_{P}^{r}+ [j.w_{s}.L_{m} +L_{m} \frac{\mathrm{d} }{\mathrm{d} t}]I_{P}^{s}- j.\Omega_{r,0} \frac{\mathrm{P} }{\mathrm{2}} [L_{m} I_{P}^{s}+ L_{r}.I_{P}^{r}] - j.\Omega_{r,2}  \frac{\mathrm{P} }{\mathrm{2}} [L_{m} I_{n,s}^{*}+ L_{r}.I_{n,r}^{*}]$$

$$V_{n}^{*} = [r_{s} - j.w_{s}.L_{s} + L_{s} \frac{\mathrm{d} }{\mathrm{d} t} ]I_{n,s}^{*}+ [-j.w_{s}.L_{m} +L_{m} \frac{\mathrm{d} }{\mathrm{d} t}]I_{n,r}^{*}$$

$$ 0 = [- j.w_{s}.L_{m} +L_{m} \frac{\mathrm{d} }{\mathrm{d} t}]I_{n,s}^{*} + [r_{r} - j.w_{s}.L_{r} + L_{r} \frac{\mathrm{d} }{\mathrm{d} t} ]I_{n,r}^{*} - j.\Omega_{r,0} \frac{\mathrm{P} }{\mathrm{2}} [L_{m} I_{n,s}^{*} + L_{r}.I_{n,r}^{*}] - j.\Omega_{r,2}^{*} \frac{\mathrm{P} }{\mathrm{2}} [L_{m} I_{P}^{s}+ L_{r}.I_{P}^{r}] $$

$$ J.\frac{\mathrm{d} }{\mathrm{d} t}.\Omega_{r,0} = \frac{\mathrm{P} }{\mathrm{2}}.L_{m}(I_{P}^{s}.I_{P}^{r} + I_{n,s}^{*}.I_{n,r}^{*})- B.\Omega_{r,0} - T_{L} $$

$$ J.\frac{\mathrm{d} }{\mathrm{d} t}.\Omega_{r,2} = \frac{\mathrm{P} }{\mathrm{4}}.L_{m}(I_{P}^{s}.I_{n}^{r} + I_{n,s}^{*}.I_{p,r})-( B + j. 2.J.w_{s}).\Omega_{r,2} $$

Case 1
Case 1 simulates a step change in mechanical torque at constant grid voltage. A torque step is applied at time t=10 sec. Fig 1. demonstrates constant quadrature axis voltage. Fig.2 indicates step change in torque. Following are the simulation results. Fig. 3 shows the impact of a step change in torque on direct axis current. Fig. 4 shows the impact of a step change in torque on quadrature axis current. Fig. 5 and Fig.6 show dc and second harmonic component of speed respectively.













Case 2
Case 2 simulates a step change in grid voltage. A constant load torque is considered. Following are the simulation results. Fig. 9 shows impact of step change in voltage on direct axis current. Fig. 10 shows impact of step change in voltage on quadrature axis current. Fig.11 and Fig.12 shows dc and second harmonic component of speed respectively.













=References=

P. Krause et al. Analysis of electric machinery and drive systems. Vol. 75. John Wiley & Sons, 2013.