Induction Motors¶

Pulsim ships a three-phase squirrel-cage induction motor (IM) as part of the v1.5 Phase 2 physics-parity release. The model is a 5th-order dq stationary-frame representation that plugs into the same observer pattern already used by the PMSM and BLDC motors.

Quick start¶

import pulsim as p

# 4 kW / 400 V / 50 Hz / 4-pole nameplate → starting parameter set.
kw = p.im_parameters_from_nameplate(P_rated_W=4_000.0,
                                          V_LL_V=400.0, f_Hz=50.0,
                                          pole_pairs=2)
diag = kw.pop("_diagnostics")
print(f"Synchronous speed: {diag['omega_sync_rad_s']:.2f} rad/s")

b = p.CircuitBuilder()
# ... 3-φ source + R_leak on the star point ...

motor = p.add_induction_motor(
    b, name="IM",
    phase_nodes=("a", "b", "c"),
    neutral_node="n",
    T_load=0.0,
    **kw,
)

obs, b_extra = p.make_induction_motor_observer(b, motor, dt=DT)
res = p.simulate(b, t_end=1.5, dt=DT,
                  switch_fn=lambda t: p.SwitchStateMask(0),
                  step_observer=obs, b_extra_fn=b_extra)

print(f"Final mechanical speed: {motor.mech.omega_rad_s:.2f} rad/s")
print(f"Final rotor flux: |ψ_r| = {math.hypot(motor.psi_r_alpha_Wb, motor.psi_r_beta_Wb):.3f} Wb")

End-to-end runnable example: examples/scripts/run_im_direct_online_start.py. On a 4 kW machine alimentada por 230 V RMS @ 50 Hz the script reaches the synchronous speed of 1500 rpm at 0 % slip in ~1.5 s sim / 0.2 s wall-clock (Apple M-series).

Model¶

Stationary-frame αβ rotor-flux state equations (Krause §6.6):

\[ \begin{aligned} \frac{d\psi_{r\alpha}}{dt} &= -\frac{1}{T_r}\psi_{r\alpha} + \frac{L_m}{T_r}i_{s\alpha} - \omega_e\psi_{r\beta} \\ \frac{d\psi_{r\beta}}{dt} &= -\frac{1}{T_r}\psi_{r\beta} + \frac{L_m}{T_r}i_{s\beta} + \omega_e\psi_{r\alpha} \\ T_e &= \frac{3}{2}p\frac{L_m}{L_r}\left(i_{s\beta}\psi_{r\alpha} - i_{s\alpha}\psi_{r\beta}\right) \end{aligned} \]

where \(T_r = L_r/R_r\) is the rotor time constant, \(\omega_e = p \cdot \omega_m\) is the electrical speed, and \(p\) is the number of pole pairs.

Topology decomposition¶

Each phase contributes \(R_s + \sigma L_s\) in series with a modulated "back-EMF" source between the phase terminal and the star neutral, where \(\sigma = 1 - L_m^2/(L_s L_r)\) is the leakage factor and \(\sigma L_s\) is the stator transient inductance. The mutual-coupling dynamics live inside the observer (the \(L_m/L_r \cdot d\psi_r/dt\) term injected via b_extra); the MNA matrix sees only the linear \(\sigma L_s\).

This split lets us reuse the existing linear-inductor path in the kernel without adding a coupled-inductor device — the same architectural trick the PMSM / BLDC observers use for back-EMF injection.

Parameter identification¶

im_parameters_from_nameplate(P_rated_W, V_LL_V, f_Hz, ...) derives a starting (R_s, L_s, R_r, L_r, L_m, J) set from the motor nameplate using NEMA-B rules of thumb. The split is approximate (R_s : R_r : X_σs : X_σr : X_m ≈ 0.10 : 0.05 : 0.08 : 0.08 : 0.95 of the rated per-phase impedance); precise design requires a locked-rotor + no-load test or a manufacturer- provided equivalent-circuit.

The returned dict also carries _diagnostics with the synchronous speed, rated torque, rated current, and per-phase impedance for sanity checks.

Operating modes covered¶

Mode	What works	Showcase
DOL start (direct-on-line)	✅ — drives by 3 sine sources at nominal V/f	`run_im_direct_online_start.py`
V/f open-loop ramp	⚠️ partial — DOL serves as a proxy; explicit V/f ramp showcase deferred	n/a
IFOC closed-loop	⚠️ planned for v1.5.2 — needs the BlockChain wiring with Park/Clarke/PI/SVM	n/a
Sensorless MRAS speed observer	⚠️ observer present (`FluxMRASObserver`) with `Rr` + leaky-integrator parameters; bootstrap for low-speed operation needs more tuning	n/a

Known limitations (v1.5)¶

No C++ port — the observer is pure-Python. Performance is fine at v2's typical sub-µs dt (the IM observer adds ~5 µs / step on M-series), but a port is queued for v1.6.0 if profiling shows a hotspot.
No YAML support — the device_type: induction_motor parser entry is queued for v1.6.0. Use the Python API meanwhile.
Synchronous-speed singularity — at exactly slip = 0 the rotor flux dynamics decay with no driving term. In practice this is fine because any load forces a non-zero slip, but the helper's s_floor = 1e-6 clamp is documented in the docstring.