Induction Motor Design & Equivalent Circuit Calculator

The model combines a linear single-cage equivalent circuit with a fundamental-flux sizing check. All impedances are per actual winding phase, referred to the stator. Star uses $V_\mathrm{ph}=V_\mathrm{LL}/\sqrt3$; delta uses $V_\mathrm{ph}=V_\mathrm{LL}$ and $I_\mathrm{line}=\sqrt3|I_1|$.

1. Form $Z_s=R_1+jX_1$, $Y_m=1/R_c+1/(jX_m)$ and $Z_r=R'_2/s+jX'_2$. Solve the parallel network for $I_1$, internal voltage $E_g$ and referred rotor current $I'_2$. Disabling the core branch sets its conductance to zero.
2. Calculate $P_g=3|I'_2|^2R'_2/s$, $P_\mathrm{Cu,r}=sP_g$, converted power $(1-s)P_g$, and $T_e=P_g/\omega_s$. Subtract mechanical and stray-load losses to get shaft output. The five-loss total closes the real-power balance. Kumari (2025), PDF pp. 131–133, supplies the circuit equations and Thevenin peak-slip expression; the extra loss branch and power accounting are derived here from circuit conservation.
3. Use $E_g=\sqrt2\pi fN k_w\Phi$ and integrate a sinusoidal radial field over one pole to obtain $\hat B_g=\Phi P/(2DL)$. Tooth envelopes follow flux per slot pitch divided by effective iron tooth area. Rotor-surface field uses the rotor diameter so pole flux is conserved. Each stator yoke carries half the pole flux. Required tooth widths and yoke thickness use the selected material-dependent field limits.
4. Estimate the gap-only excitation from $F_g=\hat B_g k_Cg/\mu_0$ and the fundamental three-phase winding MMF. This excludes iron MMF and is a consistency check, not a replacement for a B–H iteration. Binder, SS 2017, PDF p. 90, eq. 4.4.1-3 provides the winding MMF relation. The sizing equations are independently derived here from Faraday's law and flux conservation, consistent with the general method in Pyrhönen et al.
5. Catalogue mode minimizes relative residuals in shaft power, power factor, efficiency and locked-rotor current. It uses two deterministic starts of a damped finite-difference least-squares iteration in log parameters; positivity and an imposed leakage split reduce the problem to four unknowns. This implementation follows the identification principle described by Haque and Kumari; it does not reproduce either author's optimizer. The displayed maximum residual is a fit diagnostic.
6. Stray-load loss is a user-calibrated lumped estimate, $P_\mathrm{sll}=P_\mathrm{ref}(|I'_2|/I_\mathrm{ref})^2$, allocated after fundamental power conversion. Hagen (2014), pp. 132–137, explains why detailed additional losses require harmonic fields, tooth pulsations and inter-bar effects. This calculator does not implement KLASYS or claim its accuracy. Binder, PDF p. 88, separates core, winding, cage, mechanical and additional losses.

Catalogue inputs also obey the necessary energy bound $\eta_N < 1-s_N$: shaft output cannot exceed $(1-s_N)P_g$, and input power is at least $P_g$ (Binder, §4.2, PDF p. 84). The input guard allows 0.05 percentage points, half a 0.1-percentage-point reporting increment, solely for catalogue rounding; this is not an allowance for model or measurement error.

Torque and current sweeps share an adaptive slip grid: a broad interval from standstill, a dense shoulder around peak torque, and a logarithmic tail extending four decades below the exact peak slip. The exact motoring peak is always included, even when rotor resistance makes it much narrower than a uniform speed grid.

• Balanced sinusoidal three-phase supply; constant hot winding resistances and reactances at the entered frequency; positive motoring slip. Changing frequency requires new circuit parameters.
• One cage, no skin-effect or leakage-saturation correction. Catalogue identification fixes the stator leakage share and treats the entered losses as known. Identified parameters may absorb unmodeled losses and need not be unique.
• Core loss is represented by a linear shunt resistance. Friction/windage is constant at the entered operating point. The squared-current stray-loss law is an explicit engineering approximation, not a standard-prescribed allowance.
• Magnetic sizing uses an ideal radial fundamental, uniform effective stack length and stacking factor, user-supplied winding and Carter factors, negligible slot flux, no skew or leakage correction to the pole flux. Tooth results are peak envelopes; local tooth-tip fields can be higher.
• The circuit parameters do not change automatically when dimensions, turns or field limits change. Iterate the circuit separately after a geometry redesign.
• Defaults: circuit values from Kumari's rounded GA example; dimensions, core resistance and additional loss estimates chosen here for an illustrative preliminary concept. The reference cases disable losses omitted by that thesis model.
• The rotating drawing is an original schematic. The angle advances ten electrical cycles; rotor angle is $(1-s)\theta_e/p$. The field chart shows the stator-coordinate fundamental. The mechanical air gap is exaggerated and slot marks may be simplified at high counts.
• Radial arrow sampling uses at least eight points per pole pair (24–96 arrows over the supported pole counts). Arrow depth and stroke are reduced as sampling density increases to keep adjacent arrowheads distinct; lengths show normalized field shape, not a fixed physical length scale.

For preliminary steady-state screening of balanced three-phase single-cage motors and educational circuit studies. Catalogue fitting is restricted to rated slip between 0 and 20%; normal operation is on the low-slip side of peak torque. A fit over 3% requires reviewing the inputs or choosing a richer model. Even a small residual does not validate starting performance of deep-bar or double-cage motors.

The field limits are user design targets, not universal saturation criteria. Use the actual lamination B–H and loss curves to complete the magnetic design. Carter factor and tooth-tip saturation require separate slot analysis. The tool flags high loading and an excitation inconsistency, but does not solve nonlinear fields.

Torque–speed curves give fundamental electromagnetic torque. Mechanical and stray losses affect the selected shaft operating point; these curves are not a continuous thermal rating, acceleration model or assurance that the motor will start a particular load. For high slip, harmonics, inverter supply or appreciable saturation, use detailed analysis and tests. No efficiency class or standards compliance is assigned.

The rated efficiency must satisfy the slip-dependent upper bound even if the fitted residual is small. Correct speed, efficiency, frequency or pole count when this fails. The fixed 0.05-percentage-point input allowance assumes efficiency rounded to one decimal place.