Motor Starting Calculator: DOL vs Star-Delta vs Soft Starter

Full-load line current is $I_n=P_{shaft}/(\sqrt{3}U\eta\cos\varphi)$; rated shaft torque is $T_n=P_{shaft}/\omega_n$. The nameplate-current override takes precedence. Physical unit conversions are explicit.

DOL torque ratio $r_T$ and current ratio $q$ use shape-preserving piecewise cubic Hermite interpolation (PCHIP) through 0, 50%, 80%, 95% and 100% of rated speed. The curve passes through every input point, preserves monotonicity within each interval and has a continuous first derivative. Pull-up and breakdown regions are smooth; the separate star-delta and autotransformer switching factors retain their real changeover jumps. The displayed start ends at 95% rated speed, below synchronous speed. The default PF profile is derived from an induction-motor power balance, rather than chosen independently. Let $x=n/n_r$, $h=1/(1-s_r)$ and $B=\sqrt{3}UI_n/P_{shaft,r}$. A simple positive-loss model is

The air-gap term is torque times synchronous angular speed. Fit $c_{Cu}=(Bq_0\cos\varphi_0-h r_{T0})/q_0^2$ at locked rotor and $c_{other}=B\cos\varphi_r-h-c_{Cu}$ at rated operation. Both coefficients must be nonnegative. Then $\cos\varphi(x)=[h r_T+c_{Cu}q^2+c_{other}x^2]/(Bq)$. This is an illustrative loss model, not a fitted equivalent circuit or measured motor.

Alternatively, enter manufacturer PF points at the same speed knots, also joined by PCHIP. The available torque curve is normalized by rated shaft torque. Electromagnetic torque must be at least the available shaft torque before rotational losses, so a necessary induction-motor bound is $P_{in}\geq T_{shaft}\omega_s$. Check this bound at every speed, including standstill, together with $P_{in}\leq\sqrt{3}UI$. Rated slip is therefore required in both PF modes. Checking $T\omega_m$ alone would omit rotor copper loss. This lower bound does not estimate every mechanical or stator loss; see Andy Knight's torque derivation. Each power difference is a polynomial of degree at most six on each cubic interval. Recover its coefficients at seven points in a local −1…1 coordinate, then evaluate both endpoints and every real root of its derivative inside the interval. This checks between knots as well as at them, to numerical precision. An invalid PF is bounded only inside the network arithmetic to avoid undefined square roots while the input error withholds results.

At equal starter-input voltage, star line current is one third of DOL. Its torque factor defaults to one third and may be reduced to 0.25 as a practical allowance. An ideal autotransformer tap $a$ gives supply-current and torque factors $a^2$; motor-lead current is supply current divided by $a$. Both switch to full voltage at the selected speed.

Schneider's projected drop is $\Delta U=\sqrt{3}I(R\cos\varphi+X\sin\varphi)$. For nominal DOL current $I_0$, current factor $g$ and projected series impedance $z$, solve $u=1/[1+\sqrt{3}gI_0z/U]$, $I=gI_0u$ and $T=T_{DOL}g_Tu^2$. Bus dip uses source impedance only; motor voltage includes the feeder. PF follows the chosen motor model.

The soft starter uses $I=\min(I_{limit},I_{DOL,available})$ and $T=T_{DOL,nominal}[I/I_{DOL,nominal}]^2$: an ideal immediate current-limit envelope.

Integrate $dt=Jd\omega/(T_m-T_L)$ by adaptive Simpson quadrature, splitting at every motor-curve knot, changeover and bounded-search torque minimum. Each initial interval is at most 0.5% of rated speed. For each panel, compare one Simpson estimate $S$ with two half-panel estimates $S_2$; estimate error as $|S_2-S|/15$ and use $S_2+(S_2-S)/15$. Refine until panel error is at most $10^{-7}\Delta x+10^{-5}|S_2|$ in dimensionless time. The total estimated time error must also be no more than $9.5\times10^{-8}t_{scale}+1.01\times10^{-5}t_{start}$. Limit refinement to 18 levels and 60,000 integrand samples per method. If the criterion or work limit fails, withhold that method's time and traces and show Numerical limit. Evaluate each side of changeover using its own fixed starter stage, so quadrature never blends the real jump. Feasibility checks every knot, both changeover limits, and bounded minima in each half-segment. Margins within $10^{-8}$ of rated torque count as zero. Nonpositive margin means no complete start. Each method also loses its acceleration prediction and torque curve if total projected drop exceeds 20%, regardless of animation selection.

Charts merge every feasible trajectory's own node times, exact completion times and the instants immediately before changeover. Their duration is independent of playback. Cumulative times and rotor travel are cached; animation updates interpolation and the 48-shape schematic only.

Feeder resistance uses hot-conductor values 23.7 Ω·mm²/km for copper or 37.6 for aluminium, with editable reactance. Running drop uses FLC and rated PF. Overload references are FLC in the supply line or FLC/√3 inside a star-delta winding loop.

• Balanced three-phase, fixed-frequency squirrel-cage motor; one start from rest. Supply voltage is the unloaded Thevenin voltage referred to the motor-voltage level.
• Defaults describe an illustrative 30 kW fan drive with 2% rated slip. They are not a measured motor characteristic or an approved cable installation. The power-balanced PF profile matches the entered locked-rotor and rated active power with nonnegative modeled losses.
• With nameplate current enabled, the default loss model infers rated losses from shaft power, nameplate current and rated PF; the efficiency input is used only for the alternative power-derived FLC.
• The motor curve represents available shaft torque. The air-gap check uses it as a lower bound on electromagnetic torque; real rotational losses require additional air-gap power. The positive-loss PF model is an approximation, not a full equivalent circuit.
• All torque and inertia are referred to the motor shaft. Reflect geared inertia by the square of load speed divided by motor speed.
• The cable is upstream of the starter. Starter-to-motor leads, including six star-delta winding leads, are excluded.
• The soft starter is in line. Inside-delta soft-starter topology is not simulated.
• Star-delta requires six accessible leads and delta operation at the supply voltage; for example, a suitable 400/690 V Δ/Y motor on 400 V. A 230/400 V Δ/Y motor must not run in delta on 400 V.
• Physical inputs and scalar result units support the metric/US switch. Chart labels state their plotted units.

Preliminary comparison for balanced low-voltage three-phase motors, 100–1100 V. Projected voltage drop is a small-drop approximation. A separate status and warning apply to each displayed method. Above 20% total source-plus-feeder drop, that method's time, time traces and torque-speed curve are withheld; its initial current/torque and bus-dip entries remain approximate screening values identified by the status.

Power-consistent data are necessary but do not establish that an entered curve describes a real motor. Use one manufacturer dataset for current, torque and PF, or validate the default loss approximation against test data. Near zero accelerating torque, small curve errors cause large time errors. Numerical convergence does not remove this sensitivity: an estimated integration error is shown in the calculation steps, and unconverged times are withheld. The optimizer searches the smooth half-segments and explicitly checks every knot and both changeover limits; a margin of 10⁻⁸ rated torque or less is treated as zero.

The model excludes asymmetric first-cycle inrush, saturation, phase-angle harmonics, open-transition reconnection peaks and dead time, transformer magnetizing current/losses, generator voltage recovery, other changing loads, mechanical resonance, thermal accumulation and repeat-start duty. Reduced-stage stall means no complete start for the selected schedule, not necessarily zero rotor speed.

Times end at 95% of nameplate rated speed. Each feasible chart includes that exact endpoint even for millisecond starts. The schematic holds the endpoint afterward. Playback has a separate 6–120 s viewing window; the charts fit the computed start durations without that minimum. No complete-start animation is shown for stalled or invalid methods.

Running feeder drop and entered continuous ampacity are screening checks only. Check starting thermal duty, fault withstand, protective conductors, disconnection times, local rules and cable data separately. Ampacity and drop limits are user inputs, not standard tables.

Installation work belongs to a qualified person. Relay position, trip class, starter duty and short-circuit coordination require manufacturer-tested combinations. This calculator does not certify compliance with IEC 60947-4-1, IEC 60947-4-2 or wiring regulations. Manufacturer guidance was consulted on 26 October 2026; check against the standards and rules in force.