VFD Soft-Start Comparison

Side-by-side comparison of direct-on-line (DOL) starting vs. variable-frequency drive (VFD) soft-starting on the same induction motor. Adjust the ramp time, the V/Hz boost, and the DOL inrush multiplier to see how each method shapes the rotor-speed and stator-current transients during start-up.

Pedagogical tool. This page is an independent re-implementation based on the experimental setup described in Turki Alzahrani et al., VFD for Induction Motor, MATLAB File Exchange #182697 (2025). The original Simulink model is closed-source; this tool uses a reduced-order analytical model and is not a port.

See the Model assumptions panel at the bottom of the page for the equations, default parameters, and known limitations.

Direct-on-Line (DOL) Start

Full voltage applied at t = 0. The motor starts at slip s ≈ 1 (locked rotor) and accelerates on the natural torque-speed curve. Inrush is high (typically 5–7× rated for a NEMA-B design-B induction motor).

Rotor speed (rad/s) Synchronous speed ωs Stator current (× rated)

Peak current

—

× rated

Settle time

—

s

Time now

—

s

VFD Soft-Start (V/Hz)

Frequency ramps linearly from 0 to fnom over the user-selected ramp time. Voltage tracks V/f ≈ const so air-gap flux stays near nominal. Synchronous speed ωs(t) follows the ramp, so the operating point stays on the low-slip side of the torque-slip curve — inrush drops.

Rotor speed (rad/s) Synchronous speed ωs(t) Stator current (× rated)

Peak current

—

× rated

Settle time

—

s

Time now

—

s

Side-by-Side Overlay

Rotor speed

Stator current

DOL VFD soft-start Synchronous speed ωs(t)

VFD Ramp

Time to ramp frequency from 0 to fnom.

Extra voltage at low frequency to compensate stator-resistance drop. 0% = pure constant V/f.

Motor

Motor + load inertia. Drives mechanical time constant.

Rated load as a fraction of rated torque. 0 = no load (worst-case for DOL — no opposing torque to limit acceleration).

DOL Starting Behavior

Typical values: NEMA A ≈ 3×, NEMA B ≈ 6×, NEMA C ≈ 6×, NEMA D ≈ 6–8×.

Pull-up torque at slip ≈ 1. NEMA B ≈ 1.5×, NEMA D ≈ 2.5×.

Speed:

Equations

Mechanical dynamics (shaft):

$$J \frac{d\omega}{dt} = T_{em}(\omega, t) - T_{load}(\omega)$$ $$T_{load}(\omega) = T_{rated} \cdot k_{load} \cdot \left(\frac{\omega}{\omega_{rated}}\right)^2$$

Quadratic (fan/pump-like) load by default. The exponent drops the load toward zero at standstill, so a no-load motor accelerates almost freely under the DOL torque curve.

Torque vs slip (Kloss curve):

$$T_{em}(s) = T_{max}\, \frac{2\, a\, (1-q)}{\frac{s}{s_{max}} + \frac{s_{max}}{s} + 2a}$$

s = (ωs − ω) / ωs is slip, smax ≈ 0.15–0.20 is slip at breakdown, Tmax ≈ 2.5·Trated.

VFD frequency ramp:

$$f(t) = f_{nom}\,\min\!\left(1, \frac{t}{t_{r}}\right)$$ $$\omega_s(t) = \frac{2\pi\, f(t)}{p}, \quad V(t) = V_{nom}\, \frac{f(t)}{f_{nom}}\,(1 + \beta\,\frac{f_{nom}-f(t)}{f_{nom}})$$

Constant V/f (β = 0) by default. β is the low-speed boost fraction from the slider.

Stator current envelope:

$$I_{stator}(s) \approx \frac{I_{mag}}{\sqrt{1 - \sigma^2}} + \frac{I_{rated}}{s_{max}}\, \mathrm{clamp}(s, 0, 1)$$

Magnetizing component + slip-dependent rotor-reflected component. At s = 1 (locked rotor) the second term gives I ≈ Ilr·Irated (locked-rotor multiplier from slider). At s → 0 the current is just magnetizing.

Model Assumptions and Limitations

Reduced-order model

  • Squirrel-cage induction motor, per-phase reduced to a Kloss torque-slip curve
  • Mechanical-only dynamics (no rotor-flux transient, no iron loss)
  • Scalar V/Hz open-loop (no current loop, no FOC, no DTC)
  • No DC-link dynamics, no SPWM switching — frequency is the input; the inverter is implicit

Default parameters

  • 1.5 kW, 50 Hz, 2 pole pairs (typical European/Asian industrial motor)
  • NEMA design-B: locked-rotor current 6× rated, starting torque 1.5× rated, breakdown 2.5×
  • Quadratic load (fan/pump), default 60% of rated at rated speed
  • Total inertia J = 0.05 kg·m² (small motor + light load)

What this tool is good for

  • Side-by-side visualization of DOL vs VFD soft-start
  • Sensitivity to ramp time, boost, load, inertia, motor design
  • Teaching the "why" of soft-starting (low-slip operating point)

What this tool is NOT good for

  • Predicting exact current/speed traces of a real motor
  • Sizing protective devices (use manufacturer curves)
  • Replacing a vendor-specific VFD commissioning tool
  • Studying sub-transient switching effects, harmonics, or thermal behavior

References: Fitzgerald, Kingsley & Umans, Electric Machinery 7th ed., Ch. 7 (per-phase equivalent circuit, Kloss curve). Krause, Wasynczyn & Sudhoff, Analysis of Electric Machinery and Drive Systems 3rd ed., Ch. 4 (dq-frame derivation; reduced to scalar for this tool). NEMA MG-1 design-B standard values for locked-rotor current, starting torque, and breakdown torque.