Starting induction motor with variable frequency

Starting an induction motor from a variable frequency supply (low frequency at first, then raised) gives a high starting torque with low starting current, because at low frequency the synchronous speed is low and the rotor slip frequency is small. But if only frequency is reduced while voltage is kept constant, the motor is over-fluxed and draws a very high magnetising current.

What happens at low frequency

Stator emf:

$$V \approx E_1 = 4.44 f N_1 k_w \phi \Rightarrow \phi \propto \frac{V}{f}$$

• Constant V, low f: $\phi$ becomes many times rated; the core saturates, the magnetising current and iron loss rise sharply, the motor overheats. Also reactances $X = 2\pi f L$ fall, so the current rises further.
• High slip at start on full frequency: at 50 Hz direct start, $s = 1$, rotor current is 5–7 times rated while torque is small (rotor pf low).
• Stator resistance effect: at low frequency $R_1$ becomes comparable to the reactance; with pure V/f, the $I_1R_1$ drop is a large fraction of $V$, so flux and maximum torque fall:

$$T_{max} = \frac{3}{2\omega_s}\cdot\frac{V^2}{R_1 + \sqrt{R_1^2 + (X_1 + X_2')^2}}$$

At rated frequency $R_1 \ll X$ and $T_{max} \propto (V/f)^2$; at low $f$, the $R_1$ terms do not reduce with $f$, so $T_{max}$ drops.

Technique to overcome these problems

1. Constant V/f control: change voltage in proportion to frequency, $V/f$ = constant, so flux stays at rated value and $T_{max}$ is (nearly) the same at every frequency.
2. Low-frequency voltage boost (IR compensation): add a fixed voltage at low frequency,

$$V = V_0 + k f, \quad V_0 \approx I_1 R_1$$

so that $E_1/f$, not $V/f$, is held constant. 3. Start at a frequency giving maximum torque at standstill. Slip for maximum torque (approx.) $s_m = R_2'/X_2'$. With $X_2' \propto f$, choose the start frequency $f_{st}$ such that $s_m = 1$:

$$f_{st} = f_r\,\frac{R_2'}{X_{2r}'}$$

The motor then starts with $T_{max}$ at modest current. The frequency is ramped up (soft start) so that slip speed $s\omega_s$ stays small and current stays near rated. 4. Closed-loop slip/current limit: the controller limits slip frequency $\omega_{sl}$; since $T \propto \phi^2\omega_{sl}$ and $I$ depends on $\omega_{sl}$, the motor accelerates at controlled torque and current.

Thus V/f control with boost and a frequency ramp gives a smooth start with high torque and low current, which a direct-on-line start cannot give.