Effect of Change in Voltage and Frequency

 Effect of Change in Voltage and Frequency

Let us see the effect of change in voltage and frequency on the torque-slip characteristics of an induction motor. This effect can be studied by analyzing two cases as,

Case 1 : Halving the applied voltage, keeping frequency normal.

When the motor is running with slip s, the torque is,

Now standstill e.m.f. E₂ is proportional to the supply voltage.

Generally on full load, slip s is very small hence (sX₂)² << R₂² hence neglecting it

If supply voltage is made half, then the torque will reduce by the factor (1/4), in the running condition. The slip at which Tmax occurs remains same but the value of Tmax reduces. The corresponding speed-torque characteristics are shown in the Fig. 5.15.1.

Case 2 : Halving both the applied voltage and frequency

For an induction motor, the air gap flux is given by,

Thus if f is changed, air gap flux also changes. This may result into saturation of stator and rotor cores. Such a saturation may leads to sharp increase in the current. But if (V/f) ratio is maintained constant, then air gap flux remains constant. Thus when both are halved air gap flux remains constant but as frequency is reduced, the shape of torque-slip characteristics remains same.

Let     V_n = Normal voltage, f_n = Normal frequency

V       = New voltage,     f = New frequency

V / f = constant  i.e. V_n/f_n = V/f   i.e. V = f / f_n Vn .

As frequency is changed, the nominal rotor standstill reactance referred to stator also changes.

X_2n = Nominal rotor reactance

X₂  = New rotor reactance

X₂  = (f/f_n) X_2n

As frequency changes, N_s changes hence,

w_s = (f/f_n) w_sn

where, w_sn = Nominal speed    w_s = New speed

s_m = Nominal slip at maximum torque = R₂/X₂

As frequency is halved with V/f constant, the maximum torque remains same but s_m

increases while the starting torque increases. Hence the torque speed characteristics are as shown in the Fig. 5.15.2. 

Example 5.15.1 A 3-phase, 4 pole, 50 Hz squirrel cage induction motor has rotor leakage impedance of 1 + j2 Ω /Ph, standstill voltage of 100 V per phase driving a constant torque load at 0.03 slip, what is speed of the motor, if

i) Supply voltage is increased by 25 % and frequency is constant.

ii) Supply voltage is increased by 25 % and frequency is decreased by 25 %.

Solution : P = 4, f = 50 Hz, R₂ = 1 Ω, X₂ = 2 Ω, E_2ph = 100 V, s₁ = 0.03

Initially with rated voltage the torque is,

As voltage increases, E₂ increases as E_{2 ∝} V, due to transformer action. i) Torque constant, frequency constant, supply voltage increased by 25 %.

E₂ increases by 25 % = 100 + 0.25 × 100 = 125 V

Example 5.15.2 A 3-phase induction motor has operating p.f. of 0.85 at full load speed of 960 r.p.m. and at 400 V supply voltage. In case the supply voltage falls to 380 V, find the operating p.f. at the same full load torque.

Solution :

Example for Practice

Example 5.15.3 The rotor resistance and standstill reactance per phase of a 3 phase induction motor are 0.015 and 0.09 ohm respectively. At normal voltage full load slip is 3 %. Estimate the percentage reduction in stator voltage to develop the full load torque at half the full load speed. Also calculate the power factor.

[Ans.: 22.85 %, 0.308 lagging]

Review Question

1. Discuss briefly the effect on the speed-torque characteristics of a 3 phase induction motor produced by : i) Halving the applied voltage at normal frequency ii) Halving both the applied voltage and frequency.