Efficiencies of a D.C. Machine

Efficiencies of a D.C. Machine

AU: Dec.-07.09,15,19, May-09

• In case of a d.c. generator, following three efficiencies are defined.

i) Mechanical efficiency: It is the ratio of total power generated in armature to the total mechanical power input to the generator.

ii) Electrical efficiency: It is the ratio of total power supplied to the load to the total power generated in armature.

iii) Overall or commercial efficiency: This is the ratio of total power supplied to the load to the total mechanical power input to the generator. This is called efficiency of a d.c. machine which is generally obtained.

It can be seen that % η = % η_m × % η_e

The overall efficiency of a generator and motor are obtained as,

Such three efficiencies can be defined for a d.c. motor also.

1. Condition for Maximum Efficiency

In case of a d.c. generator the output is given by,

The efficiency is maximum, when the denominator is minimum. According to maxima-minima theorem,

Thus for the maximum efficiency, the condition is,

Variable losses = Constant losses

The graph of losses and efficiency against load current is shown in the Fig. 5.3.1.

2. Current at Maximum Efficiency

• From the condition of maximum efficiency, the current through the d.c. machine at the time of maximum efficiency can be obtained.

• For shunt machines: The I_sh is constant and the loss VI_sh is treated to be the part of constant losses. The variable losses are I_a²R_a.

• At maximum efficiency, I_a²R_a = P_i = (Stray + Shunt field losses)

• This is the armature current at maximum efficiency. Neglecting I_sh, I_a = I_L is the line current of the machine.

• For series machines: The current through series field is same as armature current which is same as line current. Hence the constant losses are only mechanical losses while the variable losses are the copper losses in armature as well as series field winding due to the armature current.

At maximum efficiency,

I_a² (R_a + R_se) = P_i = Mechanical losses

I_a = √P_i /R_a + R_se

• Let us study now the various methods of testing the d.c. motors from the losses and efficiency point of view.

Ex. 5.3.1 A 220 V, 12 kW, DC shunt motor has a maximum efficiency of 90 % and a speed of 800 r.p.m. When delivering 80 % of its rated output. The resistance of its shunt field is 80. Determine the efficiency, speed when the motor draws a current of 70 A from mains.

Sol.

Ex. 5.3.2 A 500 V series motor takes current of 180 A to develop 80 kW. The armature and series field resistances are 0.1 Ω and 0.04 Ω respectively. If the output is reduced to 40 kW, find the input current and efficiency.

Sol.:

Ex. 5.3.3 A DC shunt motor rated 10 kW connected to 250 V supply is loaded to draw 35 A armature current running at a speed of 1250 rpm. Given Ra = 0.5 Ω.

a) Determine the load torque if the rotational loss is 500 W.

b) Determine the motor efficiency if the shunt field resistance is 250

AU: Dec.-09, 19, Marks 8

Sol. :

Review Questions

1. Derive a condition to obtain maximum efficiency for d.c. machine. AU: Dec.-07.15, May-09, Marks 4

2. A 400 V, d.c. shunt motor has an armature nib resistance of 0.4 Ω and shunt field resistance of 100 Ω . If the stray losses amount to 2000 W, what will be the efficiency when the motor takes 100 A from the mains? If the input current is lowered by 40 %, find the new losses and efficiency.

(Ans.: 4854.4 W η_m = 79.77%)

3. Define: i) Electrical efficiency ii) Mechanical efficiency iii) Overall or commercial efficiency. Derive the condition for maximum efficiency.

4. A 500 V series motor takes current of 180 A to develop 80 kW. The armature and series field resistances are 0.1 Ω and 0.04 Ω respectively. If the output is reduced to 40 kW, find the input current and efficiency. 

(Ans.: 87.61 A, 91.31 %)

5. A 400 volts shunt motor develops an output of 18.5 kW when taking 22.5 kW. Field resistance is 200 ohms and armature resistance is 0.4 ohms. What is the efficiency and power input when output is 9 kW. 

[Ans.: 74.107 %]

6. A 250 V, 15 kW shunt motor has a maximum efficiency of 90% and a speed of 750 r.p.m. when delivering 80% of its rated output. The resistance of its shunt field is 100 Ω Determine the efficiency and speed when motor draws a current of 80 A from the mains. 

[Ans.: 88.91 %, 728.19 r.p.m.]