Power Stages and Efficiency in DC Machine

Power Stages and Efficiency in DC Machine

In this article, we will discuss Power Stages and Efficiency in DC Machine. This helps to determine the performance of the DC machine.

The power flow analysis of any machine is important to determine its characteristics of the machine. In the operation of any machine, the input power is delivered to a machine at some definite rate.

Some amount of input power is transferred into heat through copper, iron, and mechanical loss. The remaining power is used for the output power and it is delivered to the load.

If the DC machine is used as a DC generator, the supplied power is mechanical and it is converted into electrical power as output power.

Similarly, if the DC machine is used as a DC motor, the supplied power is electrical power and it is converted into mechanical power as output power.

The same machine can be used as a DC generator or DC motor. The DC machine is an electro-mechanical device.

The losses in DC machines are present during the conversion of energy. These losses are transferred into the air in the form of thermal energy (heat).

Power Flow Diagram for DC Generator

The DC generator is used to convert mechanical energy into electrical energy. Hence, the input of the machine is mechanical energy.

In a DC generator, the mechanical energy is supplied to the shaft of a machine with the help of a prime mover, turbine, or engine.

During this conversion, the rotational losses occur (friction and windage loss, mechanical loss, hysteresis loss, eddy current loss, etc.)

The remaining power is used to convert mechanical power into electrical power. After that, the power is lost in armature winding and field winding (copper loss).

And finally, the remaining power is converted into useful electrical power that is used to supply the load.

The power stages for the DC generator are shown in the figure below.

power stages for the DC generator
power stages for the DC generator

Power Stages of DC Motor

In a DC machine, the same machine can be used as a DC generator or DC motor. Therefore, the power stages are reversed in DC motor compared to DC generator.

In a DC motor, the supplied power is electrical power and the output power is mechanical.

The supplied power is given to the field winding. There are some amounts of energy is lost in form of heat (field copper loss).

The remaining power is supplied to the armature (armature copper loss, series field copper loss, interpole loss).

The remaining power is used to convert it into mechanical energy. But still, this power is not useful.

There are some amounts of energy is lost in mechanical losses. After that, the remaining power is useful power and that is used to operate the load.

The power flow diagram of the DC motor is shown in the figure below.

power flow diagram of DC motor
power flow diagram of DC motor

Efficiency of DC Machines

The various efficiency of DC machines is explained below.

Efficiency of DC Generator

Mechanical efficiency is a ratio of total electrical power developed by armature and total mechanical input power.

    \[ Mechanical \, Efficiency \, \eta_m = \frac{electrical \, power \, developed \, by \, armature}{total \, mechanical \, input \, power} \]

    \[ Mechanical \, Efficiency \, \eta_m = \frac{E_g I_a}{BHP \, Prime mover \times 735.5} \]

Electrical efficiency is a ratio of useful electrical power output to the electrical power developed.

    \[ Electrical \, Efficiency \, \eta_e = \frac{useful \, electrical \, power \, output}{electrical \, power \, developed} \]

    \[ Electrical \, Efficiency \, \eta_e = \frac{V I_L}{E_g I_a} \]

Overall efficiency or commercial efficiency of DC generator is;

    \[ Overall \, Efficiency, \eta_G = \frac{useful \, electrical \, power \, output}{total \, mechanical \, input \, power} \]

    \[ Overall \, Efficiency, \eta_G = \frac{V I_L}{ BHP \, Prime mover \times 735.5} \]

Efficiency of DC Motor

Electrical efficiency is a ratio of mechanical power developed to total electrical power input.

    \[ Electrical \, Efficiency \, \eta_e = \frac{Mechanical \, power \, developed}{Total \, electrical \, power \, input} \]

    \[ Electrical \, Efficiency \, \eta_e = \frac{E_b I_a}{V I_L} \]

Mechanical efficiency is a ratio of useful mechanical power output to the mechanical power developed.

    \[ Mechanical \, Efficiency \, \eta_m = \frac{useful \, mechanical \, power \, output}{mechanical \, power \, developed} \]

    \[ Mechanical \, Efficiency \, \eta_m = \frac{BHP \, of \, motor \times 735.5}{ E_b I_a } \]

Overall efficiency of DC motor is a ratio of useful power output to the total electrical input power.

    \[ Overall \, Efficiency \, \eta_M = \frac{Useful \, mechanical \, power \, output}{Total \, electrical \, power \, input} \]

    \[ Overall \, Efficiency \, \eta_M = \frac{Total \, electrical \, power \, input - Total \, losses}{Total \, electrical \, power \, input} \]

    \[ Overall \, Efficiency \, \eta_M = \frac{VI_L - Total \, Losses}{VI_L} \]

Condition For Maximum Efficiency

For DC generator and DC motor, the conditions for maximum efficiency same. Here, we consider the machine as a generator to derive a condition for maximum efficiency.

Generator output = VIL

Where, V = terminal voltage

IL = load current

Generator input = Output + Total losses

    \[ Generator \, input = V I_L + I_a^2 R_a + P_C \]

    \[ Generator \, input = V I_L + (I_L+I_{sh})^2 R_a + P_C \]

    \[ Generator \, input = V I_L + I_L^2 R_a + P_C \]

Shunt field current is very small. Hence, we can neglect it compared to the load current.

Here, Ra is total resistance of armature circuit (it includes brush contact resistance and resistance of series, interpole, and compensating winding).

    \[ Generator \, Efficiency \, \eta_G = \frac{Output}{Input} \]

    \[ \eta_G = \frac{VI_L}{ V I_L + I_L^2 R_a + P_C } \]

    \[ \eta_G = \frac{1}{1 + \frac{I_L R_a}{V} + \frac{P_C}{VI_L} } \]

When denominator is minimum, the efficiency of generator is maximum. Therefore,

    \[ \frac{d}{dI_L} \left( \frac{I_L R_a}{V} + \frac{P_C}{VI_L} \right) = 0 \]

    \[ \frac{R_a}{V} - \frac{P_C}{VI_L^2} = 0 \]

    \[ I_L^2 R_a = P_C \]

Therefore, the efficiency is maximum when variable losses are equal o constant loss.

The load current at maximum efficiency is given by;

    \[ I_L - \sqrt{\frac{P_C}{R_a}} \]

The below figure shows the curve of variation of efficiency with a load.

Load current vs efficiency
Load current vs efficiency

From the above figure, we can say that the efficiency increases with the increase in the load current, attains a maximum value when the load current equals the value given by the above equation, and start decreasing.

The DC machines are generally designed to give maximum efficiency at or near the rated output of the machine.

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