Losses and Efficiencies

The output of a dc machine, be it a generator or a motor, is always less than the input because some amount of energy supplied to the machine is lost as heat. Power losses sum over the three main com­ponents: iron losses (core losses), copper losses, and friction losses. Iron losses and friction losses can be put into a single group called mechanical losses, or stray-power losses. Copper losses are resistance losses that form a group of electrical losses.

Iron losses P_ir are the sum of the hysteresis loss and eddy-current loss. When the machine armature revolves in the field, the steel core of the armature periodically undergoes the reversal of magne­tization. The power required per cycle of magnetization, called the hysteresis loss, appears as heat in the iron. At the same time, the emfs generated in the armature core as it revolves in the field cause the eddy currents to circulate in the steel, which give rise to heat loss called eddy-current loss.

Iron losses depend on the magnetic flux density and the rate of magnetization reversal (the frequency of cyclic variation in the core flux). The flux density determines the emf of a machine, or its voltage, and the frequency of cyclic variation in flux is proportion­al to the speed. Therefore, in the machine running as a generator or as a motor, the iron loss will be constant and independent of the load if the terminal armature voltage and speed are constant.

Copper losses, or I²R losses, are the power lost as heat and expend­ed in the conductors of field and armature windings on overcoming the resistance offered by the conductors to the current flow.

The losses in the armature circuit made up of the armature wind­ing itself, brushes, brush contacts, and commutator bars depend on the armature current, i.e. they vary with the load.

Friction losses P_f are the losses of power expended on overcoming various frictional forces when the machine is running. They include the friction losses in the bearings, at the surface of the commutator due to the rubbing of the brushes, and in the armature core due to its fanning action, the latter power loss being referred to as the wind­age loss. These losses depend on the speed but are independent of the load on the machine.

The efficiency of a machine, expressed in percentage, is 100 times the ratio of the power output P₂ (useful power) to the power input P₁ (consumed power): η = (Р₂/Р_г) 100.

If the machine is a generator, its electrical output is found as the product of the terminal voltage V and the load current I, namely, P₂ = VI. The power input is P₁ = VI + P_ir + P_c + P_f, and the efficiency is then given as

If the machine runs as a motor, its electrical input is P₁ = VI. The power output is P₂ = VI – P_ir – P_c – Pf and the efficiency is then