# Electric Machine Efficiency and Losses

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Regardless of which type of electric machine is chosen for a particular job, efficiency is important for several reasons.

First, and perhaps most obvious, a less efficient machine will cost more to operate.

Second, the losses in the machine are converted to heat, which raises the operating temperature of the machine. The life of insulation is strongly related to the operating temperature. Thus, the machine must be designed to tolerate the heat created by its losses.

Finally, when conducting analyses of the power system, we must have a model for the machine that accounts for the losses.

As always, efficiency is simply the power out divided by the power in:

$\begin{array}{*{20}{c}}{\eta = \frac{{Power{\rm{ }}out}}{{Power{\rm{ }}in}} \times 100\% = \frac{{{P_{out}}}}{{{P_{in}}}} \times 100\% }&{}&{\left( 1 \right)}\end{array}$

Defining the losses in the machine as Ploss, equation 1 can be written in other forms:

$\begin{array}{*{20}{c}}{\eta = \frac{{{P_{out}}}}{{{P_{out}} + {P_{loss}}}} \times 100\% }&{}&{\left( 2 \right)}\end{array}$

$\begin{array}{*{20}{c}}{\eta = \frac{{{P_{in}} – {P_{loss}}}}{{{P_{in}}}} \times 100\% = \left( {1 – \frac{{{P_{loss}}}}{{{P_{in}}}}} \right) \times 100\% }&{}&{\left( 3 \right)}\end{array}$

The choice of whether to use equation 1, 2, or 3 depends often on what we know about the motor and its operating condition.

It is important to note that electric machines are rated in terms of power out. Thus, a 50 HP motor is capable of delivering 50 HP to a load and a 100 kVA generator is capable of delivering 100 kVA. Clearly, the input power to the motor would be greater than 50 HP (37.3 kW) and the input to the generator would be greater than 100 kVA times the power factor of the generator load.

There are cases where we might measure the input power of a motor and calculate the approximate losses of the machine from manufacturer’s data (e.g., the no-load losses and the resistance of the windings).

Because the output of a motor is mechanical work, it is difficult to measure the output power of a motor. Thus, we could estimate the output power and efficiency using input quantities.

The efficiency of an electrical machine is frequently determined by measuring the losses. Measurement standards are defined by ANSI Standard C50, IEEE Standard 112, and NEMA Standard MG1, among others.

The techniques specified in the standards are quite elaborate and very few laboratories are qualified to do them. The types of losses in an electrical machine are basically the same regardless of the type of machine. The amount of loss in each category depends on the number of windings, type of core, and whether the machine has brushes, etc.

## Copper losses

Resistive or I2R losses in the windings of a machine are frequently referred to as copper losses. As we know, the resistance of a conductor varies with temperature and frequency. Thus, by convention, copper losses for a winding are calculated using the DC resistance of the winding at 75°C.

The actual resistance will, of course, be different, so the difference between actual and computed copper loss is accounted for as part of the stray loss category (see “stray losses”).

For synchronous and DC machines with wound fields, the losses associated with the field windings are charged to the machine; however, losses associated with the DC supplies are charged to the rest of the system.

Brush contact loss is also included in the copper losses for DC machines but is normally neglected for AC machines (synchronous and wound-rotor induction). Copper losses are a function of winding currents, so they vary widely as the machine goes from no- load to full-load.

## Mechanical losses

This category includes friction and windage losses.

Friction occurs in the bearings that support the rotor shaft and between brushes and commutators or slip rings.

Windage is basically the fluid friction due to the rotor and fan assembly rotating in the air.

These losses can be determined by driving the machine at rated speed with no load or excitation, although they are frequently lumped with the core loss and determined at the same time.

For machines that operate at constant or nearly constant speed, the mechanical losses are essentially constant. This would include most AC machines unless they are driven by a variable-speed drive.

DC machines, on the other hand, are capable of operating over a wide speed range, so the mechanical losses will change with the speed.

## Core losses

Open circuit or no-load core losses include the hysteresis and eddy current losses in the steel of the machine, measured at no-load.

The sum of the mechanical and core losses is the no-load rotational loss. The no-load losses can be determined by running the machine with rated excitation at no-load and then measuring the power in.

In DC machines, distortion of the field may significantly increase core loss as the load increases. The difference is put into the stray loss category.

## Stray losses

Stray losses include anything not accounted for by the methods used to determine the preceding categories. By convention, the stray loss is taken to be 1% of the output of DC machines. It is found by testing for AC machines.

## Efficiency Considerations

Because some of the losses of the machine are constant and some change with load, the efficiency of a given machine will change as the load is varied.

At no-load, of course, the efficiency will be zero. As the load is added to the machine, the power out tends to increase faster than the losses and the efficiency rises until it reaches a maximum value for the machine. As the load is increased further, the efficiency decreases, indicating the losses are growing faster than the load.

Generally, the point of maximum efficiency is somewhere in the vicinity of 70% to 80% of rated load, especially for motors. Fortunately, the efficiency curve tends to be fairly flat from 50% to 100% of rated load. Thus, a slightly oversized motor will not cause a significant efficiency penalty.

One other consideration with respect to efficiency is that motors are manufactured in assembly lines and, like most manufactured goods, certain tolerances are allowed. This means that two of the same model motor from a manufacturer will probably have slightly different efficiencies because of variations in the components of the motors.

Because losses create heat in the machine, it is important to consider the effects of heat on the lifetime of the machine and to provide methods to remove the heat.

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