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8.4 Electric Motor Efficiency

This section reviews the efficiency of the connected loads.

Question How much electrical power does the motor draw from the mains? The electrical power consumption of the motor from the mains may not be clear. In this scenario, how much electricity the motor consumes from the grid? Nevertheless, we know the useful power that it can provide through its shaft and the efficiency at which it accomplishes this. For example, 5 horsepower at 85 % efficiency (η = 85%).

We refer to P as the active electrical power that the motor consumes from the electrical network, and Pu as the useful or mechanical power the motor generates on its axis. The difference between these powers yields the power lost in the motor, Pp. Then, we have:

Pp = P - Pu (8.40)

On the one hand, power losses due the Joule effect when current flows through the windings were defined as:

P = R·I² (8.41)

We also know that other losses like hysteresis and eddy currents in magnetic circuits, as well as friction in the bearings and ventilation, are the two main losses. The motor's efficiency denotes the percentage relationship between its useful power and overall or electrical power, i.e.:

η = Pu / P · 100 (8.42)

In our example, the motor's electrical power consumption from the grid is:

η = Pu / P = 5·736 / (85/100) = 4329 W (8.43)

练习题

A motor provides 3 horsepower of useful mechanical power on its shaft while consuming 2800 W of electrical power from the mains. What is the motor's efficiency? (Note: 1 HP = 736 W)

A. 78.9%

B. 85.7%

C. 92.3%

D. 107.1%

A motor operates at 80% efficiency and delivers 4 HP of useful mechanical power. How much electrical power does the motor draw from the mains? (Note: 1 HP = 736 W)

A. 2355 W

B. 2944 W

C. 3680 W

D. 4600 W

An electric motor draws 5000 W of electrical power from the grid and has an efficiency of 90%. What is the power lost in the motor?

A. 450 W

B. 500 W

C. 550 W

D. 4500 W

Which of the following are identified as main sources of power loss in an electric motor?

A. Joule effect losses in the windings

B. Hysteresis losses in magnetic circuits

C. Eddy current losses in magnetic circuits

D. Friction in the bearings

E. Power factor correction losses

Motor efficiency is defined as the ratio of electrical power consumed from the mains to the useful mechanical power delivered on the shaft, expressed as a percentage.

The power lost in a motor ( $P_{p}$ ) is equal to the difference between the active electrical power consumed from the network ( $P$ ) and the useful mechanical power generated on the shaft ( $P_{u}$ ).

The Joule effect power loss in motor windings can be calculated using the formula $P = R \cdot I^{2}$ , where R is the winding resistance and I is the current flowing through it.

The motor's efficiency denotes the percentage relationship between its ___ power and overall or electrical power.

Power losses due to the ___ effect when current flows through the windings are calculated as $P = R \cdot I^{2}$ .

A three-phase motor connected to a 400 V supply with a power factor of 0.85 draws a line current of 10 A. If the motor efficiency is 88%, calculate the useful mechanical power output. (Use the three-phase power formula: $P = 3 \cdot U_{C} \cdot I_{L} \cdot cos φ$ )

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8.4 Electric Motor Efficiency