Introduction

The two parameters of importance in a motor are efficiency and power factor. The efficiencies of induction motors remain almost constant between 50% to 100% loading (Refer figure). With motors designed to perform this function efficiently; the opportunity for savings with motors rests primarily in their selection and use. When a motor has a higher rating than that required by the equipment, motor operates at part load. In this state, the efficiency of the motor is reduced. Replacement of under loaded motors with smaller motors will allow a fully loaded smaller motor to operate at a higher efficiency. This arrangement is generally most economical for larger motors, and only when they are operating at less than one-third to one-half capacity, depending on their size.

Efficiency of the Induction Motor

The efficiency of the motor is given by

Where P_out – Output power of the motor P_in – Input power of the motor P_Loss – Losses occurring in motor

While input power measurements are fairly simple, measurement of output or losses need a laborious exercise with extensive testing facilities. The following are the testing standards widely used, but will not be elaborated in this article.
Europe: IEC 60034-2, and the new IEC 61972 US: IEEE 112 - Method B Japan: JEC 37

Even between these standards the difference in efficiency value is up to 3%. For simplicity nameplate efficiency rating may be used for calculations if the motor load is in the range of 50 –100 %. Hence it is suggested that the engineer need not attempt to measure efficiency of the motor.

Determining Motor Loading

1. By Input Power Measurements

• First measure input power Pi with a hand held or in-line power meter where Pi = Three-phase power in kW
• Note the rated kW and efficiency from the motor name plate
• The figures of kW mentioned in the name plate is for output conditions.
So corresponding input power at full-rated load

ηfl = Efficiency at full-rated load
Pir = Input power at full-rated power in kW
• The percentage loading can now be calculated as follows

Example
The nameplate details of a motor are given as power = 15 kW, efficiency η = 0.9. Using a power meter the actual three phase power drawn is found to be 8 kW. Find out the loading of the motor.

Input power at full-rated power in kW, Pir = 15 /0.9
= 16.7 kW
Percentage loading = 8/16.7
= 48 %

2. By Line Current Measurements

The line current load estimation method is used when input power cannot be measured and only amperage measurements are possible. The amperage draw of a motor varies approximately linearly with respect to load, down to about 75% of full load. Below the 75% load point, power factor degrades and the amperage curve becomes increasingly non-linear. In the low load region, current measurements are not a useful indicator of load.

However, this method may be used only as a preliminary method just for the purpose of identification of oversized motors.
%load = 100 * Input load current / Input rated current,    this is valid up to 75% loading

3. Slip Method

In the absence of a power meter, the slip method can be used which requires a tachometer. This method also does not give the exact loading on the motors.

Load = 100 * Slip / (Ss - Sr)
Where:
Load = Output power as a % of rated power
Slip = Synchronous speed - Measured speed in rpm
Ss = Synchronous speed in rpm at the operating frequency
Sr = Nameplate full-load speed

Example: Slip Load Calculation
Given: Synchronous speed in rpm = 1500 at 50 HZ operating frequency.
(Synchronous speed = 120f/P) f: frequency, P: Number of poles
Nameplate full load speed = 1450
Measured speed in rpm = 1480
Nameplate rated power = 7.5 kW
Determine actual output power.

Load = 100 * (1500 - 1480) / (1500 - 1450) = 40%

From the above equation, actual output power would be 40% x 7.5 kW = 3 kW

The speed/slip method of determining motor part-load is often favored due to its simplicity and safety advantages. Most motors are constructed such that the shaft is accessible to a tachometer or a strobe light. The accuracy of the slip method, however, is limited. The largest uncertainty relates to the accuracy with which manufacturers report the nameplate full-load speed. Manufacturers generally round their reported full-load speed values to some multiple of 5 rpm. While 5 rpm is but a small percent of the full-load speed and may be considered as insignificant, the slip method relies on the difference between full-load nameplate and synchronous speeds. Given a 40 rpm “correct” slip, a seemingly minor 5 rpm disparity causes a 12% change in calculated load.

Slip also varies inversely with respect to the motor terminal voltage squared. A voltage correction factor can, also, be inserted into the slip load equation. The voltage compensated load can be calculated as shown

Load = 100 * Slip / [ (Ss - Sr) x (Vr / V)² ]
 

Where:
Load = Output power as a % of rated power
Slip = Synchronous speed - Measured speed in rpm
Ss = Synchronous speed in rpm
Sr = Nameplate full-load speed
V = RMS voltage, mean line to line of 3 phases
Vr = Nameplate rated voltage