Motor efficiency

Electric motors are responsible for 90 percent of the electric energy consumption in a typical wastewater treatment plant.(WEF 2009, — USEPA 2010).  Motor efficiency (ememm) is a measure of mechanical power (pmpm) output compared to electrical power input (pepe).

empmpe        ————————————— (1)

where

pmpm = mechanical power output (W or hp)
pepe = electrical power input (W or hp)

pmpm is also referred as motor power or brake horsepower while pepe as wire power or wire horsepower. The plant power cost is directly related to pepe.

Most electric motors are designed to run at 50% to 100% of rated load. Maximum efficiency is usually near 75% of rated load and the preferred load ranges between 60% and 90%. As a result, a 10-horsepower (hp) motor has an acceptable load range of 5 to 10 hp, peak efficiency is at 7.5 hp, and preferred load range of 6-9 hp. A motor’s efficiency tends to decrease dramatically below about 50% load, but larger motors can operate with reasonable efficiency at loads down to the 25 percent range. Since motors are often used away from the 75% of the rated load, the practical operating efficiencies are usually less than the nominal full-load efficiency identified by the motor manufacturer.

The range of acceptable efficiency varies with individual motors and tends to extend over a broader range for larger motors.  A motor is considered under loaded when it is in the range where efficiency drops significantly with decreasing load. Other factors that reduce efficiency in the field include power quality (i.e., proper voltage, amps, and frequency) and temperature. Fig. 1 shows the mean efficiency of standard and high efficiency motors at full load. More accurate efficiency can be obtained from manufacturer.

Table 1. Efficiency of motor at full load  (— USEPA, 2010)

Name Plate Power Mean Efficiency
hp kW Standard motor High efficiency motor
1 0.746 0.825 0.865
1.5 1.119 0.84 0.894
2 1.492 0.84 0.888
2.5 1.865 0.812 0.87
3 2.238 0.875 0.895
4 2.984 0.827 0.889
5 3.73 0.875 0.902
7.5 5.595 0.895 0.917
10 7.46 0.895 0.917
15 11.19 0.91 0.93
20 14.92 0.91 0.936
25 18.65 0.924 0.941
30 22.38 0.924 0.941
40 29.84 0.93 0.945
50 37.3 0.93 0.95
60 44.76 0.936 0.954
75 55.95 0.941 0.954
100 74.6 0.945 0.958
125 93.25 0.945 0.954
150 111.9 0.95 0.958
200 149.2 0.95 0.958
250 186.5 0.954 0.962
300 223.8 0.954 0.962

Many motors are designed with a service factor that allows occasional overloading. Service factor is a multiplier that indicates how much a motor can be overloaded under ideal ambient conditions. For example, a 10-hp motor with a service factor of 1.15 can handle an 11.5 hp load for short periods of time without incurring significant damage.

Variable frequency drive (VFD) also called variable speed drive (VSD) is used to closely match the speed of blowers, pumps, mechanical oxygenators, etc. to the variable flow rate. Maxium pump and blower efficiencies can be achieved by avoiding throttling and bypassing. Its efficiency stays almost constant until the relative speed decreases down to 70%, but it can decrease somewhat rapidly below the efficiency especially for the motors with lower than 50 hp. More accurate efficiency can be obtained from the VFD manufacturer.

Table 2. Motor Efficiencies with VFD control (derived from Rooks and Wallace, 2003)
motortable

Power factor

In a purely resistive AC motor, voltage and current waveforms exactly matches in phase, changing polarity at the same instant in each cycle. In actual AC motor, however, reactive elements such as capacitors or inductors are present. The energy storage in these reactive elements results in a time delay in the current. The stored energy is not consumed by motor and returns to the power source. Power factor (PF) is defined as the ration of real power (pepe) used for work to apparent power (sss).

pf        ————————————— (2)

Since an extra transmission capacity must be prepared, fees are applied in some areas for the devices with low PF. Typical PF for the motors with various size at different loads are summarized in Table 7-1.

The real power consumption,pepe , is calculated by inserting the following equation to the above equation.

3iv  ————————————— (3)

where  is the current measure (A) and Vol is voltage (V). Finally, the power consumption by a 3-phse motor is calculated by the following equation. For 2-phase motors,33  is not required in the equation.

pe3iv  ————————————— (4)

Table 3. Typical power factor of 1,800 rpm motor

Name Plate

Power (hp)

PF at different loads
50% 75% 100%
0 – 5 0.72 0.82 0.84
5 – 20 0.74 0.84 0.86
20 – 100 0.79 0.86 0.89
100 – 300 0.81 0.88 0.91

The efficiency of variable frequency drive (VFD) varies depending on the operating speed. Typically efficiency holds at 70%-100% of the full speed for the motors rated higher than 50 hp, but it declines quickly outside the range especially for small motors.

© Seong Hoon Yoon