Thermodynamics

396 | ThermodynamicsW electricMotorefficiencyh motor100%908070605040302010h motorW shaftElectrical powerconsumed per kW ofmechanical (shaft)power output,W electric = W shaft /h motor1.00 kW1.111.251.431.672.002.503.335.0010.00FIGURE 7–76The electrical energy consumed by amotor is inversely proportional to itsefficiency.h motor, %100908070605040302010Motorefficiency0 20 40 60 80 100 Load, %FIGURE 7–77The efficiency of an electric motordecreases at part load.power supplied to the electrical power consumed during operation is calledthe motor efficiency, h motor . Therefore, the electric power consumed by themotor and the mechanical (shaft) power supplied to the compressor arerelated to each other by (Fig. 7–76)W # electric W # comp>h motor(7–92)For example, assuming no transmission losses, a motor that is 80 percent efficientwill draw 1/0.8 1.25 kW of electric power for each kW of shaftpower it delivers to the compressor, whereas a motor that is 95 percent efficientwill draw only 1/0.95 1.05 kW to deliver 1 kW. Therefore, highefficiencymotors cost less to operate than their standard counterparts, butthey also usually cost more to purchase. However, the energy savings usuallymake up for the price differential during the first few years. This is especiallytrue for large compressors that operate more than one regular shift. The electricpower saved by replacing the existing standard motor of efficiency h standard bya high-efficiency one of efficiency h efficient is determined fromW # electric,saved W # W # electric,standard W # electric,efficientcomp 11>h standard 1>h efficient 2 1Rated power21Load factor2 11>h standard 1>h efficient 2(7–93)where rated power is the nominal power of the motor listed on its label (thepower the motor delivers at full load) and the load factor is the fraction ofthe rated power at which the motor normally operates. Then the annualenergy savings as a result of replacing a motor by a high-efficiency motorinstead of a comparable standard one isEnergy savings W # electric,saved Annual operating hours(7–94)The efficiencies of motors used to power compressors usually range fromabout 70 percent to over 96 percent. The portion of electric energy not convertedto mechanical energy is converted to heat. The amount of heat generatedby the motors may reach high levels, especially at part load, and it maycause overheating if not dissipated effectively. It may also cause the air temperaturein the compressor room to rise to undesirable levels. For example, a90-percent-efficient 100-kW motor generates as much heat as a 10-kW resistanceheater in the confined space of the compressor room, and it contributesgreatly to the heating of the air in the room. If this heated air is not ventedproperly, and the air into the compressor is drawn from inside the compressorroom, the performance of the compressor will also decline, as explained later.Important considerations in the selection of a motor for a compressor arethe operating profile of the compressor (i.e., the variation of the load withtime), and the efficiency of the motor at part-load conditions. The part-loadefficiency of a motor is as important as the full-load efficiency if the compressoris expected to operate at part load during a significant portion of the totaloperating time. A typical motor has a nearly flat efficiency curve between halfload and full load, and peak efficiency is usually at about 75% load. Efficiencyfalls off pretty steeply below half load, and thus operation below 50%load should be avoided as much as possible. For example, the efficiency of amotor may drop from 90 percent at full load to 87 percent at half load and 80percent at quarter load (Fig. 7–77). The efficiency of another motor of similar