1、 2016 ASHRAE 149ABSTRACTVariable-frequency drives (VFDs) are widely applied oninduction motors that drive fans, pumps, and compressors.Underpartialloads,VFDsnotonlyadjustfrequencytoreducemotor speed and mechanical output power (load) but alsoadjust voltage to reduce motor electrical input power. Tra
2、di-tionally, VFD manufacturers recommend controlling the volt-age so that it is proportional to the square of the frequency forvariable torque motor loads on fans and pumps and propor-tional to the frequency for constant torque motor loads oncompressors. The purpose of this paper is to investigateen
3、ergy-efficient voltage frequency ratios of VFDs using themotor equivalent circuit method. First, the motor load andspeed correlation are derived for different applications. Then,VFD voltage is optimized for a given VFD frequency to maxi-mizemotorefficiency.Finally,themotorefficiencyissimulatedand co
4、mpared under the optimal voltage and different presetvoltages.Thesimulationresultsshowthatthemotorefficiencywith the ratio of voltage to frequency to the power of 1.5 ismostlyclosetotheoptimalefficiencyforvariabletorquemotorloads, and the motor efficiency with the ratio of voltage tofrequencytothepo
5、werof0.5ismostlyclosetotheoptimaleffi-ciencyforconstanttorquemotorloadswithefficiencyimprove-ment by up to 3% over traditional ratios.INTRODUCTIONFans, pumps and compressors are essential componentsto move air, water, and refrigerant in heating, ventilation, andairconditioning(HVAC)systemsandrefrige
6、rationsystemsincommercialbuildings(DOE2013).Fanscanbeusedassupplyfans in air-handling unit (AHU) systems, condenser fans inpackaged air conditioners and air-cooled chillers, and coolingtowerfansforwater-cooledchillers.Pumpscanbeusedinhot-water, chilled-water, and condensing-water systems. More-over,
7、 compressors widely serve in packaged air conditioners,chillers, and other refrigeration systems.Electric motors are applied to drive fans, pumps, andcompressors. A motor transfers electrical input power tomechanical output power or load on its connected fan, pump,or compressor. In this paper, the m
8、otor electrical input poweris called the motor power while the motor mechanical outputpower is called the motor load.The annual energy consumption of electric motor-drivensystems and components in commercial sectors was1427 TWh (4.87 quads) in 2013 in the United States (DOE2013). The fans, pumps, an
9、d compressors in HVAC systemsand refrigeration systems account for 93% of motor-drivenenergyuseor1328TWh(4.533quads)incommercialsectors.Table 1 summarizes the motor energy consumptions by fans,pumps, and compressors in commercial sectors.Among electric motors, alternating current (AC) three-phase in
10、duction motors are widely used in commercial build-ings because of their low cost and reliable operation. ACinduction motors rotate at a nearly constant speed slightlydeviated from their synchronous speed by a slip speed. Theamount of motor slip increases roughly proportional to themotor load, while
11、 the synchronous speed is determined by thefrequency of power supply and the number of electricalmagnetic poles (Hughes 2006).Variable motor loads occur frequently in commercialsectors. For example, the cooling load in conditioned spacesvaries with seasons and occupant conditions. As a result, theva
12、riable space-cooling load demands variable airflow of thesupplyfansinvariable-air-volume(VAV)AHUsystems,vari-Simulated Energy-EfficientVoltage Frequency Ratios ofVariable-Frequency Drives onInduction MotorsGang Wang, PhD, PE Koosha KiamehrMember ASHRAE Student Member ASHRAEGang Wang is an assistant
13、professor and Koosha Kiamehr is a doctoral student in the Department of Civil, Architectural and EnvironmentalEngineering, University of Miami, Coral Gables, FL.ST-16-016Published in ASHRAE Transactions, Volume 122, Part 2 150 ASHRAE Transactionsable water flow of the chilled-water pumps in centrali
14、zedHVAC systems, and variable refrigerant flow of the compres-sors in packaged air conditioners and chillers. These variableflow rates lead to variable motor loads on fans, pumps, andcompressors. According to the U.S. Department of Energy(DOE 2008), electric motors operate at or below 40% of theirra
15、ted load during more than 40% of operating hours.In fact, both the flow rate and motor load of fans, pumps,and compressors decreases as the motor speed decreases.Therefore, reducing the motor speed is more energy efficientthan closing dampers, valves, and inlet guide vanes underpartial loads. A a re
16、sult, three-phase induction motors areoften paired with variable-frequency drives (VFDs) to reducemotor speed to match the reduced motor loads in commercialapplications (DOE 2013).VFDscantransformconstantfrequencyandvoltageinputpowerintovariableoutputfrequencyandvoltagetoreducethespeed, load, and po
17、wer of the connected motor. The VFDsadjust output frequency to proportionally reduce motor speedand consequently reduce the motor load on fans, pumps, andcompressors. Meanwhile the VFDs also adjust output voltageto reduce motor power to achieve maximum energy savings.Energy savings of 50% or more we
18、re observed when fixed-speed systems were modified to allow the motor speed tomatch variable load requirements (DOE 2008).Currently the most common VFD is the pulse-widthmodulation (PWM) type. AC supply voltage is converted intodirect current (DC) voltage by a rectifier, then the DC voltageissmoothe
19、dusingfiltercapacitorsinaDClink,andfinallythesmoothed DC voltage is applied to the connected motor as aseries of positive and negative pulses with varying durationand frequency. The DC voltage pulse is turned on and off at aswitching frequency between 1 and 20 kHz to result in anapproximately sinuso
20、idal current, although some distortionstill exists. The width of the pulses determines the resultantVFDoutputvoltage,whilethechangeoverfrequencybetweenpositive and negative pulses equals the VFD output frequency(DOE 2008; CEATI 2000).Typically, VFD output voltage is correlated to VFDoutput frequency
21、 based on the voltage frequency ratios presetwithinVFDsbymanufacturers.Thevoltagefrequencyratioisselected based on the motor load-speed relationship in theapplication. Currently, centrifugal fans andpumps areconsid-eredtoideallyhaveacubiccorrelationbetweenthemotorloadand its speed, while positive di
22、splacement compressors areconsidered to ideally have a linear correlation with the motorload and its speed (DOE 2008). In fact, the cubic correlationbetween motor load and speed is true only for the centrifugalfans and pumps without pressure control, such as the fans incooling towers and condensers,
23、 and the primary pumps indecoupled hot-water and chilled-water systems. For thecentrifugal fans and pumps with pressure control, such as thesupplyfansinVAVAHUs,thesecondarypumpsindecoupledhot-water and chilled-water systems, and the pumps in vari-able-flow primary systems, the change of damper and v
24、alvepositions changes the actual correlation between the motorload and speed.VFDs commonly provide two preset voltage frequencyratios. The ratio of voltage to frequency squared, called asquaredratio,isappliedforcentrifugalfansandpumps,whichare considered to have a cubic motor load with the motorspee
25、d. The linear ratio of voltage to frequency is applied forpositive displacement compressors, which are considered tohave the linear motor load with the motor speed. In addition totwo preset voltage frequency ratios, VFD manufacturers actu-ally offer another choice to control the output voltage, whic
26、his often called energy optimization or flux optimization. ItsTable 1. Summary of Motor Energy ConsumptionAppliance or Equipment TypePrimary Energy Consumption, TWh (TBtu)Fans Pumps CompressorsPackaged terminal air conditioners 5.8 (19.8) 0 17.43 (59.5)Single-packaged vertical air conditioners 0.88
27、(3.0) 0 2.67 (9.1)Commercial unitary air conditioners 85.03 (290.2) 0 340 (1160)Commercial chiller plants and hydronic systems 286.17 (976.7) 83.07 (283.5) 230.5 (786.7)Self-contained commercial refrigeration 13.89 (47.4) 0 81.1 (276.8)Beverage vending machines 23.29 (79.5) 0 28.65 (97.8)Walk-in coo
28、lers and freezers 23.38 (79.8) 0 58.01 (198)Automatic commercial ice makers 3.46 (11.8) 0.97 (3.3) 43.98 (150.1)Sum, TWh (quads) 441.9 (1.508) 84.04 (0.287) 802.35 (2.738)Total, TWh (quads) 1328 (4.533)Published in ASHRAE Transactions, Volume 122, Part 2 ASHRAE Transactions 151purpose is to actively
29、 adjust the output voltage to maximizemotor efficiency at the actual loadHowever,VFDmanufacturersdidnotgiveanysimulationor experimental supporting data for the preset ratios. It is notclear whether the recommended ratios can achieve the highestmotor efficiency and whether the recommended squared rat
30、ioworks for all centrifugal fans and pumps with different pres-sure setpoints.To evaluate the impact of VFD voltage frequency ratiosonmotorefficiency,amethodtosimulatethemotorefficiencyunder variable VFD voltage and frequency is needed. In fact,theequivalentcircuitofinductionmotorsprovidesaneffectiv
31、emethod to evaluate the motor efficiency for sinusoidal power(IEEE2004;Hughes2006;Wildi2002).Hughes(2006)statedthattheequivalentcircuitisapplicabletofrequenciesbetween10 and 60 Hz for 60 Hz motors. Even though the VFD outputpower is not perfectly sinusoidal and can induce additionalenergylossesinmot
32、ors(Carrier2005;Plessisetal.2013),thisimpactonmotorefficiencyisconsideredtobeminimal(Manzand Morgan 1999). Therefore, the efficiency of a motorpowered by a VFD can still be evaluated using the equivalentcircuit method.Thepurposeofthispaperistoinvestigateenergy-efficientvoltagefrequencyratiosofVFDsdr
33、ivingtheinductionmotorsof fans, pumps, and compressors using the motor equivalentcircuit method. First, the motor load and speed correlation isdefined or derived for each application, especially for thecentrifugal fans and pumps with pressure control. Then, volt-ageisoptimizedforagivenfrequencyandit
34、smotorspeedandload. Finally, the motor efficiency is simulated and comparedunder different voltages, including the optimal voltage as wellasthevoltagessetbydifferentpresetratios,whicharetheratioofvoltagetofrequencytothepowerof0.5,theratioofvoltagetofrequencytothepowerof1,theratioofvoltagetofrequency
35、to the power of 1.5, and the ratio of voltage to frequency to thepower of 2.MODELINGBesides the ideal cubic and linear correlations betweenthe motor load and speed, the actual correlations for centrifu-galfansandpumpswithpressurecontrolareindistinctandareexplored first. Then, the equivalent circuit
36、method of induc-tion motors is introduced to evaluate the motor efficiency atdifferent VFD output voltages and frequencies and motorloads and to consequently determine the optimal voltage atvarious VFD frequencies and their correlated motor speedsandloads.Finally,toevaluatethemotorefficiencywithpres
37、etvoltage frequency ratios, the voltage set by four voltagefrequency ratios is defined.Correlation of Motor Load and SpeedAs discussed previously, centrifugal fans and pumpswithout pressure control, such as the fans in cooling towersand condensers, and the primary pumps in decoupled hot-water and ch
38、illed-water systems, follow the ideal cubiccorrelation between the motor load and speed. The motor loadW is proportional to the cube of the relative motor speed ,aratio of actual speed to the design speed:(1)Moreover, positive displacement compressors observethe ideal linear correlation between the
39、constant torque motorload and speed. The motor load W is proportional to the rela-tive motor speed :(2)Ontheotherhand,forthecentrifugalfansandpumpswithpressurecontrol,suchasthesupplyfansinVAVAHUsandthesecondary pumps in decoupled hot-water and chilled-watersystems, the fan and pump shaft power or mo
40、tor load has to bedetermined by fan or pump performance curves as well as thesystem control curve with a given pressure setpoint.The fan or pump performance curves are presented by thefan or pump head H curve and shaft power W curve at a designspeed, which can be regressed as functions of flow rate
41、Q:(3)(4)The fan or pump head and shaft power curves under apartial speed can be deduced using the affinity laws:(5)(6)The system control curve is determined by the pressuresetpoint Hsp. Normally, a differential pressure sensor isapplied to measure differential pressure associated with thepressure se
42、tpoint. The system pressure drop includes the pres-sure drop upstream of the pressure sensor and the pressuredrop downstream of the pressure sensor. Actually, themeasured differential pressure denotes the pressure dropdownstream of the pressure sensor and is intentionally main-tained at the pressure
43、 setpoint regardless of the flow rate.Therefore, the pressure drop downstream of the pressuresensor is approximately constant and equal to the pressuresetpoint. On the other hand, the upstream of the pressuresensor does not have any modulation valves or dampers.Therefore, the pressure drop upstream
44、of the pressure sensoris proportional to the actual flow rate squared and is equal tothe design system pressure drop or the design fan or pumphead minus the pressure drop downstream of the pressuresensoratthedesignflowrate.Thefanorpumpheadwillover-come the system pressure drop.WWd3=WWd=HaHQ3bHQ2cHQd
45、H+=WaWQ3bWQ2cWQdW+=H2- aHQ-3bHQ-2cHQ-dH+=W3- aWQ-3bWQ-2cWQ-dW+=Published in ASHRAE Transactions, Volume 122, Part 2 152 ASHRAE Transactions(7)Under a given flow rate, the motor speed can be deter-mined by Equations 5 and 7. Then, the shaft power or motorload can be determined by the given flow rate
46、and calculatedmotor speed using Equation 6. Finally, the motor load andspeed can be correlated by the given flow rate. In general, themotor load can be expressed as a function of the motor speed:(8)According to Equations 5 to 7, with zero pressuresetpoint, the correlation between the motor load and
47、speedexactly follows the ideal cubic correlation. Therefore thecentrifugal fans and pumps with zero pressure setpoint alsorepresent the centrifugal fans and pumps without pressurecontrol with the ideal cubic correlation.Motor Equivalent Circuit and Optimal VoltageA three-phase induction motor can be
48、 represented bythree identical equivalent circuits. Figure 1 shows the sche-matics of an equivalent circuit with six circuit parameters,including stator winding resistance R1, rotor winding resis-tance R2, stator leakage reactance X1, rotor leakage reactanceX2, magnetizing reactance Xm, and core loss resistance Rc.In the circuit, the reactance is proportional to the VFDfrequency while the resistance is independent of the VFDfrequency. The relative VFD frequency fthe ratio of actualfrequency to the rated frequencyis identical to the relativemotor speed and is applied to calcul
