Variable-frequency drives (VFDs) are widely applied oninduction motors that drive fans, pumps, and compressors.Under partial loads, VFDs not only adjust frequency to reducemotor speed and mechanical output power (load) but alsoadjust voltage to reduce motor electrical input power. Traditionally,VFD manufacturers recommend controlling the voltageso that it is proportional to the square of the frequency forvariable torque motor loads on fans and pumps and proportionalto the frequency for constant torque motor loads oncompressors. The purpose of this paper is to investigateenergy-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 maximize motor efficiency.Finally, the motor efficiency is simulatedand compared under the optimal voltage and different presetvoltages. The simulation results show that the motor efficiencywith the ratio of voltage to frequency to the power of 1.5 ismostly close to the optimal efficiency for variable torque motorloads, and the motor efficiency with the ratio of voltage tofrequency to the power of 0.5 is mostly close to the optimal efficiencyfor constant torque motor loads with efficiency improvementby up to 3% over traditional ratios.