Publication Date



Open access

Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PHD)


Civil, Architectural and Environmental Engineering (Engineering)

Date of Defense


First Committee Member

Gang Wang

Second Committee Member

Antonio Nanni

Third Committee Member

Wangda Zuo

Fourth Committee Member

John Onyango


Air and water flow rates are key controlled variables in heating, ventilation and air conditioning (HVAC) systems and can have significant impact on overall system performance and efficiency. However, space limitations and expensive installation costs prohibit physical flow meter installations. On the other hand, motor driven fans and pumps are essential components installed in HVAC systems. Since air or water flow rate, fan or pump head and power have correlations, which are determined by fan or pump performance, theoretically the flow rate can be virtually determined by either head, shaft power, or both. Head-power-based virtual flow meters provide more accurate results by eliminating the error caused by the flat section of head and power curves. The available power is either the motor input power obtained from the connected variable frequency drive (VFD) control panel or the VFD input power measured by a power meter. In both cases, the motor efficiency has to be applied to obtain the shaft power. In current head-power-based virtual meter development, motor efficiency is simply chosen as the motor efficiency under a rated frequency fed by sinusoidal power, In fact, the power frequency and harmonic created by the VFD will impact the actual motor efficiency. The purpose of this study is to develop head-power-based virtual air / water flow meters using the power obtained from either VFD or power meter with precise motor efficiency model. To achieve this purpose, the objectives are: to project motor efficiency using equivalent circuit theory with the variable frequency impact; to identify the impact of VFD-induced harmonics on the motor efficiency; to validate flow meter using motor efficiency with consideration of both frequency and harmonics impact from both a power meter and VFD output data, and finally verify the developed meter by comparing outcome of each developed model. Approaches followed to achieve these objectives are: investigation of work conducted by others to date; exploration of a theoretical model for virtual air / water flow meter in order to identify the relationship of fan / pump flow rate with measurable fan / pump head, motor power, power frequency and voltage; application of equivalent circuit theory for motor efficiency estimation; consideration of VFD induced energy losses including harmonic motor losses and investigation of their impact on motor efficiency calculations, and finally application of these explorations for the development of multiple theoretical models for the implementation of virtual air / water flow meters along with their validation through experiments. Comparison of outcomes from different meter models developed showed that the water flow rates determined using the model with impact of VFD induced harmonics degradation considered on VFD and motor efficiencies, proved to yield consistently most reliable results for full range of operating speeds, indicated by the R-square of 0.97 for instant measurement.


head-power based; virtual air/water flow meter; pseudo pump efficiiency; VFD harmonic degraded efficiency