In-situ efficiency estimation of induction motors under unbalanced voltages using heuristic optimization algorithms

Voltage unbalance factor in three-phase power systems adversely affects induction motor performance and efficiency, particularly in industrial settings. Conventional efficiency tests based on IEEE 112 are intrusive and impractical for in-situ applications. This paper proposes a non-intrusive efficiency estimation approach for three-phase induction motors operating under unbalanced voltages, combining positive/negative sequence modeling, IEEE 112-F1/Form F2 loss calculations, and heuristic optimization. Four equivalent circuit parameters (stator leakage reactance, magnetizing reactance, core-loss resistance, and rotor resistance) are identified from terminal measurements and nameplate data. The framework is implemented using three heuristic algorithms, Particle Swarm Optimization (PSO), Harris Hawks Optimization (HHO), and Fox Optimization Algorithm (FOX), and experimentally validated on a 1.1 kW induction motor for four load factors (25%, 50%, 75%, 100%) and Voltage Unbalance Factor (VUF) levels between 0 and 5%. IEEE 112-A is used as the reference method. The results show that PSO and HHO reproduce IEEE 112-A efficiencies with high accuracy for medium and high load factors (LF ≥ 50%), with full-load deviations typically below 1% for all VUF levels, while FOX exhibits larger errors, particularly at light load. Furthermore, the experiments confirm that efficiency degradation due to VUF is most pronounced at low load factors, even when VUF remains within the 5% NEMA limit. The proposed framework enables practical in-situ efficiency monitoring under realistic unbalanced supply conditions without motor shutdown.