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This paper proposes a novel online solution, i.e. Modified-Equilibrium Optimizer-Levenberg-Marquardt (M-EO-LM) algorithm, for the symmetric and asymmetric harmonic elimination pulse width modulation (HEPWM) methods of the modular multilevel cascaded converters. A detailed comparison of the proposed M-EO-LM algorithm with nine state-of-the-art algorithms is also presented for twenty-nine unimodal, multimodal and composite benchmark test functions. M-EO-LM has proven its effectiveness by outperforming these algorithms. EO algorithm is first introduced for the solution of HEPWM method. Its comparison with several state-of-the-art algorithms depicts its superiority; but it gets stuck in the local minima. Modified-EO (M-EO) solves the problem by enhancing its exploration ability, and is then attached to a rapid calculus-based LM method to form the novel M-EO-LM algorithm. M-EO-LM algorithm initiates the solution process by solving the HEPWM equations for nine angles ( $N=9$ and $0.78\leq M\leq 6.86$ ) offline in only two iterations, depicting its remarkable convergence ability. Solution angles are then divided into several groups, serving as the search space for the online M-EO-LM algorithm. A comparison between HEPWM and nearest level modulation methods based on the output voltage THD values is provided to report the maximum number of solvable HEPWM angles for a complete online solution. These angles ( $N=8$ and $0.78\leq M< 5.18$ ) are then solved online using the M-EO-LM algorithm. Comparing the computational times of the proposed online algorithm with differential evolution-Newton Raphson algorithm proves the rapid solution behavior of the M-EO-LM algorithm, validated through the simulation and real-time experimental results.

The widespread use of three-phase cage induction motors in so many critical industrial, commercial and domestic applications means that there is a real need to develop online diagnostic systems to monitor the state of the machine during operation. This paper presents a hybrid diagnostic system that combines a model-based strategy with a fuzzy logic classifier to identify abnormal motor states due to single-phasing or inter-turn stator winding faults. Only voltage and current measurements are required to extract the fault symptoms, which are represented as model parameters variations in an equivalent virtual healthy motor, negating the need to use complex models of faulty machines. A trust-region method is used to estimate the machine model parameters, with the final decision on the type, location and extent of the fault being made by the fuzzy logic classifier. The proposed diagnostic system was experimentally verified using a 1.0 hp three-phase test induction motor. Results show that the proposal method can efficiently diagnose single phasing and inter-turn stator winding faults even when operating with unbalanced supply voltages and in the presence of significant levels of measurement noise.