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In this paper, three metaheuristic optimization algorithms: genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE) are compared in terms of minimizing the total owning cost (TOC) of the active part of a three-phase shell-type distribution transformer. The three methods use six inputs: power rating, primary voltage, secondary voltage, primary and secondary winding connections, and frequency. The TOC of the transformer, which includes the cost of the basic materials of the transformer plus the cost of losses, is minimized under the imposed constraints (excitation current, impedance, no-load losses, load losses, and efficiency) usually specified in the standards. As a case study, the three algorithms are applied to optimize the design of a three-phase shell-type distribution transformer of 750 kVA. All applied metaheuristic algorithms provide good results, while DE avoids local optima leading to better TOC reduction. The results of the optimization algorithms used are superior to those of the manufacturer, showing a 6% TOC reduction. Optimization of the design of a power transformer may have important implications for reducing greenhouse gas emissions and extending the lifetime of the equipment.

The conventional methods of parameter estimation in transformers, such as the open-circuit and short-circuit tests, are not always available, especially when the transformer is already in operation and its disconnection is impossible. Therefore, alternative (non-interruptive) methods of parameter estimation have become of great importance. In this work, no-interruption, transformer equivalent circuit parameter estimation is presented using the following metaheuristic optimization methods: the genetic algorithm (GA), particle swarm optimization (PSO) and the gravitational search algorithm (GSA). These algorithms provide a maximum average error of 12%, which is twice as better as results found in the literature for estimation of the equivalent circuit parameters in transformers at a frequency of 50 Hz. This demonstrates that the proposed GA, PSO and GSA metaheuristic optimization methods can be applied to estimate the equivalent circuit parameters of single-phase distribution and power transformers with a reasonable degree of accuracy.

In this article, the parameter identification of a brushless DC motor (BLDC) is presented. The approach here presented is based on a direct identification considering a three-phase line-to-line voltage electromagnetic torque as function of the electric currents and rotor speed. The estimation is divided into two stages. First, the electrical parameters are estimated by well-known no-load and DC tests. Consequently, estimation of mechanical parameters is performed using a recursive Least Square Algorithm. The proposed approach is validated by comparing model responses to motor real time responses. Additionally, the design, digital simulation and real time implementation of a PI rotor speed controller, based on the estimated model, validate the identification proposal presented here.

In this paper, a new analytical method using Lagrange equations for the analysis of magnetic levitation (MagLev) systems is proposed, using Thomson’s jumping ring experiment. The method establishes the dependence of the primary and induced currents, and also the equilibrium height of the levitating object on the input voltage through the mutual inductance of the system. The mutual inductance is calculated in two ways: (i) by employing analytical formula; (ii) through an improved semi-empirical formula based on both measurements and analytical results. The obtained MagLev model was analyzed both analytically and numerically. Analytical solutions to the resulting equations were found for the case of a dynamic equilibrium. The numerical results obtained for the dynamical model under transient operation show a close correspondence with the experimental results. The good precision of the analytical and numerical results demonstrates that the developed method can be effectively implemented.

The presence of harmonics in the load current considerably increases stray losses in electric transformers. In this research paper, a new model for computing the electromagnetic field (EMF) and eddy current (EC) losses in transformer tank covers is derived considering harmonics. Maxwell’s equations are solved with their corresponding boundary conditions. The differential equation thus obtained is solved using the method of separation of variables. The obtained expressions do not require the use of special functions, accommodating them for practical implementation in the industry. The obtained formulas are evaluated for different spectrum contents of the load current and losses. The results are in good agreement with simulations carried out using the Altair Flux finite element (FE) software.