There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Although the concept of variable-speed drives, based on utilization of multiphase machines, dates back to the late 1960s, it was not until the mid- to late 1990s that multiphase drives became serious contenders for various applications. These include electric ship propulsion, locomotive traction, electric and hybrid electric vehicles, ldquomore-electricrdquo aircraft, and high-power industrial applications. As a consequence, there has been a substantial increase in the interest for such drive systems worldwide, resulting in a huge volume of work published during the last ten years. An attempt is made in this paper to provide a brief review of the current state of the art in the area. After addressing the reasons for potential use of multiphase rather than three-phase drives and the available approaches to multiphase machine designs, various control schemes are surveyed. This is followed by a discussion of the multiphase voltage source inverter control. Various possibilities for the use of additional degrees of freedom that exist in multiphase machines are further elaborated. Finally, multiphase machine applications in electric energy generation are addressed.

Multiphase Electric Machines for Variable-Speed Applications

Numerical Initial Value Problems in Ordinary Differential Equations

This paper presents the evaluation of saturation and cross-magnetization effects in an interior permanent magnet synchronous motor (IPMSM) over the entire range of direct- and quadrature-axis excitations. The conventional two-axis machine model is modified in order to include the influence of saturation and cross-coupling effects on the variation of self- and cross-coupling inductances in the direct and the quadrature axis. The two-axis machine model parameters are evaluated by experiments performed on an IPMSM using a controlled voltage-source inverter and are compared with parameter values evaluated by the finite-element method. The evaluation of two-axis machine model parameters reveals significant saturation and cross-magnetization effects in both axes, especially in the flux-weakening regime.

Evaluation of saturation and cross-magnetization effects in interior permanent-magnet synchronous motor

Rating of roofs’ surfaces regarding their solar potential and suitability for PV systems, based on LiDAR data

High-temperature superconducting (HTS) material in bulk form is used to design a linear synchronous motor for an electromagnetic aircraft launch system. The motor is designed without an iron core. Stator coils are placed in the air while the permanent magnets used in conventional design of linear permanent magnet synchronous motors are replaced by the HTS bulk magnets. The physical, operational, and equivalent circuit parameters of the linear motor with HTS bulk magnets are compared with those of a linear permanent magnet synchronous motor and linear induction motor designed for the same application. Results show that utilizing superconducting magnets is only superior at temperatures below 40 K.

Design of a linear bulk superconductor magnet synchronous motor for electromagnetic aircraft launch systems

In this paper, parameters of the Jiles-Atherton (J-A) hysteresis model are identified using a stochastic search algorithm called differential evolution (DE). The J-A hysteresis model's parameters are identified by DE in such a way, that best possible agreement is obtained between the measured and model calculated hysteresis loops. This agreement is furthermore increased by improving the J-A hysteresis model. The improvement is achieved by replacing a constant pinning parameter in the J-A hysteresis model with a variable one. Here, the variable pinning parameter is written as a function of a magnetic field. By DE identified parameters are used in the J-A hysteresis model, which is included in the dynamic model of a single-phase transformer. The effectiveness of the improved J-A hysteresis model and parameters identification approach is verified with experiments and simulations.

Parameter Identification of the Jiles–Atherton Hysteresis Model Using Differential Evolution

This paper deals with the two-axis sun tracking system for a photovoltaic system. The trajectories of the sun tracking system are determined in an optimization procedure. The optimization goal is maximization of an electric energy production in the photovoltaic system considering the tracking system consumption. Determination of the tilt angle and azimuth angle trajectories is described as a nonlinear and bounded optimization problem, where the objective function is not available in the explicit form. A stochastic search algorithm called Differential Evolution is used as an optimization tool. In the optimization procedure, the objective function is evaluated by using the models of available solar radiation, tracking system consumption, and the efficiency of solar cells with the appropriate dc/dc converters. The problem bounds are given in the form of lower and upper bounds for both angles and time and angle quantization. The results presented in the paper show, that the optimal trajectories for the tilt and azimuth angle depend on the available solar radiation, solar cell efficiency, tracking system consumption and the optimization bounds.

Gorazd Štumberger

Papers

Evaluation of saturation and cross-magnetization effects in interior permanent-magnet synchronous motor

Rating of roofs’ surfaces regarding their solar potential and suitability for PV systems, based on LiDAR data

Design of a linear bulk superconductor magnet synchronous motor for electromagnetic aircraft launch systems

Parameter Identification of the Jiles–Atherton Hysteresis Model Using Differential Evolution

Maximum Efficiency Trajectories of a Two-Axis Sun Tracking System Determined Considering Tracking System Consumption