Abstract
Time-variant inductors exist in many industrial applications, including sensors and actuators. In some applications, this characteristic can be deleterious, for example, resulting in inductive loss through eddy currents in motors designed for high efficiency operation. Therefore, it is important to investigate the electrical dynamics of systems with time-variant inductors. However, circuit analysis with time-variant inductors is nonlinear, resulting in difficulties in obtaining a closed form solution. Typical numerical algorithms used to solve the nonlinear differential equations are time consuming and require powerful processors. This investigation proposes a nonlinear method to analyze a system model consisting of the time-variant inductor with a constraint that the circuit is powered by DC sources and the derivative of the inductor is known. In this method, the Norton equivalent circuit with the time-variant inductor is realized first. Then, an iterative solution using a small signal theorem is employed to obtain an approximate closed form solution. As a case study, a variable inductor, with a time-variant part stimulated by a sinusoidal mechanical excitation, is analyzed using this approach. Compared to conventional nonlinear differential equation solvers, this proposed solution shows both improved computation efficiency and numerical robustness. The results demonstrate that the proposed analysis method can achieve high accuracy.
Highlights
Time-variant inductors exist in many industrial applications such as electric motors [1], power electronics [2], magnetic bearings [3], Linear Variable Differential Transformers (LVDT) [4], piezoelectric actuators [5] and fluidic valves [6]
The eddy current loss is a major loss in addition to Ohmic losses in the copper, hysteresis loss and mechanical loss [7,8,9], especially if a motor is running at high speed [10,11]
The industry has been expected to reduce induction loss in order to improve the power efficiency but to cancel the steady state ripples resulting from the eddy currents
Summary
Time-variant inductors exist in many industrial applications such as electric motors [1], power electronics [2], magnetic bearings [3], Linear Variable Differential Transformers (LVDT) [4], piezoelectric actuators [5] and fluidic valves [6]. In many applications, such as model predictive control with high speed motors [21,22], it is still not fast enough or economical [23] To overcome these challenges, an optimized, fast, sufficiently precise approximate solution for typical systems with variable inductance can be an alternative approach, while academia has still left it as blank. An optimized, fast, sufficiently precise approximate solution for typical systems with variable inductance can be an alternative approach, while academia has still left it as blank This investigation proposes a nonlinear technique for analyzing systems containing time-variant inductors, such as motors and solenoids, that are driven by or can be approximated as being driven by a DC source.
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