Abstract
Automated simulating of power electronics systems is currently performed by means of nodal analysis method combined with implicit numerical integration schemes. Such method allows to find transient solutions, even when the integrated system is stiff, however, it leads to some difficulties when simulating big systems and sometimes to the deterioration of computations quality, that is reflected in decrease in accuracy, oscillations of solutions, which are not present in the initial model. This paper analyzes the shortcomings of this approach, and proposes to apply explicit numerical schemes with stability control on the integration step and with reduction of some of state variables. A brief description of the method of finding transient solutions and an example of the analysis are also given in the present paper.
Highlights
Automated simulating of power electronics systems is currently performed by means of nodal analysis method combined with implicit numerical integration schemes
This paper analyzes the shortcomings of this approach, and proposes to apply explicit numerical schemes with stability control on the integration step and with reduction of some of state variables
If we reduce the state variable x, i.e. remove the capacitor from the circuit, you will obtain the trivial solution x = 0, which is more accurate than: an explicit Euler scheme, with h > τ; an implicit Euler scheme, with h > 1.7 τ; a trapezoidal scheme, with h > 2τ; a Runge-Kutta-Merson scheme, with h > 2 τ
Summary
Implicit schemes have proven to be so popular, because they partially solve the problem of “stiff” [3] occurring when trying to integrate equations with time constants of transient response, spread out onto several orders of mag-. At the same time the explicit Euler scheme and Runge-Kutta-Merson scheme (hereafter RKM) will have the oscillations grow exponentially, while the trapezoidal schemes will have them dampen slightly—the bigger is the step, the slower is the dampening. The latter property of trapezoidal schemes, combined with the problem of “excess Q-factor” mentioned above may give rise to significant fluctuations in solutions which will not be present in the actual device. Note that the Runge rule [5] according to which the accuracy of the integration by other methods is evaluated, ceases to operate in the case of stiff systems
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