Adaptive time-step control algorithm for nonlinear time-domain envelope transient

Abstract

This thesis outlines a general method to analyze circuits with several time variables using a technique known as Multi Partial Differential Equation, MPDE. The key idea of MPDE is to convert the system of ordinary differential equations that describes a circuit into a system of partial differential equations using multiple time dimensions. Multivariate Finite Difference Time Domain (MFDTD) and Time Domain Envelope following (TD-ENV) methods are based on the MPDE and give faster simulation time and reduce the memory requirements for a system with widely separated time scales. In this research, a novel time-step control method in one of the time dimensions is proposed. The algorithm uses two models: the first is the set of differential algebraic equations that represent the circuit. The second is a ‘coarse’ model that is cheap to evaluate. The main difference between the traditional and the proposed method is the dynamic tolerance changes and coarse model representation. The optimum time step is estimated from an error term obtained from the coarse model. An estimation of the Local Truncation Error (LTE) is used to optimize the time step size. The simulations show that fewer time steps are rejected, i.e. faster computation, compared with a traditional time step control algorithm. A rectifier circuit is simulated to show the difference between the conventional method and the MFDTD method for steady state analysis. The MFDTD method is used in steady state analysis and the TD-ENV method is used in transient simulations. A DC-DC converter circuit simulation using adaptive TD-ENV and its advantages are presented. Simulations of a switched rectifier circuit and DC-DC converter circuit with different controllers (P and PI) are presented. The PI controller circuit experiences a duty cycle oscillation and higher LTE, which increases the simulation time with the proposed model. The FDTD method is used to solve the problem in one of the dimensions (fast time axis) and the Backward Euler (BE) method is used on the other dimension (slow time axis).