Circuit simulation analysis (modeling) method for switching power supply

The main circuit simulation analysis methods include: state variable method, node analysis method, improved node analysis method, state space averaging method, etc.

1) Simulation technology based on state variable method

The state variable method can easily obtain the transient performance of the circuit and evaluate the stability of the circuit. The state variable method uses the voltage and current of certain branches in the circuit as state variables to establish the state equation of the circuit. Generally, the voltage on the capacitor and the current in the inductor are taken as unknown state variables, and then the equations are listed using graph theory to determine the proper tree of each circuit. The circuit variables are not directly included in the state variables, but are obtained using a set of explicit algebraic equations.

For discrete circuits such as switching converters, the piecewise linear state equations of the circuit should be listed first, and then the state transfer law should be found, and the nonlinear differential equations describing the circuit should be derived from this. This method is called discrete time domain method. COSMIR, a system-oriented switching converter simulation software developed by the Virginia Power Electronics Center in the United States, belongs to this type. It idealizes the switching device, and each operating mode of the converter is described by a set of linear time-invariant state equations. After considering the switching conditions, the steady-state response or large-signal transient response can be quickly obtained by using direct digital integration or analytical methods. There are also discrete time domain simulation programs based on the mesh method or node method.

The disadvantages of simulation technology based on the state variable method are: it is not compatible with general circuit simulation programs such as SPICE; due to the idealization of switching devices, it is not possible to analyze the changes in electrical stress on the switching devices when the devices are turned on or off.

2) Simulation technology based on node analysis method

The simulation technology based on the node analysis method can be applied to the simulation of large systems such as power systems. There are programs such as EMTP, ATP, and PECAN. EMTP is a tool for transient analysis of power systems, and ￣｛＼TP is a simulation tool for power converters and electric drives. PECAN is an analysis program dedicated to simulating power electronic closed-loop systems. The main disadvantages of simulating power electronic circuits based on the node analysis method are: insufficient processing of power supply, failure to include power supply-related components; inconvenience in obtaining branch currents; difficulty in achieving effective digital integration; special techniques are required to analyze the zeros and poles of linear circuits; and difficulty in quickly analyzing the steady state of power electronic circuits.

3) Simulation technology based on improved node analysis method

The node analysis method is improved by introducing appropriate branch currents, including voltage sources and various current-related components. The corresponding branch relationships become additional circuit equations, which partially improves some of the shortcomings of the above-mentioned node analysis method. The SPICE general circuit simulation program is based on this method. In this technology, the direct method is used to solve the equations, that is, the nonlinear algebraic-differential equations are converted into a set of nonlinear difference equations, the Newton-Raphson method is used to iteratively solve the equations, and the sparse LU decomposition technology is used to continuously solve the linear algebraic equations. Its main disadvantages are still: the steady-state analysis of power electronic circuits is time-consuming; the zero and pole analysis of linear circuits requires special techniques and more circuit variables.

4) Simulation technology based on state space averaging method

The state space averaging method is currently internationally recognized as an effective method for analyzing PWM switching converters. Its essence is: using the average state variable within a cycle to transform a nonlinear, time-varying, switching circuit into an equivalent nonlinear, time-invariant, continuous circuit, so that large signal transient analysis can be performed on the switching converter, and its small signal transfer function and zero and pole configuration can be determined to establish a state space average circuit model. The Switching CONverter Analysis Program (SCAP) developed by the California Institute of Technology is based on the state space averaging method and can perform DC and small signal analysis on personal computers.

When using the SPICE (Simulative Program With Integrated Circuit Emphasis) general circuit program to simulate a switching converter, the concept of state-space averaging is also combined to establish simulation models of the switching converter power circuit and control integrated circuit. SPICE simulation subroutines are compiled and attached to the SPICE program to perform large-signal, small-signal transient analysis and DC analysis.