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Power Electronics Development Center
StarSim: Why the state-space method is a better choice for the power electronics system simulation
StarSim is a state-space based fixed-step electrical system simulation software.
EMTP Method
The EMTP (Electromagnetic Transients Program) is the most classical power system simulation method. The basic idea of EMTP is to use the trapezoidal integration rule to discrete each circuit element and then form the system nodal matrix.
For example, the inductor will be transformed into a resistor and a current source.
The inductor is actually equivalent to a resistor and a current source. And it is observed that this current source is related with the inductor voltage.
State-Space Method
The state-space method is also a very classical electrical system simulation method. It first forms the state-space equations for the system, and then discretes the state-space equation with certain integration rule. For example, for the above simple circuit, the below state-space equation is formed.
StarSim then uses the implicit trapezoid rule to discrete state-space equations.
The Challenge of Power Electronics System Simulation
EMTP method and state-space method are equivalent for the linear time-invariant（LTI) systems. However, for the nonlinear system, such as the power electronics system, their performance will be quite different. The topology of power electronics system changes frequently. Handling the topology change poses a very big challenge of EMTP method. At the topology changing point (the switching instant), state variables (inductor currents and capacitor voltages) remain unchanged, however, inductor voltages and capacitor currents are not continuously.
where tz is the switching instant. The current sources of EMTP method usually contain variables such as inductor voltages and capacitor currents. It means that the value of current sources are not continuously either. If this discontinuity are not handle properly, the simulation software will produce less accurate results and even the numerical oscillation after switching events[1].
Unlike the EMTP method, the state-space method forms equations for state variables' differential, and state variables (inductor currents and capacitor voltages) remain unchanged, so it is easy to use state-space equations to accurately calculate dx/dt(tz+), i.e., inductor voltages and capacitor currents right after the switching instant. This is the core reason why the state-space will be superior than EMTP method for handling switching events.
The topology of power electronic system is frequently changing, so the state-space method is an ideal method for handling this kind of system simulation.
One core technology of StarSim is that it has a powerful compiler to form the state-space equations for the power grid and power electronics system.
Examples:
This is a simple buck circuit. Because of its simplicity, the analytic solution of its inductor current can be deduced. Then people can use this analytic result to compare and benchmark results produced by simulation software. It can be clear observed that StarSim does a very good simulation job for handling switching events (blue circles). It is very hard for other simulation software to produce such good results.
References:
[1] M.Hermann W.Dommel, Suppression of Numerical Oscillations in the EMTP
Kevin.Wang | kevin.wang@modeling-tech.com
R&D Director
ModelingTech Energy Technology Company
