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Simulating Discretized Electrical Systems

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Introduction Limitations of Discretization with Nonlinear Models

Introduction

You implement discretization by selecting Discretize electrical model in the Powergui block dialog box. The sample time is specified in the block dialog box. The electrical system is discretized using the Tustin method, which is equivalent to a fixed-step trapezoidal integration. To avoid algebraic loops, the electrical machines are discretized using the Forward Euler method.

The precision of the simulation is controlled by the time step you choose for the discretization. If you use too large a sample time, the precision might not be sufficient. The only way to know if it is acceptable is to repeat the simulation with different sample times or to compare with a continuous method and to find a compromise for the largest acceptable sample time. Usually sample times of 20 µs to 50 µs give good results for simulation of switching transients on 50 Hz or 60 Hz power systems or on systems using line-commutated power electronic devices such as diodes and thyristors. However, for systems using forced-commutated power electronic switches, you must reduce the time step. These devices, the insulated-gate-bipolar transistor (IGBT), the field-effect transistor (FET), and the gate-turnoff thyristor (GTO) are usually operating at high switching frequencies. For example, simulating a pulse-width-modulated (PWM) inverter operating at 8 kHz requires a maximum time step of 1 µs or less.

Note that even if you discretize your electric circuit, you can still use a continuous control system. However, the simulation speed is improved by use of a discrete control system.

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Limitations of Discretization with Nonlinear Models

There are a few limitations to discretizing nonlinear models.

Minimal Load Is Required at Machine Terminals

When using electrical machines in discrete systems, you might have to use a small parasitic resistive load, connected at the machine terminals, to avoid numerical oscillations. Large sample times require larger loads. The minimum resistive load is proportional to the sample time. As a rule of thumb, remember that with a 25 µs time step on a 60 Hz system, the minimum load is approximately 2.5% of the machine nominal power. For example, a 200 MVA synchronous machine in a power system discretized with a 50 µs sample time requires approximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 µs, a resistive load of 4 MW should be sufficient.

Lon = 0 Is Used for Power Electronic Devices

Naturally commutated devices (diodes and thyristors), as well as forced-commutated devices (IGTO, IGBT, FET), used in a discretized circuit must have a zero internal inductance. If you discretize a circuit containing power electronic devices with Lon > 0, SimPowerSystems software prompts you with a warning indicating that Lon will be reset to zero.

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Simulating with Continuous Integration Algorithms

Simulating Power Electronic Models

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