SimPowerSystems

Simulating with Continuous Integration Algorithms

Simulink provides a variety of solvers. Most of the variable-step solvers will work well with linear circuits. However circuits containing nonlinear models, especially circuits with circuit breakers and power electronics, require stiff solvers.

Choosing an Integration Algorithm

Fastest simulation speed is usually achieved with ode23tb or ode15s with default parameters.

• Solver : ode23tb or ode15s
  Relative tolerance = 1e-3
  Absolute tolerance = auto
  Maximum step size = auto; Initial step size = auto.
  Initial step size = auto
  Maximum order (for ode15s) = 5
  

Normally, you can choose auto for the absolute tolerance and the maximum step size. In some occasions you might have to limit the maximum step size and the absolute tolerance. Selecting too small a tolerance can slow down the simulation considerably. The choice of the absolute tolerance depends on the maximum expected magnitudes of the state variables (inductor currents and capacitor voltages). For example, if you work with high-power converters where expected voltage and currents are thousands of volts and amperes, an absolute tolerance of 1e-1 or even 1.0 should be sufficient. If you are working with low-power circuits involving maximum values of 100 V and 10 A, you should use a smaller absolute tolerance, such as 1e-3 or 1e-2.

Simulating Switches and Power Electronic Devices

Two methods are used for simulation of switches and power electronic devices:

• If the switch is purely resistive the switch model is considered as part of the linear circuit. The state-space model of the circuit, including open and closed switches, is therefore recalculated at each switch opening or closing, producing a change in the circuit topology. This method is always used with the Breaker block and the Ideal Switch block because these elements do not have internal inductance. It is also applied for the Diode block and the Thyristor block, with Ron > 0 and Lon = 0, and for the Universal Bridge with forced commutated devices.
• If the switch contains a series inductance (Diode and Thyristor with Lon > 0, IGBT, MOSFET, or GTO), the switch is simulated as a current source driven by voltage across its terminals. The nonlinear element (with a voltage input and a current output) is then connected in feedback on the linear circuit, as shown in Figure 3-2.

You have therefore the choice to simulate diodes and thyristors with or without Lon internal inductance. In most applications, it is not necessary to specify an inductance Lon. However, for circuit topologies resulting in zero commutation or overlap angle you will have to specify a switch inductance Lon in order to help commutation.

Consider for example the circuit shown in the following figure. This circuit is available in the psbrectifier_ideal model. The thyristor bridge is fed from an infinite source (zero impedance) so that the commutation between thyristors is quasi instantaneous.

Figure 3-3: Three-Phase Thyristor Rectifier on Infinite Source

If you simulate this circuit without internal thyristor inductances (Lon = 0), you will observe high current spikes flowing in the three lines. This happens because during commutation two thyristors connected to the same positive or negative terminal of the bridge are in conduction for a short period of time, applying a line-to-line short circuit on the source (see Figure 3-4 following). During commutation, the current is limited only by the internal resistance of thyristors (with Ron = 0.01 ohms, the current reaches 7.35 kA (208²*sin(30) / (2*0.01) = or 245 times the normal DC current of 30 A). These short circuits can be avoided by using a small Lon = 1 µH in the thyristor model. If you repeat the simulation, you will get square current waveforms with a peak value of 30 A.

If you zoom on the line current during a commutation, you discover that the commutation is not instantaneous. The commutation time depends on the Lon value and the DC current.

Figure 3-4: Source Currents and DC Load Voltage with Lon = 0 and Lon = 1 µH

Choosing an Integration Method: Continuous or Discrete

Simulating Discretized Electrical Systems