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Simulating Discretized Electrical Systems
Discretization is performed by dragging the Discrete System block in your system. The sample time is specified in the block dialog box. Next time that you start the simulation, the electrical system will be discretized using the Tustin method, which is equivalent to a fixed-step trapezoidal integration. In order to avoid algebraic loops, the electrical machines are discretized using the Forward Euler method.
When you discretize your system, the precision of the simulation will be controlled by the time step. If you use too large a sample time, the precision may 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 will 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 will have to reduce the time step. These devices, the insulated-gate-bipolar-transistor (IGBT), the field-effect-transistor (FET), and the gate-turn-off thyristor (GTO) are usually operating at high switching frequencies. For example, simulating a pulse-width modulated (PWM) inverter operating at 8 kHz would require a 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 will be improved by using a discrete control system.
Limitations with Nonlinear Models
Discretization of circuits containing forced-commutated power electronic
devices (IGBT GTO or FET) is permitted only with the Universal Bridge
block. Discretization of circuits containing individual forced commutated
devices is not allowed.For example, an attempt to discretize the buck DC
chopper circuit saved in the psbbuckconv.mdl demonstration file will
produce a warning message as shown on Figure 3-5.
Figure 3-5: A Circuit Containing Individual Forced Commutated Electronic Switches Cannot be Discretized
In this circuit, opening of the GTO will force quasi instantaneous conduction of the free wheeling diode. If the circuit was discretized, the diode would be fired with one step delay, an the inductive current chopping would produce large overvoltages.However, for conventional converter topologies as in the case of the Universal Bridge, the switch interactions are known in advance. For example, in a six-switch IGBT/Diode inverter (Figure 3-6), opening of IGBT1 causes instantaneous conduction of diode D2 in the same arm. As the circuit topology is predetermined, it is possible to force firing of the diode in the same step that the IGBT opens. If you prefer to use individual IGBT and Diode blocks to simulate a complete inverter, you should use a continuous method.
Figure 3-6: IGBT Inverter Simulated by the Universal Bridge
When using electrical machines in discrete systems, you may have to use a small "parasitic" resistive load, connected at the machine terminals in order to avoid numerical oscillations. Large sample times request larger loads. The minimum resistive load is proportional to the sample time. As a rule of thumb, remember that with a 25 us 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.
Diodes and thyristors used in a discretized circuit must have a zero internal inductance. If you discretize a circuit containing diodes or thyristors with Lon>0, the Power System Blockset will prompt you a warning, indicating that Lon will be set to zero.
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