Circuit Simulation Parameters PLECS 1.5 Online Help Circuit Simulation Parameters PLECS allows you to specify various simulation options, such as the method used for simulating a circuit and related parameters. To open the parameter dialog, select PLECS parameters from the Simulation menu of the schematic editor. Working Principle of PLECS PLECS is based on a piece-wise linear state-space approach: A circuit containing only linear components can be described mathematically by one set of time-invariant equations: where is the state variable vector with the inductor currents and capacitor voltages, and is the input vector with the source voltages and currents. The output vector contains voltages and currents measured in the circuit. If a circuit consists not only of linear components but also of one or more ideal switches, every combination of switch positions (i.e. open/closed) is described by a different set of matrices. The basic working principle of PLECS is outlined in the figure below. When you start a simulation, PLECS analyzes your circuit schematic and builds the state-space model for the initial switch positions (i.e. in general: all open). During the simulation, the Switch Manager monitors the gate signals of the switches and the currents and voltages measured in the circuit and decides whether a switching action is necessary. If any switching occurs, a new set of state-space matrices is calculated on the fly. Diode Turn-On Threshold Voltage This parameter globally controls the turn-on behavior of line commutated devices such as diodes, thyristors, GTOs and similar semiconductors. A diode starts conducting as soon as the voltage across it becomes larger than the sum of the forward voltage and the threshold voltage. Similar conditions apply to the other line commutated devices. The default value for this parameter is 1e-3. For most applications the threshold voltage could also be set to zero. However, in certain cases it is necessary to set this parameter to a small positive value to prevent line commutated devices from bouncing. Bouncing occurs if a switch receives an opening command and a closing command repeatedly in subsequent simulation steps or even within the same simulation step. Such a situation can arise in large, stiff systems that contain many interconnected switches. Continuous State-Space Method When simulating a circuit with the continuous method, PLECS employs the Simulink solver to solve the differential equation and integrate the state variables. The Switch Manager communicates with the solver in order to ensure that switching occurs at the correct time. This is done with Simulink's zero-crossing detection capability. For this reason the continuous method can only be used with a variable-step solver. In general, the default solver of Simulink, ode45, is recommended. However, your choice of circuit parameters may lead to stiff differential equations, e.g. if you have large resistors connected in series with inductors. In this case you should choose one of Simulink's stiff solvers. Discrete State-Space Method When simulating a circuit with the discrete method, PLECS transforms the circuit into a discrete state-space model with fixed time steps. The continuous state-space equations are discretized using the bilinear transformation (also known as Tustin's method). The integration of the state variables is thus replaced with a simple update rule: where is the discretization time step. With line commutated power electronic devices such as diodes and thyristors, the natural switching instants will generally not coincide with a time step of the discretized circuit model. The Switch Manager detects such non-sampled events and uses an interpolation scheme to ensure that the state variables are always consistent with the switch positions. Options Sample time This parameter determines the rate with which Simulink samples the circuit. A setting of auto or -1 means that the sample time is inherited from the Simulink model. Refine factor This parameter controls the internal step size which PLECS uses to discretize the state-space equations. The discretization time step in the equations above is thus calculated as the sample time divided by the refine factor. The refine factor must be a positive integer. The default is 1. Choosing a refine factor larger than 1 allows you to use a sample time that is convenient for your discrete controller while at the same time taking into account the usually faster dynamics of the electrical system. ZC step size This parameter is used by the Switch Manager when a non-sampled event (usually the zero crossing of a current or voltage) is detected. It controls the relative size of a step taken across the event. The default is 1e-9. Tolerances The error tolerances are used to check whether the state variables are consistent after a switching event. The defaults are 1e-3 for the relative tolerance and 1e-6 for the absolute tolerance. Note  The discrete method cannot be used with circuits that contain direct non-linear feedbacks because in conjunction with Tustin's method this would lead to algebraic loops. This applies for instance to the standard models for the induction machine and the two synchronous machines with wound rotor. For these machines the library contains discretizable equivalents, in which the feedback loops have been broken using the Integrator block.