SimPowerSystems

Modeling a Nonlinear Resistance

The technique for modeling a nonlinear resistance is similar to the one used for the nonlinear inductance.

We use as an example a metal-oxide varistor (MOV) having the following V-I characteristic defined by the equation

where

v, i =	Instantaneous voltage and current
Vo =	Protection voltage
Io =	Reference current used to specify the protection voltage
=	Exponent defining the nonlinear characteristic (typically between 10 and 50)

The following figure shows an application of such a nonlinear resistance to simulate a MOV used to protect equipment on a 120 kV network. In order to keep the circuit simple, only one phase of the circuit is represented.

Figure 1-27: Nonlinear Resistance Applied on a 120 kV Network

Using blocks of the powerlib and Simulink libraries, build this circuit. Group all components used to model the nonlinear model in a subsystem named Nonlinear Resistance. Use an X-Y Graph block to plot the V-I characteristic of the Nonlinear Resistance subsystem.

Notice that the model does not use a Look-Up Table block as in the case of the nonlinear inductance model. As the analytical expression of current as function of voltage is known, the nonlinear I(V) characteristic is implemented directly with a Fcn block from the Fcn & Tables library of Simulink.

This purely resistive model contains no states. It produces an algebraic loop in the state-space representation of the circuit, as shown in the next figure. See Power System Block Reference, for more details on how the Power System Blockset works.

Figure 1-28: Algebraic Loop Introduced by the Nonlinear Resistance Model

Although Simulink is able to solve algebraic loops, this could result in slow simulation times. It is therefore recommended that you break the loop with a block that will not change the nonlinear characteristic. We have introduced a first-order transfer function H(s) = 1/(1+Ts) in the system, using a fast time constant (T = 0.01 µs).

Use the technique explained for the nonlinear inductance block to mask and customize your nonlinear resistance block as shown.

Figure 1-29: Dialog Box of the Nonlinear Resistance Block

Open the dialog box of your new masked block and enter the parameters shown in Figure 1-29. Notice that the protection voltage Vo is set at 2 p.u. of the nominal system voltage. Adjust the source voltage at 2.3 p.u. by entering the following peak amplitude:

• 120e3/sqrt(3)*sqrt(2)*2.3
  

Save your circuit as circuit8.

Using the ode23tb integration algorithm, simulate your circuit8 system for 0.1 s. The results are shown below.

Figure 1-30: Current and Voltage Waveforms and V-I Characteristic Plotted by the X-Y Graph Block

Customizing Your Nonlinear Model

Creating Your Own Library