## How to model an inrush limiter with PSIM

An NTC is typically used to limit inrush currents, it is essentially a resistor that has temperature dependency. When the element is cold the resistance is larger and when it is hot the resistance is lower. This is the key functionality that needs to be modeled an element that heats up, that has a changing impedance with this heating. We need:

• a lookup table with resistance as a function of temp
• model the thermal equivalent circuit of power, in watts, dissipated by the element and what the resulting temperature will be.

This is relatively straightforward and can be modelled with a controlled current source. This video explains how to model a variable resistor with a lookup table, we just need to properly calculate the device temperature to lookup what the resistance will be.

This is an NTC model

The variable resistor is this part where we measure the voltage across the current source, then divide by the resistance from the lookup table to determine what the current for the current source will be. With the controlled sources we model I = V/R. One source does the division while the other sets the current of the branch.

The area highlighted in Green shows the thermal equivalent circuit. The power dissipated by the element is P = V*I, so we need the (voltage across)*(current through). The node "t" is the temperature of the device which then drives the lookup table which then gives us the resistance for the above part of the model.

This value drives a standard thermal equivalent circuit where:

• Temperature (dC) = Voltage; 1dC = 1V
• Power (Joules/s) = Current (Amps); 1W = 1Amp
• Thermal impedance, R theta, (dC/W) = Resistance (ohms); 1 dC/W = 1 Ohm
• thermal time constant in seconds

In the figure the R and the C are representing the thermal impedance and the thermal time constant.

We can directly convert the thermal impedance and use this to define the "R"

The C is defined by (Thermal time constant) / (Thermal impedance).

We can use an example from  Ametherm SL22to calculate.

So R = 30.864 ohms  (1/32.4m) we need W/dC not mW/dC

C = 94/30.864= 3.045; 94 being the time constant = R*C

IMPORTANT: you need to give the capacitor an initial condition which is the initial ambient temp!

You can use the curve extraction tool to pull out the T vs R curve or just download the data. In this example I took the "A" curve and scaled by the 25dC resistance.

Example is attached.