CST – Computer Simulation Technology

State-Space Modeling and Simulation of a Saturated Core Fault Current Limiter

Fault Current Limiters (FCL) are designed to limit the fault currents in electrical networks and this article summarizes the CST EM STUDIO® (CST EMS) simulation of a particular type of current limiter, a saturated core FCL, which takes advantage of the change in the permeability between the saturated and unsaturated states of a magnetic core.

Two possible techniques can be applied to the simulation of an FCL. It is assumed that the core is laminated and hence suppresses induced eddy currents. In this case, an efficient method for FCL simulation, based on the generation of an equivalent non-linear circuit (ECE), can be applied. However, as a validation, the ECE may be validated by performing also a transient EM simulation and comparing the results. The ECE can be exported for use in circuit simulators with the benefits of arbitrary circuit complexity and efficiency. The re-use of the ECE in various circuit simulations offers, in such a case, a distinct advantage over an EM-based transient simulation....



Figure 1: 3D Model of the fault current limiter

A requirement of an FCL is the need to limit currents whilst maintaining, in contrast to conventional reactors, a negligible impedance under normal conditions. Power losses under normal state also need to be considered. Saturated FCLs can be either superconducting or non-superconducting [1].

A simple model of a single-phase FCL, shown in Figure 1, was created in CST EMS and consists of a DC bias coil, two AC current carrying coils and two steel cores. The principle of operation is as follows. The DC bias coil forces both cores into saturation but, under normal, non-fault conditions, the AC load current is too low to de-saturate the cores which behave as air-core inductors (with a relative core permeability of 1). However, desaturation of the core, with a significant change in the permeability, occurs under fault conditions i.e. high fault currents in the AC coil. As a result, the impedance limits the fault current in the AC coils. Two cores are required to limit both the half-cyclic positive and negative polarities of the fault current. The frequency of operation in this example is 50 Hz.



Figure 2: Core Non-Linear BH Curve

Figure 2 shows the non-linear BH curve used for the core.

With this model, two simulations are possible. A transient EM analysis is performed to firstly demonstrate the behavior of the device by checking the voltages and currents in the limiter as well as visualizing the permeability of the core as a function of time. Eddy currents are assumed to be negligible due to the laminated core. The setup of the model for the transient simulation requires the definition of the signals in both the AC and DC coils. To avoid an inrush effect and hence speed up the time required to reach steady state, a linearly rising sinusoidal voltage is applied to the AC coil as shown in the top curve in Figure 3. As a result, steady state is achieved after only 3 periods. The DC coil is excited with a constant current signal.



Figure 3: CST EM Transient LT Results for AC Coil: Top - Voltage; Bottom - Current - Variation with time

The measured current in the AC coil is shown in the bottom curve of Figure 3. The current limiting and non-linear effects can be clearly seen.

Another approach to solving this problem is the generation of an equivalent electric circuit (ECE) which may be used in circuit simulation. The benefit to such an approach, is that once a single equivalent circuit has been created, circuit simulations are rapid and allow analyses and optimization to be efficiently performed without the need to perform further EM simulations. Power system level simulation software, commonly referred to as ElectroMagnetic Transients Program (EMTP) [2] and applied to large and complex systems, require a large number equivalent circuits of transformers, reactors and rotating electric machinery such as generators.



Figure 4: Animation of permeability versus time indicating level of saturation in the core

The behavior of the device may be checked by not only observing the electrical response of the FCL but also the field distribution. In this case, Figure 4 shows the variation of the permeability as a function of time (in steady-state) which is a measure of the degree of saturation in both cores. Maximum permeability is in regions of low saturation and vice-versa.



Figure 5: Variation of inductance as a function of AC coil current

In order to generate the state-space model, a parameter sweep of the current in the AC coil is performed using the CST EMS Magnetostatic solver. For each value of current, an system inductances are automatically extracted. Figure 5 shows the non-linear variation of the inductance in the AC coil as a function of current. The State-Space feature is then used to generate either a CST DS or Synopsys® SABER RD equivalent circuit model.



Figure 6: Synopsys® Saber RD Schematics of the FCL for transient circuit simulation: with FCL State-Space Model (Top) and without (bottom)

The equivalent circuit can be generated for use in the integrated CST DS circuit simulation tool or for other commercially available circuit and system level simulators such as Synopsys Saber. Figure 5 shows two Synopsys® SABER RD schematics. The one for the modeling of the fault condition (top) with the CST EMS exported SABER equivalent circuit block. The lower schematic, for the simulation without an FCL model. A transient analysis is performed on both schematics to allow the current limiting effect of the FCL to be seen.



Figure 7: Synopsys® Saber Results - with FCL, peak current 500 A (Top) and without FCL, peak current 30 kA (Bottom)

The results in Figure 7 clearly show the effect of the FCL on the currents in the AC coils. In the upper curve, the FCL limits the fault current to 500 A peak which matches the value obtained from the transient simulation shown in Figure 3. In the lower curve, with no current limiter, the current reaches 30 kA peak.

This article serves to primarily demonstrate the ability to create an equivalent circuit of a magnetic device for use in system and circuit level simulation. The results for a simple, single phase FCL obtained by magnetostatic state-space analysis were confirmed by transient analysis. More complex devices with multiple coil / phase systems can also be easily extracted with CST EMS and its State-Space export feature. Other useful applications of the state-space model include the generation of models for use in power system level studies e.g. for analysis of sympathetic inrush current behavior in transformers.

References

[1] Moscrop, J.W., "Experimental Analysis of the Magnetic Flux Characteristics of Saturated Core Fault Current Limiters", IEEE Transactions on Magnetics, Vol.49, Issue 2, Feb. 2013.

[2] http://en.wikipedia.org/wiki/Emtp

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