Current Interruption Basics

Abstract

In this chapter, the principle of current interruption in power switching devices with mechanically separating contacts is presented. The interruption is associated with initiation and extinction of a switching arc. First, a qualitative description of current interruption in power networks with various load types is given, and important parameters and concepts are introduced.

Appendices

Exercises

Problem 1—Switchgear Introduction

What are the main requirements for a switching device?

What are the main differentiators between different types of switching devices?

Problem 2—Energy Dissipation in Arc

Assume a constant arc voltage of 600 V and a sinusoidal current with the frequency of 50 Hz peak value of 50 kA. The arc burns for a half period before it is extinguished.

Calculate the total energy dissipated in the arc.

What is the maximum and mean power dissipation?

Problem 3—Derive Current Density Equation for Moving Charge Carriers

Consider the arc cross-section in Fig. 2.25.

Fig. 2.25

Figure of problem 3

The charge carriers in the arc with the charge q _e and the density n _e move with a velocity, v _e . Show that the current density, J, can be expressed as:

$$J = q_{e}n_{e } v_{e}$$

Problem 4—Conductivity in Gaseous Media

Figure 2.11 shows the relation between temperature and conductivity (in air). Why is there such a big difference in conductivity at different temperatures?

Explain in your own words the process of transition (a) from insulating to conducting state and (b) from conducting to insulating state by explaining the role of different physical processes including dissociation, ionization, recombination and heat transport.

Problem 5—Thermal Conductivity

Considering Fig. 2.26, please explain why H₂ and SF₆ have distinct peaks at in their thermal conductivity in contrast to the inert gas Argon.

Fig. 2.26

Figure of problem 5

Computer Exercises

In the following computer exercises, MATLAB/Simulink is used to model a switching arc and the resulting transient recovery voltage. A demonstration model that exists in the MATLAB package (power_arcmodels) will serve as the starting point for this exercise.

Problem 1

Implement the circuit of Fig. 2.27 in Simulink. Use existing Cassie and Mayr arc models to simulate the current interruption process. The parameters of the Cassie and Mayr models are set to, tau = 1.2 μs and Uc = 2 kV, and tau = 0.3 μs and P = 30.9 kW, respectively. The following starting values are used for different parameters:

$$\begin{aligned} & L_{s} = 3. 5 2\,{\text{mH}},L_{p} = 5. 2 8\,{\text{mH}},L_{l} = 0. 6 2 5\,{\text{mH}},C_{p} = 1. 9 8\,{\text{mF}},C_{l} = 1. 9 3\,{\text{nF}},R_{p} = 30\,{\text{W}},R_{l} = 4 50\,{\text{W}} \\ & \quad {\text{and}}\quad U = 60\,{\text{kV}}. \\ \end{aligned}$$

Fig. 2.27

Figure of problem 1

Explain the difference in arc voltage and current resulting from the two models. Which one is able to model a successful interruption? Which gives a more realistic arc voltage before current zero? Which one gives a realistic voltage after current zero?

Problem 2—Cooling Power and Time Constant in the Mayr Model

In this problem, only the Mayr model is considered. By double-clicking the breaker model, you can set new values to the parameters:

• Arc time constant, tau

• Cooling power, P

If the cooling power is reduced, the interruption capability of the breaker is reduced.

• Find the minimum cooling power needed to interrupt this circuit.

If the arc time constant is increased the recovery of insulation medium is slower, and the interruption capability is reduced.

• Set P back to the original, 30,900 W. Find the critical arc time constant.

Problem 3—Transient Recovery Voltage, TRV (Using the Mayr Arc Model)

• (a) In this problem, a terminal short circuit fault is investigated. The short circuit is simply generated by reducing the value of the load impedance (the arc model does not allow for zero impedance between its output and ground). Replace the load RLC combination in Fig. 2.27 by a 1 mΩ resistor.

  • Set cooling power, P, to 10,000 W

  • Set arc time constant, tau, to 0.6e−6

  • Run the model and find:

    • Peak of the TRV U _peak

    • Approximate rate of rise of recovery voltage, RRRV (given in V/µs)

• (b) In a case like this, the RRRV is very dependent on the capacitance of the supply circuit (left side)

  • Adjust the supply side capacitance to increase the RRRV.

  • What is the maximum RRRV that this breaker can interrupt at this given current?

Problem 4—Current Limiting Circuit Breakers

The Mayr arc model gives a good description of the arc behaviour near current zero. In this problem, a series combination of Cassie and Mayr arc models as shown in Fig. 2.28 is used to model the arc voltage during the entire arcing time. The parallel resistor R _p is used to avoid numerical instabilities; its value can be set 100 kΩ, so the current flowing through this path is negligible.

Fig. 2.28

Figure of problem 4

• (a) Set the value of the capacitance C _p back to the original 1.98 μF.

  • Run the model and find:

    • The peak current

    • The arcing time

    • The TRV amplitude and RRRV (approximate)

• (b) Reduce the source voltage and the value of the source side inductor L _s by a factor 10.

  • Run the model and find:

    • The peak current

    • The arcing time

    • The TRV amplitude and RRRV

• (c) Change the circuit breaker separation time to 0.017 (in both models). Run the model and find:

  • The peak current

  • The arcing time

  • The TRV amplitude and RRRV

• (d) Compare the results of (a), (b) and (c) in terms of interactions between the arc voltage and the short circuit current. In which switching components are high arc voltages desirable, what are drawbacks of high arc voltages? Explain.