Study of switching electric circuits with DC hybrid breaker, one stage

The paper presents a method of extinguishing the electric arc that occurs between the contacts of direct current breakers. The method consists of using an LC type extinguishing group to be optimally sized. From this point of view is presented a theoretical approach to the phenomena that occurs immediately after disconnecting the load and the specific diagrams are drawn. Using these, the elements extinguishing group we can choose. At the second part of the paper there is presented an analyses of the circuit switching process by decomposing the process in particular time sequences. For every time interval there was conceived a numerical simulation model in MATLAB-SIMULINK medium which integrates the characteristic differential equation and plots the capacitor voltage variation diagram and the circuit dumping current diagram.


Introduction
In the DC circuits that contain power breakers, a big problem is the disconnecting the loads, because an electric arc that can destroy its contacts occurs. In these situations we can use an additional circuits that are connected in parallel over the main breaker. These circuits generate a counter current injection which opposes the current breaker and results a current zero through the main breaker and the electric arc will be extinguished.
The basic electric circuit for switching DC systems is shown in figure 1:  The circuit from figure 1 contains a DC power E s which has the intern parameters R s and L s , in series with a main breaker S 1 . S 3 is an electric separator and at initial moment, a load with R L and L L parameters is connected. In parallel with S 1 a switching circuit is connected. This consists in the capacitor C, the inductivity L and the auxiliary switch S 2 (usually is a semiconductor).
For limiting the over voltages, the VAR varistor is applied across the main breaker, and the freewheeling diode D will take the current when its slope is negative.
The auxiliary switch S 2 is closed immediately after disconnection to extinguish the arc in the main breaker S 1 . Energy stored in the capacitor C, is released and that generates a current that opposes the current through the breaker, resulting a zero current through its contacts. If the arc is not extinguished at the first current zero, the capacitor C and the inductor L form an oscillating circuit which will produce a second current zero. After arc extinguishing, the capacitor C is loaded again from the source E s and is ready for a new circuit switching.

Analysis of circuit switching
We consider the continuous equivalent voltage across of the extinguishing circuit U lc . In this case the equivalent resistance R, the voltage differential equation is given by (1): where the capacitive current is: Equation (1) can be written in the equivalent form: Based on equations (2)  The above scheme (figure 2) generates currents diagram from Figure 3. As is shown in figure 3, the current value i t1 is reached at time t 1 (reported at the time of load disconnection), At this moment voltage capacitor C is U C1 value. At this time t 1 a counter current injection in opposite to i s occurs through the main breaker and the breaker current begins to decrease. At time t 2 it becomes zero and the capacitor voltage decreases to U C2 value.  Forcing zero current through the main breaker lids to arc extinguishing. The SIMULINK models presented were made for the following values of electric parameters: U c =2000[V]; R=0.1Ω; C=500µF; L=500µH.

Analyses of switching process
For the study of switching process there is used the circuit from figure 4. The current interrupting process can be splitted in intervals, where every interval is described by a differential equation. These differential equations can be integrated using the MATLAB-SIMULINK medium, which allows plotting the variation curves for the current and capacitor voltage.
There are considered the following time periods: -t 1 -time after that S 2 closed and dumping process begins; -t 2 -time after that occurs the first current zero through the main breaker S 1 ; -t 3 -time after that the source current was zero and C capacitor is fully charged at maximum.

Variation of electric parameters in the time interval [0 -t 1 ]
Throughout this time interval, the E s source current passes the loop in figure 5 and is described by the differential equation (4): If the initial conditions for this interval are took into account, the circuit current expression is: Where T = L s /R s is circuit time constant. Its variation is an exponential function.

Variation of electric parameters in the time interval [t 1 -t 2 ]
At the t 1 moment the oscillation in extinguishing circuit begins, and counter current through the main breaker occurs. The capacitor voltage which belongs to the extinguishing circuit is described by the second order differential equation: Where U c1 is the voltage at which the C c capacitor is charged at t 1 moment. Differential equation (6) is integrated using MATLAB-SIMULINK medium. The numerical simulation scheme which plots the capacitor voltage variation and the current through the extinguishing circuit is presented in figure 7:

Variation of electric parameters in the time interval [t 2 -t 3 ]
In this interval, source current becomes equal to the capacitor current. The capacitor voltage at the initial moment is U c2, and the current is I t2 . After the opening of main breaker, current flowing occurs according to scheme in figure 10: Thy S1 Figure 10. Current flowing for [t 2 -t 3 ] interval.
The capacitor voltage which belongs to the extinguishing circuit, is described by the second order differential equation: Differential equation (7) is integrated using MATLAB-SIMULINK medium. Numerical simulation model which plots the capacitor voltage variation and the current through the extinguishing circuit is presented in figure 11: Figure 11. SIMULINK model for oscillating voltage and current through the capacitor for [t 2 -t 3 ] interval.
The SIMULLINK model in figure 11 generates the following diagrams:

Conclusions
The auxiliary switch S2 was chosen unidirectional (solid state switch -thyristor) and the countercurrent from a resonant LC circuit could provide two current-zeros. From this point of view exist two opportunities for circuit interruption.
Another way of interrupting the load current, involves the using of a bidirectional switch (vacuum breaker). In this case, after the source current was commutated, the current oscillation occurs for several time periods according to the circuit damping, until the final capacitor voltage becomes equal with the supply voltage. During oscillation, energy is transferred between source and LC circuit.
Depending on the commutation current value chosen, an appropriate switch might be found from the available power semiconductors. Solid-states switches were commonly vulnerable to increasing slope currents. But the switch had to be able to withstand surge counter-currents when switching on and surge voltages when switching off. The power semiconductors allow high current to be switched by lowering its frequency. When the frequencies of LC circuit are high, a good method for interrupting the load current, consists of using a vacuum breakers.