Methods of overvoltage limitation in modern dc semiconductor switching apparatus and their calculation

The study considers switching surges at semiconductor switches of semiconductor devices of the direct current at the time of switching electric circuits; such surges occur due to the energy accumulated in the inductive elements of the mains at the load disconnection. As the cost of power semiconductor devices is determined not only by the voltage that they are able to handle but also by the class of the device that determines the amount of the blocked voltage, an important task is to use special measures to reduce these surges down to levels that are close to the network parameters. The aim of this study was to develop a methodology for calculating the parameters of a regulator of switching surges on the basis of a series of parallel-connected energy-intensive varistors used in semiconductor devices of the direct current. On the basis of studying the transient processes that occur in such surge restrictors of voltage in semiconductor devices of the direct current at load switching, analytical expressions have been developed for calculating the basic parameters of the voltage regulator. As a result, an engineering method has been devised for calculating the parameters of varistor surge regulators in hybrid and contactless semiconductor devices of the direct current at a given level of surge admissible for this class of devices. The research findings facilitate high accuracy at a small amount of time in choosing fully controlled semiconductor devices with regard to the current and voltage when designing modern switching semiconductor apparatus that work with the direct current; this helps solve the basic tasks of planning. The suggested voltage regulator for semiconductor switching apparatus of the direct current effectively limits switching surges in the circuits of power semiconductor devices to below 2.5 U nom . It significantly surpasses such parameters as the dimensions, weight and cost of resistive-capacitive surge limiters previously used in semiconductor contactors. Moreover, it can reduce the class level of fully controlled power semiconductor devices that are used in semiconductor switches of such apparatus.


Introduction
In the 1980s, a new stage began in the development of power electronics associated with the creation of powerful fully controlled semiconductor devices (SDs), primarily including a double-gate turn-off (D-GTO) thyristor, a GCT-thyristor (gate communicated turn-off thyristor) and, especially, a high-speed power insulated gate bipolar transistor (IGBT-transistor). The high level of modern electronic technology has made it possible to organize mass production of these devices in the form of compact integrated module structures such as IGCTs (GCT-based thyristors) and IGBTs (BTIZ-based thyristors), which are characterized by high reliability and reasonable price. The combination of power devices and circuits for their control in a single package with different degrees of integration has created favourable conditions to implement various laws of controlling superpower electricity flows [1,2].
The aforementioned devices have given a powerful impetus for further improvement of the previously developed hybrid and contactless switching power semiconductor devices (SDs) for the direct current (DC) by applying in their main circle new fully manageable semiconductor trans-

Analysis of previous studies and statement of the problem
In semiconductor apparatus of the direct current, damping of the switching surge caused by stored energy in the inductance of the circuit and the load at the switch-off time can be practically performed in the following ways: -by applying switching capacitors (condensers) [10]; -by using the same capacitors but shunted with linear resistors (condenser-resistive) [10]; -by using energy-intensive variable resistors (varistors) [11,12].
In all the above-listed methods for scattering the energy stored in the inductive load, it is traditional to use either a reverse diode or a reverse thyristor (in the case of a reverse execution system) that are switched on simultaneously with the load [13]. Transient electromagnetic processes taking place along have been studied in sufficient detail [11]. Moreover, it should be noted that, due to high energy stored in the inductive load at the time of switching, other methods are unsuitable because of impossibility to implement them (usually the energy stored in the inductive load is much higher than the energy stored in the circuit inductance) [14]. Thus below we shall analyse the above methods, provided that it is necessary to dampen only the energy stored in the circuit inductance.
The use of capacitors to limit switching surges by transferring the energy stored in the circuit inductance into potential energy of the charged capacitors is a classic method used in SA of the direct current with compulsory capacitive switching of the primary semiconductor switch of the SA made on the basis of thyristors [10]. To obtain an admissible level of surge, it was necessary to use bulky, unreliable and expensive special impulse capacitors, with a limited temperature operating range (it especially concerns electrolytic pulse capacitors). This method can be justified when SA already have capacitive compulsory switching; however, in modern SA, which are constructed using fully controlled STs, the use of this method would not be expedient [15].
The use of protective capacitors with linear resistors that are enabled by a special scheme in parallel to the capacitors has allowed significant reduction of their size. However, in addition to the problems connected with deficiencies of the special capacitors, there have appeared difficulties involving the need to create special schemes for switching linear resistors that would allow their switching on and off at the right time [10]. Therefore, this method is also impractical to use for reducing switching surges in modern SA.
Voltage regulators that are made on the basis of the two discussed principles are fully analysed in [10]. The study considers the methods of their calculation subject to constraining switching surges to a level acceptable for SA of the direct current.
At present, due to the development of energy-intensive varistors that allow dissipating the energy of several hundred kJ and that are suitable in size and cost, sufficiently favourable conditions have been created for their use in modern switching SA for the dissipation of stored energy in the circuit inductance at switching off the device [11,16].
The above-disclosed critical analysis of the various methods of damping switching surges in the circles of power switching devices of the direct current shows that while using SA of the direct current in which STs are fully controlled it is expedient to limit voltage surge to the level established for this class of devices (down to 2.5U nom ) [17] by dissipating the energy stored in the inductive load by means of the voltage regulator (VR) VR1 made on the basis of the feedback diode turned on parallel to the load, and the energy stored in the circuit inductance should be dissipated with the help of the VR2 based on powerful varistors switched on at the apparatus inlet.
Since there are no methods currently used for calculating varistor VRs integrated into the work of SA of the direct current using fully controlled power SA, there is a need for a detailed study of the electromagnetic transient processes that occur in the limiters of these devices while switching the load. Therefore, it is necessary to develop a method of calculating the parameters of varistor VRs that reduce switching surges to the level established for this class of devices.

Research aim and objectives
The aim of this study is to develop a method of calculating the parameters of voltage regulators made on the basis of energy-intensive varistors at a given switching surge level in SA of the direct current with fully manageable STs.
Therefore, it is necessary to solve the following problems: -to study transients that occur in the voltage regulators for SA of the direct current at the load switching; -to determine the analytical expressions to calculate the basic parameters of VRs and to formulate them as the basis of an engineering method of calculation; -to provide examples of calculating the parameters of VRs and switching surges for the most common types of SA of the direct current.

Research of transients in voltage regulators on semiconductor switches of semiconductor apparatus at switching the load
An equivalent embodiment of switching a VR in the SA power supply circuit is shown in Fig. 1.
where nom U is the nominal voltage in the circuit, scmax I is the maximum admissible short circuit current and t is the time constant of the short circuit current ( 0.01 t = s) [17].
Parallel to the VR1 in this circuit, there is the connected capacitor C that limits the growth rate of the switching surge in STs of semiconductor switches at the break of the load current. The value of this capacitor capacitance is determined by the obvious expression: where SI I is the maximum admissible switched current of the apparatus, for example, for a contactor and a modern high speed circuit breaker (usually, SI where c t is the duration of the varistor current, I c adm and t adm are the admissible amplitude and duration of the current impulse of the varistor at which its energy . Therefore, to increase the admissible energy for the VR1, the authors of the study suggest a parallel connection of a varistor series, which is shown in Fig. 2.
Such a VR has n parallel branches, each containing m consecutively connected varistors RU1-RUm and one ballast resistor b R that aligns the currents in the parallel branches.
Calculation of the maximum energy released in one varistor of the VR in Fig. 2, a is done for the limiting case of uneven current distribution in the parallel branches, which corresponds to determining the minimum values of the parameters in an n-th branch while and the maximum values are determined in the other branches.
The current in the n-th branch will be the maximum, and the currents in the other branches will be minimal. It is ob-vious that the energy released in one varistor proportionally to the square of the current will be maximal for the varistor that is set in the n-th branch with the maximum current.
The calculation diagram of replacing the switching circuit of the VR1 (Fig. 2, a), which has a given distribution of the current, at the stage of limiting the surge looks like in Fig. 2 R ,R are the maximum and minimum resistances of the ballast resistor; S1 is the switch simulating the operation of the VR1 (it switches off the branches with the currents cmin i at the declining voltage in the VR1 u vr below emax U ).
For the current to flow in the VR, it is necessary to increase the voltage u vr to the value of emin U and the switch S1 can be locked to allow the current flow in all the n branches if the inequality is the following:

I, u VR
The experience of operating varistors CH2-2 for big energy volumes to scatter in them shows that it is advisable to choose the varistor value U c as its I-V curve at the current of 1

Analytical expressions to calculate the basic parameters of the VR and their inclusion into the engineering method of calculation
To fulfil inequality (3), the process in the equivalent circuit (Fig. 2, а, sc 0 t t ≤ ≤ ) with the locked switch S1 at the time interval of sc 0 t t ≤ ≤ (Fig. 2, c) where vr u is the voltage in the voltage regulator; nom E kU = is the maximum admissible electromotive force (emf) of the circuit (k=1.1).
The calculation of the parameters of the protection circuit is given below.
The solution is subject to the initial condition of The amplitude of the limited VR voltage at the device input is: Within the time interval sc 0 t t ≤ ≤ (Fig. 2, c), the switch S1 in the equivalent circuit is unlocked, and the current i declines to zero. Meanwhile, the process in the equivalent circuit can be described through the equations [ The time of the current flow through the VR is: The maximum energy b.max W released in the ballast resistance of the same branch is: sc sc r.s.
On the basis of the above-obtained expressions, we suggest the following engineering method of calculation.
1. It is initially necessary to select from the VR varistors the type whose main parameters correspond to restriction (3) and then to apply expression (2) to determine the value of the capacitor capacitance that shunts the VR.
2. The parameters are determined to calculate the VR operation, provided that the deviation in the parameters с U , d R and b R is within the range of ±5 %, and b d R R . ≈ 3. Expression (7) helps to determine с.max с.adm. I I ≤ (for the varistor СН2-2 с.adm с.adm I 120 A, W 150 J ≤ ≤ ). 4. Expression (6) on the basis of the known с.max I and SI I helps to find out the number of the parallel-connected varistors n; the n is rounded up to the next whole number. The values of с.max I and v.max U are specified. 5. Expressions (8)-(10) determine the time of the current flow through the varistor (the decline time) t d .
6. Expression (11) determines the maximum energy released in the varistor.
7. If at least one of the varistor parameters does not meet the accepted restrictions, the calculation is repeated until all varistor settings satisfy the specified restrictions (3) and (7).
Below are the results of calculations on a varistor VR and the switching surges determined by the developed method for the case of using the specified VR in hybrid DC contactors for a voltage of 220 V, which are the most common power switching SA.
Calculations were made in an environment Mathcad on the basis of such output data: nom.r. kA. In this case, the basic voltage regulating element of the VR is the varistor of the type СН2-2, 330 V. Table 1 contains the basic calculation parameters for this type of the VR.
The analysis of the calculation parameters listed in Table 1 shows that the use of inexpensive and compact energy-intensive varistors CH2-2 in creating a VR can limit the level of switching surges to below 2.5 U nom while using hybrid DC contactors to switch boundary currents that are equal to 4 I nom. r. . In this case, even in the loaded contactor (with the effect of the stored circuit energy on the VR) when nom I 630 A, = the maximum energy released in the loaded varistor is three times less than the admissible level, and the weight of the components that are part of the VR is less than 0.1 kg at their price of about 10 USD [4].
In comparison, for example, in the previously developed hybrid contactor KP81-39 (I nom =630 A), the resistivecapacitive VR has 14 enabled parallel capacitors of the type K75-17 (1000 V, 50 µF, and the weight of 1.25 kg) [1]. Accordingly, the weight of the VR is at least 17.5 kg, which is much bigger than the considered varistor VR. It should be added that the level of restricting voltage surges by this VR amounts to 4.5 U nom , which means that it exceeds the admissible level for the existing switching devices.
Certainly, a varistor VR can be based not only on varistors CH2-2; varistors of other types and companies can be used if they comply with the requirements (2.24): for example, promising in this regard are the varistor types SKP6.5.110SA and BYZ50A22.50K39 produced by Semicron. Since they are designed for cl U 6.5 110 = − V, they should be enabled in the VR as in a parallel series connection, and the varistor, operating in the most adverse working conditions, must conform to the restrictions (3).

Analysis of the research results on switching surges in power SA of the direct current
The main advantage of the study is that it has resulted in developing an engineering method of calculating the parameters of varistor voltage regulators for hybrid and contactless SA of the direct current at a given for this class of devices admissible surge levels. It should also be noted that the results of this study, as well as previous studies of the thermal mode of power circuits working in SA [19], facilitate high accuracy at a small amount of time in choosing fully controlled STs with regard to the current and voltage when designing modern switching SA that work with the direct current. This helps solve the basic tasks of planning.
However, the research findings concern only low-voltage SA (up to 1000 V), so it is difficult to extrapolate them onto SA that are designed for higher voltage, which have been made possible with the development of high-voltage STs based on silicon carbide [8]. It is expedient to continue research on this issue in order to eliminate this shortcoming.
The practical recommendations arising from the results of this study and the suggested calculation methods are being used by the joint stock company ENAS, Kharkiv, Ukraine, to modernize hybrid DC contactors of the KP81 series so that the size and cost can be significantly reduced. This study refers to the stage of developing design documentation.

Conclusion
1. The suggested VR with a series of parallel-connected varistors is a highly reliable device that effectively limits switching surges in the circuits of power SA of the direct current to below 2.5 U nom . It significantly surpasses such parameters as the dimensions, weight and cost of resistive-capacitive surge limiters previously used in semiconductor contactors. Moreover, it can reduce the class level of fully controlled PSDs that are used in switches of semiconductor devices for the voltage of 220 V from class 10, previously common, down to class 6.

Таble 1
The main calculation parameters of the VR 2. An engineering method has been developed to calculate the VR parameters of a parallel-connected series of varistors. Unlike the previously researched cases, the present study has considered calculation for only the worst case of distributing varistors on the branches with various deviations of their parameters from the nominal ones. This allows creating VRs on the basis of quite simple calculations to provide a suitable level of switching surges in SA of the direct current at different operation modes, which is quite useful for technical professionals.
3. The method of calculation that has been developed in the study can be further used in calculating surges in fully controlled PSDs that work in an impulse mode within power electronic devices.