Comparative Analysis of Measures and Technical Means for Suppressing the Aperiodic Current Component in Circuit Breaker

Electromagnetic transients are considered in the implementation of three-phase automatic reclose on the transmission line of extra high voltage 750 kV. The influence of automatic shunting of phases and pre-insertion active resistance for limiting the characteristics of the aperiodic component of the current, which obstructs the transition of full current through zero, is evaluated. The paper analyses measures taking into account the effect of changing the degree of compensation of charging power and the angles of switching on an SF6 circuit breaker. Sub-schemes of disconnected undamaged phases of the extra high voltage transmission line for the investigation of the aperiodic current component have been developed. The values of the pre-insertion active resistances of different connection and automatic shunting of the phases are determined at which there is an effective reduction of the characteristics of the aperiodic component of the current. In the software environment, a model was developed and switching transient processes were simulated in the 750 kV transmission line. Operating modes that are potentially dangerous for SF6 circuit breakers are determined and recommendations are given to avoid them. Currently the technical and economic requirements for power transmission lines designed for the transport of electricity from large power plants and for the communication of powerful energy systems are increasing. Today there is the importance of reducing specific investment in the construction of new and reconstruction of existing lines. The solution of these issues is associated with the maximum use of power lines by increasing their power transfer capability and controlling modes, especially in operating emergency conditions and post-emergency operation of power systems.


Introduction
Due to the modernization of the switching equipment, viz. replacement of air circuit breakers with SF6 circuit breakers in the bulk electrical networks, there was a need to analyze the switching transients in 750 kV extra high voltage (EHV) transmission lines. Due to the lacks of experience in operating SF6 circuit breakers at 750 kV EHV substations, accidents have occurred which have significantly reduced the reliability of the bulk electrical networks operation [1][2][3][4][5][6]. One of the typical examples of switching that causes damage of SF6 switch is the fast on/off cycle [1][2][3].
Such a typical switching example is the cycle of a three-phase automatic recloses (TPAR) in the event of a non-liquidated metal short circuit in one of the phases. In case of unsuccessful TPAR, the damaged phase is switched on to the non-liquidated short circuit and the damaged phases are switched-off. After switching on the non-damaged phases, there may be an aperiodic current component i acc (ACC) with characteristics values are significantly higher than the maximum permissible operation data of the SF6. Exceeding the value i acc and duration T ap of the ACC leads to a delay in the transition due to zero full transient current (Fig. 1). A durable damping process i acc with a value exceeding the maximum allowed prevents the full current from passing through zero, resulting in damage to the gas switch chamber. According to the requirements specified in [7], the ACC value may not exceed 58 %. It is assumed that when the switch is off, arc extinguishing occurs in each phase at the moment when the current passes through a zero value. Since the dispersion in the action of the poles of a SF6 circuit breaker when switched on does not exceed 0.001 s, the contacts are simultaneously closed. So, in the case of an unsuccessful TPAR, when the arc on the overhead line during the TPAR pause did not go out, it is possible to delay significantly the process of arc extinction [1][2][3].
A significant aperiodic component in the switching currents occurs not only with whole groups of shunt reactors. As a result of a series of transient calculations, the most unfavorable moments of contact closure after a TPAR pause and the moments of disconnection of an uncorrected failure by the value of the aperiodic component were found.
The objective of this work is to identify the conditions for the appearance of an aperiodic component in the current, to analyze the process of damping it using pre-insertion resistors, and also to analyze alternative solutions to the problem as a whole

The reason for the appearance of the aperiodic component of the current during switching
In the studies [7][8][9][10], the simultaneous influence of the above measures on the significance of the ACC characteristics was not considered. The studies analyzed the effect of pre-insertion active resistances on the gas switch on magnetization currents and resonant over-voltages when switching on the EHV power line to the unloaded autotransformer. There are also studies [11,12] devoted to the estimation of the influence of pre-insertion active resistances and the moment of switching on the value of the ACC characteristics without analyzing the effect of changing the degree of the line charging power compensation. It should be noted that there are known works on the use of automatic phase shunting (APS) during single phase automatic re-closure (SPAR) to compensate for the recharge arc and elimination of abnormal resonance over-voltages [12][13][14][15][16]. Studies on the evaluation of the effects of ASF when performing the TPAR are also given. There are also no studies to compare the different types of connection of pre-insertion active resistors to the values of the characteristics of the AC current. A As it was shown by the previous studies, the application of only reducing the degree of charge power compensation and the use of controlled switching do not always effectively reduce the ACC [1-3, 7, 8].
This paper deals with the switching off / switching on of the low-voltage transmission line to short-circuit one of the phases, which leads to the activation of TPAR. Studies have shown that the changes in the switching angle of the gas switch and the change in the degree of compensation of the charging power of the low voltage transmission line cannot effectively reduce the aperiodic component to the given values [17].
The total current value in the switch i C (t) is determined by the expression The initial value of the current aperiodic component depends on the moment the circuit breaker closes (for example, if the switch-on occurs when the instantaneous value of the mains voltage is close to zero, then the aperiodic component has the largest value equal to the amplitude of the periodic component of the current). The damping time constant of the aperiodic current is determined by the ratio of the active and inductive resistances in its circuit.
The aperiodic time constant of the aperiodic component depends on the ratio of the inductance and resistance of the circuit where L Σ -equivalent inductance of an equivalent circuit; R Σ -equivalent resistance of the equivalent circuit. So, the initial value of the ACC current component depends of values (1). In Fig. 2 the aperiodical (AP) current in phase A in cycle of TPAR are shown. The permissible value of ACC component for SF6 circuit breakers 750 kV is 58 % of total current at the transition process. On the figure I a -current of the A phase.

Measures and technical means of improving the reliability and efficiency of EHV power transmission lines due to switching
The main task of existing measures and means used in EHV power transmission lines is to increase the reliability and operational efficiency of the operating modes of the main electric networks that they form. There are innumerable modes of operation of power lines, especially for operational normal operating modes. Normal modes of electrical networks mean those that allow long-term operation without any restrictions for both consumers and equipment of the networks themselves. But when critical deviations of parameters values of an electric network are reached, it is necessary to speak already about occurrence of an abnormal mode for which the use of traditional controls methods will be inadequate and therefore ineffective. The consequences of uncontrolled abnormal mode can be not only the deterioration of the technical and economic performance electrical network, but also damage to the equipment of responsible consumers, as well as failure of the main equipment of the network itself with the further development of a system crash.
It should be noted that classification of abnormal modes, which occur in the abnormal nonsinusoidal and nonsymmetrical modes of EHV power lines is given in [12][13][14][15][16]. The use of the term of abnormal mode is not accidental, because when working out literary sources [1][2][3][4][5][6][7][8][9][10] and studies of experimental results [12][13][14]16], it was concluded that this kind of modes is fundamentally different from traditional ones. The difference and the special characteristics of mode is that they are caused by an abnormal regime, primarily due to the effect of the distortion source. In [15,16], the division of this mode type into two main categories, depending on the resonance at a certain frequency, is shown on the basic harmonic and higher harmonic components.
Also, this developed classification of abnormal modes includes the considered form of the TPAR operation mode. An abnormal mode of operation exists during the implementation of the TPAR cycle and until the breaker is possibly damaged. In EHV power lines, the following measures and technical measures apply, shown Fig. 3: а) the use of pre-insertion resistances in SF6 circuit breakers, which can be connected in series or in parallel (Fig. 3a, b); b) applications of automatic phase shunting when a phase disconnected is shunted by circuit breakers (Fig. 3c); c) the controlled switching to ensure switching moments at the required time (Fig. 3d); d) disconnecting of groups of shunt reactors, as well as the use of open-phase modes of groups shunt reactors (Fig. 3e).
At Fig. 3 L M , L E -inductance of the shunt reactor which compensate capacitance between phases and capacitance between phase and earth, H; L Linductance of the transmission line, H; R L -active resistance of the transmission line, Ω; L S1 , L S2 -equivalent inductance, H; R S1 , R S2 -active resistance, Ω; R pre -active pre-insertion resistance of SF6 circuit breaker.
where R pre-ins -resistance of pre-insertion resistance, Ω. The above measures have proven themselves well in suppressing and limiting the characteristics of abnormal resonant over-voltages in non-sinusoidal and asymmetric operating modes [13][14][15][16][18][19][20]. It should be noted that today there is no work to assess the impact of measures and means on the aperiodic component of the total transient current (1) and especially aperiodic time constant (2).
Switch with pre-insertion active resistor can be used to extinguish large multiple voltages on the second harmonic. As shown by research [18][19][20][21], overvoltages on the second harmonic can exist for a long time, so the decisive factor in determining the scattering energy is the time of the emergence of an abnormal regime with unloaded autotransformer.
The method described in the article solves the problem of putting the line under voltage, avoiding the danger of damage to electrical equipment by resonant overvoltages on the second harmonic. The use of pre-insertion resistors can reduce the amplitude and duration of this type of overvoltage. It is important to note that the decision to use pre-insertion resistors in each case must be supported by the results of mathematical analysis.
Thus, the use of pre-insertion resistances in SF6 circuit breakers has not been verified by influencing the characteristics of the aperiodic component.
The objective of the ASP is to reduce the electrostatic as well as the electromagnetic components of the feed current in order to ensure a successful SPAR [22][23][24][25].
Compared to air circuit breakers, SF6 circuit breakers have certain advantages, the main ones being performance and high switching capacity, as well as the possibility of installing an additional controlled switching device. This device enables the switching of the gas switch at a predetermined moment in order to reduce the negative effects of transients. The switching moment of the air switch is random and it is not possible to open or close it at the right time. Such a fault during operation led to emergency situations, including the occurrence of resonant overvoltages in non-sinusoidal modes [15, 16, 18-21, 26, 27]. Initial It should be noted that the paper considers the worst case when the voltage in the intact phases goes beyond zero and the case when the voltage reaches its maximum value. In the first case, such initial conditions of the electromagnetic switching transient cause the maximum initial value of the aperiodic component of the current. As it is shown by the damping the study of the aperiodic component of the current is determined by the ratio of the circuit's active resistance to the total inductance [1][2][3]. According to the data, the damping process for certain lines continues to 0.003-0.04 s. A controlled switching device for aperiodic suppression can be used in combination with the above.
As we can see from (1) i ap (t) depends on α -moment of commutation. So, we can say that controlling switch device can reduce these two components. All circuit breakers are equipped controlled switching device Switch Sync F236. The sinusoid with possible moments of commutation is depicted in Fig. 4. To assess the impact of the switching moment on the characteristics of the aperiodic component, a simulation model is developed and the description of which is given in the next section. δ, electrical degree When using controlled switching, the time constant will be equal to In case of switching-off the shunt reactor group, the decay time constant will be ( ) In case of application APS decay time constant will be ( ) ( ) To perform the time constant calculations, the following EHV power line data were adopted for the next lines: Khmelnytsky nuclear power plant (Ukraine) -Rzeszow (Poland), South-Ukrainian nuclear power plant (Ukraine) -Isaccea (Romania), Western Ukrainian (Ukraine) -Albertshire (Hungary). The resistance is R pre-ins = 400 Ω for both cases shown in Fig. 3a, b. Parameters of equivalent systems and shunt reactors are shown in Tab. 1. The calculations of the aperiodic time constant according to the expressions (3), (4), (6)-(8) are given in Tab. 2. The task of using technical means is to reduce the duration and value of the aperiodic component. The duration of the aperiodic component is ensured by the highest value of the constant damping time. As it can be seen from the results in Tab. 2, the lowest constant time value is observed when using controlled switching. In the case of ASP, the lowest value will be observed, which will lead to the longest running of the aperiodic component.
For example, in [1][2][3][4][5][6][7][8][9][10] it is recommended to disable the shunt reactor group to reduce the characteristics of the aperiodic component. As you can see from the results, such an event reduces the time constant thereby increasing the duration of the transient. In fact, shutting down the bypass reactor group is ineffective. To test the efficiency, the results which are shown in Fig. 5 were evaluated.
As it can be seen from Fig. 5, the use of shutdown of the shunt reactor group does not lead to a significant change in the time constant, while further dragging on the value of the impedance resistance does not lead to the required increase in the time constant.
In order to verify the correctness of the equations and theoretical statements, a simulation model was developed for the analysis of electromagnetic transients in the TPAR cycle.

Modelling of cycle three phase auto-reclose of extra high voltage transmission line
The model was developed to study the processes at single phase auto-reclose in the environment MatLab-Simulink which are illustrated on Fig. 6. Calculations were made to find the effective measure to prevent this kind of overvoltages. The three-phases power system is simulated by voltage sources with fixed voltage and inductance. The overhead line is simulated by two parts, which are given complex matrices with distributed elements or values on the forward and reverse sequence.  As it can be seen from Fig. 7-10, the simulation results confirm the theoretical assumptions about the duration of existence of the aperiodic component and the derived formulas (3), (4), (6)- (8). The shortest duration of the aperiodic component is observed when using controlled switching (Fig. 9). The highest duration is observed with the use of automatic phase shunting (Fig. 10). The use of pre-insertions witched resistors also does not produce the required result (Fig. 7, 8). CONCLUSION 1. When designing extra high voltage power lines, a careful analysis of the electromagnetic transients accompanying the switching during operation is necessary. Quick on-off cycles (symmetric or non-phase) should be avoided in case of TPAR. In particular, in such cases it is necessary to pay attention to the cycle of fast three-phases automatic reconnection, in which the switch may be damaged due to the aperiodic component of the current.
2. The results of the work confirm the theoretical principles, which consist in the inefficiency of using pre-insertion resistances and automatic phase shunting to reduce the characteristics of the aperiodic component of the current for the total transient process. This also applies to the disconnection of a group of shunt reactors as measure. The derived formulas for the determination of the aperiodic time constant of the aperiodic component confirm the above mentioned. Value resistance сhanging of the pre-insertion resistor when disconnecting the group of shunt reactors also confirmed the inefficiency of using the same means even when used together. This analysis without any significant assumptions was performed based on the mathematical models developed in MatLab which confirm the theoretical propositions.