Reduction of Overvoltages under Connection on a High-Voltage Cable Line Due to Optimal Controlled Switching

. The purpose of the work is to develop a mathematical model of a cable transmission line, which allows modeling and choosing the optimal conditions for controlled switching to limit overvoltage at the development and design stage. The goal is achieved by solving the problem of determining the initial angle of each phase, so that each phase has an initial switching angle equal to zero with a time delay. A high-voltage cable line for a voltage of 330 kV, implemented using Matlab, has been chosen as the object of study. The most significant result is the method of numerical simulation of the cable line that allows you to analyze transients when each phase of a three-phase cable line is connected to a three-phase source with a time delay, the switching angle of all phases is zero. This, in turn, makes it possible to limit switching overvoltages. The significance of the results obtained lies in the possibility of the proposed technique to choose the optimal conditions for controlled switching, which makes it possible to use it in the design of switching nodes, as well as the use of controlled switching to eliminate unwanted electrical transients during planned switching. The simulation results showed that the greatest effect of using numerical simulation is when each phase of a three-phase cable line is connected to a three-phase source with a time delay of 1/150 second, then the switching angle of all phases is zero, which makes it possible to limit switching overvoltages.


INTRODUCTION
One of the modern methods of increasing the reliability and safety of high and ultra-high voltage power transmission cable lines is the use of cables with cross-linked polyethylene insulation, which is characterized by increased operational characteristics, especially in areas with dense construction and extensive communications.
When using ultra-high voltage cable lines, it is necessary to take into account the highfrequency transient processes of current and voltage, which arise as a result of commutative switches. It is extremely important to take into account the influence of this transitional process on the design requirements for the entire power transmission system [1][2][3][4][5].
Controlled switching, or synchronous switching, allows to reduce the load on the power line and switch during switching and minimize interference in the system. Thanks to this, the cable line lasts longer and wears out less. A smaller number of damages in the system (for example, repeated insulation breakdowns) increases the operational readiness of the power system. The switching operation (on and/or off, depending on the task to be performed) is carried out phase-selectively at predetermined switching angles [6][7][8][9][10][11][12][13][14][15][16][17][18].
It should be noted the great interest of the scientific community in the development and research of high-voltage cable power lines. Both simulation mathematical models and physical prototypes of ultra-high-voltage cable lines were developed [19][20][21][22][23][24]. In works [25,26,30] studies of electromagnetic processes in a powerful power transmission system, in which a cable line of ultra-high voltage is used, different modes of operation are analyzed. Models have been developed to estimate the transient process when ultra-high voltage cable lines are turned on [27][28][29]. However, the scientific community pays little attention to the study of transient processes when changing the initial phase of switching on a high-voltage cable line. This work is distinguished by the fact that elements of the theory of multipoles and numerical methods of mathematical modeling, implemented in the Matlab program, were used in the development of the high-voltage cable line model. This significantly simplifies both conducting numerical calculation studies and obtaining generalizing results.
On the basis of modeling and analysis of transient voltages and currents in three-phase circuits of the type of long cable power transmission lines, which have distributed parameters and interphase mutual inductive and capacitive couplings, it is possible to determine the features of the appearance of inherent electromagnetic oscillations under complex boundary conditions and commutations.
The setting of such a scientific task is justified by the modern tendency in theoretical electrical engineering to consider multiphase electric circuits as a series-parallel connection of various n-poles, which ensures an increase in the efficiency of the calculation of transient electromagnetic processes. Fig. 1. The electrical equivalent circuit in the form of equivalent multiport network.

MATERIALS AND METHODS OF RESEARCH
In the work, a simulation model of a highvoltage cable power transmission line has been developed. This model consists of an equivalent circuit and is implemented in Matlab/Simulink. Such an implementation makes it possible simulate and analyze electromagnetic transients in normal and emergency modes of cable line operation. Depending on the desired result and the accuracy of solutions for simulation may be chosen rational method for solving partial differential equations, and the method of changing the simulation time (fixed or variable pitch). During the simulation, it is possible to follow the processes occurring in the electrical circuit.
When studying low-frequency transients in a three-phase cable power line, transient analysis is usually performed on the basis of a P-or Tshaped equivalent circuit with lumped parameters. The longitudinal and transverse parameters R, L, C of the line equivalent circuit are functions that depend on the frequency. At the same time, if one characteristic frequency can be distinguished for the investigated transient process, then the parameters at this frequency are used in the calculations. If the transient process is characterized by a wide range of frequencies, then for each of the parameters an additional equivalent circuit with lumped parameters is synthesized, which implements its frequency response. To calculate the transients in a long line, it is possible to use the calculated method of dividing this line into short sections of such a length that allows the use of an equivalent circuit with lumped parameters for each section.
The electric circuit of the equivalent section of the length Lmeters, is implemented in the form of an equivalent multiport network on the Fig. 1, taking into account the mutual inductive connections existing between the inductances of the cores and screens.
In terms of analysis, the line is a six-wire system (three cores and three screens) with an additional seventh wireground.
The described model is simplified because it does not take into account the dynamic characteristics of energy sources and loads. However, using the user-friendly Simulink user interface, the open structure of the model allows you to quickly change its topology and block parameters depending on the specific task. In particular, the topology of the constructed model can be used in the future to study two-phase, three-phase and other complex short circuits in the cable transmission line. This model also allows for a comprehensive study of the readings of virtual instruments when including in the model of parallel nodes and loads with dynamically changing parameters, which allows calculations of various modes of operation of the power system of this type in the initial stages of design.
The investigated high-voltage power line has a power supply of 330 kV, the length of the line is 3000 m. The parameters of the line replacement scheme are calculated taking into account the geometric parameters of a singlephase cable (Fig. 2) r1=17.4 mm, r2=42.8  The calculation expressions for the parameters of a single-phase cable are obtained from the known formulas for the linear activeinductive resistances of a multi-wire wire-ground system, which are presented in [31]. When calculating the capacitive parameters of the cable, it is assumed that the cable is laid underground (the depth in this case does not matter).
The matrix of cable parameters, voltage drops along the conductors Uc and screens Us, related to the currents in them, is represented by the matrix equation: where IA, IB, ICare the currents of the cable cores; IsA, IsB, IsCcable shield currents; Zc, Zslinear internal resistances of the core and screen; Zcsis the linear mutual resistance between the core and the screen of the same cable. The calculation of the parameters was carried out using the geometric mean distance between the axes of the phases of the cables A, B, C.
To accurately calculate the electrical parameters of cables Z, taking into account the mutual influence of phases and circuits on each other, as well as taking into account the frequency dependences of these parameters, the following assumptions were made: • the cable line consists of metal conductors, the axes of which are mutually parallel and parallel to the ground surface; • the line is homogeneous along its axis; • for the lines under consideration, we neglect the propagation of the electric field in the radial direction in the earth.
Calculation formulas for the parameters of the cable line, taking into account their dependence on frequency and actual geometric location in the ground: Linear longitudinal parameters are represented by resistances Z1…Z7, the formulas for calculating which in the range of relatively low frequencies are presented in [31].

RESULTS AND DISCUSSION
The oscillograms of the transient process of voltage and current in the shields of single-phase cables when the cable line is connected to the source in the idle mode are shown in fig. 3 and 4. From the given oscillograms in fig. 3 shows that the overvoltage on the cable shields at the moment of switching will be 4 kV. This is explained by superimposing the form of oscillations of different frequencies, caused by the effect of the mutual induction of the cores of all phases of the cable on the screen. Rapid attenuation of transient phenomena in screens of a three-phase cable line of single-phase execution is observed due to the presence of active components of all elements.
The appearance of currents is caused by the grounding of the screens at the end and at the beginning of the cable line. Since at the moment of switching, due to the magnetic connection between the core and the screen, the EMF of the mutual induction increases, which contributes to the flow of currents in the screens of about 280 A.
After the attenuation of the main components of the switching transient process in the cores of the cable, induced in the circuit due to mutual inductance, the emf of each core decreases, which leads to the attenuation of the voltage and current curves in the cable shield to minimum values. To limit the switching voltage, the principle of selecting favorable initial conditions of the transition process, in which the amplitudes of free oscillations have minimum values, is used, for example, control of the switching moment by changing the initial angle of each phase.
Let us consider the oscillograms of the transient processes of currents and voltages in the shields of a three-phase cable line of singlephase execution when the cable line is turned on to a three-phase voltage source when the initial angle changes.
The switching of each phase took place at different moments of time, so that each phase had an initial switching angle equal to zero. At the angle of inclusion φ=0 О , the phase amplitude has a nominal value, which can be seen on the oscillograms of Fig. 5.
Analyzing the oscillograms of Fig. 5, we can conclude that if each phase of a three-phase cable line is connected to a three-phase source with a frequency of f=50 Hz with a time delay equal to 1/150 sec, then the angle of inclusion of all phases will be zero, which will lead to a limitation of the switching voltage. Changing the initial angle of each phase during switching does not affect the increase in voltage on the cable screen (Fig. 6), but at the same time, induced currents appear in the screens (Fig. 7), the transition process curves of which are subject to investigation in order to understand the processes, happening in cable screens. From fig. 6, 7, it can be seen that at the first moment of time at t1, phase A is turned on and a current begins to flow through the conductive core, as a result of which a variable magnetic field is created around the conductor, which leads to the appearance of a current in the screen of Fig. 7. The current in the screen causes a drop in the voltage of its phase, under the action of magnetic induction, causes a drop in the voltage on the screens of phases B and C (Fig. 6). Similarly, the voltage on the screens of phases B and C, which are not turned on, is due to the capacitive and electromagnetic connection with phase A. At the moment of switching on one phase, induced currents begin to flow in all screens of each phase. Since only the voltage of phase A acts, the transposition of the screens does not compensate for the EMF of the mutual induction, which leads to a strong increase in the current.
At the moment of time t2, phase B is connected, which leads to an increase in the EMF of the mutual induction on the phases. This can be seen from the oscillogram (Fig. 6), the voltages UA and UB have a large initial amplitude compared to the disconnected voltage UC.
The appearance of voltage on phase B, as a result of the transposition of the screens, compensates for the longitudinal currents flowing through the screens, but does not lead to a balance of phase voltages.
At the moment of time t3, all three phases are connected to the line, and therefore the EMF of the mutual induction, which is shown in the screens of the three sections of the transposition, due to the phase shift by 120 o and 240 o , is zero. Therefore, the currents induced in the screens, after a slight transient process, take values close to zero.
Oscillations caused by the connection of each phase at times t1, t2, t3 by the recharging of the capacitors, and by the electromagnetic connection between the cores and shields of the three-phase cables.

CONCLUSION
Optimal conditions of controlled switching when switching on a three-phase cable line prevent the appearance of an aperiodic current component, which allows limiting switching overvoltage.
It is convenient to analyze the switching processes of each phase by bringing the initial conditions to zero. Given that the very principle of controlled switching rids the current in the line of free components, the analysis of controlled switching can be carried out in the schemes of the established mode.
Synchronization of switching processes is carried out with the voltage of phase A and is carried out in the sequence A→B→C when switching the three-phase cable line to the generator. Such sequences are due to the desire to minimize the total switching time.
The oscillograms of the transient processes of currents and voltages in the shields of a threephase cable line of single-phase execution when the cable line is turned on to a three-phase voltage source when the starting angle is changed are considered. When each phase of a three-phase cable line is connected to a threephase source with a time delay equal to 0.006 (6) (1/150) of a second, the angle of inclusion of all phases is zero, which makes it possible to limit switching voltages.
The significance of the obtained results lies in the possibilities of the proposed method to select optimal conditions of controlled switching, which allows it to be used in the design of switching nodes, as far as in controlled switching to eliminate unwanted electrical transients during planned switching.
Changes in the initial angle of each phase during switching does not lead to an increase in the voltage on the cable shield, but at the same time, induced currents appear in the shields, the transition process curves of which are subject to additional research to analyze the processes occurring in the cable shields.