Constructing a Method of Multi-Coordinate Control Over the Static Thyristor Compensators With Forced Commutation

The configuration and the principle of operation of the static thyristor compensator of reactive power with the forced commutation and voltage addition for networks with a compensated neutral have been considered. The integrated indicators of the compensator energy process have been defined for the case when it is powered by a rectangular-shaped voltage in the case of independent control over the switching thyristors. At certain values of thyristor control angles, the specific losses of active power become less than the similar specific losses when the compensator is powered by a sinusoid voltage. This ensures its competitiveness relative to other static compensators.<br><br>A method of multi-coordinate control over the static thyristor compensators with forced commutation has been proposed. It implies independent control over all switching thyristors in a compensator in accordance with the objective function of the system, which is determined under condition that the specific losses of active power do not exceed their economically justified level.<br><br>A circuit to control the static thyristor compensator with forced commutation and voltage addition has been suggested. The application of the circuit makes it possible to reduce active power losses in the compensator when controlling the reactive power and to execute independent control over the phase reactors. Real-time microprocessor control over all elements of the system makes it possible to enable the required algorithm for switching commutation thyristors and to implement multi-coordinate control over the compensator energy processes. An algorithm for operating the microprocessor system of the static compensator when controlling the reactive power has been constructed. The algorithm, due to an increase in the voltage addition coefficient during the action of a negative half-wave of supply voltage, makes it possible to reduce the specific losses of active power in the electrical network and compensator.


Introduction
The industrial production of recent years has been accompanied by an ever-increasing consumption of reactive power, as compared with the active power, and the growing share of sharply variable loads, which is why the issue of reactive power compensation is of special importance. Static thyristor compensators (STCs) that act as a source of reactive power is an effective tool for resolving the tasks of transmitting and distributing electrical energy, associated with the large and rapid fluctuations in the reactive power. Most power reactive sources are characterized by the dependence of active power specific losses on the mode of operation [1].
The sharply variable loads are characterized by the asymmetry of power consumption in the phases of supply voltage, as well as the surges in reactive power. Voltage fluctuations that occur in this case adversely affect consumers and increase the losses of electrical energy. It is possible to ensure the permissible level of voltage fluctuations and to reduce the losses of electrical energy through the rapid phase-to-phase reactive power compensation.
To improve the efficiency of using STC as a source of reactive power, it is necessary to reduce the losses of active power in it and in the network, to ensure independent control over the opening and closing angles of its commutation thyristors. In addition, it is required to refine a mathematical model of STC as a system with the variable parameters and structure, as well as to develop the systems of multi-coordinate reactive power control. Therefore, these fields of research into static compensators are important for the development of electricity generation and are relevant.
The static thyristor compensators with forced commutation employ a direct or indirect compensation of reactive power.
The STCs with a direct compensation of the reactive power require specialized fast thyristors with a short-time recovery of shut-off properties; they have a complicated circuit configuration, low reliability, a small overvoltage margin [5,6], and a poor overload capacity [7][8][9]. Currently, compensators with a direct compensation of reactive power are fabricated based on a voltage converter with the forced commutation, which use, as power switching devices, the bipolar transistors with an insulated shutter or two-operating thyristors [10]. Control over reactive power is carried out by changing the amplitude of output voltage at the expense of pulse-width modulation.
A promising direction in the development of STCs with direct compensation is the use of STATCOM as an independent device or a base element for other devices. Paper [11] reports the results of examining the STATCOM circuit, containing two bridge voltage inverters, the same phases of which are connected to the opposite clamps of the secondary winding of the transformer. The primary windings of this transformer are connected to a three-phase electrical network. It is shown that this circuit, due to the pulse-width modulation, ensures high-quality spatial vector control over the voltage and active power in an electric network. However, the unresolved issue is the reduction of active power losses, since the application of the pulse-width modulation algorithms with a frequency much greater than the frequency of the network leads to the increased active losses in the valve part of the compensator.
The reactive power compensator with an induction energy storage unit [12] employs a three-phase bridge converter is used with the inductance on the DC side and the D-shaped LC low-frequency filter on the AC side. Reactive power is controlled in it by changing the opening angle of the transistors relative to the network voltage. This compensator has a step-less adjustment of reactive power, is insensitive to the voltage higher harmonics and is simpler structurally compared to the STATCOM-type systems.
The disadvantages of the compensator with an inductive energy storage unit include: 1) the narrow adjustment range of the opening angle of transistors, which is about half the electrical degree; 2) the impossibility to adjust power down from rated; 3) high specific losses of active power during reactive power adjustment.
Three schemes of power circuits of hybrid static compensators were proposed in work [13]. All of them include the thyristor-controlled reactors and differ in the configuration of active filters. In the scheme with a passive LC filter with a sequential active filter, the additional active losses to install the active filter is 1.4 % of the power of a three-phase load. The scheme with a phase conduction capacitor with a consistent active filter differs from the previous one by greater losses constituting 4 % of the power of a three-phase load. The least energetically efficient scheme employs a parallelly-enabled static synchronous compensator. The active losses in it reach 80 % of the power of a three-phase load. An analysis of the above circuits reveals that they do not solve the issue of reducing the active losses when controlling reactive power and do not ensure the multi-coordinate control over static compensators.
The hybrid compensation of reactive power was examined in paper [14]. It is implemented through a stepped-man-aged shunt reactor. The compensator is composed of the high-ohm transformers, consistently connected reactors, mechanical switches, and thyristors. Reactors are consistently connected to the linear secondary winding. The available number of successive reactors changes by thyristors and mechanical breakers to adjust the power. Rapid control over the power of the reactor with a controlled shunt is provided by thyristors, while mechanical switches are used to bypass them during operation without drastic changes in reactive power to simplify the cooling system of the thyristors. Using this scheme does not reduce active losses in the compensator during the adjustment of reactive power and ensure independent control over the opening and closing angles of the commutation thyristors.
Study [15] considered an industrial controller specifically designed for two-and three-level converters, which is adapted for the use on the asymmetric nine-level active power filter. An important advantage of this controller is the low-frequency switching of the nine-level converter. Given this, the active losses during switching were reduced. At the same time, the unresolved issue is the possibility of reducing the active losses in the compensator when controlling the reactive power.
The indirect compensation of reactive power can be implemented on the base of thyristor controllers of variable voltage with forced commutation [16], which enable the time-steady commutation capability and the independence of the switching node parameters on the load parameters. Using the forced commutation makes it possible to improve the energy performance of thyristor controllers of variable voltage and obtain various shapes of voltage on the load. Increasing the frequency of thyristor switching makes it possible to remove the shift of the basic harmonic of the network current during regulation and to reduce the mass and dimensions of filters. However, these schemes have two drawbacks. The synchronous switching of phase reactors decreases performance speed as the steady mode of operation is achieved not over a single but over several periods of power supply voltage, and there is no possibility of independent phase control over the reactive capacity of the static compensator.
Our analysis of special features in the operation of the examined static compensators indicates the need to design controllers with forced commutation and phased control over reactive power at small losses of the active power in them. Since the reactive power control is executed mainly by changing the opening angles of commutation thyristors, it is necessary to improve a method of independent control over the opening and closing angles of the commutation thyristors in STC with the forced commutation. Little attention has been paid to the techniques of multi-coordinate control over reactive power in the static compensators with forced commutation.

The aim and objectives of the study
The aim of this study is to optimize the operational modes of the static thyristor compensators with forced commutation and to improve the techniques for the multi-coordinate phased control over reactive power in order to improve the efficiency of using the static compensators.
To accomplish the aim, the following tasks have been set: -to build a mathematical model of STC with the forced commutation and voltage addition and to investigate the energy processes in it in order to ensure the possibility of reducing the active power losses when controlling the reactive power; -to construct a method for the multi-coordinate control over STC with the forced commutation and voltage addition, using which the switching of power thyristors is carried out depending on the system objective function; -to improve the scheme of phased control over the reactive power in STC with the forced commutation and voltage addition and to devise a flowchart of the operation algorithm of its controlling microcontroller in order to ensure the optimization of the compensator operation modes.

A mathematical model of STC with the forced commutation and voltage addition
The bipolar voltage addition is used for the cases where it is necessary to control the STC output voltage relative to the rated voltage. In this case, it is necessary that, during the use of voltage addition, the reactive power should increase while the specific loss of active power should decrease [17]. This is only possible when using a specific algorithm for applying the voltage addition. A scheme of the static controller over reactive power [18], which implements this algorithm, is shown in Fig. 1.
The reactive power static controller operates in the following way. When the power voltage is supplied, the С1-С9 capacitors are charged from the secondary windings w2 and w3 in transformer T through the single-phase bridge rectifiers VD1-VD9 at the polarity indicated in Fig. 1 without parentheses. When exposed to a positive half-wave of the supply voltage, the opening of thyristor VS1 enables the equipotentiality of points a1 and neutral N of the transformer; the phase reactor LR1 is fed with voltage. The capacitor С1 is recharged via the thyristor VS1 and the winding of throttle L1, acquiring the polarity indicated in Fig. 1 in parentheses. To close the VS1 thyristor, the thyristor VS3 opens and the capacitor С3 is recharged via the thyristor VS3 and the winding of the throttle L3. The winding of the throttle L3 is induced with an electromotive force under which the thyristor VS1 closes. When one opens the VS3 thyristor, there is the equipotentiality of points a3 and the neutral N of the transformer; the phase reactor LR1 would be closed through the rectifier VD3, thereby providing for the current continuity for the case of an active-inductive load. To close the VS3 thyristor, one opens the thyristor VS2. In this case, there is the equipotentiality of points a2 and the neutral N of the transformer; the LR1 phase reactor is given a negative half-wave of the supply voltage. The capacitor С2 is recharged via the thyristor VS2 and the throttle L2 winding, acquiring the polarity indicated in Fig. 1 in parentheses. To close the VS2 thyristor, one opens the thyristor VS3 and the capacitor С3 is recharged via the thyristor VS3 and the winding of the throttle L3. This winding is induced with an electromotive force, under the action of which the thyristor VS2 closes. The processes that occur in phases b and c of the static controller of reactive power during switching the thyristors VS4, VS5, VS6 and VS7, VS8, VS9 proceed similarly and independently. The positive half-wave of the supply voltage is determined by the output voltage of the secondary winding of the transformer w2, and the negative halfwaveby the output voltage of the secondary winding of the transformer w3. Under the action of the positive half-wave of the supply voltage the static controller is a consumer of active power, and in the case of the negative half-wave of the supply voltagea generator of active power. In this case, due to the voltage addition when changing the angles of control over the commutation thyristors, it is possible to reduce the losses of active power. At the same time, the reactive power would increase while the steepness of the adjusting characteristic of the controllerincrease.
In accordance with the operation algorithm of an STC with the forced commutation, under the action of a bipolar supply voltage, the first to open is the first commutation thyristor, followed by the second commutation thyristor that closes the first one. For all existing techniques to adjust the reactive power, the angles of opening and closing these thyristors depend on the angle of control of the first commutation thyristor. Thus, such regulation of the reactive power is carried out by means of only one coordinate -control angle and, therefore, does not make it possible to solve the optimization problems for an STC with the forced commutation effectively.
A unique feature of the STC with forced commutation is the possibility of independent control over the opening and closing angles of commutation thyristors. The purpose of this control can be characterized by a certain objective function, which would depend on the scalar set of control angles of the commutation thyristors. The objective function can be derived on the basis, for example, of the necessity to ensure the reduced specific losses of active power when controlling the reactive power of STC or its proper performance speed for the compensation of fast-changing reactive loads. Control over reactive power depending on the objective function is the multicoordinate control over an STC with the forced commutation as the control process is carried out through an independent change in all angles of control over the commutation thyristors.
Theoretically, the considered STCs with the forced commutation can produce four independent angles of control over the commutation thyristors: α 1 , α 2 , α 3 and α 4 . Moreover, the α 1 and α 3 angles are the angles of opening the first commutation thyristor, respectively, under the action of the positive and negative half-wave of the supply voltage, and the α 2 and α 4 angles are the angles of opening the second commutation thyristor and, accordingly, closing the first commutation thyristor. Practically, only the α 1 , α 2 and α 3 control angles are independent. The control angle α 4 should be determined by the moment when the phase reactor current passes through zero. In this case, a quasi-established mode of the power circuit occurs over a single period of the supply voltage. Otherwise, the current through the phase reactor would be different from zero, and over the next half-period of the supply voltage during the opening of the first commutation thyristor, the initial conditions for the current would not be zero. That would lead to the disruption of the quasi-established mode of the compensator power circle.
The electromagnetic processes in the power circuit of an STC with the forced commutation for networks with a compensated neutral in the presence of voltage addition are described by the generalized differential equation of the first order: where n=1, 2, 3 is the number of the plot at the time diagram of voltage and current; m U is the amplitude value of a rectangular voltage; ν is the voltage addition coefficient. The equation (1) holds for all control techniques of STC with the forced commutation.
The shapes of control voltages 1 , Fig. 2, a, b), the supply voltage and the current through the load (Fig. 2, c) in an STC with the forced commutation for networks with a compensated neutral in the presence of voltage addition in the case of independent control over the commutation thyristors. In the first section 1 2 , α £ θ £ π − α the total active-inductive resistance of the secondary winding of the transformer and phase reactor is fed with voltage m U . In the second section 2 3 , π − α £ θ £ π + α there is no voltage. In the third section 3 , O π + α £ θ £ θ the total active-inductive resistance of the secondary winding of the transformer and phase reactor is fed with voltage . Based on equation (1) and the corresponding initial conditions, the currents in the first, second, and third plots of the time diagram (Fig. 2) will take the form: Equating expression (4) to zero, we obtain the angle of closing the commutation thyristor: e e ρ α +α −π −ρ α +α θ = π + α + ν + − ⋅ + ρ ν Considering expressions (2), (4), and (5), the reactive power and losses of active power constitute, in relative units: where ( ) ( ) It follows from expressions (6) and (7) that the integrated indicators of the energy process ( ) , , P * ∆ α α α are functions of the scalar set of control angles α 1 , α 2 , α 3 . Therefore, by using these indicators, it is possible to estimate the effectiveness of energy processes in an STC with the forced commutation for any techniques of their control.

A method of multicoordinate control over an STC with the forced commutation and voltage addition
To improve the efficiency of an STC with the forced commutation as the source of reactive power, it is necessary that the specific losses of active power in it should not exceed the level of the basic variant when the static compensator is powered by a sinusoid voltage: 2  3  1  2  3  1  1  2  3 , , , , , , , The objective control function of an STC with the forced commutation should not be larger than 0: ( ) 0 z x, y ≤ . The objective control functions and the boundaries of their transition to the region of negative values for an STC with the forced commutation for networks with a compensated neutral in the presence of voltage addition for values 1.6;1.9; 2.2 ν = are shown in Fig. 3, 4, respectively. The expression for curves that determine the boundaries of the transition of the objective control functions to the region of negative values and the boundary control surfaces for different coefficients of voltage addition for STC are given, respectively, in Tables 1, 2.   If the control angle α 3 is located below the boundary surface, then, when controlling the reactive power, the specific losses of active power by STC would be reduced compared to the basic variant. Moreover, the further this angle is from the boundary control surface, the less the specific losses of active power. When the coefficient of voltage addition ν increases, the boundary control surfaces are shifted upwards, which makes it possible to increase the adjustment range of the control angle α 3 .
The multi-coordinate control method makes it possible to choose the angle α 3 with such a margin that would ensure when executing the phased control over reactive power, a decrease in the specific losses of active power in the STC. One can also employ a change in the α 1 and α 2 angles to resolve other local tasks.

Developing a control circuit and a flowchart of the algorithm to operate the controlling microcontroller of an STC with the forced commutation and voltage addition
The static controller of reactive power, which is included in an STC with the forced commutation in the presence of voltage addition, makes it possible to reduce the specific losses of active power by the compensator by increasing the coefficient of voltage addition ν [19].
These conclusions were drawn for those techniques to control the reactive power of a static compensator, which are partial cases of a multicoordinate control method. Applying the multi-coordinate control method to the static thyristor compensator with the forced commutation in the presence of voltage additions makes it possible to expand its functionality through the emergence of an additional control channel -the voltage addition channel.
Multi-coordinate control over a static thyristor compensator with the forced switching for networks with a compensated neutral in the presence of voltage additions can be ensured by using the control circuit, which is shown in Fig. 6.
The static compensator control circuit includes a microprocessor system. It is composed of microprocessor MP, RAM storage device RAM SD, permanent storage device PSD, terminal T, address bus AB, data bus DB, command bus CB. The conjugating devices CD1, CD2, CD3, CD4, CD5, CD6, digital-analog converters DAC1, DAC2, DAC3, and analog-digital converters ADC1, ADC2 enable processing the signals from sensors and the generation of control signals. The structure of the device circuit, which enables the synchronization and execution of the required algorithm for switching the commutation thyristors, includes: voltage transformer Т2, voltage sensors VSD1, VSD2, single-phase bridge rectifiers VD1, VD2, VD3. In addition, the device is equipped with the generators of saw-like voltage GSLV1, GSLV2 and rectangular uni-polar voltage GRUPV, zero-organs ZO1, ZO2, ZO3, ZO4, logical elements "OR", "BAN", cycle D-trigger, and pulse generators PG1, PG2, PG3.
The flowchart of the operation algorithm for the controlling microcontroller of an STC with the forced commutation when controlling reactive power is shown in Fig. 7. The terminal T is used to enter, to the microcontroller, the static compensator's configuration parameters, that is, the values of resistances of the phase reactors and the secondary winding of the transformer Т1 r r , x r , r 2 , x 2 . One also enters the values of control angles of the commutation thyristors α 1 , α 2 and the discrete set of control angles α 3i , which, when the index i increases from 1 to n, decreases from π to 0. In addition, the microcontroller receives the values of phase voltages 21 , from two split windings 21A w and 22 A w from the voltage sensors VSD1, VSD2. The phase voltages are found by means of DAVUL on two split windings from the low voltage side.
The microcontroller calculates the coefficient of voltage addition , ν specific resistances 0 , ρ 1 , ρ the boundary control surface ( ) By increasing the coefficient of voltage addition ν by using DAVUL, it becomes possible to ensure a further reduction of the specific active power losses and an increase in the static compensator performance.
The time diagrams of the operation of individual elements from the control circuit of an STC with the forced commutation for networks with a compensated neutral in the presence of voltage addition are shown in Fig. 8. The transformer T2 synchronizes the operation of the logical unit of the control system with power voltage (Fig. 8, a). Voltages at the output from rectifiers VD4 and VD5 (Fig. 8, b, c) trigger the generators of saw-like voltage GSLV1 and GSLV2, respectively, over the odd and even half-periods of the supply voltage. The saw-like voltages generated by GSLV1 and GSLV2 are compared at the zero-organs ZO1, ZO2 and ZO3 with the control voltages, which are acquired from the outputs DAC1, DAC2, and DAC3 of the microcontroller (Fig. 8, d-f). At the time of equality between the saw-like voltages and control voltages at the outputs ZO1, ZO2 and ZO3, the control pulses are generated (Fig. 8, g-i). The control pulse from the output of the pulse generator PG1 is received by the control electrode of the commutation thyristor VS1, thereby opening it. Due to this, the rectangular voltage of the first split secondary winding 21A w in the transformer Т1 is fed to the phase reactor LR1 and current is induced in it (Fig. 8, l).
To prevent the unwanted opening of thyristor VS3 when opening the thyristor VS1, the blocking of the pulse is implied, which is formed at this time at the output ZO4. This is accomplished by a cyclic D-trigger with potential control and a key built on the "BAN" logical element. When the pulse from the output of the logical element "OR" arrives at the synchronization input C of the cyclic D-trigger, the signal at its direct output Q would repeat the signal, which is fed to the information input D from GRUPV (Fig. 8, k, l). Since in this case, the direct output of the D-trigger produces a logical unity, the key would be open while the pulse from the output ZO4 would be blocked.
The commutation thyristor VS1 closes after opening the thyristor VS3 at the time when its control electrode receives, through the logical element "OR" and the generator PG3, the control pulse from ZO3 (Fig. 8, i), which occurs when comparing the saw-like voltage 1 GSLV U with the control voltage 3 C U (Fig. 8, f). At this point, the first split secondary winding 21A w of the transformer Т1 opens, and the phase reactor is short-closed, which ensures the current continuity through it. When the pulse from the output of the generator PG2 (Fig. 8, h) arrives, the thyristor VS2 opens while the thyristor VS3 closes. Next, the second split secondary winding 22 A w of the transformer Т1 is connected to the phase reactor and it is fed with the phase voltage of the opposite polarity, the amplitude of which, due to DAVUL, can vary within the established limits. When the current through the phase reactor is reduced to zero, the output ZO4 produces a control pulse, which, through the closed key and the logical element "OR", would arrive at the control electrode in the thyristor VS3. In this case, the thyristor VS3 opens and the thyristor VS2 closes.
Thus, the proposed scheme to control an STC with the forced commutation makes it possible to independently control the phase reactors of each phase. In addition, it provides the required algorithm for switching the commutation thyristors and microcontroller control in real-time over all the elements of the system, thereby making it possible to reduce the specific losses of active power in the static compensator and electrical network. c -the shapes of voltage at the output from the rectifier VD5; d -the saw-like voltage GSLV1 compared to the control voltage U C1 ; e -the shape of voltage GSLV2 compared with the control voltage U C2 ; f -the saw-like voltage GSLV1 compared with the control voltage U C3 ; g -control pulse U PG1 ; h -control pulse U PG2 ; i -control pulse U PG3 control; j -the signal sent to the information entrance D from GRUPV; k -the signal at the direct output Q of the cyclic D-trigger; l -the shapes of voltage of the first split secondary winding of the transformer T1 and the current of the phase reactor LR1

Discussion of results of studying the mathematical model of an STC with the forced commutation and voltage addition
It is known that when an STC with the forced commutation is powered by a sinusoid voltage the specific losses of active power do not depend on the thyristor opening angle α and remain constant. That does not make it possible to implement the efficient technologies of reactive power control in these static compensators. The use of a rectangular-shape voltage to power an STC with the forced commutation and independent control over the angles of power thyristor switching gives it new features. Therefore, a mathematical model of a given compensator was constructed, which is described by the generalized differential equation of the first order (1). With the help of this equation, I have derived the main energy indicators: the reactive power (6) and the losses of active power (7), which are the functions of control angles of the commutation thyristors α 1 , α 2 and α 3 .
For the existing methods of regulating reactive power [16], the opening angle of the second commutation thyristor depends on the opening angle of the first commutation thyristor. To overcome this drawback, a method of multi-coordinate control over an STC with the forced commutation and voltage addition was developed. This method implies the following. When the specific losses of active power do not exceed the economically justified level (8), it is possible to build an objective function of the system (9), which depends on the control angles of commutation thyristors α 1 , α 2 and α 3 . The objective function z(x, y), depending on the value of the voltage addition coefficient , ν determines some control surfaces in a three-dimensional space (z, x, y). This function implicitly depends on the angle of control of the thyristors as it is defined by the formalized variables (x, y). The control surfaces z(x, y) (Fig. 3), when the coefficient ν is increased, are shifted downwards and are transferred to the region of negative values earlier. The transition of the control surfaces to the region of negative values follows the curves y(x) (Fig. 4), approximated in the region 0 2 , y < £ π 0 x < < π by the fifth-order polynomials using the least-squares method (Table 1). Substituting x and y in the polynomials with their values has produced the ratio for the boundary control surfaces that are explicitly dependent on angles α 1 , α 2 , α 3 ( Table 2). The boundary control surfaces ( )