Asymmetric Compensation of Reactive Power Using Thyristor-Controlled Reactors

: The thyristor-controlled reactor (TCR) compensator for smooth asymmetric compensation of reactive power in a low-voltage utility grid is proposed in this work. Two different topologies of compensator were investigated: topology based on a single-cored three-phase reactor and topology with separate reactors for every phase. The investigation of the proposed TCR compensator was performed experimentally using a developed experimental test bench for 12 kVAr total reactive power. The obtained results show that employment of separate reactors for every phase allows us to control the reactive power in every phase independently, and that the TCR compensator with three single-phase reactors is suitable for smooth and asymmetric compensation of reactive power in a low-voltage utility grid.


Introduction
The number of small grid-connected photovoltaic and wind power plants is constantly growing. These plants supply energy to low-voltage lines of the utility. The quantity of energy supplied by these power plants depends on natural conditions, which often change. On the other hand, the electrical grid loads in low-voltage lines are not just three-phase but single-phase as well, and many of them use reactive power. This leads to the fact that one of the main present-day problems of the electrical grid is compensation of the reactive power in the low-voltage grid [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and since the lowvoltage three-phase lines are often loaded asymmetrically [14,[19][20][21], the reactive power, which has to be compensated, is different in different phases.
At present, most parts of reactive power compensation systems in low-voltage lines of the utility are based on the electro-mechanical commutation technology of capacitor banks, which are split into steps connected in parallel to the utility grid [22,23]. However, capacitor banks have fixed discrete reactive power capacity, i.e., the reactive power produced by the capacitor bank cannot be changed smoothly. Therefore, it is impossible to fully compensate reactive power of the utility grid using capacitor banks [24].
Smooth reactive power compensation can be achieved by employing static synchronous compensators (STATCOMs) based on a voltage source inverter [24][25][26][27][28][29][30]. STATCOM devices are capable of compensating for both capacitance and inductance reactive power. The inverter of a STATCOM device produces PWM voltage to the utility grid employing a low pass filter. Capacitance reactive power is supplied if the magnitude of the voltage provided by the inverter is higher than the voltage magnitude of the utility grid. In cases when the magnitude of the inverter voltage is lower than the magnitude of the utility grid voltage, inductive reactive power is consumed. The STATCOM compensator based on inverter has a fast response time and is capable of full reactive power compensation. The main disadvantages are its high price [19,20,31] and that STATCOM devices can provide just symmetric compensation of reactive power in all three phases of the grid [32].
Smooth reactive power compensation can be performed by employing the static VAR compensator (SVC), a shunt-connected variable reactance, which either generates or consumes reactive power. The static VAR compensator is a power electronic device based on thyristor-switched capacitors (TSCs) for discrete control of generated reactive power and thyristor-controlled reactors (TCRs) for smooth control of consumed reactive power [24][25][26][27]. A TCR consists of a reactor and a bidirectional thyristor connected in series. Consumed inductive reactive power is controlled by variation of the thyristor firing angle α, where = 90° corresponds to full reactive power and = 180° corresponds to zero reactive power [24][25][26][27][33][34][35][36][37]. The first step in this approach is to overcompensate the utility grid using the TSC (to make the utility-grid load slightly capacitive) and after that, by consuming the required amount of inductive reactive power by the TCR, the total compensation of reactive power is achieved.
Despite the fact that research in the field of SVCs has been carried out for many years, the topic is still relevant. This fact is evidenced by many new publications devoted to the theory and application of SVCs, e.g., [4,8,12,[38][39][40][41][42][43]. One of the directions of recent research works in this field is the expansion of SVC application areas [8]. A new area of expansion could be the development and application of the SVC for smooth asymmetric compensation of reactive power in low-voltage grids as a cheaper alternative to the inverter-based STATCOM compensator. The novelty of such work can be proved by the following facts: 1. No one on the market offers the SVC, which is based on TSCs and TCRs, for smooth asymmetric compensation of reactive power in low-voltage grids. 2. There are few publications dedicated to the SVC for smooth compensation of reactive power in low-voltage grids [5][6][7][8][9]44]. However, all these publications are dedicated to symmetric compensation of reactive power in all three phases, and in most of them, just the simulation results are presented. 3. The TCR compensator, which is an essential part of the SVC that allows us to achieve smooth compensation, is developed only for the symmetric compensation of the reactive power and practically is employed just for high and medium voltage lines of the utility grid [4,[24][25][26][27]35,39,41,[45][46][47]. The novelty of this work is that the proposed TCR compensator is capable of compensating reactive power in a three-phase low-voltage grid utility asymmetrically and that the proper operation of the proposed compensator is proved experimentally, using developed experimental reactors and the test bench of the compensator.

The Topology and Operation of the TCR Compensator
The block diagram of the experimental test bench for the investigation of the developed TCR compensator for smooth asymmetric compensation of reactive power for a low-voltage utility grid is presented in Figure 1. It consists of a three-phase power supply (| | = 230V, = 50Hz); commutation switches SW1-SW3; zero crossing circuits for each phase; thyristor switches T1-T3 for each phase; control block. The test bench was designed for the experimental investigation of the TCR compensator operation with the three-phase single-cored reactor and with separate reactors for every phase. Therefore, the single-cored three-phase Y-connected reactor (L1) with the middle point connected to neutral, three-phase Y-connected separate phase reactors (L2-L4) with the middle point connected to neutral and switches SW2 and SW3 for commutation of reactors were included into the structure of the reactive power compensator ( Figure 1). The power quality analyzer and oscilloscope were used for the measurement of the reactive and active power and waveforms of utility-grid voltage and current. The investigation was performed in low-voltage lines of the utility for symmetric and asymmetric phase load reactive power compensation. The ∆ connection of coils as well as Yconnection with an unconnected midpoint were not used because they are not suitable for asymmetric compensation of the reactive power.

Investigation Results
The experimental investigation results of the proposed TCR compensator for smooth asymmetric compensation of reactive power in a low-voltage utility grid are presented in this section. Two different topologies of compensator are investigated: topology based on a single-cored threephase reactor and topology with separate reactors for every phase. The main goal of investigations is to prove the possibility of smooth asymmetric compensation of consumed reactive power in a threephase low-voltage utility grid using a TCR. The experimental test bench of the TCR compensator with a single-cored three-phase reactor is presented in Figure 2.

Investigation of the Compensator Based on a Single-Cored Three-Phase Reactor
The single-cored three-phase air-gaped reactor was designed in order to achieve sufficient reactive power compensation and low consumption of active power and to avoid core saturation. Cores with air gaps are usually used for reactors to avoid their saturation. The theory dedicated to the design of magnetic materials with the air gap, including the cores of reactors, can be found in [48][49][50][51]. The three-phase EI-shaped reactor was designed for total reactive power = 4.8kVAr that corresponds to the RMS of phase current = 7 for the low-voltage utility-grid phase voltage | | = 230V. The impedance of the reactor has to be | | = | | | | ≈ 32Ω. The inductive resistance of the coil was much higher than active; therefore, Z ≈ XL and the approximate inductance of the coil can be obtained using the equation = ≈ 100 , where ω is the angular frequency of grid voltage. In order to avoid core saturation, the air-gaped core was used. To obtain the desired inductance of the reactor, the approximate design parameters of the reactor coil were chosen using the equation: where is the free space permeability, is the relative magnetic permeability of iron core, N is the number of turns, S is the winding area and l is the length of coil. The parameters of the singlecored three-phase air-gaped reactor are presented in Table 1. By adjusting the air gap, the inductance of every coil was set to 100 mH. The active resistance of every coil is = 1Ω. The active resistance in the equivalent circuit of the reactor was connected in series with the inductive one; therefore, the current was the same for both elements. The values of consumed active power | | = 54 and reactive power | | = 1.7 for each phase coil were determined by employing the following equations: The structure and view of the designed single-cored air-gaped reactor are presented in Figure 3. The reactive power consumed by the reactor is determined by the duration the reactor is connected to the grid. This duration can be controlled by variation of the thyristor firing moment in relation to the grid-voltage zero-value-crossing moment. Usually this moment is named as the thyristor firing angle, , and is expressed in angular degrees. The obtained reactive power dependences on the firing angle of thyristors, when firing angles in all three phases are changed simultaneously (in the case of symmetric compensation), are presented in Figure 4. The waveforms of utility-grid voltage, reactor current and thyristor firing pulses are given in Figure 5. The obtained results show that the reactive power consumed by the reactor changes in all phases by the same law. The dispersion of the reactive power between individual phases, which is about 17%, is caused by the dispersion of the parameters of the reactor coils. The obtained results allow us to conclude that the TCR compensator based on a single-cored three-phase reactor is suitable for the smooth symmetric compensation of reactive power in all three phases within appropriate error, determined by the dispersion of parameters of reactor coils.
The investigation results prove that the TCR technique can be implemented in a low-voltage utility grid for symmetric compensation of reactive power within appropriate error and that the reactive power consumed by the reactor can be controlled smoothly by control of the thyristor firing angle. Additionally, it can be stated that commutation of the reactor does not introduce any highfrequency disturbances of the reactor current and grid voltage ( Figure 5) [52]. However, for the smooth control of the reactive power consumed by the reactor, it was necessary to pass the current only for a certain part of the period. As a result, the reactor current shape was distorted ( Figure 5), resulting in low-frequency harmonics.  Spectrum analysis was carried out employing an FFT toolbox by importing oscilloscope data into MATLAB/Simulink. The spectrums were obtained experimentally; therefore, harmonic 0 can appear because of measurement error or because the current curve is slightly asymmetric with respect to the time axis, i.e., some DC bias may exist. The asymmetry can be introduced by nonlinearity of our facility network, which can be caused by other devices powered from the same network. The spectrums of reactor current at various thyristor firing angles are presented in Figure 6, and the total harmonic distortion (THD) in Table 2. When a reactor consumes a large amount of reactive energy, which requires the current to flow through the reactor for practically the whole period, the current shape is distorted slightly (Figure 5a). However, for the reduction of the consumed reactive energy, it is necessary for the current to flow through the reactor only for part of the period, so the current shape distortion increases (Figure 5c,d). On the other hand, as the current through the reactor decreases, its effect on the overall distortion of the grid current also decreases.  The next experiment was conducted to determine whether it is possible to control the consumed reactive power in every phase independently, using a single-cored three-phase air-gaped reactor. This is important because only the possibility of independent consumption of reactive power in each phase allows us to implement asymmetric compensation. The experiment was performed for the case when the firing angles of two phases were fixed: the firing angle of one phase was fixed at 165° (corresponds to minimal reactive power), while the firing angle of another phase at 99° (corresponds to maximal reactive power). The firing angle of the remaining phase was varied. The obtained dependences are presented in Figure 7. It is seen that variation of the firing angle of one phase does not just change the reactive power of the controlled phase but also influences the reactive power of phases with fixed firing angles. The nature of reactive power dependences for the phases with the fixed firing angle depends on the phase sequence. For one sequence, the reactive power was influenced only in one of the phases with a fixed angle (Figure 7a-c). For another sequence, the reactive power of both phases with the fixed firing angles was affected (Figure 7d-f).
During the next experiment, the firing angles of two phases were varied and the angle of the remaining phase was fixed. The investigation was performed for the case when the fixed firing angle was set to = 165°. Dependences of reactive power consumed by the single-cored three-phase reactor on firing angles of two phases are presented in Figure 8. It is seen that reactive power dependences of the phases with the variable firing angle strongly differ in spite of the fact that the firing angles of the thyristors are varied simultaneously. This happens due to one phase being influenced by another through the common core of the reactor.
Summarizing the obtained experimental investigation results, it can be concluded that it is impossible to control the reactive power in every phase independently using a compensator based on a single-cored three-phase reactor. This happens because phases influence each other through the common core of the reactor; therefore, separate reactors must be used for each phase for the asymmetric compensation of reactive power in a low-voltage utility grid.

Investigation of the Compensator Based on Separate Reactors for Every Phase
The structure and view of the designed air-gaped reactor for single phase are presented in Figure  9. Every single-phase reactor is capable of consuming4.2 of reactive power, which corresponds to phase current RMS I=18.5A for the low-voltage utility-grid phase voltage |U|=230V. Total reactive power of all three reactors is 12.6 kVAr . The impedance of the reactor is | | = | | | | ≈ 12.5Ω; the inductance = ≈ 40 . The required 40 mH inductance value was achieved by adjusting the reactor air gap. The parameters of the single-phase air-gaped reactor are presented in Table 3. Table 3. Parameters of the single-phase air-gaped reactor.

Parameter Value
Relative magnetic permeability of iron core ( ) 100 Number of turns of coil (N) 160 Winding area (S) 71.5 cm 2 Length of coil (l) Wire cross-section Inductance of coil at core air gap length d=0 Inductance of coil at d=5mm Inductance of coil at d=10mm Inductance of coil without core  The TCR compensator based on three single-phase air-gaped reactors was investigated experimentally. Firstly, the reactive power dependences on the firing angle of thyristors, when firing angles in all three phases were changed simultaneously (in case of case of smooth symmetric compensation), were obtained ( Figure 10). It is seen that the reactive power consumed by the singlephase reactors changes in all phases by the same law. The dispersion of the reactive power between individual phases was about 3%. The next experiment was performed in the same way as in the case of the TCR based on a single-cored three-phase air-gaped reactor, i.e., the firing angles of two phases were fixed: The firing angle of one phase was fixed at 165°, while the firing angle of another phase was fixed at 99°. The firing angle of the remaining phase was varied. The obtained dependences of reactive power consumption of every phase on the firing angle are presented in Figure 11. It is seen that the reactive power consumption of the phase with the variable firing angle has no impact on the reactive power consumption of the remaining two phases with the fixed firing angles. Therefore, this conclusion can be drawn: The employment of three single-phase reactors allows us to control the reactive power in every phase independently, and the compensator with three single-phase reactors is suitable for the smooth asymmetric compensation of reactive power in a low-voltage utility grid. It should be mentioned that the investigation also covered the TCR compensator with ∆ connection of single-phase reactor coils as well as Y-connection with an unconnected midpoint; however, the investigation results showed that these topologies of the TCR compensator are not suitable for asymmetric load compensation.

Efficiency of the TCR Compensator
The dependences of reactive and active power of single-cored three-phase and separate-phase air-gaped reactors were measured by applying a symmetric load ( Figure 12). The efficiency of reactors was calculated as a ratio of reactive power to total power. Dependencies of reactor efficiency on the firing angle are given in Figure 13.  It could be observed ( Figure 13) that the efficiency of the reactors varies from 0.955 to 0.975 when power consumed by the reactors changes from the maximal to minimal value. It is seen that efficiency decreases with increasing of the reactive power (with decreasing of the thyristor firing angle). This appears due to the fact that as the reactive power increases, the reactor current increases, and as a consequence, the active reactor losses increase as well.

Conclusions
1. TCR compensators, which typically are used in high-and medium-voltage utility grids, can be implemented in a low-voltage utility grid employing air-gapped reactors using a Y-connection connected to the neutral midpoint. 2. Variation of the thyristor firing angle of one phase of single-cored three-phase reactor does not just change the reactive power of the controlled phase but influences the reactive power of phases with fixed firing angles. This fact shows that it is impossible to control the reactive power in every phase independently using a TCR compensator based on a single-cored three-phase air-gaped reactor, i.e., a compensator with such a reactor is not suitable for the asymmetric compensation of reactive power. 3. Employment of three single-phase air-gaped reactors allows us to control the reactive power in every phase independently; therefore, a developed TCR compensator based on three singlephase reactors is suitable for smooth and asymmetric compensation of reactive power in a lowvoltage utility grid. 4. Commutation of the reactor using thyristor switches does not introduce any high-frequency disturbances of the reactor current and grid voltage. 5. TCR compensator topologies with ∆ connection of coils of single-phase reactors as well as Yconnection with unconnected midpoint are not suitable for asymmetric compensation of reactive power in a low-voltage utility grid. 6. The developed single-cored three-phase reactor and single-phase reactors are characterized by 0.955-0.975 efficiency.

Author Contributions:
The results presented in this paper were obtained in the framework of a PhD thesis by M.S., who was supervised by A.B. The experimental measurements performed at the Laboratory of Electronic Sytems, Center for Physical Sciences and Technology were supervised by M.S., V.B., N.P. and A.D. The conceptualization was introduced by S.P., A.B., V.M. and E.B. All authors contributed to the writing of this paper as well as the analysis of the results. All authors have read and agreed to the published version of the manuscript.