**3. 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 three-phase 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 three-phase 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.

**Figure 2.** Experimental test bench of the TCR compensator with a single-cored three-phase reactor.

### *3.1. 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 [48–51]. The three-phase EI-shaped reactor was designed for total reactive power *Q* = 4.8 kVAr that corresponds to the RMS of phase current *I* = 7*A* for the low-voltage utility-grid phase voltage |*U*| = 230 V. The impedance of the reactor has to be |*Z*| = |*U*| |*I*| ≈ 32 Ω. The inductive resistance of the coil was much higher than active; therefore, *Z* ≈ *X*L and the approximate inductance of the coil can be obtained using the equation *L* = *XL*ω ≈ 100 *mH*, 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:

$$L = \mu\_{\rm I} \,\mu\_0 \frac{N^2 \cdot S}{l},\tag{1}$$

where μ0 is the free space permeability, μI 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 single-cored three-phase air-gaped reactor are presented in Table 1.


**Table 1.** Parameters of the single-cored three-phase air-gaped reactor.

By adjusting the air gap, the inductance of every coil was set to 100 mH. The active resistance of every coil is *R* = 1 Ω. 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 |*P*| = 54*W* and reactive power |*Q*| = 1.7*kVAr* for each phase coil were determined by employing the following equations:

$$|P| = \frac{\left(|lI| \cdot \frac{R}{|Z|}\right)^2}{R},\tag{2}$$

$$|Q| = \frac{\left(|\iota I| \cdot \frac{X\_L}{|Z|}\right)^2}{X\_L}.\tag{3}$$

The structure and view of the designed single-cored air-gaped reactor are presented in Figure 3.

**Figure 3.** Structure (**a**) and view (**b**) of the single-cored three-phase air-gaped reactor.

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, α, 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 high-frequency 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.

**Figure 4.** Dependences of reactive power consumed by the single-cored three-phase reactor on the firing angle of the thyristors.

**Figure 5.** The waveforms of the utility-grid phase voltage (violet) and the reactor current (cyan) on thyristor firing angle (α): (**a**) 95◦ (**b**) 110◦ (**c**) 140◦ and (**d**) 160◦. Voltage zero crossing is displayed in yellow, thyristor control signal in green.

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.

**Figure 6.** The spectrums of the reactor current at various thyristor firing angles: (**a**) 95◦ (**b**) 110◦ (**c**) 140◦ and (**d**) 160◦. The frequency of the fundanental harmonic is 50 Hz.

**Table 2.** Total harmonic distortion of the single-cored three-phase air-gaped reactor current.


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.

**Figure 7.** Dependences of reactive power consumed by the single-cored three-phase reactor on the firing angle when the firing angle of one phase is variable and the angles of the remaining two phases are fixed. The Firing angle is variable for Phase 1 (**<sup>a</sup>**,**d**), for Phase 2 (**b**,**<sup>e</sup>**), for Phase 3 (**<sup>c</sup>**,**f**).

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 α = 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.

**Figure 8.** Dependences of reactive power consumed by the single-cored three-phase reactor on the firing angle when the firing angles of the two phases are variable and the angle of the remaining phase is fixed. The Firing angle is variable for Phase 1 (**a**), for Phase 2 (**b**).

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.

### *3.2. 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 consuming 4.2 *kVAr* of reactive power, which corresponds to phase current RMS *I* = 18.5 A for the low-voltage utility-grid phase voltage |*U*| = 230 V. Total reactive power of all three reactors is 12.6 kVAr. The impedance of the reactor is |*Z*| = |*U*| |*I*| ≈ 12.5 Ω; the inductance *L* = *XL*ω ≈ 40 *mH*. 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.

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 single-phase 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.

(**a**) (**b**)

**Figure 9.** Design (**a**) and view (**b**) of the single-phase air-gaped reactor.

**Table 3.** Parameters of the single-phase air-gaped reactor.


**Figure 10.** Dependencies of reactive power consumed by the single-phase air-gaped reactors on the firing angle of thyristors.

**Figure 11.** Dependences of reactive power consumed by each single-phase air-gaped reactor on the firing angle when the firing angles of the two phases are fixed and the angle of the remaining phase is variable. The Firing angle is variable for Phase 1 (**a**), for Phase 2 (**b**).

It should be mentioned that the investigation also covered the TCR compensator with Δ 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.

### *3.3. E*ffi*ciency 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.

**Figure 12.** Dependences of reactive and active power consumed by (**a**) the single-cored three-phase reactor and (**b**) three single-phase air-gaped reactors.

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.

**Figure 13.** Dependencies of reactor efficiency on the firing angle.
