*Article* **Analysis and Mitigation of Subsynchronous Resonance in a Korean Power Network with the First TCSC Installation**

**Minh-Quan Tran 1, Minh-Chau Dinh 1, Seok-Ju Lee 1, Jea-In Lee 1, Minwon Park 1,\*, Chur Hee Lee <sup>2</sup> and JongSu Yoon <sup>2</sup>**


Received: 19 June 2019; Accepted: 22 July 2019; Published: 24 July 2019

**Abstract:** This paper presents a detailed analysis results of the effect of a thyristor-controlled series capacitor (TCSC) on subsynchronous resonance (SSR), which was first applied to a Korean power system. First, the TCSC parameters were calculated, the structure of TCSC with synchronous voltage reversal (SVR) controller was presented, and the torsional characteristics of Hanul nuclear power generator rotor were studied to investigate the natural frequency and mode shape. The test signal method was used to determine the electrical damping in the frequency range of SSR operation through an electromagnetic transient analysis program in various system configurations. The SSR phenomenon was analyzed by comparing the electrical and mechanical damping of a conventional fixed series capacitor (FSC), and the case of a TCSC installed, and the effectiveness of the TCSC without any risk of SSR was demonstrated. As a result, when installing FSC, SSR occurred under sensitive operating conditions, but SSR was prevented in the case of TCSC compensation with SVR. The results obtained in this study can be effectively applied to the installation of TCSC in real power systems.

**Keywords:** korean power system; subsynchronous resonance (SSR); synchronous voltage reversal (SVR); thyristor controlled series capacitor (TCSC); test signal method

#### **1. Introduction**

Nowadays, electric power transmission lines are under the stress of reaching the thermal limit due to the increase of the transmission power. A flexible alternating current transmission system (FACTS) is well known as an effective solution to improve the power transfer capability. One of the FACTS devices, the thyristor controlled series capacitor (TCSC) not only improves power transfer capability but also helps mitigate the subsynchronous resonance (SSR) problem [1]. In 1971, the first SSR accident occurred at the Mohave generator in Arizona, where the generator shaft caused a large vibration and led to shaft fatigue [2]. Since that problem, the mitigation of the SSR effect into power system become an important issue.

A number of studies have been conducted so far on SSR mitigation using TCSC [3–7], the authors in Ref. [8] introduced that TCSC is attractive to SSR mitigation. However, the benefits of TCSC for SSR mitigation depend heavily on TCSC control methods and power system configurations, and may also affect the SSR mitigation characteristics when the grid has significant changes. The influence of control methodology on SSR was also introduced in [9]. The first IEEE benchmark model had three control methods, consisting of constant impedance, constant current and constant power control. This indicates that a TCSC device under constant impedance control can stimulate SSR vibrations. The paper also proposed a solution called synchronous voltage reversal (SVR) control. However, under the SVR control, the TCSC impedance characteristic has a transition frequency band of electrical

frequency, and it turns into a negative damping band in the mechanical frequency range and poses a risk of the SSR problem [10,11]. In Ref. [12], the authors analyzed the SSR induced by TCSC through a real-time digital simulator (RTDS) in a China power system, and showed that the TCSC system accessed without SSR damping could have the SSR problem. The Korea Electric Power Corporation (KEPCO) plans to install TCSC for the first time in a Korean power system by taking advantage of TCSC [13,14]. However, installing TCSC on an actual power system could threaten system stability, including SSR issues. Also, many nuclear and thermal power plants were installed in the Korean grid near the TCSC facility, so detailed analysis of the SSR is needed before installing the TCSC in the actual grid.

In this paper, the SSR behaviors of the real power network with the TCSC compensations were analyzed and compared with a fixed series capacitor (FSC) under various system configurations. As the first step of the study, the configuration of a 345 kV power network with the TCSCs was presented in a PSCAD/EMTDC (power systems computer aided design/electromagnetic transients in DC) simulation model which was simplified based on the power system presented in PSS/E (power system simulator for engineering). All the 345 kV transmission lines were represented by the 'pi' equivalent model. The system with a radial connection as seen from a generator to a compensated line has been identified as the most vulnerable due to the SSR [15,16]. The units #3 and #4 of the Hanul nuclear power plant were located at the Hanul station, which can be radial with the compensated transmission line. Therefore, the units #3 and #4 of Hanul nuclear power plant were selected for this study, they were presented by a detailed generator model while all other generators were represented by a voltage source. A TCSC model with the SVR control method was implemented to vary the TCSC capacitance proportional to the compensated line from 50% to 70%, which was required by the KEPCO. The modal analysis method was applied to investigate the torsional characteristics of the rotor of the units #3 and #4. Mechanical damping constants corresponding to each natural frequency were also calculated. For the SSR study, frequency scanning methods were applied. A comparison of different frequency scanning methods, including the simplified analytical, two-axis analytical, and test signal methods was performed in [2]. In this study, the test signal method was selected, which was implemented in the PSCAD/EMTDC program as a time-domain digital simulation. The PSCAD/EMTDC simulation can build a detailed generator and complex load model for a real power network, which is very important for the accuracy level of results. The test signal method was used to inject a multi-sine signal with various frequencies in a range of the SSR behavior into the generator speed, the response of electrical torque delivered from the generator was recorded, the fast Fourier transform (FFT) analysis was used to calculate the electrical damping corresponding to the subsynchronous frequency of the SSR behavior. Finally, the contingencies under different operational conditions in the 345 kV power network, including normal and sensitive conditions were defined to analyze the SSR behavior. Under severe conditions such as the loss of some transmission lines, it appears almost radial when looking at ShinYoungju-Hanul transmission line from the units #3 and #4. These conditions are unlikely to occur; however, they were defined to highlight any potential issues of the SSR in the real power network. The conventional FSC compensation was also implemented equal to the compensation levels of the TCSC to compare the SSR mitigation efficiency. In each simulation case, the responses of electrical damping at each natural oscillation frequency were used to calculate the net damping of mechanical and electrical damping.

As a result, under normal operation, both FSC and TCSC compensation did not pose a risk to SSR. However, in sensitive cases, the electrical damping clearly showed the SSR in the system with the FSC compensation. In the case of the TCSC with the SVR control at the same compensation level, there was no SSR in the power network. These results are necessary for the first TCSC installation in Korean power system.

#### **2. Configuration of a 345 kV Transmission System Equipped with TCSCs**

#### *2.1. Study Model of the 345 kV Transmission System*

The single line diagram of the 345 kV power network with the TCSCs compensation is shown in Figure 1, and the transmission line data are described in Table A1. The power system model provided by KEPCO was simplified and converted from the PSS/E network model to the PSCAD/EMTDC model. The Hanul nuclear power plant and Samcheok coal-fired power plant are important to supply the power for Seoul's load demand [17]. If TCSCs are installed in two 345 kV transmission lines, including ShinJecheon-Donghae and ShinYoungju-Hanul, it is expected that the power flow will increase and the system stability will be improved as well.

**Figure 1.** Simplified 345 kV transmission system with thyristor-controlled series capacitors (TCSCs) compensation.

#### *2.2. Detailed Design of the TCSCs*

The TCSC module has a capacitor bank and a parallel branch, which consists of an inductor connected to back to back thyristors. The TCSC impedance can be changed according to the conduction angle of the thyristors when the two thyristors are triggered. Figure 2 describes the design process of a TCSC.

The design objectives of the TCSCs were determined of 50% compensation level for normal operation and 70% compensation level for the first swing operation. The terminologies related to the TCSC design are shown in below equations [18,19]:

$$k(\%) = \frac{X\_{T\text{CSC}}}{X\_{L\text{im}}} \times 100\tag{1}$$

$$k\_b = \frac{X\_{TCCS}}{X\_{\mathbb{C}}} \tag{2}$$

$$
\lambda = \sqrt{\frac{X\_C}{X\_L}} \tag{3}
$$

where *XL* and *XC* are the inductor reactance and the capacitor reactance of TCSC. *XLine* is the reactance of the compensated transmission line. The compensation level (*k*) of TCSC was defined in the project objectives. Another parameter related to the design is the boost factor (*kb*) that was selected as 1.05 for the two TCSCs, and the resonance factors (λ) were selected as 2.6 and 2.68 for ShinYoungju-Hanul and ShinJecheon-Donghae, respectively. The results of the TCSCs parameters for two transmission lines can be seen in Table 1.

**Figure 2.** The TCSC design flow chart.

**Table 1.** The TCSCs parameters for ShinYoungju-Hanul and ShinJecheon-Donghae transmission lines.


As recommended for the SSR mitigation method [20,21], the SVR control method was selected as a controller for the TCSCs in the 345-kV power network. The concept of the SVR control is shown in Figure 3. A phasor measurement was used to measure line current and capacitor voltage. Based on these measurement values, the appearance impedance of the TCSC was calculated at the fundamental frequency. This apparent impedance was then divided to the physical impedance of the series capacitor to get the measured boost level, *kbmeas*. The boost reference was compared to the measured boost value.

The boost controller uses the PI control, which is based on the error between the reference and measured boost factor for sending angular displacement ϕ*<sup>C</sup>* to the SVR trigger pulse generation, and the outputs are the firing time for forward and reverse thyristors. The strategy of the SVR trigger pulse generation block is to control the instant when the capacitor voltage becomes zero. The detailed description of the block is given in the following equations [21]:

$$
\mu\_{\rm CZ} = \mu\_{\rm CM} + X\_0 i\_{\rm LM} \lambda a \nu\_{\rm N} (\text{tz} - \text{t}\_{\rm M}) \tag{4}
$$

$$\mathbf{u}\_{\mathbb{C}\mathbb{Z}} = X\_0 i\_{LM} [\lambda \beta - \tan(\lambda \beta)] \tag{5}$$

$$\mathbf{t}\_F = \mathbf{t}\_Z - \frac{\beta}{a\nu\_N} \tag{6}$$

where:

*X*<sup>0</sup> = *<sup>L</sup> <sup>C</sup>*, <sup>λ</sup> <sup>=</sup> *<sup>X</sup>*<sup>0</sup> <sup>ω</sup>*NL* , and <sup>ω</sup>*<sup>N</sup>* = <sup>2</sup>π*f*,

*tZ*: the desired time when the capacitor voltage becomes zero,

*tM*: the sampling time when the capacitor voltage *uCM* and line current *iLM* are measured, *tF*: the thyristor firing time,

*uCZ*: the capacitor voltage at the desired time *tZ,*

*uCM*: the capacitor voltage at the sampling time *tM, iLM*: the line current at the sampling time *tM,* β: the conduction angle of the thyristor.

**Figure 3.** The synchronous voltage reversal (SVR) control strategy.

The SVR control modules were implemented in the PSCAD/EMTDC program by the Fortran codes. The reaction of the SVR control in case of a DC current and a sub-frequency current injected into the line current was shown in Figures 4 and 5. The first case is illustrated in Figure 4, the TCSC operates in a steady state when a DC current is injected into the line current. As shown in the second graph from the top of Figure 4, there is an offset of line current caused by a DC injected current.

**Figure 4.** The TCSC-SVR operation with a DC current injection.

**Figure 5.** The TCSC-SVR operation with a sub-frequency sine wave current injection.

The SVR operates depending on the set of Equations (4)–(6) for calculating the different firing time for two thyristors which can be seen in the third graph of Figure 4. Thus, the TCSC voltage was kept stable with a DC current added to the line current.

A sine wave with a frequency of 10 Hz was also injected into the line current, as shown in the upper graph of Figure 5. The second graph from the top shows the total of the line current and the sub-frequency current. The thyristor currents and the TCSC voltage were shown in the third and bottom graph of Figure 5, respectively. The SVR control depends on the values of the line current and capacitor voltage for calculating the next firing time of a thyristor. Therefore, in the third graph of Figure 5, the conduction angles are different for two thyristors. So, there is a similar result in the case of a DC current injected, the TCSC voltage was also kept constant with the disturbance (sub-frequency current) in the system. That means with the SVR control, a disturbance of a DC or a sub-frequency current cannot affect to the TCSC operation, which is the advantage of the SVR controller.

#### **3. Analysis Method of Subsynchronous Resonance**

#### *3.1. Torsional Natural Frequency and Mode Shapes Analysis*

The simplified 345 kV transmission system was used to present the Hanul nuclear power plant and the Samcheok coal-fired power plant. It has been mentioned that, when a generator is a radial connection with series compensation such as the FSC and TCSC, the generator is the worst case to the excitation of the SSR at one or more shaft modes. Thus, in this study, the units #3 and #4 of the Hanul power plant were considered as detail generator model while the voltage sources represented the other generators. This is a 1219.6 MVA synchronous generator with a rated RMS line to line voltage of 22 kV, the generator was presented by a synchronous machine component. It included two damper windings in the q axis, the multi-mass interface was enabled, and the completed generator input data are presented in Table A2. The multi-mass system shown in Figure 6 configures the shafts of the generator

units #3 and #4 of Hanul nuclear power plant. A multi-masses system including a high-pressure (HP), an intermediate pressure (IP) turbine, two low-pressure (LP-A, LP-B) and generator (GEN) turbines together combined a five-mass spring system with detailed data given in Table 2.

**Figure 6.** Structure of units #3 and #4 multi-mass shaft system model. HP: high-pressure; IP: intermediate pressure; LP-A, LP-B: low-pressure; GEN: generator.


**Table 2.** The mechanical data of Hanul nuclear generator units #3 an #4 for shaft model calculation.

The relationship between the electrical torque and mechanical torque of a synchronous generator can be expressed by the motion equation:

$$J\frac{d\omega\_m}{dt} = \sum T = T\_m - T\_\varepsilon \tag{7}$$

For a detailed study of a multi-mass model of a steam turbine generator, a set of equations of individual masses are illustrated in the following equation [22]:

For generator:

$$J\_1 \frac{d\omega\_1}{dt} = -T\_\varepsilon + k\_{12}(\delta\_2 - \delta\_1) - D\_1\omega\_1 \tag{8}$$

For LP-B section:

$$J\_2 \frac{d\omega\_2}{dt} = T\_2 + k\_{23}(\delta\_3 - \delta\_2) - k\_{12}(\delta\_2 - \delta\_1) - D\_2\omega\_2 \tag{9}$$

For LP-A section:

$$J\_3 \frac{d\omega\_3}{dt} = T\_3 + k\_{34}(\delta\_4 - \delta\_3) - k\_{23}(\delta\_3 - \delta\_2) - D\_3\omega\_3 \tag{10}$$

For IP section:

$$J\_4 \frac{d\omega\_4}{dt} = T\_4 + k\_{45}(\delta\_5 - \delta\_4) - k\_{34}(\delta\_4 - \delta\_3) - D\_4\omega\_4 \tag{11}$$

For HP section:

$$J\_5 \frac{d\omega\_5}{dt} = T\_5 - k\_{45}(\delta\_5 - \delta\_4) - D\_5\omega\_5 \tag{12}$$

where, *Ji* is the moment of inertia, ω*<sup>i</sup>* is the angular velocity, δ*<sup>i</sup>* is the rotor angle, *Ti* is the mechanical torque, and *Di* is the damping torque coefficient with *i* from 1 to 5 indicates the individual sections of GEN, LP-B, LP-A, IP, and HP, respectively. *kij* is the stiffness between two connected shaft sections. The damping torques between masses are assumed to be negligible in this study.

An eigenvalue analysis was performed for the generator units #3 and #4 based on the shaft system equations given above. The eigenvalues and shaft model parameters such as natural frequency (*fm*), modal inertial (*Hm*), and mechanical damping (*Dm*) are given in Table 3, and the rotor natural frequencies with mode shaft of the turbine generator are shown in Figure 7. The relative rotational displacements are shown for one normal operation mode (mode 0) and four oscillation modes which are presented with natural frequencies at 8.3 Hz, 14.6 Hz, 22.2 Hz, and 23.8 Hz, respectively. For the first SSR mode, the mass IP has a strong interaction with the mass LP−A, and the mass LP−B has a strong interaction with the GEN in the second SSR mode. The third SSR mode has three interaction points, and the strongest point lies between the mass LP−B and GEN. Similarly, the fourth SSR mode has four interaction points with the strong interaction between the mass HP and IP.


**Table 3.** The shaft model parameters of Hanul nuclear generator units #3, #4 for the SSR analysis.

**Figure 7.** Rotor natural frequencies and mode shapes of the units #3 and #4.

#### *3.2. Frequency Scanning Method for SSR Analysis*

The SSR behavior can occur when the electrical power grid is compensated by a series capacitor. The resonance between electrical synchronous machines shaft and electrical grid can happen at subsynchronous frequencies, which are lower than the fundamental frequency (60 Hz for the study power network). Frequency scanning is a method of getting the frequency response of a system. These techniques determine the total impedance of the system viewed from the studying generator as a function of frequency. From that, the scanned impedance and the mechanical parameters of the turbine generator are used for calculating electrical damping of the system [2]. Another type of frequency scanning is the test signal method, which was used in this paper. As it is a method based on time domain simulation, it conforms to the detailed model of a real system application for getting the

electrical damping of the system. There is no risk of the SSR if the total net damping of the system is positive [23,24], which means that the system satisfies the equation:

$$D(\omega) = D\_\varepsilon(\omega) + D\_\mathfrak{m}(\omega) > 0\tag{13}$$

where, *Dm(*ω*)* and *De(*ω*)* are the damping of the mechanical and electrical system, respectively.

The relationship between the mechanical and electrical systems can be described by the closed−loop diagram shown in Figure 8, with Δ*Te* is the electrical torque deviation in per unit and Δω*<sup>r</sup>* is generator rotor speed deviation in per unit.

**Figure 8.** Relationship between the electrical and mechanical system.

The electrical dynamic as a function of frequency can be expressed as the following equation:

$$\mathcal{G}\_{\mathfrak{C}}(j\omega) = D\_{\mathfrak{C}}(\omega) + j\mathbb{K}\_{\mathfrak{C}}(\omega) \tag{14}$$

where, *Ke(*ω*)* is the electrical coefficient.

The transfer function between the electrical torque and the generator rotor speed is *Ge(s)*. Thus, the damping torque coefficient (electrical damping) is defined as follows:

$$D\_t(\omega) = \Re \left[ \frac{\Delta T\_t(j\omega)}{\Delta \omega\_r(j\omega)} \right] \tag{15}$$

In this method, a multi−sine signal is injected into the synchronous generator rotor as the speed deviation, and the obtained output is an electrical torque. Thus, the transfer function represents the electrical damping as the function of frequency as given in Equation (15). The injected multi−signals are described as the following Equations (16)–(18):

$$
\Delta\omega\_{\rm I} = A\_{\rm u} \sum\_{n=n\_0}^{N} \sin[2\pi (f\_{\rm sub\\_min} + nf\_{\rm sub\\_qap})t + \delta\_n] \tag{16}
$$

$$\delta\_n = -\frac{(n - n\_0)(n - n\_0 + 1)}{(N - n\_0 + 1)}\pi \tag{17}$$

$$N = \frac{f\_{sub\\_max} - f\_{sub\\_min}}{f\_{sub\\_app}} + 1\tag{18}$$

where, the spectrum injected frequencies range [*fsub\_min*, *fsub\_max*] must cover all the range of subsynchronous frequency from 5 Hz to 55 Hz, and the *fsub\_gap* is the increment of each injected frequencies. The amplitude *A*ω could be chosen to be very small. With the selected *A*ω, the Schroeder multi−sine can be applied to choose δ*<sup>n</sup>* as the function of *n* in (17) for reducing overall amplitude [25].

Figure 9 shows a simple circuit of a synchronous generator connected with a TCSC through the 'pi' model of a transmission line. A multi−sine signal is injected into the speed input of the generator, the measurement as the output of the electrical torque is for carrying out the electrical torque corresponding to the injected signal. This multi−sine signal was implemented in the time−domain simulation in

PSCAD/EMTDC, which is an interesting tool for frequency screening studies where FACTs devices are located.

**Figure 9.** A model for subsynchronous resonance (SSR) analysis using a multi−sine signal injection.

#### **4. Simulation and the Results**

In this section, we analyzed and described the effects of the series compensation for the SSR behavior in case of using the FSC and TCSC. The FSC compensation was used to confirm the advantages of the TCSC compensation with the SVR control method. As the requirements from KEPCO, the compensation levels are 50% and 70% for the normal and dynamic operations, respectively. The signal injection method was used to obtain the electrical damping *De*, these values are compared to the mechanical damping *Dm* values presented in Table 3. Thus, we can indicate the risks of the SSR in the system as the equation (13).

As discussed in Section 3.1, the selected generators are the Hanul nuclear units #3 and #4. The simulation scenarios are shown in Table 4.


**Table 4.** The simulation scenarios for the subsynchronous resonance analysis.

Each case was studied with no compensation, the FSC compensation, and TCSC compensation, and all results are shown in Figures 10–14. In the figures, the mechanical damping constants of the nuclear generator units #3 and #4 with the torsional frequencies of modes 1 and mode 2 are given. The oscillation modes 3 and 4 have large values of the mechanical damping as 18.52 p.u and 17.22 p.u, respectively, so they were neglected in the figures. These values are negative of the mechanical damping in range of [*fm* − 1 Hz, *fm* + 1 Hz] with each torsional frequency. The risk of the SSR can be easily seen from the graphs, the SSR occur if any part of the electrical (*De*) line extends below the mechanical (*Dm*) line.

#### *4.1. Normal Operation of the 345 kV Power Network*

The simulation results of normal operation for the 345 kV power network are shown in Figure 10a. The figure shows the normal operation of the system in cases of no compensation and compensated by the FSC or TCSC. In that case, the FSC and TCSC were set as 50% of the compensation level. In Figure 10a, it can be seen that the electrical damping in the study power network with the FSC or TCSC compensations is similar to the no compensation case, and the total of the electrical and mechanical damping are positive for all cases. These results confirmed that in the normal operation condition, the system was stable with TCSC installation.

**Figure 10.** Comparison of *De* for different types of compensation of no compensation, fixed series capacitor (FSC), and TCSC compensation: (**a**) The compensation of *De* for case 1; (**b**) The compensation of *De* for case 2.

#### *4.2. Sensitive Cases of the 345 kV Power Network*

In this section, two sensitive simulation cases (case 2 and case 3) were performed to quantify the effects of the FSC and TCSC on the SSR behavior. The case 2 disconnected one line between two buses 5151–5152, and the case 3 disconnected all transmission lines between buses 5151−5152 and 5151−5150. The case 3 (worst case) is unlikely to occur, but it was defined to analyze any potential issues. In this case, the system becomes radial as seen from the Hanul nuclear power plant #3 and #4 to the compensated transmission line. If the TCSC operation destabilized the torsional mode of the Hanul nuclear power plant, it would be more likely to occur under this worst case.

Figure 10b shows the first sensitive case of the 345 kV power network. As a result, one transmission line between two buses 5151−5152 was disconnected but it did not affect the electrical damping. All the results were also similar to the base case in Figure 10a, there was not any risk of the SSR when one line between two buses 5151−5152 was disconnected. There is a different electrical damping characteristic of FSC compensation at 60 Hz due to a result of the electrical torque increased rapidly in case of disconnecting one transmission line. As compared in Figure 10, the plots of electrical damping in normal operation and the outage of one line nearby the Hanul nuclear power plant are the same with no compensation on the line. That means the series compensation cannot affect the SSR problem in the power network even one−line outage condition.

In the second sensitive simulation case, all transmission lines between buses 5151−5152 and 5151−5150 were disconnected. This is a radial system, as seen from the considered generator to the compensation line. As shown in Figure 11, in case of without any compensation, the electrical damping is positive. But in the case of 50% FSC compensation level, there is a negative point of the electrical damping at 39 Hz. In this case, the impedance *Z*(*j*ω) of the electrical system is shown in Figure 12. The system reactance is zero at an electrical resonance frequency of 21 Hz, which corresponds to 39 Hz at the rotor frame frequency.

The red line in the Figure 11 describes the TCSC compensation level of 50%. It can be seen that at 39 Hz, the electrical damping is also around zero which is the same as without compensation, this shows the advantage of the SVR control method. In the frequency range [5 Hz, 20 Hz] of the TCSC compensation, the electrical damping curve has negative points, but this is also higher than the mechanical damping, that means no risk of the SSR with the TCSC compensation. The simulation results of the system with different FSC compensation levels are shown in Figure 13. When the compensation levels were increased from 50% to 70% with the increment of 5%, the electrical damping was deeper more than normal operation at 50% compensation level. The difference with the FSC compensation, the electrical damping in case of the TCSC compensation, as shown in Figure 14 has not been affected by the compensation

levels. As the concept of the SVR control, the TCSC appearance impedance changes to the transient zone and become inductive impedance in the range from 40 Hz to 60 Hz of electrical frequency. So, it can be seen in Figure 11, the electrical damping was negative from 6 Hz to 25 Hz of mechanical frequency, but all of them are higher than mechanical damping curve, i.e., there is no risk of the SSR with the TCSC compensation. Two sensitive simulation results confirmed that the system was stable with TCSC compensation. The detailed data of net damping of all different TCSC compensation levels in different cases were listed in Table 5.

**Figure 11.** Comparison of *De* for a different type of compensations in case 3.

**Figure 12.** Frequency spectrum of the impedance of network in case of 50% FSC.

**Figure 13.** Comparison of *De* for different FSC compensation levels in case 3.

**Figure 14.** Comparison of *De* for different TCSC compensation levels in case 3.


**Table 5.** Net damping of different TCSC compensation levels in different cases.

#### **5. Conclusions**

This study analyzed the SSR problem in the case of installing TCSC in a Korean power system. In order to verify the effect of the TCSC introduced in a 345 kV transmission network for the first time in Korea, the analysis results of the SSR behavior are presented in the case of FSC and TCSC compensations. The detailed design of the TCSC was carried out with the calculated capacitor values of 198.94 μF and 186.93 μF for ShinYoungju-Hanul and ShinJecheon-Donghae, respectively. The inductor was chosen to be equal to 5.23 mH for the two transmission lines. We implemented the TCSC with SVR controller and confirmed the performance of the controller by injecting DC and sub frequency current. The Hanul nuclear power plant #3 and #4 were selected as target generators. The torsional frequency and mode shaft were also analyzed to show the interaction when the oscillation mode was excited.

Based on the time domain simulation software PSCAD/EMTDC, the test signal injection, one of the frequency scanning methods, has been applied to perform the electrical damping of the system within the sub−frequency range from 5 Hz to 55 Hz. Simulation of the basic case and two sensitive cases of the power network were performed with different types of compensation and the compensation level from 50% to 70%. There was no risk of SSR in normal case and the first sensitive operation. However, when the Hanul nuclear power plant was radially connected to the compensated transmission line, an SSR occurred at around 35 Hz to 39 Hz of the rotor frame frequency with the FSC compensation. Nonetheless, the TCSC with the SVR control method avoided the risk point. The results obtained in this study can be effectively applied to the TCSC installations in real power networks in the future.

**Author Contributions:** Conceptualization and investigation M.-Q.T. and M.-C.D.; visualization, S.-J.L.; software, J.-I.L.; writing—original draft preparation and editing, M.-Q.T.; supervision, M.P.; funding acquisition, C.H.L. and J.Y.

**Funding:** This work was funded by Korea Electric Power Corporation.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**


**Table A1.** Data of transmission line for the modified Korean power network.

Table A1 shows the per unit quantities converted based on the rating of 345 kV and 100 MVA.



#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Reactive Power Compensation and Imbalance Suppression by Star-Connected Buck-Type D-CAP**

#### **Xiaosheng Wang 1,2, Ke Dai 2,\*, Xinwen Chen 3, Xin Zhang 2, Qi Wu <sup>2</sup> and Ziwei Dai <sup>4</sup>**


Received: 5 March 2019; Accepted: 16 May 2019; Published: 18 May 2019

**Abstract:** Reactive power and negative-sequence current generated by inductive unbalanced load will not only increase line loss, but also cause the malfunction of relay protection devices triggered by a negative-sequence component in the power grid, which threatens the safe operation of the power system, so it is particularly important to compensate reactive power and suppress load imbalance. In this paper, reactive power compensation and imbalance suppression by a three-phase star-connected Buck-type dynamic capacitor (D-CAP) under an inductive unbalanced load are studied. Firstly, the relationship between power factor correction and imbalance suppression in a three-phase three-wire system is discussed, and the principle of D-CAP suppressing load imbalance is analyzed. Next, its compensation ability for negative-sequence currents is determined, which contains theoretical and actual compensation ability. Then an improved control strategy to compensate reactive power and suppress imbalance is proposed. If the load is slightly unbalanced, the D-CAP can completely compensate the reactive power and negative-sequence currents. If the load is heavily unbalanced, the D-CAP can only compensate the positive-sequence reactive power and a part of the negative-sequence currents due to the limit of compensation ability. Finally, a 33 kVar/220 V D-CAP prototype is built and experimental results verify the theoretical analysis and control strategy.

**Keywords:** dynamic capacitor; inductive unbalanced load; reactive power compensation; imbalance suppression; compensation ability

#### **1. Introduction**

There are a large number of inductive unbalanced loads in three-phase three-wire power systems generating reactive power and negative-sequence current, which not only increase line loss, but also cause malfunctions in overload protection devices triggered by negative-sequence current, thus threatening the safe operation of the power system. It is particularly important to compensate reactive power and negative-sequence current [1,2].

Reactive power compensation is an important means to improve power quality. Shunt power capacitors and shunt reactors have been widely used in power grid [3], but they can only provide constant reactive power. Different from fixed capacitors, static Var compensator (SVC) has advantages of adjustable reactive power and rapid response speed. Elements which may be used to make SVC typically include thyristor-controlled reactor (TCR) and thyristor-switched capacitor (TSC). In [4,5], two kinds of reactive power compensation schemes along with harmonic reduction techniques for unbalanced loads are addressed. Although with novel solutions, harmonic problems produced by TCR obtain some improvement, while high energy loss and large volume further limit its development.

Compared with SVC, the static synchronous compensator (STATCOM) has higher compensation accuracy, faster regulation speed, stronger compensation ability, and lower harmonic content based on a fully-controllable power semiconductor device and high switching frequency [6]. Two control strategies for star-connected and delta-connected STATCOMs under an unbalanced load are proposed in [7,8]. However, the ability of a STATCOM compensating negative-sequence current is affected by its structure. In [9], the compensation ability of STATCOM with star and delta configurations is indicated and analyzed. The third-harmonic injection method proposed in [10] achieves a significant improvement in STATCOM ability of simultaneous compensation for reactive and negative-sequence current. Considering unbalanced grid voltages, an improved regulation scheme with positive and negative sequence control for modular multilevel converter (MMC) in medium-voltage distribution static synchronous compensator (DSTATCOM) application is proposed in [11].

Although the compensation characteristic of a STATCOM for reactive and negative-sequence currents is good, it is complicated to stabilize and balance DC-link electrolytic capacitors' voltages, which will influence the reliability of STATCOMs [12,13]. Additionally, the high cost of STATCOMs affect their application in low-power applications. Although a matrix converter can be designed as a dynamic compensator without the bulky electrolytic capacitors, large numbers of bi-directional switches have to be used [14,15].

In [16–18], a magnetic energy recovery switch (MERS) is applied in reactive power compensation due to its characteristic equivalent to a variable capacitor. However, it will produce some harmonics because it adopts a phase-shifting control method. Additionally, electrolytic capacitor voltage fluctuation will further increase the harmonic contents of the output current. Similar to MERS, another VAr generator is analyzed in [19,20], which can be equivalent to a variable capacitor with a H-bridge inverter and DC capacitance. The same as with STATCOMs, the voltage fluctuation of the electrolytic capacitor on the DC side will affect their reliability.

Considering a large number of fixed capacitors in a distribution system, it is economical if power electronic technology can be used to reconstruct them to achieve better performance. Compared with the above compensators, the dynamic capacitor (D-CAP) is a simple, reliable, and economical solution without bulky electrolytic capacitors, which is composed of a power capacitor and a thin AC converter (TACC) [21–23]. Furthermore, the TACC could be configured with a simple topology, such as a Buck, Boost, or a Buck-Boost circuit, so the D-CAP has great potential to be used in low-power applications. Extending cells with a series connection, it is also feasible for the D-CAP to be applied in high-voltage applications [24]. Considering harmonic contents in the grid voltage, the output currents of the D-CAP will contain some distortions due to the impacts of self-resonance and on-state voltage drop of the switches. In order to reduce the harmonic content of the output currents, a waveform shaping strategy and a resonance damping method are proposed in [25,26], respectively.

Although reactive power compensation has got some focus for D-CAP, load imbalance suppression has not been discussed. Since the D-CAP is equivalent to a capacitor controlled by the duty ratio, it is meaningful to study how to suppress the load imbalance by capacitors. Reference [27] shows that only adopting capacitors cannot compensate for all unbalanced load, but it does not specify its compensation range. Using a delta-connected D-CAP to compensate the unbalanced load has been studied in the author's previous article [28]. Although the voltage in each phase is the same for a delta-connected D-CAP without the potential deviation at the neutral point, the line voltage of the delta structure is larger than the phase voltage of the star structure. For a star-connected D-CAP, the operating voltage of the switching device is lower than a delta-connected D-CAP, and the number of cascaded units is less, especially in high-voltage applications [24]. Due to the cost advantages, it is also of great significance to study star-connected D-CAPs. In this paper, reactive power compensation and imbalance suppression for a three-phase star-connected Buck-type D-CAP are explored.

The innovations of this paper can be described as follows: In Section 2, the relationship between power factor correction and load imbalance suppression in three-phase three-wire system is analyzed. In Section 3, the theoretical compensation ability of the D-CAP for negative-sequence current is derived. Considering that the rated voltage of the D-CAP is limited, the actual compensation ability of the D-CAP is also analyzed. In Section 4, an improved control strategy is proposed, which can make the D-CAP compensate negative-sequence current the best. Finally, experimental results verify the correctness of the theoretical analysis and the effectiveness of the control strategy.

#### **2. Principle of the D-CAP Compensating for Reactive Power and Suppressing the Load Imbalance**

#### *2.1. Relationship between Power Factor Correction and Imbalance Suppression*

For the system of a three-phase star-connected Buck-type D-CAP and inductive unbalanced load, shown in Figure 1, in order to simplify the analysis, only fundamental components are considered. The load is linear and the three-phase voltages on the grid side [*uTa uTb uTc*] are balanced and symmetrical, where:

$$\begin{cases} \begin{aligned} \boldsymbol{\mu\_{Ta}} &= \boldsymbol{\mathcal{U}}\_{\text{ff}} \sin(\omega t) \\ \boldsymbol{\mu\_{Tb}} &= \boldsymbol{\mathcal{U}}\_{\text{m}} \sin(\omega t - \mathbf{1} \mathbf{2} \mathbf{0}^{\circ}) \\ \boldsymbol{\mu\_{Tc}} &= \boldsymbol{\mathcal{U}}\_{\text{m}} \sin(\omega t + \mathbf{1} \mathbf{2} \mathbf{0}^{\circ}) \end{aligned} \end{cases} \tag{1}$$

**Figure 1.** (**a**) Three phase star-connected Buck-type D-CAP compensating for inductive unbalanced load; and (**b**) the structure diagram of the three-phase star-connected Buck-type D-CAP.

As shown in Figure 2, according to the symmetric component method, the three-phase grid side currents [*iSa iSb iSc*] can be decomposed into positive-sequence components [*i* + *Sa i* + *Sb i* + *Sc*] and negative-sequence components [*i* − *Sa i* − *Sb i* − *Sc*], where:

$$\begin{cases} \begin{array}{l} i\_{\text{Sr}} = i\_{\text{Sa}}^{+} + i\_{\text{Sa}}^{-} \\ i\_{\text{Sr}}^{+} = I\_{\text{Sm}}^{+} \sin(\omega t - \varphi^{+}) \\ i\_{\text{Sr}}^{-} = I\_{\text{Sm}}^{-} \sin(\omega t - \varphi^{-}) \end{array} \tag{2}$$

**Figure 2.** Grid currents phasor decomposition into positive and negative sequence currents.

Reactive power *QSa* of phase A can be decomposed into reactive power generated by *i* + *Sa* acting on *uTa* and reactive power generated by *i* − *Sa* acting on *uTa*. Similarly, *QSb* and *QSc* can be decomposed in this way. Reactive power at the grid side can be expressed as:

$$\begin{cases} Q\_{Sa} = \mathcal{U}\_{\mathcal{W}} (I\_{Sm}^{+} \sin \varphi^{+} + I\_{Sm}^{-} \sin \varphi^{-}) / 2 \\\ Q\_{Sb} = \mathcal{U}\_{\mathcal{W}} [I\_{Sm}^{+} \sin \varphi^{+} + I\_{Sm}^{-} \sin (120^{\circ} + \varphi^{-})] / 2 \\\ Q\_{Sc} = \mathcal{U}\_{\mathcal{W}} [I\_{Sm}^{+} \sin \varphi^{+} - I\_{Sm}^{-} \sin (120^{\circ} - \varphi^{-})] / 2 \end{cases} \tag{3}$$

In Equation (3), ϕ<sup>+</sup> is the phase angle of *i* + *Sa* lagging behind *uTa*, ϕ<sup>−</sup> is the phase angle of *i* − *Sa* lagging behind *uTa*. If power factors of phases A, B, and C on the grid side are 1 under the effects of the D-CAP, which means *QSa* = 0, *QSb* = 0, *QSc* = 0, then:

$$\begin{cases} I\_{Sm}^+ \sin \varphi^+ = 0\\ I\_{Sm}^- = 0 \end{cases} \tag{4}$$

Equation (4) shows that both positive-sequence reactive components and negative-sequence components of the three-phase grid side currents are 0 at this time, and only positive-sequence active components are left at the grid side.

Consequently, in three-phase three-wire system with unbalanced load, if three-phase power factors at the grid side are equal to 1 under the effects of the D-CAP, then the D-CAP can compensate the reactive power and suppress load imbalance.

#### *2.2. Principle of the D-CAP Suppressing the Load Imbalance*

The D-CAP is equivalent to the capacitance of *D*<sup>2</sup> *k Ck* under the control of the constant duty ratio [21,22]. Considering that the neutral potential drift of the star-connected D-CAP will bring more complexity and trouble to the analysis, the equivalent capacitance of the D-CAP can be transformed into delta-connected capacitors, shown in Figure 3a, if delta-connected capacitors meet Equation (5):

$$\begin{cases} \mathbf{C}\_{ab} = D\_a^2 D\_b^2 \mathbf{C}\_a \mathbf{C}\_b / (D\_a^2 \mathbf{C}\_a + D\_b^2 \mathbf{C}\_b + D\_c^2 \mathbf{C}\_c) \\ \mathbf{C}\_{bc} = D\_b^2 D\_c^2 \mathbf{C}\_b \mathbf{C}\_c / (D\_a^2 \mathbf{C}\_a + D\_b^2 \mathbf{C}\_b + D\_c^2 \mathbf{C}\_c) \\ \mathbf{C}\_{cd} = D\_c^2 D\_a^2 \mathbf{C}\_c \mathbf{C}\_d / (D\_a^2 \mathbf{C}\_d + D\_b^2 \mathbf{C}\_b + D\_c^2 \mathbf{C}\_c) \end{cases} \tag{5}$$

**Figure 3.** The principle of the D-CAP suppressing load imbalance: (**a**) Transformation from the star-connected D-CAP equivalent circuit to delta-connected capacitors; and (**b**) the phasor decomposition of *iCab,* and *iCac*.

Shown in Figure 3b, *iCab* can be decomposed into active component *i p Cab* parallel with *uTa*, and reactive component *i q Cab*, perpendicular to *uTa*. Similarly, *iCac* can be decomposed into *i p Cac* and *i q Cac*. Then the reactive and active components of *iCa* can be expressed with *i q Cab* + *i q Cac* and *i p Cab* + *i p Cac*. Similarly, *iCb* and *iCc* also contain active and reactive components. The total active power absorbed by the three-phase D-CAP is 0, which provides feasibility for the D-CAP to suppress load imbalance by transferring active power and compensating reactive power if the duty ratio can be controlled reasonably.

From Figure 3b, reactive powers absorbed by the D-CAP can be calculated:

$$\begin{cases} Q\_{\rm Ca} = -3\mathcal{U}\_m^2 \omega (\mathcal{C}\_{\rm ab} + \mathcal{C}\_{\rm ca}) / 4\\ Q\_{\rm Cb} = -3\mathcal{U}\_m^2 \omega (\mathcal{C}\_{\rm ab} + \mathcal{C}\_{\rm bc}) / 4\\ Q\_{\rm Cc} = -3\mathcal{U}\_m^2 \omega (\mathcal{C}\_{\rm ca} + \mathcal{C}\_{\rm bc}) / 4 \end{cases} \tag{6}$$

Supposing *iLa* can be decomposed into the positive-sequence component *i* + *La* and negative-sequence component *i* − *La*:

$$\begin{cases} \begin{aligned} \dot{\mathbf{i}}\_{La} &= \dot{\mathbf{i}}\_{La}^{+} + \dot{\mathbf{i}}\_{La}^{-} \\ \dot{\mathbf{i}}\_{La}^{+} &= I\_{Lm}^{+} \sin(\omega t - \Theta^{+}) \\ \dot{\mathbf{i}}\_{La}^{-} &= I\_{Lm}^{-} \sin(\omega t - \Theta^{-}) \end{aligned} \end{cases} \tag{7}$$

In Equation (7), θ<sup>+</sup> is the phase angle of *i* + *La* lagging behind *uTa*, and θ<sup>−</sup> is the phase angle of *i* − *La* lagging behind *uTa*. Three-phase reactive powers at the grid side after the D-CAP put into operation can be deduced:

$$\begin{cases} Q\_{\rm Sd} = Q\_{\rm Cd} + Q\_{\rm Ld} = \mathcal{U}\_{\rm m}(I\_{L\rm m}^{+} \sin \theta^{+} + I\_{L\rm m}^{-} \sin \theta^{-})/2 - 3\mathcal{U}\_{\rm m}^{2} \omega (\mathcal{C}\_{\rm ab} + \mathcal{C}\_{\rm m})/4\\\ Q\_{\rm Sb} = Q\_{\rm Cb} + Q\_{\rm Lb} = \mathcal{U}\_{\rm m}[I\_{L\rm m}^{+} \sin \theta^{+} + I\_{L\rm m}^{-} \sin (120^{\circ} + \theta^{-})]/2 - 3\mathcal{U}\_{\rm m}^{2} \omega (\mathcal{C}\_{\rm ab} + \mathcal{C}\_{\rm bc})/4\\\ Q\_{\rm Sc} = Q\_{\rm Cc} + Q\_{\rm Lc} = \mathcal{U}\_{\rm m}[I\_{L\rm m}^{+} \sin \theta^{+} - I\_{L\rm m}^{-} \sin (120^{\circ} - \theta^{-})]/2 - 3\mathcal{U}\_{\rm m}^{2} \omega (\mathcal{C}\_{\rm ca} + \mathcal{C}\_{\rm bc})/4\end{cases} (8)$$

Assuming *QSa* = 0, *QSb* = 0 and *QSc* = 0, then:

$$\begin{cases} \mathsf{C}\_{ab} = \left[ I\_{Lm}^{+} \sin \theta^{+} + 2I\_{Lm}^{-} \sin(120^{\circ} - \theta^{-}) \right] / (3\omega \mathsf{U} I\_{m})\\ \mathsf{C}\_{bc} = \left( I\_{Lm}^{+} \sin \theta^{+} - 2I\_{Lm}^{-} \sin \theta^{-} \right) / (3\omega \mathsf{U} I\_{m})\\ \mathsf{C}\_{ca} = \left[ I\_{Lm}^{+} \sin \theta^{+} - 2I\_{Lm}^{-} \sin(120^{\circ} + \theta^{-}) \right] / (3\omega \mathsf{U} I\_{m}) \end{cases} \tag{9}$$

If three-phase equivalent capacitances of the D-CAP meet Equation (9), the power factors of the three-phase grid side will be corrected to 1. According to the relationship between power factor correction and imbalance suppression in Section 2.1, reactive power will be compensated and load imbalance will be suppressed absolutely.

#### **3. Compensation Ability of a Star-Connected D-CAP for Negative-Sequence Currents**

#### *3.1. Theoretical Compensation Ability of a Star-Connected D-CAP*

In Equation (9), we can find *I* + *Lm*sinθ<sup>+</sup> is the positive-sequence reactive component amplitude of the load currents, and *I* − *Lm*sinθ−, *I* − *Lm*sin(120◦ + θ−), −*I* − *Lm*sin(120◦ − θ−) are the negative-sequence reactive components amplitude of the load currents. For example, under some load conditions, the positive-sequence reactive components' amplitude is smaller than two times of negative-sequence reactive components amplitude. Then the value of *Cbc* is negative according to Equation (9), which is unachievable for the D-CAP. Therefore, the compensation ability of the D-CAP is limited.

Take phase A as another example shown in Figure 4. Draw vertical line relative to *uTa* from the end point of *i* + *La* and dividing line 1 parallel to *uTa* at the midpoint of vertical line. The value of *Cab* is positive if *i* − *La* is in the zone 1 which is above dividing line 1. Similarly, the values of *Cca* and *Cbc* are positive if *i* − *Lb* and *i* − *Lc* are in zone 2 and zone 3, respectively. Considering that *i* − *La*, *i* − *Lb*, and *i* − *Lc* are symmetrical, the value of *Cab*, *Cbc*, and *Cca* are all greater than 0 if and only if *i* − *La*, *i* − *Lb*, and *i* − *Lc* are all in the ΔRST.

**Figure 4.** Theoretical and actual compensation ability of the D-CAP for negative-sequence currents.

Consequently, in the three-phase three-wire system, if the negative-sequence components of the load currents are located in the ΔRST, shown in Figure 4, meaning the value of equivalent capacitances calculated by Equation (9) are positive, the D-CAP can completely compensate the reactive power and suppress the load imbalance. Otherwise, the D-CAP can only compensate the positive-sequence reactive components and a part of the negative-sequence components of the load currents lying in the scope of ΔRST.

Additionally, the circle with radius *i* + *Lq*/4 in Figure 4 refers to the actual compensation ability of the D-CAP, which will be illustrated in Section 3.2.

#### *3.2. Actual Compensation Ability of a Star-Connected D-CAP*

Deviation of potential at the neutral point will occur when the star-connected D-CAP suppresses the load imbalance, which will make one of the voltages between the grid side and the D-CAP neutral point higher. In practice, the rated voltage of each phase D-CAP is generally 1.1–1.3 times higher than the grid voltage in order to maintain a safety margin, so the actual compensation ability of the D-CAP under an unbalanced load will be limited by the rated voltage.

Shown in Figure 5, the coordinate expressions of three phase grid voltages are:

$$\begin{cases} \dot{\mathcal{U}}\_{Ta} = (\mathcal{U}\_{m}, 0) \\ \dot{\mathcal{U}}\_{Tb} = (-\mathcal{U}\_{m}/2, -\sqrt{3}\mathcal{U}\_{m}/2) \\ \dot{\mathcal{U}}\_{Tc} = (-\mathcal{U}\_{m}/2, \sqrt{3}\mathcal{U}\_{m}/2) \end{cases} \tag{10}$$

In order to compensate reactive power and negative-sequence currents, the coordinate expressions of [*iCa iCb iCc*] can be described as:

$$\begin{cases} \dot{I}\_{Ca} = \left(-I\_{Ln}^{-}\cos\theta^{-}, I\_{Ln}^{-}\sin\theta^{-}\right) + \left(0, I\_{Ln}^{+}\sin\theta^{+}\right) \\ \dot{I}\_{Cb} = \left[-I\_{Ln}^{-}\cos\left(120^{\circ}-\theta^{-}\right), -I\_{Ln}^{-}\sin\left(120^{\circ}-\theta^{-}\right)\right] + \left[\sqrt{3}(I\_{Ln}^{+}\sin\theta^{+})/2, -I\_{Ln}^{+}\sin\theta^{+}/2\right] \\ \dot{I}\_{Cc} = \left[-I\_{Ln}^{-}\cos\left(120^{\circ}+\theta^{-}\right), I\_{Ln}^{-}\sin\left(120^{\circ}+\theta^{-}\right)\right] + \left[-\sqrt{3}(I\_{Ln}^{+}\sin\theta^{+})/2, -I\_{Ln}^{+}\sin\theta^{+}/2\right] \end{cases} \tag{11}$$

**Figure 5.** Voltage and current phasor of the star-connected D-CAP with the deviation of the potential at the neutral point for load imbalance suppression.

If the coordinate of the D-CAP neutral point potential is (x, y), then:

$$\begin{cases} \left[ (\mathcal{U}l\_{\rm m}, 0) - (\mathbf{x}, \mathbf{y}) \right] \perp \dot{I}\_{\rm Ca} \\ \left[ (-\mathcal{U}l\_{\rm m}/2, -\sqrt{3}\mathcal{U}l\_{\rm m}/2) - (\mathbf{x}, \mathbf{y}) \right] \perp \dot{I}\_{\rm Cr} \\ \left[ (-\mathcal{U}l\_{\rm m}/2, \sqrt{3}\mathcal{U}l\_{\rm m}/2) - (\mathbf{x}, \mathbf{y}) \right] \perp \dot{I}\_{\rm Ca} \end{cases} \tag{12}$$

According to the mathematical condition that two phasors are mutually orthogonal, it can be solved:

$$\begin{cases} x = l l\_m [1 - k \sin \theta^- - 2 (\sin \theta^-)^2] / (1 - k^2) \\ y = l l\_m \cos \theta^- (-2 \sin \theta^- + k) / (1 - k^2) \\ k \triangleq l\_{Lm}^+ \sin \theta^+ / l\_{Lm}^- \end{cases} \tag{13}$$

Therefore, if the D-CAP can absolutely compensate the reactive power and negative-sequence currents of the load, the neutral point potential of the D-CAP will be affected by the phase angle θ− and the reactive/imbalance index *k*, where *k* is the ratio of the positive-sequence reactive components' amplitude *I* + *Lm*sinθ<sup>+</sup> to the negative-sequence components amplitude *<sup>I</sup>* − *Lm*.

With the coordinate of *uT* and *N*1, the amplitudes of [*uaN*<sup>1</sup> *ubN*<sup>1</sup> *ucN*1] can be calculated. Here, drift factor *d* is introduced and defined as max(*uaN*<sup>1</sup> *ubN*<sup>1</sup> *ucN*1)/*uTa*. Figure 6 presents the relationship between drift factor *d* and reactive/imbalance index *k*, θ−. Because the rated voltage of the D-CAP is generally 1.1–1.3 times as high as the grid voltage, the ratio of positive-sequence reactive components amplitude to negative-sequence components amplitude of the D-CAP compensation currents is limited. In Figure 6b, we can find if reactive/imbalance index *k* is greater than 4, the effect of θ− to drift factor *d* is small. To simplify analysis and make the voltages at both ends of the D-CAP not exceed the rated

voltage, θ− is assumed to be kept at a value producing the maximal potential deviation at the neutral point. Therefore, for D-CAP currents, the positive-sequence reactive components' amplitude should be greater than four times the negative-sequence components amplitude to ensure the voltages at both ends of the D-CAP do not exceed its rated voltage.

**Figure 6.** Relationship between drift factor *d* and reactive/imbalance index *k*, θ−: (**a**) Three-dimensional graphics of *d*(*k*, θ−) = max (*uaN*<sup>1</sup> *ubN*<sup>1</sup> *ucN*1)/*uTa*; and (**b**) projection of the curved surface on the *k-d* plane.

As shown in Figure 6b, Point A is the intersection of the rated voltage limit line (*d* = 1.3) and the compensation ability limit line (*k* = 4). Area 1 is below the rated voltage limit line (*d* = 1.3) and on the right of the compensation ability limit line (*k* = 4). Here, area 1 is equivalent to the circle whose radius is *i* + *Lq*/4 in Figure 4. If the negative-sequence components of the load currents are in the scope of the circle, that means θ− and the reactive/imbalance index *k* are in area 1, and D-CAP can compensate the reactive power and suppress the load imbalance without exceeding the rated voltage limit.

#### **4. Proposed Control Strategy of the D-CAP to Compensate the Reactive Power and Suppress Load Imbalance**

For the three-phase star-connected Buck-type D-CAP, the proposed control strategy to compensate the reactive power and suppress load imbalance is shown in Figure 7.

Firstly, we transform the load currents [*iLa iLb iLc*] with Equations (14) and (15), respectively. Then passing through a low-pass filter, the positive-sequence active and reactive components [*i* + *Ld i* + *Lq*], and negative-sequence active and reactive components [*i* − *Ld i* − *Lq*] are obtained:

$$
\begin{pmatrix} i\_{\rm Lq}^{+} \\ i\_{\rm Lq}^{+} \end{pmatrix} = 2/3 \begin{pmatrix} \sin\omega t & \sin(\omega t - 120^{\circ}) & \sin(\omega t + 120^{\circ}) \\ \cos\omega t & \cos(\omega t - 120^{\circ}) & \cos(\omega t + 120^{\circ}) \end{pmatrix} \begin{pmatrix} I\_{Ln}^{+} \sin(\omega t - \varphi^{+}) \\ I\_{Ln}^{+} \sin(\omega t - \varphi^{+} - 120^{\circ}) \\ I\_{Ln}^{+} \sin(\omega t - \varphi^{+} + 120^{\circ}) \end{pmatrix} = \begin{pmatrix} I\_{Ln}^{+} \cos\varphi^{+} \\ -I\_{Ln}^{+} \sin\varphi^{+} \end{pmatrix} \tag{14}
$$

$$
\begin{pmatrix} i\_{Lt}^{-} \\ i\_{Lq}^{-} \end{pmatrix} = 2/3 \begin{pmatrix} -\sin(\omega t) & -\sin(\omega t + 120^{\circ}) & -\sin(\omega t - 120^{\circ}) \\ \cos(\omega t) & \cos(\omega t + 120^{\circ}) & \cos(\omega t - 120^{\circ}) \end{pmatrix} \begin{pmatrix} I\_{Ln}^{-} \sin(\omega t - \varphi^{-}) \\ I\_{Ln}^{-} \sin(\omega t - \varphi^{-} + 120^{\circ}) \\ I\_{Ln}^{-} \sin(\omega t - \varphi^{-} - 120^{\circ}) \end{pmatrix} = \begin{pmatrix} -I\_{Ln}^{-} \cos \varphi^{-} \\ -I\_{Ln}^{-} \sin \varphi^{-} \end{pmatrix} \tag{15}
$$

Since the actual compensation ability of the D-CAP for negative-sequence currents is limited by its rated voltage, it is necessary to add an amplitude limit on the negative-sequence currents. The processing method of the negative sequence currents is derived as follows:

$$i\_{Lq}^{+-} = \begin{cases} i\_{Lq}^{-} & \text{if } k \sqrt{(i\_{Ld}^{-})^2 + (i\_{Lq}^{-})^2} < i\_{Lq}^{+} \\\ i\_{Lq}^{-} i\_{Lq}^{+} / [k \sqrt{(i\_{Ld}^{-})^2 + (i\_{Lq}^{-})^2}], \text{ if } k \sqrt{(i\_{Ld}^{-})^2 + (i\_{Lq}^{-})^2} > i\_{Lq}^{+} \end{cases} \tag{16}$$

$$i\_{Ld}^{\*-} = \begin{cases} i\_{Ld'}^{-} & \text{if } k\sqrt{(i\_{Ld}^{-})^2 + (i\_{Lq}^{-})^2} < i\_{Lq}^{+}\\ i\_{Ld}^{-} i\_{Lq}^{+} / [k\sqrt{(i\_{Ld}^{-})^2 + (i\_{Lq}^{-})^2}], \text{ if } k\sqrt{(i\_{Ld}^{-})^2 + (i\_{Lq}^{-})^2} > i\_{Lq}^{+} \end{cases} \tag{17}$$

If the D-CAP can compensate the reactive power and negative-sequence currents to the utmost, the amplitudes of [*iCa iCb iCc*] are uniquely determined. Command current amplitudes of the D-CAP can be obtained with *i* ∗+ *Lq* , *i* ∗− *Ld*, and *i* ∗− *Lq* as follows:

$$\begin{cases} \left| \begin{matrix} \left| \mathbf{i}\_{\rm Ca}^{\*} \right| = \sqrt{\left( \mathbf{i}\_{\rm Ld}^{\*-} \right)^{2} + \left( \mathbf{i}\_{\rm Lq}^{+} + \mathbf{i}\_{\rm Lq}^{\*-} \right)^{2}} \\ \left| \mathbf{i}\_{\rm Cb}^{\*} \right| = \sqrt{\left( \mathbf{i}\_{\rm Ld}^{\*-} / 2 - \sqrt{\mathfrak{N}} \mathbf{i}\_{\rm Lq}^{\*-} / 2 \right)^{2} + \left( -\sqrt{\mathfrak{N}} \mathbf{i}\_{\rm Ld}^{\*-} / 2 - \mathbf{i}\_{\rm Lq}^{\*-} / 2 + \mathbf{i}\_{\rm Lq}^{+} \right)^{2}} \\ \left| \mathbf{i}\_{\rm Cc}^{\*} \right| = \sqrt{\left( \mathbf{i}\_{\rm Ld}^{\*-} / 2 + \sqrt{\mathfrak{N}} \mathbf{i}\_{\rm Lq}^{\*-} / 2 \right)^{2} + \left( \sqrt{\mathfrak{N}} \mathbf{i}\_{\rm Ld}^{\*-} / 2 - \mathbf{i}\_{\rm Lq}^{\*-} / 2 + \mathbf{i}\_{\rm Lq}^{+} \right)^{2}} \end{cases} \tag{18}$$

We compare the command currents amplitudes calculated by Equation (18) with the actual current amplitudes of [*iCa iCb iCc*], which can be extracted and calculated with the RDFT method [29]. Then we regulate the error through a PI controller to control the duty ratio of the D-CAP. Finally, the switches of the Buck-type AC-AC converter are driven through the modulated output signal. By adjusting the duty ratio, the positive-sequence reactive power and negative-sequence currents of the load can be effectively compensated.

**Figure 7.** Proposed control strategy of a star-connected D-CAP compensating the reactive power and suppressing the load imbalance.

#### **5. Experiment Verification**

In order to verify the effectiveness of the control strategy, experimental tests with a 33 kVar/220 V three-phase Buck-type D-CAP are carried out. Figure 1b shows the system configuration. The D-CAP

parameters are given in Table 1, which can be determined by the methods in [30]. The experimental prototype is shown in Figure 8. In the front view of Figure 8a, the three-phase main circuits of the prototype are divided into three layers, where the A-phase, B-phase, and C-phase circuits are arranged from the top to the bottom layers, respectively. The A-phase circuit is shown in the top view of Figure 8b.


**Figure 8.** Three-phase Buck-type D-CAP prototype: (**a**) front view; and (**b**) top view.

Experiments are implemented with three different cases in which the load is star-connected with the resistor and inductor in series, as shown as Table 2. Case 1 is implemented under a balanced load, which only needs reactive power compensation. Case 2 is used to verify the feasibility of the D-CAP to compensate the negative-sequence currents, so an unbalanced load is adopted, which corresponds to a reactive/imbalance index k > 4. To verify the compensation ability of the D-CAP, Case 3 is operated under a heavily unbalanced load, whose negative-sequence currents are beyond the compensation ability of the D-CAP, which corresponds to a reactive/imbalance index k < 4. Only the inductive part of the load is unbalanced in this experiment; it is also effective for the proposed control strategy if the resistive part is unbalanced even if both of the resistive and inductive parts are unbalanced.



#### *5.1. Case 1: D-CAP for Inductive Balanced Load*

Only reactive power is needed if the load is inductive and balanced. Shown in Figure 9a,b, currents at the load side can be considered balanced with values 23.0 A, 23.2 A, and 22.3 A, respectively and lag behind grid voltages. Figure 9c shows the three-phase power factors are 0.74, 0.74, and 0.76. In this case, the reactive/imbalance index *k* is toward positive infinity, represented as Point 1 in Figure 6b. When the D-CAP is used to compensate the reactive power with the proposed control strategy, shown in Figure 7, the phase angle of the currents and voltages at the grid side become the same (Figure 9d,e) and the three-phase power factors are regulated to 1 (Figure 9f). In Figure 9h, the D-CAP currents' lead voltages by 86◦, but not 90◦, because of active power loss when the D-CAP operates. The three-phase duty ratios of the D-CAP are 0.51, 0.47, and 0.47, respectively. Therefore, the reactive power compensation can be achieved under the effects of the D-CAP if the load is balanced and inductive.

**Figure 9.** D-CAP for inductive balanced load: (**a**) A-phase voltage and current at the load side; (**b**) voltage and current phasor at the load side; (**c**) power and energy at the load side; (**d**) A-phase voltage and current at the grid side after compensation; (**e**) voltage and current phasor at the grid side after compensation; (**f**) power and energy at the grid side after compensation; (**g**) D-CAP currents; (**h**) voltage and current phasor at the D-CAP side; (**i**) grid voltages; (**j**) A-phase duty ratio; (**k**) B-phase duty ratio; and (**l**) C-phase duty ratio.

#### *5.2. Case 2: D-CAP for Slightly Unbalanced Inductive Load*

Comprehensive control of reactive power compensation and imbalance suppression are implemented under a slightly unbalanced load in this case. Calculated by Equation (13), the reactive/imbalance index *k* is equal to 5.4, which corresponds to Point 2 in Figure 6b. Shown in Figure 10, currents at the grid side are unbalanced (Figure 10a) and lag behind grid voltages (Figure 10b) when the D-CAP is not put into operation with power factors 0.81, 0.85, and 0.72, respectively (Figure 10c). Currents at the grid side become balanced (Figure 10d,e) and the three-phase power factors are regulated to 1 (Figure 10f) after the D-CAP is put into operation. The three-phase equivalent capacitances can be regulated properly under different duty ratios, whose values are, respectively, 0.38, 0.47, and 0.62. In the Figure 10g,h, the output currents of the D-CAP are unbalanced due to different equivalent capacitances. Since the negative-sequence components' amplitude is smaller than one quarter of the positive-sequence reactive components' amplitude in this case, which is not constrained by the negative-sequence components' amplitude limit shown in Equations (16) and (17), the greatest voltage at both ends of the three-phase D-CAP is 262.7 V in Figure 10i.

**Figure 10.** D-CAP for slightly unbalanced inductive load: (**a**) currents at the load side; (**b**) voltage and current phasor at the load side; (**c**) power and energy at the load side; (**d**) currents at the grid side after compensation; (**e**) voltage and current phasor at the grid side after compensation; (**f**) power and energy at the grid side after compensation; (**g**) currents at the D-CAP side; (**h**) voltage and current phasor at the D-CAP side after compensation; (**i**) voltages [*uaN*<sup>1</sup> *ubN*<sup>1</sup> *ucN*1) after compensation; (**j**) A-phase duty ratio (**k**) B-phase duty ratio; and (**l**) C-phase duty ratio.

#### *5.3. Case 3: D-CAP for Heavily Unbalanced Inductive Load*

This case is implemented under a heavily unbalanced load. Calculated by Equation (13), the reactive/imbalance index *k* is equal to 1.7, which corresponds to Point 3 in Figure 6b. Shown in Figure 11, currents at the load side are unbalanced (Figure 11a) and lag behind grid voltages (Figure 11b) with power factors 0.89, 0.95, and 0.76, respectively (Figure 11c). After the D-CAP is put into operation, the positive-sequence reactive power and a part of the negative-sequence currents are compensated. We can find that the amplitude of the three-phase currents at the grid side become more balanced (Figure 11d) and the phase angle difference between grid voltages and currents become smaller (Figure 11e). Power factors are regulated to 0.99, 0.99, and 1, respectively (Figure 11f). In Figure 11i, the greatest voltage at both ends of the three phase D-CAP is 274.8 V, which is constrained in the range of the rated voltage by the negative-sequence components' amplitude limit shown in Equations (16) and (17). Comparing with Case 2, we can find if the ratio of the negative-sequence components' amplitude to the positive-sequence reactive components' amplitude of the load currents is smaller than 0.25, then the D-CAP can compensate its positive-sequence reactive components and negative-sequence components. If not, the D-CAP can only compensate the positive-sequence reactive power and a part of the negative-sequence currents due to the limit of its compensation ability.

**Figure 11.** The D-CAP for heavily unbalanced load: (**a**) Currents at the load side; (**b**) voltage and current phasor at the load side; (**c**) power and energy at the load side; (**d**) currents at the grid side after compensation; (**e**) voltage and current phasor at the grid side after compensation; (**f**) power and energy at the grid side after compensation; (**g**) currents at the D-CAP side; (**h**) voltage and current phasor at the D-CAP side after compensation; (**i**) voltages [*uaN*<sup>1</sup> *ubN*<sup>1</sup> *ucN*1] after compensation; (**j**) A-phase duty ratio; (**k**) B-phase duty ratio; and (**l**) C-phase duty ratio.

#### *5.4. Summarization and Comparison of Three-Phase Power Factors and the Unbalanced Degree*

A summary of the experimental results of the above three cases are shown in Table 3.



In Case 1, it can be found that three-phase power factors are corrected to 1 with the inductive balanced load. The parameters of the load are not exactly the same, so the unbalanced degree of the load current is 2.3%. Additionally, there are some active power loss and sampling errors when the D-CAP operates, so there is still a slight imbalance on the grid currents after compensation. Although the unbalanced degree increases from 2.3% to 3.9%, we can think the grid currents are balanced and reactive power compensation is achieved under the inductive balanced load. In Case 2, the load is slightly unbalanced with reactive/imbalance index *k* = 5.4, the three-phase power factors are corrected from 0.81, 0.85, and 0.72 to 1, and the unbalanced degree drops from 9.8% to 2.9%. Reactive power compensation and imbalance suppression are realized. In Case 3, the load is heavily unbalanced with reactive/imbalance index *k* = 1.7, and negative-sequence currents cannot be compensated completely due to the amplitude limit of *i* ∗− *Ld* and *i* ∗− *Ld*. Only positive-sequence reactive components and a part of the negative-sequence components of the load currents are compensated, so the unbalanced degree decreases from 27.9% to 12.6%, power factors increase from 0.89, 0.95, and 0.76 to 0.99, 0.99, and 1.

#### **6. Conclusions**

In this paper, reactive power compensation and imbalance suppression by a 33 kVar/220 V star-connected Buck-type D-CAP in a three-phase three-wire system are studied. An improved control strategy is proposed, which can make full use of the rated voltage margin of the D-CAP to compensate the negative-sequence currents of the load. The following conclusions are obtained through theoretical analysis and experimental verification:

(1) In the three-phase three-wire system, if three-phase power factors at the grid side are equal to 1 under the effects of the D-CAP, then the D-CAP can suppress load imbalance.

(2) If the negative-sequence currents of the load are located in the ΔRST shown in Figure 4, the D-CAP can theoretically completely compensate the reactive power and suppress load imbalance. However, the actual compensation ability is limited by its rated voltage.

(3) If the load is inductive balanced, only reactive power compensation is needed. Under the effect of the D-CAP, three-phase power factors can be corrected to 1.

(4) If the load is slightly unbalanced, whose negative-sequence currents' amplitude is less than 1/4 of the positive-sequence reactive currents' amplitude, the D-CAP can compensate the reactive power and suppress load imbalance.

(5) If the load is heavily unbalanced, whose negative-sequence currents' amplitude is greater than 1/4 of the positive-sequence reactive currents' amplitude, the D-CAP can only compensate the positive-sequence reactive power and a part of the negative-sequence currents due to the rated voltage limit.

**Author Contributions:** X.W. and K.D. conceived this article and designed the experiments; X.W., X.C., and X.Z. developed control routine and performed the hardware experiment; and all authors wrote the paper.

**Funding:** This research was funded by National Natural Science Foundation of China [Multimode Resonance Mechanism and Corresponding Multifunction Active Damping Control Technique for Power Electronic Hybrid Systems] grant number [51277086].

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Power Quality Services Provided by Virtually Synchronous FACTS**

#### **Andres Tarraso 1, Ngoc-Bao Lai 2, Gregory N. Baltas <sup>2</sup> and Pedro Rodriguez 1,2,\***


Received: 4 July 2019; Accepted: 26 August 2019; Published: 27 August 2019

**Abstract:** The variable and unpredictable behavior of renewable energies impacts the performance of power systems negatively, threatening their stability and hindering their efficient operation. Flexible ac transmission systems (FACTS) devices are able to emulate the connection of parallel and series impedances in the transmission system, which improves the regulation of power systems with a high share of renewables, avoiding congestions, enhancing their response in front of contingencies and, in summary, increasing their utilization and reliability. Proper control of voltage and current under distorted and unbalanced transient grid conditions is one of the most critical issues in the control of FACTS devices to emulate such apparent impedances. This paper describes how the synchronous power controller (SPC) can be used to implement virtually synchronous FACTS. It presents the SPC functionalities, emphasizing in particular the importance of virtual admittance emulation by FACTS devices in order to control transient unbalanced currents during faults and attenuate harmonics. Finally, the results demonstrate the effectiveness of SPC-based FACTS devices in improving power quality of electrical networks. This is a result of their contribution to voltage balancing at point of connection during asymmetrical faults and the improvement of grid voltage quality by controlling harmonics flow.

**Keywords:** FACTS; virtual synchronous machine; synchronous power controller; power quality; harmonics

#### **1. Introduction**

The continuously increasing penetration of renewable energies (REN), particularly wind and PV generation, is gradually reducing the conventional synchronous generation share from the energy mix. As a result, the overall power system performance degrades, since REN plants do not perform as conventional synchronous generation in terms of regulation and grid support [1]. Hence, the grid codes require modern REN plants to integrate certain grid-interactive functionalities in order to make their response compatible with the natural behavior of the electrical grid in case of grid events [2,3]. In this regard, the power converters used in modern REN plants need additional functionalities, specifically, to provide voltage and frequency support during faults by remaining connected to the grid, known as low-voltage ride-through (LVRT), and to inject instantaneous reactive power. Even so, these functionalities improve the interaction of REN power plants with the electrical grid only at the point of common coupling (PCC). Therefore, other mechanisms are necessary for improving power system performance in the area level. These mechanisms should address issues related to congestion, contingencies, oscillations, inefficiencies and instabilities resulting from the inherent intermittence and lack of inertia of REN power plants. In this regard, flexible ac transmission systems (FACTS) have demonstrated to be an effective approach that enhances controllability and increases utilization of power systems.

#### **2. FACTS Based on Virtually Synchronous Power Converters**

The FACTS concept was introduced in the late 1980s [4] and since then the relevant technologies have experienced significant advancements, both in hardware components and control methods. FACTS and High-voltage dc (HVDC) systems possess fundamental differences with respect to their operating principle. However, both are presented together as active solutions based on high-power electronics to enhance regulation and flexibility of transmission systems, and thereby to increase the capacity of power systems [5].

Depending on their configuration and application, different types of FATCS devices are described in the literature [6–8]. In general, they can be classified into two main categories, namely, series-connected and shunt-connected FACTS devices. The series-connected FACTS are installed between two buses of the power system by connecting them in series with a transmission line. Therefore, by regulating the voltage provided through the series-connected FACTS, it is possible to modify the apparent impedance of the power line; in other words, to increase/reduce its capacity and to regulate the power flow in the system. Moreover, proper control of the output voltage from the series-connected FACTS allows the improvement of the systems response against voltage distortions or sudden events, such as grid faults. The thyristor controlled series capacitor (TCSC) [9], the static synchronous series compensator (SSSC) [10], the dynamic voltage restorer (DVR) [11], and the fault current limiter (FCL) [12], among others, can be mentioned as the most popular series-connected FACTS. The shunt-connected FACTS are usually implemented through power converters that are able to control the current injected into a given bus of the system. Through appropriate controllers, the current injected in the grid can be formed by positive- and negative-sequence components at the fundamental frequency as well as harmonic components. This not only makes possible to control the magnitude of the voltage at the bus where the shunt-connected FACTS is connected, but also to compensate for unbalances and distortion. Commonly used shunt-connected FACTS devices are the static synchronous compensator (STATCOM) [13], the static var compensator (SVC) [14], the thyristor controlled reactor (TCR) [15], the thyristor switched capacitor [16], and the shunt active filter (SAF) [17]. The combination of series- and shunt-connected FACTS gives rise to cost-effective devices, which combine features from both FACTS categories. The unified power flow controller (UPFC) [18], the convertible static compensator (CSC) [19] and the unified power quality conditioner (UPQC) [20] are examples of such hybrid FACTS devices.

The majority of existing shunt-connected FACTS devices are based on detecting characteristic parameters of the grid voltage, i.e., amplitude, frequency and phase-angle, and, accordingly, to inject an appropriate current for emulating a given shunt-connected impedance. Series-connected FATCS follow the same rational where the power converter imposes a given voltage in series with the line to emulate a series-connected impedance. Nevertheless, in both cases a synchronization system, such as the well-known phase-locked loop (PLL) [21], is used to detect the grid voltage parameters. However, the conventional PLL does not perform properly under unbalanced and distorted conditions. This necessitates the use of other sophisticated implementations that can accurately detect the grid components even during these demanding operating conditions [22]. Note that the PLL is a non-linear system with a particular dynamic response, which strongly affects the grid-connected power converters response. This is particularly significant during grid faults and transients that can even give rise to hazardous interactions with other controllers in the grid.

For this reason, a new approach to design power converters controllers was proposed around one decade ago. Specifically, this approach demands the equations that define the operation of a synchronous machine to be integrated in the power converter controller [23]. It is worth mentioning that a synchronous machine can synchronize with the electrical grid or even regulate its operation without using a PLL. Recently, the aforementioned approach has materialized in several implementations. For instance, the synchronous power controller (SPC) [24] that has exhibited good performance in both HVDC [25,26] and FACTS systems [27,28] under generic operating conditions.

In this paper, we present the SPC operating principle and set of equations. Special attention is given to the configuration of its virtual output admittance to improve the power quality of the electrical grid when it is affected by harmonics and transient balance and unbalanced faults. Finally, we demonstrate the effectiveness of the SPC when used within the power converter controller of a shunt-connected FACTS device through validation by both simulations and experiments.

#### **3. Synchronous Power Controller**

The SPC has been widely used to enable electronics power converter to behave as a synchronous machine [29–32], being an interesting control solution to implement virtually synchronous FACTS. In contrast to PLL-based conventional control schemes, the SPC relies on a power balancing mechanism to maintain its synchronism with the electrical grid. As illustrated in Figure 1, where a generic dc source has been connected at the power converter dc-bus, the SPC consists of a power controller, a virtual admittance emulator, and a current controller. For the stable operation of the power converter, the parameters of these control blocks should be tuned properly. Due to the fact that these control loops have different bandwidth, they can be separately tuned to meet stability requirements as well as to conform to grid codes. Practically, the current control loop, the virtual admittance loop and the power control loop have very different bandwidth and settling time; therefore, they are decoupled and can be tuned separately.

**Figure 1.** Block diagram of a synchronous power controller (SPC)-based flexible ac transmission systems (FACTS) power converter.

The current controller is the most inner loop of the SPC. The main requirements for this controller are to track the current reference generated by the virtual admittance block and to tolerate the inherently resonant characteristic of the LCL filter. To properly tune the current controller, the LCL filter is modeled on the stationary reference frame as follows:

$$
\begin{bmatrix}
\dot{i}\_{\mathcal{L}}(t) \\
\dot{v}\_{f}(t) \\
\dot{i}\_{\mathcal{E}}(t)
\end{bmatrix} = \begin{bmatrix}
\frac{1}{L\_{\mathcal{E}}} - \frac{R\_{\mathcal{L}}R\_{f}}{L\_{\mathcal{E}}} & -\frac{R\_{\mathcal{L}}}{L\_{\mathcal{E}} + L\_{\mathcal{R}}} - \frac{R\_{f}}{L\_{\mathcal{E}}} & R\_{f}\frac{R\_{\mathcal{L}} + R\_{\mathcal{R}}}{L\_{\mathcal{E}} + L\_{\mathcal{R}}} - \frac{1}{L\_{\mathcal{E}}} \\
0 & \frac{1}{L\_{\mathcal{E}} + L\_{\mathcal{R}}} & -\frac{R\_{\mathcal{L}} + R\_{\mathcal{R}}}{L\_{\mathcal{E}} + L\_{\mathcal{R}}}
\end{bmatrix} \begin{bmatrix}
i\_{\mathcal{L}}(t) \\
v\_{f}(t) \\
i\_{\mathcal{E}}(t)
\end{bmatrix} + \begin{bmatrix}
\frac{1}{L\_{\mathcal{E}}} \\
\frac{R\_{\mathcal{L}}}{L\_{\mathcal{E}}} \\
0
\end{bmatrix} \mathbf{v}\_{\mathcal{L}}(t) + \begin{bmatrix}
0 \\
\frac{R\_{\mathcal{L}}}{L\_{\mathcal{E}} + L\_{\mathcal{R}}} \\
\end{bmatrix} \mathbf{v}\_{\mathcal{R}}(t) \tag{1}
$$

where *ic*, *vf* and *ig* denote converter-side current, capacitor voltage and grid-side current, respectively, *Rc*, *Rf* and *Rg* represent filter resistances, *Lc* and *Lg* represent filter inductances, and *Rth*, *Lth* and *vth* are

the grid equivalent parameters which can be calculated from the grid short-circuit ratio (SCR) and the quality factor (*q* = *X*/*R*) ratio as:

$$R\_{\rm llb} = \frac{V^2}{\text{SCR} \cdot P\_{\rm ll} \sqrt{1 + q^2}} \text{ and } L\_{\rm llb} = \frac{V^2 q}{\text{SCR} \cdot P\_{\rm n} \cdot \omega\_{\%} \sqrt{1 + q^2}} \tag{2}$$

The LCL filter model can be concisely expressed as:

$$\dot{\mathbf{x}}\_{lclc}(t) = \mathbf{A}\_{lclc}\mathbf{x}\_{lclc}(t) + \mathbf{B}\_{lclc}u(t) + \mathbf{G}\_{lclc}w(t) \tag{3}$$

$$\mathbf{y}\_{lcl}(t) = \mathbf{C}\_{kl}\mathbf{x}\_{lcl}(t) \tag{4}$$

where **C***lcl* = [ 001 ] is the output matrix.

Taking into account the digital implementation of the current controller, the filter model is discretized as:

$$\mathbf{x}\_{lcl}(k+1) = \mathbf{A}\_{lcl}\mathbf{x}\_{lcl}(k) + \mathbf{B}\_{lcl}u(k) + \mathbf{G}\_{lcl}w(k) \tag{5}$$

$$\mathbf{y}\_{lcl}(k) = \mathbf{C}\_{lcl}\mathbf{x}\_{lcl}(k) \tag{6}$$

The delay originated by the digital implementation can also be considered in the controller design by the dummy variable *xd* as follows:

$$
\underbrace{\begin{bmatrix} \mathbf{x}\_{kl}(k+1) \\ \mathbf{x}\_{d}(k+1) \end{bmatrix}}\_{\mathbf{x}\_{in}(k+1)} = \underbrace{\begin{bmatrix} \mathbf{A}\_{lcl} & \mathbf{B}\_{lcl} \\ 0 & 0 \end{bmatrix}}\_{\mathbf{A}\_{in}} \underbrace{\begin{bmatrix} \mathbf{x}\_{lcl}(k) \\ \mathbf{x}\_{d}(k) \end{bmatrix}}\_{\mathbf{x}\_{in}(k)} + \underbrace{\begin{bmatrix} 0 \\ 1 \end{bmatrix}}\_{\mathbf{B}\_{in}} u(k) + \underbrace{\begin{bmatrix} \mathbf{G}\_{lcl} \\ 0 \end{bmatrix}}\_{\mathbf{G}\_{in}} w(k) \tag{7}
$$

$$y\_{in}(k) = \underbrace{\begin{bmatrix} \mathbf{C}\_{lcl} & \mathbf{0} \\ \hline \\ \mathbf{C}\_{in} \end{bmatrix}}\_{\mathbf{C}\_{in}} \underbrace{\begin{bmatrix} \mathbf{x}\_{lcl}(k) \\ \mathbf{x}\_{d}(k) \end{bmatrix}}\_{\mathbf{x}\_{in}(k)} \tag{8}$$

To asymptotically track the reference current, the internal model principle is employed to model a proportional resonant (PR) as:

$$\dot{\mathbf{x}}\_{\rm prc}(t) = \underbrace{\begin{bmatrix} 0 & 1\\ -\omega\_{\mathcal{S}}^2 & 0 \end{bmatrix}}\_{\mathbf{A}\_{\rm prc}} \mathbf{x}\_{\rm prc}(t) + \underbrace{\begin{bmatrix} 1\\ 0 \end{bmatrix}}\_{\mathbf{B}\_{\rm prc}} e(t) \tag{9}$$

where *wg* denotes fundamental grid frequency, and *ei* = *i* <sup>∗</sup> − *ig* represents tracking error with *i* ∗ being reference current. The controller model can also be discretized as:

$$\mathbf{x}\_{\mathbb{PT}}(k+1) = \mathbf{A}\_{\mathbb{PT}}\mathbf{x}\_{\mathbb{PT}}(k) + \mathbf{B}\_{\mathbb{PT}}\mathbf{c}\_{l}(k) \tag{10}$$

The inverter model and the current controller model can be augmented as:

$$
\begin{bmatrix}
\mathbf{x}\_{\text{in}}(k+1) \\
\mathbf{x}\_{\text{pr}}(k+1)
\end{bmatrix} = \begin{bmatrix}
\mathbf{A}\_{\text{in}} & \mathbf{0} \\
\end{bmatrix} \begin{bmatrix}
\mathbf{x}\_{\text{in}}(k) \\
\mathbf{x}\_{\text{pr}}(k)
\end{bmatrix} + \begin{bmatrix}
\mathbf{B}\_{\text{in}} \\
\mathbf{0}
\end{bmatrix} \boldsymbol{\mu}(k) + \begin{bmatrix}
\mathbf{B}\_{d} \\
\mathbf{0}
\end{bmatrix} \boldsymbol{\nu}(k) + \begin{bmatrix}
\mathbf{0} \\
\mathbf{B}\_{\text{pr}}
\end{bmatrix} \boldsymbol{r}(k)\tag{11}
$$

or:

$$\mathbf{x}(k+1) = \mathbf{A}\mathbf{x}(k) + \mathbf{B}u(k) + \mathbf{B}\_d w(k) + \mathbf{B}\_r r(k) \tag{12}$$

*Energies* **2019**, *12*, 3292

Asymptotic tracking of current controller can be achieved by stabilizing the augmented system in (12) using the following feedback controller:

$$\mathfrak{u}(k) = \mathbf{K}\mathfrak{x}(k)\tag{13}$$

The feedback controller can be optimally calculated by minimizing the following quadratic cost function:

$$J\_{\mathbb{S}^\infty} = \sum\_{k=0}^\infty \left\{ \mathbf{x}^T(k)\mathbf{Q}\mathbf{x}(k) + \boldsymbol{u}^T(k)\mathbf{R}\boldsymbol{u}(k) \right\} \tag{14}$$

where **Q** and *R* are tunable parameters to adjust performance of the current controller. It is worth noting that the choice of **Q** and *R* is based on the relative importance of system states and control signals, which is not always a straightforward process. To simplify the selection of **Q** and *R*, one may select R as an identity matrix i.e., *R* = 1 and **Q** as **Q** = ρ**I**. Then, ρ can be altered to achieve a desired response. For instance, the higher the value of ρ, the faster the transient response and smaller the stability margin.

The virtual impedance shown in Figure 2 is usually chosen according to voltage support requirement by the grid codes. The state space equation for the virtual impedance can be given as:

$$\dot{i}\_{\mathcal{S}}^{\*}(t) = -\frac{R\_{\upsilon}}{L\_{\upsilon}}\dot{i}\_{\mathcal{S}}^{\*}(t) + \frac{1}{L\_{\upsilon}}e(t) - \frac{1}{L\_{\upsilon}}\upsilon\_{\mathcal{S}}(t) \tag{15}$$

where *Rv* is the virtual resistance, *Lv* is the virtual inductance, *i* ∗ *<sup>g</sup>* is the reference current for current controller, and *e* is the reference voltage coming from power control loop.

**Figure 2.** Simplified model of a current-controlled grid-connected power converter with virtual admittance.

The power controllers consisting of an active power and a reactive power controller are the main elements of the SPC scheme. The active power controller is based on the electromechanical swing equation to synchronize the power converter with the electrical grid. The transfer function of swing equation is given by:

$$
\omega\_{\rm spc} = \frac{1}{\omega\_s (Js + D)} (P\_{\rm m} - P\_c) + \omega\_\delta \tag{16}
$$

where *Pm* and *Pe* are the mechanical and the electrical power, respectively, ω*spc* and ω*<sup>s</sup>* are the SPC and synchronous angular speed, respectively, *J* is the virtual polar moment of inertia and *D* is the damping factor.

The reactive power controller is based on a proportional integral (PI) controller defined as follows:

$$E = \frac{k\_p s + k\_i}{s} (Q\_m - Q\_c) + E\_r \tag{17}$$

where *E* is the amplitude reference for the virtual electromotive force (emf) voltage of the virtually synchronous FACTS, *Er* is a feed-forward reference for such emf voltage and *kp* and *ki* are the proportional and the integral gains of the controller.

To simplify the analysis of the power controller loop, the dynamics of inner control loop are neglected and replaced by static gains. To calculate these gains, the powers exchanged between the SPC-based virtually synchronous FACTS and the electrical grid can be written as:

$$P\_{\varepsilon} = \frac{EV}{Z}\cos(\phi - \delta) - \frac{V^2}{Z}\cos(\phi) \tag{18}$$

$$Q\_{\varepsilon} = \frac{EV}{Z}\sin(\phi - \delta) - \frac{V^2}{Z}\sin(\phi) \tag{19}$$

where *Z* = *R*2 *<sup>v</sup>* + *X*<sup>2</sup> *<sup>v</sup>* is the magnitude of the virtual impedance, φ is the phase-angle of such an impedance, *V* denotes the rms value of the grid line voltage, *E* the rms value of the virtual emf and δ is the grid load angle, i.e., the angle between *E* and *V* phasors.

The above equations can be rewritten for small-signal analysis as:

$$P\_{d0} + \Delta P\_{\varepsilon} = \frac{(E\_0 + \Delta E)V}{Z} (\cos\phi\cos(\delta\_0 + \Delta\delta) + \sin\phi\sin(\delta\_0 + \Delta\delta)) - \frac{V^2}{Z}\cos(\phi) \tag{20}$$

$$Q\_{c0} + \Delta Q\_{\xi} = \frac{(E\_0 + \Delta E)V}{Z} (\sin \phi \cos(\delta\_0 + \Delta \delta) - \cos \phi \sin(\delta\_0 + \Delta \delta)) - \frac{V^2}{Z} \sin(\phi) \tag{21}$$

In steady-state, when synchronism takes place, δ<sup>0</sup> = 0, and also Δδ ≈ 0, then cos(Δδ) ≈ 1 and sin(Δδ) ≈ Δδ. Therefore:

$$P\_{t0} + \Delta P\_{\varepsilon} = \frac{E\_0 V \cos(\phi)}{Z} - \frac{V^2 \cos(\phi)}{Z} + \frac{E\_0 V \sin(\phi)}{Z} \Delta \delta + \frac{V \cos(\phi)}{Z} \Delta E + \frac{V \sin(\phi)}{Z} \Delta E \Delta \delta \tag{22}$$

$$Q\_{\mathcal{E}} + \Delta Q\_{\mathcal{E}} = \frac{E\_0 V \sin(\phi)}{Z} - \frac{V^2 \sin(\phi)}{Z} - \frac{E\_0 V \cos(\phi)}{Z} \Delta \delta + \frac{V \sin(\phi)}{Z} \Delta E - \frac{V \cos(\phi)}{Z} \Delta E \Delta \delta \tag{23}$$

Omitting the zero- and second-order terms, the small-signal component of the electrical power can be written as:

$$
\Delta P\_{\varepsilon} = \frac{E\_0 V \sin(\phi)}{Z} \Delta \delta + \frac{V \cos(\phi)}{Z} \Delta E \tag{24}
$$

$$
\Delta Q\_c = -\frac{E\_0 V \cos(\phi)}{Z} \Delta \delta + \frac{V \sin(\phi)}{Z} \Delta E \tag{25}
$$

From Equations (16), (17), (24) and (25), the state-space representation of the power control loop is given by:

$$
\begin{bmatrix}
\Delta\dot{o}\_{\rm spec} \\
\dot{\Delta\delta} \\
\dot{\Delta Q\_{\varepsilon}}
\end{bmatrix} = \begin{bmatrix}
1 & 0 & 0 \\
0 & -\frac{k\_{q1}}{k\_{p}k\_{q2} + 1} & -\frac{k\_{p}k\_{q2}}{k\_{p}k\_{q2} + 1}
\end{bmatrix} \begin{bmatrix}
\Delta a\_{\rm spec} \\
\Delta\delta \\
\Delta Q\_{\varepsilon}
\end{bmatrix} + \begin{bmatrix}
\frac{1}{\omega\_{\mathcal{J}}} & -\frac{k\_{p}k\_{p2}}{(k\_{p}k\_{q2} + 1)\omega\_{\mathcal{E}}} \\
0 & 0 \\
0 & 1 - \frac{k\_{p}k\_{p2}}{k\_{p}k\_{q2} + 1}
\end{bmatrix} \begin{bmatrix}
\Delta P\_{\rm m} \\
\Delta Q\_{\rm m}
\end{bmatrix} \tag{26}
$$

$$
\begin{bmatrix}
\Delta P\_{\varepsilon} \\
\Delta Q\_{\varepsilon}
\end{bmatrix} = \begin{bmatrix}
0 & k\_{p1} - \frac{k\_{p}k\_{p2}k\_{q1}}{k\_{p}k\_{q2} + 1} & k\_{i} - \frac{k\_{p}k\_{p2}k\_{q2}}{k\_{p}k\_{q2} + 1} \\
0 & \frac{k\_{q1}}{k\_{p}k\_{q2} + 1} & \frac{k\_{p}k\_{q2}}{k\_{p}k\_{q2} + 1}
\end{bmatrix} \begin{bmatrix}
\Delta \omega\_{\text{spc}} \\
\Delta \delta \\
\Delta Q\_{\varepsilon}
\end{bmatrix} + \begin{bmatrix}
0 & \frac{k\_{p}k\_{p2}}{k\_{p}k\_{q2} + 1} \\
0 & \frac{k\_{p}k\_{q2}}{k\_{p}k\_{q2} + 1}
\end{bmatrix} \begin{bmatrix}
\Delta P\_{m} \\
\Delta Q\_{m}
\end{bmatrix} \tag{27}
$$

where *kp*<sup>1</sup> <sup>=</sup> *<sup>E</sup>*0*<sup>V</sup>* sin(φ) *<sup>Z</sup>* , *kp*<sup>2</sup> <sup>=</sup> *<sup>V</sup>* cos(φ) *<sup>Z</sup>* , *kq*<sup>1</sup> <sup>=</sup> *<sup>E</sup>*0*<sup>V</sup>* cos(φ) *<sup>Z</sup>* , *kq*<sup>2</sup> <sup>=</sup> *<sup>V</sup>* sin(φ) *<sup>Z</sup>* , and δ is the grid load angle, as previously defined.

Due to the fact that the three control loops have very different bandwidths, their dynamics are nearly decoupled. Thus, these control loops can be designed separately. The stability of the current control loop can be ensured by choosing a proper value of ρ. Since the current control loop is stable, the voltage control loop is also stable, as the virtual admittance is in a form of a low-pass filter. The same analogy is applied to the power control loop.

Even though the dc-bus voltage level of SPC-based FACTS is naturally regulated thanks to the inherent power balance-based principle of the SPC controller, the dc-bus voltage level might experience dramatic changes due to unexpected events, such as line trips. To prevent the dc-bus voltage of SPC-based FACTS from surpassing safe operational limits, the control loop shown in Figure 3 is added to the SPC schema already shown in Figure 1. This protection loop has two PI controllers devoted to directly change the phase-angle of the virtual emf of the SPC, and thereby its output power, to keep the dc-bus voltage level within given limits. In this way, the protection range for the dc-bus voltage can be adjusted by just setting the *v*limmin and *v*limmax parameters. In addition, a saturation block is added at the output of each PI controller to ensure the protection loop only acts in case the dc-bus voltage level is out of the safe operational range, and to limit the maximum power reference in case of activation. This control loop has a very fast response, since it directly changes the phase-angle of the virtual emf, being its dynamics set by the parameter *kphase*.

**Figure 3.** Proportional integral (PI) strategy for dc voltage protection.

#### **4. Simulation Results**

The setup structure for the simulation results is presented in Figure 4. It is composed by a 100 kVA power converter, a harmonic load and a voltage sag generator. The devices will be connected and disconnected from the PCC during the different simulation tests. In a first simulation case, voltage support results under balanced and unbalanced voltage dips will be presented, where the harmonic load is not connected to the PCC, thus not generating any harmonic disturbances in the grid voltage. In a second simulation case, the voltage sag generator will be disconnected from the system, and the harmonic load will be connected. This load will consume harmonic current which will distort the grid voltage.

**Figure 4.** Simulation results setup. PCC: point of common coupling.

The parameters of the 100 kVA power converter and the grid connection are presented in Table 1, which specifies the inductance parameters of the grid and the voltage sag generator.


**Table 1.** Of the SPC-based FACTS power converter, the voltage sag generator and the grid.

In the upcoming subsections, the balanced and unbalanced low voltage ride through (LVRT) simulation results are presented, as well as the harmonic compensation results during harmonic distortions at the grid voltage.

#### *4.1. Balanced LVRT*

To simulate the performance of an actual voltage sag generator, which is composed by inductors and contactors changing their connection, the voltage sag has two voltage steps during the connection and disconnection of contactors. Figure 5 presents the voltage dip generated at the PCC of the SPC-based FACTS connected to the grid. On the left side, Figure 5a presents the voltage dip at the PCC without the interaction of the SPC-based FACTS. It is possible to see how the voltage drops to zero at the PCC when the SPC-based FACTS does not support the grid voltage. On the right side, Figure 5b presents the voltage dip at the PCC when the SPC-based FACTS interacts with the electrical grid by injecting reactive currents during the voltage disturbance. In this case, once the voltage dip is detected by the control system, the power converter starts injecting reactive currents thanks to the effect of the virtual admittance controller. This allows the power converter to support the grid voltage during voltage sags. The third plot in Figure 5b shows the injected current in the synchronous reference frame, evidencing the injection of reactive current *iq* during the voltage sag. Once the grid fault is released, the power converter stops injecting reactive current to the grid, and returns to the steady state operation set-point.

**Figure 5.** Balanced low-voltage ride-through (LVRT) test. Voltage sag to 0% of the voltage (**a**) LVRT without SPC-based FACTS compensation. (**b**) LVRT with the compensating current injected by the SPC-based FACTS.

#### *4.2. Unbalanced LVRT*

The unbalanced voltage sag is one of the most common voltage disturbances affecting the grid voltage, as it appears when one or two phases of the grid are faulted. This perturbation generates negative-sequence voltages along the grid, which can be observed as unbalanced voltages at the PCC. Figure 6 presents an unbalanced voltage dip at the PCC. On the left, Figure 6a presents the PCC voltage when the SPC-based FACTS does not provide any support to the grid voltage. In this case, the negative-sequence component of the gird voltage reached 70 V. Figure 6b displays the PCC voltage when the SPC-based FACTS supports the grid voltage in front of unbalances. In this case, the SPC-based FACTS injects negative-sequence currents to keep the grid voltage balanced. Comparing Figure 6a and Figure 6b, it is possible to appreciate that there is a significant reduction of the negative-sequence component of the grid voltage, which is reflected in reducing the imbalance degree among phases at the PCC.

**Figure 6.** Unbalanced LVRT test. (**a**) LVRT without SPC-based FACTS. (**b**) LVRT with the compensating current injected by the SPC-based FACTS.

#### *4.3. Harmonic Compensation*

Harmonics can be generated by a large amount of systems, commonly the ones using power converters to process power. Systems such as diode rectifiers, charging systems or even computers produce harmonics that flow through the grid and distort the grid voltage. In addition to hazardous grid resonances, such distorted voltages can damage to the equipment connected to the grid. By enabling several parallel virtual admittances in a SPC-based FACTS, it is possible to control harmonics flow and to minimize their impact on the grid. Figure 7 presents the PCC voltage resulting from the connection of a harmonic load to the grid, and the effect of the SPC-based FACTS in conditioning such a voltage. Figure 7a displays the PCC voltage waveform resulted from the connection of a harmonic load. The amplitude for the 5th and the 7th voltage harmonic arises to 14 V and 16 V, respectively. Once the harmonic admittances of the SPC-based FACTS are enabled, the power converter starts injecting compensating currents. Figure 7b, shows the compensating currents injected by the SPC-based FACTS and how they dramatically reduce the grid voltage distortion. A comparison between Figure 7a and Figure 7b shows the significant reduction of 5th and 7th harmonic components of the grid voltage.

The simulation results shown in this section have demonstrated how SPC-based FACTS can improve the power quality of the electrical grid in front of voltage transients and distortions. In the following section, some experimental results are presented to validate such simulation results. In this manner, the same tests shown in simulation are now conducted in the lab by using real equipment.

**Figure 7.** Harmonic control simulation result. (**a**) Harmonic load without SPC-based FACTS compensation. (**b**) Harmonic load with SPC-based FACTS injecting harmonic current to the PCC.

#### **5. Experimental Results**

The experimental setup used for obtaining experimental results consists of two 100 kVA power converters connected to the PCC, a dc-voltage generator, a voltage sag generator and a harmonic load to absorb harmonic currents from the grid, as shown in Figure 8.

**Figure 8.** Experimental setup.

By following the sequence as in simulations, the first test to be conducted will deal with the grid support provided by the SPC-based FACTS when a balanced voltage sags happens in the grid, i.e., when the three phases of the grid are affected equally by the voltage sag. In a second test, the response of the SPC-based FACTS in front of unbalanced voltage sags will be shown. After that, the impact of the SPC-based FACTS when conditioning a distorted grid voltage due to harmonic currents will be evaluated experimentally. These test will show how the SPC-based FACTS perfectly withstand voltage transients and distortions, inject reactive currents and harmonics to improve the quality of the voltage waveform.

#### *5.1. Balance LVRT*

In this experiment, voltage sags are generated through a voltage sag generator, which consists of several inductances and tap switches to generate different voltage levels at the PCC. In the case of a balanced voltage sag, the three phases decease the voltage amplitude to a certain value during the sag time. In this experiment, the SPC-based FACTS will inject reactive current to restore the voltage level at the PCC. Figure 9 presents the scheme of the experimental setup used for this experiment.

**Figure 9.** Scheme of the SPC-based FACTS connected to the grid for the balance LVRT test.

As shown in simulations, the SPC-based FACTS presents an inherit capability to inject reactive current in the electrical grid during voltage sags thanks to the effect of the virtual admittance. Once the virtual admittance controller detects a significant difference between the measured gird voltage, *v*1(*t*), and the virtual emf, *e*(*t*), it generates an instantaneous reference current to counteract such a difference by injecting reactive current into the electrical grid. Figure 10a shows the beginning of the voltage sag. During this transient, the SPC-based FACTS detects the grid voltage reduction at the PCC and start increasing the reactive current injected into the grid. Later, once the voltage sag is released, the SPC-based FACTS stops providing reactive current and returns to its regular state. Figure 10b presents the end of the voltage sag, when the SPC-based FACTS returns to steady-state operation set-point.

**Figure 10.** Response of the SPC-based FACTS to a balanced sag. Voltage sag to 0% (**a**) Beginning of the voltage sag. (**b**) End of the voltage sag.

Analyzed the system on the synchronous reference frame, it can be appreciated how the SPC-based FACTS inject reactive current *iq* during the grid fault to contribute to restore the voltage at the PCC. In Figure 11, the *dq* current components *idq* are plotted. It can be appreciated in this figure how the current *iq* is triggered at *t* = 2.18 s, when the voltage sag is detected by the SPC-based FACTS controller. The system remains injecting reactive current to the grid until the voltage sag is cleared at *t* = 2.7 s. Once the voltage dip is cleared, the current *iq* goes to zero.

**Figure 11.** SPC-based FACTS dq currents during a balanced LVRT test.

#### *5.2. Unbalanced LVRT*

Single-phase and phase-to-phase faults generate unbalanced voltages, which gives rise to negative-sequences components in the grid voltage, which affects negatively to all the connected elements. The control algorithm of the SPC-based FACTS is able to detect the negative-sequence component of the grid voltage and provides a negative-sequence reference current aimed to restore the unbalanced grid voltage. This response in front of unbalanced voltage sags due to the action of the virtual admittance controller, which, after calculating the negative-sequence component of the grid voltage, sets such a voltage component as an input for a virtual admittance block, which generates a negative-sequence reference current addressed to reduce the negative-sequence component of the gird voltage at the PCC. Figure 12 shows the scheme of the setup used for conducting the unbalanced LVRT test. In this case, two SPC-based FACTS are connected to the PCC, which will experience the unbalanced voltage sag created through the sag generator. During the fault, the SPC-based FACTS will inject reactive currents to contribute to balance the grid voltage. Additionally, both SPC-based FACTS will share the amount of negative sequence current injected into the grid as a function of the parameters set for the virtual admittance in each SPC-based FACTS.

**Figure 12.** Electrical schematic for two SPC-based FACTS affected by an unbalanced voltage sag.

In this experiment, a voltage sag generator is used to generate the unbalanced grid voltage. In a first test, the SPC-based FACTS does not inject any reactive current into the grid when the unbalanced sag happens. Plots for this test are shown in Figure 13a, where unbalanced voltages can be seen at the PCC when the SPC-based FACTS do not provide any support. In Figure 13b, the two SPC-based FACTS are enabled to provide support to the electrical grid. In this test, once the sag is detected by the virtual admittance controller, the SPC-based FACTS starts injecting negative-sequence current into the grid in order contribute to balance the grid voltage at the PCC.

**Figure 13.** Response of the SPC-based FACTS to an unbalanced sag. (**a**) Unbalanced voltage sag without SPC-based FACTS (**b**) Two SPC-based FACTS inject reactive current to balance the gird voltage at the PCC.

The positive- and negative-sequence components of the voltage and current resulting from this experiment can be analyzed to assess the support provided to the electrical grid by the SPC-based FACTS. Figure 14a presents the voltage sag components when no reactive current is injected by the SPC-based FACTS. In this case, the positive-sequence component of the grid voltage decreases to 81% of its rated value, whereas the amplitude for the negative-sequence component grows until 20% of the rated grid voltage. As shown Figure 14b, once the SPC-based FACTS controllers are enabled to compensate unbalanced grid voltages, the positive-sequence component of the grid voltage at the PCC during the unbalanced sag decreases to the 92% of its rated value, while the negative-sequence component of the unbalanced voltage at the PCC just increases to the 5% of the rated grid voltage. Those effects can be seen in the difference between the sinusoidal waveforms from Figure 14. In this experiment, both SPC-based FACTS inject the same amount of reactive current since both of them set the same values for the virtual impedance used for processing the negative-sequence component of the PCC voltage.

#### *5.3. Harmonic Compensation*

The SPC-based FACTS can integrate multiple virtual admittances, each of them tuned to a given frequency, which can generate compensating currents addressed to the minimize distortion of the grid voltage at the PCC. To do that, the frequency components of the grid voltage should be measured, e.g., using band-pass filters tuned to the frequencies of interest, and provided as inputs to corresponding harmonic admittances in order to generate the compensating harmonic currents to be injected into the grid.

In this experiment, a non-linear load connected to the PCC, which will generate some harmonic components at the PCC voltage. The admittance controller of the SPC-based FACTS is enabled to detect such a voltage distortion at the PCC, and to inject compensating currents to attenuate the distortion of the grid voltage at the PCC. Figure 15 presents the setup used in this experiment, where a harmonic load is connected to the PCC in parallel to the SPC-based FATCS. Additionally, a 400 μH line inductance has been added to increase distortion at the PCC voltage.

**Figure 14.** Response of the SPC-based FACTS to an unbalanced voltage sag. (**a**) Positive- and negative-sequence components of the PCC voltage and current when the SPC-based FACTS is disabled. (**b**) Positive- and negative-sequence components of the PCC voltage and current when the SPC-based FACTS is enabled.

**Figure 15.** Electrical schematic for harmonic compensation control test.

In this experiment, a non-linear load is connected, giving rise to a notable amount of 5th and 7th harmonic in the current absorbed form the electrical grid. The SPC-based FACTS is able to detect the harmonic components at the PCC voltage, e.g., using multiple band-pass filters, and to inject proper currents reduce the voltage distortion at the PCC. Figure 16, from top to bottom, shows the grid voltage at the PCC, the current injected by the SPC-based FATCS and the current absorbed by the non-linear load. As appreciated in this figure, the current injected by the SPC-based FACTS compensates the one demanded by the load and the quality of the voltage at the PCC is improved. This is evidenced when the SPC-based FACTS is disabled at *t* = −0.73 s. From that time on, the harmonic load currents flow through the line impedance, instead through the SPC-based FACTS, which notably increases the grid voltage distortion.

A more detailed analysis of the grid voltage, paying special attention to the 5th and 7th harmonic components, allows assessing the effectiveness of the SPC-based FACTS in improving power quality. Figure 17a,b show the PCC voltage spectrum in case the SPC-based is disabled and enabled, respectively. As Figure 17a shows, when the harmonics control of the SPC-based FACTS is disabled, the grid voltage at the PCC presents remarkable levels for the 5th and 7th harmonic components, namely, 12 V and 7 V, respectively. However, once the harmonics compensation function is enabled in the SPC-based FATCS, the quality of the PCC voltage improves significantly. In such a case, Figure 17b shows how

the amplitude levels for the 5th and 7th harmonic components has been reduced to 6 V and 2.5 V, respectively, which can be also appreciated on the sinusoidal waveform shape.

**Figure 16.** Grid voltage distortion reduction by the SPC-based FATCS.

**Figure 17.** Effect of the SPC-based FACTS in grid voltage reduction (**a**) Harmonics compensation disabled. (**b**) Harmonics compensation enabled.

#### **6. Conclusions**

This paper has presented the application of the synchronous power controller (SPC) to FACTS with the aim of improving power quality in electrical grids. This paper has conducted an overview on FACTS devices and has highlighted that the virtual synchronous power has gained notable popularity among engineers and researchers in the last years to interface power converters to ac synchronous electrical grid. The control scheme and the main equations governing the SPC, which are essential to implement simulation models and analyses, have been presented in the paper. Based on such models, the paper has presented some simulations results addressed to evaluate the performance of a SPC-based FACTS when improving power quality in the electrical grid. In such an evaluation, the positive impact of the SPC-based FACTS to improve the grid voltage quality during balanced and unbalanced voltage sags, as well as in case of current harmonics flowing along the grid, has been illustrated by representative simulations. Moreover, such simulation results have been validated through experiments in the lab, obtaining satisfactory results. As a conclusion, this paper has presented

the SPC formulation and has evidenced the interest of the SPC-based FACTS for improving power quality in electrical grids.

#### **7. Patents**

The Synchronous Power Controller technology is protected by the following patents:


**Author Contributions:** G.N.B. conducted an overview of FACTS systems. N.-B.L. developed the SPC's formulation and simulation models. A.T. conducted simulations and lab experiments. P.R. provided conceptual and technical support as the inventor of the SPC. All the co-authors contributed to writing and reviewing the paper. Conceptualization, P.R., A.T. and N.-B.L.; methodology, A.T. and N.-B.L.; software, N.-B.L. and G.N.B.; validation, A.T. and P.R.; formal analysis, A.T. and N.-B.L.; investigation, N.-B.L. and P.R.; resources, A.T.; data curation, G.N.B.; writing—original draft preparation, A.T. and N.-B.L.; writing—review and editing, G.N.B. and P.R.; visualization, G.N.B.; supervision, P.R.; project administration, P.R.; funding acquisition, P.R.

**Funding:** This work was supported by the European Commission under the project FLEXITRANSTORE - H2020-LCE-2016-2017-SGS-774407 and by the Spanish Ministry of Science Innovation and Universities under project SMARTNODES ENE2017-88889-C2-1-R. Any opinions, findings and conclusions or recommendations written in this work are those of the authors and do not necessarily reflect those of the host institutions and funders.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
