A Proposed Supercapacitor Integrated with an Active Power Filter for Improving the Performance of a Wind Generation System under Nonlinear Unbalanced Loading and Faults

Tis study proposes the integration of a supercapacitor (SC) with the DC link of a three-phase four-wire active power flter (APF) by using an interfaced three-level bidirectional buck-boost converter controlled by the fuzzy control approach. APF is a fexible alternating current transmission system (FACTS) device that enhances power quality in the electrical network by reducing the load current harmonics and compensating the reactive power. Regulating the DC voltage of the APF’s DC link and absorbing fuctuations in compensated reactive power during disturbances are the major objectives of the integration of an SC circuit to APF. Te studied model is a wind farm of Gabal El-Zeit with a total capacity of 580MW, connected to unbalanced nonlinear loads. Te Gabal El-Zeit wind farm is divided into three projects with a capacity of 240MW, 220MW, and 120MW. Te model is simulated by the MATLAB/SIMULINK program, and the efectiveness of the proposed methodology is proved by applying diferent types of faults such as single-line-to-ground, double-line-to-ground, and three-line-to-ground faults. In addition, an additional SC circuit with a two-level converter is connected to the generators coupled to the wind turbines to enhance the performance of the wind farm during disturbances. Te results show that SC-integrated APF can reduce the harmonic distortion and compensate the reactive power for high or low inductive loads. Also, it can regulate the DC voltage and absorb the fuctuations in the reactive power during faults. Finally, the performance and the stability of the overall electric system are improved.


Introduction
Te majority of the network's loads are non-linear and unbalanced loads that draw not only active current but also harmonic and reactive current from the AC network, harming the electrical system and other connected devices.Consequently, harmonic suppression and reactive power compensation have gained attention and have been thoroughly researched.Currently, active power flters (APFs) become one of the most efcient tools for controlling harmonics and with a special control, and they can compensate for reactive power consumption.Tere are many topologies of APF which are shunt APF, series APF, and hybrid APF, as proposed in [1][2][3][4][5][6].Te shunt APF, which essentially consists of a voltage source inverter (VSI) with a DC link connected to a large capacitor, is said to be a tried-and-true method for bringing the current harmonics down to the advised standard limitations [7].Te study in [8] discusses a novel control of a three-phase half-bridge interleaved buck shunt APF.For a single-phase shunt APF, a fractional-order sliding mode technique method that relies on a double-hidden layer recurrent neural network is suggested in [9].Te research in [10] suggests a new artifcial neural network control for APF using the genetic algorithm and employing an optimization technique to adapt the pa-rameters of the PI control for APF's DC-voltage regulation.Recent studies have focused on the modifcation of an APF technique; as in [11], the authors designed a universal APF with an adaptive fltering method based on the least mean mixed norm to efciently extract reactive currents and harmonics.Te single-phase shunt APF is proposed in [12] with an enhanced modulated carrier control with on-time double that removes harmonic and reactive currents pulled by nonlinear low frequency.In [13], it is suggested to produce the reference current and control APF using a new deadbeatbased DPC approach.Te concept for a shunt APF is suggested in [14] using a single source of power fed to a multilevel inverter with fewer transformers needed.To lower the overall size and cost, a new four-switch two-leg VSI scheme for a three-phase shunt APF is developed in [15].Te current reference control approach for the shunt APF under unbalanced situations is suggested in [16] that uses a combination of the symmetrical component approach and the Kalman flter to determine the fundamental sequence component of the source voltage.Te authors in [17] suggest a fault-tolerant control, which combines multicellular topology and two-level topology to boost the dependability of multicellular converters.Te study in [18] suggests a predictive power control to reduce fuctuations in DC voltage of the APF using two metaheuristic methods, namely, grey wolf optimizer and ant lion optimizer algorithms.Te design of the APF is presented as an optimization problem with many goals, such as enhancing the response time, lowering DC-link voltage overshoot and undershoot, maintaining it at the reference value, and minimizing source current harmonics.Te authors in [19] modify a 3-level H-bridge APF with a direct connection to the distribution network.Other recent works of the literature look into ways to enhance APFs by creating new topologies or controller design as in [20]; this study suggests a double-resistive APF which consists of a terminal-resistive APF and an attenuation-resistive APF for each particular harmonic.To prevent harmonic propagation at all harmonic frequencies, the terminal-resistive APF, which acts as the feeder's characteristic impedance, is put at the end bus.To attenuate the appropriate harmonic voltages, the attenuation-resistive APF, whose control gain can be adjusted in accordance with the harmonic voltage distortion limit specifcations, is mounted at a precise location for each unique harmonic.Te study in [21] investigates how to reduce LCL flter resonance produced by an APF.Novel active damping with a grid-side current component feedback is proposed to address the faw that typical active damping based on the flter capacitor current or capacitor voltage feedback requires the addition of extra sensors.In [22], a novel high-order passive flter for single-phase half-bridge active power flters is proposed.Parallel resonance is created by paralleling a tiny capacitor with a gird-side inductor, and series resonance is created by adding a small inductor to the capacitor branch loop.In [23], a control technique was proposed to allow the LC-coupling hybrid APF to function satisfactorily with a small-rating active inverter part for a range of loads.In order to balance active power and compensate for reactive power, the thyristor-controlled LC-coupling component is designed with distinct fring angles for each phase.In [24], the triangular orthogonal principle algorithm serves as the foundation for the new harmonic detection approach presented.Te suggested approach has advantages over traditional harmonic current detection methods, such as a simple structure, low calculation requirements, and quick execution times.Te shunt APF system is developed in [25] with a faulttolerant control technique based on improved switch redundancy, and fault tolerance is attained by circuit reconstruction.
As compared to the literature, this research examines how various fault types afect the performance of the APF and suggests a novel method for enhancing performance during fault occurrence by combining the APF with an energy storage system (ESS).Tis study presents a proposed methodology that suggests using a three-phase four-wire APF integrated with the ESS which is composed of a supercapacitor (SC) and a three-level buck-boost converter controlled by the fuzzy logic control (FLC).Tis combination technique is named in this study as an SC-integrated APF.Te main purposes of the SC circuit are the fuctuation absorption of the compensated reactive power and the regulation of the DC voltage of the APF's capacitor notwithstanding disruptions.Te system studied in this study is the wind farm of Gabal El-Zeit with a total capacity of 580 MW.Te Gabal El-Zeit wind farm is divided into three projects with a capacity of 240 MW, 220 MW, and 120 MW.Tere are unbalanced nonlinear loads connected at the point of common coupling (PCC).Te wind turbines are driven by the doubly fed induction generator (DFIG) that is composed of a direct grid-connected stator and a rotor connected to the network through a back-to-back converter that is composed of a grid-side converter (GSC) and a rotor-side converter (RSC) with a DC-link capacitor.First, the SC-integrated APF with a low inductive load is studied, and then, a high inductive load is applied.Ten, the efectiveness of the system with SC-integrated APF is studied for single-line-to-ground, double-line-to-ground, and three-line-to-ground faults.In addition, this study uses SC with a two-level buck-boost converter at the DC link of the DFIG's back-to-back converter to regulate the DC voltage and improve the performance of the wind farm.Tis study is organized as follows: Te introduction is presented in Section 1. Te APF confguration and control are presented in Section 2. Te proposed methodology and the studied model confguration are illustrated in Section 3 and Section 4, respectively.Section 5 presents the simulated results and discussion.Lastly, Section 6 displays the fndings.

Shunt Active Power Filters
Shunt APFs inject an equal but opposing harmonic compensatory current to reduce current harmonics.At the same time, the APF can take on the function of the STATCOM, 2 Journal of Electrical and Computer Engineering which is compensating the reactive power, and this is done through a special control instead of using an additional fexible alternating current transmission system (FACTS) devices.Te cost of new elements may be signifcantly lowered in this method.One of the various objectives of the APF controllers is the decrease in neutral current for unbalanced nonlinear loads.Shunt APFs are normally implemented with a VSI that works as a current-controlled voltage source.Such technologies are often implemented using two-level PWM-VSIs that are coupled through a transformer to the AC system.Figure 1 displays the APF's confguration components which are the VSI, DC-link capacitor, and fltering inductor used to decrease the harmonic currents that circulate as a result of inverter switching and control units.
Te control confguration scheme of the APF is illustrated in Figure 2. Te main parts of the control are calculation of the compensated currents, current reference generator, DC voltage control, and current control [26].
To create reference currents, the principle of instantaneous reactive power is used.Tis theory uses equations (1) and (2) to convert the instantaneous load current (i a , i b , and i c ) and phase voltage (v a , v b , and v c ) to αβ coordinate components of voltages (v α , v β ) and currents (i α , i β ) [26]: Using equations ( 3) and ( 4), current and voltage are used in the αβ-coordinate to compute time-dependent active and reactive power (p, q): A new instantaneous space vector is provided by vector equation ( 5) in order to calculate the immediate reactive power: where q is a vector perpendicular to the α, β coordinates plane; the following equation provides the formula for the currents in the plane in terms of the instantaneous power: where i αp , i αq , i βp , and i βq are the diferent components of the currents in the α, β plane relating to active and reactive power.Each of the instantaneous power p and q is expressed as a summation of the DC component (p, q) and the AC component ( p,  q) as expressed in the following equations: where p and q are concerned with the fundamental active and reactive component of current, respectively,  p and  q are concerned with the harmonic currents produced by the active and reactive instantaneous power's AC component.Equations ( 9) and ( 10) are used to determine the compensating reference currents in the αβ-reference frame Te hysteresis current control receives these reference currents in order to produce switching pulses.To reduce voltage fuctuations without increasing the DC capacitor's capacitance, a control unit for the DC voltage of the capacitor is necessary.Te DC-voltage control unit is responsible for maintaining the DC voltage constant which is Journal of Electrical and Computer Engineering necessary for tracking compensation requirements.Tis control generates ∆p which indicates the active power that is transferred between the compensator and the source, and this value is necessary for the DC voltage of the capacitor to be maintained at or close to the predetermined normal value.As a result, to make the APF comfortably run, the DC voltage at the DC capacitor needs to be strictly managed.Figure 3 shows another topology that uses a three-phase four-wire APF with a DC capacitor split into two-identical capacitors (C1 and C2) [27].Te voltages on these capacitors are equal and represented by v 1 and v 2 .Tis arrangement aids in minimizing the neutral current.

Proposed Methodology
Te proposed methodology suggests the integration of SC with the DC link of APFs by using an interfaced three-level bidirectional buck-boost converter.Te main objectives of the SC circuit are to keep the DC voltage of two-split capacitors constant under disturbances and absorb fuctuations in the compensated reactive power.Te control technique used with the proposed methodology in this study is the fuzzy control approach.Te topology confguration of the SC-integrated APF system employed in this work is shown in Figure 4.

4
Journal of Electrical and Computer Engineering It appears that there are four charging states: In state 1, C2 is charging when Q2 is on and Q3 is of.In state 2, C1 is charging when Q2 is of and Q3 is on.In state 3, C1 and C2 are charging when Q2 and Q3 are both of.In state 4, C1 and C2 are not afected, that is, when Q2 and Q3 are both on.It is possible to write the instantaneous output voltage between a and b (V ab ) as follows: where Sf 2 and Sf 3 are the switching functions of switches Q2 and Q3 and V 1 and V 2 are the voltages on C1 and C2.It is clear from the diagram that V ab is suited for displaying the capacitor that is now charging, which illustrates how this converter works.In a carrier period at a steady state, i L (current through the inductor) increases and declines equally.Terefore, according to the volt-second balancing principle, input and output voltages are connected to duty cycles D q2 and D q3 as follows: where V sc is the SC voltage, D q2 and D q3 are the duty cycles of Q2 and Q3, T stands for the carrier period, and L is the inductance value of the inductor.Since D q2 and D q3 are equivalent to D and V 1 and V 2 are equivalent to V, equation ( 12) can be written as follows: Te following equation explains what the step-up ratio (K) is Te zone of K identifes three scenarios: when K � 1, Q2 and Q3 are turned of, the SC charges C1 and C2 auto- 6(a) illustrates the scenario when 1 < K < 2, V 1 , V 2 < V sc , and i L rises, charging the output like a buck circuit, this occurs in paths (1) and (3).In path (2), where V 1 + V 2 > V sc , i L decreases, and it operates as a buck circuit to each capacitor.Figure 6(b) illustrates the scenario when K > 2, V 1 , V 2 > V sc , and i L drops, charging the output like a boost circuit, this occurs in paths (1) and (3).In path (2), where V ab � 0, similar to the boost circuit charging the inductance procedure, i L rises.It equals a boost circuit for each capacitor as a consequence.

Control Methodology.
Te following main goals that the SC-integrated APF serves are the basis for developing the control mechanism: (1) To maintain the DC voltage constant during disturbance (2) To absorb reactive power fuctuations during faults and disturbance In this study, the fuzzy control is applied for balancing the DC voltage instead of using conventional control methods.Te fuzzy control can deal with the complexity and uncertainty of the system.Figure 7 illustrates the closed-loop control of the SC circuit.
Te voltage at the DC link of the APF is measured and compared with its reference value to calculate the voltage error.Te error and its diferential value are the inputs to the fuzzy control which determines the required value of the change in the duty cycle.Te pulse generator generates the signal required to control the IGBT switches of the threelevel converter connected to the SC.Te membership functions of the fuzzy inputs and outputs are shown in Figure 8, where the fuzzy sets of the inputs are positive (P), zero (Z), and negative (N).Te fuzzy sets of the change in the duty cycle are positive big (PB), positive (P), zero (Z), negative (N), and negative big (NB).Te fuzzy rules are illustrated in Table 1 that shows the ninth linguistic fuzzy rules which have been used in the fuzzy control structure using "IF-Ten" format.

Additional SC Circuit Connection.
In order to improve the system as a whole, this study suggests adding an additional ESS to the back-to-back converter of the DFIG driven by wind turbines.Te applied ESS is composed of SC with a two-level buck-boost converter, as shown in Figure 9.
By charging and discharging SC through the buck-boost converter, the DC-link voltage remains constant during disturbances.As a result, the performance and stability of the wind farm are improved.Te control of the two-level buck-boost converter using the fuzzy control is shown in Figure 10.

Studied Model Configuration
Te studied model confguration in this study is a large-scale wind farm of Gabal El-Zeit, as illustrated in Figure 11

Application of Nonlinear Unbalanced
Loads.First, the nonlinear unbalanced loads are applied to the electric network to deduce the efectiveness of the system to suppress harmonics and compensate for the reactive power.Power systems must consider total harmonic distortion (THD), which must be kept as low as possible.Higher power factor, lower peak currents, and more efciency result from decreased THD in power systems.Te nonlinear load model consists of a bridge rectifer connected to a resistive and inductive load.Two types of loads are studied: low inductive loads and high inductive loads.

Low Inductive Load.
First, the SC-integrated APF is applied with a low inductive load connected to PCC. Figure 12(a) illustrates the voltage waveform at B575 that has a THD of 2.84% without the SC-integrated APF.Te load current waveform and its FFT analysis are illustrated in Figures 12(b) and 12(c), respectively, which illustrate that the current is highly nonsinusoidal and that the load current's THD equals 44.37%.Te reactive power absorbed by the load equals 2.9 kVAR, as shown in Figure 12(d).Te impact of adopting the SC-integrated APF is illustrated in Figure 13, which appeared in the load current and absorbed reactive power.Te voltage waveform at B575 is shown in Figure 13(a) that illustrates that the THD equals 2.84%.Figures 13(b) and 13(c) illustrate the load current waveform and its FFT analysis, and in this case, the current waveform is improved and becomes more sinusoidal and the THD decreased to 7.8%.With the SC-integrated APF, the load does not absorb reactive power but instead delivers about 4 kVAR, as shown in Figure 13(d).

High Inductive Load.
In this case, a high inductive load coupled at the PCC is used in conjunction with an SC-integrated APF application.Figure 14(a) shows the voltage waveform at B575 which has a THD of 4.25% without the SC-integrated APF.Figures 14(b) and 14(c) depict the load current waveform and its FFT analysis, respectively, indicating that the current is highly nonsinusoidal and much distorted and that the load current's THD is 38.68%.According to Figure 14(d), the load's reactive power absorption is 370 kVAR.Figure 15 presents the SC-integrated APF impact, which is manifested in the load voltage, current, and absorbed reactive power.Figure 15(a) displays the voltage waveform at B575 and depicts the THD, which equals 3.92%.Te load current waveform and its associated FFT analysis are shown in Figures 15(b) and 15(c), and in this case, the current waveform is improved and becomes less distorted and the THD decreased to 16.67%.Te SCintegrated APF enables the load to deliver approximately 145 kVAR rather than absorbing reactive power, as shown in Figure 15(d).

Application of Diferent Types of Faults.
To deduce the efectiveness of the integration of the SC with the APF, diferent types of faults such as single-line-to-ground, double-line-to-ground fault, and three-line-to-ground faults are applied to the network.Te results with using the SCintegrated APF are compared with that using a simple APF.

Single-Line-to-Ground Fault.
A single-line-to-ground fault is applied at B575 at 1 sec time with a fault duration of 250 msec.Te AC voltage at B575 is shown in Figure 16(a) that illustrates that a fault occurred in phase A and that the voltage at phases B and C dropped to 50% of its normal value.Te DC voltage of APF capacitor performance is shown in Figure 16(b).Without the SC circuit, the DC voltage dropped to 1180 V during faults and returned to its normal value (1200 V) at 1.6 sec.However, the DC voltage almost remained unchanged during the fault with using the SC circuit.Figure 16(c) shows that the load active power performance is the same whether with employing SC or without.However, utilizing SC had an impact on the load's reactive power since it absorbed 500 VAR during the fault, as shown in Figure 16(d).On the other side, it absorbed 700 VAR without SC, but with or without SC, overshoot equals 1380 VAR. Figure 16(e) illustrates the DC-link voltage of the back-to-back converter capacitor performance.Without SC, the overshoot equals to 1.4 kV, and then, the voltage oscillated between 1.2 kV and 1.4 kV; however, overshoot equals 1.18 kV with SC, and the voltage returned to its steady-state value (1.15 kV).Te total active power of the wind farm performance is illustrated in Figure 16(f ).Te total active power dropped to 200 MW before returning to the steady condition at 1.45 sec with using SC.However, it dropped to 160 MW and reached the steady state without using SC at 1.9 seconds.Utilizing SC has the efect of bringing the total reactive power to the steady state faster than it would without SC, as it reached its steadystate value at 1.45 sec with using SC and at 1.9 sec without using SC, as illustrated in Figure 16(g).

Double-Line-to-Ground Fault.
At B575, a doubleline-to-ground fault is applied at 1 sec time with 250 msec fault duration.Figure 17(a) depicts the AC voltage at B575, which illustrates that a fault occurred in phase A and B and that the voltage at phase C dropped to less than 50% of its normal value.Figure 17(b) depicts the DC voltage performance of the APF capacitor.Without the SC circuit, the DC voltage decreased to 1163 V during the fault and then recovered to its original level (1200 V) at 1.67 sec.However, when a fault occurred with using the SC circuit, the DC voltage has very low oscillation and nearly stayed unchanged.Figure 17(c) shows that there is no noticeable efect of using SC on the load active power performance.However, as can be seen in Figure 17(d), using SC had an infuence on the load's reactive power since it absorbed only 500 VAR with an overshoot of 8 kVAR during the fault.On the other side, it absorbed 2000 VAR without SC with an overshoot of 8.7 kVAR.Te DC-link voltage of the back-to-back converter capacitor performance is shown in Figure 17(e).Without SC, overshoot reached 1.95 kV and then reduced to 1.088 kV and returned to its normal value (1.15 kV) at 1.25 sec.However, with SC, the DC-link voltage has very low oscillation between 1.16 and 1.13 kV during fault duration.Figure 17(f ) shows that the total active power decreased to 81 MW until stabilizing with SC at 1.45 seconds.However, without SC, it decreased to 52 MW, and after 1.9 seconds, it achieved a stable state.Te instant at which the total reactive power has reached its steady-state value is 1.45 sec with SC and 1.9 sec without SC, as illustrated in Figure 17(g).Figure 18(a) indicates the AC voltage at B575 that illustrates how much the voltage sag occurred in the three phases.Figure 18(b) illustrates the performance of the DC voltage of the APF capacitor.During the fault, the DC voltage reduced to 1185 V without using SC and then returned to 1200 V (which is the normal value) at 3.12 sec.However, because of the SC circuit efect, the DC voltage essentially stayed unaltered.As in the previous cases (single and double-line faults), the active power has no efect with using SC, as shown in Figure 18(c); however, the impact of SC appears on reactive power performance, as illustrated in Figure 18(d).
With SC, the overshoot of reactive power is −3350 VAR and then has a zero VAR value during the fault; however, the overshoot of reactive power is −3800 VAR without SC, and then, it has oscillated between 230 VAR and -164 VAR.Te DC-link voltage of the back-to-back converter capacitor performance is illustrated in Figure 18(e).Without SC, overshoot equals 1771 V during the fault and then returned to its normal value (1150 V) at 1.57 sec; however, it has very little oscillation between 1200 V and 1029 V with SC and then recovered its normal value at 1.3 sec.Te total active power of the wind farm dropped to 36 MW during the fault and returned to the steady condition at 2.5 sec with using the SC circuit, as shown in Figure 18(f ).Without SC, the active power dropped to 2 MW and returned to the steady condition at 3.2 sec.Figure 18(g) shows that the total reactive power has reached its steady value at 2 sec with SC and 3 sec without SC.

. Conclusions
Te integration of SC with the three-phase four-wire APF is suggested in this study utilizing an interfaced three-level bidirectional buck-boost converter that is fuzzy controlassisted.Te basic objectives of the SC-integrated APF are to regulate the DC voltage of the APF's DC link and absorb fuctuations in the compensated reactive power during disturbances.A wind farm of Gabal El-Zeit with a capacity of 580 MW that is connected to unbalanced nonlinear loads serves as the study model.First, a low inductive load connected to PCC is applied.Without the SC-integrated APF, the load current's THD equals 44.37%, the load voltage's THD equals 2.84%, and the reactive power absorbed by the load equals 2.9 kVAR.With the SCintegrated APF, the current's THD equals 7.8%, the load voltage's THD equals 2.84%, and the load does not absorb reactive power but instead delivers about 4 kVAR.Ten, a high inductive load is applied at PCC.Without the SCintegrated APF, the load current's THD is 38.68%, the load voltage's THD equals 4.25%, and the load's reactive power absorption is 370 kVAR.With the SC-integrated APF, the load current's THD is 16.67%, the load voltage's THD equals 3.92%, and the load does not absorb reactive power but instead delivers about 4 kVAR.For deducing the  efectively of SC integration, a single-line-to-ground fault is applied at PCC at 1 sec for 250 msec.Without the SC circuit, the DC voltage dropped to 1180 V during the fault and returned to its normal value (1200 V) at 1.6 sec and the load absorbed 700 VAR during the fault.With the SC circuit, the DC voltage of the APF almost remained unchanged and the load absorbed 500 VAR during the fault.Te load active power performance is the same whether with employing SC or without.Without SC, the DC-link voltage of the back-to-back converter capacitor has overshot to 1.4 kV and then oscillated between 1.2 kV and 1.4 kV; however, overshoot has got to 1.18 kV with SC and returned to its steady-state value (1.15 kV).Te total active power of the wind farm dropped to 200 MW before returning to the steady condition at 1.45 sec with SC.However, it dropped to 160 MW and reached the steady state without SC at 1.9 seconds.Ten, a double-line-toground fault is applied at PCC at 1 sec for 250 msec.Without an SC circuit, the DC voltage of the APF decreased to 1163 V and then recovered to its original level at 1.67 sec and the load absorbed 2000 VAR with 8.7 kVAR overshoot.With the SC circuit, the DC voltage has very low oscillation and nearly stayed unchanged and the load absorbed only 500 VAR with 8 kVAR overshoot during the fault.Te total active power of the wind farm decreased to 81 MW until stabilizing with SC at 1.45 seconds.However, without SC, it decreased to 52 MW, and after 1.9 seconds, it achieved a stable state.Te time when the total reactive power has reached its steady value is at 1.45 sec with SC and 1.9 sec without SC.A three-line-to-ground fault is applied at B25 at 1 sec for 250 msec.Without SC, the DC voltage reduced to 1185 V and then returned to 1200 V at 3.12 sec and the overshoot of reactive power is −3800 VAR, and it has oscillated between 230 VAR and −164 VAR.With SC, the DC voltage essentially stayed unaltered and the overshoot of reactive power is −3350 VAR and then has a zero VAR value during the fault.Te total active power of the wind farm dropped to 36 MW during the fault and returned to the steady condition at 2.5 sec with using the SC circuit.Without SC, the active power dropped to 2 MW and returned to the steady condition at 3.2 sec.Te total reactive power has reached its steady value at 2 sec with SC and 3 sec without SC.Te results indicate a satisfactory performance of the proposed methodology to increase the system's stability.

Figure 5 :
Figure 5: Te confguration of the three-level buck-boost converter.

Figure 7 :Figure 8 :
Figure 7: Closed loop control of the SC circuit.

Figure 13 :
Figure 13: Performance during light nonlinear loading with SC-integrated APFs.(a) Load voltage waveform, (b) load current waveform, (c) FFT analysis of load current, and (d) reactive power of the load.

Figure 14 :
Figure 14: Performance during heavy nonlinear loading without SC-integrated APFs.(a) Load voltage waveform, (b) load current waveform, (c) FFT analysis of load current, and (d) reactive power of the load.

Figure 15 :
Figure 15: Performance during heavy nonlinear loading with SC-integrated APFs (a) Load voltage waveform, (b) load current waveform, (c) FFT analysis of load current, and (d) reactive power of the load.

Figure 16 :
Figure 16: Performance during a single-line-to-ground fault.(a) Te AC voltage at B575, (b) the DC voltage of the APF capacitor, (c) the load active power, (d) the load reactive power, (e) the DC-link voltage of the back-to-back converter, (f ) the total active power of the wind farm, and (g) the total reactive power of the wind farm.

Figure 17 :
Figure 17: Performance during a double-line-to-ground fault.(a) Te AC voltage at B575, (b) the DC voltage of the APF capacitor, (c) the load active power, (d) the load reactive power, (e) the DC-link voltage of the back-to-back converter, (f ) the total active power of the wind farm, and (g) the total reactive power of the wind farm.

Figure 18 :
Figure 18: Performance during a three-line-to-ground fault.(a) Te AC voltage at B575, (b) the DC voltage of the APF capacitor, (c) the load active power, (d) the load reactive power, (e) the DC-link voltage of the back-to-back converter, (f ) the total active power of the wind farm, and (g) the total reactive power of the wind farm.