Three-phase amplitude adaptive notch filter control design of DSTATCOM under unbalanced/distorted utility voltage conditions

Abstract

This paper deals with a control design based on amplitude adaptive notch filter (AANF) for a four-leg distributed static compensator (DSTATCOM) in a three-phase four-wire distribution grid to overcome current-related problems of power quality. Extracted reference currents of DSTATCOM are obtained using AANF because of its simple structure, exact measuring of frequency and amplitude, suitable estimation of the desired signal, and capability of tracking the changes of the input signal amplitude. To improve the dynamic performance of DSTATCOM, two fuzzy logic controllers are utilized to regulate DC link voltage and the voltage of point of common coupling (PCC). Furthermore, an adaptive hysteresis band current controller is applied for generating the gate pulses of IGBT switches. The proposed control scheme is robust to power system oscillations, especially when the main voltage suffers from disturbances and unbalancing. Different surveys are performed to study the efficacy of the proposed method, and results are verified through the simulation results in MATLAB/Simulink environment.

Keywords

DSTATCOM power quality amplitude adaptive notch filter fuzzy logic controller adaptive hysteresis band current controller

1 Introduction

Due to the influence of modern innovations and rapid evolutions in power electronics industry, the application of devices such as adaptive speed drivers (ASDs), power supplies, and cycloconverters has extensively increased. This type of loads can be classified as linear, nonlinear, unbalances, and a combination of them containing reactive components and usually drawing non-sinusoidal currents from the network. As a result, these loads make various severe power quality issues including harmonic pollution, load unbalancing, weak voltage regulation, high reactive power, and exorbitant neutral current in three-phase four-wire distribution networks [1, 2].

DSTATCOM is normally employed as a shunt compensator to reduce power quality issues related to the current. DSTATCOM operation depends directly to the design of power circuit elements, its control algorithm for extracting the reference signals, the switching algorithm for generating switching pulses, and the stability of the designed control method [3].

Accurate identification and extraction of the compensation signals are prerequisites for the suitable performance of a DSTATCOM. To extract the reference signals, advanced signal processing techniques either in time or frequency domain are presented. In frequency domain techniques, most of the algorithms based on Fourier transform such as discrete Fourier transform (DFT) [4] and Kalman Filtering (KF) [5] are utilized for harmonic currents estimation. Nonetheless, these algorithms usually suffer from slow time responses. The control strategies in the time domain are based on the extraction of instantaneous currents/voltages harmonic. The conventional time-domain algorithms include instantaneous reactive power theory (IRPT) [6] and synchronous reference framework (SRF) [7]. The basic of IRPT algorithm is to calculate active and reactive powers through transforming three-phase currents and voltages to their two-phase counterparts, where it lacks the desired performance under non-sinusoidal supply conditions [8]. The SRF method is formed according to the changing of three-phase contents to the corresponding DC components, and low-pass filters (LPFs) are used for harmonic filtering and this leads to time delays and exacerbates the controller performance [9].

Phase lock loops (PLL)-based control algorithms have been conventional methods for the estimation of harmonic components of disturbed power signals. However, under unbalanced or disturbed voltage conditions, PLL shows a phase delay which leads to a slow response and equipment failure in the power system. In general, a trade-off between fast tracking and proper filtering is applied in the PLL optimization methods. Most of these methods are very sensitive to harmonic distortions. Subsequently, achieving fast tracking and strong robustness against harmonics, simultaneously, seems to be very challenging [10 –12].

Most of the advanced methods of signal processing and analysis are precise and show a superior dynamic reaction compared to FFT. However, they need a huge number of calculations that lack a suitable performance under variable frequency conditions [13 –16]. The Adaptive notch filter (ANF) is one of the advanced algorithms, introduced as an effective control method for extracting the reference sinusoidal components from the disturbed input signal because it can follow the frequency variations of the input signal by changing the Notch frequency [17 –19].

The modified Notch filter in the time-continuous form was first introduced by Hsu [20]. This was a new frequency extraction algorithm for varying signals and has obtained much consideration during recent years since noise cannot affect its performance. An adaptive low-pass notch (LPN-PLL) was presented in [21] which benefits from both quick and smooth transient responses to the network voltage transients and robust under distorted and unbalanced power supply conditions. An algorithm was suggested in [22] to improve the performance of ANF, analyze the frequency estimation and optimize the dynamic equations for modifying its operation. State-space structure of frequency estimation analysis, dynamics of the notch filter, and the tracking features are described thoroughly, and an improved method is presented to cancel the adaptive frequency [22, 23].

Notch filter has a linear time-invariant structure that multiplies its input signal in a gain equal to unity in all frequencies except the notch frequency, in which the gain is null. Therefore, all frequencies except the notch frequency will exist in the frequency spectrum of the filter’s output signal. If the filter becomes capable of locking the notch frequency on the fundamental frequency of the input signal and tracking it properly, it is then called an adaptive notch filter (ANF) that can be used to extract the desired sinusoidal component of a given signal.

The use of Notch filter for active filters was presented in [24], which is performed properly because for extracting the desired signals, it does not need any phase-locked loop (PLL) and shows a superior time response compared to control algorithms based on PLL. In [25], a control algorithm based on Notch filter was considered for DSTATCOM operation assuming a very limited range of variations (i.e., ±0.2 Hz) for the network frequency. Although this consideration may be valid in particular applications, it may not be true under weak grid conditions.

On the other hand, the ANF-based algorithm does not take into account the factor of input signal amplitude variations during the estimation process [26]. Consequently, the amplitude adaptive notch filter (AANF)-based DSTATCOM control algorithm is presented in this paper to extract the three-phase reference currents from non-ideal input signals. The presented AANF-based control design is capable of estimating the amplitude and frequency and extracting other useful information while the amplitude of the input signal is varying. In addition to its simple structure, AANF performance will not be deteriorated by the power system disturbances such as harmonics in the network signals.

The contribution of this paper is the real-time implementation of a novel control method for DSTATCOM based on the mixture of AANF technique and a method for extracting the reference currents. Additionally, to boost the dynamic performance of the DSTATCOM, an adaptive hysteresis band current (AHBC) control system is used to generate switching signals. The proposed control design does not require any PLLs, coordination transformations or high/low-pass filters for extracting the fundamental and harmonic components. This leads the DSTATCOM to detect and compensate the harmonics with high accuracy and suitable convergence speed, without lacking the robustness against the harmonics in the presence of linear and nonlinear loads. Furthermore, DSTATCOM is responsible for regulating the voltage, obliterate the effect of poor power factor, and balancing the power supply currents under different operation conditions. In other words, power factor correction (PFC) and zero voltage regulation (ZVR) tasks are performed by DSTATCOM even under disturbed and unbalanced power supply conditions with unbalanced linear/nonlinear loads.

The rest of this paper is arranged as follows. Section 2 describes the configuration of the DSTATCOM in a three-phase four-wire distribution network. The proposed AANF control design is explained in Section 3 and its formulation for achieving the desired switching signal is described. In Section 4, the control system is investigated to show its performance. The evaluation of the employed control strategy for DSTATCOM under unbalanced/distorted utility conditions in MATLAB software is given in Section 5.

2 System configuration

The schematic diagram of a four-leg DSTATCOM in a three-phase four-wire distribution network is depicted in Fig. 1. Different topologies are presented for three-phase four-wire DSTATCOM such as four leg voltage source converter (VSC) topology, capacitor midpoint VSC topology and H Bridge VSC topology. Here, a four-leg voltage source converter configuration is chosen as DSTATCOM because it is the most applicable topology because of its less complex and more reliable control, less solid state devices and efficient compensation of neutral wire current [27].

Fig.1

Schematic diagram of four-wire DSTATCOM connected to the distribution system.

Eight switches in Fig. 1, are switched according to the compensation strategy of DSTATCOM. The system includes a three-phase voltage source with the source resistor (R_s) and inductor (L_s). A fixed capacitor (C_dc) four-leg voltage source converter (VSC) is connected to the network in parallel through interface inductances (L_f, L_n). The interfacing inductances are used for filtering the ripples of the injected currents. A high-pass RC filter (R_f, C_f) is also connected for high-frequency ripples filtering of the PCC voltage.

3 Amplitude adaptive notch filter

3.1 Three-phase AANF-based algorithm

To achieve power quality purposes, an advanced algorithm is required for detection of amplitude, phase, and frequency and to extract the constitutional components of the input signals. In general, the input signal for DSTATCOM control system is defined as: $u_{α} (t) = \sum_{(i = 1)}^{n} A_{α i} \sin (i ω_{0} t + φ_{α i}); α = a, b, c$ (1) where i denotes the harmonic components, A_αi is the amplitude of each component, φ_αi is the initial angle, and ω₀ represents the fundamental angular frequency. The main aim of the Notch filter is to estimate unknown parameters (A_αi, φ_αi), especially under non-ideal supply conditions. The estimation process has to be completely accurate and insensitive to the presence of harmonics, inter-harmonics, and noise so the desired sinusoidal components can be extracted. In addition, the system frequency deviation must be tracked with suitable speed and accuracy.

The conventional ANF provides the accurate and fast extraction of the frequency and other information of the considered signal [19]. However, when the input signal amplitude is fluctuated, ANF is not able to follow the alterations adequately. Therefore, the ANF equation is modified to increase the performance of ANF in the presence of amplitude variations.

Based on the presented Equations in [19, 26], the behavior of AANF is specified by: ${\begin{matrix} {\ddot{x}}_{α} = - i^{2} θ^{2} x_{α} + 2 ξ_{α} θ e_{α} (t); α = a, b, c \\ \dot{θ} = - γ θ \sum_{α}^{n} x_{α} e_{α} (t) \\ e_{α} (t) = u_{α} (t) - \sum_{m = 1}^{n} {\dot{x}}_{ma} \\ γ = \frac{ɛ}{(1 + A^{2}) (μ θ^{2} + 1)} \end{matrix}$ (2) where e_α (t) indicates the error signal and θ denotes the common angular frequency of three-phase signals. Also in the above equations, μ, ɛ and ξ are the real adjustable positive parameters that describe the AANF behavior with regard to accuracy and convergence speed. Here, ξ is the damping factor and determines the sensitivity to the AANF noise. Furthermore, γ defines the convergence speed and as a result, determines the ability of AANF in tracking the changes of the signal characteristics. By adjusting ξ and γ parameters, a compromise should be made between the speed and accuracy of the estimation method. A small ξ increases the convergence speed but leads to higher overshoots. Also, a higher γ results in smaller variations, yet reduces the convergence speed.

For the measured three-phase voltage or current, the dynamics of system Equation (2) is converged to a unique periodic orbit as follows: $P (t) = (\begin{matrix} P_{a} (t) \\ P_{b} (t) \\ P_{c} (t) \\ ω_{0} \end{matrix})$ (3) where $P_{α} (t) = (\begin{matrix} - \frac{A_{α}}{ω_{0}} cos (ω_{0} t + φ_{α}) \\ A_{α} sin (ω_{0} t + φ_{α}) \end{matrix})$

In the above equation, A_α shows the input signal amplitude, ω₀ is the angular frequency, and φ_α is the phase angle of the input signal. This system provides robustness against the power system pollutions such as noise, distortions, and disturbances, and can successfully follow the frequency variations of the input signal.

According to Equation (2), the amplitude and phase of the fundamental component of the input signal ( ${\dot{x}}_{i α}$ ) are calculated as. ${\begin{matrix} A_{i α} = \sqrt{(i θ x_{i α})^{2} + ({\dot{x}}_{i α})^{2}} \\ φ_{i α} = {tan}^{- 1} (\frac{{\dot{x}}_{i α}}{i θ x_{i α}}) \end{matrix}$ (4) where θx_iα is 90° phase-shifted form of ${\dot{x}}_{i α}$ .

Here three AANF are separately applied to extract desired components including frequency, phase angle, and amplitude for three phases. Moreover, an advanced combination of n parallel adaptive sub-filter is utilized to extract the required i^th harmonic components and the corresponding active and reactive currents. Selective harmonic extraction/elimination objectives can also be utilized using this structure.

Referring Equation (2), each AANF contains a three-order dynamic system; nonetheless, since the frequency ω₀ of the power system in three phases are identical, the AANF control system possesses an order of seven.

The schematic of the proposed algorithm is illustrated in Fig. 2. This figure is depicted for amplitude and phase extraction of phase ‘A’ voltage/current, which is representative of recursive equations in Equation 2 for the same phase. For Phase ‘B’ and ‘C’ the same figures can be illustrated. The method includes a frequency estimation section and sub-filter (1), which is responsible for estimating the frequency and fundamental component of the input signal. Besides, the algorithm includes multiple sub-filters to estimate the desired components of the voltages/currents according to the estimated frequency by sub-filter (1).

With regard to the fact that the input signal is periodic and no additional information is available, the extraction/elimination of the selected harmonic and tracking the changes of the input signal can be performed in an accurate and fast way using the proposed configuration. Besides, the structure is independent under different load and supply conditions and does not require any synchronization tools such as PLL.

Fig.2

The proposed AANF method.

The detailed stability investigation of ANF is accomplished in [22]. The parameters of the power circuit including the DC link voltage and AC inductors for four-leg DSTATCOM are selected according to the system configuration [28].

3.2 The-proposed compensation strategy

The inputs to this section are the phase angle and amplitude of the fundamental components of the network voltages and currents which are calculated in Section 3.1.

The fundamental component of each phase’s line current, i_b (t), can be divided into two components, the active current, i_ba (t), and the reactive current, i_br (t): $i_{b} (t) = i_{ba} (t) + i_{br} (t)$ (5)

The active and reactive currents in Equation (5) are calculated as follows: ${\begin{matrix} i_{ba} (t) = I_{m} cos (φ_{i} - φ_{v}) . sin (φ_{v}) \\ i_{br} (t) = I_{m} sin (φ_{i} - φ_{v}) . cos (φ_{v}) \end{matrix}$ (6) where I_m is the amplitude ofi_b (t), φ_i is the total phase angle of i_b (t), and φ_v is the total phase angle of the fundamental component of relative phase-to-ground voltage.

In addition, the amplitude of phase voltage (V_t), in-phase unit templates (u_ap, u_bp, u_cp), and quadrature unit templates (u_aq, u_bq, u_cq) are evaluated by the fundamental component of PCC voltage driven by the AANF algorithm [29].

The proposed RLES algorithm is employed in different operating modes of DSTATCOM including enhancing power factor, regulating voltage, harmonics current elimination, and load balancing.

3.3 Power factor correction (PFC) operation mode of DSTATCOM

Control system design for DSTATCOM in this mode includes injecting the average amount of the active component of the load current as well as switching losses current (I_loss), needed for DC link of VSC voltage regulation, from the supply side. The fundamental active power components of load currents based on Equation (6) are as Equation (7). ${\begin{matrix} i_{aa} (t) = I_{ma} cos (φ_{ia}) . cos (φ_{va}) + I_{ma} sin (φ_{ia}) . sin (φ_{va}) . sin (φ_{va}) \\ i_{ab} (t) = I_{mb} cos (φ_{ib}) . cos (φ_{vb}) + I_{mb} sin (φ_{ib}) . sin (φ_{vb}) . sin (φ_{vb}) \\ i_{ac} (t) = I_{mc} cos (φ_{ic}) . cos (φ_{vc}) + I_{mc} sin (φ_{ic}) . sin (φ_{vc}) . sin (φ_{vc}) \end{matrix}$ (7)

To omit unbalancing from the reference currents, amplitude of calculated three-phase currents in Equation (7) should be fed from all phases equally. Therefore, the average amplitude of the active component of load currents is obtained as: $I_{ad} (t) = (i_{aa} (t) + i_{ab} (t) + i_{ac} (t)) / 3$ (8)

The output of fuzzy controller at the DC side of VSC is taken as the loss component of the current (I_loss) to compensate for active power losses of DSTATCOM which is evaluated in Section 3.5.

The amplitude of the reference active currents is calculated by summation of average amplitude current (I_ad (t)) to the switching losses current as: $I_{as} (t) = I_{ad} (t) + I_{loss}$ (9)

The instantaneous reference active source current components are evaluated by multiplication of the reference currents amplitude in-phase unit templates as: $i_{sap}^{*} = I_{as} * u_{ap}, i_{sbp}^{*} = I_{bs} * u_{bp}, i_{scp}^{*} = I_{cs} * u_{cp}$ (10)

These generated reference active source current components are in the same phase with three-phase voltages for PFC operation mode. In such a case, DSTATCOM provides the reactive power of the load thoroughly.

3.4 Zero voltage regulation (ZVR) operation mode of DSTATCOM

The Control system design for DSTATCOM in ZVR mode includes injecting the same active current components as well as the summation of reactive current components and the current component for the PCC voltage regulating, obtained from the fuzzy controller (I_vt), from the source side. The PCC voltage amplitude (V_t) is maintained to its predefined value ( $V_{t}^{*}$ ) by applying the fuzzy controller. The fundamental components of three-phase reactive power components of load are as Equation (11): ${\begin{matrix} i_{ra} (t) = I_{ma} sin (φ_{ia}) . cos (φ_{va}) - I_{ma} cos (φ_{ia}) . sin (φ_{va}) . cos (φ_{va}) \\ i_{rb} (t) = I_{mb} sin (φ_{ib}) . cos (φ_{vb}) - I_{mb} cos (φ_{ib}) . sin (φ_{vb}) . cos (φ_{vb}) \\ i_{rc} (t) = I_{mc} sin (φ_{ic}) . cos (φ_{vc}) - I_{mc} cos (φ_{ic}) . sin (φ_{vc}) . cos (φ_{vc}) \end{matrix}$ (11)

The average amplitude of the reactive component of load currents is calculated by: $I_{rq} (t) = (i_{ra} (t) + i_{rb} (t) + i_{rc} (t)) / 3$ (12)

For regulating the PCC voltage, the average amplitude of the supply voltage is calculated and subtracted from the reference magnitude value, and the error and deviation of error are fed to the AC voltage fuzzy controller as the inputs. The fuzzy controller output defines as the reactive power component used for the regulation of the voltage at PCC.

The total reactive current component is calculated by the subtraction of average fundamental reactive current component from the reactive power component as: $I_{rs} (t) = - I_{rq} (t) + I_{vt} (t)$ (13)

The reference reactive source current components are obtained by: $i_{saq}^{*} = I_{rs} * u_{aq}, i_{sbq}^{*} = I_{rs} * u_{bq}, i_{scq}^{*} = I_{rs} * u_{cq}$ (14)

Finally, by adding the reference reactive and active source current components of each of the three-phases, the reference source currents are expressed as: $i_{sa}^{*} = i_{sap}^{*} + i_{saq}^{*}, i_{sb}^{*} = i_{sbp}^{*} + i_{sbq}^{*}, i_{sc}^{*} = i_{scp}^{*} + i_{scq}^{*}$ (15)

The reference neutral current at the source side is taken as: $i_{sn}^{*} = 0$ (16)

The schematic diagram of the proposed control design is illustrated in Fig. 3. The schematic diagram of the proposed control design is illustrated in Fig. 3, which is shown in detailed for phase ‘A’. Based on Equations (7, 11), I_aa and I_ra is calculated, consequently, I_ad and I_aqis evaluated according to Equations (8, 12). Having calculated reference currents using Equations (10, 14), and comparing them with the sensed currents, the gate pulses are obtained through an adaptive hysteresis current controller.

Fig.3

Schematic diagram of the compensation strategy.

3.5 Fuzzy logic controller

Here, two fuzzy logic control (FLC) systems are employed to control DC link and AC voltage load terminal since these controllers show a superior and more robust performance compared to the linear controllers such as PI controller. Fuzzy controller does not require any accurate details of the proposed control scheme and its rules are derived according to the performance of DSTATCOM. Here, triangular membership functions are used as inputs and outputs due to their simplicity and ease of use. Moreover, Mamdani method is utilized for the inference part of fuzzy control system. Seven input and output membership functions (PB (positive big), PM (positive medium), PS (positive small), NB (negative big), NM (negative medium), NS (negative small), and ZE (zero)) and the rules table are illustrated in Fig. 4 and Table 1, respectively.

Fig.4

Membership function for inputs and output.

Table 1. provides the details of 49 rules to perform successful control process, and each rule indicates a different condition in the control system. In general, 49 rules can assure an acceptable operation.

Table 1

Fuzzy decision table

e	ce
	NB	NM	NS	Z	PS	PM	PB
NB	NB	NB	NB	NB	NM	NS	Z
NM	NB	NB	NB	NM	NS	Z	PS
NS	NB	NB	NM	NS	Z	PS	PM
Z	NB	NM	NS	Z	PS	PM	PB
PS	NM	NS	Z	PS	PM	PB	PB
PM	NS	Z	PS	PM	PB	PB	PB
PB	Z	PS	PM	PB	PB	PB	PB

3.6 Switching algorithm

As it is observed in Fig. 3, the current errors between the reference currents ( $i_{sa}^{*}, i_{sb}^{*}, i_{sc}^{*}$ ), calculated in section 3.3 and 3.4, and the measured currents (i_sa, i_sb, i_sc) are fed to an adaptive hysteresis-band current controller for generating the gate pulses for IGBT switches. In typical hysteresis band current control system, the bandwidth is usually considered between 1% to 5%. Narrow bandwidth results in a fast and fairly tracking of currents, whereas significantly raising the switching frequency. A wide bandwidth also does not offer an accurate tracking and may cause instability. The adaptive hysteresis controller facilitates the hysteresis band to modulate with the parameters of system to hold the switching frequency to about a fix value. The adaptive hysteresis band current controller changes the hysteresis bandwidth according to modulation frequency, supply voltage, dc capacitor voltage and slope of the source reference current.

For almost constant switching frequency, the hysteresis band is calculated as [30, 31]: $HB = \frac{V_{dc}}{8 . f_{c} . L_{f}} [1 - \frac{4 L^{2}}{V_{dc}^{2}} {(\frac{V_{s} (t)}{L_{f}} + m)}^{2}]$ (17) where f_c is the modulation frequency and $m = {di}_{sa}^{*} / - dt$ represents the slope of current waveform. In adaptive hysteresis band current controller, hysteresis band (HB) can be modulated at different points of fundamental frequency cycle to control the switching pattern of the inverter.

4 Performance evaluation

This section investigates the AANF-based control scheme performance of DSTATCOM by means of computer simulations in MATLAB/Simulink environment. Tracking and harmonic decomposition capability of the presented AANF are evaluated in this part, and the performance of the whole system for load balancing, the harmonic compensation, the neutral current elimination, and the power factor correction will be investigated in Section 5.

4.1 Initiatory performance

Consider the input signal of the proposed AANF as: $\begin{matrix} y (t) = sin (ω_{0} t + φ_{1}) + 0.2 sin (5 ω_{0} t + φ_{5}) + \\ 0.3 sin (7 ω_{0} t + φ_{7}) + 0.3 sin (30 ω_{0} t + φ_{30}) \end{matrix}$ (18) where ω₀ = 100π rad/s and the initial phase angles φ_i’s are chosen randomly between zero and 2π rad. Four extracted signals including fundamental, the 5th and the 7th harmonic components which are the control algorithm response to Equation (18) are displayed in Fig. 5, i.e. four extracted signals including the fundamental, the 5th and the 7th harmonic components are demonstrated in Fig. 5.

Fig.5

The input signal and its fundamental, 5th and 7th harmonic components of the input signal using AANF.

4.2 Tracking capability

The tracking aspects of the proposed AANF algorithm considering amplitude and frequency variations are demonstrated here. Considering (18) as an input signal, changes in the fundamental frequency from 50 to 52 Hz and+0.2 pu in the fundamental component at t = 0.2 s, with a comparison between ANF and AANF applications, are illustrated in Fig. 6. It is clear that, compared to ANF method, the proposed method performs satisfactorily with regard to tracking amplitude and frequency changes of the input signal within a transient time of about one cycle.

Fig.6

Tracking of amplitude and the frequency of the input signal.

4.3 Harmonic detection capability

Here, the proposed control algorithm is employed to track and extract harmonic components of an input signal as follows: $\begin{matrix} y (t) = sin (ω_{0} t + φ_{1}) + 0.3 sin (5 ω_{0} t + φ_{5}) \\ + 0.2 sin (7 ω_{0} t + φ_{7}) \end{matrix}$ (19)

An amplitude step change of (– 0.2 pu) of the fundamental and the 5th harmonic component, and (+0.2 pu) in the amplitude of the 7th harmonic are considered at t = 0.2 s. As seen in Fig. 7, the proposed algorithm adequately tracks the variations in one cycle of the fundamental, the 5th, and the 7th components. The total harmonic components of the input signal, γ, and the estimated frequency of the AANF algorithm are shown in Fig. 8.

Fig.7

Amplitude tracking changes of the fundamental, 5th and 7th harmonic component.

Fig.8

Total harmonic component of the input signal, γ, and the estimated frequency.

5 Analytic studies and discussion

The four-leg DSTATCOM performance using the proposed AANF-based control strategy is surveyed for PFC and ZVR as well as load balancing, harmonic elimination, and neutral current elimination. The model is surveyed under linear and non-linear loads under non-ideal supply conditions. Four different worst possible conditions are discussed in this section. Voltage source is unbalanced and distorted and unbalanced linear and non-linear loads are presented to survey the performance DSTATCOM with AANF-based control algorithm.

The three-phase unbalanced distorted source voltages consisting of the harmonic voltage components and negative-sequence component are expressed in (20).

5.1 PFC operation of DSTATCOM under linear lagging power factor load condition (Case A)

The PFC and load balancing operation of the proposed AANF-based algorithm of the four-leg DSTATCOM is discussed here. At t = 0.4 s, phase ‘A’ and at t = 0.5s phase ‘B’ are disconnected, respectively, and at t = 0.7 s and t = 0.8 s phases ‘A’ and ‘B’ are applied again. The three phase source voltage (V_source), three-phase load currents (i_load), the compensating currents (i_DSTATCOM), the source currents (i_source) and the DC bus voltage (V_dc) are observed in Fig. 9. It is shown that under unbalanced distorted voltage source condition and after t = 0.4, DSTATCOM injects compensating currents in order to maintain the three-phase source currents balanced despite unbalancing in load currents. Therefore, the three-phase source currents become balanced and during load unbalancing, DC link voltage regulated at reference level without any variation. It shows the function of DSTATCOM for load balancing and also observed the fast action of AANF during sudden load injection. Fast action of AANF can be seen at a time of load injection in the estimation of reference supply current with other signals. Just at the time of load injection, nature of DSTATCOM current is changed quickly which validates the fast action of this proposed control method. These results show satisfactory performance of the proposed control algorithm used in DSTATCOM for reactive power compensation and harmonics suppression under linear and nonlinear loads respectively.

Fig.9

DSTATCOM performance for load current balancing in Case A.

Figure 10 shows the source neutral currents (I_Sn), injected compensator currents (I_Cn) and load neutral current (I_Ln) where fourth leg current (I_Cn) and load neutral current both are equal and opposite to make supply neutral current almost zero. These results show the functions of DSTATCOM for load balancing and neutral current compensation with fast response of control algorithm during sudden removal of the load. ${\begin{matrix} V_{a} = 250 sin (ω t) + 25 sin (ω t) + 3.7 sin (3 ω t) + 18.6 sin (5 ω t \\ - 120^{\circ}) + 4.5 sin (7 ω t) + 3.1 sin (11 ω t - 120^{\circ}) \\ V_{b} = 250 sin (ω t - 120^{\circ}) + 25 sin (ω t + 120^{\circ}) + 3.7 sin (3 ω t) \\ + 18.6 sin (5 ω t) + 4.5 sin (7 ω t - 120^{\circ}) + 3.1 sin (11 ω t) \\ V_{c} = 250 sin (ω t) + 25 sin (ω t - 120^{\circ}) + 3.7 sin (3 ω t) + 18.6 sin \\ (5 ω t + 120^{\circ}) + 4.5 sin (7 ω t + 120^{\circ}) + 3.1 sin (11 ω t - 120^{\circ}) \end{matrix}$ (20)

Fig.10

DSTATCOM performance for neutral current compensation in Case A.

Figure 11 depicts reactive power compensation efficiency of DSTATCOM. DSTATCOM compensates zero-sequence current components, reactive current of the load, and enhances the power factor. It is observed that although the power factor of the load is around 0.8, the source side power factor is maintained equal to unit, and subsequently the supply voltage and currents are in-phase.

Fig.11

DSTATCOM performance for power factor correction in Case A.

5.2 ZVR operation of DSTATCOM under linear lagging power factor load condition (Case B)

The ZVR performance of DSTATCOM for linear unbalanced load currents is displayed in Fig. 12. The performance indices include load currents (i_load), compensator currents (i_DSTATCOM), source currents (i_source), amplitude of the PCC voltages (V_PCC) and DC link voltage (V_dc) under dynamic load condition. This figure shows the balanced source currents at PCC and its smooth change over when load currents are not balanced. It means that during load dynamics (removal), the reference source currents generated through control algorithm is exactly follow the sensed source currents. It shows almost balanced supply currents when load currents are unbalanced. These results show satisfactory performance of the AANF used in DSTATCOM for load balancing under non-linear loads in voltage regulation mode. The source current becomes sinusoidal and balanced, and the DC link voltage and PCC voltage amplitude remain nearly their predefined values. The power factor on supply side is leading as the terminal voltage is regulated by the DSTATCOM. It is observed that PCC voltage is regulated near to rated value. In this mode, supply currents are slightly leading with respective voltages because extra leading reactive power is required to regulate PCC voltages. These results demonstrate satisfactory performance of the control algorithm used for PCC voltage regulation with harmonics elimination in DSTATCOM under nonlinear load. The neutral current of the load (i_Ln), the injected compensator currents (i_Cn) and the source neutral currents (i_Sn) are also presented in this figure. The source side neutral current is about zero, which justifies the adequate compensation performance.

Fig.12

DSTATCOM performance for load balancing and zero voltage regulation in Case B.

5.3 PFC operation of DSTATCOM under non-linear load condition (Case C)

The dynamic performance of the proposed AANF-based control system for PFC operation of DSTATCOM under non-linear load condition is depicted in Fig. 13. The unbalanced load is made by removing phase ‘A’ (during t = 0.4 s to 0.7 s) and ‘B’ loads (during t = 0.5 s to 0.8 s). DSTATCOM injects compensating currents in order that the three phase source currents become harmonic free and balanced. It exhibits sinusoidal balanced source currents, despite unbalanced and distorted load currents. It also affirms the quick performance of the AANF strategy while two phases of the load are disconnected. These obtained results represent the proficient performance of the proposed system and justify the function of DSTATCOM for enhancing power factor, load balancing, and harmonic compensation under dynamic non-linear loads. The indices in this case include the three-phase load currents (i_load), the compensating currents (i_DSTATCOM), the sinusoidal source currents (i_source), the DC link voltage (V_dc), the load neutral current (i_Ln), the injected neutral current through DSTATCOM (i_Cn), and the source neutral current (i_Sn). It is obvious that the neutral current at the source side is remained at about zero due to the convenient compensation of the neutral current.

Fig.13

DSTATCOM performance for load current balancing, harmonic compensation, and neutral current compensation in Case C.

The THD% level of the phase ‘A’ load and source currents for PFC operation of DSTATCOM in Case C are illustrated in Figs. 14 and 15, respectively. While the THD% of the source current is 3.03%, the THD% of the load in phase ‘A’ is 20.51% for the non-linear load.

Moreover, by observing PCC voltage phase ‘A’ (V_sa) along with its respective source current (I_sa) in Fig. 16, it can be concluded that both are in-phase, and the source side power factor is maintained equal to unit. This can prove the suitable PFC mode of the operation of DSTATCOM under load variations.

Fig.14

THD% of the load current in Case C.

Fig.15

THD% of the source current in case C.

Fig.16

DSTATCOM performance for power factor correction in Case C.

5.4 ZVR operation of DSTATCOM under non-linear load condition (Case D)

Figure 17 depicts the dynamic behavior of the proposed control scheme of DSTATCOM for load balancing, harmonic current elimination, voltage regulation, and neutral current elimination under non-ideal supply condition and non-linear load. In the ZVR mode, the performance indices include the load currents (i_load), the compensator currents (i_DSTATCOM), the source currents (i_source), the PCC voltage amplitude (V_PCC), the DC link voltage (V_dc), the load, the DSTATCOM injected, and the source neutral currents (i_Ln, i_Cn, i_Sn). In this mode, balanced and sinusoidal source currents are achieved. It also shows the appropriate performance of DSTATCOM in neutral current compensation. Furthermore, the PCC voltage amplitude is set to its predefined value by provision of leading reactive power.

Fig.17

DSTATCOM performance for load balancing, harmonic compensation, zero voltage regulation, and neutral current compensation in Case D.

These results show satisfactory performance of the proposed control algorithm in four-leg DSTATCOM for its multi-functions such as reactive power compensation, harmonics suppression and neutral current compensation under non-linear loads, respectively.

The source current waveform in phase ‘A’ and harmonics spectra are exhibits in Fig. 18. The THD of phase ‘A’ at source current is equal to 2.64%. The waveforms illustrate the sinusoidal source currents after compensation, even while the supply voltage is unbalanced and distorted. These results indicate successful function of the presented control strategy of DSTATCOM for load balancing, harmonic elimination, and compensating reactive power of linear and nonlinear loads.

Fig.18

THD% of the source current in Case D.

For a better comparison of PI and Fuzzy logic controllers, the DC voltage regulator with both PI and fuzzy logic controller is shown in Fig. 19. In this paper, one of the powerful and famous optimization algorithms (e.g. Genetic Algorithm) is applied for precise calculation of optimized coefficients (PI gains) and accurate comparison between PI and Fuzzy controllers. In the first step individuals with random chromosomes are generated that set up the initial population. In this step, initial population of 20, 50 100 are used and compared which the solutions are similar. Furthermore, integral time absolute error (ITAE) criterion is employed to find the optimum PI controller gains. The new PI coefficients, calculated in these ways, are implemented in controller to demonstrate the improvement of convergence speed, reduction of error, the overshoot in capacitor voltage and other circuit parameters. It is shown that the DC link voltage fuzzy logic controller is able to perform successfully to keep the voltage of DC link around its reference value.

Fig.19

DC voltage regulator with both PI and Fuzzy logic controllers.

Figure 20 demonstrates the performance of the fuzzy logic control system in comparison with the PI controller for PCC amplitude voltage under ZVR operation of DSTATCOM. It is exhibited that the fuzzy system performance is more successful compared to the PI controller in terms of steady-state error and maintaining the PCC voltage amplitude close to its reference value.

Fig.20

Comparison of fuzzy logic controller with PI controller for zero voltage regulation.

A comparison in terms of THD% between AANF and ANF algorithm is done in for case D. It can be seen from Table 2 that AANF algorithm perform more successful than ANF algorithm during transients.

Table 2

Comparison of AANF and ANF algorithms in terms of THD%

Three	THD% of source currents
phases	(0.4 < t < 0.5)
	AANF algorithm	ANF algorithm
Phase A	4.21%	4.72%
Phase B	3.4%	4.43%
Phase C	3.48%	4.15%

To survey the load and source currents and comparison of using different controllers in terms of harmonic components and THD% value, harmonic measurements are performed with the endorsed constraints in the IEEE Std. 519-2014. $F_{n, vs} = \sqrt{\frac{1}{15} \sum_{i = 1}^{15} F_{n, i}^{2}}$ (21) where F represents an rms value of voltage/current, n represents the order of harmonic. Here, vs denotes “very short” [32, 33]. Harmonic measurement result is shown in Table 3, where the THD% values are computed according to the IEEE Std. 519-2014 recommendations. Table 3 illustrates the three-phase load and source currents with comparisons of the PI controller, fuzzy controller, adaptive hysteresis current controller, and conventional hysteresis band current controller under non-ideal supply condition.

Table 3

The harmonic measurements result for load and source currents under non-ideal supply condition

Very short time harmonics measurement according to the IEEE Std 519-2014
Non-ideal supply condition
Harmonic	Load current			Source current
order				PI Controller						Fuzzy Controller
				Conventional hysteresis controller			Adaptive hysteresis controller			Conventional hysteresis controller			Adaptive hysteresis controller
	Phase A	Phase B	Phase C	Phase A	Phase B	Phase C	Phase A	Phase B	Phase C	Phase A	Phase B	Phase C	Phase A	Phase B	Phase C
1	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00
2	0.25	0.19	0.29	0.15	0.02	0.06	0.18	0.05	0.18	0.07	0.14	0.11	0.20	0.14	0.08
3	5.39	6.94	7.71	1.07	0.87	0.41	0.54	0.42	0.99	0.20	0.66	0.90	0.11	0.23	0.26
4	0.14	0.17	0.32	0.03	0.04	0.07	0.05	0.04	0.07	0.07	0.03	0.03	0.03	0.04	0.03
5	16.12	21.95	25.30	0.14	1.24	1.86	0.47	1.20	1.29	0.85	1.26	1.67	0.31	1.04	1.30
6	0.35	0.25	0.24	0.12	0.03	0.07	0.16	0.04	0.11	0.09	0.13	0.16	0.02	0.05	0.03
7	9.22	10.06	5.66	0.96	0.79	1.12	1.16	1.04	0.79	1.00	1.15	1.10	0.88	0.72	0.88
8	0.33	0.19	0.29	0.11	0.05	0.06	0.14	0.04	0.12	0.05	0.13	0.17	0.06	0.04	0.06
9	5.42	3.17	5.10	0.34	0.27	0.21	0.42	0.37	0.32	0.40	0.37	0.22	0.42	0.37	0.31
10	0.09	0.13	0.24	0.06	0.06	0.04	0.03	0.07	0.05	0.06	0.04	0.02	0.04	0.05	0.04
11	2.52	6.88	7.36	0.54	0.39	0.34	0.45	0.19	0.51	0.34	0.20	0.50	0.55	0.39	0.49
12	0.34	0.33	0.23	0.07	0.01	0.06	0.03	0.08	0.08	0.05	0.08	0.10	0.11	0.06	0.11
13	3.02	3.05	0.45	0.14	0.13	0.12	0.06	0.09	0.21	0.16	0.13	0.17	0.24	0.15	0.38
14	0.28	0.20	0.26	0.03	0.10	0.09	0.05	0.06	0.10	0.05	0.06	0.04	0.04	0.05	0.03
15	3.53	2.17	3.74	0.48	0.40	0.40	0.35	0.33	0.47	0.22	0.43	0.37	0.51	0.43	0.42
16	0.07	0.11	0.15	0.08	0.06	0.05	0.08	0.06	0.04	0.06	0.06	0.06	0.05	0.02	0.05
17	0.89	3.07	2.29	0.33	0.35	0.33	0.26	0.43	0.33	0.50	0.18	0.14	0.44	0.37	0.27
18	0.50	0.47	0.36	0.08	0.03	0.09	0.03	0.20	0.06	0.11	0.07	0.04	0.07	0.05	0.03
19	1.42	1.50	0.68	0.21	0.18	0.15	0.12	0.28	0.13	0.32	0.11	0.24	0.26	0.20	0.24
20	0.15	0.24	0.06	0.03	0.06	0.09	0.03	0.07	0.09	0.02	0.10	0.07	0.08	0.15	0.05
21	1.60	2.04	2.42	0.45	0.49	0.33	0.24	0.50	0.40	0.44	0.38	0.30	0.36	0.45	0.40
22	0.09	0.10	0.17	0.07	0.10	0.02	0.06	0.06	0.10	0.06	0.02	0.07	0.05	0.07	0.06
23	1.09	1.29	0.92	0.21	0.19	0.11	0.22	0.16	0.07	0.26	0.15	0.17	0.30	0.22	0.17
24	0.16	0.35	0.21	0.14	0.14	0.03	0.06	0.06	0.10	0.11	0.04	0.05	0.04	0.04	0.03
25	0.29	0.76	0.81	0.15	0.11	0.13	0.14	0.18	0.04	0.08	0.11	0.04	0.12	0.20	0.13
26	0.15	0.20	0.25	0.14	0.07	0.04	0.07	0.12	0.09	0.14	0.10	0.04	0.03	0.07	0.04
27	0.57	1.05	1.11	0.39	0.34	0.29	0.24	0.32	0.27	0.29	0.16	0.18	0.23	0.31	0.26
28	0.26	0.22	0.16	0.07	0.06	0.04	0.06	0.06	0.06	0.08	0.05	0.04	0.03	0.06	0.07
29	1.09	1.14	0.72	0.24	0.14	0.17	0.16	0.11	0.29	0.25	0.09	0.15	0.23	0.08	0.18
30	0.23	0.17	0.22	0.10	0.08	0.11	0.06	0.03	0.09	0.09	0.08	0.11	0.07	0.06	0.02
31	0.55	0.10	0.58	0.13	0.17	0.02	0.03	0.20	0.08	0.20	0.05	0.06	0.07	0.20	0.18
32	0.11	0.13	0.08	0.08	0.05	0.08	0.02	0.04	0.08	0.06	0.04	0.04	0.07	0.10	0.04
33	0.30	0.51	0.59	0.20	0.31	0.10	0.15	0.13	0.18	0.06	0.15	0.18	0.10	0.16	0.14
34	0.21	0.07	0.18	0.08	0.08	0.07	0.11	0.10	0.08	0.05	0.02	0.09	0.02	0.04	0.03
35	0.77	0.52	0.38	0.17	0.06	0.08	0.09	0.20	0.14	0.26	0.08	0.07	0.19	0.06	0.16
36	0.20	0.13	0.10	0.04	0.02	0.05	0.02	0.04	0.04	0.10	0.10	0.08	0.04	0.05	0.10
37	0.32	0.29	0.22	0.08	0.11	0.21	0.03	0.13	0.19	0.09	0.05	0.06	0.06	0.17	0.20
38	0.12	0.06	0.07	0.09	0.03	0.07	0.06	0.06	0.08	0.05	0.06	0.04	0.05	0.03	0.07
39	0.19	0.30	0.29	0.09	0.13	0.08	0.12	0.06	0.09	0.10	0.17	0.03	0.07	0.08	0.04
40	0.09	0.08	0.09	0.10	0.07	0.03	0.03	0.05	0.15	0.03	0.04	0.03	0.03	0.03	0.04
41	0.24	0.32	0.17	0.14	0.09	0.13	0.12	0.11	0.08	0.13	0.09	0.05	0.17	0.15	0.10
42	0.06	0.07	0.02	0.04	0.01	0.10	0.03	0.09	0.05	0.03	0.04	0.06	0.01	0.06	0.06
43	0.09	0.12	0.16	0.04	0.11	0.18	0.11	0.16	0.13	0.05	0.10	0.20	0.09	0.09	0.15
44	0.11	0.07	0.08	0.04	0.10	0.05	0.05	0.02	0.07	0.05	0.03	0.04	0.02	0.03	0.03
45	0.19	0.16	0.09	0.10	0.16	0.10	0.07	0.16	0.06	0.10	0.07	0.01	0.09	0.03	0.06
46	0.06	0.10	0.04	0.09	0.13	0.04	0.03	0.06	0.05	0.04	0.04	0.04	0.03	0.05	0.04
47	0.11	0.27	0.17	0.09	0.16	0.11	0.10	0.17	0.06	0.08	0.08	0.04	0.06	0.10	0.05
48	0.17	0.18	0.08	0.07	0.07	0.05	0.01	0.07	0.14	0.03	0.08	0.06	0.02	0.09	0.06
49	0.18	0.10	0.17	0.13	0.04	0.09	0.06	0.08	0.15	0.11	0.03	0.06	0.14	0.04	0.07
50	0.04	0.03	0.05	0.04	0.03	0.04	0.04	0.05	0.05	0.04	0.06	0.05	0.04	0.03	0.02
THD%	21.02	26.92	29.03	1.93	2.06	2.42	1.70	2.00	2.17	1.78	2.05	2.39	1.59	1.73	1.97

It is shown that under non-ideal voltage supply conditions, DSTATCOM control system using fuzzy logic controller along with the adaptive hysteresis band current controller performs better than the other controllers in terms of THD% values.

6 Conclusion

A two-step combinational method is used in this paper to derive the reference signals of a four-leg DSTATCOM in a three-phase four-wire distribution network. In the first step, AANF is applied for estimating the fundamental and harmonic components of input currents and voltages. In the second step, the reference signals are extracted using the outputs of first step. Adaptive hysteresis band current control system is applied to generate the switching signals and two fuzzy controllers are employed to improve the dynamic operation of DSTATCOM. Simulation results of the control scheme and also operation of DSTATCOM in PFC and ZVR operation modes under abnormal supply conditions with unbalanced linear and nonlinear loads prove that the proposed scheme is robust against harmonics and frequency variations in addition to providing accurate and quick response. Furthermore, simulation results verify the efficacy of the control system for correcting power factor, harmonic compensation, balancing loads, and neutral current compensation. Moreover, the proposed strategy achieves a superior harmonic compensation performance in terms of THD% in comparison to conventional schemes.

Footnotes

Appendix

Ripple Filter: R_f =5 Ω and C_f = 5μF; Linear load: 20 kVA, 0.80-pf lag; Non-linear Load: three single-phase bridge rectifier with R_out = 9 Ω and L_out =1 mH; C_dc = 3000μF; V_dc = 700 V; L_f = 3.5 mH, L_n = 2.5 mH. Gains of PI controller for dc-bus voltage: K_pdc = 1.65, K_idc = 0.21; Gains of PI controller for PCC voltage: K_pac = 1.1, K_idc = 0.2; ξ_α=0.7; ɛ=8000; μ=0.00001.

References

Fabricio

, Junior

, Jacobina

and Correa

, Analysis of Main Topologies of Shunt Active Power Filters Applied to Four-Wire Systems, IEEE Trans Pow Electron 33(3) (2017), 1–1.

Al-Emadia

N.A.

, Buccella

, Cecati

and Khalid

H.A.

, A novel DSTATCOM with 5-level CHB architecture and selective harmonic mitigation algorithm, Electr Power Syst Res 130 (2016), 251–258.

Mahela

O.P.

and Shaik

A.G.

, Power quality improvement in distribution network using DSTATCOM with battery energy storage system, Int J Electric Pow Energy Syst 83 (2016), 229–240.

Mishra

, Das

, Kumar

and Sumathi

, A Power-Line Interference Canceler Based on Sliding DFT Phase Locking Scheme for ECG Signals, IEEE Trans Instrum Meas 64(1) (2015), 132–142.

Panigrahi

and Subudhi

, Performance Enhancement of Shunt Active Power Filter Using a Kalman Filter-Based H_∞ Control Strategy, IEEE Trans Power Electron 32(4) (2017), 2622–2630.

Boussaid

, Nemmour

A.L.

, Louze

and Khezzar

, A novel strategy for shunt active filter control, Electr Power Syst Res 123 (2015), 154–163.

Swain

S.D.

and Ray

P.K.

, Harmonic current and voltage compensation using HSAPF based on hybrid control approach for synchronous reference frame method, Int J Electric Pow Energy Syst 75 (2016), 83–90.

Revuelta

, Litrán

and Thomas

Active Power Line Conditioners: Design, Simulation and Implementation for Improving Power Quality, Elsevier Science & Technology Books, 2015.

Singh

, Jayaprakash

and Kothari

D.P.

, New control approach for capacitor supported DSTATCOM in three-phase four wire distribution system under non-ideal supply voltage conditions based on synchronous reference frame theory, Int J Electric Pow Energy Syst 33(5) (2011), 1109–1117.

10.

Golestan

, Guerrero

J.M.

, Vidal

, Yepes

A.G.

, Gandoy

J.D.

and Freijedo

F.D.

, Small-Signal Modeling: Stability Analysis and Design Optimization of Single-Phase Delay-Based PLLs, IEEE Trans Power Electron 31(5) (2016), 3517–3527.

11.

Xiao

, Dong

, Li

and Liao

, A Frequency-Fixed SOGI-Based PLL for Single-Phase Grid-Connected Converters, IEEE Trans Power Electron 32(3) (2017), 1713–1719.

12.

Abasi

, Seifossadat

S.G.

, Razaz

and Moosapour

S.S.

, Determining the contribution of different effective factors to individual voltage unbalance emission in n-bus radial power systems, International Journal of Electrical Power & Energy Systems 94 (2018), 393–404.

13.

Singh

, Arya

S.R.

, Chandra

and Al-Haddad

, Implementation of Adaptive Filter in Distribution Static Compensator, IEEE Trans Ind Appl 50(5) (2014), 3026–3036.

14.

Kumar

A.P.

and Mangaraj

, and D.S.T.A.T.C.O.M., employing hybrid neural network control technique for power quality improvement, IET Pow Electron 10(4) (2017), 480–489.

15.

Ray

A.S.

and Bhattacharya

, Improved tracking of shunt active power filter by sliding mode control, Int J Electric Pow Energy Syst 78 (2016), 916–925.

16.

Badoni

, Singh

and Singh

, An implementation of variable step-size least-mean-square based control algorithm for DSTATCOM, International Transactions on Electrical Energy Systems 26(17) (2016), 1540–1554.

17.

Chilipi

, Al sayari

N.A.

Al Hosani

K.H.

and Beig

A.R.

Adaptive Notch. Filter Based Multipurpose Control Scheme for Grid-Interfaced Three-Phase Four-Wire DG Inverter, IEEE Trans Ind Appl PP(99) (2017), 4015–4027.

18.

Khazraj

, da Silva

F.F.

Bak

C.L.

and Golestan

Analysis and design of notch filter-based PLLs for grid-connected applications, Electr Power Syst Res 147 (2017), 62–69.

19.

Yazdani

, Mojiri

, Bakhshai

and JoÓs

, A Fast and Accurate Synchronization Technique for Extraction of Symmetrical Components, IEEE Trans Power Electron 24(3) (2009), 674–684.

20.

Hsu

, Ortega

and Damm

, A globally convergent frequency estimator, IEEE Trans Automat Control 44(4) (1999), 698–713.

21.

Shin

, Lee

K.J.

, Lee

J.P.

, Yoo

D.W.

and Kim

H.J.

, Implementation of Fault Ride-Through Techniques of Grid-Connected Inverter for Distributed Energy Resources Adaptive Low-Pass Notch PLL, IEEE Trans Power Electron 30(5) (2015), 2859–2871.

22.

Mojiri

, Karimi-Ghartemani

and Bakhshai

, Time Domain Signal Analysis Using Adaptive Notch Filter, IEEE Trans Signal Process 55(1) (2007), 85–93.

23.

Nishimura

, Mvuma

and Hinamoto

A continuous time adaptive notch filter: Transient and Tracking analyses, In:

Proceedings of IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS), (2012), pp. 262–265.

24.

Ketabi

, Farshadnia

, Malekpour

and Feuillet

, A new control strategy for active power line conditioner (APLC) using adaptive notch filter, Int J Electric Pow Energy Syst 47 (2013), 31–40.

25.

Singh

, Kant

and Arya

S.R.

, Notch filter-based fundamental frequency component extraction to control distribution static compensator for mitigating current-related power quality problems, IET Pow Electron 8(9) (2015), 1756–1766.

26.

Yin

, Guo

and Li

, An Amplitude Adaptive Notch Filter for Grid Signal Processing, IEEE Trans Power Electron 28(6) (2013), 2638–2641.

27.

Sreenivasarao

, Agarwal

and Das

, Neutral current compensation in three-phase, four-wire systems: A review, Electric Power Systems Research 86 (2012), 170–180.

28.

Singh

, Chandra

and Al-Haddad

, Power quality: Problems and mitigation techniques, John Wiley & Sons; 2014.

29.

Singh

, Arya

S.R.

, Jain

and Goel

, Implementation of four-leg distribution static compensator, IET Gener Transm Distrib 8(6) (2014), 1127–1139.

30.

Panda

A.K.

and Patel

, Adaptive hysteresis and fuzzy logic controlled-based shunt active power filter resistant to shoot-through phenomenon, IET Pow Electron 8(10) (2015), 1963–1977.

31.

Biricik

and Komurcugil

, Three-level hysteresis current control strategy for three-phase four-switch shunt active filters, IET Pow Electron 9(8) (2016), 1732–1740.

32.

IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems, IEEE Std 519-2014 (Revision of IEEE Std 519-1992), 2014.

33.

Khorasani

P.G.

, Joorabian

and Seifossadat

S.G.

, Smart grid realization with introducing unified power quality conditioner integrated with DC microgrid, Electr Power Syst Res 151 (2017), 68–85.

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