Analysis of Fractional Order Sliding Mode Control in a D-STATCOM Integrated Power Distribution System

 ABSTRACT:

At present, the disturbances like the voltage fluctuations, resulting from the grid's complexities and unbalanced load conditions, create severe power quality concerns like total harmonic distortion (THD) and voltage unbalance factor (VUF) of the grid voltage. Though the custom power devices such as distribution-static compensators (D-STATCOMs) improve these power quality concerns, however, the accompanying controller plays the substantial role. Therefore, this paper proposes a fractional-order sliding mode control (FOSMC) for a D-STATCOM to compensate the low power distribution system by injecting/absorbing a specific extent of the reactive power under disturbances. FOSMC is a non-linear robust control in which the sliding surface is designed by using the Riemann-Liouville (RL) function and the chattering phenomenon is minimized by using the exponential reaching law. The stability of FOSMC is evidenced by employing the Lyapunov stability criteria. Moreover, the performance of the proposed FOSMC is further accessed while doing its parametric variations. The complete system is demonstrated with a model of 400V, 180kVA radial distributor along with D-STATCOM under two test scenarios in MATLAB/Simulink environment. The results of the proposed controller are compared with the fixed frequency sliding mode control (FFSMC) and conventional proportional-integral (PI) control. The results validate the superiority of the proposed controller in terms of rapid tracking, fast convergence, and overall damping with very low THD and VUF.

 KEYWORDS:

1.      Power quality

2.      Custom power devices

3.      Distribution static compensator

4.      Fractional order

5.      Sliding mode control

6.      Total harmonic distortion

7.      Voltage unbalance factor

SOFTWARE: MATLAB/SIMULINK

SCHEMATIC DIAGRAM:

Figure 1. Simplified Model Of D-Statcom Configuration.

 EXPECTED SIMULATION RESULTS:

Figure 2. (A) Three-Phase Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid (B) Rms Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid (C) Load Active And Reactive Power Under Voltage Sag/Swell Of

Main Grid.

Figure 3. (A) Three-Phase Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid With D-Statcom While Employing Pi Control (B) Rms Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid With D-Statcom While Employing Pi Control (C) Three-Phase Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid With D-Statcom While Employing Ffsmc (D) Rms Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid With D-Statcom While Employing Ffsmc (E) Three-Phase Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid With D-Statcom While Employing Fosmc (F) Rms Voltage At Lv Ac Bus Under Voltage Sag/Swell Of Main Grid With D-Statcom While Employing Fosmc.

Figure 4. (A) Load Active And Reactive Power Under Voltage Sag/Swell With D-Statcom While Employing Pi Control (B) Load Active And Reactive Power Under Voltage Sag/Swell With D-Statcom While Employing Ffsmc (C) Load Active And Reactive Power Under Voltage Sag/Swell With D-Statcom While Employing Fosmc.

 

Figure 5. (A) Injected/Absorbed Reactive Power By D-Statcom Under Voltage Sag/Swell While Employing Pi Control (B) Injected/Absorbed Reactive Power By D-Statcom Under Voltage Sag/Swell While Employing Ffsmc.

 

Figure 6. (A) Injected/Absorbed Reactive Power By D-Statcom Under Voltage Sag/Swell While Employing Fosmc With _ D 0:2 And Kd , Kq D 5 _ 106 (B) Injected/Absorbed Reactive Power By D-Statcom Under Voltage Sag/Swell While Employing Fosmc With _ D 0:5 And Kd ; Kq D 5 _ 106 (C) Injected/Absorbed Reactive Power By D-Statcom Under Voltage Sag/Swell While Employing Fosmc With _ D 0:8 And Kd , Kq D 5 _ 106 (D) Injected/Absorbed Reactive Power By D-Statcom Under Voltage Sag/Swell While Employing Fosmc With _ D 0:5 And Kd , Kq D 3 _ 104:

CONCLUSION:

In this paper, the authors have proposed a FOSMC based DSTATCOM to compensate the low power distribution system under disturbances such as voltage sag/swell and unbalanced load conditions. Besides, the performance of the FOSMC under its parametric variations is discussed as well. The complete system is demonstrated with a model of 400V, 180kVA radial distributor along with D-STATCOM under two test scenarios in MATLAB/Simulink environment. In the first test scenario, the grid transients (voltage sag/swell) are considered at the LV AC bus. Likewise, in the second test scenario, the unbalanced load conditions are considered at the LV AC bus. D-STATCOM sustains the voltage at LV AC bus by injecting/absorbing a certain extent of reactive power under voltage sag/swell and unbalanced load conditions. The results of the proposed controller are compared with fixed frequency sliding mode control (FFSMC) and conventional proportional-integral (PI) control. The results validate the superiority of the proposed controller in terms of rapid tracking, fast convergence, and overall damping with very low THD, and VUF. In the first test scenario, the voltage THD of proposed FOSMC during voltage sag/swell results in 0.52% in contrast to FFSMC and PI control which have THD of 0.84% and 2.17% respectively. In the second test scenario, the voltage THD of proposed FOSMC during unbalanced load conditions results in 0.97% in contrast to FFSMC and PI control which have THD of 1.96% and 3.63%. Likewise, the VUF under unbalanced load conditions with proposed FOSMC is 0.0014% in contrast to FFSMC and PI control which have VUF of 0.02% and 0.71%. In terms of assessment with existing SMC schemes, the proposed FOSMC has a very high response time, very high accuracy, very high robustness, lowest chattering along with low THD and VUF. The proposed model could be realized on the hardware platform for real-time verification purposes in future applications.

REFERENCES:

[1] A. Q. Al-Shetwi, M. A. Hannan, K. P. Jern, A. A. Alkahtani, and A. E. P. Abas, ``Power quality assessment of grid-connected PV system in compliance with the recent integration requirements,'' Electronics, vol. 9, no. 2, p. 366, Feb. 2020.

[2] A. D. J. C. Leal, C. L. T. Rodríguez, and F. Santamaria, ``Comparative of power calculation methods for single-phase systems under sinusoidal and non-sinusoidal operation,'' Energies, vol. 13, no. 17, p. 4322, Aug. 2020.

[3] E. Hossain, M. R. Tür, S. Padmanaban, S. Ay, and I. Khan, ``Analysis and mitigation of power quality issues in distributed generation systems using custom power devices,'' IEEE Access, vol. 6, pp. 16816_16833, 2018.

[4] F. R. Islam, K. Prakash, K. A. Mamun, A. Lallu, and H. R. Pota, ``Aromatic network: A novel structure for power distribution system,'' IEEE Access, vol. 5, pp. 25236_25257, 2017.

[5] A. A. Alkahtani, S. T. Y. Alfalahi, A. A. Athamneh, A. Q. Al-Shetwi, M. B. Mansor, M. A. Hannan, and V. G. Agelidis, ``Power quality in microgrids including supraharmonics: Issues, standards, and mitigations,'' IEEE Access, vol. 8, pp. 127104_127122, 2020.

Analysis and Design of Hybrid Harmonic Suppression Scheme for VSG Considering Nonlinear Loads and Distorted Grid

 ABSTRACT:

 The power quality of virtual synchronous generator (VSG) inevitably deteriorates in the presence of local nonlinear loads and distorted grid. In this paper, the conflict involved in the simultaneous elimination of distortion for both the inverter local load voltage and the grid exchanged current is first described. A unified control structure is presented that enables a tunable tradeoff between the two constrained harmonic sources. Then, a hybrid harmonic suppression scheme is proposed to enable the further improvement of the adaptability of VSG, which mainly consists of a local voltage harmonic control loop and an adaptive grid current-controlled loop. The local voltage harmonic control loop aims to scale down the inverter output impedance via a negative feedback loop, while the grid current-controlled compensator is intended to counteract the adverse effects from a weak grid via an additional voltage, which leads to substantially lower total harmonic distortion for both the local load voltage and the grid current at the same time. Small-signal modelling is performed to investigate the system stability and its robustness to parameter perturbations. The effectiveness of the proposed methodology is verified using hardware-in-the-loop simulations.

KEYWORDS:

1.      Distorted grid

2.      Harmonic suppression

3.      Harmonic observer

4.      Nonlinear load

5.      Virtual synchronous generator

SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAM:

 

Fig. 1. Structural diagram of grid-connected DG

 EXPECTED SIMULATION RESULTS:

 Fig. 2. Simulation results of voltage and current harmonics suppression. (a) Results without harmonic suppression. (b) Results with proposed voltage control loop only. (c)Results with proposed hybrid harmonic suppression method.

 

Fig. 3 Simulation results of the robustness against Lg variation. (a) Results without harmonic suppression. (b) Results with proposed voltage control loop only. (c)Results with proposed hybrid harmonic suppression method.

Fig. 4 Simulation results of the robustness to load variation of the proposed method. (a) Before load increases. (b) With increased linear load. (c) With increased nonlinear load. (d) Linear load current.

Fig. 5 Simulation results of the robustness to load variation of the comparison method. (a) Before load increases. (b) With increased linear load. (c) With increased nonlinear load. (d) Linear load current.

 

CONCLUSION:

In view of the inherent contradiction involved in attenuating adverse effects in the presence of nonlinear loads and distorted grid, this paper presents tunable tradeoff between constrained harmonic sources. A hybrid harmonic suppression scheme is then proposed and consists of a local voltage harmonic control loop and an adaptive grid current-controlled loop, with a concurrent distortion inhibition capability. Compared with the existing approaches, the proposed methodology provides high-quality power supplies for both the grid and local loads.

REFERENCES:

[1] Q. Zhong, and G. Weiss, “Synchronverters: inverters that mimic synchronous generators,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1259-1267, Apr. 2011.

[2] J. Ailpoor, Y. Miura, and T. Ise, “Power system stabilization using virtual synchronous generator with alternating moment of inertia,” IEEE Journal Emerg. Sel. Topics Power Electron., vol. 3, no. 2, pp. 451-458, June 2014.

[3] J. Liu, Y. Miura, and T. Ise, “Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter-based distributed generators,” IEEE Trans. Power Electron., vol. 31, no. 5, pp. 3600-3611, May 2016.

[4] D. Arricibita, P. Sanchis, and L. Marroyo, “Virtual synchronous generators classification and common trends”, in Proc. IECON, 2016, pp. 2433-2438.

[5] J. Fang, Y. Tang, H. Li, and X. Li, “A battery/ultra-capacitor hybrid energy storage system for implementing the power management of virtual synchronous generators,” IEEE Trans. Power Electron., vol. 33, no. 4, pp. 2820-2824, Apr. 2018.

 

An Uninterruptable PV Array-Battery Based System Operating in Different Power Modes with Enhanced Power Quality

ABSTRACT:

 This work aims to develop a solar- battery energy storage (BES) based system, which ensures an uninterruptable supply to loads irrespective of availability of the grid. This system comprises of a solar photovoltaic (PV) array, a BES, the grid and local residential loads. A new control is implemented such that the active power demand of residential loads, is fed from the PV array, a BES unit and the utility grid. In this system, the power control operates in different power modes, which delivers the benefits to the end users with an integration of BES and an excess of PV array power, which is sold back to the grid. For this, an effective control logic is developed for the grid tied voltage source converter (VSC). Moreover, this system deals with the issue of an integrating power quality enhancement along with the power generation from the solar PV source. The cascaded delayed signal cancellation (CDSC) based phase locked loop (PLL) is implemented for grid synchronization during the grid voltage distortion. The developed control is easily implemented in a real time controller (dSPACE-1202). Test results validate the performance of the implemented control in different operating conditions such as varying solar power generation, load variations and unavailability of the grid.

KEYWORDS:

 

1.      Energy Storage

2.      Power Quality

3.      Quadrature Signal Generation

4.      Solar PV Generation

5.      Synchronization

6.      Voltage Control Mode

SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAM:

Fig. 1 System configuration

 

EXPECTED SIMULATION RESULTS:

Fig.2 Dynamic performance at different operating modes during PV hour

Fig. 3 Dynamic performance of the grid interfaced PV-BES system during SVPM

Fig. 4 Performance of PV-BES system under SVPM (a) IPV and VPV (b) ig and vg (c) iL and vg(d) ivsc and vvsc (e) load power (PL), (f) grid power Pg (g) Ibat and Vbat, (h) Pbat, (i) harmonic spectral of iL (j) harmonic spectral of ig (k) harmonic spectral of vg and (l) grid voltage and grid current phasors diagram

 

Fig 5 Dynamic response of the system under CGPM (a) vg, VDC, ig, IPV (b)VPV, iL, Ibat, iVSC and (c) Pg, PL, PPV and IPV

 

Fig. 6 Dynamic performance of the system during non-PV hours (a) vg, VDC, ig, iVSC (b) ig, IPV, iL, Pg and (c) IPVFF, ID, ILoss and isα

CONCLUSION:

The main contributions of this work are on the robustness of the system operating in different operating modes. The performance of a grid interfaced PV-BES system is validated through experimental results where the worst case of PV array insolation, load variation and grid unavailability are used for transition between modes. In addition, the system is operating in constant and variable power modes to provide power smoothening and a decrease the burden on the distribution grid during peak demand. This system is also found capable to work in an islanding mode to deliver the uninterruptable power to the load. The CDSC-PLL provides synchronization to the grid and MNSOGI-QSG-DQ control uses for current harmonics elimination and power quality improvement. The THD of ig and vL are achieved within limits of an IEEE-519-2014 standard.

REFERENCES:

[1] J. T. Bialasiewicz, “Renewable Energy Systems with Photovoltaic Power Generators: Operation and Modeling,” IEEE Trans. Industrial Electronics, vol. 55, no. 7, pp. 2752-2758, July 2008,

[2] R. Panigrahi, S. Mishra, S. C. Srivastava, A. K. Srivastava and N. Schulz, “Grid Integration of Small-Scale Photovoltaic Systems in Secondary Distribution Network- A Review,” IEEE Trans. Industry Applications, Early Access, 2020

[3] J. Krata and T. K. Saha, “Real-Time Coordinated Voltage Support with Battery Energy Storage in a Distribution Grid Equipped with Medium-Scale PV Generation,” IEEE Trans. Smart Grid, vol. 10, no. 3, pp. 3486-3497, May 2019.

[4] N. Liu, Q. Chen, X. Lu, J. Liu and J. Zhang, “A Charging Strategy for PV-Based Battery Switch Stations Considering Service Availability and Self-Consumption of PV Energy,” IEEE Trans. Ind. Elect., vol. 62, no. 8, pp. 4878-4889, Aug. 2015.

[5] Y. Shan, J. Hu, K. W. Chan, Q. Fu and J. M. Guerrero, “Model Predictive Control of Bidirectional DC-DC Converters and AC/DC Interlinking Converters - A New Control Method for PV-Wind-Battery Microgrids,” IEEE Trans. Sust. Energy, Early Excess 2018.

 

 

An MPC Based Algorithm for a Multipurpose Grid Integrated Solar PV System With Enhanced Power Quality and PCC Voltage Assist

ABSTRACT:

The continuously fluctuating energy output and varying power demands in the renewable energy systems have led to the degradation of power quality. This work presents a model predictive based control for a solar PV system integrated to the grid for optimal management and control of the power transfer. The double stage three-phase configuration is controlled using model predictive control (MPC) strategy, which considers the power converters’ switching states to predict the next control variable. The control uses a modified-dual second-order generalized-integrator for estimation of the power requirements based on the continuously varying system parameters. The PCC voltages assist and the ride through operation are performed based on the drops in voltage levels and optimum switching state is selected based on the minimization of the cost function to deliver the required active and reactive powers to the grid. The performance of the controller is validated through simulation and is also shown using hardware implementation. The IEEE-519 standard is followed throughout and a comparative analysis shows the remarkable performance of the presented grid controller.

KEYWORDS:

1.      MDSOGI

2.      Model predictive control

3.      PCC voltage assist

4.      Ride through, solar photovoltaic

5.      Voltage source converter

SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAM:

 

Fig. 1. Circuit diagram of system.

EXPECTED SIMULATION RESULTS:

Fig. 2. Steady State UPF operation. (a) vg_ab-iinv_a (b) Inverter Power (c) THD of inverter current (d) vg_ab-ig_a (e) Grid Power (f) Grid voltage THD (g) Grid Current THD (h) Load Power (i) Load Current THD.

Fig. 3. Load current unbalance (a)-(c): (a) Phase ‘a’ PCC line voltage, Grid current, Load Current and VSC current (b) Phase ‘b’ PCC line voltage, Grid current, Load Current and VSC current (c) Internal Components Φloss, Φpvg, Φload and Φnet. (d) Grid current THD in steady state, (e) Load Current THD in steady state. (f) Solar Irradiation variation: PV current (IPV ), PV Voltage (V PV ) and DC link Voltage (V dc).

Fig. 4. Waveforms during grid voltage variations (a) Overvoltage: iL_a, V dc, vg_ab, ig_a (b)Undervoltage: iL_a, V dc, vg_ab, ig_a. (c) Grid current THD after overvoltage, (d) Load current THD after overvoltage, (e) Grid current THD after undervoltage, (f) Load current THD after undervoltage.

Fig. 5. High grid distortion (a) extracted fundamental voltage, highly distorted grid voltage, load current, current in the grid, (b) THD in voltage in the grid, (c) grid currentTHDfor Damped SOGI control based on [24] (d)LCS-MPC [25] (e) Presented MDSOGI-MPC control.

CONCLUSION: 

A modified dual second order generalized integrator based model predictive control (MDSOGI-MPC) is presented in this work for the control of two stage three phase grid tied solar PV system. Various adverse grid variations are performed to highlight the performance of the control technique. The robustness and simple configuration as well as the implementation of the control make its performance superior to present control methods based on MPC. Themodified-dual second order generalized integrator has estimated the power requirements based on system parameters. The performance during the sag in the voltage is shown while the controller demonstrates the PCC voltage assist operation as well as the ride through performance. Optimum switching states are predicted based on the minimization of the cost function. The performance is tested on simulation as well as hardware setup and the results show that the implementation of this control is advantageous. The harmonic spectrum of the current in the grid network is maintained within the prescribed limits of IEEE-519 std. limits. A generic comparison is made with the current modern control strategies, which shows that it works well as compared to other techniques.

REFERENCES:

[1] Y. Chen et al., “From laboratory to production: Learning models of efficiency and manufacturing cost of industrial crystalline silicon and thin-film photovoltaic technologies,” IEEE J. Photovoltaic, vol. 8, no. 6, pp. 1531–1538, Nov. 2018.

[2] V. Saxena, N. Kumar, B. Singh, and B. K. Panigrahi, “A rapid circle centre-line concept-based MPPT algorithm for solar photovoltaic energy conversion systems,” IEEE Trans. Circuits Syst. I: Regular Papers, vol. 68, no. 2, pp. 940–949, Feb. 2021.

[3] A. Tazay and Z. Miao, “Control of a three-phase hybrid converter for a PV charging station,” IEEE Trans. Energy Convers., vol. 33, no. 3, pp. 1002–1014, Sep. 2018.

[4] IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems - Amendment 1. IEEE Standard 1547a-2014 (Amendment to IEEE Standard 1547-2003), pp. 4–16, May 21, 2014, doi: 10.1109/IEEESTD.2014.6818982.

[5] V. L. Srinivas, B. Singh, and S. Mishra, “Fault ride-through strategy for two-stage grid-connected photovoltaic system enabling load compensation capabilities,” IEEE Trans. Ind. Electron., vol. 66, no. 11, pp. 8913–8924, Nov. 2019.

 

 

An Improved Deadbeat Control Strategy Based on Repetitive Prediction Against Grid Frequency Fluctuation for Active Power Filter

ABSTRACT:

In order to improve the harmonic compensation performance of active power filter (APF) in distribution network, based on deadbeat control theory, the command current prediction algorithm and current tracking control strategy are optimized in this article. Firstly, the command current repetitive prediction in abc coordinate system is transferred to dq for improving its accuracy in lead compensation, and the equivalent for fractional delay beat is achieved by Lagrange Interpolation Polynomial to solve the problem of inaccurate prediction caused by grid frequency fluctuation. Then, considering the inherent half-sampling-period delay of sinusoidal PWM (SPWM), an improved deadbeat control strategy for current tracking is proposed by estimating the output current of next sampling period. Because the output current in next sampling period is replaced by that in current sampling period with traditional deadbeat control strategy, this estimation could make up for the defect of low control precision caused by that replacement. After that, adding error repetitive correction into the improved deadbeat control channel to reduce the periodic tracking error of output current. Finally, the stability and accuracy of the improved control system are analyzed theoretically, and its feasibility and effectiveness are verified by the simulation and hardware-in-the-loop (HIL) experiments.

KEYWORDS:

1.      Deadbeat control

2.      Frequency fluctuation

3.      Harmonic compensation

4.      Lagrange interpolation polynomial

5.      Error repetitive correction

SOFTWARE: MATLAB/SIMULINK

BLOCK DIAGRAM:

Figure 1. Three-Phase Apf Topology And Overall Control Structure.

 EXPECTED SIMULATION REUSLTS:

Figure 2. Predicted Command Current With Traditional Or Proposed Prediction Algorithm At Different Grid Frequency. (A) Grid Frequency of 50hz. (B) Grid Frequency Of 50.5hz. (C) Grid Frequency Of 49.5hz.

 

Figure 3. Simulation Results For The Improved Deadbeat Control Strategy With Traditional Or Proposed Repetitive Prediction. (A) With Traditional Prediction At Grid Frequency Of 50.5hz. (B) With Proposed Prediction At Grid Frequency Of 50.5hz (C) With Traditional Prediction At Grid Frequency Of 49.5hz. (D) With Proposed Prediction At Grid Frequency Of 49.5hz.

 

Figure 4. Power Grid Voltage And Nonlinear Load Current. (A) Power Grid

Voltage. (B) Nonlinear Load Current.

 

Figure 5. Grid-Side Current And Output Current Of Phase A With Traditional Or Improved Deadbeat Control Strategy. (A) Traditional Deadbeat. (B) Improved Deadbeat (Krc D 0).

 

Figure 6. Grid-Side Current And Output Current Of Phase A With Different Value Of Krc. (A) Krc D 0:15. (B) Krc D 0:30. (C) Krc D 0:45.

 

CONCLUSION:

 In order to improve the harmonic compensation performance of APF, command current prediction algorithm and dead-beat control strategy for current tracking are optimized in this article. The feasibility and effectiveness of the proposed method are verified by theoretical analysis, simulation, and experiment. The conclusions are as follows:

(1) The accuracy of command current prediction is the pre- requisite for optimizing the current tracking control strategy. Compared with the traditional command current repetitive prediction algorithm, the proposed one exhibits higher prediction accuracy and stronger adaptability to the fluctuation of grid frequency.

(2) Compared with the traditional deadbeat control, because the APF output current in the next sampling period has been estimated, the effective controlled frequency band of the control system is enlarged on the premise of ensuring system stability.

(3) When current tracking error repetitive correction is added into the improved deadbeat control channel, the periodic tracking error could be reduced to some extent, and the control accuracy is increased as well.

(4) The simulation and experiment results demonstrate that the proposed control method has a fine steady-state performance to grid frequency fluctuation and a satisfactory dynamic response to the sudden change of load current.

 REFERENCES:

[1] Y. Fang, J. Fei, and T. Wang, ``Adaptive backstepping fuzzy neural controller based on fuzzy sliding mode of active power filter,'' IEEE Access, vol. 8, pp. 96027_96035, Jun. 2020.

[2] J. Chen, H. Shao, Y. Cheng, X. Wang, G. Li, and C. Sun, ``Harmonic circulation and DC voltage instability mechanism of parallel-SVG system,'' IET Renew. Power Gener., vol. 14, no. 5, pp. 793_802, Apr. 2020.

[3] J. Fei and Y. Chu, ``Double hidden layer output feedback neural adaptive global sliding mode control of active power filter,'' IEEE Trans. Power Electron., vol. 35, no. 3, pp. 3069_3084, Mar. 2020.

[4] W. U. K. Tareen and S. Mekhielf, ``Three-phase transformerless shunt active power filter with reduced switch count for harmonic compensation in grid-connected applications,'' IEEE Trans. Power Electron., vol. 33, no. 6, pp. 4868_4881, Jun. 2018.

[5] Z.-X. Zou, K. Zhou, Z. Wang, and M. Cheng, ``Frequency-adaptive fractional-order repetitive control of shunt active power filters,'' IEEE Trans. Ind. Electron., vol. 62, no. 3, pp. 1659_1668, Mar. 2015.