ISSN Vol.08,Issue.18, October-2016, Pages:

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1 ISSN Vol.08,Issue.18, October-2016, Pages: Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters SWAPNIL BALASAHEB VADER 1, G SATISH GOUD 2, S. RAJESH 3 1 PG Scholar, Dept of EEE, Siddhartha Institute of Engineering & Technology, Ibrahimpatnam, Hyderabad, Telangana, India. 2 Asst. Professor, Dept of EEE, Siddhartha Institute of Engineering & Technology, Ibrahimpatnam, Hyderabad, Telangana, India. 3 Associate Professor, Dept of EEE, Siddhartha Institute of Engineering & Technology, Ibrahimpatnam, Hyderabad, Telangana, India. Abstract: Active power filter (APF) has been proved as a flexible solution for compensating the harmonic distortion caused by nonlinear loads in power distribution power systems. Digital repetitive control can achieve zero steadystate error tracking of any periodic signal while the sampling points within one repetitive cycle must be a known integer. However, the compensation performance of the APF would be degradation when the grid frequency varies. In this paper, an improved repetitive control scheme with frequency adaptive capability is presented to track any periodic signal with variable grid frequency, where the variable delay items caused by time-varying grid frequency are approximated with Pade approximants. Additionally, the stability criterion of proposed repetitive control scheme is given. A threephase shunt APF experimental platform with proposed repetitive control scheme is built in our laboratory. Simulation and experimental results demonstrate the effectiveness of the proposed repetitive control scheme. Keywords: Active Power Filter (APF), Fractional Order, Frequency Variation, Repetitive Control (RC). I. INTRODUCTION Power quality has become a serious concern in power distribution power system due to harmonic currents pollution caused by various nonlinear loads such as adjustable speed drives, arc furnaces and other power electronic-related devices. These harmonic currents increase the power losses, deteriorate the quality of the voltage waveform, and may cause resonance problem. Active power filter (APF) that operates as controllable current sources and provides fast dynamic response to load variations has been widely used to suppress the harmonic current produced by nonlinear loads. APF has been proved to be a flexible solution to suppress the harmonic currents due to its simplicity and effectiveness. The key technology of the APF system is tracking of the periodic reference signals. To solve this issue, numerous current control strategies have been introduced, such as hysteresis control, proportional-integral (PI) control, proportional-resonant (PR) control, repetitive control, etc. PI control has good tracking capability for DC and lowfrequency signals. However, the reference signals are composed of many frequency components (fundamental and its multiples) in APF. The PI control is not an optimum 2016 IJATIR. All rights reserved. solution for APF, due to the limitation of control bandwidth and the adverse effect of delay time. Repetitive control technique, based on internal model principle (IMP), is particularly suitable for this situation since it introduces infinite gains at the interested harmonic frequencies. The composite control strategy combing repetitive control with PI feedback control is an effective approach for APF. PI controller is utilized to enhance the dynamic response to the load variations. Repetitive controller is adopted to improve the steady-state accuracy. The faster dynamic performance of PI controller will not be affected by the slower repetitive controller. Nowadays, this control structure has been widely adopted in power electronic related equipments, such as uninterruptible power supply (UPS) systems, unity power factor rectifiers, Pulse-Width Modulation (PWM) inverters and distributed generation. In repetitive control, the signal generator z -N /1-z -N must be included. N = f s / f is the order of the repetitive controller, f s is the sampling rate; f is the fundamental frequency of the reference signal. Repetitive control can achieve zero steady-state error tracking of any periodic reference signals when N is a known integer. However, the grid frequency is time-varying within a certain range, for instance 49.5~50.5Hz. The order of repetitive control often contains a decimal at a fixed sampling rate. Therefore, the compensation performance of APF would have a great recession when conventional repetitive control technology is employed. Ensuring the N keeps a known integer in the presence of grid frequency variations, several approaches have been introduced to solve this problem. These solutions could be divided into two groups: fixed sampling rates and variable sampling rates. Variable sampling rates can keep the constant sampling points within one repetitive control cycle by adjusting the changed sampling period with the grid frequency variations. However, the discrete control plant model would change with the sampling period varies. In the literatures, authors introduce a special designed finite impulse response (FIR) filter, which is cascaded with a traditional delay time item, to replace the conventional low-pass filter (LPF) with function for system stabilization.

2 In the literatures, the fractional-order filter is approximated by a Lagrange Interpolation method with an integer number. Their coefficients can be easily updated online. However, this method need higher order approximants to maintain repetitive control open-loop gains without attenuation. In the literature, authors used Pade approximants to approximate the fractional delay item in repetitive control. This paper presents an improved repetitive control scheme with frequency adaptive capability to enhance the steady-state compensation accuracy. The variable-delay items in repetitive controller are approximated by using Pade approximants. Their coefficients can be earlier updated online and the nominal part keeps a constant. So, the proposed control scheme can track any periodic signal with variable grid frequency. A shunt APF experimental system is built in our laboratory. Various simulation and experimental results demonstrate the feasibility and effectiveness of the proposed repetitive control scheme. II. THREE-PHASE SHUNT APF WITH FREQUENCY ADAPTIVE CAPABILITY A. Problem description Fig.1. Three-phase shunt APF: (a) Circuit structure of shunt APF with LCL filter; (b) Block diagram of the proposed control scheme; (c) The implementation of proposed repetitive controller in DSP. SWAPNIL BALASAHEB VADER, G SATISH GOUD, S. RAJESH A complete system circuit structure of three-phase shunt APF with LCL output filter is illustrated in Fig. 1(a). The shunt APF operates as a controllable current source parallel with nonlinear diode rectifier loads connected at the point common coupling (PCC). The subscript k denotes phase a, b and c. u sk is the grid voltage, u k is the voltage at the PCC, the system inductance L s is normally neglected due to its low value relatively, thus u sk = u k. i sk, i lk and i fk are the grid, load and converter current of each phase. L ff is the converter-side filter inductors, L gf is the grid-side filter inductors, C f is the filter capacitors, and R d is the damping resistors. C and V dc are the dc-link capacitor and voltage, respectively. Fig. 1(b) shows the block diagram of the proposed control scheme with frequency adaptive capability for three-phase shunt APF. The control system contains a phase-locked loop (PLL), a dc-link voltage regulator with PI control, a reference current calculator and the proposed current controller. The PLL is used to produce the phase information q of the grid voltage and the ratio N of the sampling frequency to the grid frequency. The dc-link voltage regulator forces the dc-link voltage V dc to track the reference voltage V dcref. The reference current calculator detects the harmonic components of grid currents and produces reference current signals. The proposed current controller with grid voltage feed-forward and output current feedback cross decoupling is shown in Fig. 1(b). The implementation of proposed repetitive controller in DSP is shown in Fig. 1 (c), where e(cur) is the current error, e(cur -1) is the error of last control period, e 1 (cur) is the error of last time delay period, u r1 (cur) is the repetitive error of last time delay period, u r (cur) is the output of repetitive controller. The register array is updated after calculation of current control period. B. PLL In the proposed repetitive control scheme, the time delay coefficient d is updated online relying on the real-time grid frequency, which is measured by PLL. The accuracy of the PLL, as shown in Fig. 1(b), will affect the performance of the control system. Therefore, the output error of the PLL should be as small as possible. The bandwidth is much slower than the inner current loop and is much faster than the grid frequency. The coefficient d will change only a very little bite and can be treated as constant within a control period, so the proposed repetitive control scheme can be analysis in stability. In practical application, the grid voltage is not pure sinusoidal, which may affect the output accuracy of the PLL. To overcome this problem, a low pass filter (LPF) is introduced to make its output contains only dc component, which is used as the input of the PLL. The PLL is calculated at the sampling rate, for example 9.6 khz. In this paper, a first-order Pade approximants is chosen, which means that only two coefficients need to be calculated online. It will just take a little time for the 144 MHz DSP. III. EXPERIMENTAL VALIDATION A. Experimental Setup To validate above theoretical analysis, a dspace based single-phase shunt system has been built in our

3 Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters laboratory. The grid voltage is generated by a programmable ac power source. The system parameter values are listed in Table I. The phase-lead compensation filter G f (z) = z 2 is employed. The bandwidth for LPF Q(z) = 0.1z z 1 and the FD filter are about 1630 and 1875 Hz, respectively, and enable FORC to efficiently compensate up to the 30thorder current harmonics. Table.1. SYSTEM PARAMETERS that, if fundamental frequency changes from 50 to 50 ± 0.2 Hz, CRC cannot exactly compensate harmonic frequencies of (50 ± 0.2)n Hz (n = 1, 2,...) due to its low gains at these frequencies. That means CRC is sensitive to grid frequency variations. With listed parameters, the DB controller for the shunt APF can be given as follows: u c (k) = v g (k) (i ref (k) i c (k)). (1) Assuming that L t = L+ΔL is the actual inductance of the filter inductor with ΔL being the uncertainty inductance and L being the nominal inductance, the transfer function of the DB-controlled current loop without plug-in FORC will change from H(z) = z 1 to Ht(z) = ic(z) = L iref (z) Ltz ΔL (2) Fig.2. Magnitude response of the FD filters and the LPF Q(z). As two examples, when the grid frequency changes from 50 to 50 ± 0.2 Hz in the case of a fixed sampling frequency of 5 khz, i.e., the period N will change from integer N = 100 to fractional N = 100 ± 0.4. The magnitude-frequency responses of Q(z) and FD filters of z 99.6 and z are plotted in Fig. 2. Bode diagrams for CRC (N = 100) and FORC with FD filters of z 99.6 and z are shown in Fig. 3. It can be noted that, both CRC and FORC have expected large gains at their harmonic frequencies of 50n and (50 ± 0.2)n Hz (n = 1, 2,...), respectively. Moreover, the phase shifts at these interested frequencies are zero. Fig. 3 indicates Fig.3. Bode diagrams of CRC, FORC with N = and 99.6 within (a) low frequency band and (b) neighboring frequency band around seventh-order harmonics. Fig. 4(a) shows the pole map of H t (z) with the parameter uncertainty. Fig. 4(b) shows the amplitude of the stability criteria for the DB-plus-plug-in-FORC-controlled current loop. It is seen that, if inductance uncertainty ΔL 0.5L and k r < 1.4, DB-plus-FORC-controlled current loop is stable.

4 SWAPNIL BALASAHEB VADER, G SATISH GOUD, S. RAJESH Fig.5. Steady-state responses at 50 Hz without an APF. (a) Grid voltage vg and grid current i g. (b) Harmonic spectrum of v g. (c) Harmonic spectrum of i g. B. Experimental Results Fig.5 shows the steady-state responses of the system without an APF under grid frequency of 50 Hz: the grid voltage v g and the grid current i g, the harmonic spectrum of v g, and the harmonic spectrum of i g. Fig.4. Robustness analysis. (a) Pole map of H t (z). (b) Amplitude of stability criteria. Fig.6. Steady-state responses at 50 Hz with a CRCcontrolled (b) Harmonic spectrum of compensated i g. Fig. 6 shows the steady-state responses of the system with a CRC-controlled APF (i.e., FORC with F = 0) under grid frequency of 50 Hz: grid voltage v g and the grid current i g, and the harmonic spectrum of i g, where the period of N = 100. Figs. 5 and 6 indicate that the CRC-controlled APF

5 Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters efficiently reduce the total harmonic distortion (THD) of the grid current i g from 44.15% to 3.719% under integer period grid voltage v g with THD of 2.41%. Fig.7 shows the steadystate responses of the system with a CRC-controlled APF under grid frequency of 49.8 Hz: grid voltage v g and the grid current i g, the current tracking error of the compensation current i c, and the harmonic spectrum of i g. Fig.8 shows the steady-state responses of the system with a FORC-controlled APF under grid frequency of 49.8 Hz: grid voltage v g and the grid current i g, the current tracking error of the compensation current i c, and the harmonic spectrum of i g, where N = Fig.8. Steady-state responses at 49.8 Hz with a FORCcontrolled (b) Compensation current i c, reference current i ref, and current tracking error. (c) Harmonic spectrum of i g. Fig.7. Steady-state responses at 49.8 Hz with a CRCcontrolled (b) Compensation current i c, reference current i ref, and current tracking error. (c) Harmonic spectrum of i g. Figs. 7 and 8 indicate that, in the case of fractional period grid voltage, the grid current i g compensated by the CRCcontrolled APF contains considerable THD(= 7.179%), and FORC enables the APF to provide much better quality sinusoidal grid current with THD = 2.987%. Figs. 7(b) and 8(b) indicate that FORC offers much better control accuracy in the case of fractional period grid voltage. Fig. 9 shows the steady-state responses of the system with a CRC-controlled APF under grid frequency of 50.2 Hz: grid voltage v g and the grid current i g, the current tracking error of the compensation current i c, and the harmonic spectrum of i g. Fig. 10 shows the steady-state responses of the system with a FORC-controlled APF under grid frequency of 50.2 Hz: grid voltage v g and the grid current i g, the current tracking error of the compensation current i c, and the harmonic spectrum of i g, where N = Figs. 9 and 10 indicate that, in the case of fractional period grid voltage, the grid current i g compensated by a CRCcontrolled APF contains considerable THD(= 8.749%), and FORC enables the APF to provide much better quality sinusoidal grid current with THD = 2.795%. Figs. 9(b) and 10(b) indicate that FORC offers much better control accuracy in the case of fractional period grid voltage.

6 SWAPNIL BALASAHEB VADER, G SATISH GOUD, S. RAJESH and the grid current i g compensated by a FORC-controlled APF is immune to the step grid frequency in these cases. Therefore, Fig. 11 implies that, Fig.9. Steady-state responses at 50.2 Hz with a CRCcontrolled (b) Compensation current i c, reference current i ref, and current tracking error. (c) Harmonic spectrum of i g. Table II lists the experimental THD data of steady-state compensated grid current ig under grid frequency from 49.5 to 50.5 Hz. The THD data in Table II indicates that, in the cases of various grid frequencies, the FORC-controlled APF offers very good current harmonics compensation capacity, whereas the CRC-controlled APF fails to provide satisfactory current harmonics compensation capacity. Generally speaking, Figs and Table II show that CRC is sensitive to grid frequency variations, whereas FORC is not. Fig. 11 shows the transient responses of the system with a FORC-controlled APF to step changes of grid frequency between 49.5 and 50.5 Hz: grid voltage v g and the grid current i g, and the PLL detected grid frequency f. Fig. 11 indicates it takes FLL-based PLL about 50 ms (i.e., the settling time) to detect the step changes of grid frequency, Fig.10. Steady-state responses at 50.2 Hz with a CRCcontrolled (b) Compensation current i c, reference current i ref, and current tracking error. (c) Harmonic spectrum of i g. TABLE II : PERFORMANCE UNDER DIFFERENT FUNDAMENTAL FREQUENCIES

7 Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters for the FORC-controlled shunt APF with a sufficiently large fundamental period N, the upper bound for system robustness to grid frequency disturbances is actually determined by the operation frequency range of PLL since the tuning rate of the proposed FORC is much faster than the transient response of PLL. Fig.12. Responses to step load changes at 49.8-Hz fundamental frequency. (a) R15Ω 30Ω, (b) R30Ω 15Ω. IV. SIMULATION RESULTS Fig.11. Responses to step changes of grid frequency. (a) 49.5 Hz 50.5 Hz. (b) 50.5 Hz 49.5 Hz. Fig. 12 shows the transient responses to step load changes between rectifier resistor R = 15Ω and R = 30Ω: dc bus voltage vdc, the load current i L, and the grid current i g. It is seen that the FORC-controlled APF maintains a sinusoidal line current even during the step load change. The recovery time of dc bus voltage in both two cases is about 250 ms. The dynamic responses of FORC are promising. Fig. 7. Simulation design of proposed system Fig. 8. Voltage and current waveforms of grid side

8 The proposed frequency-adaptive fractional-order repetitive control of shunt active power filters and its control circuit is implemented using MATLAB/SIMULINK. Fig. 7 shows the simulation model of the proposed system. Voltage and current waveforms of grid side of the proposed system is shown in Fig.8. Harmonic spectrum of vg is shown in Fig. 9. The simulation waveforms are in good agreement with the theoretical analysis. Fig.9. Harmonic Spectrum of vg. IV. CONCLUSION In this paper, an improved repetitive control scheme with frequency adaptive capability for three-phase shunt APF has been presented. The variable-delay items in repetitive control are approximated by Pade approximants. The proposed repetitive control scheme can achieve zero steady-state error tracking of any periodic signal with variable grid frequency at the fixed sampling rate. The criteria of stability proposed repetitive control system is given, which is similar to the conventional repetitive control system. Simulation and experimental results demonstrated that the proposed repetitive control scheme is an effective solution to improve the tracking performance and reduce the harmonic distortion during grid frequency variation. V. REFERENCES [1] Zhi-Xiang Zou, Student Member, IEEE, Keliang Zhou, Senior Member, IEEE, Zheng Wang, Member, IEEE, and Ming Cheng, Senior Member, IEEE, Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters, IEEE Transactions on Industrial Electronics, Vol. 62, No. 3, March [2] H. Akagi, New trends in active filters for power conditioning, IEEE Trans. Ind. Appl., vol. 32, no. 6, pp , Nov./Dec [3] H. Akagi, Active harmonic filters, Proc. IEEE, vol. 93, no. 12, pp , Dec [4] Y. Han et al., Robust deadbeat control scheme for a hybrid APF with resetting filter and ADALINE-based harmonic estimation algorithm, IEEE Trans. Ind. Electron., vol. 58, no. 9, pp , Sep [5] M. Angulo, D. A. Ruiz-Caballero, J. Lago, M. L. Heldwein, and S. A. Mussa, Active power filter control strategy with implicit closed loop current control and SWAPNIL BALASAHEB VADER, G SATISH GOUD, S. RAJESH resonant controller, IEEE Trans. Ind. Electron., vol. 60, no. 7, pp , Jul [6] P. Mattavelli and F. P. Marafao, Repetitive-based control for selective harmonic compensation in active power filters, IEEE Trans. Ind. Electron., vol. 51, no. 5, pp , Oct [7] L. R. Limongi, R. Bojoi, G. Griva, and A. Tenconi, Digital current control schemes, IEEE Ind. Electron. Mag., vol. 3, no. 1, pp , Mar [8] A. D. Le Roux, H. Mouton, and H. Akagi, DFT-based repetitive control of a series active filter integrated with a 12- pulse diode rectifier, IEEE Trans. Power Electron., vol. 24, no. 6, pp , Jun [9] K. Zhou et al., Zero-phase odd-harmonic repetitive controller for a single-phase PWM inverter, IEEE Trans. Power Electron., vol. 21, no. 1, pp , Jan [10] P. C. Loh, Y. Tang, F. Blaabjerg, and P. Wang, Mixedframe and stationary-frame repetitive control schemes for compensating typical load and grid harmonics, IET Power Electron., vol. 4, no. 2, pp , Feb [11] D. Chen, J. Zhang, and Z. Qian, An improved repetitive control scheme for grid-connected inverter with frequency-adaptive capability, IEEE Trans. Ind. Electron., vol. 60, no. 2, pp , Feb [12] M. Rashed, C. Klumpner, and G. Asher, Repetitive and resonant control for a single-phase grid-connected hybrid cascaded multilevel converter, IEEE Trans. Power Electron., vol. 28, no. 5, pp , May Author s Profile: Swapnil Balasaheb Vader, received the B.E degree in Electrical Engineering from Jayan T Rao Sawant College of Engineering Pune University, India. Presently he is pursuing his M.Tech in Electrical Power Systems from Siddhartha Institute of Engineering and Technology, JNTU Hyderabad, Telangana India. G. Sathish Goud has received his B.Tech degree in Electrical and Electronics Engineering from JNTUH, Hyderabad, India and M.Tech degree in electrical power systems from JNTU Hyderabad.India.He is life member of Indian Society for Technical Education. Presently He is working as Assistant Professor In Siddhartha Institute of Engineering & Technology; Hyderabad. His is doing currently research in Fuzzy Logic Controllers, ANN and electrical power systems power electronics & drive. S. Rajesh received M.Tech degree in Power Electronics from Jawaharlal Nehru Technological University Hyderabad, Telangana, India in 2010 respectively. He has presented nearly 5 papers in National level conferences. His research interests are power electronics applications in distributed power generation and analysis of power

9 Frequency-Adaptive Fractional-Order Repetitive Control of Shunt Active Power Filters converters, control and estimation in induction motor drive and wind turbine driven induction generator. Currently he is working on stability studies of Double Fed Induction Generator in Wind power Generation. He is a Student member of IEEE and life Member of ISTE (India). He currently serving as Associate Professor & Head of the Department of Electrical and Electronics engineering in Siddhartha institute of engineering and Technology Hyderabad, Telangana, India. He has 8 years experience in teaching.