A Single-Stage Active Damped LCL-Filter-Based Grid-Connected Photovoltaic Inverter With Maximum Power Point Tracking

A Single-Stage Active Damped LCL-Filter-Based Grid-Connected Photovoltaic Inverter With Maximum Power Point Tracking Sandeep N, Member, IEEE Research Scholar Department of Electrical Engineering NITK Surathkal, India sandeep.1991.in@ieee.org P S Kulkarni Associate Professor Department of Electrical Engineering VNIT Nagpur, India pskulkarni@eee.vnit.ac.in Udaykumar R Y, Member, IEEE Professor Department of Electrical Engineering NITK Surathkal, India udaykumarry@yahoo.com Abstract In this paper, a simple single-phase grid-connected photovoltaic (PV) inverter topology consisting of a three-level inverter, an LCL filter, and a new current feedback method for active damping is considered. A dynamically rapid method is used for tracking the maximum power point (MPP) of photovoltaic arrays, known as ripple correlation control. The algorithm uses the current and voltage low-frequency oscillations as the perturbation signals, which are introduced in the output of PV array due to the sinusoidal power being injected into the single-phase utility grid, to enable operation at MPP. The capacitor of the conventional LCL filter is split into two parts and the current flowing between these two parts is used as the feedback for regulation of grid current being injected. By doing so the V I transfer function of the grid connected inverter system degrades to first-order one from third order function. Due to which, wide control-loop bandwidth can be achieved with a large proportional control-loop gain ensuring good stability. Proportional-resonant (PR) current controller is suggested to provide power to the line with unity power factor and the PV inverter offers much less total harmonic distortion. The entire system has been numerically simulated in MATLAB/SIMULINK platform and the performance results are presented for variation in insolation levels and grid voltage profile showing the effectiveness of the proposed system. Index Terms Active damping, current control, grid-connected inverter, LCL-filter, new current feedback (NCF), PR controller. I. INTRODUCTION Increase of energy demand yields in an increased development of power distribution systems and concerns about the environmental conservation has led to the use of alternate energy sources in power generation that are cleaner and renewable [1]. Among the alternative sources Photovoltaic (PV) energy is presently considered to be one of the most useful natural energy sources since it is free, abundant, pollutionfree and distributed throughout the earth. In a single-stage grid connected PV system, inverter acts as the power conditioning system (PCS) to have a controlled power flow between the PV panels and the single-phase grid. The efficiency of energy conversion of PV panel is low, since it depends on many factors such as insolation, temperature, dirt, shadow and so on. So in order to maximize the efficiency of energy conversion the PCS must keep the operating point of the PV source close to MPP. This can be achieved by employing a suitable maximum power point tracking (MPPT) algorithm which keeps the power extracted from the PV source at MPP. Ripple correlation control MPPT exploits the voltage and current oscillations caused due the pulsation of the sinusoidal power being injected into the grid for tracking MPPT [2] - [3]. The MPPT algorithm varies the dc link reference voltage according to the environmental conditions in order to extract maximum power from the PV panels. When connecting the PV inverter to the utility grid, either a L or LCL filter can be used as the interfacing stage. The LCL filter is more attractive than L filter since it can provide higher high-frequency harmonic attenuation with the same inductance value. System with LCL filter is of order three, which may cause the instability of the current controller if not designed properly due to inherent resonance peak of the filter. To address this stability problem active or passive damping methods have been applied by the researchers [4]. A proportional-integral (PI) controller for the regulation of grid current has the following drawbacks: inability to track a sinusoidal reference without steady-state error and poor disturbance rejection capability due to the limited loop gain for system stability at LCL resonance frequency [5]. A PR controller introduces an infinite gain at the grid frequency which eliminates the steady state error and serves as a better solution to grid current control [6]. Passive damping is most widely used for maintain system stability, however it results in increased cost, losses and degrades the filter performance. In this paper principle of active damping is first presented and applied to single-phase single-stage grid connected PV system with LCL filter. The capacitor of LCL-filter is split into two parts and the current flowing between these two parts is used as the feedback of a current controller [7]. Ripple correlation control algorithm is used for tracking the MPP. Design of MPPT and PR controller is presented. The transient response of the proposed system for various grid disturbances and change in insolation levels is presented to demonstrate the viability of the control strategy. The characteristics of the PV inverter system with the LCL controller and RCC 978-1-4799-5141-3/14/$31.00 c 2014 IEEE

Fig. 1. Single-phase single-stage grid connected LCL type inverter based on active damping. Schematic diagram Block diagram model. MPPT are investigated and compared with the traditional grid current feedback strategy. The analysis and design of the proposed system has been successfully demonstrated through the MATLAB/SIMULINK simulation. II. S YSTEM S TRUCTURE AND C HARACTERISTICS Fig. 1 shows the topology of 60 Wp single-phase grid connected PV inverter system. An LCL is used as an interface between grid and the inverter. Compared with an L filter, an LCL filter can bypass the high-frequency harmonics through an additional capacitor branch. The selection of the parameters depends upon the dominant harmonics nearer to the switching frequencies. The various transfer functions for the system can be derived as follows Z1 = L1 s + R1 (1) Z2 = L2 s + R2 (2) 1. (3) Cs Where L1 is the inverter side inductance L2 is the grid side inductance of the filter and R1, R2 are their equivalent series resistors (ESR) and C is the capacitance of the LCLfilter. Fig. 2 shows the conventional feedback technique which uses the grid current as the feedback parameter. Considering L = L1 + L2, α = L1 /L and neglecting the ESR of the filter inductors the transfer function for the grid current and the inverter output voltage can be derived as follows: Fig. 2. Block diagram of conventional current feedback scheme. Zo = Fig. 3. Bode plot of undamped LCL filter. (4) damping method is more attractive and the transfer function of the LCL filter with Rd in series with C as the passive damping resistance is given as The characteristics of the filter for different parameters are demonstrated using the bode plots as shown in Fig. 3. From the figures it can be inferred that as the filter is of third order there exists a peak amplitude response at the resonant frequency of the LCL filter, a more careful design of LCL-filter parameters and current control strategy is required to maintain system stability. Due to the simplicity and the cost the passive I2 (s) Rd Cs + 1 =. Vinv (s) L1 L2 Cs3 + (L1 + L2 )CRd s2 + (L1 + L2 )s (5) The filter response with passive damping (Rd = 1.5Ω) and for different filter parameters are as shown in Fig. 4. The output voltage of the PV inverter is controlled in a manner to inject sinusoidal current into the grid irrespective I2 (s) 1 =. Vinv (s) α(1 α)l2 Cs3 + Ls

current controller. Assuming C 1 = βc and C 2 = (1 β)c then the current i 12 between the two capacitors is given as i 12 = i 2 + (1 β)i C (7) Fig. 4. Bode plot of LCL filter with passive damping. of the grid disturbances which is taken care by the grid synchronizer. The amplitude of the reference current to be injected is generated by the dc link voltage controller on the basis of error between V mpp,ref and V pv. The MPPT controller varies the V mpp,ref according to the environmental conditions in order to keep the power drawn from the panels near point of maximum power. The basic principle of the RCC MPPT algorithm is to exploit the oscillations present in the voltage and current due to the pulsation of the power being injected into grid which are inherent in power converter. which provides information about the power slope and evaluate if the PV system operates close to the maximum power point. The variation of V pv can be related to active power P, grid frequency ω and dc link capacitor C dc by the following relationship P ω = C dc(vpv,max 2 V 2 III. CONTROL DESIGN OF SINGLE PHASE GRID CONNECTED VSI A. Conventional Control Scheme. pv,min). (6) Conventionally, the grid current is used as a feedback of the current controller to regulate the current injected into the grid. Fig. 2 shows one of the conventional current feedback schemes. Where, Ig is the grid current reference, G i (s) is the proportional-resonant (PR) current regulator, G inv (s) is the transfer function of the inverter bridge, which is modeled as a first order lag system with time constant equal to 1.5 times the switching period. G V I (s) is the transfer function of passive damped LCL filter as given in (5). As Compared to PI compensator, PR compensator can provide larger gain at the fundamental frequency to eliminate the steady state error. The proportional gain of the PR controller is limited by the peak due to the peak amplitude existing at the resonant frequency of the filter. By the use of passive damping this peak can be reduced with the cost of increased power losses and hence with low value of R d, however the control loop gain for the traditional scheme is quite small leading to steady state error. B. New Current feedback Scheme. The capacitor C is split into two parts and the current flowing between them are used as the feedback current for the or i 12 = (1 β)i 1 + βi 2. (8) Where i C is the total currents of filter capacitor and the current i 12 is the weighted average of the inverter current and the grid current. The transfer function for V inv and i 12 can be derived as follows I 12 (s) V inv (s) = (1 β)(1 α)lcs2 + 1 α(1 α)l 2 Cs 3 + Ls. (9) Considering β = (1 α) the capacitor C 1 can be expressed as C 1 = (1 L 1 )C. (10) L By substituting (10) in (9) the transfer function degrades from third order to first order I 12 (s) V inv (s) = 1 Ls. (11) Considering the ESRs of inductor in LCL filter the transfer function becomes I 12 (s) V inv (s) = 1. (12) Ls + R 1 + R 2 C. Design of PR Current Regulator. The merits of the NCF scheme can be demonstrated by a comparison of current controller designs for the system. There are three major output current control techniques for the single phase VSI: hysteresis band, predictive and sinusoidal pulse width modulation (SPWM) control. The traditional method of SPWM control uses a PI compensator in the feedback loop to regulate the output current. However, while PI compensators have excellent performances on regulating DC quantities, tracking a sinusoidal current reference would lead to steady state magnitude and phase errors. Using the PR controllers, the converter reference tracking performance can be enhanced and shortcomings associated with conventional PI controllers can be alleviated. The bode plots of the loop transfer function under conventional control scheme is shown in the Fig. 5. The structure of the PR controller is as follows 2K ir ω o ξs G i (s) = K pr + s 2 + 2ω o ξs + ωo 2. (13) The primary design guide for the inverter output filter is to make the magnitude of the major harmonic current of the inverter less than 0.3% of the rated current. LCL filter values are chosen based on these guidelines. The values of the controller parameters for both conventional current feedback scheme and NCF scheme are listed in Table I. The loop gain

TABLE I C OMPARISON OF C ONTROL D ESIGN PERFORMANCE FOR T WO C ASES OF C URRENT C ONTROLLER VALUES Case Kpr Kir 1 2 6 10 100 100 Conventional feedback NCF scheme Loop gain@50hz (db) Bandwidth (Hz) Loop gain@50hz (db) Bandwidth (Hz) 47 49 769 1250 50 53 1970 2300 Fig. 5. Bode plot of passive damped inner current loop with conventional current feedback for various controller parameters. Fig. 6. Bode plot of inner current loop with NCF scheme for the case of different current controller parameters. at fundamental grid frequency and the crossover frequency are also tabulated. All the control schemes have a phase margin more than 450, but the proportional gains of the PR regulators are quite different to maintain the system stability. The ESRs of inductor in LCL is considered to be 0.1 Ω. Fig. 6 shows the bode plots of the loop transfer function under NCF scheme for the same controller parameters. From the Table I, it is clear that the the loop gain and the cross-over frequency with new control strategy is much higher than those with conventional control strategies, resulting in minor steady-state error and a better dynamic response in close-loop control. Fig. 7. Block diagram of outer voltage loop. D. Design of Voltage Controller. In general using electrolytic capacitors are less desirable for their short operational lifetime. Hence Long lifetime film capacitors serves as a substitute, however their high prices limit the size that can be used in PV inverters. This causes a significant double line frequency ripple on the DC link voltage which may further couple through the control loop. Therefore a band stop filter is placed on the dc voltage feedback loop to attenuate the ripple. A simple PI controller is used as a voltage controller Gv (s) to regulate the dc link voltage [3]. The value of the proportional gain of the voltage controller is selected such that the closed loop bandwidth of the voltage control loop is about 1/150th of the closed current loop [8]. Fig. 7 shows the Bode plot of the voltage control loop with and without voltage controller. The proportional gain of the PI controller is tuned based on the stability of the closed loop and the integral gain is tuned to set the gain crossover frequency or the bandwidth. E. Ripple Correlation Control MPPT. The objective of MPPT is to extract the maximum power from PV panel. The condition p/ v = 0 is adopted to track the peak power point since power-voltage characteristics of PV panel shows unique global peak power point. The basic principle of RCC MPPT algorithm is to estimate the voltage corresponding to maximum power point by exploiting the module voltage and current ripples which are inherent in power electronic converters. It correlates the module voltage and power in order to determine whether V is above or below Vmpp. dv dp > 0 V < Vmpp dt dt (14)

TABLE II ELECTRICAL SPECIFICATIONS OF MSX-60 PV MODULE Parameter Symbol Values Peak power P max 60 W Peak power voltage V mpp 17.1 V Current at peak power I mpp 3.5 A Short circuit current I sc 3.8 A Open circuit voltage V oc 21.1 V Solar irradiation S 1000 W/m 2 Fig. 8. Block diagram of RCC-MPPT and V mpp,ref generator. dv dp dt dt < 0 V > V mpp. (15) Ripple present in power and voltage can extracted by subtracting average value of signal over a period T from the signal as shown below ṽ(t) = v(t) 1 T p(t) = p(t) 1 T T 0 T 0 v(t)dt (16) p(t)dt. (17) Considering the frequency of ripple is known, a filtering approach can be employed to extract the ripple content in voltage and power. High-pass filters are used as an approximation of the (17) and (18) and the cutoff frequency of the filter must be higher than the switching frequency in order to eliminate the switching frequency components and electromagnetic inference problems. The block diagram of RCC MPPT is shown in Fig. 8. A hysteresis comparator with a small band of values around zero is used to extract the sign of p/ v. An integral controller is used to eliminate the steady state error in the estimation of V mpp, whose gain (k) is tuned according to the requirement of speed and trajectory of convergence. IV. SIMULATION RESULTS To examine the performance of the designed system simulation studies of the single phase grid connected PV system with conventional feedback and NCF scheme are carried out on MATLAB/SIMULINK platform. The specifications for the solar module used in the simulations study are provided in Table II. The parameters of the grid connected PV inverter system and the values of the control parameters are as shown in Table III. The grid connected PV inverter system subjected to a step change in irradiation level which is changed from 1000 W/m 2 to 600 W/m 2 at t = 2 s and reverted to 800 W/m 2 at t = 3 s. The temperature of the array is considered to be constant (25 0 C) during the simulation. The variation in the PV panel power, current and dc link voltage are shown in Fig. 9. Fig. 10 and Fig. 11 show the TABLE III PV INVERTER PARAMETERS Parameter Symbol Values Grid voltage(rms),frequency V g, f g 10 V, 50 Hz Rated output current(rms) I g 6 A DC link capacitor C dc 3300 µf Grid side inductor L 2 0.6 mh Inverter side inductor L 1 0.6 mh Filter capacitor C f 2 µf Filter damping resistor R d 1.5 Ω Switching frequency f sw 10 khz Damping ratio of current controller ξ 0.01 Proportional gain of voltage controller k p 0.5 Integral gain of voltage controller k i 5 (c) Fig. 9. Simulation results for step change in irradiation levels: Power Current (c) voltage.

Fig. 10. Steady-state response of the grid current with NCF scheme. Fig. 12. Simulation results emulating weak grid situation: with conventional feedback scheme with NCF scheme. Fig. 11. Simulation results for step change in irradiation levels: with conventional feedback scheme with NCF scheme. steady state and transient response of grid current for change in insolation levels. From the results it is seen that the response time with NCF scheme is lesser by 6 cycles over conventional feedback strategy. The %THD in grid current with weak grid voltage situation is shown in Fig. 12. It is seen that with the NCF scheme the %THD in the injected current is improved as compared to conventional feedback scheme. V. C ONCLUSION In this paper the application of NCF scheme and conventional grid current feedback scheme for single-phase grid connected PV system has been presented. The characteristics and design method of the injected grid current regulator and voltage controller for both passive and active damping of the LCL-type filter has been presented. With the NCF scheme the inverter control system degrades from third order to first order, which allows one to increase the loop gain and bandwidth making the system steady state error minimum with reduced harmonic distortion. With RCC-MPPT operating point converges asymptotically at maximum speed to the maximum power point. Simulation results for both steady state and dynamic conditions have been presented and it shows that the current injected into the grid is in-phase with grid voltage even under weak grid situation and varying environmental conditions. The results show good performance of the control system and confirm the viability and effectiveness of the control design of PV generation system for any operating condition. Future work is aimed at developing hardware prototype of the proposed system. R EFERENCES [1] F. Blaabjerg, R. Teodorescu, and M. Liserre, Overview of control and grid synchronization for distributed power generation systems, IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1398 1409, Oct. 2006. [2] D. Casadei, G. Grandi, and C. Rossi, Single-phase single-stage photovoltaic generation system based on a ripple correlation control maximum power point tracking, IEEE Trans. Energy. Convers., vol. 21, no. 2, pp. 562 568, Jun. 1999. [3] N. Sandeep, M. K. Murthy, and P. S. Kulkarni, Single-phase gridconnected photovoltaic system based on ripple correlation control maximum power point tracking, in Electrical, Electronics and Computer Science (SCEECS), 2014 IEEE Students Conference on, March 2014, pp. 1 6. [4] W. Wu, T. T. Y. He, and F. Blaabjerg, New design method for the passive damped lcl and llcl filter-based single-phase grid- tied inverter, IEEE Trans. Ind. Electron., vol. 60, no. 10, pp. 4339 4350, Oct. 2013. [5] R. Teodorescu, F. Blaabjerg, M. Liserre, and P. Loh, Proportionalresonant controllers and filters for grid-connected voltage-source converters, Electric Power Applications, IEE Proceedings, vol. 153, no. 5, pp. 750 762, Sep. 2006. [6] G. Shen, X. Zhu, J. Zhang, and D. Xu, New feedback method for pr current control of lcl-filter-based grid-connected inverter, IEEE Trans. Ind. Electron., vol. 149, no. 6, pp. 449 458, Nov. 2002. [7] G. Shen, D. Xu, L. Cao, and X. Zhu, An improved control stratergy for grid-connected voltage sorce inverters with an lcl filter, IEEE Trans. Power. Electron., vol. 23, no. 4, pp. 1899 1906, Jul. 2008. [8] A. Dell Aquila, V. M. M. Liserre, and P. Rotondo, Overview of pi-based solutions for the control of dc buses of a single-phase hbridge multilevel active rectifier, IEEE Trans. Ind. Appl., vol. 44, no. 3, pp. 857 866, Jun. 2008.