Two Degrees of Freedom Active Damping Technique for - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 6, JUNE 2014

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Two Degrees of Freedom Active Damping Technique for LCL Filter-Based Grid Connected PV Systems Moin Hanif, Member, IEEE, Vinod Khadkikar, Member, IEEE, Weidong Xiao, Member, IEEE, and James L. Kirtley, Jr., Fellow, IEEE

Abstract—In grid connected photovoltaic (PV) systems, lowpass filters are utilized to reduce injected current harmonics. LCL filters have recently drawn attention for PV system grid interfaces due to their small size and they have shown better attenuation to switching harmonics than simple L filters. However, the LCL filter causes resonance resulting in oscillation and instability issues. This paper proposes an effective active damping technique by introducing a two-degree-of-freedom (2DOF) PID control structure. The 2DOF control structure allows the independent action of PI and D terms giving two degrees of freedom. The design is based on a typical three-phase grid-tied PV system. The active damping control loop is formed by using the existing grid side inductor currents and thus eliminating the need of additional sensors. The relative stability is illustrated in frequency domain by using bode plots. A real-time hardware-in-loop study is performed to validate the performance of the proposed 2DOF technique to damp out the LCL filter resonance. Index Terms—Active damping, LCL filter, photovoltaic (PV) system and resonance damping.

I. I NTRODUCTION

C

ONCERNS related to the increasing costs of conventional energy, greenhouse gas emissions, and security of centralized power generations have forced the power industry to move toward a decentralized distributed generation (DG) system. These DG units are integrated into the low voltage (LV) power distribution systems and are used to deliver renewable and clean energy such as PV power, wind power, and fuel cell power to the utility through the interfacing inverters. Gridconnected DG systems come as pulse width modulated (PWM) voltage source inverters (VSIs) that can inject controlled active and reactive powers as required. Output currents of such an inverter need to be filtered to prevent the current harmonics around the switching frequency from entering the utility grid [1]. A third order LCL filter is preferred over an L or LC filter due to the 60 dB/decade attenuation of the frequencies above the resonance frequency and the reduction in physical Manuscript received November 23, 2012; revised February 18, 2013 and April 21, 2013; accepted June 24, 2013. Date of publication July 24, 2013; date of current version December 20, 2013. This work was supported by Masdar Institute of Science and Technology under MI-MIT grant (Award 10PAMA1). M. Hanif is with the Department of Electrical Engineering, University of Cape Town, Rondebosch 7701, South Africa (e-mail: [email protected]). V. Khadkikar and W. Xiao are with the Institute Center for Energy, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates (e-mail: [email protected]; [email protected]). J. L. Kirtley, Jr. is with the Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2274416

size of the inductor [2]. A small inductance in an LCL filter is effective, as the capacitor impedance is inversely proportional to the frequency of the current. The LCL filter exhibits first order inductive behavior to allow proper current control and high frequency rejection to guarantee proper filtering. However, an LCL filter can cause stability problems due to the undesired resonance caused by zero impedance at certain frequencies. To avoid this resonance from contaminating the system, several damping techniques have been proposed [1]–[14]. One way is to incorporate a physical passive element, such as, a resistor in series with the filter capacitor [3]. This passive technique, however, causes power loss in the added passive element and reduces the overall LCL-based system efficiency. A second approach is to modify the LCL inverter control structure such that the damping is achieved without any power loss [1], [2], [4]–[14]. An active damping control loop is introduced around the inverter to introduce a negative peak that compensates the positive peak caused by the presence of the LCL filter. In [13], a design procedure is given to optimize the LCL filter parameters that make the system stable at certain switching frequencies without implementing any passive damping. The active damping techniques in the literature [1], [2], [4]– [14] can broadly be categorized as techniques that either do [4]–[8] or do not require additional sensors [1], [2], [9]–[14]. In [4]–[6], the measured filter capacitor voltage is used as a feedback variable for active damping. Similarly, the measured filter current is used to form “virtual resistance” in [7] and [8]. An attempt is made to eliminate the capacitor voltage or current sensor by estimating either the capacitor voltage as in [1] and [9] or the capacitor current as in [10]. Such an estimation, however, depends on the accuracy of the plant model parameters, which, may be sometimes unknown or vary with temperature and/or system operating conditions. Another interesting approach, which is the main focus of this work, is to modify the inverter control structure so that the need for capacitor voltage or current information (either measurement or estimation) is eliminated. Liserre et al. have proposed a sensorless technique utilizing high order digital filters in the forward path of inverter current control loop [2], [11]. The performance of this technique is further evaluated in [12]. It is noticed from [2], [11], [12] that a tuning method (such as genetic algorithm which adds complexity) may be required to tune such high order digital filters. In [14], an approach, in which the existing grid side inductor currents are used in the inverter current control loop, is utilized to achieve sensorless active damping. This method preserves the meaning of “filtering the resonance” by using the grid side

0278-0046 © 2013 IEEE

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Fig. 1. Configuration of LCL filter based grid connected PV VSI.

inductor currents as feedback, and achieves active damping simply by modifying the inverter current control loop. However, as highlighted in [14], the proposed digital infinite impulse response (IIR) filter based sensorless active damping technique has the following challenges [14]. • It is based on a “true” digital control system with a full Z-transform representation of the plant and the controller. In reality, the system comprising of inverter and LCL filter are analog in nature, therefore, the full digitalization is an approximation process. • Iterative optimization is required in [14] to meet the specified design of the second order IIR Butterworth filter which increases the control complexity, the computing burden and also requires optimization expertise. • In [14] the LCL damped system achieves a limited reduction (68%) in the current oscillations compared to the undamped LCL system. This paper proposes a two-degree-of-freedom (2DOF) PID control structure to achieve effective active damping for three phase grid-connected PV inverters. The proposed analysis uses the existing grid side inductor currents and focuses on the system dynamics in continuous time. This 2DOF PID controller is a general approach and can be easily tuned, using conventional techniques to obtain the required stability margin. The proposed technique is validated both by simulation and a real time hardware-in-loop (HIL) experimental study. II. OVERALL S YSTEM C ONFIGURATION Fig. 1 shows the diagram of a three phase grid-tied PV power system, which adopts the dual stage conversion topology. The LCL filter is the interface between the VSI and the point of common coupling (PCC). For ac filtering analysis in a dual stage PV system with a dc-dc converter (not shown in Fig. 1), the dc side can be considered as a finite voltage source, therefore its dynamics are decoupled from the ac side. Voltage-oriented control is adopted to control the PV inverter systems [1]–[3]. For unity power factor operation, the grid side inductor current, ILg , is regulated to be a sinusoidal waveform and in-phase with the grid voltage. The detail control is discussed later in Section V. Using the design guidelines from [15] and considering a maximum total harmonic distortion, THD of 5% at current output, the LCL parameters are chosen and shown in Table I (Appendix). We define: f1 , the fundamental frequency of the grid voltage; fres , resonance frequency; fc , controller sampling frequency

and fsw , switching frequency. The following design constraints are considered [2]. • For good filtering performance: the resonance frequency should be in the range of 10f1 < fres < (fsw /2). • The controller sampling frequency should be at least 2fsw . • Stability of the LCL filter is dependent on the ratio of fres /fc . If the grid side inductor current is used for the inverter control, then the following relationship should be maintained for a stable operation: (fres /fc ) > (1/4) (i.e., (fres /fsw ) > (1/2)). Since there is no alternative to achieve a good filtering performance except by having fres < (fsw /2), the switching frequency, fsw is chosen such that it is about five times the filter resonance (≈5fres ) for effective attenuation of higher order current harmonics. However, since fc is set to at least 2fsw , it causes the ratio fres /fc to be less than 1/4, which, consequently causes resonance (instability). Therefore, the LCL filter resonance needs to be damped to achieve a stable operation. III. U NDAMPED LCL F ILTER BASED S YSTEM R ESPONSE The LCL-based system is modeled in the s-domain to evaluate the system dynamics. For modeling purposes and to derive the transfer function of the LCL system, it is assumed that the three phase voltages at the PCC are sinusoidal and balanced. Therefore, for stability analysis the grid voltage is neglected, i.e., the grid voltage is treated as a disturbance, which is a short circuit in the high frequency range. Nevertheless, as grid voltages are always not sinusoidal and balanced, the grid voltage (Vg ) is fed forward within the control structure, which is explained later in Section VI. Another assumption is that the equivalent series resistances of the passive components including the inverter side inductor Linv , grid side inductor Lg and the filter capacitor C are neglected for clarity. These parasitic elements may provide an additional passive damping effect that would improve the overall system stability. The system without passive resistances thus, represents the “worst case” for the design process. Fig. 2(a) gives the block diagram representation of the undamped LCL system including the inverter. The open loop transfer function (OLTF), GLCL , for this system in the frequency domain can be written as GLCL (s) =

Vdc /2 ILg (s) = Vm (s) Linv Lg Cs3 + (Linv + Lg )s

(1)

where Vdc is the dc link voltage, Vm is the normalized modulating signal, ILg is the grid side inductor current. The average model for the inverter is represented by a gain of Vdc /2 that is applied to the PWM reference signal. Following the parameters shown in Table I, the bode plot of the transfer function in (1) is shown in Fig. 2(b). A sharp peak is noticeable in the bode diagram at the resonance frequency of 1.949 kHz. This peak needs to be compensated to have a flattened low-pass response. It can be clearly noticed from GLCL (s) in (1) that the denominator has a polynomial without an s2 term. Therefore, the overall closed loop system is not stable according to the Routh’s stability criterion. It can also be confirmed from the bode plot analysis. This suggests that an

HANIF et al.: TWO DEGREES OF FREEDOM ACTIVE DAMPING TECHNIQUE

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Fig. 2. Block diagram and frequency response of undamped LCL filter based grid connected PV system. (a) Block (b) Bode plot.

additional damping term should be incorporated to stabilize the system. As highlighted above, to satisfy Routh’s criterion for stabilizing the overall closed loop system, a finite s2 term needs to be introduced into the denominator. This can be done by calculating the second derivative of the controlled current ILg , which passes through a damping gain k, and adding it to the modulating signal Vm as shown in Fig. 3(a). This leads to a transfer function that can be written as ILg (s) Vdc /2 = Vm (s) − (ks2 ILg (s)) Linv Lg Cs3 + (Linv + Lg )s

(2)

Vdc /2 ILg (s) = . Vm (s) Linv Lg Cs3 + (Vdc /2) ks2 + (Linv + Lg )s

(3)

Due to the noise in any measured signal, especially when using digital controllers such as a digital signal processor (DSP), the calculation of derivatives does not lead to a reasonable result. Therefore, in [14] an approximation of the derivative term (s2 ) by means of a digital filter is made. The challenges associated with such an implementation are already discussed in the introduction section. In addition to the challenges, the approach in [14] shows difficulty to reduce the resonance peak. As shown in the bode diagram of Fig. 3(b), the recommended method in [14] lowers the resonance peak and reduces 68% of the current oscillations, but still shows considerable gain at the resonance frequency (7.7 kHz). The next section proposes a 2DOF PID controller. This is an alternative way of achieving the missing “s2 term” in the denominator of the OLTF of the damped LCL system. In contrast to the active damping technique in [14], the proposed 2DOF PID active damping technique is simple to implement and can achieve a well damped system (i.e., a well reduced resonance peak) without any additional sensors. This 2DOF PID controller can be realized by analog or digital methods.

Fig. 3. Block diagram and frequency response of actively damped LCL filter based system using approximated s2 term by means of a digital filter as suggested in reference [14]. (a) Block diagram with finite s2 term. (b) Bode plot.

Fig. 4. Block diagram of the 2DOF PID controller.

IV. P ROPOSED 2DOF ACTIVE DAMPING M ETHOD A 2DOF PID control structure shows flexibility to achieve a better control performance compared to traditional one degree of freedom (1DOF) PID control [16]. This extra freedom separates the set-point response from the disturbance rejection response and allows harmless pole-zero cancellations [17]. In traditional 1DOF PID control structure, PI (kp and ki ) and D (kd ) actions are interrelated such that they cannot be controlled separately. On the other hand, the 2DOF control structure allows the independent action of PI and D terms giving two degrees of freedom. We propose a 2DOF PID structure to regulate the inverter current following a given set-point and perform the function of active damping. Fig. 4 shows the block diagram representing the LCL filter based PV inverter system including the proposed active damping loop. The proposed 2DOF PID controller consists of a PI controller in the main forward loop and a derivative term in the feedforward loop. For practical implementation, the D action is achieved by an ideal derivative term using a low-pass filter. This low-pass filter attenuates the high frequency noise and therefore, the filter derivative term is expressed as (kd td s)/(1 + td s), where kd is the derivative gain

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good control feature in terms of command following and lowfrequency disturbance rejection. Further, the noticeable change in phase in the low frequency range (below fres ) indicates highly damped gains around the resonance frequency and guarantees the closed loop system stability. It can be further noticed that there is no change in gain or phase at higher frequencies above fres , which maintains the attenuation performance to avoid the higher order harmonics from being injected into the grid by the PV inverter. Another comparison of the reduction in the resonance peak by the proposed method [see Fig. 5(b)] to the method proposed in [14] [see Fig. 3(b)] shows that the proposed method is capable of better resonance reduction. The next section describes the approach used to determine the unknown parameters kd , td , kp and ki for the proposed 2DOF PID controller. V. P ROPOSED 2DOF PID C ONTROLLER D ESIGN

Fig. 5. Block diagram and frequency response of actively damped LCL filter based system using proposed 2DOF PID controller. (a) Block diagram (b) Bode plot.

(or damping gain) and td is the time constant of the first order low-pass filter. Vg is fed forward within the control structure. Fig. 5(a) shows the block diagram of the inverter, LCL filter and the filtered derivative term. The filtered derivative term represents the feedforward loop of the 2DOF PID controller. The feedforward loop is added to the modulating signal Vm as shown in Fig. 5(a). The new transfer function that includes the derivative action can be written as IL (s) Vdc /2 = g . 3 +(L td k d s L L Cs inv g inv +Lg )s Vm (s)+ ILg (s) 1+td s

(4)

The new damped LCL transfer function GLCL_damped constitutes, a fourth order polynomial in the denominator that contains all the orders of the “s term” and can be derived as in (5), shown at the bottom of the page. The bode plot of the transfer function in (5) is shown in Fig. 5(b). Comparing Fig. 5(b) to Fig. 2(b), the positive peak of the gain at the resonance frequency fres , in the undamped LCL system has been damped by about 98%. Additionally, the increased gain in the low frequency range (below fres ) shows

GLCLdamped =

Gsystem =

ki kp + s

· (e

Substituting (5) into (6), we get (7), shown at the bottom of the page. To tune the four unknown parameters kd , td , kp and ki of the 2DOF PID controller in (7), the following two steps are carried out. 1) Step 1—Tuning of Gains kp and ki : In [7], a detailed procedure to tune kp and ki values is given. However, taking into account the effect of sampling and transport delay as well as additional delay caused by signal sensing following, the controller synthesis considers the modified expressions: kp ≈

2πfco (Linv + Lg ) Vdc

(8)

ki ≈

kp 10/2πfco

(9)

Vdc (1 + td s)/2 Linv Lg Ctd s4 + Linv Lg Cs3 + (Linv td + Lg td )s2 + Linv + Lg −

Fig. 6 shows the expanded version of Fig. 5, which is the block diagram of the proposed 2DOF PID control structure, applied to the undamped LCL system. The derivative feedforward loop of the 2DOF PID filters the controlled current, ILg . To design a stable 2DOF PID controller for the plant (inverter with LCL), the systems’ OLTF needs to be formulated and analyzed. The OLTF comprises the PI current controller, kp + (ki /s), a 1.5Ts delay [consists of sampling delay (Ts ) and transport delay (0.5Ts )] that is modeled as e−1.5Ts s in the forward path and GLCL_damped as expressed in ki Gsystem = kp + · (e−1.5Ts s ) · GLCL_damped . (6) s

−1.5Ts s

)·

Vdc kd td 2

Vdc (1+td s) 2

Linv Lg Ctd s4 + Linv Lg Cs3 + (Linv td + Lg td )s2 + Linv + Lg −

(5)

s

Vdc kd td 2

s

(7)


Fig. 6.

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Block diagram of the actively damped LCL system (2DOF PID + 1.5Ts + plant).

where fco is the system cross over frequency. To decide the fco for the calculation method, it can be noted from Fig. 5(b) that the control bandwidth cannot exceed or even closely approach the resonance frequency fres as that would create a 180◦ phase lag, which then, would result in unstable oscillation in the closed loop system. Nonnegligible delays caused by digital sampling and pulse width modulation would also further constrict the fco . Therefore, the value of fco is assigned to be 0.3fres , which is fairly a conservative value [7]. This prevents the interference between the LCL resonant component and the maximum harmonics of the currents that need to be controlled. The gains kp , ki , and kd are for the actual current values of the model. When per unit (p.u.) values are used within the controller with a base power of 10 kVA and a base voltage of 240 V, then the gains kp = kp × puaf , ki = ki × puaf and kd = kd × puaf are transformed using the p.u. attenuation factor (puaf = 19.64). The calculated values for the gains kp and ki are 0.54 and 198, respectively, for the above system. 2) Step 2—Tuning of Gains kd and td : According to the Routh’s criteria, in a stable system, all the coefficients of characteristic equation of (7) should be positive. To guarantee the system stability, the tuning on kd and td can be expressed by using the coefficient of the last term of the denominator in (7), as follows: kd td ≤

2(Linv + Lg ) . Vdc

Fig. 7. Bode diagram of the system showing gain and phase margins (PI + 1.5Ts + damped LCL).

(10)

The derivative gain kd (kd × puaf ) is considered as 1 and td is calculated by considering kd td as half of the right hand side of (10). This gives the value of td = 1.47 × 10−4 and thus, the cutoff frequency of LPF becomes 1080 Hz. The derived control parameters are summarized in Table II in the Appendix. Following (7), the system bode diagram is shown in Fig. 7. The system relative stability is demonstrated by the phase margin and gain margin, which are 48.9◦ and 4.57 dB, respectively. Fig. 8. Control diagram (2DOF PID for active damping).

VI. S IMULATION P ERFORMANCE Simulation was carried out in the Matlab/Simulink environment based on the system shown in Fig. 1 and the parameters given in Tables I and II. Table II gives the system parameters including grid voltage, line frequency, dc link voltage, and system capacity. The performance of the proposed 2DOF PID based active damping method with the designed controller parameters, determined in the previous section, is verified by

simulation. The 10 kW PV inverter supplies 5 kW of passive resistive load and the grid. Fig. 8 shows the overall controller diagram of the three phase grid-tied system including the proposed active damping loop and dq reference frames. The inverter controller consists of an outer dc link voltage control loop with an inner current loop that guarantees a good dynamic and steady state performance. In this paper, the dc link is represented by a finite source of 800 V dc. A phase

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Fig. 9. Simulation results of the undamped LCL filter based grid connected PV system.

locked loop (PLL) is used to determine the reference frequency and phase of the grid voltage at the PCC. The three grid side inductor currents are transformed using dq synchronous reference frame to Id_CC and Iq_CC . The currents Id_CC and Iq_CC are compared to the Id_ref which adjusts the active power and the Iq_ref = 0 for zero reactive power, respectively. The generated errors are then passed through the current controller (PI controller) to generate the voltage references for the inverter. To get a good dynamic response, Vd_CC and Vq_cc are both fed forward, as shown in Fig. 8. A gain of “2/Vdc ” is used on the three phase grid voltages before the dq transformation to extract the modulating signals (i.e., modulation indexes) for each of the phases as V ac = mVdc /2). Since the feedforward voltage in the control loop now considers the grid voltage disturbance (the grid voltage was neglected during modeling in the Section III), the control is immune to the impact from the grid distortion disturbances. Therefore, an improved quality of the controlled current is expected when the practical system is tested under grid voltage harmonic disturbances. The generated reference voltages in dq reference frame are then transformed back into a stationary reference frame that can be used as command voltages to generate high frequency PWM voltages. For comparison, the LCL system without active damping control is simulated and the result is shown in Fig. 9. For simplicity, results of only phase-A in p.u. values are shown. The oscillations in the grid side inductor current (ILg−A ) with significant amplitude can be noticed due to inadequate damping. Fig. 10 gives the simulated results with the proposed 2DOF active damping method. Note that the power delivered by the PV system to the main grid is shown as out-of-phase injected current. It demonstrates that the proposed method effectively suppresses the oscillations providing a stable system performance. The THD of gird side inductor current (ILg_A ) is noticed as 2.6% at rated output power injection. The effectiveness of the 2DOF active damping technique is compared with another well-known capacitor voltage based active damping technique [1], [9]. To test the robustness of the controller, the system is tested with a three phase distorted and unbalanced load. A single-phase full bridge rectifier is connected between phase-A and -N. The load on the dc side

Fig. 10. Simulation results of the actively damped LCL filter based grid connected PV system with proposed 2DOF active damping technique.

Fig. 11. Performance of proposed 2DOF PID active damping technique under distorted and unbalanced three phase load.

of the rectifier is composed of an inductor (100 mH), resistor (10 Ω) and a parallel connected capacitor (200 μF). The loads on the Phase-B and Phase-C are a resistor (80 Ω) and series combination of resistance-inductor (30 Ω + 10 mH), respectively. The load currents (ILoad_ABC ) due to the non-linear and unbalanced load combination are shown in Fig. 11. The LCL filter based system performance with the proposed 2DOF PID active damping method and with the capacitor voltage based active damping technique is shown in Figs. 11 and 12, respectively. For both cases, the active damping control loop is activated at 0.02 s. As noticed from Figs. 11 and 12 (expanded results, after time 0.04 s), both the active damping techniques give satisfactory performance. However, the capacitor voltage based technique requires estimation of capacitor voltage that depends on the accuracy of the plant model parameters. The proposed 2DOF active damping technique uses the existing grid side currents to achieve the desired performance. The THD of ILg is noticed as 3.4% using the proposed technique, which is better than 4.8% that is achieved with the capacitor voltage based technique. The proposed method shows a fast


Fig. 12. Performance of capacitor voltage based active damping technique under distorted and unbalanced three phase load.

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Fig. 13. state.

HIL experimental result of the undamped LCL system during steady

response entering steady state by comparing Figs. 11 and 12. This comparison shows that the proposed 2DOF PID controller is effective in damping the LCL resonance and is not affected by the distortion in the load current. VII. R EAL -T IME HIL E XPERIMENTAL VALIDATION A real-time hardware-in-the-loop (HIL) experiment is carried out to validate the effectiveness of the proposed 2DOF damping technique. The HIL system consists of an FPGA based digital simulator from OPAL-RT and a DSP. The plant is allocated within one core of the 8-core OPAL-RT system. The plant represents the power system, which includes the inverter, LCL filter, three-phase load and grid as given in Fig. 1. The controller (Fig. 8) of this PV VSI system is implemented on a separate DSP, DS1103 of dSPACE. The input/output limits of the OPALRT and DS1103 are +/−16 V and +/−10 V respectively. The three phase PCC voltages and grid side inductor currents are the analog outputs of the OPAL-RT plant which are sent to the DS1103 controller via its own ADC’s. The DSP decides the PWM reference signals via the PI controller such that all the 10 kW active power is transferred to both the load and the grid as described in Section VI. The PWM output from DS1103 is sent to the inverter gate drivers within the OPAL-RT plant via its own time stamped digital inputs (TSDI’s). The TSDI’s are capable of precisely realizing the high frequency PWM pulses. The setup is run with the same gains kp , ki , kd and the time constant td that were used for simulation. Furthermore, the identical parameters, as given in Table II, are used for HIL experimental systems. The dSPACE DSP controller is run at a discrete fixed time step of 50 μs (TS ). In all the experimental results, the voltages and currents are represented in p.u. where 1 p.u. = 1 V. Fig. 13 shows the HIL experimental result obtained at steady state for the undamped LCL system. As expected, the system is unstable and the output oscillations are saturated to 5 p.u. for safe OPAL-RT and DSP operation. Fig. 14 shows HIL experimental results that the system stabilizes as expected when the active damping 2DOF PID loop is enabled while the system is running without any damping.

Fig. 14. HIL experimental result when the active damping loop for the LCL system is enabled.

Fig. 15. HIL experimental result the actively damped LCL system during steady state.

Fig. 15 depicts the steady state results of the actively damped LCL system where 1 p.u. grid side inductor current is the output from the inverter. Current of 0.5 p.u. is transferred to the 5 kW load and remaining 0.5 p.u. is injected into the grid. The capacitor current is high frequency current harmonics absorbed

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Fig. 16. HIL experimental result: transition of the inverter power supply level from 50% to 100%.

Fig. 18. Effect of grid voltage distortion on the quality of controlled current (without feedforward). TABLE I S YSTEM PARAMETERS U SED FOR S IMULATION AND E XPERIMENT

Fig. 17. Effect of grid voltage distortion on the quality of controlled current (with feedforward).

with “close to zero” fundamental current. ILg and Ig are well filtered by the LCL filter as expected. The THD of grid voltage is 2.4% while the THD of the ILg is 2.5%. Using the proposed 2DOF active damping technique, the magnitude of the current oscillations is reduced by about 98% in comparison with the undamped system. Fig. 16 shows the experimental results obtained when a step change in the current reference from 0.5 p.u. to 1 p.u. is made. The actively damped 2DOF PID current controller tracks the reference satisfactorily within one power cycle. In Fig. 17, the experimental results show a distorted grid voltage with 5% of 5th harmonic and 5% of 7th harmonic. The test of grid voltage feedforward discussed earlier demonstrates that the controller responds well toward any grid distortion that may occur in any real system. The result shows that the grid voltage has THD of 8.1% and the injected current (ILg ) has 3.8% THD (which is well below the considered 5% THD limit). For comparison purposes, the system is tested without the feedforward loop and the result for this case is shown in Fig. 18. A THD of 8.7% is noticed in the controlled current (ILg ) without the feedforward loop. For further improvement of the harmonic contents of the controlled current, ILg , selective harmonic current compensators may be considered, which lies

outside the scope of this paper. Also, the robustness of the above 2DOF PID current controller (active damping) is analyzed with different grid impedance values. Initially the grid impedance consisted of 0.1 Ω resistance and 1 mH inductance. The system is tested with varied grid impedance (2 mH, 5 mH, and 10 mH) and has no effect on the THD of the controlled current. THD of ILg remains between 2.4% to 2.6%. VIII. C ONCLUSION In this paper, a two-degree-of-freedom (2DOF) PID active damping method is proposed to attenuate the resonance that is caused by the LCL filter based PV system. The proposed method is straightforward to design and uses the existing grid side inductor currents by eliminating the need for additional sensors. It is shown that oscillations are damped by about 98% using proposed 2DOF PID technique. A general controller tuning process is also presented without compromising on the filtering performance of the LCL filter. The control loop secures a phase margin of 49◦ with consideration of the time delay (1.5Ts ) caused by digital control. The simulation and HIL experiment results validate the effectiveness of the proposed active damping technique. The proposed 2DOF PID controller does not affect the quality of the controlled current during practical grid voltage distortion, grid impedance variation and unbalanced/distorted load. The HIL experimental study validates the controller design considering a digital controller delay to tune the 2DOF PID gains and simulation results.


TABLE II C ONTROLLER PARAMETERS FOR SIMULATION AND EXPERIMENT

A PPENDIX The system parameters and controller coefficients are listed in Tables I and II, respectively.

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Moin Hanif (M’11) received the 1st class B.Eng. (Hons.) degree in electrical and electronic engineering with High Achievers Award scholarship from University of Nottingham, Nottingham, U.K., in 2007, and the Ph.D. degree from Dublin Institute of Technology, Ireland, in 2011. He worked as a Postdoctoral Researcher at Masdar Institute of Science and Technology, Abu Dhabi, UAE, from October 2011 to 2012. From November 2012, he has been appointed as a Senior Lecturer at the Department of Electrical Engineering, University of Cape Town, Cape Town, South Africa. His research interest is in the area of power electronics converters and their control, MPPT of photovoltaic power, Islanding detection, grid integration of renewables, and micro/smart grid operation. Dr. Hanif has received a number of research grants from the University of Cape Town’s Research Committee and also serves as a member on the editorial board of International Journal of Applied Control, Electrical, and Electronics Engineering (IJACEEE).

R EFERENCES [1] M. Malinowski and S. Bernet, “A simple voltage sensorless active damping scheme for three-phase PWM converters with an LCL filter,” IEEE Trans. Ind. Electron., vol. 55, no. 4, pp. 1876–1880, Apr. 2008. [2] J. Dannehl, M. Liserr, and F. W. Fuchs, “Filter-based active damping of voltage source converters with LCL filter,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3623–3633, Aug. 2011. [3] S. Wei, W. Xiaojie, D. Peng, and Z. Juan, “An overview of damping methods for three-phase PWM rectifier,” in Proc. ICIT, Apr. 21–24, 2008, pp. 1–5. [4] K. Jalili and S. Bernet, “Design of LCL filters of active-front-end twolevel voltage-source converters,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1674–1689, May 2009. [5] J. L. Agorreta, M. Borrega, J. López, and L. Marroyo, “Modeling and control of N-paralleled grid-connected inverters with LCL filter coupled due to grid impedance in PV plants,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 770–785, Mar. 2011. [6] M. H. Bierhoff and F. W. Fuchs, “Active damping for three-phase PWM rectifiers with high-order line-side filters,” IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 371–379, Feb. 2009. [7] Y. Tang, P. C. Loh, P. Wang, F. H. Choo, F. Gao, and F. Blaabjerg, “Generalized design of high performance shunt active power filter with output LCL filter,” IEEE Trans. Ind. Electron., vol. 59, no. 3, pp. 1443– 1452, Mar. 2012. [8] Y. A.-R. I. Mohamed, M. A.-Rahman, and R. Seethapathy, “Robust line-voltage sensorless control and synchronization of LCL-filtered distributed generation inverters for high power quality grid connection,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 87–98, Jan. 2012. [9] M. Malinowski, S. Stynski, W. Kolomyjski, and M. P. Kazmierkowski, “Control of three-level PWM converter applied to variable-speed-type turbines,” IEEE Trans. Ind. Electron., vol. 56, no. 1, pp. 69–77, Jan. 2009. [10] W. Gullvik, L. Norum, and R. Nilsen, “Active damping of resonance oscillations in LCL-filters based on virtual flux and virtual resistor,” in Proc. Power Electron. Appl. Conf., Sep. 2–5, 2007, pp. 1–10. [11] M. Liserre, A. Dell’Aquila, and F. Blaabjerg, “Genetic algorithm-based design of the active damping for an LCL-filter three-phase active rectifier,” IEEE Trans. Power Electron., vol. 19, no. 1, pp. 76–86, Jan. 2004. [12] J. Dannehl, C. Wessels, and F. W. Fuchs, “Limitations of voltage-oriented pi current control of grid-connected PWM rectifiers with LCL filters,” IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 380–388, Feb. 2009. [13] R. Teodorescu, F. Blaabjerg, M. Liserre, and A. Dell’Aquila, “A stable three-phase LCL-filter based active rectifier without damping,” in Conf. Rec. IEEE 38th IAS Annu. Meeting, Oct. 12–16, 2003, vol. 3, pp. 1552–1557. [14] C. P. Dick, S. Richter, M. Rosekeit, J. Rolink, and R. W. De Doncker, “Active damping of LCL resonance with minimum sensor effort by means of a digital infinite impulse response filter,” in Proc. Power Electron. Appl. Conf., Sep. 2–5, 2007, pp. 1–8. [15] M. Liserre, F. Blaabjerg, and S. Hansen, “Design and control of an LCLfilter-based three-phase active rectifier,” IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1281–1291, Sep./Oct. 2005. [16] M. Araki and H. Taguchi, “Two-degree-of-freedom PID controllers,” Int. J. Control, Autom. Syst., vol. 1, no. 4, pp. 401–411, Dec. 2003. [17] K. J. Åström and T. Hägglund, PID Controllers—Theory, Design, and Tuning, 2nd ed. Research Triangle Park, NC, USA: Instrum. Soc. Amer., 1995.

Vinod Khadkikar (S’06–M’09) received the B.E. degree from the Government College of Engineering, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India, in 2000, the M.Tech. degree from the Indian Institute of Technology (IITD), New Delhi, India, in 2002, and the Ph.D. degree in electrical engineering from the École de Technologie Supérieure (E.T.S.), Montréal, QC, Canada, in 2008, all in electrical engineering. From December 2008 to March 2010, he was a Postdoctoral Fellow at the University of Western Ontario, London, ON, Canada. Since April 2010 he has been an Assistant Professor at Masdar Institute of Science and Technology, Abu Dhabi, UAE. From April to December 2010, he was a Visiting Faculty at Massachusetts Institute of Technology (MIT), Cambridge, MA, USA. His research interests include applications of power electronics in distribution systems and renewable energy resources, grid interconnection issues, power quality enhancement, active power filters and electric vehicles.

Weidong Xiao (M’07) received the M.Sc. and Ph.D. degrees from the University of British Columbia, Vancouver, Canada, in 2003 and 2007, respectively. He is a Faculty Member with the electric power engineering program at the Masdar Institute of Science and Technology, Abu Dhabi, UAE. In 2010, he spent eight months working as a Visiting Scholar at Massachusetts Institute of Technology (MIT), Cambridge, MA, USA. Prior to his academic career, he worked with the MSR Innovations Inc. in Canada as an R&D Engineering Manager focusing on projects related to integration, research, optimization and design of photovoltaic power systems. His research interest includes photovoltaic power systems, dynamic systems and control, power electronics, and industry applications.

James L. Kirtley, Jr. (F’91) received the S.B. and Ph.D. degrees from Massachusetts Institute of Technology (MIT), Cambridge, MA, USA, in 1968 and 1971, respectively. He is a Professor of Electrical Engineering at MIT. He has worked for General Electric, Large Steam Turbine Generator Department and for Satcon Technology Corporation. He is a specialist in electric machinery and electric power systems. Dr. Kirtley served as Editor in Chief of the IEEE T RANSACTIONS ON E NERGY C ONVERSION from 1998 to 2006 and continues to serve as Editor for the journal and as a member of the Editorial Board of the journal Electric Power Components and Systems. He was awarded the IEEE Third Millenium medal in 2000 and the Nikola Tesla prize in 2002. He is a Registered Professional Engineer in Massachusetts and is a member of the United States National Academy of Engineering.