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Abstract-- The grid-connected LCL-filtered inverter is widely used in distributed power generation systems based on renewable energies. Single inverter-side ...
9th International Conference on Power Electronics-ECCE Asia June 1 - 5, 2015 / 63 Convention Center, Seoul, Korea

An Improved Inverter-Side Current Feedback Control for Grid-Connected Inverters with LCL Filters A. Jinming Xu , B. Shaojun Xie , C. Jiarong Kan and D. Lin Ji College of Automation Engineering Nanjing University of Aeronautics and Astronautics, China Abstract-- The grid-connected LCL-filtered inverter is widely used in distributed power generation systems based on renewable energies. Single inverter-side current feedback control only needs to sample one current to realize both current control and inverter protection. However, with single inverter-side current feedback control, the closedloop system is under-damped or even unstable due to the digital control delay. In this paper, an active damping control based on only inverter-side current feedback is proposed. With the novel control, the resonance in the digitally-controlled LCL-filtered inverter is successfully solved while only inverter-side current is sampled. Comparisons of the proposed and typical single inverterside current feedback control have verified the improvement of the proposed control. Thus, the proposed control has good application prospect in grid-connected LCL-filtered inverters. Index Terms-- active damping, Grid-connected inverter, inverter-side current feedback control, LCL filter

I. INTRODUCTION Grid-connected inverter is widely used in the distributed power generation system based on renewable energy [1]. The switching harmonics can be highly suppressed by LCL filter so that the filter volume and weight are reduced and the power density is increased [2]. Thus, grid-connected LCL-filtered inverter has gained wide attention. The current control of such inverter is a research focus in recent years. The existing current control can be classified into grid-side and inverter-side current feedback control. Besides the sampling of grid-side current, the grid-side current control still needs to sample the inverter-side current for the power device protection purpose [3-4]. On the contrary, the inverter-side current control only needs to sample the inverter-side current to realize both control and protection, which is more convenience to be implemented [5-6]. Although the inverter-side current control has these characteristics, the research and application are still lacking due to the resonance of LCL filter. The LCL resonance introduces a high resonance peak in the system open-loop transfer function. In practice, there are always many noise disturbances, and the step variation of grid voltage, input voltage or current reference will also arouse harmonic disturbances around the resonance frequency. If the LCL-filtered inverter is not controlled properly, the current is easily resonated. Therefore, the damping of LCL-resonance peak is

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necessary and is widely discussed. Good damping can be achieved by the inverter-side current control when filter parameters meet a certain condition [5]. In [6], it is also pointed out that single inverter-side current feedback control can promise stable operation. However, the inherent digital control delay in digital control system is ignored in previous studies. The stability with only inverter-side current control is aggravated when the ratio between resonance frequency of filter and control frequency keeps high [7]. It is necessary to adopt extra damping into the inverter-side current control [8]. In a word, the system adopting inverter-side current feedback control is stable when the control delay is ignored; however, the control delay seriously affects the stability and dynamic. Thus, the high suppression of LCL resonance is a precondition for high-quality grid current with only inverter-side current feedback control. However, there are still shortcomings in the commonlyused passive or active damping methods. The design of passive damping method by adding resistor in series with the capacitor needs to make a tradeoff between the power loss and damping effect [9]. Otherwise, a larger resistor will cause large amount of power loss and reduce the efficiency at light load. In addition, this method also affects the suppression of harmonics at switching frequency. The filter-based active damping method which adds digital filter on the forward path can also damp the LCL resonance [8, 10, 11]. However, this method relies on accurate filter parameters. Although the robustness can be improved by online parameter estimation, extra disturbance for parameter estimation needs to be injected into the inverter, and finally aggravates the current quality [11]. Besides, the filter-based active damping reduces the system bandwidth [10] so that the dynamic performance and the suppression of low-frequency harmonics are affected. Another kind of active damping methods improves the LCL damping factor by introducing extra state feedback, including the feedback of injected grid current [4], capacitor voltage [12] and capacitor current [13, 14]. However, this method needs extra high-precision sensor to sample the extra state when it is applied in the inverter-side current control. In summary, with the typical inverter-side current control, the inverter performance is unsatisfactory. Therefore, an active damping method is needed. However, the existing methods either show a poor performance or require extra high-precision sensors. In this paper, an active damping control based on only inverter-side current feedback is proposed. Comparisons of the

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proposed and typical inverter-side current control demonstrate the improvement of the proposed control. II. GRID-CONNECTED LCL-FILTERED INVERTERS AND CONVENTIONAL CURRENT CONTROL A. Grid-connected LCL-filtered Inverters Fig. 1 shows the structure of a full-bridge gridconnected inverter with an LCL output filter consisting of inverter-side inductor L1, filter capacitor C1 and grid-side inductor L2, where Udc denotes the DC voltage, uinv denotes the inverter output voltage, iL1 is the inverter-side current, ug is the grid voltage, and ig represents grid current. In practical applications, the DC side is connected to the input source in a single-stage gridconnected system or the output of a DC-DC inverter in a dual-stage system. Current reference is obtained by the injected grid power control or the DC voltage control. Then, the reference multiplied by the output of a phaselocked loop generates the instantaneous current reference iref.

B. Conventional Inverter-side Current Control In the digital control system, there is a delay between the signal sampling and the generation of duty cycle. Thus, a large control delay is always introduced in the digital control system. In previous studies, the current sampling is always executed at the beginning of the control period and the modulation wave is reloaded at the end of the control period. Therefore, the delay time is equal to a control period, namely Ts=1/fs. The structure of single inverter-side current feedback control is shown in Fig. 2 where Gc(s) represents the current regulator and u is the output of Gc(s). Gc ( s )

e − sTs

Ginv ( s )GuiLinv1 ( s )

Fig. 2. Conventional single inverter-side current control

The open-loop transfer function from iref to iL1 with the conventional control (denoted as ‘S1’) is expressed as:

GiirefL1 _ o _ S1 ( s) = Gc ( s)GuiL1 ( s) = Gc ( s)e− sTs Ginv ( s)GuiLinv1 (s) ( 4)

Fig. 1.

as

Grid-connected LCL-filtered inverter

The transfer function from uinv to iL1 can be expressed

GuiLinv1 ( s) =

L2 C1 s 2 + 1 L1 L2 C1s 3 + ( L1 + L2 ) s

(1)

Clearly, a pair of under-damped conjugate resonant poles at the frequency Ȧres appears. The expression of Ȧres is given in (2). The parameters of filter in this paper are L1=0.6mH, L2=0.36mH, and C1=7ȝF. In addition, the switching frequency and control frequency (denoted as fs) are equal to 15 kHz.

ωres = 2π f res =

L1 + L2 L1 L2 C1

(2)

The inverter is equivalent to a first order inertial element: Ginv ( s ) =

kPWM TPWM s + 1

(3)

where kPWM stands for the proportional gain (and equals 1 for simplification in this study), TPWM stands for the delay time which equals 1/(2fs).

Without loss of generality, the conventional proportional-integral regulator (PI) is used as Gc(s), as shown in (5), where kp is the proportional gain, Ti represents the time constant of PI regulator. The performance of fundamental current tracking and harmonics suppression can be improved by increasing kp or decreasing Ti. However, both parameters are restricted for the system stability. In this paper, considering that the control frequency is equal to 15 kHz, parameters of PI regulator can ensure that the open-loop lowest cut-off frequency where the open-loop amplitude-frequency curve crosses the 0dB line is around 1 kHz. Then, the widely-used resonant controller can be added to further improve the fundamental current tracking and harmonics rejection. Gc ( s) = k p (1 +

1 ) Ti s

(5)

The open-loop bode plots with the conventional control are given in Fig. 3. As can be seen from the dotted lines in the figure, without the control delay, the phase-frequency curve does not intersect with the í180°line in the range where the magnitude gain is larger than 0dB. Thus, the closed-loop system is stable according to the Nyquist stability criterion in bode plot [15]. However, if the control delay is considered, there is an intersection between the phase curve and í180°-line around the resonance peak (the magnitude gain is over 0dB). Thus, the closed-loop system becomes unstable and a serious resonance is activated. In summary, the control delay greatly decreases the open-loop phase with the conventional control and leads to closed-loop instability. In this case, if the resonance peak can be supressed below the 0dB-line by proper damping control, the system will

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remain stable. In next section, a proper active damping control strategy with only inverter-side current feedback will be given.

harmonics, the aliasing of iL1 real-time sampling is not obvious. In addition, HAD(s) can suppress the distortion of low-frequency harmonics caused by aliasing. Ginv ( s )

e − sTd 1

e− sTd 2

GuiLinv1 ( s )

H ( s) Fig. 4.

Proposed active damping control with inverter-side current feedback

The transfer function with the proposed control (denoted as ‘S2’) from u to iL1 can be expressed as: GuiL_1 S2 ( s )

Fig. 3.

Open-loop Bode plots with conventional single inverter-side current control

III. PROPOSED ACTIVE DAMPING CONTROL AND ANALYSIS The active damping control is used to shape the magnitude and phase characteristics at the resonance frequency. Therefore, it damps the LCL peak due to the feedback of the components of the controlled state at the resonance frequency essentially. Accordingly, an active damping control based on the feedback of iL1 is given in Fig. 4, where kAD is the feedback coefficient. Moreover, the expression of HAD(s) is given as follow:

H AD ( s) =

s2 s 2 + 2ζωh s + ωh2

(6)

where, Ȧh and ȗ are the turnover frequency and damping ratio of the second order high-pass filter, respectively. The main idea of such active damping control is to extract the components of iL1 around the resonance frequency by HAD(s) to realize the LCL-resonance peak damping. Clearly, no additional state is needed. Since the control delay between the signal sampling and the modulation wave reloading leads to the phase lag of sampled signal, the thought of real-time sampling in [13] is used to extract the resonance component of iL1 accurately. The sampling instant of iL1 in Fig. 3 is moved toward the reloading instant of um so that the control delay denoted as Td1 is decreased. The notation Td2 in Fig. 3 denotes the delay time between the outer-loop current tracking control and the inner-loop active damping control. In other words, the inner-loop control delay Td1 is decreased by real-time sampling of iL1, and Td2 in Fig. 3 denotes the delay time between the outer-loop iL1 sampling and the inner-loop one. Compared with Fig. 2, in the proposed strategy, Td1 and Td2 equals Ts. It should be noted that the component of iL1 at the switching frequency are not the major part. Thus, compared with the real-time sampling of capacitor current containing a large proportion of switching

=

e − s (Td 1 +Td 2 ) Ginv ( s )GuiLinv1 ( s ) 1 + kAD H AD ( s )e − sTd 1 Ginv ( s )GuiLinv1 ( s )

(7)

Note that the delay time of inner-loop Td1 and outerloop Td2 satisfy: Td1+Td2=Ts. Because Td1 is not an integral multiple of Ts, the time exponential function in the denominator of (7) cannot be transformed to the form zíN (N is an integer) in the Z-domain. Therefore, the analysis in this paper is simply carried out in the s-domain with a proper linear approximation of the control delay. Considering that the phase lag is the major factor that influences the active damping performance, a secondorder approximation given in (8) is adopted to replace the control delay with time constant T. This second-order approximation matches the control delay in phase well. In the following study, for analysis purpose, Td1 and Td2 are equal to 0.1Ts and 0.9Ts, separately. e −Ts =

1 1 ≈ eTs 1 + Ts + (Ts) 2 2

(8)

In theory, the digital filter HAD(s) will be sensitive to the noise around Ȧh if the damping factor ȗ is small. Thus, the value of ȗ should not be too small. In this study, ȗ is chosen as 0.4. In practical applications, the resonance frequency may be largely reduced [8, 14] because of the widely-varied grid impedance and the variation of LCLfilter parameters. Thus, HAD(s) should promise that the component of iL1 around the real resonance frequency are extracted accurately. Considering the existence of grid inductive impedance Lg, the natural resonance frequency can be calculated by:

L1 + L2 + Lg

ωres _ L =

L1 ( L2 + Lg )C1

g

(9)

It is seen from (9) that the resonance frequency decreases gradually with the increase of Lg until it reaches the minimum value expressed as:

ωres _ L

g

_ min

=

1 L1C1

(10)

Accordingly, the parameter Ȧh of HAD(s) should meet the following requirement:

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ωh ≤ ωh _ max = ωres _ Lg _ min

(11)

The resonance component around Ȧres will be accurately obtained through HAD(s) if Ȧh satisfies (11) in default case. When Ȧh decreases, the actual phase at Ȧres can be regained more accurately via HAD(s). However, a too small Ȧh reduces the ability of HAD(s) in filtering the low-frequency harmonics. In fact, low-frequency components are not the necessary imformation for active damping purpose. Thus, in order not to introduce some low-frequency current harmonics through the inner loop, the minimum value of Ȧh should be kept higher than the highest angular frequency of the major low-frequency current harmonics in iL1. In this study, in order to ensure a certain margin, Ȧh is selected to be 0.7Ȧh_max. For the design of kAD, the system open-loop characteristics with different kAD are depicted in Fig. 5. Compared with Fig. 3, the magnitude-frequency curve no longer intersects with the í180°-line in the range where the gain is larger than 0dB. Thus, the closed-loop system is stable. The magnitude curve around the resonance frequency becomes gentler with the increase of kAD. However, over damping will be caused by a too large kAD. As seen from the phase curves, large kAD means relatively samll PM. Thus, kAD needs to be selected properly. For instance, the phase and gain margins equal to 47.4° and 6.9dB separately when kAD is chosen to be 21. In summary, compared with the conventional control, the proposed control solves the resonance problem without the need of additional hardware costs so that it is capable of maintaining satisfactory performance.

Fig. 5.

Open-loop Bode plots with the proposed control

Another focus in the control for grid-connected inverters is robustness while the parameters of controller keep invariant and the variation of filter parameters and grid impedance exist. Here, the robust performance with the proposed control is presented. The open-loop bode plots with the increase of Lg are given in Fig. 6. The open-loop amplitude and phase curves move towards lower frequency direction with the increase of Lg. The resonance peak is always highly attenuated. The phase curve does not intersect with the í180°-line in the range where the magnitude gain is larger than 0dB. Therefore, the closed-loop system is always stable and the phase and gain margins are almost unchanged. Because the increase

of grid inductance equivalently reduce the system openloop gain, the cut-off frequency is surely decreased. In conclusion, the proposed control has good robustness when the grid impedance varies.

Fig. 6.

Open-loop Bode plots with the proposed control in presence of large grid impedance

IV. EXPERIMENTAL RESULTS In order to validate the effectiveness of the proposed method, a single-phase grid-connected inverter platform has been constructed. The DC voltage is 380V, and the AC side is the grid with 220V/50Hz. The digital signal processor (DSP) TMS320F28035 is adopted to realize the closed-loop control. The switching and control frequency are both 15 kHz. The inverter switches are the IGBT from Infineon (IKW40N120T2). Comparative experiments with the conventional inverter-side current control and the proposed control have been tested. The parameters of LCL filter are the same as previously used. Ti of PI regulator in the following tests is equal to 0.0006. First, waveforms with the conventional control are shown in Fig. 7. In Fig. 7a, severe resonance is observed and the protection is suddenly activated when the PI gain is relatively high. In Fig. 7b, many resonance harmonics still exists in the grid current although the protection is not activated when the PI gain is reduced to 5.1. When the PI gain is further reduced to 4, the current harmonics are more highly suppressed, as shown in Fig. 7c. However, the resonance can still be observed at the top and bottom of the current waveform. These results indicate that the inverter with the conventional control is under damped or resonated so that the bandwidth is hard to be improved. Next, steady-state waveforms with the proposed control is shown in Fig. 8a. Compared with Fig. 7, better current quality is achieved by the proposed inner-loop active damping even when the PI gain is 7.2. No resonance is observed. Transient waveforms with the proposed control is given in Fig. 8b while the reference changed suddenly. No resonance is excited and the current returns to steady-state operation rapidly. All the results above suggest that the proposed control promise a high bandwidth and satisfactory stability margin.

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(a) kp =7.2

(a) Steady state waveform

(b) kp =5.1

Fig. 8.

Fig. 9. (c) kp =4 Fig. 7.

Experimental waveforms with the conventional control

(b) Transient waveforms Experimental waveforms with the proposed control and kp =7.2

Experimental waveforms with the proposed control in presence of 1.4mH-grid impedance

V. CONCLUSION

At last, in order to validate the robustness, the proposed control is tested on the same platform with 1.4mH grid impedance. The results are given in Fig. 9. The current still has no resonance harmonics. In summary, the proposed control promises good robustness even when the grid impedance varies largely.

With the conventional single inverter-side current control, the inverter is under damped or resonated so that the current quality is unsatisfactory. In this paper, a novel and effective solution without the need of extra highprecision sensors is proposed. By adding an inner-loop active damping with only inverter-side current feedback, the aforementioned problem is solved. Compared with the conventional control, the proposed control works better even when a large control delay exists in the digital

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control system. Moreover, the robustness design of the proposed control is given in this paper. The robustness of proposed method is discussed. It is proved that the proposed control is also robust. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (grant number 51477077, 51077070). REFERENCES [1] Z. Zeng, H. Yang, R. Zhao, and C. Cheng, “Topologies and control strategies of multi-functional grid-connected inverters for power quality enhancement: A comprehensive review,” Renewable Sustainable Energy Rev., vol. 24, pp. 223-270, Aug. 2013. [2] W. Wu, Y. Sun, Z. Lin, T. Tianhao, F. Blaabjerg, and H.S.H. Chung, “A new LCL-filter with in-series parallel resonant circuit for single-phase grid-tied inverter,” IEEE Trans. Ind. Electron., vol. 61, no.9, pp. 4640-4644, Sep. 2014. [3] S.G. Parker, B.P. McGrath, and D.G. Holmes, “Regions of active damping control for LCL filters,” IEEE Trans. Ind. Appl., vol. 50, no. 1, pp. 424-432, Jan./Feb. 2014. [4] J. Xu, S. Xie, and T. Tang, “Active damping-based control for grid-connected LCL-filtered inverter with injected grid current feedback only,” IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 4746-4758, Sep. 2014. [5] Y. Tang, P. C. Loh, P. Wang, et al, “Exploring inherent damping characteristic of LCL-filters for three- phase gridconnected voltage source inverters” IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1433-1442, Mar. 2012. [6] R. Teodorescu, F. Blaabjerg, U. Borup, and M. Liserre, “A new control structure for grid-connected LCL PV inverters with zero steady-state error and selective harmonic compensation,” in Proc. IEEE APEC, Anaheim, CA, USA, 2004, vol. 1, pp. 580–586.

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