Sliding-Mode Control in dq-Frame for a Three-Phase Grid-Connected Inverter with LCL-Filter

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Sliding-Mode Control in dq-Frame for a Three-Phase Grid-Connected Inverter with LCL-Filter Chaoliang Dang , Xiangqian Tong , Weizhang Song PII: DOI: Reference:

S0016-0032(19)30909-3 https://doi.org/10.1016/j.jfranklin.2019.12.022 FI 4339

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Journal of the Franklin Institute

Received date: Revised date: Accepted date:

21 January 2019 29 September 2019 11 December 2019

Please cite this article as: Chaoliang Dang , Xiangqian Tong , Weizhang Song , Sliding-Mode Control in dq-Frame for a Three-Phase Grid-Connected Inverter with LCL-Filter, Journal of the Franklin Institute (2020), doi: https://doi.org/10.1016/j.jfranklin.2019.12.022

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Sliding-Mode Control in dq-Frame for a Three-Phase Grid-Connected Inverter with LCL-Filter Chaoliang Dang, Xiangqian Tong*, Weizhang Song School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi Province, China ∗ Corresponding author E-mail addresses: [email protected] (C.L. Dang), [email protected] (X.Q. Tong). Abstract: The three-phase LCL-filter-based grid-connected inverter (LCL-GCI) is a third-order and multi-variable system, and claiming a higher demand to the control system design. Aiming at this, an improved current sliding mode control (SMC) strategy combing with capacitor current feed-forward control is proposed to eliminate the distortion of the grid current for a three-phase LCL-GCI control system. Meanwhile, the modified exponential reaching law is presented to effectively alleviate the shaking shock effect caused by the traditional SMC strategy. The detailed theoretical analysis and design method of the proposed SMC strategy are presented. A simulation model and hardware-in-the-loop experimental platform on a 50kW three-phase LCL-type grid inverter is built with Matlab/Simulink and RT-LAB, which are compared with the traditional control strategy for verifying the accuracy of the proposed SMC strategy. The simulation and experimental results show that with the proposed SMC strategy, the steady and transient performances of the grid current are effectively improved. Keywords: Three-phase grid-connected inverter; LCL-type filter; PI control; sliding-mode control (SMC).

1.

Introduction

In the increasing application of renewable energy conversion technologies, the grid-connected inverter acts as the interface between the new power generation system and the power grid, which has become an important research topic all over the world [1-3]. The conventional voltage source inverter (VSI) is usually used to process dc energy generated by a renewable energy source and inject it to the grid. To decrease the influence of current harmonic components, the VSI is tied to the grid via either L or LCL filter with the aim of attenuating the switching frequency harmonics. Compared with the L-type grid-connected inverter, the LCL-filter-based Grid-connected inverter (LCL-GCI) has some matchless features such as the high frequency attenuation, the high power density and the characteristic which make it widely used in the micro power grid and new energy field [4-5]. As a third-order system, the LCL filter can effectively reduce the harmonic distortion with the excellent high frequency attenuation characteristic. However, due to the resonance hazard of the LCL filter [6], damping solutions are needed for the grid-connected inverters to stabilize the system. To solve the above defects effectively, various digital control strategies have been proposed. The tradition methods can be divided into passive and active damping [7-9]. In [10], the damping resistance method is employed to suppress the high frequency resonance. Nevertheless, its application is limited for increasing additional power loss and reducing the efficiency of the whole system. As a result, this method is not conducive to the practical engineering applications. Compared with the resistance damping control method, the active damping control strategy is widely promoted due to its higher reliability, lower cost and higher efficiency. In [11], the current feedback of the LCL network capacitor branch is utilized to optimize the performance of signal-phase LCL-GCI. Although this method has good performance in controlling and flexibility, an additional current sensor is needed. Therefore, it is not suitable to the industrial application. In [12], the predictive capacitive current of LCL filter is adopted to regulate the grid current. Although the additional hardware is not needed, the forecast of capacitance current is complex, and additional compensation measures are required to eliminate the error of system noise and control system. A new current control method named single current feedback is proposed in [13] to improve the grid-current quality. It effectively restrains the LCL type high frequency resonant, while improve the stability of the whole system. Nonetheless, the grid current differential link should be introduced more than once, and consequently, the controller design is complex. In addition to the aforementioned control strategies, some nonlinear control strategies are also presented, such as model predictive algorithm [14-15], fuzzy algorithm [16], sliding mode control (SMC) algorithm [17-19], and so on. As an effective control algorithm, SMC has been widely applied in the power converters and drives with the advantages of fast dynamic response, periodic interference suppression, and easy inclusion of nonlinear constraints [20-22]. In [23], the SMC strategy is utilized for transformer-less single-phase inverter for photovoltaic (PV) application with the active power decoupling to minimize the capacitance requirement. In [24], a SMC method is introduced to enhance the voltage stability margin of dc systems and guarantee the grid-current quality. The results shows that the presented SMC method has good performance to keep the voltage stability and the grid-currents represent good sinusoidal waveforms. However, no experimental validation was presented. In [25], the SMC method is proposed to improve the speed-regulation performance of the permanent-magnet

synchronous motor (PMSM) system under uncertainties and disturbances. All of the above shows that SMC methods provide a systematic approach to deal with the constraints of inputs and states, which is vital to control the complex power electronic systems with multiple variables in a simple way. It is worthy to point out that SMC can also restrain the periodic interference and ensure a high degree of grid power factor [26]. In [27], the Kalman filter algorithm is implemented in SMC for three-phase grid-connected inverters with LCL filter. Whereas, no experimental validation was presented, but the influence of reaching law is not considered. In [26], a fixed switching frequency multi-resonant SMC (MRSMC) is presented for single-phase grid-connected inverter to suppress the harmonics. However, this complex method is hardly implemented. A variable structure control method is proposed in natural frame, where Kalman filter is employed in estimating the variables needed in the sliding surface function formation [28]. In [28], the relative degree associated with the grid current (output variable) is three. However, the performance of the Kalman filter is sensitive to the LCL filter parameters. Aforementioned discussion indicates that SMC can effectively optimize the output waveform, and reduce the specific harmonic pollution for complex power electronics. Despite the multitude of these works, as a current force rectifier, the detailed theoretical analysis and design method of the SMC strategy in the synchronously rotating dq-frame applied to control the LCL-GCI was rarely reported. Moreover, with a direct control of the grid-side current high robustness against the distortion phenomenon of grid current is achieved, consequently, a reduction of the THD of the currents injected to the grid. Then, with this method, digital filters in the closed-loop system are not required. Therefore, to overcome the above drawbacks of the conventional control strategy while maintaining SMC merits, an improved current sliding mode control (SMC) strategy combing with capacitor current feed-forward control without increase the computational burden will be presented in this paper. First, the working mechanism of the LCL-GCI is analyzed. Afterwards, to improve the performance of system effectively without increasing the computational burden, an improved exponential approach is introduced in the current SMC to eliminate the vibration of the traditional SMC. Then, a new control method by controlling the grid-side current indirectly through the inverter-side current is presented. Finally, to verify the correctness and superiority of the proposed control strategy, both the simulation model and the prototype of the LCL-GCI are built. The effectiveness and correctness of the proposed SMC strategy is verified by comparing the results with the traditional current feedback control strategy. The rest is organized as below: The modeling and influence of resonances for LCL-GCI is presented in Section II. Section III presents the design principle of the current loop based on the proposed SMC control strategy. The performances of the improved SMC are verified through simulations and experimentally evaluation in Sections IV. Section V concludes the whole paper.

2. Circuit topology and mathematic model of three-phase LCL-GCI Without loss of generality, the topology of a three-phase LCL-GCI [29] is depicted in the Fig. 1, and the VSI consists of six switches (T1-T6) which are controlled with the pulse width modulation signals. A dc-link capacitor (Cs) is on the left, and a three-phase voltage source, representing the voltage at the point of common coupling (PCC) of the ac system, is on the right. The utilized symbols are listed below: us represent the voltage of dc source, is is the current of dc-link, Lf is the inverter-side inductor, Cf is the filter capacitor, and Lg is the grid-side inductor, Rf, Rg and Rc denote the parasitic resistance, n is the neutral points. VSI

is

T3

T1

T5 iLx

a

us

Cs

LCL Filter Lf , Rf Lg , Rg

b

igx ugx n

c

T4

T6

T2

 uc 

C f , Rc

Fig.1 Schematic circuit of the three-phase LCL type grid inverter

To simplify the analysis, the following assumptions are made: 1) the switching frequency is much higher than the grid frequency and the grid current are all in steady state. Assuming the variables Sx (x= a, b, c) denote the switching state of each bridge switch Tn(n=1-6) in the Fig. 1, and the expression of Sx is defined as below:  0 if Tn is on Sx   (1)  1 if Tn is off According to the Kirchhoff equations of the elementary circuits, in the d−q frame, the VSI equations can be obtained from the circuit as follows:

di   sx )  uc  Lf Lx us ( sx  x=a,b,c dt  digx  u =L i  ugx   c g dt gx  i  C dus  i s gx  Lx dt  i =C dus   i s  s s dt x  a ,b ,c Lx x 

(1)

Where，sx denote the switching state . According to Eq. (1), the control block diagram of the LCL-GCI studied in this paper is as shown in the Fig.2. ug (s) uc iL ig ( s) us + d (s) G (s) + G (s) G (s) + 1

3

2

Fig.2 Block diagram of LCL -GCI

Where, G1(s)  1/ ( Lf s  Rf ) , G2 (s)  1/ sCf  Rc , G3 (s)  1/ ( Lg s  Rg ) . According to the Mason formula [30], the transfer function G(s) between igx(s) and d(s) is derived as igx ( s) us G2 ( s)G3 ( s)G1 ( s) G(s)  = =us (1  sCf Rc ) / ( s3 Lf Cf Lg +s 2Cf ( Lg  Lf )  s 2Cf ( Lf Rf  Rg Lg ) d ( s) 1+G1 ( s)G2 ( s)  G2 ( s)G3 ( s)

(2)

 s( Rc Lf +Rc Lg  Cf ( Rf Rg +Rf Rc +Rc Rg )  Rc ( Rf  Rg )) When the filter capacitance is ignored, the system can be equivalent to a single L-type grid-connected inverter, then, the transfer function G(s) will be obtained as:

G( s) 

igx ( s) d (s)

=

us s( Lf +Lg） Rf  Rg

(3)

(dB)

Magnitude(dB)

According to the comparison between Eq. (2) and Eq. (3), it can be seen that the LCL-GCI is a third-order system, while the L-type is a first-order system. Unless otherwise noted, in all the simulation and experiment cases, the parameters are consistent with the theoretical analysis. The parameters of LCL filter involved is as below: Lg=0.04mH, Rg=0.001 ,Cf=650uF, Rc=0.03 ,Lf=0.70mH,Rf=0.01 . The amplitude-frequency characteristic curve of LCL-type and L-type filter is shown as Fig.3. LCLfilter

100

L filter

0

(deg)

Phase(deg)

-100 -90 -135 -180 -225 -270 2 10

3

10

4

Frequency(Hz) (Hz)

10

5

10

Fig.3 Amplitude-frequency characteristic curve of LCL and L filter

It can be seen that the LCL-type and L-type filter shows equivalent filtering properties at the low and high-frequency band. However, as shown in the Fig.3, the LCL filter is a three-order system, it will generate a large overshoot at the resonance frequency, resulting in the amplification of the harmonic amplitude at the resonance frequency, thus increasing the content of high-order harmonics in the grid connected current. Therefore, if the drawbacks of the LCL filter can be avoided while maintaining their merits, and the performance of LCL-GCI can be effectively improved with low computational burden and high-power quality. This is the motivation of this paper, which will be discussed in the sub-sequent sections.

3. The design method of the improved current SMC strategy To suppress the influence of the resonance peak, various control schemes have been presented by worldwide scholar, including passive damping (capacitor branch concatenated resistance) [31], capacitance current prediction [32], and single current feedback control [12], and so on. The performance of system is effectively improved by the aforementioned

discussion, however, the tradition control methods increase the design costs and losses of system, and there is still a phase angle between the grid-connected current and the voltage. Meanwhile, it is difficult to guarantee the unit power factor control. As an effective control algorithm, SMC has been widely used for the current control of power converters with the advantages of the "structure" is not fixed, but changing with the change of the system status, the sliding mode variable structure has good adaptability for the current control of grid inverter[34]. However, the detailed analysis and design method of the three-phase LCL-type grid inverter with SMC method was rarely reported. In this section, the detail design method of traditional current loop and the proposed SMC strategy will be discussed, respectively. 3.1 The traditional closed-loop current control strategy The three-phase LCL-type grid inverter allows for the generation of grid current with lower harmonic distortion and high power density, this characteristics makes it is widely used in the energy conversion technologies. However, to improve the performance of system effectively, the aforementioned schemes suffer from an apparent lack of systematic design procedures. And high sampling frequency is essential in order to reduce the current harmonics and achieve good steady-state performance. The traditional current closed-loop control method is shown as Fig. 4. ugm igm u u * + igm Gi (s ) + igm G2 ( s ) c + Gi (s ) + G3 ( s ) iLk uc

* + iLm

iLm

a. Closed-loop control based on grid current feedback ugm igm u u Gi (s ) + G2 ( s ) c + Gi (s ) + G3 ( s ) uc

igm

b. Closed-loop control based on converter current feedback Fig.4 The traditional closed-loop current control structure

According to the described in Ref.[33], due to the poles are always distributed in the right half plane of the complex plane, the overall system shown in the Fig.4(a) is difficult to be closed-loop stable. Meanwhile, the close-loop control method based on the converter current iLm (m=d,q) feedback is mainly adopted in the real system. The converter current can alternatively be sensed for feedback control as shown in Fig. 4(b). Since the grid current is not directly controlled, the q-axis current reference is not zero. As analyzed in the above, the stable operation of system can be achieved by selecting the appropriate controller parameters. However, its adoption for open-loop stability analysis is not convenient because the feedback variable is tapped from the middle of the open-loop path rather than at the end. Furthermore, the traditional control strategy relies too much on the single modulated wave output by the current inner loop, which undoubtedly increases the burden of the inner loop and the accuracy requirement of parameter. 3.2 The design method of the proposed SMC strategy To avoid the unstable performance caused by the LCL-type filter, a series damping resistance may be introduced to the filter capacitor branch. However, the power loss of the system is increased. What’s more, the performance of steady-state and transient is poor. In order to improve the whole performance of system effectively，an improved SMC control strategy is presented, the proposed control diagram block of three-phase LCL-type grid inverter is shown as Fig.5. The details are discussed as below.

is

T3

T1

T5

Lf , Rf

iLx

us

Lg , Rg

igx ugx

Cs

n

T4

T6

T2

T1 SVPWM uβ uα dq/αβ uq ud SMC SMC         * igq

C f , Rc

T6

 abc/dq PLL LPF LPF LPF LPF uga , ugb , ugc iLd i Lq icd icq abc/dq

* igd

Fig.5 Block diagram of the proposed control system

However, the direct control of grid current igx may cause instability problem of system, the grid current iLx is used to indirect control the grid current igx in this paper. The control diagram of the improved SMC designed in this paper is shown as Fig.5. To achieve unit power factor control, the d axis component of the grid-connected current in the two-phase synchronous rotating coordinate system is oriented according to the system power, and the q axis component of the grid-connected current is set to zero. The sum of the converter current and capacitor current processed by the low-pass filter (LPF) is as the given signal of the inner loop. Once the reference is computed, the reference current and the estimated inverter-side current are used in a sliding surface, and the output ud and uq of the internal current loop regulator are converted by parker to obtain the modulating signals uα and uβ . Finally, the generated control signal is applied to control the switching signal of the VSI, generating a current without oscillations. The control block diagram with the proposed improved SMC strategy in this paper is shown as Fig.6. The details are discussed as below. * + iLm +

ugm

igm

* iLm

SMC

+u

G1 (s ) uc

+ iLm

G2 ( s )

uc +

G3 ( s )

igm

icm

Fig.6 Control block diagram of the current inner loop with the proposed SMC strategy

3.2.1 SMC in the synchronously rotating dq-frame The design method of SMC mainly divided into the design of switching surface, control law and reaching law, etc. The dynamic performance of system is mainly depended by the reaching law, and the main task of the sliding-mode control law is to force the system state trajectory to reach the sliding surface. To simplify the analysis, the influence of parasitic resistance is ignored, according to the Kirchhoff equations of the elementary circuits, the circuit equation of the LCL-type grid inverter describes in Fig.6 is written as:  I gd (k  1)=      I gq (k  1)=   

Rf I gd (k )  I gq (k )  us Sd  ucd (k ) Lf Rf I gd (k )  I gd (k )  us Sq (k )  ucq (k ) Lf

(4)

while their capitalized notations are for representing them in the s-domain. The measured inverter-side current is used to compute the estimation error, and the equation for the estate estimation is expressed as follows: (5) x(k  1)  Ax(k )  Bu(k )  Fe(k ) Where, X =[igd (k ) igq (k )]T , u(k )  [udeq (k ) udeq (k )]T

  Rf / Lf  

, F  Ts / Lf , e(k )  [ucd (k ) ucq (k )]T , A  

   Rf / Lf 

0  u B s  , Ts being the sampling time, udeq(k) and udeq(k) is the equivalent control of the grid-current igq and igd. 0 u s   As it was explained, in order to achieve a damped dynamics the estimated inverter-side current can be used in a SMC controller. Then, the following sliding surface vector used to control the grid-currents can be defined as:

* * x1  I gd  I gd ，x2  I gq  I gq

(6)

* * where I gq and I gd are the reference current in the d-q domain, respectively.

From Eq. (6) and Eq. (5), the expression of the sliding surface can be rewritten as follows: s(k )  Cx(k )

(7)

T

T

Where, C =[c1 c2 ] , c1 and c2 are constant value, x(k) = [igd (k ) igq (k )] is the space-state vector. 3.2.2 Selection of sliding surface constants in the synchronously rotating dq-Frame It is necessary to point out that the control law is needed to control the system to reach the sliding surface quickly and accurately when the system without reaching the sliding surface. For the practical control systems, due to factors such as system exists inertia, time delay, the sliding mode variable structure control in the existence of the sliding mode condition inevitably high-frequency chattering. Reaching law of sliding mode variable controller often used to improve the dynamic performance of system, the commonly reaching law mainly consists of constant speed reaching law, exponential reaching law, the exponential reaching law and generally reaching law [35]. Appropriate reaching law is very important for the dynamic and static performance, increase the control effect when the system away from the sliding mode surface, reduce or even cancel the control effect on surface of the sliding mode, not only can obtain good dynamic characteristics, also can weaken the chattering phenomenon. For the discrete-time dynamic model of LCL-type grid inverter, the integral-type sliding surface is rearranged as below: ds (8) =-k3 s-k0sgn(s), k3  0, k0  0 dt Where, sgn(s) is the switching function. However, it is clearly that the sgn(s) is a hard switching function. To eliminate the chattering phenomenon, a new continuous switching function is selected to instead of the traditional switching function. Then, the expression of the exponential reaching law in continuous-time domain is given by:

s(k  1)=  k s(k )

 sat( s ( k ) -1)



s  T s(k ) sat(s(k )) k  0,   0,1    0，  0

(9)

Where, the expression of sat(s) described in the Eq. (9) is:  1, s(k )    (10) s at( s(k ))   s(k ) / , s( k )  (  0) 1, s(k )    When the system state reaches to the switching surface, it is obvious that the expression of sliding mode control law should meet Eq. (11), the expression yields as:  sat( s ( k ) -1)



s =Cx(k )  Bu(k )=  k s(k ) s  T s(k ) sat(s(k )) Based on the Eq. (6)-Eq. (7), the discretized output signal equation of the proposed control strategy is derived as: 

(11)

sat( s 1)

u(k )  (CT B)-1[CT ( A  I ) x(k )  CT Fe(k )   s sat(s)  k s ] (12) When the system is in sliding regime, the converter dynamics is forced to evolve over the sliding surface, and the new dynamics can be derived according to the invariance conditions, s(k+1)=s(k)=0.Then, taking into account the aforementioned expression, the discrete equivalent control can be found by using Eq.(5) and Eq.(10) in Eq.(12). Then, the expression of control law of SMC is obtained as:  ( RLTs  L)igd (k )  LTigq (k )  ucd     u deq (k )   c1usTs  (13) u (k )      ( R T  L)i (k )  LTi (k )  u  u ( k ) qeq L s gq gd cq     c2usTs   Where, udeq(k) and uqeq(k) are the equivalent control of the grid-current igq and igd, which is the solution of Δs = s(k + 1) − s(k) = 0. 3.2.3 Stability of the SMC In this section, the stability of the SMC control system is analyzed by Lyapunov method, the expression of Lyapunov functions is written as below:

1 V = s2 2

(14)

The last requirement in the design of SMC is to satisfy the reaching conditions. The most often used reaching conditions for each grid-current in the d-q domain are given by ss <0, based on the Eq. (14) and Eq. (17), the expression of dV / dt is

obtained as: sat( s 1)



sat( s 1)

1

V ( x)  ss  s(k s s   s sat(s))  k s s2   s sat(s)<0 (15) Where, k and  are the parameters of the reaching law, respectively. Based on the above analysis, it is clearly that the change of the sliding surface s(x) is contrary with the change of dV ( x) / dt , the state variables could reach the sliding surface with the introduction of disturbance, and the proposed SMC control method in this paper meets the global asymptotical stability criterion. In addition, according to Ref. [36-37], the response time for the system reached from the initial state to the sliding surface is depended by the variable parameter of SMC. The response of system will be decreased with the increasing of k. However, the anti-interference ability will be declined. When the value of  is increased, the anti-interference ability will be enhanced, and the chattering phenomenon is obvious. In this paper, the value of k and  are selected to 5 and 3, respectively.

4. Simulation and experiment discussion 4.1 Simulation results discussion To verify the performance of the proposed SMC strategy, simulation studies based on the Matlab/Simulink simulation software with the novel SMC strategy and the convention methods are built, respectively. Unless otherwise noted, in all simulation cases, the simulation and experimental parameters are consistent with the theoretical analysis. The parameters of converter module involved are show as Table.1. Table.1 Circuit parameters of the LCL-GCI involved Parameter Description Values usx(V/Hz)

Grid voltage

380/50

Lg(uH)

Grid equivalent inductance

40

Rg(

Grid equivalent resistance

0.001

Filter inductor

700

Inductor equivalent resistance

0.01

Filter capacitor

50

Capacitor equivalent resistance

0.004

fs(kHz)

Sampling frequency

20

us(V)

DC voltage

720

)

Lf(uH) Rf (

)

Cf(uF) Rc(

)

400 200 0 -200 -400 100

-100 100

iga

0 0.22

0.24

0.26

0.28

0.3

Mag (% of Fundamental)

iLa

0

-100 0.2

Fundamental (50Hz) = 96.84 , THD= 2.07%

uga 0.8 0.6 0.4 0.2 0

0

Time(0.02s/div) a. Grid current waveforms with full load Fig.7 Steady-state simulation waveforms with half load and FFT analysis

2

4

6

8 10 12 Harmonic order

14

16

18

20

b. FFT analysis result of grid current

Just take phase A as example, the related simulation results when the system working in full power with the traditional PI control method is shown as Fig.7. From top to bottom，the curves shown in the Fig. 7(a) is the grid voltage (uga), converter current (iLa) and grid-current (iga). According to the simulated waveforms in Fig.7 (a), the input current is in phase with the input phase voltage, which agrees well with the case of unity input power factor. The FFT analysis result of iga is shown as Fig.7 (b). However, there is still a small distortion in current peak.

400 200 0 -200 -400 100

Mag (% of Fundamental)

iLa

0 -100 100

iga

0 -100 0.2

Fundamental (50Hz) = 98.79 , THD= 1.41%

uga

0.22

0.24

0.26

0.28

0.6

0.4

0.2

0

0.3

0

Time(0.02s/div) a. Grid current waveforms with full load Fig.8 Steady-state simulation waveforms with half load and FFT analysis

2

4

6

8 10 12 Harmonic order

14

16

18

20

b. FFT analysis result of grid current

Meanwhile, the steady-state simulation result under the same working conditional is shown as Fig 8.a. The results show that the quality of grid current with the proposed SMC control method is significantly improved and its THD is decreased from 2.07% to 1.41%. The proposed control strategy can suppress the grid current distortion effectively when compared the Fig.7 and Fig.8.According to the simulated waveforms in Fig.8 and Fig.7, the input current is in phase with the input phase voltage, which agrees well with the case of unity input power factor. The results when operated in the rated power show that the quality of grid current with the SMC strategy is effectively improved, consequently. Comparatively, the grid-current waveforms in Fig. 7 diverging a little worse than that in Fig.8, which has demonstrated that the SMC presented is sufficiently superiority of the traditional strategy when working in the same conditional. Obviously, the characteristic of current spectrums are better than those in using the existing control strategy. 400 200 0 -200 -400 50

Fundamental (50Hz) = 45.96 , THD= 5.67% Mag (% of Fundamental)

uga

iLa

0 -50 50

iga

0 -50 0.2

0.22

0.24

0.26

0.28

1 0.8 0.6 0.4 0.2 0

0.3

0

2

4

6

8

10

12

14

Time(0.02s/div) Harmonic order a. Grid current waveforms with convention control b. FFT analysis result of grid current Fig.9 Steady-state simulation waveforms with traditional control method under full load

16

18

20

The steady-state simulation and FFT analysis result with the traditional method when the system working in half power are shown as Fig.9.The THD of the grid current is approximately 5.67% when the traditional control method adopted. 400 200 0 -200 -400 50

Mag (% of Fundamental)

iLa

0 -50 50

iga

0 -50 0.2

Fundamental (50Hz) = 45.98 , THD= 3.20%

uga

0.22

0.24

0.26

Time(0.02s/div)

0.28

0.3

2 1.5 1 0.5 0

0

2

4

6

8 10 12 Harmonic order

14

16

18

20

a. Grid current waveforms with convention control b. FFT analysis result of grid current Fig.10 Steady-state simulation waveforms with the proposed control under full load

Further, the simulation waveform and FFT analysis result with the proposed method under half load are shown as Fig.10. It is clearly that the performance of system with the proposed control method is excellent when compared the Fig.9 and Fig.10. Obviously, the grid-current waveform with the proposed SMC is smoother than that response with the convention control. In comparison, with the same sampling frequency, the performance based on the SMC methods achieves much better results than the convention strategy. For SMC, the THD is significantly decreased to 3.20%, which is nearly half of the convention control. The proposed SMC presents better result by achieving lower THD and power ripple than that of conventional strategy.

400 200 0 -200 -400 100

uga

iLa

0

uga

iLa

0

-100 100

iga

0 -100 0.1

400 200 0 -200 -400 100

-100 100

iga

0

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-100 0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time(0.05s/div) a. Transient output with traditional control b. Transient output with the proposed method Fig.11 Transient simulation output waveforms of load change between half load and full load conditions

0.5

Time(0.05s/div)

In order to further prove the effectiveness of the proposed strategy, the system loads are changed from full load to half load at t =0.3s. Comparing the response waveform shown in the Fig.11 (a) and Fig.11 (b), the transient response of the grid-current is largely consistent, there is almost no overshoot, and the time for the current to achieve a smooth transition to a new stable state is 0.008s and 0.005s under the condition of transient changing 50% load, and however, the presented SMC presents lower current harmonics. It is clearly seen that the system has good anti-jamming performance and good control performance. These results further verify the correctness and superiority of the SMC control strategy in this paper. 4.2 RT-Lab experiment results analysis In this section, the performance of the proposed SMC and comparison with the existing method with respect to dynamic response and static response, are analyzed and discussed in the experiment results, respectively. A hardware-in-the-loop experimental platform on a 50kW LCL-GCI based on the RT-LAB has been developed. Note that in all the simulation cases, the simulation and experimental parameters are consistent with the theoretical analysis. The main parameters involved are consistent with the simulations. The main parameters adopted are as shown in Tab.1.

iga

iga

iLa

iLa

uga

uga

a. Convention control method Fig.12 Experimental output waveforms with full load

b. Proposed SMC control

Fig.12 shows the static response waveform by using different control methods. The current total harmonic distortion (THD) is as high as 3.65% when the convention control method adopted. The conventional control has certain drawbacks. One of the main drawbacks is that high sampling frequency is essential in order to reduce the current harmonics and achieve good steady-state performance. The performance of system is deeply depended on the controller parameters. In comparison, with the same sampling frequency, the performance based on the improved SMC methods achieves much better results than the existing method. For SMC, the THD is significantly decreased to 1.85%, which is nearly half of the convention control strategy. The proposed SMC presents better result by achieving lower THD and power ripple than that of conventional control strategy.

iga

iga

iLa

iLa

uga

uga

a. Convention control method Fig.13 Experimental output waveforms with half load

b. Proposed SMC control

For comprehensive comparisons, the steady performance when the system operated in half load with the traditional PI and the proposed SMC control methods is also presented as shown in Fig. 13. The THD of the grid current is approximately 5.13% when the traditional current control method is adopted; the THD is approximately 3.54% with the proposed method. In comparison, with the same sampling frequency, the performance based on the SMC methods achieves much better results than convention control method. iga iga

uga ugb ugc

uga ugb ugc

a. Convention control method Fig.14 Experimental output waveforms with the unbalanced grid voltages

b. Proposed SMC control

The responses waveform of grid current and grid voltages with the unbalanced grid voltages (grid voltage of phase A is kept 178rms, grid voltage of phase B and C are 220rms). As described above, the improved SMC strategy is based on the sliding surface functions formed in d and q frames using the capacitor voltage error and its rate of change. By comparing Fig.14 (a) and Fig.14 (b), the performance with the unbalanced grid voltages based on the SMC methods achieves much better results than the convention strategy.

iga

iga

iLa

iLa

uga

uga

a. Convention control method Fig.15 Experimental output waveforms with the change of active current

b. Proposed SMC control

To show the dynamic performance of the presented SMC-DPC, Fig.15 shows the transient response waveform when *

the active current reference signal id steps from 75A (full load) to 37.5A (half load). The curves involved in the Fig. 15 are the active current, grid voltage and current of phase A, respectively. As shown in the Fig.15 (b), there is almost no overshoot, and the time for the current to achieve a smooth transition to a new stable state within 0.0010 s under the condition of transient changing 50% load. By comparisons, it is obviously that the grid-current can track the reference value quickly, the

transient response of system is largely consistent, and however, the presented SMC presents lower current harmonics and overshoot. The experimental results are agreed very well with the simulated results. Besides, the proposed SMC method has the advantages of easy implementation, as well as a low computational burden and design complexity. As a result, the theory analysis is demonstrated. All the simulation and RT-LAB experimental results show that the performance of three-phase LCL-GCI is effectively improved by the proposed improved SMC control strategy. At the same time the proposed control method shows great steady-state and transient performance. Besides, the proposed SMC method could also be used for other three-phase topologies.

5. Conclusions Aiming at the performances of LCL-GCI with the traditional control method has poor dynamic, a current compound control strategy based on the current feedforward and sliding mode variable is proposed in this paper, and it applied to the current inner loop control of LCL-GCI, the theoretical basis and realization method of the proposed SMC method is presented. The detailed theoretical design steps are given, and the reliability of the SMC presented was also tested in the synchronously rotating dq-frame by comprehensive simulation and experiment. The following conclusions are obtained: (1) Compared with the convention control strategy, the harmonic and the overall THD of the grid-current with the presented SMC method is reduced. (2) The overshoot phenomenon of grid current is significantly reduced when the load changed; What’s more, no additional sensor is required. In conclusion, the proposed SMC control strategy not only improves the transient and steady-state of grid current quality, but also the overshoot phenomenon of grid current is significantly reduced. In a future work, this method will be applied to other converters with the LCL filter as rectifiers or active power filters by finding the appropriate reduced model for each converter.

Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Acknowledgment This work was supported by the National Natural Science Fund of China (No. 51677151) and International Exchange and Cooperation Project of Key R&D Program in Shaanxi (No. 2017KW-035).

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