VOLUME XX, 2017 1

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Digital Object Identifier 10.1109/ACCESS.2017.Doi Number

A Robust Second-Order Sliding Mode Control for Single-Phase Photovoltaic Grid-Connected Voltage Source Inverter BIN GUO, (Student Member, IEEE), MEI SU, YAO SUN, (Member, IEEE), HUI WANG, HANBING DAN, (Member, IEEE), ZHONGTING TANG, (Student Member, IEEE), AND BIN CHENG School of Automation, Central South University, Changsha 410083, China Hunan Provincial Key Laboratory of Power Electronics Equipment and Grid, Changsha 410083, China

Corresponding author: Hanbing Dan (e-mail: daniel698@sina.com).

This work was supported in part by National Natural Science Foundation of China under Grant 51677195, the Key Technology R&D Program of Hunan Province of China under Grant 2018SK2140 and the Project of Innovation-driven Plan in Central South University under Grant 2019CX0003.

ABSTRACT In this paper, a super-twisting algorithm (STA) second order sliding mode control (SOSMC) is proposed for single-phase photovoltaic grid-connected voltage source inverters. The SOSMC approach is aimed to inject sinusoidal current to grid with low total harmonic distortion (THD), strong robustness to parameter variations, fast dynamic response to solar irradiance changes. As the discontinuous sign function in the traditional sliding mode control (SMC) is replaced by the continuous super-twisting function, the chattering problem is eliminated. Furthermore, a robust sliding mode differentiator (SMD) is proposed to acquire the derivative of current reference which is difficult to obtain in practice. The stability of the system under the proposed method is proved through the Lyapunov theory. Experimental results validate that the proposed method has satisfactory performance in both dynamic and steady-state conditions, as well as disturbance rejection.

INDEX TERMS Super-twisting algorithm (STA), second order sliding mode control (SOSMC), sliding mode differentiator (SMD), single-phase photovoltaic grid-connected system.

I. INTRODUCTION Nowadays, distributed power generation systems (DPGS) based on renewable energy (solar and wind energy) have received more and more attention due to the increasing electricity demand and growing interest in environmental problems [1], [2]. Owing to the government policies, feed-in-tariff and the cost-reduction of photovoltaic (PV) installations, the PV power generation system has attracted considerable attention in recent years [3], [4]. The objective of such system is to deliver power from PV array to the unity grid usually by means of a grid-connected voltage source inverter (VSI) [5]. The VSI injects an ac current with the requirement of specified frequency and minimum THD into the grid via a filter [6].

Generally, LCL-filter or L-filter is applied to attenuate the switching harmonics of grid-connected inverter. Compared with L-filter, LCL-filter has the advantages on small volume and strong attenuation of high-frequency switching ripples [7]. However, due to the resonance hazard of the LCL-filter,

damping solutions are needed to stabilize the system [8], which increases the control complexity and requires extra sensors. Alternatively, the L-filter is easily implemented in practice because it is a first-order system. However, the L-filter increases size and cost due to relatively larger inductor value to meet the harmonic limits [9]. Therefore, the design of an appropriate control strategy for PV grid-connected VSI with a small L-filter is a challenging issue due to the performance specifications like preferably zero steady-state error, low THD in grid current, fast dynamic response and strong robustness under system parameters variation and external disturbance [10].

To achieve the aforementioned performance requirements, many control strategies have been proposed in [11-18]. Proportional-integral (PI) regulator [11] is widely used in engineering practice due to easy implementation and strong robustness. However, the steady-state error with related to the reference value of the sine wave is reduced but can’t

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2 VOLUME XX, 2017

become zero [12]. Although proportional resonant (PR) controller can achieve zero steady-state error, it is sensitive to frequency variations in the grid [13], [14]. Due to the fast dynamic response and easy inclusion of system constraints and nonlinearities, model predictive control (MPC) has become an attractive control for power inverters [3]. However, it suffers from model mismatch and parameter uncertainty. To address that issue, an adaptive parameter identification technique is introduced in MPC [15] at the cost of computation burden. The plug-in repetitive control (RC) in [16] is an effective way to eliminate multiple harmonics, but it complicates the controller design. Due to the inherent nonlinearity of the system, the aforementioned control methods yield various advantages and drawbacks related to steady-state error, dynamic response, control complexity, robustness and can only fulfill parts of the performance requirements.

Alternatively, as a nonlinear control method, the sliding mode control (SMC) has gained special interest due to its superior performance such as robustness against parameter variations, fast dynamic response, simplicity in implementation and good regulation capability [17], [18]. In [19], SMC has been proposed to provide good performance in the mitigation of voltage oscillations between the dc-dc converter and the inverter, and to ensure the tracking of the voltage reference provided by the maximum power point tracking (MPPT) algorithm. The SMC approach is used to achieve MPPT and serve the function of reactive power injection in commercial PV inverters [20], [21]. However, chattering phenomenon is their major drawback, which can result in instability and electromagnetic interference (EMI) noise issues. To eliminate the chattering effect, SMC has been implemented with the double-band hysteresis control [6]. However, the switching frequency is mitigated but cannot be fixed. Chattering problem can also be overcome by replacing the sign function with a similar smooth function such as the practical saturation function [22], ideal saturation function [23] or sigmoid function [24]. Although these approaches can eliminate the chattering effect, they suffer from the degradation of robustness and tracking performance. Second order sliding mode control (SOSMC) [25], [26] is a potential solution to reduce the chattering phenomenon without affecting system performance [27]. However, compared with the first order SMC, the increasing information demand limits its widespread application.

To cope with the shortcomings mentioned above, the super-twisting algorithm (STA) SOSMC is proposed in this paper. It eliminates the chattering problem by reducing discontinuous input through the enforcement of continuous control action. Owing to this merit, STA has been widely applied to all works of life. Liang et al. [28] have demonstrated the application of STA to online observe the stator resistance of permanent magnet synchronous machines. Mishra et al. [29] have proposed a cascaded inner-loop STA based SMC and outer-loop PI speed controller for induction

motor, which lies in the simplicity of control design in the presence of operational constraints. Kchaou et al. [30] have applied the algorithm for MPPT of PV system, the simulation results produced excellent tracking performance in MPPT compared to the conventional SMC. In addition, an adaptive STA is implemented for wind energy conversion system [31] to maximize the energy production simultaneously reducing the mechanical stress on the shaft. In practice, different applications have different requirements, the standard STA should be tailored to cater to the specific problem. To the best of authors’ knowledge, there are no references in the literature about the use of STA applied to control the PV grid-connected inverter. In fact, the proposed method is suitable for PV application due to the following reasons: 1) Fast dynamic response and strong robustness: The proposed method has fast dynamic response to solar irradiance variations, strong robustness to system parameter uncertainties and external disturbances (such as distortion of grid voltage). 2) Simple realization: The method does not require heavy computation burden like repetitive controller and multi-resonant controller to realize good performance.

Therefore, the main contribution of this paper lies in the design of PV grid-tied controller which achieves chattering suppression, maintains robustness and finite time convergence properties under the conditions of solar irradiance variations, parametric uncertainties and external disturbances. A robust SOSMC is designed in the current loop of inverter to realize strong robustness and low THD. In addition, SOSMC method is proposed in the current loop of boost converter to achieve fast tracking and eliminate the adverse effect of dc-link voltage pulsation on MPPT. Moreover, the detailed parameters design guidelines of the proposed method are given, which contribute to engineering implementation. The feasibility and superiority of the proposed strategy are verified by experimental results and comparative analysis.

This paper is organized as follows: The system model analysis and operation principle of single-phase PV generation system are presented in Section Ⅱ. In Section Ⅲ, the detailed design of controller and the stability analysis of the proposed method are introduced. Section Ⅳ presents the experimental results in a 4.5-kW single-phase PV system to verify the effectiveness of the proposed control strategy. At last, Section Ⅴ draws the conclusions.

II. SYSTEM CONFIGURATION AND OPERATION PRINCIPLE The topology of the studied single-phase PV grid-tied VSI is shown in Fig. 1, which is made up of two-stage converters. A boost converter is adopted in the front-end stage to control the input voltage according to the MPPT algorithm, while the rear-end one is a Heric-based inverter to transfer power to the grid. The main role of the two auxiliary switches S5 and S6 is to achieve adequate leakage current suppression.

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2 VOLUME XX, 2017

VgUdc

S1

S2

S3

S4

S5

S6

L1

a

b

iL

r

+

L2

ipv

CdcS7

L3

CpvUpv

D1

Boost Converter Heric-Based Inverter

iL3

i1

FIGURE 1. Topology of single-phase PV grid-connected VSI with L filter (L1=L2).

0 π 2π

0

S5

S6

0S1, S4

0

Vg

0

S2, S3

Ⅰ ⅣⅡ Ⅲ

iL

ωt

ωt

ωt

ωt

ωt

FIGURE 2. Schematic of the gate drive signals for HERIC inverter with non-unity power factor.

In order to achieve reactive power regulation and improve the efficiency of the system, the modulation strategy proposed in [4] is adopted in this paper. Fig. 2 presents the principle operation of Heric topology in non-unity power factor (PF). As shown in Fig. 2, region Ⅰ and region Ⅲ are negative power region (Vg and iL are opposite polarity), while region Ⅱ and region Ⅳ are positive power region (Vg and iL are same polarity). When the system operates in unity power factor, region Ⅰ and Ⅲ become zero.

In region Ⅰ and Ⅲ, S1, S2, S3 and S4 are turned off, S5 and S6 are turned on/off when the modulation wave is larger/smaller than the carrier wave. Therefore, the zero-state voltage can be generated during the negative power region.

In region Ⅱ, S6 is on all the time, when the modulation wave is larger than carrier wave, S1 and S4 are turned on, otherwise turned off. Similarly, in region Ⅳ, S5 is on all the time, S2 and S3 are turned on when the modulation wave is larger than carrier wave, otherwise turned off. From Fig. 2, it can be concluded that the zero-voltage state can be realized not only in positive power section but also in negative power section.

Neglecting the total series equivalent resistance r of inductor L1 and L2 to simplify the derivation, the mathematical model of the dc-dc converter and dc-ac inverter based on pulse-width modulation (PWM) can be written as

3pv

pv pv L

dUC i i

dt (1)

33 1(1 )L

pv dc

diL U u U

dt (2)

Lab g dc g

diL U V uU V

dt (3)

1 3(1 ) dcdc L L

dUC u i ui

dt (4)

where L=L1+L2, Upv, ipv, iL3, Udc, Uab, Vg and iL are ac filter inductor, PV output voltage and current, boost current, dc-link voltage, inverter output voltage, grid voltage and grid current, respectively. u1 and u represent the control input of boost converter and inverter, respectively.

III. DESIGN AND CONTROL OF PV SYSTEM

A. PROPOSED ROBUST SOSMC FOR INVERTER In single-phase PV grid-connected inverter, a cascade control structure is used to govern the system presented by (3)-(4). The controller is made up of an inner current loop and an outer voltage loop. For the current tracking loop, the proposed method ensures the grid current convergence fast to its reference with low THD and zero steady-state error. For the voltage regulation loop, a traditional PI controller is implemented to regulate the dc-link voltage to its desired value. Meanwhile, a notch filter is adopted in the voltage loop to eliminate the grid current harmonics caused by secondary pulsation in dc-link voltage [32]. Due to the limited space, the detailed analysis and design process of the outer loop PI controller are not included in this paper, which can be referred to [20].

1) SLIDING SURFACE OF SOSMC Since the control objective of the SOSMC for single-phase grid-connected VSI is to control the grid current, and to add a degree of freedom to adjust the bandwidth of the system, an additional current error integral term is included as a state variable. Therefore, the sliding surface can be defined as follows:

1 2S X X (5)

where 1 L LX i i , 2 1X X d and λ is a positive sliding

coefficient. In the X1-X2 plane, S=0 means a line passing through the origin with a slop equal to λ. The first time derivative of (5) can be written as

1 2

1 1=

S X X

X X

(6)

During the sliding mode, S=0 and S =0, the grid current error can be expressed as

1 1( ) (0) tX t X e (7)

It can be concluded that the value of λ affects the dynamic response of closed-loop system.

2) CONTROLLER DESIGN The STA which has the advantage of finite-time convergence to the set point and rejecting smooth

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disturbances of arbitrary shape has been developed for the systems of relative degree-1.

The global control law u(t) consists of two terms: the equivalent control term ueq and the super-twisting control term ust. Therefore, the global control law can be defined as

eq stu u u (8)

where the equivalent control term ueq can be obtained by solving the following equation:

=0S (9) Substituting (3) and (6) into (9), the ueq can be calculated

as follows:

1( ) geq L

dc dc

V L du i X

U U dt (10)

where sin( ) L mi I t is the reference of grid current, the

amplitude Im comes from the output of voltage loop, the phase angle of grid current reference is obtained through a phase-locked loop .

The expression of STA term ust is given as 1

21

2

( )

( )stu c S sign S v

v c sign S

(11)

where c1, c2 are positive constants. The selection of these parameters are discussed in Section Ⅲ-A-(5).

However, as mentioned above, the control law (10) depends on the derivative of current reference, which comes from the voltage loop. In practice, it is not easy to get the derivative of a signal in the presence of high frequency noise. It has been known that the Levant’s high-order sliding mode differentiator (HOSM) features the best possible asymptotic in the presence of Lebesgue-measurable sampling noises. Therefore, a sliding mode differentiator (SMD) is applied in this paper to obtain the first-order derivative of current reference. To improve the accuracy of first-order differentiation, the SMD is artificially set to second order.

Considering that the current reference Li consists of a

bounded Lebesgue-measurable noise and its third-order derivative has a known Lipschitz constant L>0. To obtain

Li in finite time, a second-order SMD is adopted as follows

2/31/30 0 0 0 0 0 1

1/21/21 1 1 1 1 0 1 0 2

2 2 2 1

, ( )

, ( )

( )

L Lz L z i sign z i z

z L z sign z z

z Lsign z

(12)

if the parameters β0, β1, and β2 are properly chosen as proposed in [33], the following equalities are true in the absence of input noise, after a finite time transient process:

0 0 1,L L

dz i z i

dt (13)

3) MODEL UNCERTAINTY AND ROBUSTNESS

Let’s consider the system model in (3) with uncertainties as

1 2( ) ( ) gdcLVUdi

udt L L

(14)

where Δ1, and Δ2 are parametric uncertainties, ξ is any external disturbance.

Equation (14) can be rewritten as

2gdcL

VUdiu d

dt L L (15)

where

1 2 d u (16)

The perturbation term d includes parametric uncertainties, unmodeled quantities and external disturbance.

Considering the physical limitation of the system in practice and its behavior during the operation, the following assumptions are introduced.

Assumption: The inductance parameter L in (3) is uncertain with bounded, and the external disturbance ξ is bounded such as

;

LL L L L

(17)

where the upper notation “－” represents the nominal value, Δ is its uncertainty and δ(.) are bounding known positive constants.

From the assumption, it can be assumed that the perturbation d is bounded such as

d (18)

where δ is a known positive constant.

4) STABILITY ANALYSIS Considering the aforementioned perturbation in the actual system, the first order derivative of sliding variable S can be rewritten as

1 1 S X X d (19)

From (8) and (19), the closed loop system is given as 1

21

2

( )

( )

S c S sign S v d

v c sign S

(20)

To prove the stability of system, the Lyapunov function is chosen as [34]

1/22 22 1

1 12 ( ( ) )

2 2

T

V c S v c S sign S v

P

(21)

where 1/2( ) T S sign S v ,

212 1

1

41

22

cc cP

c

.

Its time derivative alone the solution of (11) results as follows

1/2 1/2

1 T TdV Q q

S S (22)

where 2

12 11

1

2

12

cc ccQ

c

, 21 1

2(2 )2 2

T c cq c

.

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2 VOLUME XX, 2017

Applying the bounds on the disturbance (18), as demonstrated in [34], we can get that

1/2

1 TV QS

(23)

where 2 2

2 1 1 111

1

42 ( ) ( 2 )

12( 2 )

c

c c c cccQ

c

.

Obviously, V is negative if 0Q , which represents the

system is strongly globally asymptotically stable if the gains satisfy

1

21

2 11

2

5 4

2( 2 )

c

cc c

c

(24)

5) PARAMETERS SELECTION There are three parameters related to SOSMC, λ, c1 and c2, which play a significant role in obtaining a fast dynamic response as well as ensuring a stable system.

According to (7), λ denotes the pole of sliding mode dynamics. Thus, it is clear that the controller is beneficial to select the λ as large as possible, but it will degrade the tracking performance such as cause large overshoot in the system states. In contrary, the controller with the smaller sliding surface slope λ leads to longer tracking time and slower error convergence. The detailed design guideline for parameter λ is presented in [35], which is not discussed here.

Parameters c1 and c2 are the coefficients of the STA term, which are related to the system stability and the required convergence time of the application. As analyzed in section Ⅲ-A-(4), the gain coefficients c1 and c2 can be easily selected based on the bounded perturbation (18).

B. CONTROL OF THE BOOST CONVERTER The boost converter is used not only to achieve the voltage lifting, but also to realize MPPT. In this study, the perturb and observe (P&O) algorithm that has been widely used in practical application is employed to realize MPPT. For high power boost converters (typically over 1kW), a cascaded control is usually adopted in PV system, which can avoid current transients and reduce failure rates. In the cascaded structure, a conventional PI controller is adopted in voltage loop to generate reference command for the corresponding inner current loop controller; while, the proposed SOSMC method is used in the current loop to enhance the robustness and rapidity of the system. Due to the limited space, the design process of outer loop PI controller is not exhibited here, which can be referred to [20].

1) INNER CURRENT LOOP DESIGN The control objective of inner current loop is to track the current reference iL3ref with zero steady-state error and fast transient response. Similar to the controller design of inverter,

the sliding surface for current control of boost converter can be selected as

1 1 2s x x (25)

where x1=iL3-iL3ref, x2=∫x1dτ, and λ1 is a positive sliding coefficient.

Considering the system model in (2) with uncertainties as

3 11

3 3

(1 )pvL dcUdi u U

ddt L L

(26)

where the perturbation term d1 includes parametric uncertainties, unmodeled dynamics and external disturbance. Considering the physical limitation in practical system and its behavior during the operation, it can be assumed that the perturbation d1 is bounded as |d1|<δ1, where δ1 is a known positive constant.

Then the control law u1 can be obtained as

33 31 1 1 11 ( )

eq st

pv L refst

dc dc dc

u u

U diL Lu x u

U U dt U (27)

where ueq is the equivalent control term, which can be obtained by solving 0s without the perturbation term d1, and u1st is the super-twisting control term.

The first order derivative of sliding variable s can be obtained as

1 1 sts u d (28)

where u1st takes the following form 1

21 3

4

( )

( )stu c s sign s w

w c sign s

(29)

where c3 and c4 are the designed positive constants. Equations (28) and (29) result into STA SOSMC, hence,

the stability of controller can be proved as in section Ⅲ-A-(4). It should be noted that the designed current loop controller

contains the term ueq according to (27), which can be regarded as a feedforward term. It can improve the dynamic performance and reduce the disturbance effect of double-line frequency ripple generated by the rear-end inverter. Furthermore, the gain coefficients of STA controller u1st will be reduced accordingly, which is beneficial to diminish chattering. The overall control block diagram of the boost converter is shown in Fig. 3.

IV. EXPERIMENTAL RESULTS A prototype of a 4.5kW single-phase PV system is developed in the laboratory as shown in Fig. 4. The PV system is controlled by a floating-point digital signal processor (TI TMS320F28335) and the driver signals of insulated-gate bipolar transistors are generated by field programmable gate array (Altera EP2C8T144C8N). Solar simulator (Chroma 62150H-600S) and programmable ac source (Chroma 61830) are used as a PV array and grid, respectively. The parameters of the system and controller are listed in Table Ⅰ, and control block diagram of the proposed control strategy in the inverter is shown in Fig.5. Kpwm is the inverter gain, which is equal to Udc in this paper.

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2 VOLUME XX, 2017

iL3ref λ1

x1 x2

L3/Udc

s

-C3

-C4

Ueq

Ust

+

-

-

+

+

++ +

++

Equivalent term

Super-twisting term

λ1

iL3

Eq.(12)

Sliding mode differentiator 1-Upv/Udc

+

L3/Udcu1+

kup

kui/s

+Upv

-UpvrefP&Oalgorithm

Upv

ipv

Voltage loopMPPT Current loop

+-

vtri

S7

Pulsewidth modulator

+

+

FIGURE 3. Control block diagram of the boost converter.

i*L λ

X1 X2

L

Vg

S

-C1

-C2

Ueq

Ust

kpwm 1/(LS+r)

Vg

iL+-

-

+

+ +

++

-

++

+ +

Equivalent term

Super-twisting term

VSI with L- filter

Uab

1/Udc

λ

PLL

PI

Udc

Vg sin(θ)

Udc*+

-

iL

Voltage loopEq.(12)

Im

Sliding mode differentiator

+

FIGURE 5. Control block diagram of the single-phase grid-connected VSI with the proposed method.

Power Analyzer

L-Type Filter

Controller ProgrammableAC Source

Oscilloscope

PV Simulator

FIGURE 4. Experimental setup.

TABLE I EXPERIMENTAL PARAMETERS

Parameters Values

dc-link voltage: Udc 360 V

Grid voltage: Vg 220 V

Grid frequency: f 50Hz

Switching frequency: fs 20 kHz

Filter inductance: L 1.5 mH

Equivalent resistance: r 0.06 Ω

Sampling time: T 50 µs

Dead-time: Td 1 µs

SOSMC parameter 1: λ SOSMC parameter 2: c1

SOSMC parameter 3: c2

Voltage loop proportional: Kp

Voltage loop integral: Ki

500 0.1 20

1.107 246

A. STEADY-STATE PERFORMANCE OF PV GRID-CONNECTED INVERTER

(a)

(b)

FIGURE 6. Steady-state performance of PV system with the proposed control strategy. (a) Experimental waveform. (b) Harmonic spectrum of grid current.

Fig. 6 shows the experimental waveforms of dc-link voltage, grid voltage, grid current and its harmonic spectrum with the proposed control strategy. It is clear that, although the dc-link voltage has secondary pulsation, the

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2 VOLUME XX, 2017

S5

S6

S1, S4

S2, S3

A

Ⅰ Ⅱ Ⅲ Ⅳ

S5

S6

S1, S4

S2, S3

(a) (b) (c)

S5

S6

S1, S4

S2, S3

B

S5

S6

S1, S4

S2, S3

(d) (e) (f)

FIGURE 7. Experimental results. (a) Experimental waveforms of grid voltage and current at PF of 0.95 (Lagging), (b) Driving signals for the switching devices S1-S6, (c) Zoom-in waveforms of point A. (d) Experimental waveforms of grid voltage and current at PF of 0.95 (Leading), (e) Driving signals for the switching devices S1-S6, (f) Zoom-in waveforms of point B.

20ms

15ms

-1

0

1u

-0.5

0

0.5 X1

-2

0

2 10-3

0 0.02 0.04 0.06 0.08 0.1

-0.2

0

0.2

X2

S

(a) (b) (c)

FIGURE 8. Experimental results of the dynamic waveform with the proposed method in PV system. (a) Waveforms of grid voltage and current when solar irradiance changes from 1000 W/m2 to 700 W/m2, (b) Waveforms of grid voltage and current when solar irradiance changes back to 1000 W/m2. (c) Waveforms of control input u, sliding variable X1, X2 and sliding surface S for the case of solar irradiance changes from 1000W/m2 to 700W/m2.

grid current is almost sinusoidal with low THD, which verifies the robustness of the proposed control method to voltage disturbance.

Figs. 7 (a) and (d) show the waveforms of grid voltage and grid current when the experimental prototype operates at PF of 0.95 (lagging) and (leading), respectively. Figs.7 (b), (c), (e), (f) show the experimental driving signals (S1-S6) for the switching devices under the above condition, respectively. In Fig 7 (b), when in region Ⅰ and Ⅲ, S1-S4 are turned off, then when modulation wave is larger than carrier wave, S5 and S6 are turned on. Otherwise, S5 and S6 are turned off. When in region Ⅱ, the drive signals are generated in such a way that the switching device S1 and S4 are switched on and off, while S6 is always on, and S5 is always off. Similarly, when in region Ⅳ, S2 and S3 are switched on and off, while S5 is

always on, and S6 is always off. It is clear that such switching leads to a fixed switching frequency than that obtained by the hysteresis scheme [6], which is beneficial to design the filter and achieve reactive power regulation.

B. DYNAMIC PERFORMANCE OF PV SYSTEM Figs.8 (a) and (b) show the dynamic response of the grid voltage and current for a step change in solar irradiance from 1000W/m2 to 700W/m2 and back to 1000W/m2, respectively. It clearly shows that the system has very short tracking time with less than one power frequency cycle and without overshoot. What’s more, to show the superior performance of the proposed robust second order sliding mode control strategy, the experimental data of the control input u, state variables X1, X2 and sliding surface S

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2 VOLUME XX, 2017

ˆ=0.7 nL LTHD: 1.64

ˆ=1.3 nL LTHD: 1.51

(a) (b)

40msˆ=0.7 nL L

ˆ=1.3 nL L30ms

(c) (d)

FIGURE 9. Experimental results of grid current for the following: (a) and (c) The value of filter inductance in the controller is reduced by 30%, (b) and (d) The value of filter inductance in the controller is increased by 30%.

(a) (b)

FIGURE 10. Experimental results of the steady-state waveform with the proposed SOSMC under the THD of grid voltage is 2.9%. (a) Experimental waveform of grid voltage and current, (b) Experimental spectrum of the grid current.

70ms

75ms

(a) (b) (c)

FIGURE 11. Experimental waveforms of the grid voltage and grid current with the quasi-PR controller. (a) Irradiance changed from 1000 W/m2 to 700 W/m2, (b) Irradiance changed from 700 W/m2 to 1000 W/m2, (c) Steady-state waveform of grid voltage and grid current under the THD of grid voltage is 2.9%.

are obtained under the case of solar irradiance step changes from 1000W/m2 to 700W/m2 at 0.045s, which are shown in Fig.8(c). Although the irradiance suddenly changes, it is obvious that the state variable X1, X2 are nearly zero all the

time, this is because the response speed of outer loop is lower than that of the inner loop. The results show that the proposed method has fast dynamic performance and zero steady-state error. In addition, the chattering issue of the

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TABLE Ⅱ COMPARISONS OF INVERTER CHARACTERISTICS: THREE COMMON CONTROLLERS

AND THE PROPOSED CONTROL STRATEGY

Reference PR [14] MPC[3] SMC[6] Proposed SOSMC

Udc (V) 400 300 400 360 Vg (rms) 220 133 230 220 Number of phases 1 1 1 1 Total power (kVA) 1 2 3.3 4.5 Fswitching (kHz) 20 1.7 (average) 18.8 (average) 20 Fsampling (kHz) 20 20 - 20

Filter type L L LCL L Filter inductor (mH) 3 4.7 L1: 1.74, L2: 0.68 1.5 THD (%) 1.67 3.64 1.4 1.3 Robustness High Low Very high Very high Transient response Fast Very fast Very fast Very fast

FIGURE 12. Experimental results of steady-state waveform with traditional SMC.

system is eliminated by the proposed control strategy.

C. ROBUSTNESS AGAINST INDUCTANCE PARAMETERS VARIATION To evaluate the robustness of the proposed controller, the parameter value of filter inductance is changed to 30% in the controller. The experiment results are shown in Fig.9. It can be seen from Fig. 9 that, although the performance of the system has declined, it still exhibits good steady-state and dynamic performance in the case of 30% change in L, indicating that the proposed method is robust.

D. TEST OF PV INVERTER IN DISTORTED GRID Fig. 10 (a) gives the experimental results of the steady-state waveform of grid current with the proposed method at the condition that the THD of grid voltage is 2.9%. Fig. 10 (b) shows the steady state spectrum of the grid current under the above condition. Clearly, the proposed control strategy offers very good harmonic suppression capability.

E. COMPARISON WITH PR CONTROL AND CONVENTIONAL SLIDING MODE CONTROL In order to exhibit the superior performance of the proposed control strategy, a conventional PR controller proposed in [14] is built to make a comparison. Fig 11(a) and (b) show the dynamic response of PR controller under the condition that solar irradiance suddenly changes from 1000W/m2 to 700W/m2 and back to 1000W/m2. It can be seen that, compared with Fig. 8, the settling time of the conventional PR controller is nearly 75ms, which is far slower than the proposed controller. Fig. 11(c) shows the experimental

results of the steady-state waveform of grid current with the PR controller at the THD of grid voltage is 2.9%, the THD of grid current is 2.7%. Compared with Fig. 10, it can be concluded that the proposed SOSMC strategy has an excellent steady-state performance even with a small value of filter inductance.

To demonstrate the effectiveness of the proposed SOSMC in chattering elimination, a traditional SMC is adopted to make a comparison, that is, using the discontinuous sign function to replace the proposed STA controller. Therefore, the global control law can be defined as u=ueq-αsign(s), where ueq is equivalent control term and α is a positive constant. Fig.12 shows the experimental result of the steady-state waveforms using the conventional SMC. It is obvious that the grid current is chatting due to the discontinuous sign function, which further demonstrates the superiority of the proposed robust SOSMC strategy in chattering suppression.

Table Ⅱ shows the comparison of the proposed control method with classical first-order SMC and other common controllers. The proposed approach not only shows an improvement in terms of reducing THD and settling time, but also eliminates the chattering problem without additional information of any derivative of the sliding variable.

V. CONCLUSION The second order sliding mode technique is a promising control strategy for single-phase PV grid-connected system due to its merits of finite time convergence and robustness. Considering the dynamic and steady-state performance requirements of the grid current in a PV system, the distortion of grid voltage, variation of solar irradiance and uncertainty inductance parameters are regarded as disturbances for the current control loop, which directly affects the performance of the whole system. To improve the disturbance rejection ability and dynamic response, a robust SOSMC is proposed for the current loop. Moreover, a sliding mode differentiator is adopted to realize the derivation of current reference which is difficult to obtain in practice. With the proposed method, the chattering problem of conventional SMC is eliminated, and the fixed switching frequency is

Author Name: Preparation of Papers for IEEE Access (February 2017)

VOLUME XX, 2017 10

achieved. Various experimental results and comparisons with conventional controller demonstrated that the proposed control strategy achieved a shorter settling time to solar irradiance variations, strong robust to parameter uncertainties, and better grid current quality. What’s more, the proposed control strategy can also be applied to wind power generation, active front end and vehicle to grid.

REFERENCES [1] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus,

“Overview of control and grid synchronization for distributed power generation systems,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1398–1409, Oct. 2006.

[2] H. Komurcugil, N. Altin, S. Ozdemir, and I. Sefa, “Lyapunov-Function and Proportional-Resonant-Based Control Strategy for Single-Phase Grid-Connected VSI with LCL Filter,” IEEE Trans. Ind. Electron., vol. 63, no. 5, pp. 2838–2849, May. 2016.

[3] J. Hu, J. Zhu, S. Member, D. G. Dorrell, and S. Member, “Model predictive control of grid-connected inverters for PV systems with flexible power regulation and switching frequency reduction,” IEEE Trans. Ind. Appl. vol. 51, no. 1, pp. 587–594, Jan. 2015.

[4] T. K. S. Freddy, J. H. Lee, H. C. Moon, K. B. Lee, and N. A. Rahim, “Modulation technique for single-phase transformerless photovoltaic inverters with reactive power capability,” IEEE Trans. Ind. Electron., vol. 64, no. 9, pp. 6989–6999, Sep. 2017.

[5] R. Guzman, L. G. de Vicuna, M. Castilla, J. tomas Miret, and J. de la Hoz, “Variable structure control for three-phase LCL-filtered inverters using a reduced converter model,” IEEE Trans. Ind. Electron., vol. 65, no. 1, pp. 5–15, Jan. 2018.

[6] H. Komurcugil, S. Ozdemir, I. Sefa, N. Altin, and O. Kukrer, “Sliding-mode control for single-phase grid-connected LCL-filtered VSI with double-band hysteresis scheme,” IEEE Trans. Ind. Electron., vol. 63, no. 2, pp. 864–873, Feb. 2016.

[7] Z. Xin, X. Wang, P. C. Loh, and F. Blaabjerg, “Grid-current-feedback control for LCL-filtered grid converters with enhanced stability,” IEEE Trans. Power Electron., vol. 32, no. 4, pp. 3216–3228, Apr. 2017.

[8] D. Pan, X. Ruan, C. Bao, W. Li, and X. Wang, “Optimized controller design for LCL-type grid-connected inverter to achieve high robustness against grid-impedance variation,” IEEE Trans. Ind. Electron., vol. 62, no. 3, pp. 1537–1547, Mar. 2015.

[9] D. Pan, X. Ruan, C. Bao, W. Li, and X. Wang, “Capacitor-current-feedback active damping with reduced computation delay for improving robustness of LCL-type grid-connected inverter,” IEEE Trans. Power Electron., vol. 29, no. 7, pp. 3414–3427, Jul. 2014.

[10] H. Komurcugil, N. Altin, S. Ozdemir, and I. Sefa, “An extended lyapunov-function-based control strategy for single-phase UPS inverters,” IEEE Trans. Power Electron., vol. 30, no. 7, pp. 3976–3983, Jul. 2015.

[11] X. H. Wang, X. B. Ruan, S. W. Liu, and C. K. Tse, “Full feedforward of grid voltage for grid-connected inverter with LCL filter to suppress current distortion due to grid voltage harmonics,” IEEE Trans. Power Electron., vol. 25, no. 12, pp. 3119–3127, Dec. 2010.

[12] K. Sayama, S. Anze, K. Ohishi, H. Haga, and T. Shimizu, “Robust and fine sinusoidal voltage control of self-sustained operation mode for photovoltaic generation system,” in Proc. IEEE Conf. Ind. Electron. (IECON), Oct 29-Nov 1, 2014. pp. 1760–1765.

[13] G. Q. Shen, X. C. Zhu, J. Zhang, and D. H. Xu, “A new feedback method for PR current control of LCL-filter-based grid-connected inverter,” IEEE Trans. Ind. Electron., vol. 57, no. 6, pp. 2033–2041, Jun. 2010.

[14] Q. L. Zhao, X. Q. Guo and W.Y.Wu, “Research on control strategy for single-phase grid-connected inverter,” Proc. CSEE, vol. 27, no. 16, pp. 60–64, 2007.

[15] S. Kwak, U. C. Moon, and J. C. Park, “Predictive-control-based direct power control with an adaptive parameter identification technique for improved AFE performance,” IEEE Trans. Power Electron., vol. 29, no. 11, pp. 6178–6187, Nov. 2014.

[16] B. Guo, M. Su, J. Yang, J. Ou, Z. T. Tang and B. Cheng “A hybrid control strategy based on modified repetitive control for single-phase photovoltaic inverter in stand-alone mode,” in Proc IEEE Int. Conf Ind. Electron. Sustain. Energy Syst. (IESES), Jan 32-Feb 2, 2018, pp.308-313.

[17] M. Pichan and H. Rastegar, “Sliding-mode control of four-leg inverter with fixed switching frequency for uninterruptible power supply applications,” IEEE Trans. Ind. Electron., vol. 64, no. 8, pp. 6805–6814, Aug. 2017.

[18] B. Wang, J. Xu, R. J. Wai, and B. Cao, “Adaptive sliding-mode with hysteresis control strategy for simple multimode hybrid energy storage system inelectric vehicles,” IEEE Trans. Ind. Electron., vol. 64, no. 2, pp. 1404–1414, Feb. 2017.

[19] D. G. Montoya, C. A. Ramos-Paja and R. Giral, “Improved design of sliding mode controllers based on the requirements of MPPT techniques,” IEEE Trans. Power Electron., vol. 31, no. 1, pp. 235–247, Jan. 2016.

[20] M. Rezkallah, S. K. Sharma, A. Chandra, B. Singh and D. R. Rousse, “Lyapunov function and sliding mode control approach for the solar-PV grid interface system,” IEEE Trans. Ind. Electron., vol. 64, no. 1, pp. 785–795, Jan. 2017.

[21] B. Liu, M. Su, J. Yang, D. R. Song, D. Q. He and S. J. Song, “Combined reactive power injection modulation and grid current distortion improvement approach for H6 transformer-less photovoltaic inverter,” IEEE Trans. Energy Convers. vol. 32, no.4, pp. 1456–1467, Dec. 2017.

[22] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: a survey,” IEEE Trans.Ind. Electron, vol. 40, no. 1, pp. 2–22, Feb.1993.

[23] A. Abrishamifar, A. A. Ahmad, and M. Mohamadian, “Fixed switching frequency sliding mode control for single-phase unipolar inverters,” IEEE Trans. Power Electron., vol. 27, no. 5, pp. 2507–2514, May. 2012.

[24] A. Msaddek, A. Gaaloul, and F. M’Sahli, “Comparative study of higher order sliding mode controllers,” 15th Int. Conf. Sci. Tech. Autom. Control Comput. Eng., Dec. 21-23, 2014, pp. 915–922.

[25] R. Ling, Z. Shu, Q. Hu, and Y. D. Song, “Second-order sliding-mode controlled three-Level Buck DC-DC converters,” IEEE Trans. Ind. Electron., vol. 65, no. 1, pp. 898–906, Jan. 2018.

[26] M. I. Martinez, A. Susperregui, and G. Tapia, “Second-order sliding-mode-based global control scheme for wind turbine-driven DFIGs subject to unbalanced and distorted grid voltage,” IET Electr. Power Appl., vol. 11, no. 6, pp. 1013–1022, Jul. 2017.

[27] A. Levant,”Principles of 2-sliding mode design” Automatica., vol. 43, no. 4, pp. 576-586. Apr. 2007.

[28] D. Liang, J. Li, and R. Qu, “Adaptive second-order sliding mode observer for PMSM sensorless control considering VSI nonlinearity,” IEEE Trans. Power Electron., vol. 33, no. 10, pp. 8994–9004, Oct. 2018.

[29] J. Mishra, L. P .Wang, Y. K. Zhu, X. H. Yu, and M. Jalili, “A novel mixed cascade finite-time switching control design for induction motor,” IEEE Trans. Ind. Electron., vol. 66, no. 2, pp. 1172–1181, Feb. 2019.

[30] A. Kchaou, A. Naamane, Y. Koubaa, and N. M’sirdi, “Second order sliding mode-based MPPT control for photovoltaic applications,” Sol. Energy, vol. 155, pp. 758–769, 2017.

[31] C. Evangelista, P. Puleston, F. Valenciaga and L. M. Fridman, “Lyapunov-designed super-twisting sliding mode control for wind energy conversion optimization,” IEEE Trans. Ind. Electron., vol. 60, no. 2, pp. 538-545, Feb. 2013.

[32] Y. L. Liu, M. Su, F. Liu, M. Zheng, X. Liu, G. Xu and Y. Sun, “Single-phase inverter with wide input voltage and power decoupling capability,” IEEE Access., vol. 7, pp. 16870–16879, 2019.

[33] A. Levant, “Higher-order sliding modes, differentiation and output-feedback control,” Int. J. Control, vol. 76, no. 9–10, pp. 924–941, 2003.

[34] J. A. Moreno, and M. Osorio, “Strict Lyapunov functions for the super-twisting algorithm,” IEEE Trans. Autom. Control., vol. 57, no. 4, pp. 1035–1040, Apr. 2012.

[35] H. Komurcugil, “Rotating-sliding-line-based sliding-mode control for single-phase UPS inverters,” IEEE Trans. Ind. Electron., vol. 59, no. 10, pp. 3719–3726, Oct. 2012.