1456 IEEE TRANSACTIONS ON ENERGY CONVERSION, …pe.csu.edu.cn/lunwen/Combined Reactive Power Injection... · 2017-12-13 · Abstract—In this paper, ... mode variable structure control

1456 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 4, DECEMBER 2017

Combined Reactive Power Injection Modulation andGrid Current Distortion Improvement Approach for

H6 Transformer-Less Photovoltaic InverterBin Liu , Mei Su, Jian Yang , Member, IEEE, Dongran Song, Deqiang He, and Shaojian Song

Abstract—In this paper, a combined reactive power modulationand grid current distortion improvement approach is proposedfor an H6 transformer-less full-bridge single-phase photovoltaic(PV) grid-connected inverter. H6 transformer-less inverters withtraditional modulation and control strategies may not satisfy therequirement of reactive power compensation or may result in moresevere zero-crossing current distortion. Therefore, contrary to thetraditional modulation, a novel reactive power injection space vec-tor pulse width modulation (SVPWM) is proposed, which consistsof two operation stages—inverter modulation and reactive powermodulation. The implementation of SVPWM for reactive powermodulation using a digital signal processor is also investigated.Furthermore, to suppress the current zero-crossing distortion inthe reactive power injection mode, a global sliding mode functionbased on the proportion-integration-resonance current controlleris designed, and the control law of the global sliding mode is de-rived. Using the segment modulation and grid current distortionimprovement approach, the function of reactive current injection isimplemented in commercial PV inverters, and the total harmonicdistortion of the grid current is decreased significantly by morethan 5% in the low-power segment, under the operating condi-tions of a lagging or leading power factor of 0.95. The effectivenessand feasibility of the proposed approach are verified through sim-ulation and experiment using a 5-kVA prototype.

Index Terms—Global sliding mode control, H6 topology PV in-verter, reactive power injection, zero-crossing distortion.

I. INTRODUCTION

OWING to the depletion of fossil fuels, distributedgeneration, and local use, the photovoltaic (PV) power

Manuscript received September 13, 2016; revised February 28, 2017 andMay 21, 2017; accepted May 29, 2017. Date of publication June 7, 2017; dateof current version November 22, 2017. This work was supported in part bythe Program for New Century Excellent Talents in University under NCET-13-0599, in part by the Innovation-Driven Plan in Central South Universityunder Grant 2016CXS004, and in part by the Natural Science Foundation ofGuangxi Province under Grant 2016GXNSFBA380241. Paper no. TEC-00784-2016. (Corresponding author: Jian Yang.)

B. Liu is with the School of Information Science and Engineering, Cen-tral South University, Changsha 410083, China, and also with the School ofElectrical Engineering, Guangxi University, Nanning 530004, China (e-mail:[email protected]).

M. Su, J. Yang, and D. Song are with the School of Information Scienceand Engineering, Central South University, Changsha 410083, China (e-mail:[email protected]; [email protected]; [email protected]).

D. He is with the School of Mechanical Engineering, Guangxi University,Nanning 530004, China (e-mail: [email protected]).

S. Song is with the School of Electrical Engineering, Guangxi University,Nanning 530004, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TEC.2017.2712741

generation system has become the most promising renewableenergy source [1], [2]. In residential applications of the single-phase distributed PV power generation system, a single-phasegrid-connected inverter is used as the interface between thephotovoltaic arrays and the single-phase utility grid. In recentyears, owing to their low cost, high power density, highperformance, and super high efficiency, single-phase inverterswith H6 transformer-less full-bridge topology have been widelyused in single-phase grids.

Most traditional single-phase PV transformer-less grid-connected inverters can only operate with a power factor (PF)of unity. The increased penetration of PV systems in residentialsingle-phase grids has attracted increasing attention to powerquality and reliability. Single-phase PV inverters should be ableto conduct voltage regulation through a reactive power control(injecting or absorbing reactive power) acting as the static gridsupport [3], [4]. Therefore, some countries have updated theirgrid-connected PV standards to include the function of regu-lating reactive power, such as the German standard VDEAR-N4105. According to the new standards, when the power levelis between 3.68 kVA and 13.8 kVA, the commended PF of agrid-connected inverter is from 0.95 leading to 0.95 lagging;further, reactive power should be provided to the utility grid,and its power quality should be improved.

H6-type topology (H4 full-bridge with ac bypass topology),was proposed to eliminate the leakage current that exists in thetransformer inverters [5]. During the freewheeling period of H6inverter, its dc-side was isolated from the ac-side [6], [7]. Byusing the traditional modulation and control methods, the ac-side of the H6 inverter was isolated from the dc-side after thezero-crossing of the grid voltage. Therefore, the H6 inverter canonly work under a PF of unity in the grid-connected mode [8],[9]. Thus, enabling the H6 inverter to inject or absorb reactivepower from the grid, while maintaining a low leakage current,is of utmost importance.

Contrary to the single-phase H4 full bridge topology with aPF of unity, the zero-crossing points of the H6 inverter outputvoltage and grid current no longer overlap when the H6 inverteroperates at a non-unity PF. Hence, the grid current waveform dis-tortion becomes more significant. In order to solve the problemof grid current distortion at zero-crossing related to nonlinearmodulation, the study in [10] introduced a repetitive control inthe inner current-loop control. Consequently, the current dis-tortion in the dual-buck PV inverter was alleviated. Based on

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LIU et al.: COMBINED REACTIVE POWER INJECTION MODULATION AND GRID CURRENT DISTORTION IMPROVEMENT APPROACH 1457

the characteristic that the rate of current variation of bipolarmodulation is larger than that of unipolar modulation, the stud-ies in [11]–[13] reduced the current zero-crossing distortion byusing a combined unipolar and bipolar pulse width modulation(PWM). Recently, as a nonlinear control method, the slidingmode variable structure control strategy has been widely ap-plied to the control of power electronic devices. Some favorableresults have been obtained, such as ideal control effects, gooddynamic response, strong robustness, and good regulation prop-erties over a wide range of operating conditions [14], [15]. In[16], the sliding mode control was used to improve the dynamicperformance of a dc-coupled distributed power generation sys-tem. Many sliding mode control methods for inverters have beenproposed [17]–[20].

The H6 inverter bridge arm outputs voltage by modulating DCbus voltage. Similarly, electromotive force can be generated bymodulating the residual current in the ac additional freewheelingpath. Based on this principle, this paper proposes a novel modu-lation technique with low leakage current for reactive powerinjection, and its space vector PWM (SVPWM) realization.The proposed PWM modulation technique for the H6 inverteris composed of two stages—inverter modulation and reactivepower modulation. Furthermore, when the H6 inverter outputsreactive power, the mechanism for grid current distortion of theH6 inverter in the vicinity of voltage zero-crossings and cur-rent zero-crossing is analyzed. It is well known that the slidingmode controller can track a predetermined trajectory. Therefore,by constructing a proportional-integral-resonance (PIR) globalsliding surface with a sliding trajectory, the dc component ofthe grid current is suppressed, smooth two-stage modulationswitching is achieved, and grid current distortion can be reducedsignificantly.

This paper is organized as follows. The operating principle ofthe proposed modulation technique and its SVPWM implemen-tation are introduced in Section II. The reason for grid currentwaveform distortion of H6 inverter is analyzed in Section III.Followed by Section IV, the control strategies for grid currentwaveform quality improvement are proposed. Finally, experi-mental results measured from a H6 inverter are presented inSection V, and the conclusions are drawn in Section VI.

II. REACTIVE POWER INJECTION MODULATION FOR H6INVERTER BASED ON SVPWM

A. H6 Inverter Topology and Traditional Modulation

The topology of an H6 inverter is shown in Fig. 1. S1−S6are the power switches; D1 and D2 are the freewheeling diodes;L1 and L2 are the filter inductors at the ac-side; Udc is the dcvoltage. The common-mode (CM) ground leakage current iscaused by the existence of a parasitic capacitor (Cp) betweenthe PV panels and earth. Since the PV arrays, parasitic capac-itor Cp , and grid form a ground leakage current transmissionpath, as illustrated in Fig. 1 by the dotted line, when the CMvoltage varies, the ground leakage current ileak appears. Theleakage current ileak decreases the efficiency of the PV inverter,reduces the grid current quality, and induces severe conductedand radiated electromagnetic interference (EMI); moreover, it is

Fig. 1. Topology of the H6-type single-phase PV inverter.

Fig. 2. Schematic of the gate drive signals for the H6 inverter with unity PF.

a major safety concern according to many standards [21]. Thus,in order to suppress the leakage current ileak of the PV inverter,two additional unidirectional freewheeling paths are embeddedin the bridge arms of the H6 inverter, to separate the PV arraysfrom the grid during the freewheeling stage.

The traditional modulation scheme for the H6 inverter with aPF of unity is shown in Fig. 2, where ug is the voltage of the util-ity grid, ig is the grid current, uref is the modulation reference,and ugs1 − ugs6 represent the gate drive signals of switchesS1−S6 , respectively. Under the traditional modulation scheme,the principle of elimination of leakage current ileak in the H6inverter was stated in [22]. Moreover, to improve the inverter

1458 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 4, DECEMBER 2017

TABLE ITABLE OF MODULATION SECTOR

Voltage direction Current direction

Positive Negative

Positive II (inverter modulation) I (reactive power modulation)Negative III (reactive power modulation) IV (inverter modulation)

efficiency, S1−S4 are chosen to be metal-oxide-semiconductorfield-effect transistors (MOSFETs) and they operate at high fre-quency; whereas, S5 and S6 , which are insulated-gate bipolartransistors (IGBTs) commutated at twice the grid frequency,form the freewheeling path with additional diodes D1 and D2 .

B. Principle and Implementation of SVPWM for H6 InverterReactive Power Injection Operation

If the H6 inverter operates in the freewheeling stages, whilepower switchers S1−S4 are turned off, the PV arrays andthe grid are separated. By modulating the IGBTs S5 or S6 tochange the freewheeling current according to the leading or lag-ging reference grid current, reactive power output is achievedwhile maintaining low leakage current in the H6 inverter. Ac-cordingly, the modulation reference wave can be divided intofour sectors according to the direction of grid voltage and gridcurrent, as shown in Table I.

In Sectors II and IV (positive power regions), the grid currentis in the same direction as the grid voltage; hence, the conven-tional modulation can be used. When the H6 inverter modulatesthe positive reference wave (Sector II), S1 and S4 are modulatedat high frequency, and S6 maintains the conduction. When theinverter modulates the negative reference wave (Sector IV), S2and S3 are modulated at high frequency, and S5 maintains theconduction. Further, in these sectors, the inverter outputs activepower, hence, Sectors II and IV are regarded as the invertermodulation stage.

Correspondingly, in Sectors I and III (negative power re-gions), the grid current in in the opposite direction to the volt-age, the inverter outputs reactive power, and these sectors areregarded as the reactive power modulation stage, while S5 andS6 are modulated at high frequency and S1−S4 are turned off.

Assuming that the grid current lags voltage by a phase angleϕ, the modulation scheme of reactive power injection is shownin Fig. 3. Moreover, the modulation technique in case the gridcurrent leads voltage can be obtained using the same principle.In Sector I, the grid voltage is positive, reference grid currentis negative, S1−S4 are turned off, and the driving signal of thefreewheeling switch S5 is a high frequency pulse generated bycomparing the reference wave with the modulation wave. In thismode, the output voltage uab of the H6 inverter is the counter-electromotive force generated by the grid ig through L1 and L2 ,during on/off of the freewheeling circuit, and its deviation fromthe grid voltage is

uab − ug = Ldigdt

. (1)

Fig. 3. Schematic of gate drive signals for the H6 inverter when grid currentlags grid voltage.

In equation (1), L is the total inductance, i.e., L = L1 + L2 .Owing to the existence of the anti-parallel diode in MOSFET S1 ,the highest value of counter-electromotive force uab is clampedto Udc , and since S6 is turned on, uab = 0. Similarly, in SectorIII, when S5 is turned on, uab = 0, and since S5 is turned off,uab = −Udc . Therefore, in Sectors I and III, the output voltageuab of the bridge arms of the H6 inverter commutates between0 and ±Udc . It can also be regarded as being generated bymodulating the dc bus voltage Udc . The relation between thetiming of the switches and the output voltage uab in Sectors IIand IV is contrary to the relation between them in Sectors Iand III. Correspondingly, in Sectors II and IV, when S1 and S4conduct (or S2 and S3 conduct), the output voltage uab of thebridge arms of the H6 inverter is Udc (or −Udc); when S1 andS4 are turned off (or S2 and S3 are turned off), uab = 0. At anytime in Sectors I and III, S1−S4 are turned off, the grid currentig varies with time following a sinusoidal law. It is assumed thatthe grid voltage and current are defined as ug = Ugsin ωt andig = Igsin (ωt − ϕ), respectively, where Ig is the amplitudeof current and ω is the grid angular frequency. In this situation,the counter-electromotive force uab can be regarded as beinggenerated by the modulation of this freewheeling current, andequation (1) yields

uab − ug =Ldigdt

= L[Ig sin (ωt − ϕ)]′ = LIgω cos (ωt − ϕ) .

(2)

LIU et al.: COMBINED REACTIVE POWER INJECTION MODULATION AND GRID CURRENT DISTORTION IMPROVEMENT APPROACH 1459

TABLE IICORRESPONDENCE RELATIONS BETWEEN Q AND SECTOR

Q 0 1 2 3

Sector IV III I II

Assuming that da , db , and d6 are the duty cycles of the bridgearms A, B, and S6 , respectively, uab in Sector III can be ex-pressed as

uab = uan − ubn = daUdc − dbUdc = d6Udc . (3)

Combining equations (2) and (3) yields d6 at steady state:

d6 =LIgω cos (ωt − ϕ) + ug

Udc. (4)

As for digital signal processor (DSP) implementation of re-active power injection modulation, similar to the three-phaseSVPWM modulation technique, the related strategy is imple-mented in the reactive power modulation of the H6 inverter.First, the location of the reference vector should be defined.Therefore, according to the directions of the grid voltage ugand the reference grid current iref , sectors can be identified inaccordance with the following rules:

IF ug > 0 THEN M = 1 ELSE M = 0;

IF iref > 0 THEN N = 1 ELSE N = 0.

where M and N are the sector identification variable symbols.Considering Q = 2M + N , the correspondence relations be-tween Q and the sectors are shown in Table II.

Further, X is defined as

X = muref

Udc=

kLIg sin (ωt − ϕ)Udc

, (5)

where uref is the modulating output reference voltage, m(m ≤ 1) is the modulation ratio, and k is a proportion fac-tor (a normalized factor) that is a function of the modulationratio, reference voltage and reference current.

Notably, under reactive power modulation, if the switchesS5 and S6 are turned on, the output voltage uab = 0. Usingequation (1), the variation rate of the grid current is in theopposite direction to the grid voltage. Further, if S5 and S6are turned off, the output voltage of the bridge arms is −Udc(or Udc). Simultaneously, the variation rate of the correspondingoutput grid current is in the same direction as the grid voltage.

When the H6 inverter operates in the reactive power modula-tion mode, the variation law of the grid current, which is causedby the switches S5 and S6 being turned on and off, is differentfrom that caused by the switches S1−S4 being turned on andoff. Therefore, by using the same modulation wave and settingX as the reference wave of S1−S4 , the reference wave of S5 andS6 is defined as

Y = 1 − X. (6)

Further, Tc represents the digital control cycle count value; TAand TB represent the switching points of the single-phase bridge

Fig. 4. Implementation of SVPWM in Sector II.

TABLE IIIDEFINING TA , TB BY X, Y, AND Q

Switching point Sector

I II III IV

TA Tc X Tc Tc

TB Tc Tc Tc XT5 Y Tc Tc 0T6 Tc 0 Y Tc

arms A and B, respectively; T5 and T6 represent the switchingpoints of the freewheeling switches S5 and S6 , respectively. InSector II, for example, Fig. 4 shows the implementation of theSVPWM. Table III describes the relations among TA , TB , sectornumber, and the reference waves X and Y.

C. Low Leakage Current Characteristics in Reactive PowerInjection Mode

According to the analysis in [5], [9], in a transformer-lessPV inverter system, the leakage current is essentially the CMcurrent. Besides the parasitic capacitor Cp of the PV arrays, thefactor deciding the value of the leakage current is the variationrate of the output CM voltage ucm . The leakage current can beexpressed as

ileak = Cpducm

dt. (7)

Hence, by selecting the appropriate modulation sequence andmaintaining the output CM voltage ucm of the H6 inverter con-stant, low leakage current characteristics of the system can beensured.

When the H6 inverter is modulated by the sequence shown inFig. 3, the output of the bridge uab has the feature of unipolarmodulation. In Sector II, modulating by +1 and 0, the outputuab is Udc and 0, respectively. In Sector IV, modulating by −1and 0, the output uab is −Udc and 0, respectively. In these twosectors, the CM voltage ucm retains half of the dc-side voltageUdc , i.e., ucm = 0.5Udc . It can be inferred from equation (7)that the leakage current of the H6 inverter is very small [22].

Fig. 5 shows the detailed operating principle of Sector III,when the H6 inverter outputs lagging reactive power. As shownin Fig. 5(a), the H6 inverter operates in the inverter modulationstage of outputting lagging reactive power, and the current flows

1460 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 4, DECEMBER 2017

Fig. 5. Operation modes of the H6 Inverter when it operates in reactive powermodulation stage.

through the path L1→ Grid →L2→ S6→ D2 → L1 . Owing tothe voltage balancing effect of the junction capacitor of switches,uan = ubn = 0.5Udc , and the CM voltage ucm is

ucm =12

(uan + ubn) =12

(12Udc +

12Udc

)=

12Udc . (8)

As shown in Fig. 5(b), when the H6 inverter operatesin the freewheeling stage, the freewheeling current flowsthrough the path L1 → Grid → L2 → parallel diode ofS3 → PV arrays → parallel diode of S4 → D2 → L1 . Dur-ing this stage, the grid voltage is reversed, but the output voltageof the bridge arms uab = −Udc , uan = 0, ubn = Udc , andthe CM voltage ucm is

ucm =12

(uan + ubn) =12

(0 + Udc) =12Udc . (9)

The above analysis shows that when the H6 inverter outputslagging reactive current, irrespective of whether it operates inthe inverter modulation stage or the freewheeling stage, if theinput voltage Udc remains unchanged, the CM voltage ucm willalways be constant. Furthermore, the same conclusion can bedrawn when the H6 inverter outputs leading reactive current.Hence, the H6 inverter has the feature of low leakage currentwhen it operates in the reactive power injection modulationmode, similar to its operation in the unity PF mode.

Notably, when the H6 inverter outputs reactive power inSectors I and III (negative power region), the inverter bridgeis separated from the PV arrays during the modulation stages.However, when the H6 inverter operates in other sectors or op-erates with a PF of unity, the inverter bridge is separated from

Fig. 6. Distortion of the grid current near the output voltage and grid currentzero-crossing points.

the PV arrays during the freewheeling stages. Therefore, thereare differences between the modulation methods.

III. ANALYSIS OF CURRENT WAVEFORM DISTORTION FOR H6IN REACTIVE POWER INJECTION MODE

The H6 inverter with unity PF modulation has high grid cur-rent waveform quality, even if the inductance value of the grid-side filter is considered to be small [23]. However, when the H6inverter operates in the reactive power injection mode, the zero-crossing points of the output voltage and grid current appearat different moments; hence, a phase difference exists betweenthem. Furthermore, near these two zero-crossing points, thewaveform of the grid current is distorted, resulting in a largertotal harmonic distortion (THD) of the grid current, particularlywhen the H6 inverter operates at low power.

A. Grid Current Distortion Caused by Dead-Time NearVoltage Zero-Crossing Point

Fig. 6 shows the distortion of the grid current near the zero-crossing points of the output voltage and grid current, whenthe H6 inverter outputs lagging reactive power. Under unipolarmodulation, during the switching dead-time, the output voltageof the bridge arms of the H6 inverter is uab = 0 and the gridcurrent is in a state of uncontrolled freewheeling; it may not trackthe reference current iref , resulting in distortion [24]. In practice,owing to the minimum pulse width limit in the operating processof the H6 inverter, the dead-time td is longer than the presetvalue, and the waveform distortion becomes more significant.

In Fig. 6, the output voltage uab cuts off at ta in the positivehalf cycle, starts at tb in the negative half cycle, and the currentduring the dead-time (td = tb − ta) can be expressed as

ig (t) =∫ tb

ta

dig (t)dt

dt + ig (ta) . (10)

The dead-time td of the H6 inverter is considered to be equiva-lent to a phase angle θ. Assuming ta = π − θ/2, tb = π + θ/2,and ug = Ugsin ωt near the zero-crossing point of the output

LIU et al.: COMBINED REACTIVE POWER INJECTION MODULATION AND GRID CURRENT DISTORTION IMPROVEMENT APPROACH 1461

voltage, the current derivative is

digdt

= −Ug sin ωt

L. (11)

Substituting equation (11) into equation (10) yields

ig (t) =Ug

ωL

∫ π

ta

d cos ωt +Ug

ωL

∫ tb

π

d cos ωt + ig (ta) , t

∈ (ta , tb) . (12)

If the H6 inverter operates in the reactive power injectionmode, the grid current lags voltage by a phase ϕ; hence, ig =Igsin(ωt − ϕ) and substituting it into equation (12) yields

ig (t) =Ug

ωL

∫ π

π− θ2

d cos ωt +Ug

ωL

∫ π+ θ2

π

d cos ωt+Ig sin ϕ, t

∈ (ta , tb) (13)

It can be inferred from the above equations that the magnitudeof the grid current ig at ta is Igsin ϕ. Under the effect of the gridvoltage alone, the grid current varies as a cosine curve. Duringthe period [ta , π], the amplitude of current decreases, attainingthe minimum value at the zero-crossing point of voltage (at thismoment, the phase angle is π), and subsequently increases dur-ing the period [π, tb ]. Correspondingly, near the zero-crossingpoint of the H6 output voltage (near the phase angle 0), the gridcurrent exhibits a similar distortion.

The aforementioned analysis shows that, during the dead-time near the zero-crossing point of the output voltage, only theac grid voltage will be applied across the ac inductors L1 andL2 , and the output voltage of the H6 inverter uab can no longercontrol the variation of the grid current. Hence, the grid currentcannot track the reference grid current, resulting in distortion.Equation (13) further illustrates that, when the H6 inverter out-puts reactive power with lower PF, the values of ϕ and Igsinϕare relatively larger, and the current distortion becomes moresignificant.

B. Current Distortion Near the Zero-Crossing Point of GridCurrent

Distortion is also observed in the grid current near its zero-crossing point, as shown in Fig. 7 in a zoomed-in view. More-over, near the zero-crossing point of the grid current, the gridcurrent cannot track the reference grid current accurately, re-sulting in distortion.

1) Current Distortion Before Zero-Crossing Point: Theanalysis Section II-A in this paper shows that before the zero-crossing point of the grid current in Sector III, only the IGBTS6 functions, and the electromotive force uab is generated byvariation of the current through the inductor. Without the ef-fect of the external voltage or counter-electromotive force, theresidual current through the inductor can only hold the originalfreewheeling direction, but cannot be commutated by modulat-ing S6 actively. As shown in Fig. 7, at the end of Sector III,although the reference current iref has already crossed the zeropoint and changed its direction, the H6 inverter has not com-pleted the sector switching, and the grid current cannot follow

Fig. 7. Grid current distortion near its zero-crossing point.

the reference current and complete the zero-crossing shift frompositive to negative, resulting in distortion.

2) Current Distortion During Sector Switching: As de-scribed in Section II-C, the reactive power injection modulationis segmented into two stages, and the ideal modulation referencewave u∗

ref is discontinuous and mutates during the sector transi-tion. However, owing to factors such as the delay of control loopand the current sampling error at zero-crossing points, the actualmodulation reference wave cannot mutate; consequently, the H6inverter may not transit between the two sectors smoothly. Asshown in Fig. 6, the output of the closed-loop control system,i.e., the modulation reference wave uref , is higher than the idealsector conversion reference wave u∗

ref in the initial period ofSector IV, such that the modulating output voltage of the H6inverter is higher than the voltage required to follow the refer-ence grid current. The variation rate of the actual grid current islarger than that of the reference grid current, i.e.

∣∣∣∣digdt

∣∣∣∣ >

∣∣∣∣diref

dt

∣∣∣∣ . (14)

Similarly, during the period when the H6 inverter convertsfrom Sector I to Sector II, the grid current exhibits a similardistortion. Hence, the current distortion near the grid currentzero-crossing point is caused by the discontinuous sector con-version, and effective control approaches should be undertakento ensure smooth sector transition.

As described above, when the H6 inverter operates in the re-active power injection mode, the grid current distortion is moresignificant. Consequently, the lower-order harmonic current andeven the dc component will significantly increase in the gridcurrent, resulting in the degradation of grid power quality andreduction of system efficiency. When the grid current distortssignificantly, the harmonic current amplified by the control loopwill cause problems in system oscillation and stability. Specifi-cally, when multiple grid-connected inverters are running simul-taneously, the zero-crossing distortion will be superimposed andamplified, easily causing disturbance to the adjacent grids, andinfluencing the operating safety of nearby electrical equipment[25]. Hence, the quality of the grid current waveform should beimproved using an advanced control strategy.

1462 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 4, DECEMBER 2017

Fig. 8. Structure and Bode diagram of the PIR controller: (a) Structure of thePIR controller and (b) Bode diagram of the PIR controller.

IV. CONTROL STRATEGY FOR GRID CURRENT WAVEFORM

IMPROVEMENT

A. PIR Sliding Mode Surface Construction for Lower OrderHarmonics

A sliding mode control can implement a high precision con-trol under changing parameters and load disturbances; therefore,it exhibits good robustness and fast dynamic response [26]. Ow-ing to these advantageous features, the sliding mode control isadopted in this study to improve the quality of the grid currentwaveform.

The analysis in Section III illustrates that the current dis-tortion is partly caused by the nonlinear PWM modulation. Thetraditional current control loop of the PV grid-connected inverteralways uses a proportional-resonant (PR) controller or quasi-PRcontroller, achieving high gain at the resonance frequency pointof the grid current, but resulting in no inhibition of the dc com-ponent. However, in the actual system, the current zero-crossingdistortion appears and results in higher lower-order harmonicsand further leads to an increase in the dc component. Fourieranalysis of the current waveform with zero-crossing distortionshows that there are low frequency and dc components in thegrid current harmonic spectrum [27]. In order to compensatethe zero-crossing distortion, suppress the dc component, andimprove the quality of the grid current waveform, an integrallink is added to the quasi PR of the current loop controller,forming a PIR controller, as shown in Fig. 8(a), whose transferfunction is expressed as:

G (s) = Kp +Ki

s+

KRωcs

s2 + 2ωcs + ω20, (15)

where Kp, Ki , and KR are the proportional, integral, andresonant controller parameters, respectively; ω0 is the systemresonance attenuation coefficient. Considering Kp = 2, Ki =50, ωc = 10, and KR = 100, its Bode diagram is shown inFig. 8(b). From the Bode diagram, it can be observed that thePIR controller has a high gain not only at resonant frequency, butalso in the low frequency band. This reflects the inhibitory effectof the controller on the current distortion and the dc component.

Therefore, this study modifies the PIR sliding mode switchingsurface into a fixed-frequency sliding mode control for the gridcurrent. First, the switching surface equation SPIR is designedas

SPIR =(

Kp +Ki

s+

KRωcs

s2 + 2ωcs + ω20

)(iref − ig ) , (16)

where s is the Laplace operator. By selecting the grid current igof the H6 inverter as the state variable X, the state equation ofthe H6 inverter can be derived from equation (1) as

dX

dt= AX + BU + D, (17)

where X = ig , B = Udc/L, and D = ug/L. Furthermore,A = 0 by neglecting the ac-side line resistor. The system isdesigned with a negative slope converging to the switching sur-face, and the saturation function sat() is used to eliminate thechattering; further, k is set to be the convergence control co-efficient of the switching surface. Subsequently, the switchingsurface derivative can be expressed as

dSPIR

dt=

dXref

dt− AX − BU − D = −k·sat (SPIR) . (18)

Assuming Δ is the boundary width of the sliding mode con-trol, the saturation function is expressed as:

sat(S) =

⎧⎪⎨⎪⎩

1, S ≥ ΔγS, |S| < Δ; γ = 1/Δ−1, S ≤ −Δ

. (19)

The sliding systems control law is obtained as

U = B−1 [E − AX − D + k·sat (SPIR)] , E =dXref

dt.

(20)

Based on the equations (17)–(20), by considering E as theunknown disturbances, the voltages applied to the converteruref can be calculated as

uref =ug

udc+ k·sat (SPIR) . (21)

The sliding mode control block diagram is shown in Fig. 9.The ac-side modulation output reference voltage uref generatedby the sliding mode controller, after modulation by SVPWM,produces the PWM pulse driving power switches. Owing to thefixed SVPWM modulation frequency, this control strategy is afixed-frequency sliding mode control.

In order to verify the stability and convergence of the slidingmode control strategy, a Lyapunov function is constructed asfollows

V = SST = S2PIR . (22)

LIU et al.: COMBINED REACTIVE POWER INJECTION MODULATION AND GRID CURRENT DISTORTION IMPROVEMENT APPROACH 1463

Fig. 9. Sliding mode control diagram for the grid current.

and it easily renders V permanently positive. Its first orderderivative is

V̇ =dSST

dt= −2 (SPIRsat (SPIR)) . (23)

Since the arithmetic product of the switching surface functionSPIR and its saturation function sat() is always greater than orequal to 0, the derivative of V in the above equation is alwaysless than or equal to 0, i.e., the Lyapunov function V decreaseswith time until it converges to 0. Hence, the system convergesto the switching surface and is convergent and stable.

B. Global Sliding Mode Control for Sector SwitchingDistortion Compensation

By setting up the model of the fixed-frequency sliding modecontrol for the grid current, the SVPWM control process canbe optimized by constructing a suitable sliding function S, ac-cording to the theory of sliding mode control; subsequently, theobjective of system optimized control can be achieved.

From Fig. 3 and the analysis of the grid current waveformdistortion of the H6 inverter, the switching process of the H6inverter from a reactive current output mode to an active in-verter mode (i.e., switching from Sector I to Sector II or fromSector III to Sector IV) is not smooth. Since these two pro-cesses occur near the zero-crossing points of the current (switch-ing from negative to positive or from positive to negative), theswitching that is less smooth leads to the grid current zero-crossing distortion. Therefore, the modulation could be so sen-sitive that the modulator has to adopt a soft transition. Duringthe global sliding mode controlling, the global function S has asliding surface gradient characteristic and can attenuate to zerorapidly. Moreover, by determining the transient state by the sec-tor switching, considering the initial value of the sliding modesurface as the initial value of the transient state, and construct-ing the dynamic nonlinear global sliding surface to smooth thesector switching process, the compensation of zero-crossing dis-tortion can be implemented. Therefore, the new global slidingmode function can be designed as

S = SPIR − f (t) . (24)

The global sliding mode function is the original sliding modefunction minus the function f(t), which is designed to achievethe global sliding mode; further, f(t) satisfies the followingthree conditions [28]:

1) f(0) = S(0);2) When t → ∞, f(t) → 0;

Fig. 10. Comparison of the waveforms when the inverter is running with andwithout the global sliding mode controller.

3) f(t) has a first-order derivative.Since the initial value of the transient state is f(0+) =

SPIR(0+), f(t) can be designed as

f (t) = f(0+)

e−λt , (25)

where λ > 0 and is a constant. The discrete equation (24) yields

f (k + 1) = f (k) e−λ. (26)

According to the definition of the global sliding mode, f(0)finally attenuates to 0 and the value of λ determines the attenua-tion rate of f(0). If the value of λ is too large, f(0) decays fast,failing to reflect the effect of global sliding. If the value of λ istoo small, f(0) decays slowly, and cannot even decrease to 0 inthe entire sector, causing an additional distortion of the ac outputreference wave uref . By considering all the aforementioned fac-tors, and assuming λ = 0.37, after approximately seven controlcycles, f(0) can decay to less than 0.1 times of the initial value,when the control frequency is 20 kHz.

Fig. 10 compares the detailed waveforms of the ac-side mod-ulation reference wave uref , in the vicinity of the current zero-crossing, when the H6 inverter operates with and without theglobal sliding mode controller. When the H6 inverter switchesbetween the reactive power injection mode and the active in-verter mode, the global sliding mode controller lowers uref inseveral control cycles just after sector switching as comparedto the conventional controller, and it is much closer to the idealreference wave. Hence, the grid current zero-crossing with the

1464 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 4, DECEMBER 2017

Fig. 11. Photograph of the prototype H6 PV inverter.

TABLE IVPARAMETERS OF 5 KVA PROTOTYPE

Parameters Value

Switching Frequency fs /Hz 20 kAC filter inductor L1 = L2 /mH 0.8DC link capacitor Cd c /mF 3Rated Capacity Se /(kVA) 5Output frequency f /Hz 50Rated grid voltage ug /V 220

global sliding mode control is more moderate than that withoutthe global sliding mode control. Consequently, the switchingprocess becomes smoother, and the mutation and distortion ofthe grid current is reduced.

V. EXPERIMENTAL RESULTS

In order to study the reactive power injection modulation ofthe H6 inverter, and verify the control algorithm for the im-provement of the grid current waveform, a 5 kVA experimentalprototype is built. Fig. 11 shows the designed H6 PV inverter,which consists of a boost converter and an H6 full-bridge in-verter. All the control algorithms are implemented by using thelow-cost 16-bit digital signal processor chip TMS320F2808.The specifications of the prototype PV inverter are listed inTable IV.

Fig. 12 shows the measured waveforms of the H6 inverter withthe traditional modulation. The inverter is expected to outputleading and lagging reactive power. Since S1−S6 are all turnedoff in the reactive power regions, the function of reactive powerregulation is not achieved.

Compared with Fig. 12, Fig. 13 shows the measured wave-forms of the H6 inverter with reactive power injection modula-tion, at 0.95 lagging PF and 0.95 leading PF. The experimentalwaveforms show that, by using the modulation strategy pro-posed in this paper, the H6 inverter can accurately and stablyoutput reactive current lagging or leading the grid voltage.

Fig. 14 shows the midpoints a, b of the H6 bridge arms voltagewaveforms relative to the ground uan , ubn , and the waveform

Fig. 12. Waveforms of the H6 inverter when it is expected to regulate thepower factor: (a) H6 inverter is expected to output leading reactive power and(b) H6 inverter is expected to output lagging reactive power.

Fig. 13. Waveforms of the H6 inverter when it operates at 0.95 PF: (a) H6inverter output leading reactive power and (b) H6 inverter output lagging reactivepower.

of voltage uan + ubn (twice the CM voltage), when the H6inverter functions under 0.95 lagging PF. The waveform of thevoltage uan + ubn shows that its amplitude remains approx-imately the same, and the variation rate of its CM voltage issmall. Furthermore, the leakage current of the H6 inverter issmall, as inferred from equation (7).

LIU et al.: COMBINED REACTIVE POWER INJECTION MODULATION AND GRID CURRENT DISTORTION IMPROVEMENT APPROACH 1465

Fig. 14. Experimental waveforms of uan , ubn and twice CM voltageuan + ubn when the H6 bridge operates under 0.95 PF.

Fig. 15. Measured waveforms of grid voltage, grid current, and leakage cur-rent when the H6 inverter operates at unity PF and ±0.95 PF: (a) At unity powerfactor; (b) at PF of 0.95 (leading) and (c) at PF of 0.95 (lagging).

Fig. 15 illustrates the leakage current waveform when theexperimental prototype is at full load (5 kW or 5 kVA) andoperates at PF of 1 and ±0.95. It can be observed from theexperimental waveforms of Fig. 15(a)–(c) that, when the H6inverter operates in the reactive power output mode, the valueof leakage current is equivalent to the value at unity power

Fig. 16. Comparison of the grid current experimental waveforms with andwithout the waveform-improving controller at PF of 0.95 (lagging): (a) withtraditional current controller; (b) with waveform-improving current controllerand (c) harmonic spectrum of grid current of (a) and (b).

factor and remains under 20 mA, and its root mean square(RMS) value remains under 15 mA. These values satisfy therequirements of standard VDE-AR-N 4105. The experimentproved that, by utilizing the proposed modulation strategy, theH6 inverter presents low leakage current characteristics whenoutputting reactive power.

Fig. 16 shows the comparison of the waveforms with andwithout the control strategy for the improvement of the gridcurrent, when the non-isolated H6 single-phase PV grid inverteroperates at an apparent power of 2000 VA and a PF of 0.95. Theanalyses show that, with the help of the waveform-improvingcontrol, the THD of the grid current is decreased by 0.6%,from 4.3% to 3.7%. The grid current distortion at the zero-crossing point is substantially eliminated. However, owing tothe limitation of minimum pulse width and dead-time, a furtherreduction of the grid current distortion is not achieved. From thefast Fourier transform (FFT) analysis of the current waveforms,by using the waveform-improving control, it can be observedthat the dc component and main characteristic harmonics havedeclined.

Fig. 17 shows the measurement results of the grid currentTHD with and without the waveform-improving controller,

1466 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 4, DECEMBER 2017

Fig. 17. Comparison of grid current THD with and without the waveform-improving controller.

TABLE VPERFORMANCE COMPARISON OF [29], [30] AND PROPOSED METHOD IN

THIS PAPER

[29] [30] This paper

Topology H6 bridge with6MOSFETs

H6 bridge with6IGBTs

H6 bridge with 4MOSFETs and 2

IGBTsCapability ofreactive powerinjection

Not involved With reactivepower injection

modulation

With reactivepower injection

modulationLeakage current Low Low LowImprovement ofcurrent distortion inzero-crossing

Not involved Not involved With waveform-improving control

methodEnergy transferpath in reactivepower injectionmode

1 MOSFET + 1diode + 2 inductors

1 IGBT + 1 diode+ 2 inductors

IGBT + 1 diode+2 inductors

Energy transferpath in invertingmode

3 MOSFETs +2inductors

3 IGBTs +2inductors

1 IGBT + 1MOSFET + 1

diode+ 2 inductorsFreewheeling pathin reactive powerinjection mode

3 diodes +2inductors

3 diodes +2inductors

1 IGBT + 1diode+ 2 inductors

Freewheeling pathin inverting mode

1 MOSFET + 1diode + 2 inductors

1 IGBT + 1 diode+ 2 inductors

3 diodes + 2inductors

MaximumEfficiency

98.10% 97.64% 97.70%

performed under conditions of full power when the H6 inverteroperates at 0.95 lagging PF. Using the proposed control strategy,the grid current waveform distortion is apparently improved inthe entire power section, particularly when outputting small re-active power. As the output power of the H6 inverter becomeshigher, the improvement of grid current quality is smaller thanthat observed in Fig. 16. The reason for this phenomenon isthat, when the output power is high, the variation rate differencebetween the actual grid current and the reference grid currentis small, and the increment of the grid current THD caused bythe zero-crossing is small. Besides, when the output power ishigh, the THD of the grid current is relatively low. Under thiscondition, the further improvement is limited.

In case of the H6-type transformer-less single-phase in-verter for grid-tied PV system, some research work was re-ported in [29] and [30]. However, the study in [29] focusedon the efficiency of the H6-type inverter, and the waveform-improving method was not described in [30]. The performance

comparison of the studies in [29] and [30], and the proposedmethod are shown in Table V.

It can be observed from Table V that, similar to the H6 topolo-gies, all the topologies have similar efficiencies, with a slightdifference caused by the difference in the performances of theIGBT and MOSFET devices. Using the reactive power injec-tion modulation and control strategy proposed in this paper, H6inverters have the capability of reactive power injection, withlow THD of grid current and improvement of grid current wave-form in zero-crossing. Moreover, the advantage of low leakagecurrent is intact.

VI. CONCLUSION

In order to extend the application of the non-isolated H6single-phase PV grid-connected inverter, this paper proposesa reactive power injection modulation for the H6 inverters.However, when an H6 single-phase PV inverter operates inthe reactive power injection mode, the distortion of the gridcurrent is aggravated. Therefore, a control strategy based onthe PIR global sliding mode control is proposed to improvethe quality of the grid current waveform. Experimental re-sults show that the proposed scheme for the H6 inverter canimplement reactive power modulation while maintaining lowleakage current characteristics. Moreover, the waveform dis-tortion of the grid current is improved. For the H6 single-phase PV inverters that have already been installed for resi-dential applications, only their control program requires to beupdated, without hardware transformation. The proposed im-proved control approach is attractive owing to its cost-savingadvantage.

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Bin Liu received the Ph.D. degree from the School ofInformation Science and Engineering, Central SouthUniversity, Changsha, China, in 2014. He is currentlya Postdoctoral Member with Central South Univer-sity, and a Lecturer with the School of ElectricalEngineering, Guangxi University, Nanning, China.His research interests include power electronics andenergy conversion, with particular emphasis on con-verter topologies, modeling, control, and various ap-plications.

Mei Su received the B.S., M.S., and Ph.D. degreesfrom the School of Information Science and Engi-neering, Central South University, Changsha, China,in 1989, 1992, and 2005, respectively. Since 2006, shehas been a Professor with the School of InformationScience and Engineering, Central South University.Her research interests include matrix converter, ad-justable speed drives, and wind energy conversionsystems.

Jian Yang (M’09) received the Ph.D. degree in elec-trical engineering from the University of CentralFlorida, Orlando, FL, USA, in 2008. He was a SeniorElectrical Engineer with Delta Tau Data Systems,Inc., Los Angeles, CA, USA, from 2007 to 2010.Since 2011, he has been with Central South Uni-versity, Changsha, China, where he is currently anAssociate Chair Professor with the School of Infor-mation Science and Engineering. His main researchinterests include control application, motion plan-ning, and power electronics.

Dongran Song received the B.S., M.S., and Ph.D.degrees from the School of Information Science andEngineering, Central South University, Changsha,China, in 2006, 2009, and 2016, respectively. He wasan Electrical and Control Engineer with China MingYang Wind Power, Zhongshan, China, from 2009 to2013. He is currently a Postdoctoral Member with theSchool of Information Science and Engineering, Cen-tral South University. His research interests includewind turbines, power electronics, and renewable en-ergy system.

Deqiang He received the Ph.D. degree fromChongqing University, Chongqing, China, in 2004.He is currently a Professor with the School of Me-chanical Engineering, Guangxi University, Nanning,China. His main research interests include fault diag-nosis and the intelligent maintenance of rail transit.

Shaojian Song received the B.S. and M.S. degreesfrom Guangxi University, Nanning, China, in 1994and 2001, respectively. He is currently a Professorwith the School of Electrical Engineering, GuangxiUniversity. His current research interests includemodeling, optimization and control for complex sys-tem, electric vehicle and V2G, active distribution net-work, power electronics, and energy conversion withparticular emphasis on converter modeling, control,and various applications.