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Microsoft Word Combined Reactive Power Injection Modulation and Grid Current Distortion Improvement Approach for H6 Transform See discussions, stats, and author profiles for this publication at https.

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/317417671 Combined Reactive Power Injection Modulation and Grid Current Distortion Improvement Approach for H6 Transformer-Less Photovoltaic Inverter Article  in  IEEE Transactions on Energy Conversion · June 2017 DOI: 10.1109/TEC.2017.2712741 CITATIONS READS 35 921 authors, including: Song Dongran S.j Song Central South University Guangxi University 76 PUBLICATIONS   1,221 CITATIONS    58 PUBLICATIONS   292 CITATIONS    SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Wind farms control View project Advanced Wind Turbine Systems Based on Novel Electrical Power Conversion and Control Technique View project All content following this page was uploaded by Song Dongran on 11 October 2017 The user has requested enhancement of the downloaded file This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion Combined Reactive Power Injection Modulation and Grid Current Distortion Improvement Approach for H6 Transformer-less Photovoltaic Inverter Bin Liu, Mei Su, Jian Yang, Member, IEEE, Dongran Song, Deqiang He and Shaojian Song  Abstract—In this paper, a combined reactive power modulation and grid current distortion improvement approach is proposed for an H6 transformer-less full-bridge single-phase photovoltaic (PV) grid-connected inverter H6 transformer-less inverters with traditional modulation and control strategies may not satisfy the requirement of reactive power compensation or may result in more severe zero-crossing current distortion Therefore, contrary to the traditional modulation, a novel reactive power injection space vector pulse width modulation (SVPWM) is proposed, which consists of two operation stages—inverter modulation and reactive power modulation The implementation of SVPWM for reactive power modulation using a digital signal processor (DSP) is also investigated Furthermore, to suppress the current zero-crossing distortion in the reactive power injection mode, a global sliding mode function based on the proportion-integration-resonance (PIR) current controller is designed, and the control law of the global sliding mode is derived Using the segment modulation and grid current distortion improvement approach, the function of reactive current injection is implemented in commercial PV inverters, and the total harmonic distortion (THD) of the grid current is decreased significantly by more than 5% in the low power segment, under the operating conditions of a lagging or leading power factor (PF) of 0.95 The effectiveness and feasibility of the proposed approach are verified through simulation and experiment using a kVA prototype Index Terms—H6 topology PV inverter, reactive power injection, zero-crossing distortion, global sliding mode control Manuscript received September 13, 2016; revised February 28, 2017; accepted May 29, 2017 This work was supported in part by the Program for New Century Excellent Talents in University under NCET-13-0599, in part by the Innovation-driven Plan in Central South University under Grant 2016CXS004, and in part by the Natural Science Foundation of Guangxi Province under Grant 2016GXNSFBA380241 Corresponding Author: Jian Yang Paper no.TEC-00784-2016 Bin Liu, Mei Su, Jian Yang, and Dongran Song are with the the School of Information Science and Engineering, Central South University, Changsha 410083, China (e-mail: bingo.liu@csu.edu.cn; sumeicsu@mail.csu.edu.cn; jian.yang@csu.edu.cn; humble_szy@163.com) Deqiang He is with the School of Mechanical Engineering, Guangxi University, Nanning 530004, China (e-mail:hdqianglqy@126.com) Shaojian Song is with the School of Electrical Engineering, Guangxi University, Nanning 530004, China (e-mail:57095158@qq.com) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org O I.INTRODUCTION wing to the depletion of fossil fuels, distributed generation, and local use, the photovoltaic (PV) power generation system has become the most promising renewable energy source [1]–[2] In residential applications of the single-phase distributed PV power generation system, a single-phase grid-connected inverter is used as the interface between the photovoltaic arrays and the single-phase utility grid In recent years, owing to their low cost, high power density, high performance, and super high efficiency, single-phase inverters with H6 transformer-less full-bridge topology have been widely used 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 residential single-phase grids has attracted increasing attention to power quality and reliability Single-phase PV inverters should be able to conduct voltage regulation through a reactive power control (injecting or absorbing reactive power) acting as the static grid support [3]–[4] Therefore, some countries have updated their grid-connected PV standards to include the function of regulating reactive power, such as the German standard VDEAR-N4105 According to the new standards, when the power level is between 3.68 kVA and 13.8 kVA, the commended PF of a grid-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 the transformer inverters [5] During the freewheeling period of H6 inverter, its dc-side was isolated from the ac-side [6–7] By using the traditional modulation and control methods, the ac-side of the H6 inverter was isolated from the dc-side after the zero-crossing of the grid voltage Therefore, the H6 inverter can only work under a PF of unity in the grid-connected mode [8– 9] Thus, enabling the H6 inverter to inject or absorb reactive power from the grid, while maintaining a low leakage current, is of utmost importance Contrary to the single-phase H4 full bridge topology with a PF of unity, the zero-crossing points of the H6 inverter output 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion voltage and grid current no longer overlap when the H6 inverter operates at a non-unity PF Hence, the grid current waveform distortion becomes more significant In order to solve the problem of grid current distortion at zero-crossing related to nonlinear modulation, the study in [10] introduced a repetitive control in the inner current-loop control Consequently, the current distortion in the dual-buck PV inverter was alleviated Based on the characteristic that the rate of current variation of bipolar modulation is larger than that of unipolar modulation, the studies in [11–13] reduced the current zero-crossing distortion by using a combined unipolar and bipolar pulse width modulation (PWM) Recently, as a nonlinear control method, the sliding mode variable structure control strategy has been widely applied to the control of power electronic devices Some favorable results have been obtained, such as ideal control effects, good dynamic response, strong robustness, and good regulation properties over a wide range of operating conditions [14–15] In [16], the sliding mode control was used to improve the dynamic performance of a dc-coupled distributed power generation system Many sliding mode control methods for inverters have been proposed [17]–[20] The H6 inverter bridge arm outputs voltage by modulating DC bus voltage Similarly, electromotive force can be generated by modulating the residual current in the ac additional freewheeling path Based on this principle, this paper proposes a novel modulation technique with low leakage current for reactive power injection, and its space vector PWM (SVPWM) realization The proposed PWM modulation technique for the H6 inverter is composed of two stages—inverter modulation and reactive power modulation Furthermore, when the H6 inverter outputs reactive power, the mechanism for grid current distortion of the H6 inverter in the vicinity of voltage zero-crossings and current zero-crossing is analyzed It is well known that the sliding mode controller can track a predetermined trajectory Therefore, by constructing a proportional-integral-resonance (PIR) global sliding surface with a sliding trajectory, the dc component of the grid current is suppressed, smooth two-stage modulation switching is achieved, and grid current distortion can be reduced significantly This paper is organized as follows The operating principle of the proposed modulation technique and its SVPWM implementation are introduced in Section II The reason for grid current waveform distortion of H6 inverter is analyzed in Section III Followed by Section IV, the control strategies for grid current waveform quality improvement are proposed Finally, experimental results measured from a H6 inverter are presented in Section V, and the conclusions are drawn in Section VI II REACTIVE POWER INJECTION MODULATION FOR H6 INVERTER BASED ON SVPWM A H6 Inverter Topology and Traditional Modulation The topology of an H6 inverter is shown in Fig S1–S6 are the power switches; D1 and D2 are the freewheeling diodes; L1 and L2 are the filter inductors at the ac-side; Udc is the dc voltage The common-mode (CM) ground leakage current is caused by the existence of a parasitic capacitor (Cp) between the PV panels and earth Since the PV arrays, parasitic capacitor Cp, and grid form a ground leakage current transmission path, as illustrated in Fig by the dotted line, when the CM voltage varies, the ground leakage current ileak appears The leakage current ileak decreases the efficiency of the PV inverter, reduces the grid current quality, and induces severe conducted and radiated electromagnetic interference (EMI); moreover, it is 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 embedded in the bridge arms of the H6 inverter, to separate the PV arrays from the grid during the freewheeling stage A B a  D1 U dc  L1 ig S3 S1 PV Array S5 S6 D2 S2 S4 L2 Utility Grid n ileak Cp  ug  b Fig Topology of the H6-type single-phase PV inverter ug ig uref u gs u gs1 , u gs u gs u gs , u gs Fig Schematic of the gate drive signals for the H6 inverter with unity PF The traditional modulation scheme for the H6 inverter with a PF of unity is shown in Fig 2, where ug is the voltage of the utility grid, ig is the grid current, uref is the modulation reference, and ugs1–ugs6 represent the gate drive signals of switches S1–S6, 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion ug respectively Under the traditional modulation scheme, the principle of elimination of leakage current ileak in the H6 inverter was stated in [22] Moreover, to improve the inverter efficiency, S1–S4 are chosen to be metal-oxide-semiconductor field-effect transistors (MOSFETs) and they operate at high frequency; whereas, S5 and S6, which are insulated-gate bipolar transistors (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 Inverter Reactive Power Injection Operation If the H6 inverter operates in the freewheeling stages, while power switchers S1–S4 are turned off, the PV arrays and the grid are separated By modulating the IGBTs S5 or S6 to change the freewheeling current according to the leading or lagging reference grid current, reactive power output is achieved while maintaining low leakage current in the H6 inverter Accordingly, the modulation reference wave can be divided into four sectors according to the direction of grid voltage and grid current, as shown in Table I In Sectors II and IV (positive power regions), the grid current is in the same direction as the grid voltage; hence, the conventional modulation can be used When the H6 inverter modulates the positive reference wave (Sector II), S1 and S4 are modulated at high frequency, and S6 maintains the conduction When the inverter modulates the negative reference wave (Sector IV), S2 and S3 are modulated at high frequency, and S5 maintains the conduction Further, in these sectors, the inverter outputs active power, hence, Sectors II and IV are regarded as the inverter modulation stage TABLE I TABLE OF MODULATION SECTOR Voltage direction Positive Negative Current direction Positive Negative II I (inverter modulation) (reactive power modulation) III IV (reactive power modulation) (inverter modulation) Correspondingly, in Sectors I and III (negative power regions), the grid current in in the opposite direction to the voltage, the inverter outputs reactive power, and these sectors are regarded as the reactive power modulation stage, while S5 and S6 are modulated at high frequency and S1–S4 are turned off Assuming that the grid current lags voltage by a phase angle φ, the modulation scheme of reactive power injection is shown in Fig Moreover, the modulation technique in case the grid current leads voltage can be obtained using the same principle In Sector I, the grid voltage is positive, reference grid current is negative, S1–S4 are turned off, and the driving signal of the freewheeling switch S5 is a high frequency pulse generated by comparing the reference wave with the modulation wave In this mode, the output voltage uab of the H6 inverter is the counter-electromotive force generated by the grid ig through L1 ig uref u gs u gs1 , u gs u gs u gs , u gs Fig Schematic of gate drive signals for the H6 inverter when grid current lags grid voltage and L2, during on/off of the freewheeling circuit, and its deviation from the grid voltage is di (1) uab  ug = L g dt 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 clamped to Udc, and since S6 is turned on, uab=0 Similarly, in Sector III, when S5 is turned on, uab=0, and since S5 is turned off, uab=−Udc Therefore, in Sectors I and III, the output voltage uab of the bridge arms of the H6 inverter commutates between and ±Udc It can also be regarded as being generated by modulating the dc bus voltage Udc The relation between the timing of the switches and the output voltage uab in Sectors II and IV is contrary to the relation between them in Sectors I and III Correspondingly, in Sectors II and IV, when S1 and S4 conduct (or S2 and S3 conduct), the output voltage uab of the bridge arms of the H6 inverter is Udc (or −Udc); when S1 and S4 are turned off (or S2 and S3 are turned off), uab=0 At any time in Sectors I and III, S1–S4 are turned off, the grid current ig varies with time following a sinusoidal law It is assumed that the grid voltage and current are defined as ug=Ugsinωt and ig=Igsin(ωt−φ), respectively, where Ig is the amplitude of current and ω is the grid angular frequency In this situation, the counter-electromotive force uab can be regarded as being generated by the modulation of this freewheeling current, and equation (1) yields 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion uab  ug = L dig dt =L  I g sin t      LI g cos t    (2) Assuming that da, db, and d6 are the duty cycles of the bridge arms A, B, and S6, respectively, uab in Sector III can be expressed as uab = uan  ubn  d aU dc  d bU dc  d 6U dc (3) Combining equations (2) and (3) yields d6 at steady state: LI g cos t     ug (4) d6  U dc As for digital signal processor (DSP) implementation of reactive power injection modulation, similar to the three-phase SVPWM modulation technique, the related strategy is implemented 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 ug and the reference grid current iref, sectors can be identified in accordance 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 = M + N, the correspondence relations between Q and the sectors are shown in Table II TABLE II CORRESPONDENCE RELATIONS BETWEEN Q AND SECTOR Q Sector IV III I II Further, X is defined as uref kLI g sin t    , (5) = U dc U dc where uref is the modulating output reference voltage, m (m ≤ 1) is the modulation ratio, and k is a proportion factor (a normalized factor) that is a function of the modulation ratio, reference voltage and reference current Notably, under reactive power modulation, if the switches S5 and S6 are turned on, the output voltage uab = Using equation (1), the variation rate of the grid current is in the opposite direction to the grid voltage Further, if S5 and S6 are turned off, the output voltage of the bridge arms is −Udc (or Udc) Simultaneously, the variation rate of the corresponding output grid current is in the same direction as the grid voltage When the H6 inverter operates in the reactive power modulation mode, the variation law of the grid current, which is caused by the switches S5 and S6 being turned on and off, is different from that caused by the switches S1–S4 being turned on and off Therefore, by using the same modulation wave and setting X as the reference wave of S1–S4, the reference wave of S5 and S6 is defined as (6) Y =1 X Further, Tc represents the digital control cycle count value; TA and TB represent the switching points of the single-phase bridge arms A and B, respectively; T5 and T6 represent the switching points of the freewheeling switches S5 and S6, respectively In X m Sector II, for example, Fig shows the implementation of the SVPWM Table III describes the relations among TA, TB, sector number, and the reference waves X and Y Fig Implementation of SVPWM in Sector II TABLE III DEFINING TA ,TB BY X, Y, AND Q Sector Switching point I TA TC TB TC T5 Y TC TC T6 TC Y TC II III IV X TC TC TC TC X C Low Leakage Current Characteristics in Reactive Power Injection Mode According to the analysis in [5, 9], in a transformer-less PV inverter system, the leakage current is essentially the CM current Besides the parasitic capacitor Cp of the PV arrays, the factor deciding the value of the leakage current is the variation rate of the output CM voltage ucm The leakage current can be expressed as ileak = Cp ducm dt (7) Hence, by selecting the appropriate modulation sequence and maintaining the output CM voltage ucm of the H6 inverter constant, low leakage current characteristics of the system can be ensured When the H6 inverter is modulated by the sequence shown in Fig 3, the output of the bridge uab has the feature of unipolar modulation In Sector II, modulating by +1 and 0, the output uab is Udc and 0, respectively In Sector IV, modulating by −1 and 0, the output uab is −Udc and 0, respectively In these two sectors, the CM voltage ucm retains half of the dc-side voltage Udc, 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 shows the detailed operating principle of Sector III, when the H6 inverter outputs lagging reactive power As shown in Fig 5(a), the H6 inverter operates in the inverter modulation stage of outputting lagging reactive power, and the current flows through the path L1GridL2S6D2 L1 Owing to the voltage balancing effect of the junction capacitor of switches, uan = ubn = 0.5Udc, and the CM voltage ucm is 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion ucm = 1 1  uan  ubn    U dc  U dc   U dc 22  (8) The H6 inverter with unity PF modulation has high grid current waveform quality, even if the inductance value of the grid-side filter is considered to be small [23] However, when the H6 inverter operates in the reactive power injection mode, the zero-crossing points of the output voltage and grid current appear at different moments; hence, a phase difference exists between them Furthermore, near these two zero-crossing points, the waveform of the grid current is distorted, resulting in a larger total harmonic distortion (THD) of the grid current, particularly when the H6 inverter operates at low power L1 ig  ug   U dc  L2 A Grid Current Distortion Caused by Dead-Time near Voltage Zero-Crossing Point Fig shows the distortion of the grid current near the zero-crossing points of the output voltage and grid current, when the H6 inverter outputs lagging reactive power Under unipolar modulation, during the switching dead-time, the output voltage of the bridge arms of the H6 inverter is uab=0 and the grid current is in a state of uncontrolled freewheeling; it may not track the reference current iref, resulting in distortion [24] In practice, owing to the minimum pulse width limit in the operating process of the H6 inverter, the dead-time td is longer than the preset value, and the waveform distortion becomes more significant (a) A B a  D1 U dc  L1 ig S3 S1 PV Array S5 S6 D2 S2 S4  ug  b L2 III ANALYSIS OF CURRENT WAVEFORM DISTORTION FOR H6 IN REACTIVE POWER INJECTION MODE Utility Grid n (b) Fig Operation modes of the H6 Inverter when it operates in reactive power modulation stage As shown in Fig 5(b), when the H6 inverter operates in the freewheeling stage, the freewheeling current flows through the path L1GridL2parallel diode of S3PV arrays parallel diode of S4D2 L1 During this stage, the grid voltage is reversed, but the output voltage of the bridge arms uab=−Udc, uan=0, ubn=Udc, and the CM voltage ucm is 1 ucm =  uan  ubn     U dc   U dc 2 (9) The above analysis shows that when the H6 inverter outputs lagging reactive current, irrespective of whether it operates in the inverter modulation stage or the freewheeling stage, if the input voltage Udc remains unchanged, the CM voltage ucm will always be constant Furthermore, the same conclusion can be drawn when the H6 inverter outputs leading reactive current Hence, the H6 inverter has the feature of low leakage current when it operates in the reactive power injection modulation mode, similar to its operation in the unity PF mode Notably, when the H6 inverter outputs reactive power in Sectors I and III (negative power region), the inverter bridge is separated from the PV arrays during the modulation stages However, when the H6 inverter operates in other sectors or operates with a PF of unity, the inverter bridge is separated from the PV arrays during the freewheeling stages Therefore, there are differences between the modulation methods 8A 400V iref i g 200V 4A 0A 0V uab 200V 400V ta 4A td 8A tb 11 10 12 13 t (ms) Fig Distortion of the grid current near the output voltage and grid current zero-crossing points In Fig 6, the output voltage uab cuts off at ta in the positive half cycle, starts at tb in the negative half cycle, and the current during the dead-time (td = tb−ta) can be expressed as ig  t  =  tb dig  t  dt  ig  ta  (10) dt The dead-time td of the H6 inverter is considered to be equivalent to a phase angle  Assuming ta πθ/2, tb πθ/2, and ug Ugsinωt near the zero-crossing point of the output voltage, the current derivative is dig U g sin t (11) = dt L Substituting equation (11) into equation (10) yields ta 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion ig  t  = Ug   L t d cos t  a Ug tb  L  d cos t ig  ta  , t   ta , tb  (12) If the H6 inverter operates in the reactive power injection mode, the grid current lags voltage by a phase φ; hence, ig = Igsin(ωtφ) and substituting it into equation (12) yields U  U   ig  t  = g   d cos t  g  d cos t I g sin  , t   ta , tb  L   L  (13) It can be inferred from the above equations that the magnitude of the grid current ig at ta is Igsin Under the effect of the grid voltage alone, the grid current varies as a cosine curve During the period [ta, π], the amplitude of current decreases, attaining the minimum value at the zero-crossing point of voltage (at this moment, the phase angle is π), and subsequently increases during the period [π, tb] Correspondingly, near the zero-crossing point of the H6 output voltage (near the phase angle 0), the grid current exhibits a similar distortion The aforementioned analysis shows that, during the dead-time near the zero-crossing point of the output voltage, only the ac grid voltage will be applied across the ac inductors L1 and L2, and the output voltage of the H6 inverter uab can no longer control the variation of the grid current Hence, the grid current cannot track the reference grid current, resulting in distortion Equation (13) further illustrates that, when the H6 inverter outputs reactive power with lower PF, the values of  and Igsinare relatively larger, and the current distortion becomes more significant B Current Distortion near the Zero-Crossing Point of Grid Current Distortion is also observed in the grid current near its zero-crossing point, as shown in Fig in a zoomed-in view Moreover, near the zero-crossing point of the grid current, the grid current cannot track the reference grid current accurately, resulting in distortion uref 4A 0.8 * uref 0.4 2A iref 0A ig 0.4 2A 4A 0.5 0.8 1.5 t (ms) 2.5 Fig Grid current distortion near its zero-crossing point (1) Current Distortion Before Zero-Crossing Point The analysis in Subsection A of Section II in this paper shows that before the zero-crossing point of the grid current in Sector III, only the IGBT S6 functions, and the electromotive force uab is generated by variation of the current through the inductor Without the effect of the external voltage or counter-electromotive force, the residual current through the inductor can only hold the original freewheeling direction, but cannot be commutated by modulating S6 actively As shown in Fig 7, at the end of Sector III, although the reference current iref has already crossed the zero point and changed its direction, the H6 inverter has not completed the sector switching, and the grid current cannot follow the reference current and complete the zero-crossing shift from positive to negative, resulting in distortion (2) Current Distortion During Sector Switching As described in Subsection C of Section II, the reactive power injection modulation is segmented into two stages, and the ideal modulation reference wave u*ref is discontinuous and mutates during the sector transition However, owing to factors such as the delay of control loop and the current sampling error at zero-crossing points, the actual modulation reference wave cannot mutate; consequently, the H6 inverter may not transit between the two sectors smoothly As shown in Fig 6, the output of the closed-loop control system, i.e., the modulation reference wave uref, is higher than the ideal sector conversion reference wave u*ref in the initial period of Sector IV, such that the modulating output voltage of the H6 inverter is higher than the voltage required to follow the reference grid current The variation rate of the actual grid current is larger than that of the reference grid current, i.e dig di  ref (14) dt dt Similarly, during the period when the H6 inverter converts from Sector I to Sector II, the grid current exhibits a similar distortion Hence, the current distortion near the grid current zero-crossing point is caused by the discontinuous sector conversion, and effective control approaches should be undertaken to ensure smooth sector transition As described above, when the H6 inverter operates in the reactive power injection mode, the grid current distortion is more significant Consequently, the lower-order harmonic current and even the dc component will significantly increase in the grid current, resulting in the degradation of grid power quality and reduction of system efficiency When the grid current distorts significantly, the harmonic current amplified by the control loop will cause problems in system oscillation and stability Specifically, when multiple grid-connected inverters are running simultaneously, the zero-crossing distortion will be superimposed and amplified, easily causing disturbance to the adjacent grids, and influencing the operating safety of nearby electrical equipment [25] Hence, the quality of the grid current waveform should be improved using an advanced control strategy IV CONTROL STRATEGY FOR GRID CURRENT WAVEFORM IMPROVEMENT 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion A PIR Sliding Mode Surface Construction for Lower Order Harmonics A sliding mode control can implement a high precision control under changing parameters and load disturbances; therefore, it exhibits good robustness and fast dynamic response [26] Owing to these advantageous features, the sliding mode control is adopted in this study to improve the quality of the grid current waveform The analysis in Section III illustrates that the current distortion is partly caused by the nonlinear PWM modulation The traditional current control loop of the PV grid-connected inverter always uses a proportional-resonant (PR) controller or quasi-PR controller, achieving high gain at the resonance frequency point of the grid current, but resulting in no inhibition of the dc component However, in the actual system, the current zero-crossing distortion appears and results in higher lower-order harmonics and further leads to an increase in the dc component Fourier analysis of the current waveform with zero-crossing distortion shows that there are low frequency and dc components in the grid current harmonic spectrum [27] In order to compensate the zero-crossing distortion, suppress the dc component, and improve the quality of the grid current waveform, an integral link is added to the quasi PR of the current loop controller, forming a PIR controller, as shown in Fig 8(a), whose transfer function is expressed as: K Rc s K G  s  = Kp  i  , s s  2c s  02 (15) where Kp, Ki, and KR are the proportional, integral, and resonant controller parameters, respectively; ω0 is the system resonance attenuation coefficient Considering Kp = 2, Ki = 50, ωc = 10, and KR = 100, its Bode diagram is shown in Fig (b) From the Bode diagram, it can be observed that the PIR controller has a high gain not only at resonant frequency, but also in the low frequency band This reflects the inhibitory effect of the controller on the current distortion and the dc component Therefore, this study modifies the PIR sliding mode switching surface into a fixed-frequency sliding mode control for the grid current First, the switching surface equation SPIR is designed as   K Rc s K S PIR =  K p  i  i  ig  ,   ref s s  2c s  0   where s is the Laplace operator By selecting the grid current ig of the H6 inverter as the state variable X, the state equation of the H6 inverter can be derived from equation (1) as dX  AX + BU + D , dt K R ωc s s  2ωc s  0  ig    dSPIR dX ref   AX  BU  D  k·sat  SPIR  (18) dt dt Assuming  is the boundary width of the sliding mode control, the saturation function is expressed as: (19) The sliding systems control law is obtained as uref U  B1  E  AX  D  k·sat  SPIR  ，E = Ki s dX ref (20) dt Based on the equations (17)–(20), by considering E as the unknown disturbances, the voltages applied to the converter uref can be calculated as uref = 40 Magnitude (dB) S | S | ;   /  S   1,  sat ( S )   S ,  1,  (a) iref 30   20 ig 10 90 Phase (deg) (17) where X = ig, B = Udc/L, and D = ug/L Furthermore, A = by neglecting the ac-side line resistor The system is designed with a negative slope converging to the switching surface, and the saturation function sat() is used to eliminate the chattering; further, k is set to be the convergence control coefficient of the switching surface Subsequently, the switching surface derivative can be expressed as Kp iref  (16) Kp ug udc   Ki s  k·sat  SPIR  (21) uref S  ugs1 ~ugs6 ug ug ig K R ωc s s  2ωc s  0 45 -45 -90 -1 10 10 10 10 Frequency (Hz) 10 10 (b) Fig Structure and Bode diagram of the PIR controller: (a) structure of the PIR controller and (b) Bode diagram of the PIR controller Fig Sliding mode control diagram for the grid current The sliding mode control block diagram is shown in Fig The ac-side modulation output reference voltage uref generated by the sliding mode controller, after modulation by SVPWM, 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion produces the PWM pulse driving power switches Owing to the fixed SVPWM modulation frequency, this control strategy is a fixed-frequency sliding mode control In order to verify the stability and convergence of the sliding mode control strategy, a Lyapunov function is constructed as follows (22) V  SS T  S PIR and it easily renders V permanently positive Its first order derivative is T dSS (23) V   2  SPIR sat  S PIR   dt Since the arithmetic product of the switching surface function SPIR and its saturation function sat() is always greater than or equal to 0, the derivative of V in the above equation is always less than or equal to 0, i.e., the Lyapunov function V decreases with time until it converges to Hence, the system converges to the switching surface and is convergent and stable B Global Sliding Mode Control for Sector Switching Distortion Compensation By setting up the model of the fixed-frequency sliding mode control for the grid current, the SVPWM control process can be optimized by constructing a suitable sliding function S, according to the theory of sliding mode control; subsequently, the objective of system optimized control can be achieved From Fig and the analysis of the grid current waveform distortion of the H6 inverter, the switching process of the H6 inverter from a reactive current output mode to an active inverter mode (i.e., switching from Sector I to Sector II or from Sector III to Sector IV) is not smooth Since these two processes occur near the zero-crossing points of the current (switching from negative to positive or from positive to negative), the switching that is less smooth leads to the grid current zero-crossing distortion Therefore, the modulation could be so sensitive that the modulator has to adopt a soft transition During the global sliding mode controlling, the global function S has a sliding surface gradient characteristic and can attenuate to zero rapidly Moreover, by determining the transient state by the sector switching, considering the initial value of the sliding mode surface as the initial value of the transient state, and constructing the dynamic nonlinear global sliding surface to smooth the sector switching process, the compensation of zero-crossing distortion can be implemented Therefore, the new global sliding mode function can be designed as (24) S  S PIR  f  t  The global sliding mode function is the original sliding mode function minus the function f(t), which is designed to achieve the global sliding mode; further, f(t) satisfies the following three conditions [28]: 1）f(0) = S(0); 2）When t∞, f(t)0; 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   (25) f  t   f 0 e   t , where > and is a constant The discrete equation (24) yields (26) f  k  1  f  k  e   According to the definition of the global sliding mode, f(0) finally attenuates to and the value of determines the attenuation rate of f(0) If the value of  is too large, f(0) decays fast, failing to reflect the effect of global sliding If the value of  is too small, f(0) decays slowly, and cannot even decrease to in the entire sector, causing an additional distortion of the ac output reference wave uref By considering all the aforementioned factors, and assuming = 0.37, after approximately seven control cycles, f(0) can decay to less than 0.1 times of the initial value, when the control frequency is 20 kHz 0.8 0.6 0.4 0.2 2.0 2.4 2.8 t (ms) 3.2 3.4 3.2 3.4 (a) 3A 2A 1A 0A 1A 2A 3A 2.0 2.4 2.8 t (ms) (b) Fig 10 Comparison of the waveforms when the inverter is running with and without the global sliding mode controller Fig 10 compares the detailed waveforms of the ac-side modulation reference wave uref, in the vicinity of the current zero-crossing, when the H6 inverter operates with and without the global sliding mode controller When the H6 inverter switches between the reactive power injection mode and the active inverter mode, the global sliding mode controller lowers uref in several control cycles just after sector switching as compared to the conventional controller, and it is much closer to the ideal reference wave Hence, the grid current zero-crossing with the global sliding mode control is more moderate than that without the global sliding mode control 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion Consequently, the switching process becomes smoother, and the mutation and distortion of the grid current is reduced ug V EXPERIMENTAL RESULTS In order to study the reactive power injection modulation of the H6 inverter, and verify the control algorithm for the improvement of the grid current waveform, a kVA experimental prototype is built Fig 11 shows the designed H6 PV inverter, which consists of a boost converter and an H6 full-bridge inverter All the control algorithms are implemented by using the low-cost 16-bit digital signal processor chip TMS320F2808 The specifications of the prototype PV inverter are listed in Table IV ig uab (b) Fig 12 Waveforms of the H6 inverter when it is expected to regulate the power factor: (a) H6 inverter is expected to output leading reactive power and (b) H6 inverter is expected to output lagging reactive power ug ig uab (a) Fig 11 Photograph of the prototype H6 PV inverter TABLE IV PARAMETERS OF KVA PROTOTYPE Parameters Value Switching Frequency fs/Hz 20k AC filter inductor L1 =L2/mH 0.8 DC link capacitor Cdc/mF Rated Capacity Se/(kVA) Output frequency f/Hz 50 220 Rated grid voltage ug/V Fig 12 shows the measured waveforms of the H6 inverter with the traditional modulation The inverter is expected to output leading and lagging reactive power Since S1–S6 are all turned off in the reactive power regions, the function of reactive power regulation is not achieved ug ig uab (a) ug ig uab (b) Fig 13 Waveforms of the H6 inverter when it operates at 0.95 PF: (a) H6 inverter output leading reactive power and (b) H6 inverter output lagging reactive power Compared with Fig 12, Fig 13 shows the measured waveforms of the H6 inverter with reactive power injection modulation, at 0.95 lagging PF and 0.95 leading PF The experimental waveforms show that, by using the modulation strategy proposed in this paper, the H6 inverter can accurately and stably output reactive current lagging or leading the grid voltage Fig 14 shows the midpoints a，b of the H6 bridge arms voltage waveforms relative to the ground uan, ubn, and the waveform of voltage uan + ubn (twice the CM voltage), when the H6 inverter functions under 0.95 lagging PF The waveform of the voltage uan + ubn shows that its amplitude remains approximately the same, and the variation rate of its CM 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion 10 voltage is small Furthermore, the leakage current of the H6 inverter is small, as inferred from equation (7) ug ig uan ubn ileak uan ubn ig Fig 14 Experimental waveforms of uan, ubn and twice CM voltage uan+ ubn when the H6 bridge operates under 0.95 PF Fig 15 illustrates the leakage current waveform when the experimental prototype is at full load (5 kW or kVA) and operates at PF of and 0.95 It can be observed from the experimental waveforms of Fig 15(a)–(c) that, when the H6 inverter operates in the reactive power output mode, the value of leakage current is equivalent to the value at unity power factor and remains under 20 mA, and its root mean square (RMS) value remains under 15 mA These values satisfy the requirements of standard VDE-AR-N 4105 The experiment proved that, by utilizing the proposed modulation strategy, the H6 inverter presents low leakage current characteristics when outputting reactive power Fig 16 shows the comparison of the waveforms with and without the control strategy for the improvement of the grid current, when the non-isolated H6 single-phase PV grid inverter operates at an apparent power of 2000 VA and a PF of (c) Fig 15 Measured waveforms of grid voltage, grid current, and leakage current when the H6 inverter operates at unity PF and 0.95 PF: (a) at unity power factor; (b) at PF of 0.95(leading) and (c) at PF of 0.95(lagging) ug ug ig ig (a) ug ug ig ig (b) ug ig ig ileak (a) ug ig (c) Fig 16 Comparison of the grid current experimental waveforms with and without the waveform-improving controller at PF of 0.95 (lagging): (a) with traditional current controller; (b) with waveform-improving current controller and (c) harmonic spectrum of grid current of (a) and (b) 0.95 The analyses show that, with the help of the waveform-improving control, 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 to the limitation of minimum pulse width and dead-time, a further reduction of the grid current distortion is not achieved From the fast Fourier transform (FFT) analysis of the current waveforms, by using the waveform-improving ileak (b) 0885-8969 (c) 2016 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications_standards/publications/rights/index.html for more information This article has been accepted for publication in a future issue of this journal, but has not been fully edited Content may change prior to final publication Citation information: DOI 10.1109/TEC.2017.2712741, IEEE Transactions on Energy Conversion 11 control, it can be observed that the dc component and main characteristic harmonics have declined THD/% 20 Traditional control 10 Wave-improving control 0 2000 4000 6000 Output Power/VA Fig 17 Comparison of grid current THD with and without the waveform-improving controller Fig 17 shows the measurement results of the grid current THD with and without the waveform-improving controller, performed under conditions of full power when the H6 inverter operates at 0.95 lagging PF Using the proposed control strategy, the grid current waveform distortion is apparently improved in the entire power section, particularly when outputting small reactive power As the output power of the H6 inverter becomes higher, the improvement of grid current quality is smaller than that observed in Fig 16 The reason for this phenomenon is that, when the output power is high, the variation rate difference between the actual grid current and the reference grid current is small, and the increment of the grid current THD caused by the zero-crossing is small Besides, when the output power is high, the THD of the grid current is relatively low Under this condition, the further improvement is limited TABLE V PERFORMANCE COMPARISON OF [29], [30] AND PROPOSED METHOD IN THIS PAPER [29] [30] This paper Topology H6 bridge with6 MOSFETs H6 bridge with6 IGBTs H6 bridge with MOSFETs and IGBTs In case of the H6-type transformer-less single-phase inverter for grid-tied PV system，some research work was reported in [29] and [30] However, the study in [29] focused on 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 proposed method are shown in TableV It can be observed from TableV that, similar to the H6 topologies, all the topologies have similar efficiencies, with a slight difference caused by the difference in the performances of the IGBT and MOSFET devices Using the reactive power injection modulation and control strategy proposed in this paper, H6 inverters have the capability of reactive power injection, with low THD of grid current and improvement of grid current waveform in zero-crossing Moreover, the advantage of low leakage current is intact VI CONCLUSION In order to extend the application of the non-isolated H6 single-phase PV grid-connected inverter, this paper proposes a reactive power injection modulation for the H6 inverters However, when an H6 single-phase PV inverter operates in the reactive power injection mode, the distortion of the grid current is aggravated Therefore, a control strategy based on the PIR global sliding mode control is proposed to improve the quality of the grid current waveform Experimental results show that the proposed scheme for the H6 inverter can implement reactive power modulation while maintaining low leakage current characteristics Moreover, the waveform distortion of the grid current is improved For the H6 single-phase PV inverters that have already been installed for residential applications, only their control program requires to be updated, without hardware transformation The proposed improved control approach is attractive owing to its cost-saving advantage VII References Capability of reactive power injection Not involved With reactive power injection modulation With reactive power injection modulation [1] Leakage current Low Low Low [2] Improvement of current distortion in zero-crossing Not involved Not involved With waveformimproving control method [3] Energy transfer path MOSFET + 1 IGBT + diode in reactive power diode + inductors + inductors injection mode IGBT + diode+ inductors Energy transfer path in inverting mode MOSFETs +2 inductors IGBTs +2 inductors IGBT + MOSFET + diode+ inductors Freewheeling path in reactive power injection mode diodes +2 inductors diodes +2 inductors IGBT + diode+ inductors Freewheeling 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photovooltaic non-isolateed AC module applicattions,” IEEE Tranns Power Electrron., vol 26, no 4, pp 1253–1260, Aprr 2011 [30] M Islam and S Mekhilef, “H6-tyype transformerlesss single-phase innverter for grid-tied phootovoltaic system,,” IET Power Eleectron., vol 8, pp 636– 644, 2015 Bin Liu receivedd the Ph.D degreees from the Schoool of Information Scieence and Engineeering, Central South University, Channgsha, China, in 2014 He is currrently working as a poost-doctoral mem mber in Central South University, and a Lecturer in School of Elecctrical Engineering, Guaangxi University His research intterests are in the generaal area of power electronics and eenergy conversion, withh particular em mphasis on connverter topologies, modeeling, control, andd various applicatiions M Mei Su received the B.S., M.S annd Ph.D degreess from tthe School of IInformation Scieence and Engineeering, C Central South U University, Changgsha, China, in 1989, 1992 and 2005, rrespectively Since 2006, she has bbeen a pprofessor with thhe School of Infformation Sciencce and E Engineering, Central South Uniiversity Her ressearch iinterests includee matrix converrter, adjustable speed ddrives, and wind energy conversion systems Jian Yang (M’099) received the Phh.D degree in Elecctrical Engineering from m the Universityy of Central Fllorida, Orlando, in 20088 He was a Seniior Electrical Enggineer with Delta Tau D Data Systems, Innc., Los Angeless, CA, from 2007 to 20110 Since 2011, hee has been with C Central South University,, Changsha, Chinaa, where he is currrently an Associate Chair C Professor with the School of Information Sciennce and Engineerring His main ressearch interests include control applicattion, motion plannning, a power electroonics and and M and Ph.D deegrees Dongran Song reeceived the B.S., M.S from the School oof Information Sccience and Engineeering, Central South U University, Changgsha, China, in 2006, 2009 and 2016,, respectively, w where he is currrently working as a postt-doctoral membeer He was an Elecctrical & Control Engineeer with China M Ming Yang Wind Power, P Zhongshan, from m 2009 to 2013 His research intterests include wind turbbines, power elecctronics and renewable energy system D Deqiang He received PhD deggree from Chonngqing U University, Chonngqing, China, inn 2004 Now hee is a pprofessor of thee School of Meechanical Engineeering, G Guangxi Universsity His main reesearch interests are in ffault diagnosis aand the intelligennt maintenance oof rail ttransit Shaojian Song reeceived the B.S., and M.S degreess from Guangxi Universsity, Nanning, Chhina, in 1994 andd 2001 respectively Now w he is a professor of the Schoool of Electrical Engineeering, Guangxi University U His cuurrent research interestts include modelling, optimizationn and control for compplex system, elecctric vehicle and V2G, active distributionn network, powerr electronics and eenergy conversion withh particular em mphasis on connverter modeling, controol, and various 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