Novel LCL Filter for Non-Isolated Photovoltaic

THIS WORK HAS BEEN ACCEPTED BY THE 44TH ANNUAL CONFERENCE OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY (IECON 2018). THIS IS A PREPRINT

Novel LCL Filter for Non-Isolated Photovoltaic Inverters with CM Current Trapping Capability for Weak Grids Ahmad Khan†, ‡, Atif Iqbal†, Mohammad B. Shadmand‡ † Department of Electrical Engineering, Qatar University, Doha, Qatar ‡ Electrical and Computer Engineering Department, Kansas State University, Kansas, USA Abstract— In this work, a novel LCL filter topology for nonisolated Photovoltaic (PV) applications is developed. This topology has the ability to trap the High-Frequency (HF) Common Mode (CM) current inside the PV inverter. Consequently, suppressing the ground leakage current. Furthermore, the proposed solution is immune to ground leakage current resonance issues (i.e. effective for applications where the utility grid is characterized as a weak grid). Moreover, the theoretical analyses were validated on a 10 kW grid-connected PV system. The results demonstrated that at resonance conditions, the proposed system reduced the leakage current root-mean-square (RMS) value from 1 A to 25 mA. Thus, satisfying the VDE standard’s leakage current limit. Keywords— Photovoltaic (PV), Non-isolated, Transformer-less, Grid-Connected, Ground leakage current, LCL filter

LIST OF SYMBOLS

DC-Link capacitor Filter capacitor PV negative terminal stray capacitor to the ground PV positive terminal stray capacitor to the ground CM resonance frequency DM resonance frequency Controller sampling frequency Switching frequency Grid fundamental frequency Anti-resonance (trap notch) frequency Filter capacitors’ CM current Filter capacitors’ DM current Inverter-side inductors’ CM current Inverter-side inductors’ DM current Ground leakage current Grid current Filter inductor Grid terminals stray inductor Grid-side filter inductor Inverter side inductor Rated power Ground resistance Controller sampling time DC-Link voltage Grid voltage Inverter output voltage Inverter’s CM noise Inverter’s DM output voltage Point of common coupling voltage The CM impedance of the PV stray capacitors The CM impedance of the grid-side inductances

I. INTRODUCTION

N

owadays, the utilization of transformer-less inverters in grid-connected PV applications is becoming more dominant [1]. This is due to their higher power density, improved efficiency, and lower cost compared to transformer based topologies [2]-[4]. Nevertheless, the galvanic connection in transformer-less technologies consequences in hazardous ground leakage current circulation [5]. Essentially, this stray current is imposed by PV modules’ stray capacitors existence [6], [7]. These stray capacitors are formed between the PV panel terminals and the ground conductor [8]. Accordingly, for safety assurance, grid-connection codes introduced strict requirements regarding the maximum acceptable ground leakage current magnitude [8]. For instance, the VDE standard considers a leakage current exceeding 300 mA RMS for a duration more than 0.3 sec as a system fault; and it demands tripping the grid regardless of the amount of active power transfer [9], [10]. Thus, excessive leakage current circulation not only affects system’s safety it also influences the total energy yield by the PV system indirectly [11]. The leakage current suppression techniques in the literature are divided into three methods: (A) CM voltage decoupling, (B) common grounding, and (C) CM current bypassing. II. LEAKAGE CURRENT SUPRESSION TECHNIQUES

A. CM Voltage Decoupling CM voltage decoupling technique is introducing a supplementary active circuitry to the H-bridge inverter topology in Fig. 1. These active switches form a decoupling network for disconnecting the PV terminals (P and N nodes in Fig. 1) from the inverter two poles (A and B nodes in Fig. 1) during the zero ) [6], [7]. As voltage level generation in the inverter output ( a result, the HF CM voltage that appears on the PV stray capacitors will be reduced and accordingly it’s associated leakage current amount. The major advantage of this methodology is that it can be easily implemented on the Hbridge inverter. For example, the HERIC [12], H5 [13] and H6 [14] topologies are variations of the conventional H-bridge inverter with slightly modifying the modulation strategy. However, the major drawbacks of this method are the need for additional gate drives and switches [15]. Additionally, complicated control schemes must be adopted to support reactive power flow [16]-[20] and avoid current distortion in low solar irradiance operation conditions [19]-[22]. Furthermore, CM voltage decoupling only is not adequate to mitigate the S1

CPVG +

P

ig Split Passive + ½Lg Low Pass vpcc vg Filter - L, LC, LCL, - ½Lg B or LLCL A

2CDC

vDC CPVG −

S3

C S2

PV

+ vinv S4

C

2CDC N

RE iE

Fig. 1. Transformer-less grid-connected voltage source H-Bridge inverter involving grid and PV stray elements


leakage current completely. As an extra clamping cell implementation is mandatory to suppress the leakage current generated by the transistors’ junction capacitance resonance [6], [7]. This clamping cell reduces the reliability of the system since it requires a split DC-Link structure to access the neutral point (Node C in Fig. 1) [23]. In other words, double the initial electrolytic DC-Link capacitors’ capacitance is required with a split DC-Link structure. B. Common Grounding In the common grounding method, the grid negative terminal is directly connected to the negative DC-Bus. Vast number of common ground based topologies exist in the literature, such as the topologies proposed in [24]-[41]. These common ground topologies are based on two operation principles; either on flying-inductor or flying-capacitor concept. However, most of the common ground inverters are based on a non-conventional structure that use more active switches compared to the 4-switched H-bridge topology. Only [40], [41], provide an H-bridge based common ground inverter. This topology is termed as Siwakoti-H inverter [41]. Nonetheless, the Siwakoti’s topology uses two non-conventional active switches with reverse blocking capability and an additional large electrolytic unreliable flying capacitor. These factors make the design of the Siwakoti’s topology more complex compared to the conventional H-bridge. Hence, common ground topologies are in the developing stage and they need further improvements. C. CM Current Bypassing The principle of suppressing the ground leakage current with this approach is based on deviating the HF CM current from the ground leakage loop [6]. Precisely, this approach is achieved by introducing shunt capacitors in the HF CM equivalent circuit of the filter [6]. For example, the modified filter proposed by [42] that is illustrated in Fig. 2(a); utilizes the CM current bypassing method [42]. Additionally, this filter is equivalent to a conventional LCL filter in the Differential Mode (DM) because of its’ symmetrical structure; whereas, the HF CM equivalent circuit appears as Fig. 2(b) depicts. Moreover, since practically and ) are much smaller the PV stray capacitors ( than the two filter capacitors (2 ) and the ground resistance is in range of 10Ω-15Ω for stiff grids [43]-[46]; the ground leakage loop possesses larger impedance compared to the capacitive shunt branch at the switching frequency in Fig. 2(b). As a result, the ground leakage current ( ) is negligible. Actually, the HF CM model can be simplified further as illustrated in Fig. 2(c) where the leakage current is considered zero. The most attractive feature of the CM current bypassing technique is that it allows utilizing the conventional 4-switched H-Bridge inverter with the unipolar modulation effectively [23]. Meaning that, it does not require additional active circuitry and gate drives for leakage current suppression. Furthermore, reactive power flow is possible and grid current distortion issue is non-existing [11], [17], [18], [23]. Thus, compared to the earlier methods – i.e. CM voltage decoupling and Common Grounding – this method is more promising. Actually, even higher order trap filters were introduced that are based on this mitigation method, such as the LLCL [23], [47] and LCL-LRCR [48]. Nevertheless, a serious problem is neglected with the CM current bypassing method in [42]. This issue is related to ground leakage current resonance occurrence. If this resonance is triggered; the leakage current mitigation principle will be breached. Specifically, if the PV stray capacitors are resonating at the switching frequency ( ) or it’s multiple with the equivalent inductance of the ground leakage loop; the HF CM -

S1

CPVG +

S3

P A

2CDC + vinv -

C

vDC

S2

CPVG −

S4

B

2CDC

PV

ig

N

C

½Linv 2Cf 2Cf ½Linv

½Lgf +

½Lg

vg

vpcc ½Lgf

-

½Lg

Modified LCL filter with CM Current bypassing Capability

RE

iE

(a)

iCM

½Linv

½Lgf

½Lg

½Linv

½Lgf

½Lg

vinv (CM)

iC (CM)

2Cf

RE CPVG + CPVG -

2Cf

CM Current Bypassing Branch

Ground Leakage Loop Elements

iE

(b)

½Lgf

½Lg

½Lgf

½Lg

½Linv

iCM

½Linv

vinv (CM)

iC (CM) ≈ i

2Cf

RE

CPVG +

CM

CPVG -

2Cf



iE ≈ 0

(c)

½Lgf

½Linv

iCM

½Lgf

½Linv

vinv (CM)

iC (CM)≈ 0

2Cf

2Cf


½Lg

½Lg

ZLg

Resonate at the switching frequency

RE CPVG +

ZCpvg CPVG -


iE ≈ iCM

(d) Fig. 2. Existing LCL filter with CM current bypassing capability [42]: (a) Filter structure, (b) HF CM equivalent circuit (c) Approximate HF CM equivalent circuit under non-resonance conditions (i.e. Stiff grid inter-connection) and (d) Approximate HF CM equivalent circuit when the ground leakage loop elements are resonating at the switching frequency (i.e. Weak grid inter-connection)

model will be approximated by Fig. 2(d). This condition is highly probable when considering weak grids connection. As weak grids’ possess large equivalent Thevenin inductances (i.e. grid-side inductances) [49]-[52]. Accordingly, it is extremely likely that they will resonate with the small PV stray capacitors. In more details, this resonance condition in Fig. 2(d) is represented mathematically by the equation (1). +

=0

= 1, 2, 3 = (¼ =

(

+¼ 1 +

(1)

) )

Generally, this resonance is only serious when it occurs at the switching frequency. The leakage current resonance occurrences at the 2nd or the 3rd multiple of the switching frequency are rare because such conditions require extremely low PV stray capacitors. This work proposes a novel LCL filter topology that is


S1

CPVG +

A

2CDC

vDC CPVG −

P

S3

+ vinv -

C S2

S4

½Lgf + -

vg ½Lg

RE

Proposed LCL filter with CM Current Trapping Capability

N

LCL DM resonance

½Lg

vpcc ½Lgf

C

2CDC

PV

ig

½Linv 2Cf Lf 2Cf ½Linv B

iE

(a)

Lgf + Lg

Linv

vinv

iDM

iC (DM)

(DM)

vg

Cf

ig ½ fsw

10fo

Fig. 4. Proposed LCL filter grid current to inverter’s DM output transfer function (equation (2) bode plot) (b)

½Lgf

½Linv

iCM vinv (CM)

½Linv

iC (CM)

2Cf

½Lgf

½Lg

Higher parasitic elements based resonance

Lower nonparasitic elements based resonance

½Lg

Non-parasitic elements based CM trap notch

CPVG +

2Cf

CPVG -

CM Current trapping Branch

Lf

CM bode plot when Lf = 0 CM bode plot when Lf is tuned at fsw

RE


iE

(c) Fig. 3. Proposed LCL filter with CM current trapping capability: (a) Filter structure, (b) DM equivalent circuit and (c) HF CM equivalent circuit

immune to ground leakage current resonance problems by trapping the HF CM current inside the inverter. The proposed technique is crucial in weak grid connection applications. In other words, when the ground leakage current resonance occurrence is common. The remainder of this paper is structured as follows: Section III, presents the proposed filter topology. Section IV, presents the control scheme and stability considerations with the proposed filter. Section V, discusses the results obtained on a 10 kW system. Finally, Section VI concludes the paper. III. PROPOSED FILTER TOPOLOGY The proposed filter is depicted in Fig. 3(a). The noticeable differences in the proposed filter compared to the conventional LCL filter are: (i) all filter inductances are split into two parts – This is to guarantee that the HF DM noise contribution to the CM circuit is eliminated [6], [7], (ii) the filter capacitor is split into two capacitors and (iii) the mid-point of the two filter capacitors is connected to the neutral point (Node C in Fig. 3(a)) - This is to bypass the HF CM current from the ground leakage loop - through a small inductor ( ). This added filter inductor is used to trap the HF CM current as detailed in subsection III.A. A. Proposed Filter DM and CM Equivalent Circuits 1) DM Equivalent Circuit Due to the symmetrical structure of the proposed filter (Fig. 3(a)); the mid-point of the filter capacitor connection to the neutral point circulates only a CM current component. In other words, in the DM the filter capacitors appears in series. Hence, the proposed filter is equivalent to an LCL filter as shown in Fig. 3(b). In addition, the DM control plant can be represented by (2). Moreover, this plant possesses a stability challenging resonance peak at (3) (see Fig. 4).

Fig. 5. Proposed LCL filter leakage current to inverter’s CM noise transfer function (equation (4) bode plot when = 0) 1

=

=

(

+

1 2

(

)+

+

(2)

+

+ + + )

(3)

This control plant in (2) can be stabilized passively through physical resistors or actively with the existing multi-loop control schemes [53]-[56]. Moreover, the components’ values can be selected according the optimum criteria established in the literature [57]; but considering the filter’s inductors and capacitors split that were indicated earlier in Fig. 3(a). 2) CM Equivalent Circuit Rather than depending solely on the filter capacitors to bypass the HF CM current from the ground leakage loop; an additional filter inductor ( ) is used to trap the HF CM current. This filter inductor does not interact with the DM operation. An analytic expression for the ground leakage current ( ) in ) can be used to relation to the inverter’s CM noise ( determine the optimal value for inductor ( ). Therefore, by utilizing the HF CM model in Fig. 3(c) equation (4) is deduced. = =

(

+ (

= =

(

=

(

+

) ¼ )(4

+ 4 ) + ¼( +

(

1+s 4 +

)

+ + +

)

+

+

+ 4

+1

+¼

+

) )

+

+

(4)


CPVG+ 2CDC PV

C

ig

P A

2CDC N

IGBTs H-Bridge S4 S3 S2 S1

B

CPVG-

½Linv

½Lgf

½Lg

½Linv

½Lgf

½Lg

2Cf

vDC

vg RE

vpcc iE

2Cf

ZOH

1 -1

ZOH

ZOH

Lf

Triangular Carrier

-1

PI(z)

PR(z) Resonance gain at fo

VDCRef

PLL

Sin

ϕPFRef Fig. 6. Proposed system overall control scheme

The leakage current to inverter’s CM noise transfer function in (4) contains two resonance peaks at the frequencies (5) and (6) (see Fig. 5). ≈

1 2

(¼

+

(5)

)4

1

≈ ¼

2

+

(

+

)

(6)

Practically, the lower non-parasitic elements based resonance (5) does not affect the leakage current. This is because the inverter’s CM noise does not contain any frequency component in that resonance frequency range. However, this low resonance only affects the CM control stability in case the CM operation of the inverter is utilized for active power decoupling [58], [59] or low frequency leakage current suppression [11]. Contrariwise, the parasitic based resonance (6) affects the magnitude of leakage current severely. Particularly, for weak grid cases; the second resonance may occur at the switching frequency. Fortunately, the proposed filter has an anti-resonance dip (Trap notch) at (7) that can be designed based on non-stray elements (see Fig. 5).

=

1 2

4

(7)

Hence, if this trap notch is tuned at the switching frequency; the ground leakage current will be immune to amplification due to ground leakage loop elements resonance. IV. CONTROL SCHEME STRUCTURE AND STABILITY The overall control scheme is shown in Fig. 6. The control approach adopted is the dual cascaded loops methodology. Specifically, an outer DC-bus voltage control loop that utilizes a Proportional-Integral (PI) controller and an inner current control loop that uses a Proportional-Resonance (PR) controller that is tuned at the grid fundamental frequency ( ). In more details, the outer voltage loop drives the reference for the inner current loop. Stability-wise, as aforementioned that DM has an LCL resonance that affects the stability of the control scheme.

Table I. Parameters of the proposed system Parameter

Symbol

Rated power

Value

10 kW

10 kHz

Switching frequency Controller sampling frequency

10 kHz

Nominal grid frequency

50 Hz

Grid voltage

240 VRMS 700 V

Nominal DC-Bus voltage

Inverter-side inductor

Filter capacitor

1.25 µF

Filter inductor

50.64 µH

Grid-side filter inductor Grid-side parasitic inductor

Ground resistance

3 mH 0.8 mH

DC-Link capacitor PV terminals parasitic capacitance

3.6 mH

=

5 mF 133 nF 15 Ω

However, in this work since the controllers are designed in the discrete Z-domain; the inherent 1.5 delay is harnessed for stabilizing the system by assuring the LCL DM resonance frequency is greater than one sixth of the controller sampling frequency ( ) [60]. The output of the controller is a sinusoidal modulation index (Fig. 6). This modulation index is compared with the bipolar triangular carrier as indicated in Fig. 6 to generate the switches’ gate signals (Fig. 6). Moreover, this pulse width modulation strategy is identical to the conventional unipolar modulation.


1st Case:

2nd Case:

= 0

=

iE

vpcc

ig

5 ms/div

Fig. 7. Impact of the filter inductor ( ) introduced by the proposed LCL filter on the leakage current for a 10 kW system with triggered ground leakage loop elements resonance at the switching frequency: (a) Ground leakage current ( : 600 mA/div), (b) Grid current ( : 40 A/div) and (c) Point of common coupling : 80 V/div) (The dashed vertical line indicates the instant that the filter inductor’s value changes) voltage (

V. RESULTS AND DISCUSSION The theoretical analyses developed are verified by implementing a 10 kW grid-connected PV system in PSIM software. This PV system is tied to a 240VRMS/50Hz weak grid. The weakness property of the grid is due to the large grid-side equivalent inductance value (Table I). Consequently, a PV stray capacitor in the range of nano-Farads would trigger the ground leakage loop elements resonance at the switching frequency. In fact, in Table I, the value of the PV parasitic capacitors causes resonance at the switching frequency with the grid-side = ). In addition, the CM equivalent inductance (i.e. current trapping inductor ( ) value is selected such that the proposed filter CM trap frequency occurs at the switching = ). Moreover, observing the ground frequency (i.e. leakage current waveform with and without this CM trap inductor would be enlightening. In Fig. 7, when the filter inductor ( ) is properly tuned at switching frequency the leakage current RMS value is reduced from 1 A to 25 mA. In other words, this small trap inductor reduced the leakage current 40 times and achieved the VDE standard limit (i.e. ≪ 300 mA). Also, the additional trap filter does not interact with the DM operation of the inverter. As the grid current ( ) is not influenced by the sudden change in the filter inductor value in Fig. 7

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

VI. CONCLUSION In conclusion, this paper proposed a novel LCL filter topology. This topology has the capability to trap the HF CM current inside the PV inverter. Hence, resulting in reduced ground leakage current. The proposed method is suitable for PV application where the utility grid is categorized as a weak grid. As weak grids’ inductances can easily resonate at the switching frequency with the PV stray capacitors. The theoretical analyses were validated on a 10 kW grid-tied system. The results demonstrated that at resonance conditions the proposed system reduced the leakage current RMS value from 1 A to 25 mA. Therefore, satisfying the VDE standard limit (i.e. less than 300 mA).

[10]

[11]

[12]

[13]

ACKNOWLEDGMENT This publication was made possible by NPRP grant # [X033-2-007] from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

[14]

W. Wu, Y. He and F. Blaabjerg, "A new design method for the passive damped LCL-and LLCL-filter based single-phase grid-tied inverter," IEEE Trans. Ind. Electron, vol. 60, no. 10, p. 4339–4350, 2013. F. Bradaschia et al., "Modulation for Three-Phase Transformerless ZSource Inverter to Reduce Leakage Currents in Photovoltaic Systems", IEEE Trans. Ind. Electron., vol. 58, no. 12, pp. 5385-5395, 2011. M. Cavalcanti et al., "Modulation Techniques to Eliminate Leakage Currents in Transformerless Three-Phase Photovoltaic Systems", IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1360-1368, 2010. T. Kerekes et al., “A new high-efficiency single-phase transformerless PV inverter topology,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 184– 191, Jan. 2011 A. Khan et al., "Dual Active Full Bridge Implementation on Typhoon HIL for G2V and V2G Applications," 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), Belfort, 2017 A. Khan et al., “Review and simulation of leakage Current in transformerless microinverters for PV applications,” Renew. Sustain. Energy Rev., vol. 74, pp. 1240-1256, July 2017 W. Li et al., "Topology Review and Derivation Methodology of SinglePhase Transformerless Photovoltaic Inverters for Leakage Current Suppression," IEEE Trans. Ind. Electron., vol. 62, no. 7, pp. 4537-4551, 2015 T. Kerekes, D. Séra and L. Máthé, "Leakage current measurement in transformerless PV inverters," 2012 13th International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), pp. 887892, Brasov, 2012 "VDE V 0126-1-1," Automatic Disconnection Device between a Generator and the Public Low-Voltage Grid Document 0126003, VDE Verlag, 2006 Power Generation Systems Connected to the Low-Voltage Distribution Network—Technical Minimum Requirements for the Connection to and Parallel Operation With Low-Voltage Distribution Networks, document VDE-AR-N 4105:2011-08, VDE Verband der Elektrotechnik Elektronik Informationstechnik e.V., 2010 A. Khan and F. Blaabjerg, “Novel Shunt-less Filters for Grid-Connected Transformerless Photovoltaic Applications”, IEEE 12th International Conference on Compatibility, Power and Power Engineering (CPEPOWERENG),Qatar, 2018 H. Schmidt, C. Siedle and J. Ketterer. Wechselrichter zum Unwandeln einer elektrischen Gleichspannung in einen Wechselstrom oder eine Wechselspannung, EP Patent 2086 102 A2, 2003 M. Victor et al., Method of converting a direct current voltage from a source of direct current voltage, more specifically from a photovoltaic source of direct current voltage, into a alternating current voltage. US Patent 7411802, 2008 B. Yang et al., "Improved Transformerless Inverter With Common-Mode Leakage Current Elimination for a Photovoltaic Grid-Connected Power System," IEEE Trans. Power Electron., vol. 27, no. 2, pp. 752-762, Feb. 2012


[15] A. Khan et al., "Switchless Power Decoupling and Switchless Leakage Current Elimination in Grid-Tied Inverters," 9th IEEE-GCC Conference and Exhibition (GCCCE), Manama, Bahrain, 2017 [16] T. K. S. Freddy et al., “Modulation technique for single-phase transformerless photovoltaic inverters with reactive power capability,” IEEE Trans. Ind. Electron. vol. 64, no. 9, pp. 6989–6999, 2017 [17] A. Khan et al., “Electrolytic Capacitor-less Dual Buck Inverter with CM and DM Active Resonance Damping Control for Non-Isolated GridConnected PV Applications," IEEE 12th International Conference on Compatibility, Power and Power Engineering (CPE-POWERENG), 2018 [18] A. Khan and F. Blaabjerg, “Modified Transformerless Dual Buck Inverter with Improved Lifetime for PV Applications," 2018 IEEE International Reliability Physics Symposium, California, Burlingame, 2018 [19] Z. Ahmad and S.N. Singh, "Single phase transformerless inverter topology with reduced leakage current for grid connected photovoltaic system," Electr. Pow. Syst. Res., vol. 154, pp. 193-203, Jan. 2018 [20] Z. Ahmad and S.N. Singh, “An improved single phase transformerless inverter topology for grid connected PV system with reduce leakage current and reactive power capability,” Sol. Energy, vol. 157, pp. 133146, 2017 [21] M. Islam and S. Mekhilef, "A new high efficient transformerless inverter for single phase grid-tied photovoltaic system with reactive power control," 2015 IEEE Applied Power Electronics Conference and Exposition (APEC) pp. 1666-1671, Charlotte, NC, 2015 [22] J. R. Dreher et al., "Comparison of H-bridge single-phase transformerless PV string inverters," 2012 10th IEEE/IAS International Conference on Industry Applications, pp. 1-8, Fortaleza, 2012  [23] A. Khan, A. Gastli and L. Ben-Brahim, “Modeling and Control for New LLCL Filter Based Grid-Tied PV Inverters with Active Power Decoupling and Active Resonance Damping Capabilities,” Electr. Pow. Syst. Res., vol. 155, pp. 307-319, Feb. 2018 [24] D. Karschny, "Wechselrichter", Apr. 1998. [25] J. M. Shen, H. L. Jou and J. C. Wu, "Novel transformerless grid-connected power converter with negative grounding for photovoltaic generation system", IEEE Trans. Power Electron., vol. 27, no. 4, pp. 1818-1829, Apr. 2012. [26] H. Patel and V. Agarwal, "A single-stage single-phase transformer-less doubly grounded grid-connected PV interface", IEEE Trans. Energy Convers., vol. 24, no. 1, pp. 93-101, Mar. 2009. [27] V. Gautam, A. Kumar and P. Sensarma, "A novel single stage transformerless PV inverter", Proc. IEEE Int. Ind. Tech. Conf., pp. 907912, 2014. [28] D. Schekulin, "Transformerless ac. inverter circuit for coupling photovoltaic systems or wind generator systems esp. in the low power range to current networks", Mar. 1999. [29] M. Rajeev and V. Agarwal, "Novel transformer-less inverter topology for single-phase grid connected photovoltaic system", Proc. 42nd IEEE Int. Photovolt. Spec. Conf., pp. 1-5, 2015. [30] P. Chamarthi, M. Rajeev and V. Agarwal, "A novel single stage zero leakage current transformer-less inverter for grid connected PV systems", Proc. 42nd IEEE Int. Photovolt. Spec. Conf., pp. 1-5, 2015. [31] J. C. Wu and C. W. Chou, "A solar power generation system with a sevenlevel inverter", IEEE Trans. Power Electron., vol. 29, no. 7, pp. 34543462, Jul. 2014. [32] D. Debnath and K. Chatterjee, "Neutral point clamped transformerless grid connected inverter having voltage buck-boost capability for solar photovoltaic systems", IET Power Electron., vol. 9, no. 2, pp. 385-392, 2016. [33] Y. Tang, X. Dong and Y. He, "Active Buck-Boost inverter", IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 4691-4697, Sep. 2014. [34] H. Hu et al., "A single-stage microinverter without using eletrolytic capacitors", IEEE Trans. Power Electron., vol. 28, no. 6, pp. 2677-2687, Jun. 2013. [35] A. Abramovitz, B. Zhao and K. M. Smedley, "High-gain single-stage boosting inverter for photovoltaic applications", IEEE Trans. Power Electron., vol. 31, no. 5, pp. 3550-3558, May 2016. [36] D. Meneses, et al., "Grid-connected forward microinverter with primaryparallel secondary-series transformer", IEEE Trans. Power Electron., vol. 30, no. 9, pp. 4819-4830, Sep. 2015. [37] N. Vázquez et al., "A New Common-Mode Transformerless Photovoltaic Inverter," IEEE Trans. Ind. Electron., vol. 62, no. 10, pp. 6381-6391, Oct. 2015. [38] M. Tofigh Azary, et al., "Modified Single-Phase Single-Stage Grid-Tied Flying Inductor Inverter With MPPT and Suppressed Leakage Current," IEEE Trans. Ind. Electron., vol. 65, no. 1, pp. 221-231, Jan. 2018.

[39] V. Gautam and P. Sensarma, "Design of Ćuk-Derived Transformerless Common-Grounded PV Microinverter in CCM," IEEE Trans. Ind. Electron., vol. 64, no. 8, pp. 6245-6254, Aug. 2017. [40] Y. P. Siwakoti and F. Blaabjerg, "Common-Ground-Type Transformerless Inverters for Single-Phase Solar Photovoltaic Systems," IEEE Trans. Ind. Electron., vol. 65, no. 3, pp. 2100-2111, March 2018. [41] Y. P. Siwakoti and F. Blaabjerg, "H-Bridge transformerless inverter with common ground for single-phase solar-photovoltaic system," 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), Tampa, FL, 2017, pp. 2610-2614. [42] D. Dong et al., “Leakage current reduction in a single-phase bidirectional AC-DC full-bridge inverter,” IEEE Trans. Power Electron. vol. 27, no. 10, pp. 4281-4291, 2012 [43] Y. Tang et al., "Transformerless photovoltaic inverters with leakage current and pulsating power elimination," 2015 9th International Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia), Seoul, 2015 [44] Y. Tang et al., "Highly Reliable Transformerless Photovoltaic Inverters With Leakage Current and Pulsating Power Elimination," IEEE Trans. Ind. Electron, vol. 63, no. 2, pp. 1016-1026, Feb. 2016 [45] Ó. López et al., "Eliminating Ground Current in a Transformerless Photovoltaic Application," IEEE Trans. Energy Convers., vol. 25, no. 1, pp. 140-147, Mar. 2010 [46] X. Guo et al., “Single-carrier modulation for neutral-point-clamped inverters in three-phase transformerless photovoltaic systems”. IEEE Trans. Power Electron.,vol. 28 no. 6, pp. 2635–7. 2013 [47] W. Wu et al., “A modified LLCL filter with the reduced conducted EMI noise,” IEEE Trans. Power Electron., vol. 29, no. 7, pp. 3393–3402, 2014 [48] W. Wu et al., “A new LCL-filter within-series parallel resonant circuit for single-phase grid-tied inverter,” IEEE Trans. Ind. Electron., vol 61, no. 9, pp. 4640–4644, 2014 [49] A. Adib et al., "On Stability of Voltage Source Inverters in Weak Grids," IEEE Access, vol. 6, pp. 4427-4439, 2018 [50] A. Etxegarai et al., “Review of grid connection requirements for generation assets in weak power grids,” Renew. Sustain. Energy Rev.,vol. 41, pp. 1501-1514, 2015 [51] E. N. Chaves et al.,“Design of an Internal Model Control strategy for single-phase grid-connected PWM inverters and its performance analysis with a non-linear local load and weak grid,” ISA Trans., vol. 64, pp. 373383, 2016 [52] J. Khazaei et al.,“Review of HVDC control in weak AC grids,” Electr. Pow. Syst. Res., vol. 162, pp. 194-206, Sept. 2018 [53] M. Büyük et al., “Topologies, generalized designs, passive and active damping methods of switching ripple filters for voltage source inverter: A comprehensive review,” Renew. Sustain. Energy Rev., vol. 62, pp. 46-69, 2016 [54] C. Camilo et al., “Damping techniques for grid-connected voltage source converters based on LCL filter: An overview,” Renew. Sustain. Energy Rev., vol. 81, Part 1, pp. 116-135, 2018 [55] W. Wu et al., "Damping Methods for Resonances Caused by LCL-FilterBased Current-Controlled Grid-Tied Power Inverters: An Overview," IEEE Trans. Ind. Electron, vol. 64, no. 9, pp. 7402-7413, Sept. 2017 [56] M. H. Mahlooji, H. R. Mohammadi, M. Rahimi, A review on modeling and control of grid-connected photovoltaic inverters with LCL filter, Renew. and Sustain. Energy Rev., vol. 81, Part 1, pp. 563-578, 2018 [57] R. N. Beres et al., "A Review of Passive Power Filters for Three-Phase Grid-Connected Voltage-Source Converters," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 1, pp. 54-69, March 2016 [58] W. Yao et al., "A unified active damping control for single-phase differential mode buck inverter with LCL-filter," 2015 IEEE 6th International Symposium on Power Electronics for Distributed Generation Generation Systems (PEDG), Aachen, 2015 [59] W. Yao et al., "Improved Power Decoupling Scheme for a Single-Phase Grid-Connected Differential Inverter With Realistic Mismatch in Storage Capacitances," IEEE Trans. Power Electron., vol. 32, no. 1, pp. 186-199, Jan. 2017 [60] J. Wang et al., "Delay-Dependent Stability of Single-Loop Controlled Grid-Connected Inverters with LCL Filters," IEEE Trans. on Power Electron., vol. 31, no. 1, pp. 743-757, Jan. 2016