Novel 1-$\varphi$ High-Voltage Boosting Transformerless Inverter Topology With Optimal Power Components and Negligible Leakage Currents

Inverter topologies for integrating a rooftop photovoltaic (PV) unit into a microgrid are becoming increasingly complex. This paper proposes a high-voltage boosting transformerless inverter (HVBTI) topology for enhancing such applications. The coupled inductor-based high voltage gain feature of the HVBTI configuration allows power to be delivered into the grid from a lower voltage PV source without using higher duties. In addition, HVBTI suppresses leakage current as the common connection shared between the <inline-formula><tex-math notation="LaTeX">$-ve$</tex-math></inline-formula> terminal of the PV source and the grid neutral point. In comparison to existing topologies, the HVBTI topology uses a compact pulse width modulation strategy to control only six controllable switching devices. Again, using lower-rated switching devices is more cost-effective while increasing reliability and efficiency. In a laboratory prototype of a 1 kVA grid integrated system, the proposed HVBTI configuration is validated, and the maximum efficiency of the HVBTI is estimated at approximately 95<inline-formula><tex-math notation="LaTeX">$\%$</tex-math></inline-formula>.


I. INTRODUCTION
D UE to the rapidly rising demand for power in recent years, renewable energy sources (RES) have gained immense recognition in the electricity market [1], [2], [3].In fact, solar photovoltaic (PV) systems, wind power generation systems, hybrid energy storage systems (HESS) and fuel cell systems are viewed as the primary RES.The PV system is considered to be the most effective among the RES because it requires less upkeep and has a lower system cost [4], [5].Solar PV power is fed into the AC grid and loads via DC-AC converters.In most cases, a low frequency (i.e., 50/60 Hz) transformer is used to provide galvanic isolation between the PV-fed DC-AC converter and the power grid [6].However, the use of low-frequency transformers leads to an increase in the size of the system and also to a reduction in efficiency [7].To overcome these problems, several researchers have developed transformerless inverter topologies for PV applications [8], [9], [10].To comply with IEEE standards, these transformerless inverter topologies attempted to suppress/eliminate parasitic/leakage currents and DC offset current injections into the power grid.A parasitic capacitance is typically formed between the frame of the PV module and the PV cells, as shown in Fig. 1.During the operation of the inverter, the voltage of this parasitic capacitance changes, creating the current through the parasitic capacitance.Such leakage current flows through the PV panel, the inverter, and the power grid.Consequently, it increases conduction losses in power switches and distorts the grid current [8].This leads to a decrease in PV system performance as well as issues concerning electromagnetic interference (EMI), electromagnetic compatibility (EMC), and protection of switching devices [11].
Z-source inverter-based topology mentioned in [6] can increase the output voltage of the inverter in a two-stage configuration, which cannot effectively suppress parasitic currents.Many two-stage transformerless inverter topologies, such as H5 [5], [9], H6 [7], [9], [12], [13], [14] and HERIC [9], have been introduced in the literature to suppress parasitic currents.However, the H5 inverter cannot supply reactive power, the H6 inverters have higher control complexities, and HERIC inverters add an additional filter that increases the size of the system.In [10] and [15], transformerless inverter topologies are introduced to suppress the leakage currents completely.In this inverter topology, the −ve terminal of PV is shorted to neutral of the power grid, effectively suppressing parasitic currents.The key drawback of these inverter configurations is that they require many power components such as switches, diodes, inductors and capacitors.High duty ratios are required for power transfer with low voltage PV modules (24 V to 48 V), resulting in increased power loss and deteriorated efficiency.To overcome such challenges, inverter topologies in [11], [16], [17] can provide a high gain in output voltage for suitability to the low voltage PV module and suppress the leakage/parasitic currents effectively.A flying capacitor-based voltage boosting transformerless inverter topology in [11] boosts its output voltage twice the input voltage, with an issue of DC offset current injection into the power grid due to asymmetry in the operation of the inverter.In [16], a charge pump circuit based transformerless inverter is introduced to suppress the leakage currents.However, it cannot provide a high gain in the output voltage and also suffers from high current ripple at the input due to the absence of the input inductor.A single-stage transformerless inverter based on the switched inductor principle is introduced in [17], where the output voltage gain increases with an increase in the turns ratio of the coupled inductor.Due to the increased number of power components, this inverter has a higher complexity of implementation and control, resulting in a lower overall power density and lower efficiency.Some literature claims that leakage currents can be completely eliminated [18], [19], [20].To support this concept, the DC-DC and DC-AC stages need to be cascaded together [1].The DC-DC converter steps up the low voltage PV output, while the DC-AC inverter stage corresponds to the bipolar output voltages with high-gain DC input.During DC-DC step-up conversion in [18], only one inductor is required to generate the high-gain voltage required by the inverter.However, this converter requires more switches with a higher level of complexity control that increases implementation costs and power consumption.DC-DC step-up converters in [19], [20] use only one switch to generate bipolar output voltages, reducing power device losses.The step-up converter in [19] provides bipolar outputs by using the combination of SEPIC and Cuk converters.The coupling coefficient of the coupled inductor used here is optimized to reduce the ripple in the input current.By choosing the optimal value of the coupling coefficient, the size and cost of the coupled inductor can be effectively reduced, which optimizes the overall system.However, the topology in [19] limits the gain in the output voltage to twice of the input voltage.In the step-up topology in [20], an inductor is coupled at the input, causing a large ripple in the input current, increasing conduction losses in the power components, and reducing the efficiency and lifespan of the inverter.
Fig. 2 shows the category of transformerless inverters which can provide high gain in the output voltage and supply reactive power to the power grid.However, these transformerless inverters utilize a large number of power switches.More switches involve a complicated switch control method and increase the requirement of driver circuits.From the aforementioned discussions, it can be understood that there is a necessity to introduce output voltage boosting inverter topology for PV applications with better reliability, reduced current ripple, minimized leakage current, and lower control complexity.Originally, the proposed high-voltage boosting transformerless inverter (HVBTI) topology is introduced in [21] with limited analysis and investigation.However, this article contributes the following with detailed analysis, discussions, and additional experimental validation results.
r By reducing the number of power components, the pro- posed HVBTI configuration can offer high output voltage gain and suppress parasitic currents effectively, thereby reducing system losses and improving the efficiency.
r The HVBTI is investigated with a view to finding a suitable mode of operation for switch control using a pulse width modulation scheme.As a result of lower average total power rating (TPR) of power devices, the proposed HVBTI is able to further enhance the efficiency of the system.r Compared to existing transformerless inverter topologies, the proposed HVBTI provides a high gain in the output voltage and reactive power support with a smaller TPR.This article is structured as follows.The inverter topology and its operating modes are presented in Section II.The design of all power components is given in Section III, along with developed modulation technique and current control techniques of the proposed HVBTI.Experimental verification of the proposed topology is detailed in Section IV.Critical conclusions drawn from the HVBTI configuration are presented in Section VI.

II. PROPOSED HVBTI FOR GRID INTERCONNECTION
This section describes the proposed HVBTI configuration and its operating modes in a detailed manner.

A. Configuration of HVBTI
The proposed HVBTI topology shown in Fig. 3 consists of six power switches (S 1 , S 1 , S 2 , S 2 , S 3 , S 3 ), two power diodes (D 1 , D 2 ), two auxiliary DC capacitors (C 1 , C 2 ) and one coupled  inductor.HVBTI supplies power to the utility grid through a grid inductor (L g ).The coupled inductor has primary winding and secondary windings with inductance (L 1 , L 2 ) and number of turns (n 1 , n 2 ), respectively.It is employed to boost the output voltage of the inverter by adjusting its turns ratio (n), which can be expressed as (1). ( Using the coupled inductor, it is possible to feed power into the power grid from the low voltage PV module through the proposed HVBTI.Through the proposed pulse width modulation (PWM) technique, only three switching pulses for switches {S 1 , S 2 , S 3 } can be generated.The switching pulse for switches {S 1 , S 2 , S 3 } can be produced by complementing the switching pulses {S 1 , S 2 , S 3 }.The PWM strategy for generating switching pulses is presented in Fig. 4 and the pulse patterns of each switching pulse are illustrated in Fig. 5.

B. Working Modes of HVBTI
The working of the proposed high-gain 1-φ HVBTI topology has six important modes of operation (mode-1 to 6) considering continuous conduction mode (CCM) and discontinuous conduction mode (DCM) of operation, as shown in Fig. 6.Switching states at different modes is clearly mentioned in Table I.A thorough analysis for each mode of operation is discussed by referencing the steady-state waveforms presented in Fig. 7.The modes {1, 2, 3} discuss the working of HVBTI topology in +ve half cycle of the grid voltage (v g ), whereas modes {4, 5, 6} discuss the working of the proposed topology in -ve half cycle of v g .
1) Mode-1: This mode helps in powering the grid in the +ve half-cycle while switches {S 1 , S 2 , S 3 } are ON.The coupled

TABLE I OPERATING MODES OF HVBTI TOPOLOGY
inductor stores energy in its primary winding from the input PV source through a switch S 1 .In this mode, the energy stored in auxiliary capacitors C 1 and C 2 is also supplied to utility through switches {S 2 , S 3 }.The current path for such activities in mode-1 can be interpreted through Fig. 6(a).This mode operates in between time 0-t 1 , as shown in Fig. 7(a), which can be used to deduce the expressions for the voltage across L 1 (v l 1 ), voltage across L 2 (v l 2 ), and the voltage across grid inductor (v l g ), as given in (2).
where i l 1 and i g represent the current through the inductors L 1 and L g , respectively.v c 1 and v c 2 are defined as voltages across the auxiliary capacitors C 1 and C 2 , respectively.v pv and v g indicate the instantaneous input PV voltage and grid voltage, respectively.
2) Mode-2 (i l 1 >0): This mode can be observed in between time t 1 − t 2 , as shown in Fig. 7(a).The voltage across L 1 , L 2 and L g for this mode can be derived as (3).
The freewheeling of stored energy in the inductors (L 1 , L g ) happens in this mode during the +ve half cycle of v g .The  energy stored in the coupled inductor is transferred to auxiliary capacitors C 1 , C 2 through its primary and secondary windings, respectively.The primary winding of the coupled inductor charges the C 1 through switches S 1 , S 2 and diode D 1 .Similarly, the secondary winding releases the energy to the capacitor C 2 through the diode D 2 .The stored energy in L g freewheels through S 2 , S 3 , and the grid.Fig. 6(b) depicts such currents path for mode-2.
3) Mode-3 (i l 1 =0): In this mode, the switches {S 1 , S 2 , S 3 } are switched ON during the time t 2 − T sw , as shown in Fig. 7(a).Again, the voltage across L 1 , L 2 and L g for this mode can be derived as (4).
The energy stored in the coupled inductor is completely transferred to the auxiliary capacitors C 1 and C 2 during this period.Thus, the currents in the coupled inductor gradually fall to zero and i g still continue to flow through {S 2 , S 3 }, as shown in Fig. 6(c).

4) Mode-4:
This mode-4 is observed during time 0-t 1 , as shown in Fig. 7(b).In mode-4, switches {S 1 , S 2 , S 3 } of the proposed HVBTI are in conduction mode and help in powering the grid in the -ve half cycle of v g .The coupled inductor stores its energy in the primary winding from v pv through S 1 , and the auxiliary capacitors C 1 and C 2 supply power to the grid through {S 2 , S 3 }.Fig. 5(d) depicts the current path for mode-4 and its voltage relation is similar to (2).
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5) Mode-5 (i l 1 >0):
As shown in Fig. 7(b), mode-5 operates from time t 1 − t 2 and its voltage relations are similar to (3).The energy stored in L 1 and L g freewheel in this mode, corresponding to the −ve half cycle of v g .The energy stored in the coupled inductor is fed to auxiliary capacitors C 1 , C 2 through primary and secondary windings.The energy stored in the primary winding charges the C 1 through switches {S 1 , S 2 } and diodes D 1 .Similarly, the secondary winding charges the capacitor C 2 through the diode D 2 .The stored energy in L g freewheels through S 2 , S 3 , and the grid.Fig. 6(e) depicts the current path for mode-5.
6) Mode-6 (i l 1 =0): During this mode (time t 2 − T sw in Fig. 7(b)), the current in L g freewheels through the switches {S 2 , S 3 }.At the same time, the coupled inductor transfers its stored energy completely to the capacitors C 1 and C 2 and its voltage relations can be found in (4).Thus, the coupled inductor current slowly reaches to zero and the corresponding current path is shown in Fig. 6(f).

C. Working Modes in NPA
The working modes correspond to the negative power area (NPA) are shown in Fig. 8.During +ve half cycle of v g and -ve value of instantaneous grid current (i g ), the switches {S 1 , S 2 , S 3 } are ON, as shown in Fig. 8(a).In this state, the coupled inductor stores energy from the input PV source and the current in i g freewheels through switches S 2 , S 3 and capacitors (C 1 , C 2 ).The current conduction paths for this state are indicated in Fig. 8(a) (red dotted lines).When the switches {S 1 , S 2 , S 3 } are ON, the stored energy in the coupled inductor and grid inductor (L g ) is transferred to the capacitors C 1 and C 2 as depicted in Fig. 8(a) (blue dotted lines).Fig. 8(b) shows the current conduction paths for the −ve half cycle of v g during the +ve value of i g .In this state, the switches {S 1 , S 2 , S 3 } are ON and the coupled inductor stores energy from the input PV source.The current through i g (red dotted lines) freewheels via capacitors C 1 , C 2 , S 2 , and S 3 .There is possibility of another state, where the switches {S 1 , S 2 , S 3 } are turned ON and the stored energy in the coupled inductor transferred to capacitors C 1 , C 2 .During this state, inductor current i g (blue dotted lines) freewheels through switches S 2 , and S 3 .Thus, the proposed grid connected HVBTI topology can send or receive reactive power while maintaining the grid power quality.Therefore, the HVBTI topology can meet the requirements of Volt-VAr standards (i.e.IEEE 1547-2018).

D. Voltage Across Auxiliary Capacitors
The input PV source voltage (v pv ), the primary winding of the coupled inductor L 1 , power switches (S 1 , S 1 , S 2 ) and capacitor (C 1 ) forms a conventional boost converter.From such part of circuit, the expression for the voltage across the capacitor C 1 (v c 1 ) can be deduced as (5).
where m i is the modulation ratio of the HVBTI during CCM.The higher voltage across the auxiliary capacitor C 2 (v c 2 ) can be obtained as ( 6) by properly selecting the turns ratio (n) of the multi-winding inductor.
The expression of the RMS value of the HVBTI output voltage (V o ) can be expressed as (7).
By solving ( 5)-( 7), the expression for the gain (k p,ccm ) in the output voltage that corresponds to the CCM of the HVBTI configuration can be obtained as (8).
As seen from Fig. 6(c) and (f), the coupled inductor current (i l 1 ) reaches zero at t = t 2 , whereas the grid inductor current (i g ) does not reach zero before the end of the switching cycle (T sw ).From this understanding, another duty cycle m d can be defined for which i l 1 becomes zero.As shown in Fig. 7, the voltage across inductors (v l 1 , v l 2 and v l g ) correspond to DCM can be expressed as ( 9)- (11).(10) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
By applying the volt-second balance technique for the voltage across inductors L 1 and L 2 , the expression for the voltage across capacitors v c 1 and v c 2 can be expressed as (12).
By solving ( 8)-( 12), the expressions for the RMS value of the output voltage (v o,dcm ) for DCM can be demonstrated as (13).
The gain (k p,dcm ) in output voltage corresponding to DCM of the HVBTI configuration can be obtained as (14).
It is clear from (8) and ( 14) that the overall gain (k p ) of HVBTI can be formulated as (15).
Fig. 9 shows the variation of gain in output voltage with respect to the modulation ratio for various turns ratio (i.e.n = 1, 2 and 3).Furthermore, it can be observed that the gain in the output voltage of HVBTI increases with an increase in the turns ratio.The detailed study of the output voltage gain and its effect due to sensitivity is studied in Section IV.

III. PARAMETER DESIGN AND CONTROL OF GRID CONNECTED HVBTI
The design of the multi-winding inductor, grid inductor, capacitors and power components (switches and diodes) of the HVBTI topology are discussed in this section.Additionally, control of grid connected HVBTI is discussed at the end of this section.

A. Coupled Inductor and Grid-Side Inductor Design
Consider L m be the mutual inductance of the coupled winding inductance.The design value of the coupled winding inductance needs to be calculated based on the critical value of the mutual inductance, i.e.L mc , which can be estimated as (16).
where v pv is the voltage across PV source, P o is the RMS output power and f sw is the switching frequency of HVBTI.The proposed HVBTI operates in discontinuous conduction mode (DCM) if the mutual inductance is less than its critical value, i.e., L m < L mc .The inductances of the primary winding (L 1 ) and secondary windings (L 2 ) of the coupled inductor are calculated by using its turns ratio (n = n 1 /n 2 ) and can be derived as (17).
The grid inductor (L g ) of the proposed grid-connected HVBTI is designed as (18).
where v g is the grid voltage, Δi g is the required grid current ripple and T sw (=1/f sw ) is the switching time period.

B. Design of the Auxiliary Capacitors C 1 and C 2
The operating modes of the inverter decide the charging and discharging of the capacitors connected to it.The rate of change in capacitor charge can be estimated with the help of (21).
where Δq c is the change in charge, C is the value of the required capacitance, Δv c is the change in the ripple voltage, T s is the charging and discharging time of the capacitor and i c is the average current flowing through the capacitor.It means that the AC power output of the inverter (P o ) and the ripple voltage of the capacitor decide the value of the capacitor.Considering Δv c = ≈5%, the required capacitance can be estimated as (20).
where f s (=1/T s ) is the inverter output frequency, i.e., grid frequency.To get balance level (+ve and −ve) of the output voltage, the capacitance C 1 and C 2 need to be equally distributed, i.e.,

C. Design of Power Devices Rating
In a switching cycle, the average current flowing through the power switches and diodes can be determined as (21).
where I g is the RMS value of the grid current i g .Similarly, the average voltages between power switches and diodes during the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
OFF state in a switching cycle can be derived as (22).
Now, the total current rating (TCR) and total voltage rating (TVR) of the power switches corresponding to the positive half (PH) of the grid voltage are given as ( 23)− (24).
Similarly, TCR and TVR of the power switches during the negative half-cycles (NH) of the grid voltage can be derived as ( 25)- (26).
In order to achieve the best design of the proposed HVBTI, the TCR and TVR of the switching devices should be minimized to withstand the maximum load power.With x the number of operating power devices, the total average power rating (TPR) of a converter switch can be expressed as (27).
where V s,j and I s,j are the average voltage and current of the power switches in one switching cycle T sw corresponding to the switch j.Now, the total average power rating of a switch in the proposed HVBTI can be derived as (28).
TPR can be utilized to establish a relationship for the power limit of the proposed HVBTI, which is elaborately discussed in Section IV-C.

D. Duty Cycles During CCM and DCM Operation
The proposed HVBTI is capable of operating in both CCM and DCM.The duty cycles for the CCM and DCM operations can be calculated considering the variability in the magnitudes of v pv and v g .These variations are time-dependent; thus, impacting the transition between the CCM and DCM operations.The expression for the duty cycle (m i ) in CCM operation can be formulated as (29).
The ripple in the inductor L 1 (Δi l 1 ) current controls the transition from CCM to DCM operation.Δi l 1 during CCM (Δi l 1 ,ccm ) can be expressed as (30).
During DCM operation, the average current in inductor L 1 (i l 1 ,dcm ) can be given as (31).
Now, the duty cycle (m d ) for the DCM operation can be obtained as (32).
where T sw (=1/f sw ) denotes switching period.A transition between CCM and DCM occurs below the critical values corresponding to the converter switching frequency f sw , the primary inductance L 1 , and the magnitude of the grid current i g .DCM operation may result in over-boosting the output voltage of the inverter, which needs to be considered when determining TVR, TCR, and TPR of the power devices and components of HVBTI.
It is therefore always preferable to operate in the CCM rather than in the DCM.Either limiting the double line frequency component or employing a variable duty cycle scheme can be used to narrow the DCM operation boundary [22].

E. Control of HVBTI During Grid Interconnection
The small signal analysis and state space averaging techniques are used to linearize the proposed grid integrated HVBTI.In order to design a suitable controller and obtain a desired steady state and transient responses, this linearized model will be used for the current control technique (mentioned in [21]) and is implemented as per Fig. 10 to control the grid current supplied by the proposed HVBTI topology.Such control methodology with maximum power point algorithm (MPPT) (detailed in [16]) is capable of tracking the maximum available PV power (P max pv ), which is further fed to the grid.
1) Modelling of Grid Connected HVBTI: As depicted in Fig. 7, the state variables of the state-space model are defined by the inductor currents (i l 1 , i g ) and the capacitor voltages (v c 1 , v c 2 ).For the purpose of streamlining the modeling process, ideal inductors and capacitors (L 1 , L g , C 1 and C 2 ) are considered with zero initial conditions.Additionally, the time intervals m i T sw (when switch S 1 is ON) and m d T sw (when switch S 1 is OFF) are utilized for the different modes of operation during the positive half cycle of the grid in the state space modeling.Given the symmetrical nature of HVBTI's operation, only modes corresponding to either the positive or negative half cycle of the grid are considered.With these considerations, the averaged state space model for the grid-connected HVBTI topology can be derived as Perturbations were implemented in both the duty cycles and the state variables to obtain the corresponding transfer function, as detailed below.
where perturbations and DC quantities for the state variables are denoted by using ĩl 1 , ĩg , ṽc 1 , ṽc 2 , mi , md and I l 1 , I g , V c 1 , V c 2 , M i , M d , respectively.To derive the transfer function for the grid current control, the perturbations in the input PV voltages are ignored.By ignoring the second order components, The linearized model of the grid connected HVBTI is derived as By utilizing the relations from Fig. 7, i.e., the voltage across inductors (v l 1 , v lg from ( 9)-( 11)) and current across capacitors (i r With the input inductor current reset in each switching period, a soft switching state is facilitated for the input switch (S 1 ), thereby reducing the switching losses.

2) Control Methodology of Grid Connected HVBTI:
The following methodology is provided to implement a control technique for HVBTI.
Step 1: Measure v pv and i pv and feed to the MPPT control block in PV control module.
Step 2: Compare v pv with the output voltage of MPPT block (v mpp ) and then regulate such error with a proportional-integral controller (K p,dc =0.3, K i,dc =250) to formulate the estimated grid current ( îg ).Simultaneously, use an efficient phase-lockedloop method [23] to generate the grid angular frequency ω g , grid phase θ g and sin θ g .Step 3: Obtain the reference grid current (i * g ), i.e., i * g = îg sin θ g and further compare with the measured actual grid current i g .
Step 4: Feed the error signal e g (i.e., e g = i * g − i g ) to a proportional resonant (PR) controller to produce the reference modulating waveform v m sin(ω g t).The transfer function (G P R (s)) of such PR controller can be defined as (37) [24].
where k pr , k rr and ω cr are the proportional gain, resonant gain and resonant frequency of the PR controller.The PR control scheme is adopted here to address the resonance and improve the offset error (up to 0.1%) in steady-state compensation during the reactive power support during grid interconnection [25].To reduce the steady state error, the PR controller delivers high gain at grid frequency (i.e.50 Hz).
Step 5: Utilize V m sin(ωt) further to produce the switching pulses for all the switches (S 1 -S 3 and S 1 -S 3 ) of the HVBTI with the help of developed modulation strategies in Fig. 4.
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A. Prototype Description
The practicality of the proposed HVBTI is verified through an experimental laboratory prototype of 1 kVA PV fed grid connected system.The details of the experimental setup of the proposed grid connected HVBTI topology are given in Table II.

B. Experimental Validation
The experimental results of the PV grid connected HVBTI is shown in Fig. 11(a).Such performances are observed at unity power factor (UPF) for active power reference (P * o ) and reactive power reference (Q * o ) of 1000 W and 0 VAr, respectively.In this scenario, the PV source is operating at maximum power point (mpp) while feeding it's maximum available power (i.e.1000 W) to the grid.It can be observed from Fig. 11(a) that the PV voltage and the grid current are 60 V and 9 A (rms), respectively.In order to check the reactive power capability of HVBTI, the experiments are performed corresponding leading and lagging power factors.The experimental waveforms for the lagging and leading power factors corresponding to the power references of P * o = 800 W and Q * o = ±600 VAr are shown in Fig. 11(b) and (c), respectively.It can be observed from Fig. 11 that the proposed HVBTI feeds greater quality of current into the grid with % THDs of 3.1 %, 2.85 % and 2.9 %, respectively.
As shown in Fig. 12, the dynamic response of the HVBTI is tested experimentally in order to check the transient performance   change in power reference from 0 W to 500 W and 500 W to 1000 W, respectively.Again, Fig. 13(c) and (d) show the experimental results for the variation of input PV voltage from 50 V to 65 V and 50 V to 90 V, respectively.It can be concluded from Fig. 13 that grid current has a good transient response during variation in PV voltage and has a negligible effect on grid current waveform.
The experimental results corresponding to the PV fed HVBTI topology when the grid voltage is varied from 0.9 to 1.1 pu are shown in Fig. 14.To meet the requirements of Volt-VAr setting as per IEEE 1547-2018 standard, the HVBTI topology sends the reactive power whenever the grid voltage is decreased or receives the reactive power whenever the grid voltage is increased (i.e.45% of rated power of the HVBTI).As shown in Fig. 14(a), the HVBTI absorbs reactive power of 400 VAr from the grid whenever the grid voltage is increased to 1.1 pu.Fig. 14(b) confirms that the HVBTI sends reactive power of 400 VAr to the grid whenever the grid voltage is decreased to 0.9 pu.From Fig. 14(a) and (b), it can also be observed that the PV source is operating at it's mpp voltage (i.e. 60 V) whenever the grid voltage is increased or decreased by 1 ± 0.1 pu.

C. Detailed Performance Analysis
The zoomed view of grid current waveform at unity power factor is illustrated in Fig. 15.It can be observed that the grid current has a smooth transition from +ve to -ve half cycle and vice versa.The % THD in grid current is achieved below 5 % and the measured % THD in injected grid current is limited to 3 %.The zoomed view of grid currents and instantaneous power waveforms for power factors of 0.8 lagging and 0.8 leading are  shown in Fig. 16(a) and (b), respectively.It can be observed from Fig. 16 that the grid current does not suffer from distortions at zero crossing transitions and also in the NPA areas.Hence, the harmonic components in the grid current are maintained within the IEEE 1547-2018 standards.
The parasitic leakage currents (i cp and i cn ) measured at both the terminals (+ve and -ve) of the PV are shown in Fig. 17(a).As expected, the leakage currents of the proposed HVBTI is observed with near to zero value (i.e., <2 mA).This is because the negative terminal of the PV source is directly connected to the neutral point of the 1-φ grid, as shown in Fig. 3.According to the German DIN VDE0126-01 standard, IEC-62109-2 standard and IEEE Std 2030.1.1-2021,the leakage currents must be below 300 mA, 10 mA and 12.5 mA, respectively, above which PV inverters are not allowed to connect to the utility grid.From the above discussions, it can be concluded that the proposed HVBTI topology successfully suppress/eliminate the leakage currents while providing high gain at the output voltage and Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE III HVBTI CONFIGURATION COMPARED WITH OTHER HIGH VOLTAGE GAIN TRANSFORMERLESS INVERTER CONFIGURATIONS
feeding nice quality of current into the utility grid.The results in Fig. 17(a) are based on a proposed HVBTI at a temperature of 25 • C and a solar insolation of 1000 W/m 2 .Whenever the PV panel's utilization factor decreases, the conventional inverter's boosting feature extracts a discontinuous current, making it incompatible with the MPPT strategy described in [16].However, the proposed HVBTI has the capability of operating at both CCM/DCM, resulting in the PV operation always being in MPPT mode.Based on the capacitor voltage v c 1 shown, it appears that MPPT control is being used to maintain the MPP voltage (v mpp ), which is significantly affected by variations in irradiance as opposed to temperature variations.Across a broad range of insolations (say, 100%-10%), duty ratios may vary (say, 34%-20%), which can differ between CCM and DCM operation for the proposed HVBTI.In order to provide a deeper understanding of the proposed HVBTI topology, this article does not include a detailed study of MPPT performance.The PV current waveform in Fig. 17(a) exhibits significant ripple due to the HVBTI's primary side inductor L 1 operating in DCM, which affects the MPPT operation.This condition also causes increased conduction losses as the current in L 1 passes through several switches and diodes, although this is somewhat offset by using soft switching in S 1 to reduce switching losses.To address this and enhance MPPT efficiency, a high-value capacitor across the PV source is added to smooth the current and reduce ripple.Notably, the transition between CCM and DCM hinges on the converter switching frequency, the primary inductance, and the grid current magnitude.While DCM can lead to over-boosting the inverter's output voltage and reducing the PV current, this can be mitigated by limiting the double line frequency component or employing a variable duty cycle, thereby improving MPPT operation and reducing input current ripple.Common mode voltage (v cm ) can be measured in between the capacitor midpoint and the neutral point of the 1-φ grid, as shown in Fig. 3.The terminal voltage (v t ) can be observed at the AC-side of the HVBTI.Fig. 17(b) depicts the waveforms of v t and v cm for a time duration of T s .Unusual pattern of v cm and v t are observed during phase angle difference between the v g and i g .Again, it Fig.18.Efficiency (η) curve versus output power.can be observed that there is higher v cm during the −ve half cycle of the grid voltage in comparison to its +ve half cycle.However, it can be seen from Fig. 17(a) that v cm is not impacting the leakage currents i cp and i cn .
As of limitation, the measured efficiency (i.e., ≈95.8% at 400 W for v pv = 90 V for low-power application) performance of the proposed HVBTI topology is competitive in the efficiency range of 88% to 96% compared to the other existing high voltage gain transformerless inverter topologies.In fact, it has the second-best measured efficiency among the other existing transformerless inverter topologies, as shown in Table III.Further, the maximum efficiencies of HVBTI are measured to be ≈95% and ≈95.8% for input voltages of v pv = 50 V and v pv = 90 V, respectively, as shown in Fig. 18.Fig. 19 shows the power loss distribution (P cond : total conduction loss of switches, P sw : total switching losses, P D : conduction losses in diodes, P core : total core losses, P L : total power losses, P C : total losses in capacitors, P driver : losses due to driver board) of the HVBTI at a power rating of 1000 VA.It can be observed from Fig. 19 that the major losses are contributed by the power switches S 1 -S 3 and S 1 -S 3 .Fig. 20 shows the sensitivity study of the HVBTI with a mismatch in the grid inductance (i.e.ΔL g ) and grid current %THD.It can be seen from Fig. 20 that even with the error of ±50% in the value of grid inductance, the HVBTI exhibits Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.satisfactory performance as the same as traditional grid tied PV inverter.

D. Comparative Performance Analysis
The main attributes of the existing high voltage gain transformerless inverter topologies and the proposed HVBTI are given in Table III.The HVBTI topology has a high gain in the output voltage and can provide reactive power support with an optimized number of power devices (i.e.switches and diodes) and power components.The total seven numbers of power devices are used in the proposed HVBTI, while the total power devices count of high gain transformerless inverters in [10], [11], [15], [16], [17], [18], [19], [20], [26], [27], [28], [29], [30] varies from 3∼8, as shown in Table III.However, a limited number of high gain inverters from these topologies support the reactive power as per the IEEE 1547-2018 standards.
The output voltage gain and its sensitivity analysis are presented for the proposed HVBTI and also compared with the existing high gain transformerless inverters, as shown in Fig. 21(a) and (b), respectively.It can be observed that higher output voltage gain is achieved at higher modulation ratio (m i ) that further increases the sensitivity in output voltages due to parameter variations.The more sensitive the transformerless inverter is, the greater the possibility of unstable output voltage gain.Hence, the transformerless inverter with more sensitivity in the output voltage necessitates a precise closed-loop control system and digital signal processor (DSP) or microcontroller with high resolution.As shown in Fig. 21(b), the proposed HVBTI has lower sensitivity in v o with simpler control techniques as compared to other transformerless inverters with complex control strategies.
The transformerless inverters in [10], [11], [15], [16] have a gain in the output voltage of m i .Hence, these inverters can be used in such applications where the output voltage is required to step down.The inverter in [26] has an output voltage gain of 2v pv , while the transformerless inverter in [27] [29] does not have the capability to boost the output voltage in the -ve half cycle of the grid voltage.Also, its output voltage gain is more sensitive to the change in m i .The transformerless inverters in [28], [30] can boost the output voltage higher; however, they require more power devices compared to other existing configurations.In addition, they have higher sensitivity to the change in m i .The transformerless inverters in [17], [18] can boost the output voltage; however, the gain in the output voltage is smaller and very sensitive compared to the proposed HVBTI.As depicted in Fig. 21(a), the transformerless inverter in [19] provides a higher gain with increased sensitivity compared to the proposed HVBTI topology.Evidently, the output voltage gain of the proposed HVBTI is almost similar to the inverter in [20] and this voltage gain is limitless for the input PV voltages with extremely minimal sensitivity in the output voltage.As per the requirements of Volt-VAr standards (i.e.IEEE 1547-2018), any grid-tied PV inverter must have the capability to supply or receive the reactive power during normal operation.However, the transformer-less inverters in [10], [11], [27] do not have the capability to supply/receive reactive power, which does not fulfill the requirements of Volt-VAr standards of IEEE 1547-2018.
The proposed HVBTI topology performance is evaluated through comparative study in Fig. 22(a) and (b) considering TVR and TCR of the power devices, respectively.It is observed that the proposed HVBTI has the lowest TVR of v pv and TCR of I g .Such TCR value of HVBTI power devices is lower than the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.high gain inverters (with output gain of 0.8) mentioned in [20], [27].However, the high gain inverters mentioned in [17], [18], [26] have lower TCR compared to the proposed HVBTI.With lower TCR, the inverter in [26] has limited voltage boosting feature, while inverters in [17], [18] cannot provide reactive power support to the utility grid.Further, the average TPR of power devices used in HVBTI is compared with existing high gain transformerless inverters.In order to reduce the cost of power devices (such as switches and diodes), the average TPR of each device in the transformerless inverter should be as low as possible.For the best design of the inverter, the current, and voltage stresses on each of the power devices should be minimized while feeding maximum power to the load [15].The TPR curves versus output voltage gain are plotted for the proposed HVBTI and the other high gain transformerless inverter topologies, as shown in Fig. 23.It can be clearly observed that the proposed HVBTI has the lowest device TPR compared to other high gain transformerless inverter topologies.With such device TPR, the maximum measured efficiency of 97.5% is observed for the proposed HVBTI.In this manner, the proposed HVBTI exhibits proper balance amongst power devices count, output voltage boosting range, ratings of power devices, suppression/elimination of leakage currents, and maximum efficiency.It also can be concluded that the proposed HVBTI is a promising practical solution for PV-fed grid-connected applications.
V. CONCLUSION Implementation of HVBTI configuration for 1-φ PV grid integration is presented in this article.The proposed HVBTI configuration integrates the coupled inductor-based high voltage gain converter with a conventional two-level inverter.The significant properties of the HVBTI topology are 1) boosting the lower PV voltage to a higher bipolar voltage, 2) nullifying leakage current by interconnecting the negative terminal of the input solar PV panel directly to the neutral of the grid, 3) accommodating lower rated power devices to enhance the efficiency (≈95%) of the overall system, 4) supplying reactive power till 100% of the inverter rating, 5) obtaining lower input/output current ripple with higher power quality and 6) employing simple modulation and control techniques to inject power into the grid with the least output voltage sensitivity.Further, the proposed HVBTI is validated through a laboratory prototype of 1 kVA power rating.The experimental results are in good agreement with the theoretical study.HVBTI may be used in a variety of applications, including integration of rooftop solar PV with local microgrids, in which the droop control strategy can be further explored during reactive power compensation.

Fig. 4 .
Fig. 4. Developed modulation logic to synthesize the logic functions of the proposed inverter topology.

Fig. 9 .
Fig. 9. O/P voltage gain of HVBTI versus m i for various n.
state space model from (35), the plant transfer function (i.e., i g (s)/m(s)) is derived asĩg (s) m(s) = (1.81e4)s 2 + (8.3e7)s + 8.97e10 s 3 + (4218)s 2 + (3.78e7)s + 3.41e10(36)The following requirements are met through the DCM operation of L 1 , guided by this transfer function:r Enhanced control of HVBTI is realized as the plant transfer function is devoid of any poles or zeros in the right half of the s-plane.

Fig. 11 .
Fig. 11.Experimental waveforms of the grid tied HVBTI during various loading conditions.

Fig. 13 .
Fig. 13.Experimental waveforms corresponding to transient response during change in P o and v pv .

Fig. 16 .
Fig. 16.Zoomed view of grid voltage and grid current in NPA.

Fig. 20 .
Fig. 20.Plot of %THD in I g during mismatch in L g .

Fig. 22 .
Fig. 22. Comparative study of the operating limit of HVBTI.