Closed-Loop Control and Performance Evaluation of Reduced Part Count Multilevel Inverter Interfacing Grid-Connected PV System

Multilevel inverters (MLIs) have drawn tremendous attention in the power sector. Application of MLI has grown extensively to improve the power quality and efficiency of the photovoltaic (PV) system. For an MLI interfacing PV system, the size, cost and voltage stress are the key constraints of the MLI that need to be minimized. This paper presents a novel reduced part count MLI interfacing single-stage grid-tied PV system along with a closed-loop control strategy. The proposed MLI consists of <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> repeating units and a level boosting circuit (LBC) that assists in generating <inline-formula> <tex-math notation="LaTeX">$4n+7$ </tex-math></inline-formula> voltage levels instead of <inline-formula> <tex-math notation="LaTeX">$2n+3$ </tex-math></inline-formula> levels. Three different algorithms are proposed for a proper selection of dc-link voltages to enhance the levels further. A comparative analysis is carried out to confirm the superiority of the developed MLI. The workability of the proposed MLI is investigated with a 1.3 kW PV system. The closed-loop control strategy ensures the maximum power tracking, dc-link voltage balancing, satisfactory operation of the MLI and injection of clean sinusoidal grid current under any dynamic changes. Comprehensive simulation analysis is carried out considering a 15-level MLI structure. Experimental tests further confirm the practicality of the topological advancement for a PV system under different dynamic conditions.


I. INTRODUCTION
Research attempts for the development of renewable energybased power generation systems integrated with multilevel inverter (MLI) are burgeoning. These systems developed for both the standalone and grid-tied applications [1]- [3]. The primary goal of such systems is to attain full power with reduced harmonic distortion, low power loss, and low voltage stress, unlike the commonly used three-level inverter. In retrospect, the cascaded H-bridge (CHB) MLI structures employed extensively interfacing with photovoltaic (PV) The associate editor coordinating the review of this manuscript and approving it for publication was Ramazan Bayindir .
systems [4]- [6] for higher reliability and easy modularity. Consequently, higher power rating and higher voltage levels achieved as per the requirement. CHB MLI requires multiple isolated dc sources in each H-bridge, thus making it highly suitable for PV application as individual PV panel used in each H-bridge along with distributed maximum power point tracking (DMPPT) control. It can help in harvesting maximum energy from the PV sources [4], [7], [8]. On the contrary, single dc source-based MLIs such as diode-clamped and capacitor-clamped MLI demands several components and complex control circuitry to synthesize multilevel output [9], [10]. The shortcoming of conventional MLIs is the involvement of a higher number of power devices. In such cases, the switching losses are more as the semiconductor switches generally operate at high frequency. Although the asymmetrical CHB MLI structure can reduce the number of switching devices but still, the switch count stands high and control complexity increases for higher-level applications [11], [12]. MLIs have immense capability to improve the efficiency of the solar PV system. Such a system integrated with the grid through a dc-dc converter (single-stage) or without it (two-stage). Although both the configurations have nearly the same loss factor and efficiency, the single-stage configuration can save the cost of additional dc-dc converters [13]. Several CHB MLI based single/two-stage PV power conversion systems reported in the literature. Single-stage structure in [5] adopted fuzzy logic for controlling the CHB MLI operating in standalone as well as in grid-connected mode. Individual PV panel control, dc-link voltage balancing, maximum power tracking, and phase-shifted pulse width modulation (PWM) control further explored in [14]. To deal with heavy mismatch condition in large scale two-stage PV interfaced CHB MLIs, detailed system analysis is reported in [4]. DMPPT thereby incorporated to extract maximum power, from all the sub-modules of the MLI under uniform as well as partially shaded conditions. A cascaded quasi-Z source MLI for a PV system is further explored in [15] addressing single-stage dc-dc conversion and inversion along with the second harmonic voltage and current ripples in the Z source network.
It is worth mentioning that the efficiency of the solar PV system is very low. Thus, the use of conventional MLIs in such a system is not an ideal choice. In this context, several reduced switch MLIs (RSMLIs) have been developed in recent years [16]. By reducing the number of components, the power losses reduced, and the efficiency of the standalone/grid-connected PV system can be improved [17], [18]. Several single-phase and three-phase 5-level RSMLIs using reduced power devices have been proposed in [8], [19], [20] for grid-tied PV systems. These MLIs altogether uses eight switches per phase and comprises an H-bridge for changing the polarity at the output. The DMPPT, global MPPT, and inter-phase power balancing addressed in [8]. Extending the structure proposed [19], a two-stage grid-tied PV MLI system introduced in [21]. This work deals with capacitor voltage balancing issues, and also several grid side control objectives addressed. In [20], the issues related to the reduction of leakage current and common-mode voltage investigated in detail. Three-phase asymmetrical RSMLI structures are subsequently developed in [22], [23] that uses a reduced number of switches for the generation of multilevel output.
Continuing the research trend, MLIs are further explored broadly in two forms, i.e., switched-diode based or switchedcapacitor based RSMLI. The authors in [18], [24], [25] have introduced a cascaded MLI based on the switched-diode modules for standalone applications. Use of diodes makes the circuit simple and reduces the switch count and control complexity. Several switched-capacitor based MLIs that allow dc source reduction is also witnessed in the literature with level boosting feature. The developed MLI in [26] is an example of it which is a CHB MLI, but with additional bidirectional switches used to replace the isolated dc sources by capacitors.
Nevertheless, the switch count is higher compared to a CHB MLI. The MLI topologies proposed in [27]- [31] adopt the switched-capacitor principle to reduce the source count as well as the switch count. The capacitors are self-balanced at the desired voltage by charging in parallel from the input dc source and discharging in series through the load. Appropriate charging & discharging of capacitors, capacitance sizing, and dc-link voltage balancing are the critical challenges of these MLI types [32].
Apart from reducing the switch count, minimization of voltage stress is also a key factor. Besides the above-discussed RSMLIs that address this issue, different types of level boosting circuits (LBCs) developed to optimize the MLI and addition, reduce the stress. In [3], [33]- [35], the introduced LBC doubles the number of levels and reduces the component count per level ratio (CLR). Almost all the above-cited MLIs formed by combining a low-frequency H-bridge as polarity generation unit and high-frequency level generation units. The level of generating units can be cascaded to increase the number of levels. The switches in the H-bridge withstand higher voltage stress than the level generating units. Few compact module hybrid MLI structures, therefore, realized without using an H-bridge [36], [37].
It is evident from the above discussion that there is a need for an optimized PV MLI that possibly reduces the number of semiconductor devices, device stress and power losses. In addition, the power quality and efficiency of the (PV) system can be improved. This work presents a detailed analysis of the grid-tied single-phase single-stage PV system interfaced with a novel MLI. Structural and functional analysis of the proposed MLI detailed in Section II and Section III highlights the superiority of the proposed MLI compared to the prior art topologies. In Section IV, a closed-loop PWM control strategy developed to balance the individual dc-link voltages, synthesize the desired staircase output with low distortion under any perturbations, and maintain the power quality of the grid-tied system. Extensive simulation and experimental analysis of the proposed system is presented in Section V & VI, respectively. In the end, concluding remark on the whole research work is presented.

II. PROPOSED SYSTEM CONFIGURATION
The generalized structure of the proposed voltage level boost (VLB) MLI for the single-stage grid-connected PV system shown in Fig. 1. As indicated, VLB MLI is the combination of three modules such as; repeating unit (RU), H-bridge, and LBC. RU consists of two PV strings as input sources which can be repeated in a series manner to achieve higher voltage levels. Moreover, the inclusion of LBC in the VLB MLI exactly doubles the number of levels with the addition of four extra switches. Numbers of switches (N sw ), the number of sources (N dc ) and the number of diodes (N dd )  involved in the VLB MLI in terms of RU (n) are expressed in (1)(2)(3). In this work, the VLB MLI is integrated with the grid through a small size low pass filter (inductor) to reduce further the current harmonics caused by switching action. Moreover, optimization of the proposed system attempted in two ways, i.e., use of dc-dc converter eliminated, and three different algorithms to select input source magnitude developed for reducing the source count.

Number of switches (N
Other than the component count, total blocking voltage (TBV) is an important parameter to be considered while designing an MLI. TBV is the addition of blocking voltage of each switch which decides the suitability of MLI for a different level of voltage application. In this respect, blocking voltage by the RU switches, H-bridge switches, and LBC switches expressed in (4-6), respectively considering V 1 , V 2 , . . . , V 2n−1 , V 2n , and V L as the dc-link voltages.
Magnitudes of the dc-links for RUs are selected as per the algorithms presented in Table 1. Magnitudes can be selected as asymmetrical, arithmetic and binary ratio according to PA1, PA2 and PA3, respectively. The generalized expressions for the output voltage levels (N l ), TBV, and switching loss (S loss ) in terms of RUs also included. This work analyzes the performance of the VLB MLI considering PA1. The VLB MLI produces a 15-level output with PA1 when two RUs (i.e., with ten switches) are taken into consideration. Fig. 2(a) shows the expected 15-level staircase output waveform with switching pulse duration of all the switches. The source used in the LBC is responsible for the generation of the first step while the second step is produced by turning off the switches in the RU along with deactivating the LBC. The third step can be obtained by activating the LBC source. Afterwards, RUs are switched to generate the fourth step and the further. For the 15-level case, blocking voltages  across each switch is illustrated in Fig. 2(b). Performance of the VLB MLI with the three proposed algorithms is further evaluated in Fig. 3(a) & (b). The N l increases significantly considering PA3; however, TBV also increases accordingly.

III. COMPARATIVE ANALYSIS
The prime purpose of the current work is to devise a novel MLI structure having lesser switch count and TBV. To validate the competence, the proposed VLB MLI is compared with different MLI topologies developed recently. Hereafter the MLI topologies in [18], [28], [38], [23], [36], [29], [37], [26] are termed as T1, T2, . . . , T8. The MLI presented in [26] utilizes a higher number of switches but reduces the source count. The MLIs presented in [29], [36], [37] employs lesser switch count than a conventional CHB MLI, but the reduction is not significant as compared to the presented MLIs in [18], [23], [28], [38]. Accordingly, the superiority of the proposed VLB MLI acknowledged from Fig. 4(a). Moreover, it is observed that some of the MLI topologies use diodes in the circuit. The MLIs in [18], [28], [29] employ diodes to synthesize a staircase output. It is obvious from Fig. 4(b) that, the VLB MLI requires less number of diodes among all the compared MLIs.
Addition of more number of dc sources will result in more number of voltage levels, but at the same time, TBV will increase. The MLI topologies developed in [26], [28], [29], [38] involves a single dc source and additional capacitors for generating multiple voltage levels. All these MLI topologies are corroborated for lower-level applications. Although TBV becomes less for these MLIs, but voltage balancing issue and control complexity may arise in higher-level applications. It is clear from Fig. 4(c) that, the proposed VLB MLI requires a lesser number of dc sources to synthesize the same level output. Fig. 4(d) shows there is no need for additional capacitors in the proposed MLI. Further, CLR is calculated for all the MLI topologies for evaluating a generic cost comparison. CLR is the ratio of sum of the cost deciding parameters (N sw , N d , N c , N dc , and the number of driver circuits) with N l . In this perspective, the VLB MLI exhibits a lower value of CLR among all the considered MLIs, as shown in Fig. 4(e) which indicates the cost-effectiveness of the proposed structure.
TBV is an important parameter which decides the applicability of an MLI in high voltage. In order to compute the TBV, the blocking voltages of all the individual switches are added together. The blocking voltages for the proposed MLI are summarized in (4-6) along with TBV in Table 1 for PA1, PA2, and PA3. Significant reduction in TBV can be clearly noted from Fig. 4(f). Furthermore, Table 2 presents a summary of well known standalone and grid-tied MLI interfacing PV systems.

IV. CONTROL STRATEGY
The 15-level VLB MLI utilizes two varieties of dc-link voltages (0.5V dc & V dc ). Thus it is most important to control the dc-link voltage so that they can be maintained at  desired values. In this aspect, a suitable close loop control strategy has been employed for the grid-tied PV fed VLB MLI system with critical objectives such as maximum power extraction from the PV-array, dc-link voltage balancing under dynamic change in insolation, injection of clean sinusoidal grid current at unity power factor, control of overall system under phase change and grid side perturbations. The comprehensive control system is shown in Fig. 5.

A. MPPT CONTROL
The performance of the PV systems is highly dependent on the temperature and insolation level, which are not uniform throughout the day. For harvest maximum power, MPPT control technique is adopted, which will make the sure operation of PV at MPP. Although various MPP tracking techniques have been investigated in literature [39], [40], incremental conductance MPPT [13], [40] is implemented due to its full viability and simplicity. The MPPT control then produces the reference voltage signal for the voltage control loop. For efficiently extract maximum PV power under insolation mismatch conditions, DMPPT control is performed, i.e., MPP tracking is carried out in each RUs. The required reference current is further generated by comparing the actual individual PV voltages with the total PV voltage.

B. TOTAL VOLTAGE CONTROL LOOP
Closed-loop voltage control is employed to maintain the total dc-link voltage corresponding to the reference set voltage considering any change in PV characteristics. The control loop calculates error taking the sum of the actual/measured dc-link voltages (V total ) and the sum of individual reference dc-link voltages (V total * ) that are generated from the MPPT control algorithm. The obtained voltage error is minimized by processing it through a proportional-integral (PI) controller. The parameters (K p1 , K i2n ) of this PI-controller are tuned so that the peak value of the injected grid current becomes maximum. Further, a phase-locked loop (PLL) is used to synchronize with the grid frequency.

C. INDIVIDUAL VOLTAGE CONTROL LOOP
Although the total voltage controller module maintains the total dc-link voltage at the desired value, but individual dc-link balancing is not guaranteed. Therefore, an individual control loop is also used for balancing each dc-links. The output of each individual voltage control modules is used to generate the reference signal for PD-PWM controller of VLB MLI.

D. CURRENT CONTROL LOOP
For obtain the desired power balancing in addition to the voltage control, a current controller is used to maximize the PV output. This current control loop generates the current error by comparing the reference grid current (I * s ) and the actual/measured grid current (I s ) which is then processed through a PI-controller. The parameters of the PI-controller (K p , K i ) are tuned for optimizing the error.   The output of this controller is compared with the grid voltage (V s ) for generating the reference voltage of the inverter for any change in V s . Accordingly, the inverter voltage follows the grid voltage under every unwanted circumstance.

E. PHASE-DISPOSITION PWM CONTROL OF VLB MLI
The phase-disposition PWM (PD-PWM) control scheme can be implemented in three stages such as; reference signal generator, a comparator circuit, and switching pulse decoder. For an MLI to produce N l level output, (N l − 1)/2 number of triangular carriers are required for the aforesaid control mechanism [10]. Thus, seven carriers are disposed of in-phase with a precise offset level for the 15-level VLB MLI. Thereby, the carriers are compared with the reference sinusoidal signal in the comparator circuit for producing seven switching states. The switching pulse decoder circuit comprises of several digital logic gates then generate pulses considering switching logic as illustrated in Fig. 2(a) for all the ten switches.

F. STABILITY ANALYSIS
The stable functionality of the adopted closed-loop controller for the proposed grid-tied system [11] is examined in this section. The overall equivalent block diagram shown in Fig. 6 is considered for stability analysis. The overall transfer function (TF) of the proposed system in Laplace domain (G(s)) is computed taking the product of TF of current control module (G ccm (s)), modulation delay (G MD (s)), grid (G s (s)), and L-type filter (G LF (s)). The value of the proportional gain (K p ) & integral gain (K i ) of the current control module is taken as 0.7 & 10, respectively. The integral time constant (T i ) is the reciprocal of K i . The time of modulation delay (T MD ) is considered as 1.5 times of sampling time (T s ). Fig. 6 also depicts the bode plot stability analysis of the considered system. The phase margin (PM) is computed to be 102.7 • and the phase plot stabilizes much ahead of −180 • . Therefore, the gain margin (GM) of the proposed system is infinite. It may be concluded from the figure that both GM & PM values are more significant than zero, which verifies a stable control strategy.

V. SIMULATION ANALYSIS
In this section, the operation of 15-level VLB MLI in single-stage grid-tied PV system under MATLAB/Simulink environment is investigated. The adopted closed-loop control strategy as outlined earlier makes sure maximum PV power extraction and the dc-links are maintained at desired voltage levels (0.5V dc & V dc ). PV panels are connected to the VLB MLI through the 1500 µF & 2200 µF dc-link capacitors. The values are chosen, considering 2-3 % voltage ripple and nominal output frequency. The carrier frequency and reference sinusoidal frequency are chosen as 5 kHz & 50 Hz. Several 125 W PV panels arranged in (2 × 2) and (1 × 1) are considered as an input source for the VLB MLI to obtain the desired dc-link voltage V dc & 0.5V dc , respectively. The parameters considered in the simulation are given in Table 3. Fig. 8(a) shows the output voltage of the proposed VLB MLI (V inv ) and injected grid current (I s ) at different MI values (MI = 0.5, MI ≈ 1, MI > 1). With the decrease in MI value, the MLI is able to operate at a reduced voltage level. On the other hand, overmodulation (MI > 1) causes distortion in voltage waveform. Hence, it is always desirable to operate near unity MI value. Fig. 8(b) depicts the harmonic spectra of the output voltage of the MLI and grid current. The % THD values of both output voltage and current waveform are below 5% obeying the IEEE-519 standard.
Tests are further conducted under different dynamic conditions. Fig. 8(c) shows the results with varying insolation at 0.12 s to 300 W/m 2 from 750 W/m 2 . During this, the grid voltage (V s ) remains unaffected; however, grid current magnitude changes accordingly with insolation change. MPP tracking performance is also delineated in Fig. 8(d). The dc-link voltage is automatically tracked to the reference value and maintained at the desired level even under a change in insolation level. Voltage sag is a common incident in the power system network which is generally caused by faults in the transmission line, sudden load change or excessive load demand. Under voltage sag initiated at 0.4 s, Fig. 8(e) also shows the grid current increases to an extent which ensures the power balance, i.e., the injected power to the grid is maintained Moreover; the PV fed VLB MLI continuously injects a clean sinusoidal current to the grid even under 0.94 lagging power factor (PF) condition as shown in Fig. 8(f). However, the proposed converter can result in unsatisfactory performance under very low PF due to the presence of discrete diodes in the conducting path.

VI. EXPERIMENTAL VERIFICATION
The real-time operation of the proposed VLB MLI in grid-connected mode is verified on a prototype developed in the laboratory, as shown in Fig. 7. The 12N60A4D insulated gate bipolar transistors (IGBTs) and RGP30D discrete diodes are used to build the power circuit. According to the current laboratory availability, one SAS 120/10 solar simulator and four variable dc sources are used as input sources to mimic the PV panel characteristics. Solar simulator and dc sources voltage magnitudes are so adjusted according to Table 3. The output of the VLB MLI is connected to the residential grid through an auto-transformer which steps down the grid voltage to match with the inverter output such that the current from the PV fed MLI can be continuously injected to the grid. LA-55p and LV-25 hall-effect sensors are used to sense the current and voltage, respectively. A DSP controller is used to implement the control technique. Generated pulses are further amplified using TLP250 drivers. All the waveforms are acquired with the help of a YOKOGOWA ScopeCoder. All the experimental results are obtained under similar test conditions as in the simulation analysis. The output voltage waveform with grid current at different MI values is shown in Fig. 9(a). At MI value > 1, the voltage waveforms get slightly distorted. At MI value < 0.5, the grid supply is also reduced to continuously feed power to the grid as the MLI operates at a reduced voltage level. Further tests are conducted at MI ≈ 1, where a clean voltage output is evident. Fig. 9(b) shows the steady-state results that confirm V inv, is the sum of the output voltage without LBC (V oH ) and the output voltage of the LBC (V oL ). A 15-level output voltage is produced instead of 7-level by adding V oL at the intermediate levels.
The grid voltage and grid currents which are in phase with each other are also shown in the figure. The MLI output voltage and injected grid current harmonic profile are shown in Fig. 9(c) which is following the IEEE-519 standard.
For verify the theoretically calculated blocking voltages, voltage stress across some switches (S 1 , S 2 , T 1 , T 3 , L 1 , L 3 ) are shown in Fig. 10(a). It implies the unidirectional nature of   all the switches. Under dynamic solar insolation change and grid voltage sag condition, results are further acquired. MPP tracking performance is shown in Fig. 10(b) at 750 W/m 2 and 300 W/m 2 insolation levels. These curves show the tracking efficiency is about 99.9% at MPP. In Fig. 10(c), insolation level is changed from 750 W/m 2 to 300 W/m 2 . During this, the current grid change is noticeable. The performance under grid voltage sag condition keeping the insolation level fixed is depicted in Fig. 10(d). This causes the minor change in inverter output voltage as the MI varies according to the change in grid voltage or dc-link voltage. However, the grid current increases proportionally ensuring the power balance between the grid and PV system. Moreover, Fig. 11 depicts the grid power, PF, frequency under steady-state, insolation change and voltage sag conditions. Low reactive power attests operation near unity PF in all conditions while the grid frequency is maintained at 50 Hz. Power loss is a crucial factor that dictates the system efficiency, which includes both switching and conduction losses. Switching loss occurs during the state transition of a switch [18]. Although the switching losses are high due to high-frequency PWM switching, the proposed MLI in a way minimizes the switching loss by operating the switches having higher blocking voltage at the fundamental frequency (f o ) and the switches having lower blocking voltage at switching frequency (f s ). For instance, RU and LBC switch    faceless blocking voltage operated at f s and H-bridge switches withstand a high blocking voltage are operated at f o . By considering it, switching losses for the proposed VLB MLI is calculated as per Table 1. Further, and conduction loss is also calculated for one complete cycle by considering the number of switches and diodes that conduct during any interval of time. Total power loss is accordingly computed to examine the efficiency of the proposed VLB MLI by neglecting drivers and snubber circuit losses. Fig. 12 illustrates a significantly higher efficiency of VLB MLI interfacing single-stage PV system considering parameters tabulated in Table 3. With the change in insolation level of the PV system, dc-link voltage, grid supply, switching and supply frequencies, efficiency may change.

VII. CONCLUSION
A novel VLB MLI structure introduced in this work along with three different algorithms to choose dc-link magnitude for producing higher voltage steps using the fewer part count. Using two RUs with two different varieties of sources, the proposed MLI generates a 15-level output voltage. In addition to the reduction in the number of switches, both the CLR and TBV are reduced significantly compared to the prior-art MLIs. Low CLR value verifies that the proposed VLB MLI can easily extend to any number of levels with a reduced number of components and lower TBV (16V dc for the 15-level MLI) demonstrates suitability in high-voltage/power applications. The workability of the proposed 15-level MLI is verified in integration with the 1.3 kW PV system. A closed-loop control strategy is developed, which fulfils all the control objectives, and the system operates satisfactorily for any input or output side perturbations. Simulation and experimental analysis under dynamic test cases such as; different MI values, under varying insolation, and grid voltage sag condition validates the satisfactory working of the proposed MLI interfacing PV system. The MPP tracking efficiency of the PV system is about 99.9 %, and the overall system efficiency is more than 90%.