A Comprehensive Review on Common-Mode Voltage of Three-Phase Quasi-Z Source Inverters for Photovoltaic Applications

Abstract

Inverters with Quasi-Z-Source Networks (QZSN) provide DC-DC boosting and DC-AC conversion in a single stage. It offers reduced cost, complexity, and volume compared with the classical two-stage conversion system, which is composed of a boost converter followed by a Voltage-Source-Inverter (VSI). Further, QZSI provides superior conversion characteristics for single-stage grid-connected photovoltaic transformerless systems. However, the absence of galvanic isolation in these systems makes it possible to allow leakage current through these systems’ parasitic capacitances due to the high-frequency Common-Mode Voltage (CMV) generated by the Pulse Width Modulation (PWM) nature of the inverter output voltages. As a result of this current, critical safety issues may arise with PV systems. Many PWM techniques have been presented in recent years for QZSIs. This paper is intended to provide a comprehensive analysis and review study of the characteristics of most of these PWM techniques in terms of CMV and leakage currents. In this study, closed-form equations have been derived to determine the effective CMV and leakage current analyses for all modulation techniques. Analytical and simulation approaches are used to identify schemes with the lowest CMV and current leakage effects. Moreover, the experimental setup is presented by applying the Simple-Boost Modified Space Vector Modulation (SB-MSVM) technique.

1. Introduction

In recent years, advances in power electronics converters topologies and modulations have paved the way for developing high-performance Renewable Energy Systems (RES). Among the various RES currently emerging in the world, the Photovoltaic (PV) system stands out, which is a highly reliable, clean and noiseless method of producing electricity [1,2]. PV technology has grown to solve problems related to conventional power plants. Based on the snapshot of the PV technology report in February 2022 [3], a graph showing the evolution of solar PV capacity worldwide in the last 11 years is depicted in Figure 1. It shows how solar PV power systems are expected to provide more energy worldwide. From 2010 to 2021, annual global PV capacity additions grew from 17 GWdc to about 180 GWdc, and the total cumulative installed capacity for PV at the end of 2021 reached at least 939 GWdc. In Africa, for example, solar annual PV capacity increased from 1.5 GW in 2014 to more than 8 GW in 2019 [4]. This growth is attributed to different countries in Africa. For example, the Benban complex in Upper Egypt today is the largest solar project in Africa and one of the largest solar installations in the world, with around 2 GW of AC power [5]. The Benban project comprises 41 individual plants consisting of 7.2 million PV panels. Thirty-one plants each have a capacity of 50 MW AC (64 MW DC), while the remaining ten projects have different capacities due to the shape of the area of the plant [5,6,7,8,9].

Undoubtedly, this growth has triggered the development of PV power converters. These converters are essential for interfacing PV modules with the AC loads, as shown in Figure 2 [10]. As a result, it is used to ensure efficient and reliable energy conversion. While PV power converters differ in configuration, their major functions remain the same. These functions are determined according to the type of loads.

The PV conversion systems can be predominantly classified according to the connection types of systems into (1) standalone and (2) grid-connected (on-grid) systems. Compared with standalone, grid-connected PV systems are widely used in practical applications [10,11,12]. It accounts for over 99% of installed capacity [11]. Various functions are performed by the power converters of the grid-connected systems, as shown in Figure 2, including (1) Maximum-Power-Point-Tracking (MPPT) at the PV side, (2) DC-to-AC conversion, (3) grid synchronization and power quality control at the gride side [13]. Due to cost reductions on PV modules and subsidies and incentives, PV systems are becoming more affordable. It is expected that grid-connected PV systems will soon play a major role in electrical power generation, especially from renewable energy sources [14,15,16,17]. Generally, there are two types of grid-connected PV systems: transformer (or galvanic)-isolated and transformerless (or non-isolated) systems, as shown in Figure 3 [18].

The transformers in isolated PV systems may be low- or high-frequency transformers, as classified in Figure 3 [15,18]. The schematic diagrams of both systems are shown in Figure 4a,b. As can be shown, several peripheral components are included in these systems, such as power converters, filters, and transformers. The converters include DC/DC and DC/AC topologies [19,20,21]. Since the grid-connected PV runs parallel to the grid, no storage systems are required. The Low-Frequency Transformers (LFTRs) are located directly before the grid, as shown in Figure 4a. Although LFTRs provide galvanic isolation and can develop safety issues, they suffer some drawbacks, including size, weight, and cost. They also reduce overall system efficiency. On the other hand, High-Frequency Transformers (HFTRs) are placed in the DC stage of the inverter instead of the LFTR to solve this problem, as shown in Figure 4b. The HFTRs-based converters, however, have complex constructions, and their efficiency does not differ significantly [22,23,24,25,26,27].

Transformerless-based PV systems can be achieved by removing the transformer from the isolated systems. As a result, small size, low weight, low cost, and high-efficiency systems are achieved [22,24,25,27]. Meanwhile, about a 2% increase in the overall conversion efficiency is achieved using these systems [28]. However, it is critical to note that a current will flow through the parasitic capacitance ($C_{pv}$) as shown in Figure 4c. This current is called leakage current.

This leakage current seems to be a common problem in all transformerless PV systems [29,30,31,32,33,34,35]. This results in serious safety concerns and reduces the grid’s current quality and the overall efficiency of the conversion system [34]. Practically, the leakage current should be reduced according to the safety standards such as IEC 62109-2. In transformerless PV systems, parasitic capacitance between PV panels and the ground is estimated from 200 nF to 1 µF per kW, which is panel-based and it’s base construction [36]. Sure, the actual value can be varied according to environmental conditions, but it is still in the range between nano- to micro-Farads. The leakage current is confined by the grid codes and many standards to 300 mA (peak) for safety issues. The converter protection will disconnect the system if the leakage current exceeds this limit within 300 msec [36].

Generally, transformerless PV systems can use two- or single-stage power converters, as shown in Figure 3. The first stage of the transformerless system boosts the PV voltage, while the second stage converts the boosted DC voltage to an AC waveform. On the other hand, single-stage converters perform both boosting and inversion processes. Recently, different topologies have been made to increase the power density and efficiency of single-stage inverters [20,24,25]. Among single-stage PV topologies, Impedance-Source Inverter (ZSI) was first invented in 2003 [37,38]. It represents one of the dominant and promising single-stage inverters for the transformerless grid-connected system. There has been a significant increase in publications on the ZSI topology and its developments in recent years. Based on the database of IEEE Xplore, Figure 5 shows a summary of ZSI-based topologies published over the past two decades. It can be observed from Figure 5 that extensive research was conducted to explore various aspects of the basic ZSI circuit, develop novel topologies, and propose enhanced modulation techniques to enhance conversion and switching performance [39].

Among Z-source-based inverter topologies, the Quasi-Z Source Inverter (QZSI), shown in Figure 6, offers some advantages, such as continuous supply current [40].

Consequently, QZSI is well suited to transformerless grid-connected PV systems and energy storage systems [41]. As a result of the QZSI’s common ground, a potential issue between the panel and grid is also obviated. The main disadvantage of this system is its lack of galvanic isolation, which results in leakage currents. The advancement in different research work aims to solve the leakage current problems in the traditional VSI using the following methods: adding extra switching devices [42] or modifying modulation techniques [43,44,45]. Modifying modulation techniques is the most cost-effective way to solve leakage-current problems in transformerless PV systems [45]. To improve the performance of QZSIs, various PWM techniques have been proposed. In the available literature [46,47,48,49,50], these techniques are classified, reviewed, and compared based on their performance parameters and complexity of implementation. However, it is essential to evaluate the leakage current of QZSI -based systems to analyze the generated CMV magnitude because PV systems have significant parasitic capacitance. In motor drive applications, the leakage current is more influenced by CMV transition than its voltage magnitude [44]. However, the main cause of leakage current in the PV system is the voltage magnitude of the CMV [45].

All the advancements related to this issue are focused on the traditional two-level or multilevel inverters. A few publications in this field are related to reducing CMV of the two-level three-phase QZSI [51,52,53,54]. In [51,52,53], the traditional PWM schemes used to reduce the CMV in the classical VSI are developed into QZSIs. It uses the odd, even or hybrid odd-even vectors in addition to the ST states to reduce the transition of the CMV and, consequently, reduce the leakage current effects. The work in [44] splits the boosting inductor to reduce the CMV. In [55], some conventional PWM schemes of QZSIs are compared in terms of CMV. In this study, CMV is compared for a narrow bandwidth rather than its average value. In particular, no research work, to our knowledge, has considered and fully explored the problems of CMV and leakage currents for the presented PWM schemes of the QZSI topology.

Because of its many advantages, this paper introduces a comprehensive study and review of PV-based QZSI systems. It compares their different modulation techniques from the following points of view: (1) Performance characteristics, (2) RMS value of CMV, (3) peak value, $dv/dt$, and (4) leakage current. To better understand how QZSI functions, we will provide an overview of its operating principles in Section 3. Section 4 discusses the various PWM techniques available for QZSI. An introduction to CMV analysis can be found in Section 5. The leakage current analysis is discussed in Section 6, Section 7 and Section 8. The simulation study is introduced in Section 9, while the experimental work is presented in Section 10, followed by conclusions.

2. Operating Principles of QZSI

The circuit of the QZSI connected to PV panels is shown in Figure 6 [55]. It operates in two modes called 1) Non-Shoot-Through (NST) and Shoot-Through (ST) modes. In the NST mode, the QZSI operates as a traditional VSI, while in the ST case, one or more legs can be shorted. It is worth noting that the ST mode must be used in the zero states to perform boosting action without affecting the output quality.

2.1. Non-ST Mode

In this case, the diode, $D$ is conducted, and the active switches are modulated by six active states ($V_1$ to $V_6$) and two zero states ($V_o$ and $V_7$) like the traditional inverter. The capacitors will charge, and the energy in the inductors will be realized to the load.

2.2. ST Mode

In this case, the sum of the capacitor voltages in the impedance network is much higher than the voltage on the supply $E_s$. So, the diode, $D$ is opened. As a result, the capacitive energy will be released to charge the inductors. In this mode, the DC-link voltage equals zero.

Hence, for both modes, the peak DC-link voltage, ${\widehat{v}}_{dc}$ is

$${\widehat{v}}_{dc}=B{E}_s$$

(1)

where $B$ is the boosting factor and it can be estimated from [55]

$$B=1/\left(1-2D_{ST}\right)$$

(2)

here $D_{ST}$ is the ST duty cycle.

3. Review of PWM Techniques for QZSI

Based on the method of achieving ST mode, the PWM schemes for QZSIs can be divided into Three- and Single-phase ST schemes (i.e., 3ΦST and 1ΦST, respectively), as depicted in Figure 7 [47,48,49,50]. As shown, it can be divided into a) continuous and b) discontinuous schemes. Moreover, it’s further subdivided into (i) Simple-Boost (SB), (ii) Maximum-Boost (MB), and (iii) Constant-Boost (CB) control methods. There are also classifications depending on the modulating signals used. At this level, we have sinusoidal (SPWM), third harmonic (THM), symmetrical (SYM), DC-Clamped (DCCM), and modified SVM (MSVM) schemes. The common and dissimilar aspects of most of the analyzed modulation techniques include implementation complexity, voltage gain, current and voltage stresses, the effective switching frequency, output voltage spectrum, and switching losses were examined in [48,49].

Table 1. Review summary of the modulation techniques of QZSI.

	3Φ-ST Modulation Techniques					1Φ-ST Modulation Techniques
Technique	3Φ/SB/SPWM	3Φ/SB/THM 3Φ/SB/SYM	3Φ/MB/SPWM 3Φ/MB/THM 3Φ/MB/SYM	3Φ/MCB/SPWM 3Φ/MCB/THM 3Φ/MCB/SYM 3Φ/SB/+DCCM 3Φ/SB/-DCCM	3Φ/MB/+DCCM 3Φ/MB/-DCCM	1Φ/SVM6 1Φ/SVM4(b) 1Φ/SVM2	1Φ/SVM4(a)	1Φ/SB/SPWM	1Φ/SB/THM 1Φ/SB/SYM 1Φ/SB/MSVM	1Φ/MB/THM 1Φ/MB/SYM 1Φ/MB/MSVM	1Φ/SB/-DCCM 1Φ/SB/+DCCM	1Φ/MB/+DCCM 1Φ/MB/-DCCM
${\mathit{D}}_{\mathit{sh}}$	$1-M$	$1-M\sqrt{3}/2$	$\frac{2\pi -3\sqrt{3}M}{2\pi }$	$1-M\frac{\sqrt{3}}{2}$	$\left(2\pi -3\sqrt{3}M\right)/2\pi$	$k\left(1-\frac{3\sqrt{3}}{2\pi }\times M\right)$	$3/4k\left(1-3\sqrt{3}/2\pi \times M\right)$	$1-M$	$1-M\frac{\sqrt{3}}{2}$	$\frac{2\pi -3\sqrt{3}M}{2\pi }$	$1-M\frac{\sqrt{3}}{2}$	$\frac{2\pi -3\sqrt{3}M}{2\pi }$
B	$1/\left(2M-1\right)$	$1/\left(\sqrt{3}M-1\right)$	$\frac{\pi }{3\sqrt{3}M-\pi }$	$\frac{1}{\sqrt{3}M-1}$	$\pi /\left(3\sqrt{3}M-\pi \right)$	$\frac{\pi }{\pi -k\left(2\pi -3\sqrt{3}M\right)}$	$\frac{4\pi }{4\pi -6\pi k+9\sqrt{3}Mk}$	$\frac{1}{2M-1}$	$\frac{1}{\sqrt{3}M-1}$	$\frac{\pi }{3\sqrt{3}M-\pi }$	$\frac{1}{\sqrt{3}M-1}$	$\frac{\pi }{3\sqrt{3}M-\pi }$
G	$M/\left(2M-1\right)$	$M/\left(\sqrt{3}M-1\right)$	$\frac{M\pi }{3\sqrt{3}M-\pi }$	$\frac{M}{\sqrt{3}M-1}$	$M\pi /\left(3\sqrt{3}M-\pi \right)$	$\frac{\pi M}{\pi -k\left(2\pi -3\sqrt{3}M\right)}$	$\frac{4\pi M}{4\pi -6\pi k+9\sqrt{3}Mk}$	$\frac{M}{2M-1}$	$\frac{M}{\sqrt{3}M-1}$	$\frac{M\pi }{3\sqrt{3}M-\pi }$	$\frac{M}{\sqrt{3}M-1}$	$\frac{M\pi }{3\sqrt{3}M-\pi }$
${\mathit{V}}_{\mathit{s}}$	$\left(2G-1\right)E_s$	$\left(\sqrt{3}G-1\right)E_s$	$\frac{3\sqrt{3}G-\pi }{\pi }{E}_s$	$\left(\sqrt{3}G-1\right)E_s$	$\left(3\sqrt{3}G-\pi \right)/\pi E_s$	$\frac{\left(\pi -3\sqrt{3}kG\right)}{\pi \left(1-2k\right)}{E}_s$	$\frac{4\pi -9\sqrt{3}Gk}{4\pi -6\pi k}{E}_s$	$\left(2G-1\right)E_s$	$\left(\sqrt{3}G-1\right)E_s$	$\frac{3\sqrt{3}G-\pi }{\pi }{E}_s$	$\left(\sqrt{3}G-1\right)E_s$	$\frac{3\sqrt{3}G-\pi }{\pi }{E}_s$
${\mathit{V}}_{\mathit{c}1}/{\mathit{E}}_{\mathit{s}}$	$M/\left(2M-1\right)$	$\sqrt{3}M/\left(2\sqrt{3}M-2\right)$	$\frac{3\sqrt{3}M}{6\sqrt{3}M-2\pi }$	$\frac{\sqrt{3}M}{2\sqrt{3}M-2}$	$3\sqrt{3}M/\left(6\sqrt{3}M-2\pi \right)$	$\frac{2\pi \left(1-k\right)+3\sqrt{3}Mk}{2\pi \left(1-2k\right)+6\sqrt{3}Mk}$	$\frac{8\pi \left(1-\frac{3}{4}k\right)+9\sqrt{3}Mk}{4\pi \left(1-\frac{3}{2}k\right)+9\sqrt{3}Mk}$	$\frac{M}{2M-1}$	$\frac{\sqrt{3}M}{2\sqrt{3}M-2}$	$\frac{3\sqrt{3}M}{6\sqrt{3}M-2\pi }$	$\frac{\sqrt{3}M}{2\sqrt{3}M-2}$	$\frac{3\sqrt{3}M}{6\sqrt{3}M-2\pi }$
${\mathit{V}}_{\mathit{m}}/{\mathit{E}}_{\mathit{s}}$	$M/\left(4M-2\right)$	$M/\left(2\sqrt{3}M-2\right)$	$\frac{\pi M}{6\sqrt{3}M-2\pi }$	$\frac{M}{2\sqrt{3}M-2}$	$\pi M/\left(6\sqrt{3}M-2\pi \right)$	$\frac{\pi M}{2\pi -2k\left(2\pi -3\sqrt{3}M\right)}$	$\frac{4\pi M}{8\pi -6k\left(2\pi -3\sqrt{3}M\right)}$	$\frac{M}{4M-2}$	$\frac{M}{2\sqrt{3}M-2}$	$\frac{\pi M}{6\sqrt{3}M-2\pi }$	$\frac{M}{2\sqrt{3}M-2}$	$\frac{\pi M}{6\sqrt{3}M-2\pi }$
Group	G1	G2	G3	G2	G3	G4	G5	G1	G2	G3	G2	G3

lists the performance characteristics of all modulation techniques and maximum phase voltage ($V_m$/$E_S$), the mean capacitor voltage ($V_{C1}$/$E_S$) and the boosting factor for each modulation scheme. Based on the results, the PWM techniques are classified into five groups: G1 to G5.

4. CMV in QZSI

As in the conventional VSI, the CMV, $v_{CM}$ of the QZSI is determined from [55]

$$v_{CM}=\left(v_{aN}+v_{bN}+v_{cN}\right)/3$$

(3)

where $v_{aN}$, $v_{bN}$ and $v_{cN}$ are the phase voltages.

Using (3),

Table 2. Common-mode Voltages for QZSI.

State		${\mathit{v}}_{\mathit{C}\mathit{M}}/{\mathit{v}}_{\mathit{d}\mathit{c}}$
$\mathrm{Odd} \mathrm{states} (V_1,V_3,V_5)$	{100}, {010}, {001}	$1/3$
Even ($V_2,V_4,V_6)$	{110}, {011}, {101}	$2/3$
Zero-state ($V_0)$	{000}	0
Zero-state ($V_7)$	{111}	$1$
$\mathrm{Shoot}-\mathrm{through} \mathrm{states} (V_{ST})$	-	0

lists the normalized CMV ($v_{CM}/v_{dc}$) for the possible switching states of the QZSI. As shown in Table 2, the CMV depends on the switching state of the inverter. For the sake of illustration, the typical waveforms of the common-mode voltage during one sample period for 1Φ/SB/SPWM and 1Φ/SVM6 schemes are shown in Figure 8. Similarly, the CMV waveforms of all the analyzed schemes in Figure 7 are given in Figure 9 and Figure 10, respectively. It can be observed that various PWM schemes have different waveforms and characteristics of CMV, as shown in the following subsections.

4.1. CMV—Root Mean Square

The mean squared CMV for switching interval, $v_{cm-MS}^2$ can be evaluated from [55]

$$v_{cm,MS}^2\left(M,\theta \right)=\frac{1}{T_s}{{\displaystyle \int }}_0^{T_s}{v}_{cm}^2 dt$$

(4)

where $T_s$ is the sampling time.

For the sake of illustration Figure 10a shows the CMV of 1Φ-ST/SVM6. As a result of analyzing the CMV waveforms and switching sequence of this scheme, the CMV mean square (MS) value is determined from

$$v_{cm,MS}^2=\frac{2}{T_s}{V}_{dc}^2\left(\underset{\frac{T_0}{2}}{\overset{x_1}{{\displaystyle \int }}}\frac{1}{9}dt+\underset{x_2}{\overset{x_3}{{\displaystyle \int }}}\frac{4}{9}dt+\underset{x_4}{\overset{x_5}{{\displaystyle \int }}}dt\right)$$

(5)

where $x_1=T_0/2+T_1/2$, $x_2=x_1$+$T_{sh}/6$, $x_3=x_2+T_2/2$, $x_4=x_3+T_{ST}/6$, $x_5=x_4+T_z/4-T_{sh}/4$ and $T_{ST}=k{T}_z$. Hence,

$$\begin{array}{cc}{v}_{cm,MS}^2=\frac{1}{9}{V}_{dc}^2\left[d_1+4d_2+9d_z\left(\frac{1}{2}-\frac{k}{2}\right)\right],& 0\le k\le 1\end{array}$$

(6)

where $d_1,d_2,d_z$ are the active and null vectors’ duty cycles, respectively.

The duty cycles can be determined from

$$\{\begin{array}{l}{d}_1=M\sin \left(\pi /3-\theta \right)\hfill \\ d_2=M\sin \theta \hfill \\ d_z=1-d_1-d_2\hfill \end{array}$$

(7)

The MS-CMV per fundamental period, $V_{cmf-MS}^2$ is

$$V_{cmf-MS}^2\left(M\right)=\frac{3}{\pi }{{\displaystyle \int }}_0^{\pi /3}{v}_{cm,MS}^2\left(M,\theta \right) d\theta$$

(8)

Based on (8), the analytical expression for the RMS-CMV can be governed by

$$V_{cmf-RMS}=\sqrt{\frac{3}{\pi }{V}_{dc}^2\left[\left(\frac{\sqrt{3}k}{4}-\frac{\sqrt{3}}{9}\right)M+\frac{\pi }{6}-\frac{\pi k}{6}\right]}$$

(9)

As a result of (9),

Table 3. The effective CMV for all presented modulation schemes.

	3Φ-ST Modulation Techniques				1Φ-ST Modulation Techniques
Technique	3Φ/SB/SPWM	3Φ/SB/THM 3Φ/SB/SYM 3Φ/MCB/SPWM 3Φ/MCB/THM 3Φ/MCB/SYM	3Φ/MB/SPWM 3Φ/MB/THM 3Φ/MB/SYM 3Φ/SB/-DCCM 3Φ/MB/+DCCM 3Φ/MB/-DCCM	3Φ/SB/+DCCM	1Φ/SVM6 1Φ/SVM4(a) 1Φ/SVM2	1Φ/SVM4(b)	1Φ/SB/SPWM	1Φ/SB/THM 1Φ/SB/SYM	1Φ/MB/THM 1Φ/MB/SYM 1Φ/MB/MSVM 1Φ/SB/-DCCM 1Φ/MB/+DCCM 1Φ/MB/-DCCM	1Φ/SB/MSVM 1Φ/SB/+DCCM
MS Value	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{\pi }{6}-\frac{\sqrt{3}}{9}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{\sqrt{3}\left(3\pi -4\right)}{36}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{5\sqrt{3}}{36}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{\sqrt{3}\left(6\pi -13\right)}{36}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left[\left(\frac{\sqrt{3}k}{4}-\frac{\sqrt{3}}{9}\right)M+\frac{\pi }{6}-\frac{\pi k}{6}\right]$	$\frac{3}{\pi }{V}_{dc}^2\left[\left(\frac{\sqrt{3}k}{3}-\frac{7\sqrt{3}}{36}\right)M+\frac{2\pi }{9}-\frac{2\pi k}{9}\right]$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{\pi }{6}-\frac{\sqrt{3}}{9}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{\sqrt{3}\left(3\pi -4\right)}{36}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{5\sqrt{3}}{36}\right)M$	$\frac{3}{\pi }{V}_{dc}^2\left(\frac{\sqrt{3}\left(6\pi -13\right)}{36}\right)M$
Group	CMF1	CMF2	CMF3	CMF4	CMF5	CMF6	CMF1	CMF2	CMF3	CMF4

shows the CMV-RMS for all schemes. The results are divided into six groups, from CMF1 to CMF6. It is worth noting that 3Φ-ST schemes have the same waveform as in Figure 9a, whereas 3Φ/MB schemes have a Figure 9b waveform. Furthermore, 1Φ-ST schemes have the same waveform as Figure 10e, while 1Φ/MB have the waveform of Figure 10g. The difference between them is $v_a,v_b,v_c$ and $D_{ST}$ [55].

4.2. Maximum Value of CMV and Its $dv/dt$

It is critical to note that the maximum and dv/dt of the CMV values also influence the leakage current. These values are affected by several factors, including the selection of vectors and the switching sequences. Using Figure 10a as an example, the peak CMV value and dv/dt of 1Φ/SVM6 scheme can be as follows

$${\widehat{v}}_{CM}=B{E}_s$$

(10)

$$\frac{dv}{dt}=B{E}_s$$

(11)

where $dv/dt$ presents the highest CMV difference at the switching state’s transition.

For $k=1$, the 1Φ/SVM6 method has the same CMV of MB case of Figure 8b. So, the maximum CMV and $dv/dt$ are determined from

$${\widehat{v}}_{CM}=\left(2/3\right)B{E}_s$$

(12)

$$dv/dt=\left(2/3\right)B{E}_s$$

(13)

Similarly, peak CMV and $dv/dt$ for all schemes are evaluated. The results are given in

Table 4. The peak CMV and $dv/dt$ for all presented modulation schemes.

	3Φ-ST Modulation Techniques					1Φ-ST Modulation Techniques
Technique	SB/SPWM	SB/THM SB/SYM MCB/SPWM MCB/THM MCB/SYM SB/+DCCM	MB/SPWM MB/THM MB/SYM MB/+DCCM MB/+DCCM	SB/-DCCM	MB/-DCCM	SVM6 SVM4(b) SVM2	SVM4(a)	SB/SPWM	SB/THM SB/SYM	SB/MSVM	MB/THM MB/SYM MB/MSVM MB/+DCCM MB/-DCCM	SB/+DCCM	SB/-DCCM
$\mathit{d}{\mathit{v}}_{\mathit{C}\mathit{M}}/\mathit{d}\mathit{t}$	$B{E}_s$	$B{E}_s$	$2B{E}_s/3$	$B{E}_s/3$	$B{E}_s/3$	$B{E}_s$	$B{E}_s$	$B{E}_s$	$B{E}_s$	$B{E}_s/3$	$2B{E}_s/3$	$B{E}_s$	$2B{E}_s/3$
Peak CMV	$B{E}_s$	$B{E}_s$	$2B{E}_s/3$	$2B{E}_s/3$	$2B{E}_s/3$	$B{E}_s$	$B{E}_s$	$B{E}_s$	$B{E}_s$	$B{E}_s$	$2B{E}_s/3$	$B{E}_s$	$2B{E}_s/3$
Groups	GB1	GB2	GB3	GB4	GB5	GB6	GB7	GB1	GB2	GB8	GB3	GB2	GB9

. It can be divided based on their values into nine groups (GB1–GB9).

5. Leakage Current Analysis

As we discussed before, transformerless PV systems are more efficient, lighter, and smaller due to the lack of transformers. However, leakage currents are caused by common-mode voltage fluctuations. In the analyzed system, the leakage current flows through the stray capacitance ($C_{pv}$) and ground resistance ($R_g$). The capacitance $C_{pv}$ is defined as the stray capacitance between the PV array and its grounded frame. The leakage current path and the stray capacitance in QZSI are shown in Figure 6.

5.1. Three-Phase ST Modulation Techniques

Figure 11 shows the CMV and leakage current waveforms for 3Φ ST modulation techniques. These results are taken for a given gain that satisfied 220 V output phase voltage for $E_s$ equals 150 V.

Based on these results, the following notes can be made:

• Both CMV and leakage current in cases of 3Φ/SB/THM and 3Φ/SB/SYM are similar and less than those of 3Φ/SB/SPWM.
• Both 3Φ/MB/SPWM, 3Φ/MB/THM, and 3Φ/MB/SYM have the same value as CMV. On the other hand, the value of leakage current in the case of 3Φ/MB/THM is lower than that of 3Φ/MB/SPWM and 3Φ/MB/SYM.

Both 3Φ/MCB/SPWM, 3Φ/MCB/THM and 3Φ/MCB/SYM have the same value as CMV. On the other hand, leakage current in the case of 3Φ/MCB/THM and 3Φ/MCB/SYM is higher than those of 3Φ/MCB/SPWM.

• The CMV and leakage current value of 3Φ/SB/+DCCM is greater than 3Φ/SB/-DCCM.
• The CMV and the leakage current value of 3Φ/MB/+DCCM are similar and equal to 3Φ/MB/-DCCM.
• Among all the given techniques, 3Φ/MB/-DCCM has the lowest leakage current value in the case of 3Φ ST modulation techniques.

5.2. Single-Phase Shoot-through Modulation Techniques

Figure 12 gives CMV and leakage current waveforms for 1Φ ST control methods. From the results, the following notes can be made:

• In the case of SVM schemes, 1Φ/SVM4 (a) has the most considerable value of CMV and leakage current. The lowest value of leakage current is 1Φ/SVM2. The CMV of 1Φ/SB/SPWM is more significant than those of 1Φ/SB/THM, 1Φ/SB/SYM and 1Φ/SB/MSVM. Contrary, the leakage current of 1Φ/SB/MSVM is lower than those of 1Φ/SB/SPWM, 1Φ/SB/THM, and 1Φ/SB/SYM.
• The leakage current of 1Φ/MB/MSVM is lower than 1Φ/MB/THM and 1Φ/MB/SYM.
• The CMV and leakage current of 1Φ/SB/-DCCM is lower than 1Φ/SB/+DCCM.
• Among all the given techniques, 1Φ/SVM2 has the lowest leakage current in 1Φ ST modulation techniques.

6. Spectrum Analysis of QZSI Modulation Techniques

Figure 13 and Figure 14 show the spectrum using FFT of CMV and leakage current for 3Φ ST and 1Φ ST modulation techniques at constant voltage gain.

• For 3Φ/SB/THM and 3Φ/SB/SYM spectrum, the CMV and leakage current are similar. This is due to similar waveforms, as discussed later. Further, 3Φ/SB/SPWM has a higher value of CMV and leakage current. For 3Φ/MB/SPWM, 3Φ/MB/THM and 3Φ/MB/SYM spectrum, the CMV and leakage current are similar.
• For 3Φ/MCB/SPWM, 3Φ/MCB/THM, 3Φ/SB/THM and 3Φ/MCB/SYM spectrum, the CMV and leakage current are similar.
• The 3Φ/SB/-DCCM Spectrum has lower CMV and leakage current at $f_o$. Moreover, harmonic is more petite than 3Φ/SB/+DCCM for the CMV and leakage current.
• For 3Φ/MB/+DCCM Spectrum, the leakage current is higher than 3Φ/MB/-DCCM; this is due to similar waveforms as discussed later. The CMV and leakage current spectrum of 1Φ/SB/SPWM is higher than 1Φ/SB/THM, 1Φ/SB/SYM and 1Φ/SB/MSVM.
• The leakage current spectrum magnitudes of 1Φ/MB/MSVM are lower than 1Φ/MB/SPWM and 1Φ/MB/THM.

7. The Relationship between CMV and Leakage Current

Figure 15 and Figure 16 show the leakage current magnitude and FFT analysis of all the analyzed modulation schemes at constant voltage gain. It is observed from Figure 15 that the 3Φ/MB/-DCCM has the lowest leakage current. It is important to note that the value of the leakage current depends on the rate of change of the CMV waveform, as can be defined by [29]

$$i_{leakage}=c_{pv}d{v}_{cm}/dt$$

(14)

It can be noticed from Figure 16 that:

• The low-frequency components of the CMV do not appear on the corresponding leakage current spectrum, while the HF components of the CMV leads to significant leakage current magnitudes at the same frequencies.
• The 3Φ/MB/-DCCM produces the lowest FFT components of the leakage current and CMV compared with the other schemes. This result confirms the previous conclusion from the leakage current magnitude.

8. Simulation Results

In this section, a simulation study is conducted for all the analyzed modulation schemes for QZSI in this paper. To test the validity of the presented theoretical analysis, twenty-eight MATLAB/Simulink models for the PWM schemes presented in Figure 7 were conducted with the parameters given in

Table 5. Simulation Parameters.

Parameter	Value	Parameter	Value
Input voltage	150 V	Output frequency	50 Hz
		Switching frequency	7.5 kHz
Z-network components
Inductances	$L=5$ mH	Capacitances	$C=450 \mathsf{\mu }$F
Load parameters
Resistance	10 Ω	Inductance	50 mH

. Moreover, the simulation results are obtained to compare the different techniques according to the following criteria: Performance characteristics, CMV according to (RMS value, $d{v}_{CM}/dt$ and peak value).

8.1. Comparison in Terms of Performance Characteristics

Figure 17, Figure 18, Figure 19 and Figure 20 present the performance relations for all the analyzed schemes based on simulation results and analytical study using derived relations given in Table 1. Figure 17 and Figure 18 show the dependency of the voltage gain ($G$) and the shoot-through duty ratio ($D_{sh})$ on the modulation index ($M$), respectively. Figure 17 shows the minimum value of modulation for each modulation technique. Figure 19 shows the dependency of the capacitor voltage ($v_{c1}$) to the normalized phase voltage. Figure 20 shows dependency between voltage gain and voltage stress for all modulation schemes. It can be noted that, in all cases, the simulation waveforms and the analytical study are in reasonable agreement. Moreover, the following notes can be observed:

• From Figure 17, 1Φ-ST/SVM4(a) or G5 scheme is the optimal choice because it has a wider operating region.
• From Figure 18, the G6 scheme has the highest values for the ST interval compared with other schemes.
• G6 is the best scheme because it has a higher shoot-through duty ratio and higher boosting action.
• From Figure 19, the G6 scheme is the best with lower values compared with the other scheme for capacitor voltage. G6 is the best scheme because the stress of the capacitor is low, so the capacitor has a low cost and size.
• From Figure 20, the G6 scheme is the best with lower values compared with the other scheme at the same voltage gains for voltage stress.

In the case of G6, the stress voltage of the switch is low, so the stress, losses, rating, and cost of the switch are low.

Note that the minimum value of voltage gain (G) and modulation index (M) of all presented schemes are shown in

Table 6. The minimum value of voltage gain (G) and modulation index (M) of modulation techniques.

Group (Method)	G1	G2	G3	G4	G5
$G_{min}$	$1/2$	$1/\sqrt{3}$	$\pi /3\sqrt{3}$	$\pi /3\sqrt{3}$	$4\pi /9\sqrt{3}$
$M_{min}$	$1/2$	$1/\sqrt{3}$	$\pi /3\sqrt{3}$	$\pi /3\sqrt{3}$	$2\pi /9\sqrt{3}$

.

8.2. Comparison in Terms of CMV Characteristics

Figure 21 shows the relation between the normalized RMS value of CMV ($v_{cmf-RMS})$ to DC-link voltage and modulation index, $M$ for all schemes. Both theoretical analyses and simulations are used in these results. Moreover, the dv/dt of the CMV relationship with $M$ in the analyzed schemes is shown in Figure 22. The peak value of the CMV relationship with the modulation index has the exact curve of dv/dt (Figure 22). Figure 23 shows the dependency of ($v_{cmf-RMS})$ on the voltage gain. Additionally, the peak value of CMV and its dv/dt relationships with the voltage gain for all modulation schemes are shown in Figure 24 and Figure 25, respectively. For all results, there is good agreement between simulation and analysis.

8.3. In terms of the Modulation Index

• From Figure 21, it can be noticed that the CMF3 group as well as CMF5 and CMF6 groups for $k=1$ (as defined in Table 3) has the minimum value of RMS-CMV.
• The minimum value of CMV-RMS results in the minimum value of leakage current.
• From $dv/dt$ points of view, Figure 22, 1Φ-ST/SVM4(a) or GB7 scheme is the appropriate choice with lower magnitudes when compared to the other schemes in the modulation index range between 0.4 to 0.7. For the modulation index from 0.7 to 1.2, 3Φ/SB/-DCCM and 1Φ/SB/MSVM provide minimum values of $dv/dt$ when compared with the other scheme. So, the leakage current is low.

8.4. In terms of Voltage Gain

• From Figure 23, for the same voltage gain, it can be observed that CMF3 group has the lowest value of RMS-CMV.
• From Figure 24, for the peak CMV, it is noted that GB3 and GB5. These groups provide minimum values of peak CMV compared with the other scheme.
• From Figure 25, for dv/dt, 3Φ/MB/-DCCM scheme provides minimum values compared with the other scheme.

9. Experimental Results

A laboratory setup has been established to verify the theoretical and simulation results. Figure 26a shows the main parts of implemented proposed system. The system consists of three parts, namely, power, control, and interface circuits. The power circuit consists of a traditional voltage source inverter (VSI) and impedance network. The parameters of the experimental setup are listed in

Table 7. QZSI Experimental setup parameters.

Parameter	Value	Parameter	Value
Source voltage (E)	30 V	Output frequency (f)	50 Hz
Z-inductance (L)	1.25 mH	$\mathrm{Switching} \mathrm{Frequency} (f_s)$	5 kHz
Z-capacitance (C)	$150 \mathsf{\mu }$F	Modulation index (M)	0.8
$\mathrm{Sampling} \mathrm{time} (T_s)$	2 × 10−4	Inductive load (R+L)	11 Ω + 5 mH
Voltage gain (G)	3	$\mathrm{Output} \mathrm{voltage} (V_{out})$	90 V

.

The VSI contains three power transistor modules of CM300DX-12A type. The Z-network comprises two inductors L and two capacitors C connected with a diode. The control of the QZSI has been implemented by using a DSP board of the Delfino F28379D LaunchPad Kit controller board. The interface circuits consist of the buffering circuit, gate drive circuit VLA536, and current transducer LA-25-P. Figure 26b shows a photograph of the complete experimental setup. Where A: The laptop is connected to the DSP control circuit, B: The rectifier circuit, C: The impedance network of QZSI, D: The power circuit and gate drive circuit, E: The oscilloscope, and F: The R-L load.

The 1ф/SB/MSVM has been chosen as a sample of the studied modulation schemes. Figure 27, Figure 28, Figure 29 and Figure 30 show the experimental waveforms results of gating pulses of the upper and lower switch of phase a, load current, inductor current, DC-link voltage, and common-mode voltage. A zoom for each result is shown.

For checking the experimental results, the corresponding simulations have also been obtained. From the shown figures, it can be observed that both simulation and experimental results are in good agreement for all cases. The following notes can be observed.

• Figure 27 shows the gating pulses of inverter switches of leg-a. The shown zooming clarifies the periods of non-ST (left half of figure) and ST (right half of the figure). It is noticed that in non-ST, the pulses of two switches are complimentary, while in ST, the ST period is obtained when two switches are on.
• Figure 28 shows the inductor current and load current ($i_{abc})$ waveforms.
• The inductor current, DC-link voltage, and load current of one phase are shown in Figure 29. It can be noticed that the DC-link voltage is zero during ST periods. This result is matched with the steady-state analysis mentioned in Section 2.
• The inductor current and common-mode voltage are shown in Figure 30. It can be noticed that in charging operation (ST mode), the CMV is equal to zero but in discharging operation (non-ST mode), the CMV have three voltage level ($1/3, 2/3, 1) v_{dc}$ as discussed in Table 2.

10. Conclusions

An in-depth investigation and review of Pulse Width Modulation (PWM) schemes for three-phase transformerless PV systems based on a quasi-Z-source inverter (QZSI) is presented in this paper. Since transformers are omitted from these systems, the fluctuation of the generated Common Mode Voltage (CMV) by the PWM schemes produces leakage currents in the parasitic capacitance. This paper gives a comprehensive review and evaluation of most of the applied PWM schemes for QZSI in terms of CMV characteristics using both analytical and simulation approaches. Moreover, it provides a microscopic view of how shoot-through intervals and modulation techniques influence the CMV waveform of the analyzed system. For each modulation scheme, closed-form equations are derived from RMS-CMV values. In each PWM scheme, the peak value of CMV and the corresponding dv/dt is determined.

Using the obtained results, an optimal PWM that provides a minimum CMV performance is identified. It is worth noting that the space-vector-based modulation scheme called 1Φ/SVM4(a) in this paper is the most appropriate choice to modulate the three-phase QZSI for transformerless PV systems from the CMV characteristics.