**1. Introduction**

Multilevel inverter (MLI) topologies have attracted interest in a variety of applications, including grid-connected PV applications, static VAR compensators, and active-powerfilter (APF) applications. MLIs have many advantages over conventional inverters, such as reducing the total harmonic distortion (THD) of the produced voltage and current, reducing the size of filters, reducing the switching frequency, and improving the inverter efficiency [1]. Many cascaded inverter topologies have been proposed in the literature [2]. Of these, cascaded H-bridge (CHB) topologies have advantages over other MLI topologies (e.g., layout simplicity, extreme modularity, and construction and control simplicity) because they are free of voltage-balance issues. Moreover, compared to other MLI topologies, CHB topologies use the fewest components at the same voltage levels [3,4]. Asymmetrical CHB topologies have been proposed in which the DC voltages are not symmetrical. The combination of these asymmetrical DC voltages results in the generation of increased voltage levels [5,6]. On the other hand, hybrid MLI topologies presented in the literature have been based on a three-phase voltage source inverter (VSI) unit with a CHB. In these topologies, H-bridge units are coupled to floating capacitors whose voltages must be carefully regulated. This complicates the control algorithm [7,8].

Recently, research into the development of APF applications has increased [9,10]. APFs are electronic devices that can be accurately used to eliminate the harmonic contents in a current. The harmonics in power systems can be created by nonlinear loads connected to the public grid. Some of these loads are computers with a switched-mode power supply,

**Citation:** Noman, A.M.; Alkuhayli, A.; Al-Shamma'a, A.A.; Addoweesh, K.E. Hybrid MLI Topology Using Open-End Windings for Active Power Filter Applications. *Energies* **2022**, *15*, 6434. https://doi.org/ 10.3390/en15176434

Academic Editors: Najib El Ouanjli, Saad Motahhir, Mustapha Errouha and Marco Pau

Received: 21 May 2022 Accepted: 29 July 2022 Published: 2 September 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

motor drives, and electronic light ballasts (fax machines, medical equipment, etc.). These harmonics may cause unwanted effects, such as heating of sensitive electrical equipment or of the generators and transformers, which leads to increased core loss and may cause transformer and equipment failure, random circuit breaker tripping, flickering lights, high neutral currents due to zero sequence harmonics, and conductor losses [11]. As a result, these harmonics must be eliminated. There are three different types of harmonic filters: passive, active, and hybrid. The advantages of APFs over passive filters are numerous. They can, for example, suppress supply-current harmonics as well as reactive currents. On the other hand, certain harmonics will involve their own passive filter, hence there will be more passive filters needed if there are more harmonics to remove. Because only large harmonics with lower frequencies are usually removed, the filters will be bulky due to the geometric size of the inductor [12]. In contrast to passive power filters, APFs can eliminate any harmonics by using a suitable control and the performance of APFs is unaffected by the characteristics of the power distribution system [9,11,13,14].

Several APF topologies using the conventional three-phase VSI have been proposed [15–17]. In addition, some of the proposed APFs were based on the classical three-level H-bridge inverter [18]. Recently, the use of MLI topologies in APF applications has become a hot topic [19,20]. An APF based on a seven-level neutral-point clamped (NPC) MLI was proposed in [21]. The authors used LS–PWM and fuzzy control approaches to eliminate current harmonics generated by nonlinear loads. Others [19] used a three-level NPC for activepower-filter applications. The authors used a fuzzy-logic controller and a fractional-order proportional-integral (PI) controller to control the proposed system. From another point of view, an APF based on a three level NPC-T type was proposed in [20,22]. The authors in [23] proposed a five-level HB-NPC MLI for APF applications with an experimental validation. Other authors used a CHB for APF applications due it the advantages of the CHB such as simplicity and possession of a high modularity [24,25]. Both CHN topologies were proposed for APFs either by directly connecting the H-bridges in series or by cascading the H-bridges using transformers [26–28]. Moreover, cascaded MLI topologies are used for APF applications [29,30]. The authors in [30] proposed a shunt APF based on cascaded MLI topology using a single power source with three-phase transformers. The proposed scheme could adjust for polluted loads with high harmonics and a poor power factor. To compute compensating currents, the dq theory was applied. A prototype was built to validate the simulation results by the experimental results.

In this paper, a hybrid MLI topology is proposed for APF applications. The proposed MLI topology conjoins the cascaded H-bridge MLI and the cascaded three-phase VSI topology using open-end windings and was first proposed and tested under different load parameters, as presented in [31]. In addition, this new topology has been patented, as seen in [32]. However, the previous paper focused only on the topology itself. The topology was not used in any applications. This paper is the first to detail the utilization of the new topology for the active power filter and for grid-connected PVs. The proposed MLI is used to compensate the harmonic currents of the nonlinear load, while the grid supplies the fundamental positive-sequence currents of the load. A closed-loop control is proposed for both applications—the APF and the PV–grid connection. Finally, the proposed MLI was experimentally implemented in the lab, and it was tested for the two applications.

The rest of the paper is structured as follows: the suggested APF topology and corresponding control approaches are discussed in Section 2, the simulation results are described in Section 3, and experimental validation of the proposed topology for the two applications is described in the Section 4.

#### **2. The Proposed Hybrid Active-Power-Filter Topology**

A three-phase multilevel high-voltage/high-power converter is used in this topology. It is a hybrid arrangement that combines two common multilevel configurations: a cascaded H-bridge MLI and a three-phase cascaded VSI. These two configurations are joined together to create the hybrid configuration. Figure 1 depicts the suggested cascaded

MLI architecture. This novel topology has been given a patent with the number US 10, 141, 865 B1. It is suitable for a wide variety of grid-connected applications, including power-factor correction, static-VAR compensation, and grid-connected photovoltaic (PV) systems. The proposed architecture is made up of two components linked by an open-end windings transformer.

**Figure 1.** Proposed APF topology. Upper part: This part is the conventional cascaded H-bridge MLI which consists of three-phase systems. Each phase consists of N H-bridge cells that are cascaded as shown in the stage 1 of Figure 1 such that the *ay*<sup>1</sup> terminal of H-bridge cell 1 in phase a, for example, is connected to the *ax*<sup>2</sup> terminal of the next H-bridge cell. In addition, the *ay*(*N*−1) terminal is connected to the *axN* terminal of the last H-bridge cell. The same idea is applied to phases b and c. Lower part: This part is a three-phase triple-voltage source inverter, which is made up of three VSIs. Each unit is a three-leg, two-level inverter, and the three units are linked together in a chain, as shown in the lower part of Figure 1. The three VSIs are cascaded with one another by using open-end winding transformers. Finally: The upper part and the lower part are connected to each other via open-end windings. The terminals *ayN*, *byN*, and *cyN* of stage 1 are connected together to a common point NN. The terminals *ax*1, *bx*1, and *cx*<sup>1</sup> of the upper part are connected to the points *a*1, *b*1, and *c*<sup>1</sup> of the open-end windings transformers, respectively. The three points *a*21, *a*22, and *a*<sup>23</sup> of the lower part are connected to the points *a*1, *b*1, and *c*<sup>1</sup> of the open-end windings transformers, respectively. The secondary sides of the transformer are connected in Y connection and the terminals are connected to the grid and to the nonlinear loads.

As shown in this figure, the proposed MLI is capable of supplying the extracted PV power to the nonlinear loads and of injecting power into the grid. The idea is to compensate the harmonics generated by the nonlinear loads while supplying balanced three-phase currents to the grid. The control scheme proposed in [33] has been extended to be used for the proposed APF in this paper. The proposed control scheme is used to inject balanced three-phase low harmonic currents into the grid. If the three-phase loads are nonlinear, then the load currents will contain harmonics, which may reduce the current quality of the grid. Therefore, the harmonic contents of the load currents must be extracted to be compensated by the MLI. Consequently, the grid current will be balanced and contain low harmonic contents. The current of the nonlinear loads may contain positive-, negative-, or zero-sequence harmonics.

Therefore, the following steps are considered:

1. Extract the fundamental positive-sequence component of the load current using the following equation:

$$
\begin{bmatrix} i\_{Lzro} \\ i\_{Lpos} \\ i\_{Lne\_X} \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & a^2 \\ 1 & a^2 & a \end{bmatrix} \begin{bmatrix} i\_{La} \\ i\_{Lb} \\ i\_{Lc} \end{bmatrix} \tag{1}
$$

where *a* = *ej*2*<sup>π</sup>*/3, *iLzero*, *iLpos*, and *iLneg* are the zero, positive, and negative components of the load currents, respectively.

2. The maximum value of the fundamental component of the load current is extracted, and the harmonic contents of the load currents can be extracted by the following equation:

$$
\begin{bmatrix} i\_{LA(harm)} \\ i\_{LB(harm)} \\ i\_{LC(harm)} \end{bmatrix} = i\_{L\text{pos\\_max}} \begin{bmatrix} \sin(\Theta) \\ \sin(\Theta - 120^\circ) \\ \sin(\Theta + 120^\circ) \end{bmatrix} - \begin{bmatrix} i\_{La} \\ i\_{Lb} \\ i\_{Lc} \end{bmatrix} \tag{2}
$$

where *iLA*(*harm*), *iLB*(*harm*), *and iLC*(*harm*) are the extracted harmonic components of the load currents of phases a, b, and c, respectively.

3. The extracted harmonic components of the load currents are then converted into a dq frame as shown in Figure 2.

**Figure 2.** Extraction of the load harmonic currents.

From another perspective, the main goal of the control scheme is to produce reference currents that deliver only available active power to the grid while maintaining unity power factor. The DC links share the same active phase grid currents. These DC-link voltages are compared to their respective reference voltages.

If the DC-link voltages are accurately regulated by the control system, then:

$$V\_{dcA} = V\_{dcB} = V\_{dc\mathbb{C}} = V\_{dctot} \tag{3}$$

where *VdcA*, *VdcB*, and *VdcC* are the corresponding DC-link voltages of the phases a, b, and c, respectively.

The d-q components of the terminal voltages of the proposed MLI are given by:

$$\begin{cases} V\_d = L\_s \frac{di\_d}{dt} - (\omega L\_s) i\_\emptyset + d\_{nd} V\_{dctot} \\ V\_\emptyset = L\_s \frac{di\_\emptyset}{dt} + (\omega L\_s) i\_d + d\_{n\emptyset} V\_{dctot} \end{cases} \tag{4}$$

The sequential function *dnX* is given by:

$$
\begin{bmatrix} d\_{nA} \\ d\_{nB} \\ d\_{n\gets} \end{bmatrix} = \begin{bmatrix} \mathbf{C}\_A \\ \mathbf{C}\_B \\ \mathbf{C}\_C \end{bmatrix} - \frac{1}{3} (\mathbf{C}\_A + \mathbf{C}\_B + \mathbf{C}\_C) \tag{5}
$$

The DC link current is defined as follows:

$$C\_{dc}\frac{dV\_{dctot}}{dt} = d\_{nd}i\_d + d\_{nq}i\_q\tag{6}$$

Analyzing nonlinearity problems requires presention of a new model. These inputs could be written as:

$$\begin{array}{rcl} \mu\_d &= (\omega L\_s) i\_q - d\_{nd} V\_{dctot} + V\_d\\ \mu\_q &= -(\omega L\_s) i\_d - d\_{nq} V\_{dctot} + V\_q \end{array} \tag{7}$$

To ensure the unity power factor, the reactive current *iq* in Equation (6) should be set to zero. Therefore,

$$
\mu\_{dc} = \mathbb{C}\_{dc} \frac{dV\_{dc\text{tot}}}{dt} = d\_{nd} \frac{u\_{dc}}{d\_{nd}} \tag{8}
$$

In normal operation the following properties apply:

$$V\_d \approx d\_{nd} V\_{dctot} = d\_{nd} V\_{dctot} = \sqrt{\frac{3}{2}} V\_{max} \tag{9}$$

where *Vmax* is the maximum grid voltage. Substituting Equation (8) in (9) yields:

$$
\dot{u}\_d = \sqrt{\frac{2}{3}} \frac{u\_{dc}}{V\_{max}} V\_{dctot} \tag{10}
$$

The active current, *id*, is used to regulate the DC-link capacitors. As shown in Equation (10), the active reference current can be given as:

$$i\_{dA} = \sqrt{\frac{2}{3}} \frac{u\_{dcA}}{V\_{max}} V\_{dcA} \tag{11}$$

The reference active current of the grid is the sum of the three *id* active currents:

$$i\_{dref} = i\_{dA} + i\_{dB} + i\_{dC} = \sqrt{\frac{2}{3}} \frac{u\_{dcA}}{V\_{max}} V\_{dcA} + \sqrt{\frac{2}{3}} \frac{u\_{dcB}}{V\_{max}} V\_{dcB} + \sqrt{\frac{2}{3}} \frac{u\_{dcC}}{V\_{max}} V\_{dcC} \tag{12}$$

The DC-link voltage controllers of the proposed topology based on the analysis above can be seen in Figure 3. As seen in the analysis, the resulting signal from the DC-link controllers is the reference active current of the inverter, *idre f* . The inner current controller can be seen in Figure 4.

Where the proposed MLI is used in a PV application, the reference active grid current *idre f* is compared with the actual grid current, and the reference grid reactive current *iqre f* = 0 is compared with the actual reactive grid current *iq* to ensure unity power factor. However, where the proposed MLI is used in an APF application, the harmonic load current in the d axes *iLd*(*harm*) given from Figure 2 is then added to the reference current in the d axes *idre f* generated form the DC-link controllers. The total reference inverter currents are given as:

$$\begin{array}{l} i\_{drefTOT} = i\_{dref} + i\_{Ld(harm)}\\ i\_{qrefTOT} = i\_{Lq(harm)} \end{array} \tag{13}$$

**Figure 3.** Proposed voltage control scheme.

**Figure 4.** The current controllers. *Vdc*<sup>∗</sup> is the reference DC voltage.

Equation (13) states that the reference active current of the inverter equals the active current produced by the DC-links and the active harmonic load current. The complete proposed control scheme for APF application can be seen in Figure 5.

**Figure 5.** The proposed control scheme for APF application.

According to the proposed control scheme, two cases can be applied:
