**1. Introduction**

The participation of renewable energy sources (RESs), battery storage systems, and other flexible loads, commonly referred to as prosumers, changes the character of distribution networks (DNs) from passive to active. For this reason, both generating units and loads are included in the determination of power flow and voltage profile. The nature of prosumers is unpredictable and intermittent, so existing DNs are not adapted to their influence. This is particularly evident in frequent voltage violations [1]. A voltage rise is addressed as a major issue caused by prosumers and impacts DNs [2]. The distribution system operator (DSO) is responsible for maintaining voltage within the allowable limits for the secure operation of DNs [3]. However, voltage control mechanisms that were once applicable in passive DNs become less valid and new mechanisms are required [4–6].

While DG can cause voltage violation in the DN, the same DG can help solve the problem of voltage violation, for example by managing active or reactive power. This problem/solution principle is especially interesting in the case of reactive power management [7]. When it comes to RESs in DNs, the main representative is a photovoltaic (PV) system [8,9]. Traditionally, most DSOs require PVs to operate with the unit or fixed power factor [1]. PV inverters have several modes of operation, but volt–VAR control has become certainly significant for voltage optimization. A major advantage of using a PV inverter and volt–VAR control is that reactive power can be injected/absorbed even where there is no production. Since prosumers contribute to the complexity and unpredictability of such DNs, it is crucial to use optimization methods and analyzed software tools that allow DN monitoring and finding suitable and optimal set points for PV inverters. In addition,

**Citation:** Dubravac, M.; Fekete, K.; Topi´c, D.; Barukˇci´c, M. Voltage Optimization in PV-Rich Distribution Networks—A Review. *Appl. Sci.* **2022**, *12*, 12426. https://doi.org/ 10.3390/app122312426

Academic Editors: Luis Hernández-Callejo, Jesús Armando Aguilar Jiménez and Carlos Meza Benavides

Received: 4 November 2022 Accepted: 1 December 2022 Published: 5 December 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/).

optimal power flow (OPF) has proven to be an efficient tool for the operation of active DNs. In order to illustrate the problem/solution principle of PV inverters, a case study is developed in this paper presenting the low voltage DN with the connected PVs. Different power flow simulations are presented and they include:


Nowadays, optimal management of active DNs represents an attractive topic, and a large and growing body of literature focuses on this topic. Some related reviews on the optimization DNs are listed in Table 1. Refs. [10,11] show the impact of PV on DNs, the related problems, and possible solutions. Refs. [12–14] study voltage violation mitigation and voltage control strategies. Ref. [12] deals with voltage control methods in DNs with PVs and their advantages and disadvantages. In addition to [12], a comprehensive review of voltage control methods is given in [13]. In [14], voltage control models and methods are divided according to the communication strategy. The application of OPF in DNs is discussed in [15,16]. The researchers in [15] address a probabilistic approach to solving OPF in active DN. The authors in [16] study OPF in smart DNs and microgrids according to objectives, methods, and future challenges.


**Table 1.** Related review papers on the optimization of DNs.

While refs. [15,16] present interesting and useful reviews of OPF application to modern DNs, they are mainly focused on active power objectives [16] and probabilistic OPF [15]. So far, the research gap is present in the area of voltage optimization objectives in the case of using PV inverters for reactive power management. The problem/solution principle of using PV inverter reactive power for voltage mitigation motivated the authors of this paper to focus their review on scientific papers that applies OPF for voltage optimization in the DN using PV inverter reactive powers. The contributions of this review paper are:

1. Summary and classification of OPF objectives and variables in the case of voltage optimization in the DNs using PVs reactive power.


This paper aims to provide the readers with starting points for OPF applications in PV-rich DNs and, in some way, to compare with conventional OPF. Therefore, the authors searched several bibliographical databases—IEEE Xplore, ScienceDirect, and MDPI.

The paper is structured as follows: Section 2 gives a prosumer definition, describes the voltage control capabilities of PV inverter, and presents the case study that illustrates the impact of PVs on the DN voltages. Section 3 addresses OPF in PV-rich DN—objectives and variables. OPF formulation and solution methods are discussed in Section 4. Test network models used in the literature are presented in Section 4. Conclusions with a note on future research are given in Section 5.

#### **2. PV Prosumers in Distribution Network**

In this section, various definitions and configurations of prosumers are presented. Then, the focus is on PVs and their voltage control capabilities. Finally, theoretical foundations are supported by the case study in which the part of the low voltage DN is presented and various cases are simulated.
