**1. Introduction**

In terms of harmonics, the loads are classified into two types, linear loads and nonlinear loads. A linear load [1] is one which, when supplied by an AC source at fundamental frequency, can produce only fundamental AC currents. Non-linear loads, however, generate harmonic currents. The use of non-linear loads can inject harmonic currents into URDN. These harmonic injections can cause overheating of the equipment, insulation stress on winding in electric machines, added power loss in the equipment, and interference with the communication. Therefore, HPFAs are essential for finding the harmonic distortion level on URDN. In [2], based on current injection, graph theory, and the sparse matrix technique, a three-phase HPFA is proposed. The authors of [3] utilized the decoupled harmonic power flow (DHPF) algorithm to present the results of harmonic power flow calculations. In [4,5], a forward/backward-based HPFA for DN is proposed that considered the special topology of radial distribution networks (RDN). The authors of [6] developed an iterative time-dependent, computer-aided HPFA by combining the time-dependent cross-coupled

**Citation:** Satish, R.; Vaisakh, K.; Abdelaziz, A.Y.; El-Shahat, A. A Novel Three-Phase Harmonic Power Flow Algorithm for Unbalanced Radial Distribution Networks with the Presence of D-STATCOM Devices. *Electronics* **2021**, *10*, 2663. https:// doi.org/10.3390/electronics10212663

Academic Editor: Christos Volos

Received: 6 October 2021 Accepted: 28 October 2021 Published: 30 October 2021

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harmonic model. To obtain this model, large data are received from the practical DNs. Tracing THD in secondary RDN with photovoltaic uncertainties by multiphase HPFA is discussed in [7]. The authors of [8] propose a new combined analytical technique (CAT) for HPFA in the presence of correlated input uncertainties from photovoltaic (PV) systems in RDN. In [9], static capacitors are allocated in shunt along RDN using a Cuckoo search optimization method. For allocating and sizing of capacitors optimally, a flower pollination algorithm is proposed in [10].In [11,12], a novel three-phase power flow algorithm for URDN with multiple integrations of distributed generations (DGs) and a D-STATCOM device is presented. In [13], an electrical energy management in unbalanced distribution networks using virtual power plant concept is presented. In [14], an efficient multi-objective optimization approach based on the supervised big bang–big crunch method for the optimal planning of a dispatchable distributed generator is presented. This approach aims to enhance the system performance indices by the optimal sizing and placement of distributed generators connected to balanced/unbalanced distribution networks. The optimal planning of distributed generators in unbalanced distribution networks using a modified firefly method is presented in [15].

The authors of [16] examine the utilization of D-STATCOM without a capacitor to compensate for power quality in DNs. The optimal D-STATCOM allocation in DNs is discussed in [17,18]. In [19], an optimal algorithm to control a three-phase D-STATCOM is proposed. This algorithm can give harmonic compensation as well as reactive power compensation in linear and non-linear loads, which are connected in three-phase. In [20], for minimizing the total real power loss in DNs with the interfacing of DGs, plug-inhybrid electric vehicles (PHEVs), and D-STATCOM, a genetic algorithm is proposed. A control technique is developed in [21] for D-STATCOM for extracting the fundamental weight components from non-sinusoidal load currents to produce grid reference currents. For harmonics elimination, the injection of reactive power and balancing of load, this D-STATCOM is developed. The D-STATCOM's performance is examined in different working modes. The combination of two problems such as the reconfiguration and interfacing of D-STATCOM can be solved by using the grey wolf optimization (GWO) method proposed in [22].

The proposed power flow algorithm (PFA) can give both fundamental and harmonic solutions. The solution of the fundamental power flow algorithm (FPFA) discussed in this paper is used in modelling the linear and non-linear loads for HPFA. The BNM and BRNM developed in this paper make the implementation of the PFA simple. The bus numbers and branch numbers of newly created sections of RDN are stored in BNM and BRNM, respectively. This paper is arranged in the following order. The network components' modelling is addressed in Section 2. The algorithm to develop BNM and BRNM is discussed in Section 3. In Section 4, the three-phase HPFA with the integration of the D-STATCOM device is discussed. Section 5 presents the test studies and discussions on the IEEE−13 bus and IEEE−34 bus URDN. Section 6 discusses the concluding remarks.
