### Literature Review  
Power-flow solutions in the literature present a vast universe of possibilities based on iterative procedures, linearization methods, and convex reformulations. Some of these approaches are presented below. The most classical power-flow methods in power-systems analysis correspond to the Gauss-Seidel (GS) and NR approaches [14]. The GS approach can be easily implemented using any programming language with its main advantage being that it can be used with complex numbers. However, it exhibits the worse performance in terms of processing time and number of iterations. With the purpose of improving the efficiency of the GS method, an accelerating factor \(\alpha\) that reduces the total number of iterations and the required overall processing time is used [17]. In the case of the NR approach, it is a methodology that is more commonly used in commercial software and is widely adopted by utilities [23]. The main advantage of the NR approach is that it converges in a few iterations, has low processing times, and can possibly be used with radial and meshed networks comprising multiple voltage-controlled nodes. The main problem with using the NR approach in distribution networks is the high dispersion of the Jacobian matrix, which may cause convergence problems when the matrix is inverted for updating the voltage magnitude and angle variables [19]. The authors of [24] proposed the use of the Levenberg-Marquardt (LM) algorithm for solving power-flow problems in electrical networks; this approach essentially comprises an alternative manner of presenting the NR formulation with the main advantage that a factor is added to the Jacobian in order to reduce the possible singularities in this matrix. For distribution networks, some of the most recognized approaches for addressing the power-flow problem are graph-based methodologies known as backward-forward and triangular methods [12; 20]. The backward-forward method is typically designed with an algorithmic structure using an iterative sweep based on currents in the backward stage to update the voltages in the forward stage [21]. An important improvement in the backward-forward approach was presented by [13], wherein radial and meshed structures were included in a matricial formulation. The triangular approach works for radial and meshed structures [12]; however, the related convergence analysis is not provided. It should be noted that in these methods, the authors do not present an analysis of the inclusion of voltage-controlled nodes, which we proposed in our matricial reformulation. A new approach based on successive approximations was recently reported in [25]. This approach demonstrates the convergence of the recursive formulation for radial and meshed networks using the Banach fixed-point theorem. However, voltage-controlled sources were not considered in this formulation, and the behavior of the \(\theta\)-coefficient was not determined to confirm the convergence at well-defined voltage conditions. Two additional important power flow contributions have been reported in specialized literature by [26; 27] regarding secondary distribution networks to study the problem of the harmonic penetration caused by higher penetration of photovoltaic sources. The authors in these approaches have proposed a harmonic power flow analysis using affine arithmetic which allows reaching better results regarding harmonic distortion estimations with low-computational effort when compared with classical Monte-Carlo simulations; in addition, these methods were validate in real secondary distribution networks with promissory results for utilities. Other approaches have also been presented in specialized literature in relation to linear and convex approximations for power-flow solutions in distribution networks. In [11], a convex approximation for a power-flow analysis of radial and meshed distribution networks was presented while considering a semidefinite programming approximation by using a rectangular representation of the power-balance equations.