**1. Introduction**

Recent deployments of power electronics have allowed the positive advancement and development of efficient renewable energy interfaces for wind and photovoltaic plants [1–3], and the large-scale usage of energy storage systems, such as batteries [4–6], supercapacitors [7,8], superconductors [3,9,10] and flywheels [11,12]. These devices can be integrated into the power system using different interface technologies; i.e., to operate in the classical alternating current (AC) or direct current (DC) grids [3,13]. The selection of the grid operative condition plays an important role in the quality of the electrical service provided to the end-users. In the case of AC grids, it is required to maintain sinusoidal voltages with adequate form (power quality criteria); i.e., magnitude, frequency, power factor, harmonics, etc. [14–16]. These characteristics in AC networks make them more complex in comparison to DC networks, since these latter only require voltage control, and reactive power and frequency are nonexistent [17,18]. An additional advantage of using DC over AC technologies is their high efficiency in terms of power loss and voltage profiles [19]. These features can be added to the fact that photovoltaic plants or some energy storage technologies (supercapacitors, batteries

and superconducting coils) work directly in the DC paradigm [17,20], which can help to reduce the number of power interfaces to integrate these technologies in DC grids in comparison to their AC counterparts [21].

In specialized literature, DC networks have taken relevance regarding optimization and control applications [21]. In the case of optimization, multiple approaches based on semidefinite programming [4], second-order cone programming [20], sequential quadratics [22] and metaheuristics have been proposed to address optimal power flow problems [23]; additionally, some classical numerical methods can be found, such as Newton-Raphson [24], Gauss-Seidel [17] or successive approximations for power flow solutions [25]. In the case of control, the most conventional approaches focus on battery control [26], renewable energy integration [27] and dynamic stability based on passivity based-control [28,29], model predictive control [30,31] and sliding mode control [32,33].

These recent studies show that DC networks are promissory technologies that require extensive research for being successfully operated and also integrated and interconnected to the conventional AC power system [34,35]. In this paper, we deal with a classical and well-studied problem of optimal location and sizing of distributed generation in power systems. Nevertheless, we focus on direct current networks in isolated areas operated with diesel generators [36,37]. Although this problem has been widely studied in AC networks with metaheuristics, such as genetic algorithms [38], tabu search [39], harmonic search [40], krill-herd algorithm [41] and population based-learning methods [42], in conjunction with exact mixed-integer nonlinear programming methods [43,44], on the topic of DC networks there are only four references that address this problem. In [45] a semidefinite programming method was proposed for binary variable relaxation associated with the location of the generators; then, its binary structure was recovered with random hyperplanes; in [46] a sequential quadratic programming model with the same binary relaxation was proposed, and the binary nature of the problem was recovered with a heuristic search that defines the optimal location of the generators. The authors of [47] have addressed the issue of optimal location and sizing of distributed generators in DC networks from the metaheuristic point of view by using a classical genetic algorithm for their locations, in conjunction with their different optimal power flow methods based on particle swarm, black hole and continuous genetic optimizers. In [48], a mixed-integer nonlinear programming model was proposed to locate and size DGs in DC microgrids, using the general algebraic modeling system (GAMS) package for its solution. The common denominator of these approaches is the fact that load or renewable generation variations are not considered, since all of them only solve the problem for a unique hour time lapse. This cannot replicate the real behavior of electrical networks, especially when renewable energy resources are introduced.

To deal with renewable energy variations in the problem of optimal location and sizing of distributed generators in DC networks, here, we propose mixed-integer nonlinear programming for location and sizing of PV plants in DC networks to minimize the total pollution and greenhouse emissions released by diesel generators feeding isolated DC networks. The main contribution of our approach is based on a multiperiod optimization problem, including expected curves of PV generation and demand consumption focused on Colombian power system characteristics. To ensure that PV generation potential was well estimated, an artificial neural network with recursive connections was employed. To solve the proposed mixed-integer nonlinear programming (MINLP) model, we used the GAMS package with multiple nonlinear solvers to compare the results, as recommended in [44,48]. Numerical results confirm that the correct placement of PV plants helps via a significant reduction of pollutants released to the atmosphere by fossil fuels, which contributes positively to the responsible plans of energy consumption for future generations; i.e., making the power system more sustainable [6].

The remainder of this document is organized as follows: In Section 2 is presented the MINLP model for the problem of optimal location and sizing of PV generators in DC networks, for the reduction of greenhouse emissions with multiperiod structure. In Section 3 it the artificial neural network employed to forecast the solar power generation is described. In Section 4 a GAMS example in a small DC network to solve the problem addressed in this paper is presented. In Section 5 the numerical simulation in a 21-nodes test feeder is shown to minimize pollutants produced by diesel generators with its corresponding analysis and discussion. In section 6 the main concluding remarks derived from this research are presented.
