###### Abstract  
This paper presents a modeling and solution approach to the static and multistage transmission network expansion planning problem considering series capacitive compensation and active power losses. The transmission network expansion planning is formulated as a mixed integer nonlinear programming problem and solved through a highly efficient genetic algorithm. Furthermore, the [PERSON]'s constructive heuristic algorithm is implemented to render the configurations of the genetic algorithm feasible. The installation of series capacitive compensation devices is carried out with the aim of modifying the reactance of the original circuit. The linearization of active power losses is done through piecewise linear functions. The proposed model was implemented in C++ language programming. To show the applicability and effectiveness of the proposed methodology several tests are performed on the 6-bus Garver system, the IEEE 24-bus test system, and the South Brazilian 46-bus test system, presenting costs reductions in their multi-stage expansion planning of 7.4%, 4.65% and 1.74%, respectively. transmission network expansion planning; DC model; series capacitive compensation; power losses; linearization; genetic algorithms +
Footnote †: journal: Applied  
used to solve the TNEP problem are the Benders decomposition method [6], Branch and Bound [7; 8], linear programming algorithms [9; 10], quadratic programming [11], mixed integer linear programming [12], and mixed integer nonlinear programming [13]. Classical mathematical techniques are able to find globally optimal solutions for small and medium-sized systems. Nonetheless, for large electrical power systems, they require a high computational effort [14]. In contrast, metaheuristic approaches are able to find high-quality solutions for real-size power systems with less computational effort. Constructive heuristic algorithms can be defined as simplified procedures that have the capacity to identify feasible solutions of good quality for problems with medium mathematical complexity. These algorithms rarely find the optimal global solution to the problem, the best known applied to the TNEP problem are: constructive algorithms using the transport model, DC model, and the hybrid model [15; 16]. In [17], a constructive heuristic algorithm is proposed, based on sensitivity indices of a hyperbolic tangent function to initiate a multimodal optimization process and solve the TNEP problem. Metaheuristic algorithms are techniques inspired by natural processes. These algorithms are used to solve complex combinatorial problems, finding high-quality or even global optimal solutions with an acceptable computational effort. Several metaheuristic techniques have been applied to solve the TNEP problem, such as: genetic algorithms (GA) [2; 18; 19], tabu search [20], simulated annealing [21], ant colony optimization [22], coronavirus optimization algorithm [23], Grasp algorithm [24], scattered search [25], path relinking [26], and variable neighborhood search [27]. Moreover, there are methodologies in the specialized literature that formulate the TNEP as a multi-objective problem. In [28], the objective function is divided into three parts: investment cost, reliability, and congestion cost. In [29], the TNEP problem is solved through as a multi-objective algorithm that considers the investment cost of lines and/or transformers, the cost of unserved wind energy, and a cost for non-supplied energy. The multi-objective nature of the models proposed in [28; 29] is solved using NSGA II (Non-dominated Sorting Genetic Algorithm-II). Hybrid algorithms are also reported in the literature, in which two metaheuristics are combined to solve the TNEP problem more efficiently.