###### Abstract
In [30], the authors combine a tabu search algorithm with an ordinal optimization algorithm; in [31], a simulated annealing algorithm is used together with a local search algorithm, and in [18], the Chu-Beasley genetic algorithm is used, combined with a path relinking algorithm to solve static and multistage TNEP considering series compensation. In the TNEP problem, there is a constant need to improve the representation of mathematical modeling, including different parameters, variables, and/or constraints that make the problem even more realistic. For example, solving the problem takes into account the natural effects that happen in the transport of energy. One of the most important effects that can be considered in expansion planning is the power losses. Power losses represent a small percentage of the total energy of the power grid; nonetheless, inaccurate estimates of power losses can alter the functioning of the power grid and lead to a greater economic imbalance, forcing utilities to buy more energy to satisfy the energy balance [32; 33]. Bearing in mind its importance, several authors have considered the effect of power losses when solving the TNEP problem. In [34], a mixed integer linear programming formulation is presented to solve the TNEP problem in a competitive electricity market, where the future demand scenarios are defined considering power losses. In [12], a mixed integer linear programming approach is presented to solve the TNEP problem considering power losses. The linearization of power losses is carried out by means of piecewise linear functions. In the same way in [35], power losses are also considered by means of piecewise linear functions within an AC mathematical model. In [36], a new mathematical modeling is presented considering power losses. In this case, a sigmoid function is considered, and to model the optimal power flow, the primal-dual interior-point technique is used. In [37], a hybrid algorithm is proposed to reduce the search space of the TNEP, using Lagrange multipliers, also considering the N-1 contingency criterion, and several loads and power loss scenarios. The authors in [38] present three mathematical models to account for power losses in the TNEP problem: (1) considering a single linear equality constraint, (2) tangent or transversal constraints of linear inequality, and (3) piecewise linear approximation. Nowadays, considering FACTS (Flexible AC Transmission Systems) devices within the TNEP problem is a topic of great interest for energy companies. These elements bring along some advantages, such as the redistribution of power flows, enhancement of transmission capacity, improvement of voltage stability and reduction of power losses [39]. Nonetheless, the installation of these devices might cause adverse effects in the network, such as resonance problems and limitations related to the thermal capacity of the transmission lines. The installation of series controllers draws special attention within the TNEP since they increase the active power flow through transmission lines keeping the same voltage angles differences. Moreover, this type of compensation can be done with minimum infrastructure adjustments and low out-of-time service. In [40], series compensation is included within the multistage TNEP problem considering N-1 security constraints. In [41], the authors introduce a continuously variable series reactor to the TNEP problem, also considering security constraints. In this case, a decomposition approach is proposed to reduce the computational burden of the model. In [42], the authors include thyristor-controlled series compensators and battery energy storage within an investment model for transmission expansion planning. The proposed planning strategy uses a linearized AC optimal power flow and a Benders' decomposition technique to find the optimal solution to the expansion plan. As evidenced in the review of the specialized literature, no TNEP model has been reported that considers simultaneously the planning of series compensation and power losses.