Transmission Network Expansion Planning Considering Optimal Allocation of Series Capacitive Compensation and Active Power Losses

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 Villasana Garver’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.

On Multistage Multiscale Stochastic Capacitated Multiple Allocation Hub Network Expansion Planning

The hub location problem (HLP) basically consists of selecting nodes from a network to act as hubs to be used for flow traffic directioning, i.e., flow collection from some origin nodes, probably transfer it to other hubs, and distributing it to destination nodes. A potential expansion on the hub building and capacitated modules increasing along a time horizon is also considered. So, uncertainty is inherent to the problem. Two types of time scaling are dealt with; specifically, a long one (viz., semesters, years), where the strategic decisions are made, and another whose timing is much shorter for the operational decisions. Thus, two types of uncertain parameters are also considered; namely, strategic and operational ones. This work focuses on the development of a stochastic mixed integer linear optimization modeling framework and a matheuristic approach for solving the multistage multiscale allocation hub location network expansion planning problem under uncertainty. Given the intrinsic difficulty of the problem and the huge dimensions of the instances (due to the network size of realistic instances as well as the cardinality of the strategic scenario tree and operational ones), it is unrealistic to seek an optimal solution. A matheuristic algorithm, so-called SFR3, is introduced, which stands for scenario variables fixing and iteratively randomizing the relaxation reduction of the constraints and variables’ integrality. It obtains a (hopefully, good) feasible solution in reasonable time and a lower bound of the optimal solution value to assess the solution quality. The performance of the overall approach is computationally assessed by using stochastic-based perturbed well-known CAB data.