Decomposition approach for generation and transmission expansion planning with implicit multipliers evaluation

Abstract

ABSTRACT.In an electric power systems planning framework, decomposition techniques are usually applied to separate investment and operation subproblems to take benefits from the use of independent solution algorithms. Real power systems planning problems can be rather complex and their detailed representation often leads to greater effort to solve the operation subproblems. Traditionally, the algorithms used in the solution of transmission constrained operation problems take great computational advantage with compact representation of the model, which means the elimination of some variables and constraints that don't affect the problem's optimal solution. This work presents a new methodology for solving generation and transmission expansion planning problems based on Benders decomposition where the incorporation of the traditional operation models require an additional procedure for evaluating the Lagrange's multipliers associated to the constraints which are not explicitly represented yet are used in the construction of the Benders cuts during the iterative process. The objective of this work is to seek for efficiency and consistency in the solution of expansion planning problems by allowing specialized algorithms to be applied in the operation model. It is shown that this methodology is particularly interesting when applied to stochastic hydrothermal problems which usually require a large number of problems to be solved. The results of this methodology are illustrated by a Colombian system case study.

A comprehensive state‐of‐the‐art survey on power generation expansion planning with intermittent renewable energy source and energy storage

“…The output of this model gives the optimal size, as well as the best location of the candidate plants on the network. Considering the literature, many studies have focused on the single‐node model, while focused on the network‐constrained GEP.…”

“…Depending on the storage medium, ESSs are categorised either as mechanical, chemical, or electrical storage systems . A survey of the literature shows that few studies have integrated ESS in GEP models …”

“…Some of the classical techniques that have been applied to GEP problems include LP, 40,125,126 DP, 19,30,37,101,113,123,[127][128][129][130] system dynamic method (SDM), 131,132 hierarchical decomposition (HD), 24,40,133 game theory (GT), 16,120,[134][135][136] NLP, 38,137 branch and bound (BB), 110,138-140 mixed-integer linear programming (MILP), 43,58,83,105,141 Dantzig-Wolfe decomposition (DWD), 22,142 quadratic programming (QP), 143,144 cross entropy (CE), 9 and the Benders decomposition method (BD). 7,26,63,65,101,103,[145][146][147] Although easy to use, the classical techniques present a challenge in real-world applications because practical problems consist of noncontinuous and/or differentiable objective functions. 36…”

Planning With Multiple Transmission and Storage Investment Options Under Uncertainty: A Nested Decomposition Approach

“…Also several decomposition schemes based on classical Benders Decomposition [29] have been applied to solve this extremely complex model [30], [31], [32], [33], [34]. By separating investment and operation costs, it is possible to exploit Benders decomposition methods in a straightforward way [35].…”

“…The distribution of the power over the network is described by the Direct Current Power Flow (DCPF) equation (33). The system balance at each node is imposed by equation (34). It requires that the sum of the injected power in each node is equal to the local demand level while also considering curtailed demand.…”