Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

ABSTRACT

This article presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a ‘hybrid’ Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its efficacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested on the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the hybrid Bernstein global optimization algorithm delivers satisfactory performance in terms of solution optimality.

KEYWORDS:

• Bernstein polynomials
• global optimization
• power system
• optimal power flow
• non-convex problem

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The word ‘hybrid’ in this context means that the algorithm is a combination of local and global optimization methods. To the best of the authors' knowledge, this is the first work that explores the use of local solving techniques for the early pruning of nodes in a B & B tree in the context of Bernstein global optimization algorithms.

Additional information

Funding

This research is supported by the National Research Foundation, Prime Minister's Office, Singapore under its CREATE programme.