A Bi-Level Branch and Bound Method for Economic Dispatch with Disjoint Prohibited Zones Considering Network Losses

Abstract

This paper proposes a bi-level branch-and-bound ((B&B) method to solve the economic dispatch problem with prohibited zones and network losses. The approach employs binary variables for each prohibited zone and utilizes the B-coefficient for network losses, which can be transformed into a mixed-integer quadratically constrained quadratic programming (MIQCQP), where linear relaxation technique is applied on each bilinear term. Due to the complexity in solving the MIQCQP problem, this paper proposes a bi-level B&B method to achieve global optimum. A spatial B&B method is utilized in the higher level to solve the quadratically constrained quadratic programming (QCQP) problem, whereas a simple B&B method is employed in the lower level to solve a mixed-integer quadratic programming (MIQP) problem. The bi-level B&B algorithm that combines spatial and simple B&B methods is actually a deterministic optimization method and can produce global optimal solutions. Numerical results on 6-unit, 15-unit, and 40-unit test systems show that the bi-level B&B method can solve the MIQCQP problem with superior solution quality and convergence characteristics.

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Complex Networks; Convergence of Numerical Methods; Electric Load Dispatching; Integer Programming; Nonlinear Programming; Numerical Methods; Optimization; Problem Solving; Quadratic Programming; Scheduling; Economic Dispatch; Mixed-Integer Nonlinear Programming; Prohibited Operating Zone; Quadratically Constrained Quadratic Programming (QCQP); Spatial Branch and Bounds; Branch and Bound Method; Mixed-Integer Nonlinear Programming (MINLP); Prohibited Operating Zones; Spatial Branch-And-Bound

International Standard Serial Number (ISSN)

0885-8950

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Nov 2015

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