Journal
IEEE TRANSACTIONS ON POWER SYSTEMS
Volume 30, Issue 6, Pages 2841-2855Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TPWRS.2014.2375322
Keywords
Economic dispatch; mixed-integer nonlinear programming (MINLP); prohibited operating zones; quadratically constrained quadratic programming (QCQP); spatial branch-and-bound
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Funding
- National Key Basic Research Program of China (973 Program) [2013CB228205]
- National Science Foundation of China [51277105]
- National Science Fund for Distinguished Young Scholars of China [51025725]
- National Science Fund of China [51428701]
- National Science Fund of US [EEC-1041877]
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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.
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