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.
- 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
Available at: http://works.bepress.com/rui-bo/6/