Bundle methods for power system scheduling with bidding strategies

Date of Completion

January 1998


Economics, Commerce-Business|Engineering, Electronics and Electrical




Lagrangian relaxation has been widely used for hydrothermal scheduling. The idea is to use Lagrangian multipliers to relax system-wide demand and reserve requirements, and decompose the problem into unit-wise subproblems that are much easier to solve. The multipliers are then updated at the high level, most commonly by using a subgradient method (SGM). Since the high level dual function is non-differentiable with many "ridges," SGM may zigzag across ridges resulting in slow convergence. One part of the thesis studies the application of bundle type methods in updating the multipliers at the high level for hydrothermal scheduling. To avoid the zigzag of SGM, bundle methods use the convex combination of subgradients accumulated in a bundle as a search direction that is usually better than a subgradient. Obtaining the combination coefficient, however, involves quadratic programming and is very time consuming. The RCBM is a kind of bundle method that enjoys faster convergence compared to SGM, but has much reduced complexity as compared to a conventional bundle method by substituting the quadratic programming with projection. Bundle Trust Region Method is another bundle type that avoids the computation time requirement of quadratic programming by solving it recursively. Both RCBM and BTRM are shown to converge faster than the SGM in optimizing non-differentiable dual functions.^ With the deregulation of power market, participants bid generation resources to the Independent System operator (ISO), and ISO decides hourly accepted generation levels for each participant and energy clearing prices with the bids. Bidding strategies have direct impact on the profit of a participant, and an algorithm that can find a good bidding strategy to effectively use its generation resources and maximize its profit is very important. Bidding may also be coupled with self-scheduling in circumstances where a participant bid only part of its generation resources and self-schedule the remaining. ^