Optimization of large-scale interconnected systems

Date of Completion

January 1993


Engineering, Electronics and Electrical




Large scale dynamic optimization problems are generally difficult to solve because of their high dimensionality and problem complexity. Those problems involving discrete decision or state variables may also belong to the class of NP-hard (Non-Polynomial) combinatorial problems where computational requirements to obtain an optimal solution grow exponentially as the problem size increases. It is the goal of this dissertation to develop new concepts and solution methodologies for the resolution of these large scale dynamic optimization problems.^ The key features of the methods are Lagrangian relaxation, coordination, and parallel processing. The idea is to relax system-wide coupling constraints by using Lagrangian multipliers according to problem context, and decompose the overall problems into many smaller subproblems. The original problem is thus converted to a two-level optimization, where the low level consists of many smaller subproblems and each can be easily solved. The coordination of subproblems is done through Lagrange multipliers and possibly some other variables. These coordinating variables are updated iteratively at the high level by using some continuous variable optimization techniques to ensure the optimality or near optimality of the overall solution. Since the low level subproblems are decoupled and can be solved in parallel, parallel processing computers can be used to speed up computation.^ There are two major thrusts of the research. The first one considers optimal control problems that involve continuous variables only, and develops a parallel algorithm based on the spatial decomposition and coordination framework. The Parallel Variable Metric and Differential Dynamic Programming (PVM/DDP) method is found to be promising for loosely coupled systems. Numerical results show that significant speed-ups are obtained in comparison with the one level DDP algorithm.^ The second one investigates the power system scheduling problem that involves both discrete and continuous variables, and develops an efficient and effective scheduling methodology. By using Lagrange multipliers to relax system-wide demand and reserve constraints, the problem is decomposed into the scheduling of individual units. Efficient methods have been developed for solving thermal, hydro and pumped-storage subproblems, and a subgradient algorithm has been modified to update Lagrangian multipliers. The salient features include non-discretization of generation levels and a systematic way to handle ramp rate constraints in the thermal subproblems, and an efficient algorithm to solve pumped-storage subproblems by relaxing pond level constraints. Test results based on data from the Northeast Utilities power system show that the methods developed are efficient and produce near optimal solutions. ^