Parallel computation for large-scale optimization problems with application to hydroelectric generation

Thesis/Dissertation · Sat Dec 31 23:00:00 EST 1988

OSTI ID:6086792

Tang, J

For static optimization, the new method solves a class of problems with linear or nonlinear equality constraints and separable structures. The idea is to relax equality constraints via Lagrange multipliers, and create a hierarchy where the Lagrange multipliers and part of the decision variables are selected as high level variables. The low level is a set of independent subproblems and can be solved in parallel. The Modified Newton's Method is adopted at the high level for fast convergence. The information needed for the high level is obtained by using a kind of sensitivity analysis. For dynamic optimization, the method solves long horizon optimal control problems. The idea is to decompose a long horizon problem into subproblems along the time axis. The requirement that the initial state of a subproblem equals the terminal state of the preceding subproblems is relaxed by using Lagrange multipliers. The Lagrange multipliers and the initial state of each subproblem are then selected as high level variables which are updated by using the Modified Newton's Method. The low level subproblems are optimal control problems with a shorter time horizon, and are solved in parallel by using the extended Differential Dynamic Programming (DDP). An efficient way for finding the gradient and Hessian of a low level objective function with respect to high level variables is developed. The method is extended for constrained dynamic optimization problems where constraints on control and state are relaxed by using multiplier method. For a given set of multipliers, the problem can be treated as an unconstrained dynamic optimization problem. The Lagrange multipliers are then updated in a simple and efficient way. The constrained algorithm is then applied to hydroelectric scheduling problems. The issue of how to handle uncertainties is also addressed.

• Research Organization: Connecticut Univ., Storrs, CT (USA)
• OSTI ID: 6086792
• Country of Publication: United States
• Language: English

Related Subjects

13 HYDRO ENERGY
130300* -- Hydro Energy-- Plant Design & Operation
ALGORITHMS
CONTROL
DECISION MAKING
DIFFERENTIAL EQUATIONS
DYNAMIC LOADS
EQUATIONS
HYDROELECTRIC POWER PLANTS
ITERATIVE METHODS
LAGRANGE EQUATIONS
LOAD MANAGEMENT
MANAGEMENT
MATHEMATICAL LOGIC
NEWTON METHOD
NUMERICAL SOLUTION
OPTIMIZATION
PARTIAL DIFFERENTIAL EQUATIONS
PERFORMANCE TESTING
POWER PLANTS
PROCESS CONTROL
SCHEDULES
SENSITIVITY ANALYSIS
STATIC LOADS
TESTING
VARIATIONS