Implementation of mixed integer linear programming for hydro-thermal generation scheduling with river and reservoir constraints

Abstract

A Short-term Hydro-thermal Scheduling (HTS) model based on Mixed Integer Linear Programming (MILP) is developed and presented in this thesis. For countries such as Malaysia that are close to the equator, high precipitation throughout the year replenishes existing water resources. The efficient scheduling of hydro and thermal units considering a large amount of water resources and river systems can significantly affect the total operation costs of the system. The HTS is a highly complex problem involving a large number of continuous and integer variables with nonlinearity and nonconvexity/nonconcavity characteristics in its objective function and constraints. A comprehensive MILP hydraulic model for unit-wise, and cascaded multi-chain reservoir system considering head variation effects has been developed. Incorporation of the detailed reservoir and river modelling with variable head makes the HTS problem even more complex with an additional number of integer/continuous variables as well as the constraints. A piecewise linear approximation is used to transform all nonlinearities into an equivalent linear model. Multi-thread computing is utilised to expedite the solution process of MILP Branch and Bound and Cut (BB & C) method using a certain number of concurrent threads. Obtained results show the successful implementation of the multi-chain river system modelling on several test cases including 69-unit, 132-unit and 287-unit. The proposed MILP-HTS algorithm is compared with a Lagrangian Relaxation (LR) algorithm that is currently employed by a real-world utility. Based on the similar input data, the MILP-HTS algorithm offers more optimal hydro-thermal generation strategy, taking into account a detailed hydraulic modelling. Based on the simulation results, the proposed MILP algorithm outperforms several other deterministic and heuristic techniques in terms of objective cost and execution time. Comparison with other equivalent MILP models over the same test conditions demonstrated that the proposed MILP model with the formulation presented in this thesis creates tighter relaxation (better cuts) in the BB & C solution process. This results in a cheaper objective value with a lesser computation time. Implementation of multi-thread computing improves the execution time performance for all case studies as compared with the serial computation time. Simulation results also suggest that the multi-threading can allow taking tighter optimality gap resulting in a more accurate solution (near-optimal) for large-scale problems in a moderate time, even with more detailed hydraulic modelling.