Identification of umbrella constraints in power generation scheduling problems

In this dissertation we propose a methodology to reduce the size of optimization problems used for market clearing and planning studies purposes in power systems. Solving these optimization problems is essential for daily operation of power systems and to ensure their security and dependability.However, the biggest challenge in solving these problems are their large sizes. Nonetheless, the empirical evidence and previous research suggest that these problems contain many redundant constraints. We propose a methodology, called umbrella constraint discovery (UCD), which identifies the constraints of these problems that contribute in forming the feasible set of solutions (umbrella constraints) and removes the ones that do not contribute. These redundant constraints do not have any effect on the solution of the problem, yet, they occupy memory and require CPU time. UCD is an optimization-based approach which identifies the umbrella constraints through the enforcement of a consistency logic on the set of constraints. In this dissertation, we apply UCD on security-constrained optimal power flow and unit commitment problems for different standard test systems. One of the advantages of UCD is that it lends itself well to decomposition. We propose decomposition techniques to further expedite the solution of UCD problems. Different decomposition approaches which exploit the structure of the parent problem are tested and the most efficient ones are identified.We also perform a sensitivity analysis on umbrella sets by varying the system load. The results show that the umbrella sets are relatively insensitive to the changes of system loads. This means that the system operators should not need to run UCD for each change of load in the system, but rather they can use the results of UCD for the similar conditions of their system.Additionally, the system operators can solve UCD problem for the entire system load profile over the span of a year and use the union of all umbrella sets corresponding to each hour. We show that the size of this set is still very small in comparison with the original constraint set.Then, we introduce a new formulation that benefits from less computational complexity than UCD, called partial UCD. This new method exploits the experience of running UCD on the network at hand and by making some reasonable assumptions, it reduces the computational burden for identifying non-umbrella constraints. This formulation is indeed an approximation of UCD and can quickly identify non-umbrella constraints. Therefore, it can be used as a pre-processing step to UCD solution.To further investigate the efficacy of the proposed methodology, we apply UCD and partial UCD on mixed-integer linear problems. We elaborate how the benefits of application of the proposed methodology can be further exploited the proposed methodology can improve the solution time of mixed-integer linear problems.Finally, we explore the possibility of predicting heuristically the umbrella set of a network if enough historical information of UCD results are available. We used neural networks to demonstrate that this task is possible and the results are encouraging.

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