PhD defence of Mohamed Awadalla – Data-Driven Constraint Learning and Screening for Operations of Sustainable Power Systems

Abstract

The ongoing deepening penetration of renewable energy sources is posing significant challenges to electric power system operation and planning. High levels of renewable energy, particularly from wind and solar sources, introduce significant variability and uncertainties that system operators must integrate into operational planning problems to ensure secure and cost-effective operation. Solving NP-hard (Non Deterministic Polynomial-time) operational planning problems such as the unit commitment, security-constrained unit commitment, and ac optimal power flow (AC-OPF) repeatedly is essential for ensuring reliable and economical daily operations. However, their numerous constraints and the inclusion of uncertainties and variability can substantially prolong solution times and may render these problems intractable for large systems. Nevertheless, existing empirical evidence and prior research indicate that these problems often include numerous unnecessary constraints.

This thesis seeks to advance the state-of-the-art of optimization-based constraint screening approaches for power system operational planning problems. We leverage constraint learning to achieve efficient constraint screening outcomes. Constraint learning embeds trained machine learning models directly into constraint screening approaches. Constraint learning is primarily led by discovering insights from previously solved operations planning instances which inherit the economical aspect of their objective functions as well as the observed demand patterns.

In optimization-based constraint screening for operational planning problems, robust optimization is often employed to ensure the operator’s ability to handle a broad range of possible scenarios, where scenarios refer to probable realizations of the system’s sources of uncertainty. In this realm, we propose polyhedral uncertainty sets that are capable of capturing spatial correlations in the uncertainty space of variable renewable energy and demand, called net load. Polyhedral uncertainty sets offer coverage levels similar to those of convex hulls without the over conservatism of multidimensional bounding boxes. Afterward, we extend the optimization-based approach known as umbrella constraint discovery (UCD), in the context of polyhedral uncertainty sets integrated in unit commitment problems. The classical UCD approach identifies non-redundant constraints by enforcing a consistency logic on the set of constraints. Furthermore, we augment UCD with an upper bound cost-driven constraint derived by fitting an appropriate regression model using past solved instances of the unit commitment problem. This new formulation called techno-economic UCD screens out redundant and inactive constraints that are not necessary to achieve optimal solutions for unit commitment with significant computational enhancement. This is a key departure from UCD, which is only capable of screening out redundant constraints.

Furthermore, we extend the optimization-based bound tightening technique for constraint screening problem in the context of the AC-OPF problem using constraint learning. Due to the non-convexity of the AC-OPF problem, we investigate how different convex relaxations of the AC-OPF perform when performing line constraint screening. Next, we propose an interpretable machine learning algorithm for real-time constraint generation for the security-constrained unit commitment problem. Our proposed approach is simplifying and accelerates the conventional constraint generation approach by leveraging machine learning approaches to learn the active set of pre- and post-contingency constraints. Those are then used to warm-start the constraint generation process used in the practical solution of security-constrained unit commitment problems to reveal the constraints set necessary and sufficient to guarantee the feasibility and optimality of the solution at a fraction of the computational cost needed by state-of-the-art approaches.

Finally, we develop a novel approach to determine the distance of an optimization problem solution to its non-redundant constraints defining its feasible region, or even its violated constraints in cases when problems are infeasible. Here, the notion of “distance” to a problem’s constraints is associated with the ability of the power system to respond to uncertain events, i.e., how flexible it is. For this purpose, we propose novel system flexibility metrics which are calculated by solving an associated inverse optimization
problem. We reveal that when applying this approach to the loadability set of a power system, it can accurately determine the feasibility of uncertain net load vector, and it is able to identify which constraints are closest to that uncertain net load vector.