Contingency-Constrained Unit Commitment with Post-Contingency Corrective Recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the well-known $N$-$k$ criterion, and dictates that at least $(1-e_ j)$ fraction of the total system demand must be met following the failures of $k$ or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art

Reinforcement Learning and Tree Search Methods for the Unit Commitment Problem

The unit commitment (UC) problem, which determines operating schedules of generation units to meet demand, is a fundamental task in power systems operation. Existing UC methods using mixed-integer programming are not well-suited to highly stochastic systems. Approaches which more rigorously account for uncertainty could yield large reductions in operating costs by reducing spinning reserve requirements; operating power stations at higher efficiencies; and integrating greater volumes of variable renewables. A promising approach to solving the UC problem is reinforcement learning (RL), a methodology for optimal decision-making which has been used to conquer long-standing grand challenges in artificial intelligence. This thesis explores the application of RL to the UC problem and addresses challenges including robustness under uncertainty; generalisability across multiple problem instances; and scaling to larger power systems than previously studied. To tackle these issues, we develop guided tree search, a novel methodology combining model-free RL and model-based planning. The UC problem is formalised as a Markov decision process and we develop an open-source environment based on real data from Great Britain's power system to train RL agents. In problems of up to 100 generators, guided tree search is shown to be competitive with deterministic UC methods, reducing operating costs by up to 1.4\%. An advantage of RL is that the framework can be easily extended to incorporate considerations important to power systems operators such as robustness to generator failure, wind curtailment or carbon prices. When generator outages are considered, guided tree search saves over 2\% in operating costs as compared with methods using conventional $N-x$ reserve criteria

Learning‑assisted optimization for transmission switching

The design of new strategies that exploit methods from machine learning to facilitate the resolution of challenging and large-scale mathematical optimization problems has recently become an avenue of prolific and promising research. In this paper, we propose a novel learning procedure to assist in the solution of a well-known compu- tationally difficult optimization problem in power systems: The Direct Current Opti- mal Transmission Switching (DC-OTS) problem. The DC-OTS problem consists in finding the configuration of the power network that results in the cheapest dispatch of the power generating units. With the increasing variability in the operating con- ditions of power grids, the DC-OTS problem has lately sparked renewed interest, because operational strategies that include topological network changes have proved to be effective and efficient in helping maintain the balance between generation and demand. The DC-OTS problem includes a set of binaries that determine the on/off status of the switchable transmission lines. Therefore, it takes the form of a mixed- integer program, which is NP-hard in general. In this paper, we propose an approach to tackle the DC-OTS problem that leverages known solutions to past instances of the problem to speed up the mixed-integer optimization of a new unseen model. Although our approach does not offer optimality guarantees, a series of numerical experiments run on a real-life power system dataset show that it features a very high success rate in identifying the optimal grid topology (especially when compared to alternative competing heuristics), while rendering remarkable speed-up factors.Funding for open access charge: Universidad de Málaga / CBU

Mathematical Programming bounds for Large-Scale Unit Commitment Problems in Medium-Term Energy System Simulations

We consider a large-scale unit commitment problem arising in medium-term simulation of energy networks, stemming from a joint project between the University of Milan and a major energy research centre in Italy. Optimal plans must be computed for a set of thermal and hydroelectric power plants, located in one or more countries, over a time horizon spanning from a few months to one year, with a hour-by-hour resolution. We propose a mixed-integer linear programming model for the problem. Since the complexity of this unit commitment problem and the size of real-world instances make it impractical to directly optimise this model using general purpose solvers, we devise ad-hoc heuristics and relaxations to obtain approximated solutions and quality estimations. We exploit an incremental approach: at first, a linear relaxation of an aggregated model is solved. Then, the model is disaggregated and the full linear relaxation is computed. Finally, a tighter linear relaxation of an extended formulation is obtained using column generation. At each stage, metaheuristics are run to obtain good integer solutions. Experimental tests on real-world data reveal that accurate results can be obtained by our framework in affordable time, making it suitable for efficient scenario simulations

Reinforcement learning and A* search for the unit commitment problem

Previous research has combined model-free reinforcement learning with model-based tree search methods to solve the unit commitment problem with stochastic demand and renewables generation. This approach was limited to shallow search depths and suffered from significant variability in run time across problem instances with varying complexity. To mitigate these issues, we extend this methodology to more advanced search algorithms based on A* search. First, we develop a problem-specific heuristic based on priority list unit commitment methods and apply this in Guided A* search, reducing run time by up to 94% with negligible impact on operating costs. In addition, we address the run time variability issue by employing a novel anytime algorithm, Guided IDA*, replacing the fixed search depth parameter with a time budget constraint. We show that Guided IDA* mitigates the run time variability of previous guided tree search algorithms and enables further operating cost reductions of up to 1%

New efficient ADMM algorithm for the Unit Commitment Problem

The unit commitment problem (UC) is an optimization problem concerning the operation of electrical generators. Many algorithms have been proposed for the UC and in recent years a more decentralized approach, by solving the UC with alternating direction method of multipliers (ADMM), has been investigated. For convex problems ADMM is guaranteed to find an optimal solution. However, because UC is non-convex additional steps need to be taken in order to ensure convergence to a feasible solution of high quality. Therefore, solving UC by a MIL(Q)P formulation and running an off-the-shelf solver like Gurobi until now seems to be the most efficient approach to obtain high quality solutions. In this paper, we introduce a new and efficient way to solve the UC with ADMM to near optimality. We relax the supply-demand balance constraint and deal with the non-convexity by iteratively increasing a penalty coefficient until we eventually force convergence and feasibility. At each iteration the subproblems are solved by our efficient algorithm for the single UC subproblem developed in earlier work and our new ADMM algorithm for the transmission subproblems. Computational experiments on benchmark instances demonstrated that our algorithm produces high-quality solutions. The computation time seems to grow practically linear with the length of the time horizon. For the case with quadratic generation cost our algorithm is significantly faster than solving the problem by a state-of-the-art MIL(Q)P formulation. For the case of linear generation cost, it outperforms the MILP approach for longer time horizons.Comment: 30 pages, 9 figure