Short Term Unit Commitment as a Planning Problem

‘Unit Commitment’, setting online schedules for generating units in a power system to ensure supply meets demand, is integral to the secure, efficient, and economic daily operation of a power system. Conflicting desires for security of supply at minimum cost complicate this. Sustained research has produced methodologies within a guaranteed bound of optimality, given sufficient computing time. Regulatory requirements to reduce emissions in modern power systems have necessitated increased renewable generation, whose output cannot be directly controlled, increasing complex uncertainties. Traditional methods are thus less efficient, generating more costly schedules or requiring impractical increases in solution time. Meta-Heuristic approaches are studied to identify why this large body of work has had little industrial impact despite continued academic interest over many years. A discussion of lessons learned is given, and should be of interest to researchers presenting new Unit Commitment approaches, such as a Planning implementation. Automated Planning is a sub-field of Artificial Intelligence, where a timestamped sequence of predefined actions manipulating a system towards a goal configuration is sought. This differs from previous Unit Commitment formulations found in the literature. There are fewer times when a unit’s online status switches, representing a Planning action, than free variables in a traditional formulation. Efficient reasoning about these actions could reduce solution time, enabling Planning to tackle Unit Commitment problems with high levels of renewable generation. Existing Planning formulations for Unit Commitment have not been found. A successful formulation enumerating open challenges would constitute a good benchmark problem for the field. Thus, two models are presented. The first demonstrates the approach’s strength in temporal reasoning over numeric optimisation. The second balances this but current algorithms cannot handle it. Extensions to an existing algorithm are proposed alongside a discussion of immediate challenges and possible solutions. This is intended to form a base from which a successful methodology can be developed

Efficient methods for solving power system operation scheduling challenges: the thermal unit commitment problem with staircase cost and the very short-term load forecasting problem

This dissertation addresses two crucial power system operational scheduling aspects: the thermal unit commitment problem and real-time load demand forecasting. These two are important challenges that need the development of models and efficient algorithms. To tackle the generator scheduling problem, we propose and develop five matheuristic methods, including four variations of local branching (LB) and one using kernel search (KS). Additionally, we have introduced a novel constructive approach named HARDUC, which effectively generates high-quality initial solutions for the matheuristic methods. To assess the effectiveness of the proposed matheuristic algorithms, tests were con ducted on instances simulating scenarios where an analyst must deliver a generation sched ule within one or two hours. A comparison with CPLEX, an off-the-shelf solver, under two scenarios (i) using the solver from scratch and (ii) using the solver with an initial feasible solution from the heuristic, revealed interesting insights. For small instances, the off-the-shelf solver outperformed the matheuristic methods. However, in medium-sized instances, the solver sometimes struggled to find a feasible solution. When solutions were found, there were no significant differences in performance between the solver and the methods. However, the proposed methods excelled and achieved remarkable results for large instances where the solver left many instances unsolved. Furthermore, we tested the proposed constructive method by comparing it with the best UCP constructive method from the literature. The results, supported by statistical tests, indicate the superiority of our proposed method. Our implementation of the KS algo rithm outperformed both the solver and the LB method in terms of relative optimality gap, especially in challenging instances. This discovery is significant as it reveals tremendous potential in utilizing KS for solving the UCP, paving the way for further research. As expected, as complexity increased, matheuristic methods outperformed the solver, delivering quicker, more e↵ective solutions. Matheuristics have a proven track record and are incorporated into commercial solvers for efficient solutions in mixed-integer linear programming problems. In our research, we customized matheuristics for the termal UCP by identifying dominant variables and addressing implementation challenges of the KS method, improving its efficacy. In addition, we introduced a novel method called the Analogue with Moving Av erage (AnMA) approach in very short-term load demand forecasting. AnMA exploits the seasonal characteristics of load demand time series by selecting the most correlated days. Its adaptability to real-time data positions it as an ideal choice for accommodating new demand patterns, rectifying biases, and enhancing accuracy. AnMA was compared against other methods recognized for their efficency and precision in the literature. The results showcased AnMA’s superiority, outperforming naive algorithms and exponential smoothing methods in accuracy, computational speed, and cost-e↵ectiveness. Addition ally, AnMA achieved comparable accuracy to ARIMA models while requiring significantly fewer computational resources and less time. Our research addresses critical challenges in power system operational scheduling, highlighting the e↵ectiveness of tailored methods that align with problem-specific char acteristics. These findings hold practical significance for the electricity industry, as our approach leverages a profound understanding of problem characteristics to improve opera tional scheduling. The success of our methods could potentially guide the development of future hybrid heuristic approaches combining mixed-integer programming or matheuris tics alongside analogy-based forecasting techniques, o↵ering substantial practical advance ments in the electricity sector

Tighter MIP formulations for the discretised unit commitment problem with min-stop ramping constraints

International audienc

Water Allocation Under Uncertainty – Potential Gains from Optimisation and Market Mechanisms

This thesis first develops a range of wholesale water market design options, based on an optimisation approach to market-clearing, as in electricity markets, focusing on the extent to which uncertainty is accounted for in bidding, market-clearing and contract formation. We conclude that the most promising option is bidding for, and trading, a combination of fixed and proportionally scaled contract volumes, which are based on optimised outputs. Other options include those which are based on a post-clearing fit (e.g. regression) to the natural optimised outputs, or constraining the optimisation such that cleared allocations are in the contractual form required by participants. Alternatively, participants could rely on financial markets to trade instruments, but informed by a centralised market-clearing simulation. We then describe a computational modelling system, using Stochastic Constructive Dynamic Programming (CDDP), and use it to assess the importance of modelling uncertainty, and correlations, in reservoir optimisation and/or market-clearing, under a wide range of physical and economic assumptions, with or without a market. We discuss a number of bases of comparison, but focus on the benefit gain achieved as a proportion of the perfectly competitive market value (price times quantity), calculated using the market clearing price from Markov Chain optimisation. With inflow and demand completely out of phase, high inflow seasonality and volatility, and a constant elasticity of -0.5, the greatest contribution of stochastic (Markov) optimisation, as a proportion of market value was 29%, when storage capacity was only 25% of mean monthly inflow, and with effectively unlimited release capacity. This proportional gain fell only slowly for higher storage capacities, but nearly halved for lower release capacities, around the mean monthly inflow, mainly because highly constrained systems produce high prices, and hence raise market value. The highest absolute gain was actually when release capacity was only 75% of mean monthly inflow. On average, over a storage capacity range from 2% to 1200%, and release capacity range from 100% to 400%, times the mean monthly inflow, the gains from using Markov Chain and Stochastic Independent optimisation, rather than deterministic optimisation, were 18% and 13% of market value, respectively. As expected, the gains from stochastic optimisation rose rapidly for lower elasticities, and when vertical steps were added to the demand curve. But they became nearly negligible when (the absolute value of) elasticity rose to 0.75 and beyond, inflow was in-phase with demand, or the range of either seasonal variation or intra-month variability reduced to ±50% of the mean monthly inflow. Still, our results indicate that there are a wide range of reservoir and economic systems where accounting for uncertainty directly in the water allocation process could result in significant gains, whether in a centrally controlled or market context. Price and price risk, which affect individual participants, were significantly more sensitive. Our hope is that this work helps inform parties who are considering enhancing their water allocation practices with improved stochastic optimisation, and potentially market based mechanisms