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In power system studies the unit commitment problem (UC) is solved to support market decisions and assess system adequacy. Simplifications are made to solve the UC faster, but they are made without considering the consequences on solution quality. In this study we thoroughly investigated the impacts of simplifications on solution quality and computation time on a benchmark set consisting of almost all the available instances in the literature. We found that omitting the minimum up- and downtime and simplifying the startup cost resulted in a significant quality loss without reducing the computation time. Omitting reserve requirements, ramping limits and transmission limits reduced the computation time, but degraded the solution significantly. However, the linear relaxation resulted in less quality loss with a significant speed-up and resulted in no difference when unserved energy was minimized. Finally, we found that the average and maximum capacity factor difference is large for all model variants.

This article analyzes how the Unit Commitment Problem (UCP) complexity evolves with respect to the number n of units and T of time periods. A classical reduction from the knapsack problem shows that the UCP is NP-hard in the ordinary sense even for \\[T=1\\]. The main result of this article is that the UCP is strongly NP-hard. When the constraints are restricted to minimum up and down times, the UCP is shown to be polynomial for a fixed n. When either a unitary cost or amount of power is considered, the UCP is polynomial for \\[T=1\\] and strongly NP-hard for arbitrary T. The pricing subproblem commonly used in a UCP decomposition scheme is also shown to be strongly NP-hard for a subset of units.

The increasing integration of variable wind generation has aggravated the imbalance between electricity supply and demand. Power-to-hydrogen (P2H) is a promising solution to balance supply and demand in a variable power grid, in which excess wind power is converted into hydrogen via electrolysis and stored for later use. In this study, an energy hub (EH) with both a P2H facility (electrolyzer) and a gas-to-power (G2P) facility (hydrogen gas turbine) is proposed to accommodate a high penetration of wind power. The EH is modeled and integrated into a security-constrained unit commitment (SCUC) problem, and this optimization problem is solved by a mixed-integer linear programming (MILP) method with the Benders decomposition technique. Case studies are presented to validate the proposed model and elaborate on the technological potential of integrating P2H into a power system with a high level of wind penetration (HWP).

Although it can be complex to integrate variable renewable energy sources such as wind power and photovoltaics into an energy system, the potential benefits are large, as it can help reduce fuel imports, balance the trade, and mitigate the negative impacts in terms of climate change. In order to try to integrate a very large share of variable renewable energy sources into the energy system, an integrated energy planning approach was used, including ice storage in the cooling sector, a smart charging option in the transport sector, and an excess capacity of reverse osmosis technology that was utilised in order to provide flexibility to the energy system. A unit commitment and economic dispatch tool (PLEXOS) was used, and the model was run with both 5 min and 1 h time resolutions. The case study was carried out for a typical Caribbean island nation, based on data derived from measured data from Aruba. The results showed that 78.1% of the final electricity demand in 2020 was met by variable renewable energy sources, having 1.0% of curtailed energy in the energy system. The total economic cost of the modelled energy system was similar to the current energy system, dominated by the fossil fuel imports. The results are relevant for many populated islands and island nations.

Power system operators are faced with the problem of unit commitment belonging to mixed integer programming, which becomes very complicated, as units become large-scale and highly constrained. Because unit commitment problem is a binary problem with commitment and de-commitment, a discrete/binary optimization algorithm with superior performance is required. This paper proposes a novel hybrid binary bat algorithm for unit commitment problem, which consists of two process. To begin with, the proposed binary bat algorithm is applied to determining the commitment schedule of unit commitment problem. Specifically, an improved crossover operator based on exponential-logic-modulo map is proposed to enhance the convergence and maintain the diversity of populations. To prevent the algorithm from falling into a local optimum, a local mutation strategy performs local perturbation. Chaotic map is responsible for updating some parameters to increase the performance of the proposed algorithm. Furthermore, Lambda-iteration method is adopted to solve economic load dispatch in continuous space. Constraint handling is performed using the heuristic constraint produce. The effectiveness of the proposed algorithm is verified by benchmark functions and test systems. Additionally, the simulation results are compared with other well-established heuristic and binary approaches.

The unit commitment problem has been a very important problem in the power system operations, because it is aimed at reducing the power production cost by optimally scheduling the commitments of generation units. Meanwhile, it is a challenging problem because it involves a large amount of integer variables. With the increasing penetration of renewable energy sources in power systems, power system operations and control have been more affected by uncertainties than before. This paper discusses a stochastic unit commitment model which takes into account various uncertainties affecting thermal energy demand and two types of power generators, i.e., quick-start and non-quick-start generators. This problem is a stochastic mixed integer program with discrete decision variables in both first and second stages. In order to solve this difficult problem, a method based on Benders decomposition is applied. Numerical experiments show that the proposed algorithm can solve the stochastic unit commitment problem efficiently, especially those with large numbers of scenarios.

This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are (1) generation limits and (2) minimum up and down times. Apart from this, the startup and shutdown processes are also modeled, using (3) startup and shutdown power trajectories for slow-start units, and (4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, power schedules are used to represent the staircase energy schedule; however, this simplification leads to infeasible energy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-based UC formulation drawing a clear distinction between power and energy. The proposed constraints can be used as the core of any power-based UC formulation, thus tightening the final mixed-integer programming UC problem. We provide evidence that dramatic improvements in computational time are obtained by solving different case studies, for self-UC and network-constrained UC problems.

Energy storage systems (ESSs) are essential to ensure continuity of energy supply and maintain the reliability of modern power systems. Intermittency and uncertainty of renewable generations due to fluctuating weather conditions as well as uncertain behavior of load demand make ESSs an integral part of power system flexibility management. Typically, the load demand profile can be categorized into peak and off-peak periods, and adding power from renewable generations makes the load-generation dynamics more complicated. Therefore, the thermal generation (TG) units need to be turned on and off more frequently to meet the system load demand. In view of this, several research efforts have been directed towards analyzing the benefits of ESSs in solving optimal unit commitment (UC) problems, minimizing operating costs, and maximizing profits while ensuring supply reliability. In this paper, some recent research works and relevant UC models incorporating ESSs towards solving the abovementioned power system operational issues are reviewed and summarized to give prospective researchers a clear concept and tip-off on finding efficient solutions for future power system flexibility management. Conclusively, an example problem is simulated for the visualization of the formulation of UC problems with ESSs and solutions.

Hydro Unit Commitment (HUC) is an important problem of power systems and when it is dealt with via a mathematical programming approach and optimization, it leads to the complicated class of mixed-integer nonlinear programming (MINLP). Many attempts have been made to solve the problem efficiently, while there is still ongoing research to come up with better solution schemes in terms of runtime and optimality. Highly nonlinear nature of the relationships and constraints in the optimization problem have forced the researchers to deal with the HUC problem in simplified manners which may result in impractical and unreliable solutions, i.e. schedules. Here in this paper we proposed a new method based on sequential mixed-integer linear programming (MILP) for solving a more realistic version of the HUC problem efficiently. We applied the proposed method to a cascade of two hydropower plants, Karun-3 and Karun-4, located in the Southwest of Iran. The sequential MILP approach was compared with several MINLP solvers of the GAMS optimization package. The results indicated that the proposed methodology outperformed the MINLP solvers in terms of efficiency, with solution time of less than 30 s, compared to 10 min that were given to the solvers, and in terms of optimality with more than 20 thousand cubic meters per day in water release. Additionally, we have explored the effect of penalizing the total number of startups on the total release, convergence of the algorithm, and the computation time. In all of the cases the total number of startups was reduced more than three times.

With the increasing penetration of renewable energy, uncertainty has become the main challenge of power systems operation. Fortunately, system operators could deal with the uncertainty by adopting stochastic optimization (SO), robust optimization (RO) and distributionally robust optimization (DRO). However, choosing a good decision takes much experience, which can be difficult when system operators are inexperienced or there are staff shortages. In this paper, a decision-making approach containing robotic assistance is proposed. First, advanced clustering and reduction methods are used to obtain the scenarios of renewable generation, thus constructing a scenario-based ambiguity set of distributionally robust unit commitment (DR-UC). Second, a DR-UC model is built according to the above time-series ambiguity set, which is solved by a hybrid algorithm containing improved particle swarm optimization (IPSO) and mathematical solver. Third, the above model and solution algorithm are imported into robots that assist in decision making. Finally, the validity of this research is demonstrated by a series of experiments on two IEEE test systems.