A fuzzy optimization-based approach to large scale thermal unit commitment

This paper proposes an innovative genetic algorithm (GA) approach to solve the thermal unit commitment (UC) problem in power generation industry through a constraint satisfaction technique. Due to a large variety of constraints to be satisfied, the solution space of the UC problem is highly nonconvex, and therefore the UC problem can not be solved efficiently by the standard GA. To effectively deal with the constraints of the problem and greatly reduce the search space of the GA, the minimum up- and down-time constraints are embedded in the binary strings that are coded to represent the on-off states of the generating units. The violations of the other constraints are handled by integrating penalty factors into the cost function. Numerical results on the practical Taiwan Power (Taipower) system of 38 thermal units over a 24-hour period show that the features of easy implementation, fast convergence, and highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach. >

A novel projected two-binary-variable formulation for unit commitment in power systems

This paper presents the solving unit commitment (UC) problem using Modified Subgradient Method (MSG) method combined with Simulated Annealing (SA) algorithm. UC problem is one of the important power system engineering hard-solving problems. The Lagrangian relaxation (LR) based methods are commonly used to solve the UC problem. The main disadvantage of this group of methods is the difference between the dual and the primal solution which gives some significant problems on the quality of the feasible solution. In this paper, MSG method which does not require any convexity and differentiability assumptions is used for solving the UC problem. MSG method depending on the initial value reaches zero duality gap. SA algorithm is used in order to assign the appropriate initial value for MSG method. The major advantage of the proposed approach is that it guarantees the zero duality gap independently from the size of the problem. In order to show the advantages of this proposed approach, the four-unit Tuncbilek thermal plant and ten-unit thermal plant which is usually used in literature are chosen as test systems. Penalty function (PF) method is also used to compare with our proposed method in terms of total cost and UC schedule.

This paper presents a new approach for the large scale unit commitment problem. The unit commitment (UC) problem plays a major role in the power system since the improvement of commitment schedule results in the reduction of operating cost. However, the unit commitment problem is one of the most difficult optimization problems in the power system, because this problem has many constraints. Moreover search space is vast. To overcome these problems, a new genetic operator based on unit characteristic classification and unit integration technique are proposed. The proposed algorithm was tested on a reported UC problem. From simulation results, better solutions are obtained in comparison with previously reported results. Numerical results for a system up to 100 units are compared to previously reported results.

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited. This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility. UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space. Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations. To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.

Evaluating the impact of sub-hourly unit commitment method on spinning reserve in presence of intermittent generators

This paper presents a new approach for thermal unit commitment (UC) using a differential evolution (DE) algorithm. DE is an effective, robust, and simple global optimization algorithm which only has a few control parameters and has been successfully applied to a wide range of optimization problems. However, the standard DE cannot be applied to binary optimization problems such as UC problems since it is restricted to continuous-valued spaces. This paper proposes binary differential evolution (BDE), which enables the DE to operate in binary spaces and applies the proposed BDE to UC problems. Furthermore, this paper includes heuristic-based constraint treatment techniques to deal with the minimum up/down time and spinning reserve constraints in UC problems. Since excessive spinning reserves can incur high operation costs, the unit de-commitment strategy is also introduced to improve the solution quality. To demonstrate the performance of the proposed BDE, it is applied to largescale power systems of up to 100-units with a 24-hour demand horizon.

The authors propose an algorithm to consider the ramp characteristics in starting up and shutting down the generating units as well as increasing and decreasing power generation. They consider the inclusion of ramping constraints in both unit commitment and economic dispatch. Since implementing ramp-rate constraints is a dynamic process, dynamic programming (DP) is a proper tool to treat this problem. To overcome the computational expense which is the main drawback of DP, this study initially employs artificial intelligence techniques to produce a unit commitment schedule which satisfies all system and unit operation constraints except unit ramp-rate limits. Then, a dynamic procedure is used to consider the ramp properties as units are started up and shut down. According to this adjustment, maximum generating capabilities of units will change the unit operation status instead of following a step function. Finally, a dynamic dispatch procedure is adopted to obtain a suitable power allocation which incorporates the unit generating capability information given by unit commitment and unit ramping constraints, as well as the economical considerations. Two examples are presented to demonstrate the efficiency of the method. >

This paper presents a new approach of particle swarm optimization (PSO) algorithm for short term hydro thermal scheduling (HTS) problems. Various possible particle selections have been studied and its effects on the global optima have been discussed. The effectiveness and stochastic nature of proposed algorithm has been tested with standard test case and the results have been compared with earlier works. This paper also describes software developed for short term hydro-thermal scheduling by considering hydro economic dispatch and thermal unit commitment. The proposed algorithm is ideally suitable for hydro-thermal co-ordination problems, hydro economic dispatch problems with unit commitment, thermal economic dispatch with unit commitment problems and scheduling of hydraulically coupled plants.

This paper presents a hybrid immune algorithm (IA)/genetic algorithm (GA) and fuzzy system (FS) method (IGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shutdown schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve and individual units. First, we combined the IA and GA, then we added the fuzzy system approach. This hybrid system was used to solve the UC problems. Numerical simulations were carried out using three cases; ten, twenty and thirty thermal unit power systems over a 24 hrs period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional tabu search (TTS). The result demonstrated the accuracy of the proposed CIGAFS approach.

The optimal scheduling of power units to meet the estimated demand is called the unit commitment problem. Of the available methods for this problem, those using Lagrangean relaxation seem most promising. A description is given of the thermal unit commitment problem. Also given is a short survey of Lagrangean duality including some new techniques, which are applied to the unit commitment problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents an algorithm for integrating and managing electrochemical energy storage systems (ESSs) on unit commitment (UC) problem. As some elements required for integrating electrochemical ESS, such as the power converter, have non-linear characteristics, its corresponding linear modeling could be difficult to be developed and included on the UC problem, which could lead to unfeasible solutions or unexpected results. In order to incorporate full models of ESS and its interface with the power system, in this paper an algorithm to incorporate electrochemical ESS management on the UC problem is presented. An insular power system of 10-units is analyzed, and conclusions are duly drawn.

An approach to solving the short-term unit commitment problem (UCP) using a neural-based tabu search (NBTS) is presented. The solution of the unit commitment problem is a complex optimisation problem. The exact solution of the UCP can be obtained by a complete enumeration of all feasible combinations of generating units, which could be a huge number. The unit commitment has commonly been formulated as a nonlinear, large-scale, mixed-integer combinational optimisation problem. The objective is to find the generation scheduling such that the total operating cost can be minimised, when subjected to a variety of constraints. This also means that it is desirable to find the optimal generating unit commitment in the power system for the next H hours. Tabu search is a powerful optimisation procedure that has been successfully applied to a number of combinatorial optimisation problems. It has the ability to avoid entrapment in local minima by employing a flexible memory system. The neural network combines good solution quality for tabu search with rapid convergence for an artificial neural network. The neural based tabu search method is used to find the unit commitment. By doing so, it gives the optimum solution rapidly and efficiently. The Neyveli Thermal Power Station (NTPS) Unit – II in India has been considered as a case study and extensive studies have also been performed for different power systems consisting of 10, 26, and 34 generating units. The data collected has been used for implementation in the above methods. Numerical results are shown, comparing the cost solutions and computation time obtained by using the intelligent techniques with the conventional methods like dynamic programming and Lagrangian relaxation to reach proper unit commitment.

This paper presents centralized control for a wind farm using model predictive control (MPC) method. In order to solve intra-day unit commitment (UC) problem, the UC problem is solved by using the MPC method with short-term wind power forecasting. We introduce a new dynamics model for the UC with some constraints to utilize the benefits of the MPC method. The objective function considering the operation and maintenance costs is formulated by adding a new variable in order to average the operating time of each wind turbine (WT) within the whole time. The proposed method could solve the UC problems on-line using the prediction time horizon that could be selected flexibly considering time horizon based on wind power forecasting errors. From the simulation study using 10 WTs, we observed that the proposed dynamics model of UC effectively provided the optimal solution to each scenario. Numerical study will validate that the proposed method can be applied to solving the UC problem of a large scale wind farm by aggregating WTs.

Solving the unit commitment (UC) problem in a computationally efficient manner is a critical issue of electricity market operations. Optimization-based methods such as heuristics, dynamic programming, and mixed-integer quadratic programming (MIQP) often yield good solutions to the UC problem. However, the computation time of optimization-based methods grows exponentially with the number of generating units, which is a major bottleneck in practice. To address this issue, we formulate the UC problem as a Markov decision process and propose a novel multi-step deep reinforcement learning (RL)-based algorithm to solve the problem. We approximate the action-value function with neural networks and design an algorithm to determine the feasible action space. Numerical studies on a 5-generator test case show that our proposed algorithm significantly outperforms the deep Q-learning and yields similar level of performance as that of MIQP-based optimization in terms of optimality. The computation time of our proposed algorithm is much shorter than that of MIQP-based optimization methods.