Solution of the unit commitment problem by the method of unit periods

This paper studies how to sample load more realistically and efficiently for security constraint unit commitment (SCUC) problems in order to achieve a high degree of robustness of the unit commitment (UC) solution. For example, given the UC solution, 95% of load profiles can be supplied. Principal component analysis (PCA) is introduced to find a clear feature of the historical load in two-dimensional space rather than the original high-dimensional load space, whose feature is hard to capture. Kernel density estimation (KDE) with Gaussian kernel is applied to form the probability density function (PDF), from which hourly load profiles are sampled. The load profiles based on sparse sampling are used to find the UC solution with high robustness while the load profiles based on dense sampling are used to verify the robustness of the obtained UC solution.

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.

Researches on the unit commitment with transmission network have been reported recently. However, most of these researches mainly discussed the security constrained unit commitment, while the relationship between unit commitment and transmission losses was not considered. However, from the standpoint of operating reserve for ensuring power supply reliability, a unit commitment considering transmission losses is required. Further, under the deregulation and liberalization of the electric power industry, not only the line's security but also transmission losses are expected to play an important role in calculating the network access charge, and unit commitment taking into account transmission losses is also desired from this viewpoint. In this paper, a unit commitment approach with both transmission losses and line flow constraint is presented. Based on a heuristic iterative optimization method, first, an initial schedule is created by using a successively decommitting unit approach that is proposed in this paper. Then, we determine constraints included in the unit commitment schedule by a heuristic iterative optimization approach, in which an algorithm able to get rid of line overload by DC optimal power flow is developed. Through numerical simulations on two test power systems, the effectiveness of the proposed method is shown. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 142(4): 9–19, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10116

Unit commitment is an efficient method to lower the total cost of the power plant by scheduling units' generation and meeting the constraint condition. However, in practice, few power plants implement the algorithm for fear that the load response in the power plant would not be fast enough to track the unscheduled load demand from the power grid if some units of the power plant are shut down. This paper proposes a new unit commitment method that tries to solve this problem effectively. The proposed method guarantees the desired speed limit by setting the plant-level load tracking speed. In this method a ‘one-at-a-time’ unit commitment is accomplished. The most expensive unit (which is determined by computing its cost) is optimized, the unit commitment schedule is updated, and the load dispatch result is re-computed. The result will be repeatedly optimized until the spinning reserve or load tracking speed is lack. The optimization loop will breaks out as well if the unit schedules of two consecutive iterations over the time period remain unchanged. The test results from 10-machine system shows that the proposed method is easy to understand and quick to solve, and is of practical use.

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. >

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

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.

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.

This paper presents a trustworthy unit commitment study to schedule both Renewable Energy Resources (RERs) with conventional power plants to potentially decarbonize the electrical network. The study has employed a system with three IEEE thermal (coal-fired) power plants as dispatchable distributed generators, one wind plant, one solar plant as stochastic distributed generators, and Plug-in Electric Vehicles (PEVs) which can work either loads or generators based on their charging schedule. This paper investigates the unit commitment scheduling objective to minimize the Combined Economic Emission Dispatch (CEED). To reduce combined emission costs, integrating more renewable energy resources (RER) and PEVs, there is an essential need to decarbonize the existing system. Decarbonizing the system means reducing the percentage of CO2 emissions. The uncertain behavior of wind and solar energies causes imbalance penalty costs. PEVs are proposed to overcome the intermittent nature of wind and solar energies. It is important to optimally integrate and schedule stochastic resources including the wind and solar energies, and PEVs charge and discharge processes with dispatched resources; the three IEEE thermal (coal-fired) power plants. The Water Cycle Optimization Algorithm (WCOA) is an efficient and intelligent meta-heuristic technique employed to solve the economically emission dispatch problem for both scheduling dispatchable and stochastic resources. The goal of this study is to obtain the solution for unit commitment to minimize the combined cost function including CO2 emission costs applying the Water Cycle Optimization Algorithm (WCOA). To validate the WCOA technique, the results are compared with the results obtained from applying the Dynamic Programming (DP) algorithm, which is considered as a conventional numerical technique, and with the Genetic Algorithm (GA) as a meta-heuristic technique.

Day-ahead unit commitment (UC) solution methods seek to determine the status and output of all available generators. In a world with an increasing integration of renewable energy sources such as wind electric generators (WEG), the UC solution process must model and include WEGs too in the decision-making process. Power output of WEGs in a day-ahead decision-making process are usually modeled using a short-term probabilistic forecast. Inclusion of WEGs introduces uncertainty in the solution that may be quantified through an imbalance risk function. Thus a UC solution method should seek a solution to minimize cost and risk in schedule. Two strategies are proposed in this paper to minimize costs and handle risks introduced due to WEGs. These formulations are posed as fuzzy optimization models and are solved using the mixed integer linear programming (MILP) technique. The proposed strategies are tested on a 26- and a 100-generator systems with associated transmission networks that have three and six wind generators each. The results with two strategies of handling WEGs are discussed.

Unified solution of a non-convex SCUC problem using combination of modified Branch-and-Bound method with Quadratic Programming

The fast-increasing introduction of renewable energy sources (RESes) leads to some problems in electrical power network due to fluctuating generated power. A power system must be operated with provision of various reserve powers like governor free capacity, load frequency control and spinning reserve. Therefore, the generator’s schedule (unit commitment schedule) should include the consideration of the various power reserves. In addition, it is necessary to calculate the annual operational costs of electric power systems by solving the unit commitment per week of thermal power generators and pumped storages in order to compare and examine the variance of the operational costs and the operating ratio of the generators throughout the year. This study proposes a novel annual analysis for the thermal power generator and pumped storages under a massive introduction of RESes. A weekly unit commitment schedule (start/stop planning) for thermal power generator and pumped storages has been modeled and calculated for one year evaluation. To solve the generator start/stop planning problem, Tabu search and interior point methods are adopted to solve the operation planning for thermal power generators and the output decision for pumped storages, respectively. It is demonstrated that the proposed method can analyze a one-year evaluation within practical time. In addition, by assuming load frequency control (LFC) constraints to cope with photovoltaic (PV) output fluctuations, the impact of the intensity of LFC constraints on the operational cost of the thermal power generator has been elucidated. The increment of the operational cost of the power supply with increasing PV introduction amount has been shown in concrete terms.

In this paper, first time ever artificial colony bee search is applied for thermal unit commitment. The main aim of doing thermal unit commitment scheduling is to optimize running while ensuring security and reliability. In recent era, lot of attention is given to the environmental conditions. All developed and few developing countries are worrying about emission of carbon dioxide from thermal generating stations. In first section of this paper unit commitment and Artificial Bee Colony (ABC) is discussed. In next section methodology for adopting ABC and general constraints of unit commitment are discussed in great detail. In last section application of ABC for unit commitment is implementation of proposed algorithm is shown and obtained results are presented. It is observed that ABC produces good results for unit commitment problem and easy to implement.

Unit Commitment solution using an optimized genetic system

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.