Thermal Unit Commitment Problem Research Articles

PROFIT–BASED UNIT COMMITMENT PROBLEM WITH BILATERAL CONTRACTS

This paper addresses the thermal unit commitment problem for power generation companies that operating in the market environment. The model for this problem is formulated as a deterministic optimization task where the optimal solution obtained using the 0/1 mixed-integer linear programming technique. The main feature of the model is that it provides a comprehensive and accurate representation of operating costs and operating constraints for thermal units. The model have been incorporated a long-term bilateral contracts with defined profiles power and price, and forecasted market for hourly prices for day-ahead auction. Solution is achieved using the homogeneous and self-dual interior point method for linear programming with a branch and bound optimizer for binary programming. The effectiveness of the proposed model is demonstrated through case study with detailed discussion.

Unit commitment with energy dispatch using a computationally efficient encoding structure

This study aims to propose a solving approach for the thermal unit commitment (UC) problem using the mutated particle swarm optimization (MPSO) combined with a novel encoding scheme. Unlike traditional straightforward encoding arrangements, the proposed encoding method applies the load demand and spinning reserve constraints to construct a small searching space, and then put the constraints of minimum up and down-time into the encoding structure so as to shorten the searching time effectively. This novel coding scheme could effectively prevent obtaining infeasible solutions through the application of stochastic search methods, thereby dramatically improving search efficiency and solution quality. Many nonlinear characteristics of power generators, and their operational constraints, such as minimum up and down-time, spinning reserve, generation limitations, ramp rate limits, prohibited operating zones, transmission loss, and nonlinear cost functions were all considered for practical operation. The effectiveness and feasibility of the proposed approach were demonstrated by three system case studies and compared with previous literature in terms of solution quality. The simulation results reveal that the proposed approach was capable of efficiently determining higher quality solutions in resolving the thermal unit commitment problems.

A Novel Solution Methodology for Solving Large-scale Thermal Unit Commitment Problems

An effective solution methodology for solving large-scale unit commitment problems is proposed. In order to model the line losses, the second-order network model is introduced into the conventional unit commitment problem. The proposed solution methodology consists of three key steps: (1) a transformed problem formulation that is based on a mixed-integer convex programming problem, (2) an improved solution method that is a combination of a modified branch-and-bound method and an interior point method, and (3) some accelerating strategies to speed up the proposed solution method. During the branch-and-bound process, the best first search and depth first search strategy are combined to expedite the required computation. In order to achieve the goal of obtaining a fast, near-optimal feasible solution of large-scale unit commitment problems, some accelerating strategies are developed. An effective scheme to partition the study period is also presented. The proposed solution methodology is applied to several test systems, including a 10-unit system and modified IEEE 118-bus system with 54 thermal units. Numerical study results indicate that the proposed solution methodology is fast and effective in dealing with various constraints and is promising for solving large-scale unit commitment problems. The proposed solution methodology finds better unit commitment solutions than most other methods. In addition, the solutions obtained by the proposed solution methodology are close to the optimal total operational cost. Especially for 60-unit and 80-unit unit commitment problems, the proposed solution methodology finds the best solutions.

Feasible Modified Subgradient Method for Solving the Thermal Unit Commitment Problem as a New Approach

The Lagrangian relaxation- (LR-) based methods are commonly used to solve the thermal unit commitment (UC) problem which is an important subject in power system engineering. The main drawback of this group of methods is the difference between the dual and the primal solutions which gives some significant problems on the quality of the feasible solutions. In this paper, a new approach, feasible modified subgradient (F-MSG) method which does not require finding an unconstrained global minimum of the Lagrangian function and knowing an optimal value of the problem under consideration in order to update dual variables at the each iteration, is firstly used for solving the thermal UC problem. The major advantage of the proposed approach is that it guarantees the zero duality gap and convergence independently from the size of the problem. In order to discuss the advantages of this method, the four-unit Tuncbilek thermal plant, which is located in Kutahya region in Turkey, is chosen as a small test system. The numerical results show that F-MSG gives better solutions as compared to the standard LR method.

An immune-tabu hybrid algorithm for thermal unit commitment of electric power systems

This paper presents a new method based on an immune-tabu hybrid algorithm to solve the thermal unit commitment (TUC) problem in power plant optimization. The mathematical model of the TUC problem is established by analyzing the generating units in modern power plants. A novel immune-tabu hybrid algorithm is proposed to solve this complex problem. In the algorithm, the objective function of the TUC problem is considered as an antigen and the solutions are considered as antibodies, which are determined by the affinity computation. The code length of an antibody is shortened by encoding the continuous operating time, and the optimum searching speed is improved. Each feasible individual in the immune algorithm (IA) is used as the initial solution of the tabu search (TS) algorithm after certain generations of IA iteration. As examples, the proposed method has been applied to several thermal unit systems for a period of 24 h. The computation results demonstrate the good global optimum searching performance of the proposed immune-tabu hybrid algorithm. The presented algorithm can also be used to solve other optimization problems in fields such as the chemical industry and the power industry.

A new decomposition approach for the thermal unit commitment problem

In this paper, we propose a new formulation based on benders decomposition approach to solve the thermal unit commitment (UC) problem. In the proposed approach, the UC problem is decomposed into a master problem, which is an integer optimization problem, and a subproblem, which is a nonlinear optimization problem. The proper on/off states of the generating units are found by solving the master problem using the mixed-integer programming method. The subproblem utilizes the solution of the master problem to form appropriate cuts and returns the cuts to the master problem for running the next iteration of the UC problem. In both optimization problems, corresponding constraints are exactly modeled. To demonstrate the effectiveness of the proposed approach, simulation results are compared with the results obtained by other methods.

Unit commitment using a new integer coded genetic algorithm

AbstractThis paper proposes a new Integer‐Coded Genetic Algorithm (ICGA) for the solution of the thermal unit commitment problem. The thermal generating units scheduling consists of the sequence of operation/reservation times of the generating units, which is coded into a sequence of alternating sign integer numbers in the proposed ICGA. The minimum up and down time constraints of the generating units are directly coded in the chromosome structure of the ICGA. The proposed ICGA has a new hybrid crossover composed of modified average bound and swapping operators. In addition, a combination of uniform and non‐uniform mutations is used as the mutation operator. As a result, the algorithm robustness is improved. Test results with systems of up to 300 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) methods justifies the effectiveness of the proposed method in light of minimizing the total operation cost. Copyright © 2008 John Wiley & Sons, Ltd.

A Computationally Efficient Mixed-Integer Linear Formulation for the Thermal Unit Commitment Problem

This paper presents a new mixed-integer linear formulation for the unit commitment problem of thermal units. The formulation proposed requires fewer binary variables and constraints than previously reported models, yielding a significant computational saving. Furthermore, the modeling framework provided by the new formulation allows including a precise description of time-dependent startup costs and intertemporal constraints such as ramping limits and minimum up and down times. A commercially available mixed-integer linear programming algorithm has been applied to efficiently solve the unit commitment problem for practical large-scale cases. Simulation results back these conclusions

Short-term thermal generation scheduling using improved immune algorithm

This paper proposes a new immune algorithm (NIA), which merges the fuzzy system (FS), the annealing immune (AI) method and the immune algorithm (IA) together, to resolve short-term thermal generation unit commitment (UC) problems. This proposed method differs from its counterparts in three main aspects, namely: (1) changing the crossover and mutation ratios from a fixed value to a variable value determined by the fuzzy system method, (2) using the memory cell and (3) adding the annealing immune operator. With these modifications, we can attain three major advantages with the NIA, i.e. (1) the NIA will not fall into a local optimal solution trap; (2) the NIA can quickly and correctly find a full set of global optimal solutions and (3) the NIA can achieve the most economic solution for unit commitment with ease. The UC determines the start-up and shut-down schedules for related generation units to meet the forecasted demand at a minimum cost while satisfying other constraints, such as each unit's generating limit. The NIA is applied to six cases with various numbers of thermal generation units over a 24-h period. The schedule generated by the NIA is compared with that by several other methods, including the dynamic programming (DP), the Lagrangian relaxation (LR), the standard genetic algorithm (GA), the traditional simulated annealing (SA) and the traditional Tabu search (TS). The comparisons verify the validity and superiority in accuracy for the proposed method.

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

This paper presents a new fuzzy optimization based approach to solve the thermal unit commitment (UC) problem. In this approach load demand, reserve requirements, and production cost are expressed by fuzzy set notations, while unit generation limits, ramp rate limits, and minimum up/down limits are handled as crisp constraints. A fuzzy optimization based algorithm is then, developed to find the optimal solution by using fuzzy operations and “if-then” rules. Some heuristics such as dividing hourly load and generating units into levels are used to speed the solution. The approach has been applied to a 38 units thermal power system. The results are compared with that obtained by the dynamic programming (DP), the Lagrangiane–relaxation (LR), constraint logic programming (CLP), and simulated annealing (SA) methods. The achieved results prove the effectiveness, and validity of the proposed approach to solve the large-scale UC problem. The effects of unit ramp rate limits and minimum up/down times are also, investigated.

A Solution to the Unit-Commitment Problem Using Integer-Coded Genetic Algorithm

This paper presents a new solution to the thermal unit-commitment (UC) problem based on an integer-coded genetic algorithm (GA). The GA chromosome consists of a sequence of alternating sign integer numbers representing the sequence of operation/reservation times of the generating units. The proposed coding achieves significant chromosome size reduction compared to the usual binary coding. As a result, algorithm robustness and execution time are improved. In addition, generating unit minimum up and minimum downtime constraints are directly coded in the chromosome, thus avoiding the use of many penalty functions that usually distort the search space. Test results with systems of up to 100 units and 24-h scheduling horizon are presented.

A solution to the unit commitment problem considering LNG fuel constraints

In this paper, an algorithm is proposed for finding a quasi-optimal schedule for the short-term thermal unit commitment problem taking LNG fuel constraints into account. In recent years, LNG fuel has been used increasingly. As a result, LNG fuel constraints should be considered in making a unit commitment schedule. Generally, unit commitment is a nonlinear combinatorial problem including discrete variables. To solve the problem, a two-step algorithm is developed using mathematical programming methods. First a linear programming problem is solved to determine the amount of LNG fuel to be consumed by each LNG unit, then a Lagrangian relaxation approach is used to obtain a unit commitment schedule. This two-step algorithm simplifies the problem and thus has good convergence characteristics. To test the effectiveness of the proposed algorithm, a numerical simulation was carried out on a 46-unit thermal system over a 24-hour period. A result with a dual gap of 0.00546 was obtained. © 1998 Scripta Technica, Electr Eng Jpn, 125(3): 22–30, 1998

Scheduling of thermal units with a nonlinear load flow network model

We describe a formulation of the thermal unit commitment problem that includes AC network constraints, which allows taking into account VAr production as a criterion for generator commitment for the first time. The formulation makes it possible to use the Lagrangian Relaxation technique as a solution algorithm even though the network constraints are not linear. Although the solution method is computationally intensive, the problem exhibits a separation structure and a price coordination schedule that suggest several ways of improving the performance. Preliminary test results are reported.

A new thermal unit commitment approach using constraint logic programming

The authors propose a constraint logic programming (CLP) algorithm to solve the thermal unit commitment (UC) problem in this paper. The algorithm combines the characteristics of the logic programming with the constraint satisfaction as well as the depth-first branch and bound search techniques to provide an efficient and flexible approach to the UC problem. Through the constraint satisfaction techniques, the constraints, which consist of the upper bound on the objective value, are propagated as much as possible to actively reduce the search space of the UC problem in a priori way. Consequently, the optimal solution can be acquired in a very early stage. To demonstrate the effectiveness of the proposed approach, the practical thermal UC problem of Taiwan Power (Taipower) 38-unit system over a 24-hour period is solved by the CLP algorithm implemented in CHIP language. The results obtained are compared with those from the established methods of the dynamic programming, the Lagrangian relaxation as well as the simulated annealing.

Hydro unit commitment in hydro-thermal optimization

In this paper, the authors develop a model and technique for solving the combined hydro and thermal unit commitment problem, taking into full account the hydro unit dynamic constraints in achieving overall economy of power system operation. The combined hydrothermal unit commitment problem is solved by a decomposition and coordination approach. Thermal unit commitment is solved using a conventional Lagrangian relaxation technique. The hydro system is divided into watersheds, which are further broken down into reservoirs. The watersheds are optimized by network flow programming (NFP). Priority-list-based dynamic programming is used to solve the hydro unit commitment (HUC) problem at the reservoir level. A successive approximation method is used for updating the marginal water values (Lagrange multipliers) to improve the hydro unit commitment convergence, due to the large size and multiple couplings of water conservation constraints. The integration of the hydro unit commitment into the existing hydro-thermal optimization (HTO) package greatly improves the quality of its solution in the PG&E power system.

A parallel genetic algorithm approach to solving the unit commitment problem: implementation on the transputer networks

Through a constraint handling technique, this paper proposes a parallel genetic algorithm (GA) approach to solving the thermal unit commitment (UC) problem. The developed algorithm is implemented on an eight-processor transputer network, processors of which are arranged in master-slave and dual-direction ring structures, respectively. The proposed approach has been tested on a 38-unit thermal power system over a 24-hour period. Speed-up and efficiency for each topology with different number of processor are compared to those of the sequential GA approach. The proposed topology of dual-direction ring is shown to be well amenable to parallel implementation of the GA for the UC problem.

Solving the unit commitment problem with a genetic algorithm through a constraint satisfaction technique

This paper proposes a genetic algorithm (GA) in conjunction with constraint handling techniques to solve the thermal unit commitment problem. To deal effectively with the constraints of the problem and prune the search space of the GA in advance, the difficult 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 other constraints are handled by integrating penalty factors into the cost function within an enhanced economic dispatch program. The proposed GA approach has been tested on a practical Taiwan Power (Taipower) thermal system over a 24-hour period for different utility factors and GA control parameters. Test results reveal that the features of easy implementation, fast convergence, and a highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach.

A genetic algorithm based approach to thermal unit commitment of electric power systems

This paper presents a new approach based on genetic algorithms to solve the thermal unit commitment problem of electric power systems. Genetic algorithms (GAs) are general search techniques based on the biological metaphor and are very suitable for solving combinatorial optimization problems. Because of its nonconvex and combinatorial nature, the unit commitment problem is difficult to solve by conventional programming methods. However, it is well suited for the application of the GAs. A key to the success of the implementation of the proposed algorithm is a newly developed knowledge-augmented mutation-like operator, named here the forced mutation. It was found to improve, significantly, the efficiency of the GA in solving the unit commitment problem. Two different coding schemes were devised and tested. In addition, the effects of GAs' control variables on convergence were extensively studied. The approach was tested on a ten-unit system. Test results clearly reveal the robustness and promise of the proposed approach.

A capacity based Lagrangian relaxation unit commitment with ramp rate constraints

This paper presents a Lagrangian relaxation based technique for solving the power system thermal unit commitment problem. As a general approach, Lagrangian relaxation has proven to be an efficient method of solving the thermal unit commitment problem. The specific technique described in this paper focuses on finding a feasible commitment, then attempting to improve on the optimality of the solution. A new method for processing ramp rate constraints is also introduced. The algorithm has been implemented on a large scale power system and results are shown using actual power system data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Unit commitment literature synopsis

Several optimization techniques have been applied to the solution of the thermal unit commitment problem. They range from heuristics such as complete enumeration to the more sophisticated ones such as Augmented LaGrangian. The heuristics have even reappeared as expert systems. The problem to solve is the optimal scheduling of generating units over a short-term horizon, typically 168 hours. This paper is an overview of the literature in the unit commitment field over the past twenty five years. >