Solving Unit Commitment Research Articles

Two-level, two-objective evolutionary algorithms for solving unit commitment problems

A two-level, two-objective optimization scheme based on evolutionary algorithms (EAs) is proposed for solving power generating Unit Commitment (UC) problems by considering stochastic power demand variations. Apart from the total operating cost to cover a known power demand distribution over the scheduling horizon, which is the first objective, the risk of not fulfilling possible demand variations forms the second objective to be minimized. For this kind of problems with a high number of decision variables, conventional EAs become inefficient optimization tools, since they require a high number of evaluations before reaching the optimal solution(s). To considerably reduce the computational burden, a two-level algorithm is proposed. At the low level, a coarsened UC problem is defined and solved using EAs to locate promising solutions at low cost: a strategy for coarsening the UC problem is proposed. Promising solutions migrate upwards to be injected into the high level EA population for further refinement. In addition, at the high level, the scheduling horizon is partitioned in a small number of subperiods of time which are optimized iteratively using EAs, based on objective function(s) penalized to ensure smooth transition from/to the adjacent subperiods. Handling shorter chromosomes due to partitioning increases method’s efficiency despite the need for iterating. The proposed two-level method and conventional EAs are compared on representative test problems.

Differential Evolution Algorithm for Solving Unit Commitment with Ramp Constraints

This article proposes a differential evolution algorithm to solve the unit commitment problem with ramp constraints. Two implementations of the proposed algorithm—the first one using the binary code, and the second one using the integer code—have been developed. Both of these implementations have been found to converge to the same optimum solution requiring a different number of generations and a different CPU time. The proposed algorithm shows competitive performance with the best of the similar methods proposed earlier.

潮流制約を考慮した火力，揚水，水力及び融通の統合翌日運用計画作成

We have developed an innovative power generation scheduling method using quadratic programming (QP). The advantage of using our method is that it simultaneously solves unit commitment and economic load dispatch. We relax the binary variables of the unit state into continuous variables to apply QP to this problem. We also add the penalty term to converge the value of those variables to 0 or 1 to the objective function; the sum of fuel costs and start-up costs. This penalty term depends on per-unit fuel cost. The possibility of its variable converging to zero increases as the cost increases. This method was applied to a test system of daily generation scheduling that consisted of 29 thermal units, two pumped-storage units, four cascaded-hydro units, and one transmission. The schedule satisfied all constraints, i.e., load-power balance, operation reserve, power flow, minimum up/down-times, and fuel consumption. This result shows that the developed method is effective.

Solving unit commitment problems with general ramp constraints

Lagrangian relaxation (LR) algorithms are among the most successful approaches for solving large-scale hydro-thermal unit commitment (UC) problems; this is largely due to the fact that the single-unit commitment (1UC) problems resulting from the decomposition, incorporating many kinds of technical constraints such as minimum up- and down-time requirements and time-dependent startup costs, can be efficiently solved by dynamic programming (DP) techniques. Ramp constraints have historically eluded efficient exact DP approaches; however, this has recently changed [Frangioni A, Gentile C. Solving nonlinear single-unit commitment problems with ramping constraints. Oper Res 2006;54(4):767–75]. We show that the newly proposed DP algorithm for ramp-constrained (1UC) problems allows to extend existing LR approaches to ramp-constrained (UC); this is not obvious since the heuristic procedures typically used to recover a primal feasible solution are not easily extended to take ramp limits into account. However, dealing with ramp constraints in the subproblems turns out to be sufficient to provide the LR heuristic enough guidance to produce good feasible solutions even with no other modification of the approach; this is due to the fact that (sophisticated) LR algorithms to (UC) duly exploit the primal information computed by the Lagrangian Dual, which in the proposed approach is ramp feasible. We also show by computational experiments that the LR [approach] is competitive with those based on general-purpose mixed-integer program (MIP) solvers for large-scale instances, especially hydro-thermal ones.

An evolutionary programming based simulated annealing method for solving the unit commitment problem

This paper presents a new approach to solve the short-term unit commitment problem using an evolutionary programming based simulated annealing method. The objective of this paper is to find the generation scheduling such that the total operating cost can be minimized, 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. Evolutionary programming, which happens to be a global optimisation technique for solving unit commitment Problem, operates on a system, which is designed to encode each unit’s operating schedule with regard to its minimum up/down time. In this, the unit commitment schedule is coded as a string of symbols. An initial population of parent solutions is generated at random. Here, each schedule is formed by committing all the units according to their initial status (“flat start”). Here the parents are obtained from a pre-defined set of solution’s, i.e. each and every solution is adjusted to meet the requirements. Then, a random recommitment is carried out with respect to the unit’s minimum down times. And SA improves the status. The best population is selected by evolutionary strategy. The Neyveli Thermal Power Station (NTPS) Unit-II in India demonstrates the effectiveness of the proposed approach; extensive studies have also been performed for different power systems consists of 10, 26, 34 generating units. Numerical results are shown comparing the cost solutions and computation time obtained by using the Evolutionary Programming method and other conventional methods like Dynamic Programming, Lagrangian Relaxation and Simulated Annealing and Tabu Search in reaching proper unit commitment.

Neural-based Tabu Search method for solving unit commitment problem for utility system

This paper presents a new approach to solving short-term Unit Commitment Problem (UCP) using Neural-Based Tabu Search (NBTS) for utility system. The objective of this paper 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 next H hours. A 66-bus utility power system with 12 generating units in India demonstrates the effectiveness of the proposed approach; extensive studies have also been performed for different IEEE test systems consisting of 24, 57 and 175 buses. Numerical results are shown to compare the superiority of the cost solutions obtained using the Tabu Search method, Dynamic Programming and Lagrangian Relaxation methods in reaching the proper unit commitment.

Genetic algorithm-based simulated annealing method for solving unit commitment problem in utility system

This paper presents a new approach to solve the short-term unit commitment problem using genetic algorithm-based simulated annealing method for utility system. The objective of this paper 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. Genetic Algorithms (GAs) are general-purpose optimisation techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as neural section, genetic recombination and survival of the fittest. In this, the unit commitment schedule is coded as a string of symbols. An initial population of parent solutions is generated at random. Here, each schedule is formed by committing all the units according to their initial status ('flat start'). Here, the parents are obtained from a predefined set of solutions, i.e., each and every solutio...

An Evolutionary Programming-Based Tabu Search Method For Solving The Unit Commitment Problem

This paper presents a new approach to solving the short-term unit commitment problem using an evolutionary programming-based tabu search (TS) method. The objective of this paper is to find the generation scheduling such that the total operating cost can be minimized, 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. Evolutionary programming, which happens to be a global optimization technique for solving unit commitment problem, operates on a system, which is designed to encode each unit's operating schedule with regard to its minimum up/down time. In this, the unit commitment schedule is coded as a string of symbols. An initial population of parent solutions is generated at random. Here, each schedule is formed by committing all of the units according to their initial status (flat start). Here, the parents are obtained from a predefined set of solutions (i.e., each and every solution is adjusted to meet the requirements). Then, a random decommitment is carried out with respect to the unit's minimum downtimes, and TS improves the status by avoiding entrapment in local minima. The best population is selected by evolutionary strategy. The Neyveli Thermal Power Station (NTPS) Unit-II in India demonstrates the effectiveness of the proposed approach; extensive studies have also been performed for different power systems consisting of 10, 26, and 34 generating units. Numerical results are shown comparing the cost solutions and computation time obtained by using the evolutionary programming method and other conventional methods like dynamic programming, Lagrangian relaxation, and simulated annealing and tabu search in reaching proper unit commitment.

Solving Unit Commitment Problem Using Hybrid Particle Swarm Optimization

This paper presents a Hybrid Particle Swarm Optimization (HPSO) to solve the Unit Commitment (UC) problem. Problem formulation of the unit commitment takes into consideration the minimum up and down time constraints, start up cost and spinning reserve, which is defined as the minimization of the total objective function while satisfying all the associated constraints. Problem formulation, representation and the simulation results for a 10 generator-scheduling problem are presented. Results shown are acceptable at this early stage.

Neural-based tabu search method for solving unit commitment problem

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.

A practical algorithm for unit commitment based on unit decommitment ranking

AbstractThis paper presents a practical algorithm for solving Unit Commitment (UC) problems with network constraints represented in Optimal Power Flow (OPF). The proposed algorithm is based on Successive Approximation Dynamic Programming (SADP) according to a Unit Decommitment Ranking (UDR) which is a priority list for unit decommitment procedure. The UDR can be determined by Dynamic Programming (DP) according to the information of OPF consisting of a set of Lagrange multipliers (dual variables). Since the set of Lagrange multipliers represents the relationship between the optimal value of objective function and OPF constraints, the proposed algorithm can determine power system resource scheduling in consideration of network constraints, such as line flow and voltage constraints. The feasibility and effectiveness of the proposed algorithm are demonstrated on a modified IEEE Reliability Test System. © 2001 Scripta Technica, Electr Eng Jpn, 138(2): 1–13, 2002

Unit commitment using hybrid models: a comparative study for dynamic programming, expert system, fuzzy system and genetic algorithms

Hybrid models for solving unit commitment problem have been proposed in this paper. To incorporate the changes due to the addition of new constraints automatically, an expert system (ES) has been proposed. The ES combines both schedules of units to be committed based on any classical or traditional algorithms and the knowledge of experienced power system operators. A solution database, i.e. information contained in the previous schedule is used to facilitate the current solution process. The proposed ES receives the input, i.e. the unit commitment solutions from a fuzzy-neural network. The unit commitment solutions from the artificial neural network cannot offer good performance if the load patterns are dissimilar to those of the trained data. Hence, the load demands, i.e. the input to the fuzzy-neural network is considered as fuzzy variables. To take into account the uncertainty in load demands, a fuzzy decision making approach has also been developed to solve the unit commitment problem and to train the artificial neural network. Due to the mathematical complexity of traditional techniques for solving unit commitment problem and also to facilitate comparison genetic algorithm, a non-traditional optimization technique has also been proposed. To demonstrate the effectiveness of the models proposed, extensive studies have been performed for different power systems consisting of 10, 26 and 34 generating units. The generation cost obtained and the computational time required by the proposed model has been compared with the existing traditional techniques such as dynamic programming (DP), ES, fuzzy system (FS) and genetic algorithms (GA).

A hybrid neural network and simulated annealing approach to the unit commitment problem

In this paper, the authors present an approach combining the feedforward neural network and the simulated annealing method to solve unit commitment, a mixed integer combinatorial optimisation problem in power system. The artificial neural network is used to determine the discrete variables corresponding to the state of each unit at each time interval. The simulated annealing method is used to generate the continuous variables corresponding to the power output of each unit and the production cost. The type of neural network used in this method is a multi-layer perceptron trained by the back-propagation algorithm. A set of load profiles as inputs and the corresponding unit commitment schedules as outputs (satisfying the minimum up–down, spinning reserve and crew constraints) are utilized to train the network. A method to generate the training patterns is also presented. The experimental result demonstrates that the proposed approach can solve unit commitment in a reduced computational time with an optimum generation schedule.

An interior-point/cutting-plane method to solve unit commitment problems

An interior-point/cutting-plane method for nondifferentiable optimization is used to solve the dual to a unit commitment problem. The interior-point/cutting-plane method has two advantages over previous approaches, such as the sub-gradient and bundle methods: first, it has better convergence characteristics; and second, does not suffer from the parameter-turning drawback. The results of a performance testing using systems with up to 104 units confirm the superiority of the interior-point/cutting-plane method over previous approaches.

系統評価のための停止ランキングに基づく電源起動停止計画手法

This paper presents a practical algorithm for solving Unit Commitment (UC) problems with network constraints represented in Optimal Power Flow (OPF). The proposed algorithm is based on Successive Approximation Dynamic Programming (SADP) according to a Unit Decommitment Ranking (UDR) which is a priority list for unit decommitment procedure. The UDR can be determined by Dynamic Programming (DP) according to the information of OPF consisting of a set of Lagrange multipliers (dual variables). Since the set of Lagrange multipliers represents the relationship between the optimal value of objective function and OPF constraints, the proposed algorithm can determine power system resource scheduling in consideration of network constraints, such as line flow and voltage constraints. The feasibility and effectiveness of the proposed algorithm are demonstrated on a modified IEEE Reliability Test System. © 2001 Scripta Technica, Electr Eng Jpn, 138(2): 1–13, 2002

Unit commitment with transmission security and voltage constraints

In this paper, optimal power flow (with transmission security and voltage constraints) is incorporated in the unit commitment formulation. Using Benders decomposition, the formulation is decomposed into a master problem and a subproblem. The master problem solves unit commitment with prevailing constraints, except transmission security and voltage constraints, by augmented Lagrangian relaxation. The subproblem minimizes violations of transmission security and voltage constraints for a commitment schedule given in the master problem. Since transmission constraints are decoupled from voltage constraints in the subproblem, the subproblem could further be decomposed into two smaller subproblems. The resulting transmission subproblem minimizes transmission flow violations for the worst contingency case by adjusting unit generation and phase shifter controls. The corresponding reactive subproblem minimizes voltage constraints by reactive power generation and tap changing controls. In the case of transmission flow or voltage infeasibility, Benders cuts are produced for unit commitment rescheduling. The iterative process between the master problem and the subproblems provides a minimum production cost solution for generation scheduling while satisfying the constraints. A comprehensive unit commitment software package is developed using Visual C++. A 36-unit system in the IEEE-118 bus network is used to demonstrate the efficiency of the method.

Transmission-constrained unit commitment based on Benders decomposition

An efficient algorithm based on Benders decomposition is proposed for dealing with the transmission-constrained unit commitment problem. Using Benders decomposition, the formulation of the unit commitment with transmission constraints is decomposed into a master problem and a subproblem. The master problem solves unit commitment without transmission constraints by augmented Lagrangian relaxation and the subproblem minimizes violations of transmission constraints by adjusting unit generation and phase shifter controls and testing the feasibility of the unit commitment schedule. In the case of infeasibility in transmission flows, a proper constraint (Benders cut) is introduced for unit commitment rescheduling based on violations in the subproblem. The iterative process between the master problem and the subproblem provides a minimum production cost solution for generation scheduling while satisfying transmission constraints. A modified IEEE-30 bus system is presented to demonstrate the efficiency of the method.

Unit commitment with voltage constraints

This paper proposes an efficient algorithm for considering reactive power and voltage constraints in unit commitment. Because the problem is formulated as a large mixed-integer programming and has a two-level hierarchical structure, the Benders decomposition method is used. Using decomposition, the master problem solves unit commitment, and the subproblem examines reactive power and voltage constraints in each hour to test the feasibility of the unit commitment solution. In the case of infeasibility, a proper constraint (Benders cut) is introduced and placed in the master problem for unit commitment rescheduling. The iterative process between the master and subproblems provides a minimum cost solution for generation scheduling while satisfying reactive power and voltage constraints. The constrained economic dispatch is used in our unit commitment. The constraints in the subproblem are formulated as linear programming with a block-angular structure. So, the Dantzig–Wolfe decomposition is applied in the subproblem to solve large-scale power system problems. A modified IEEE-30 bus system is presented to demonstrate the efficiency of the method. © 1997 by John Wiley and sons, Ltd.

Decomposition approach to unit commitment with reactive constraints

The authors propose an efficient algorithm for considering reactive power and voltage constraints in unit commitment. The inclusion of these reactive constraints in unit commitment will ensure enough commitment of real power and a feasible distribution of reactive power in power systems. Because the problem is a large mixed-integer programming and has a two-level hierarchical structure, the Benders decomposition method is used. Using decomposition, the master problem solves unit commitment and the subproblem examines reactive power and voltage constraints every hour to test the feasibility of the unit commitment solution. In the case of infeasibility, a proper constraint (Benders cut) is introduced and placed in the master problem for rescheduling the units. The iterative process provides a minimum cost solution for generation scheduling while satisfying reactive constraints. Test examples on the modified IEEE 30 bus system are presented to demonstrate the efficiency of the method.

CORRESPONDENCE: EXPERIENCE WITH ECONOMIC DISPATCHING FOR A RAPID DEVELOPING POWER SYSTEM

ABSTRACT This paper presents a method to solve unit commitment and economic dispatching problems for rapid developing power system of moderate size. The method is simple and can be used by system engineers without requirement of sophisticated expensive commercial computer codes. In spite of that the main goal of these rapid growing systems is to satisfy their demand securely, yet using this method will reduce the production cost even with one type of generation. The heat rate models for the different units have been obtained using two sets of data, the designers and the on site test data indicating the importance of site test data.