Large-scale Unit Commitment Problem Research Articles

Tight Relaxation Method for Unit Commitment Problem Using Reformulation and Lift-and-Project

This paper presents a novel method to solve the unit commitment (UC) problem by solving a sequence of increasingly tight continuous relaxations based on the techniques of reformulation and lift-and-project (L&P). After projecting the power output of unit onto [0, 1], the continuous relaxation of the UC problem can be tightened with the reformulation techniques. Then, a tighter model which is called L&P-TMIP is established by strengthening the continuous relaxation of the feasible region of the tight UC problem iteratively using L&P. High-quality suboptimal solutions can be obtained from the solutions of the relaxation for this tight model. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the proposed tight relaxation method is competitive with general-purpose mixed integer programming solvers based methods for large-scale UC problems due to the excellent performance and the good quality of the solutions it generates.

A Modified Differential Evolution Algorithm for the Solution of a Large-Scale Unit Commitment Problem

The Unit Commitment (UC) problem is a nonlinear and complex optimization problem used to determine the start-up and shutdown scheduling of power-generating units to meet the forecasted load demand and spinning reserve over a specified time horizon so that the target of production cost minimization is achieved while satisfying various system and generator-based constraints. The increase in computational burden with the system size requires more efficient meta-heuristic approaches for solving the UC problem. This paper proposes a modified differential evolution (DE) approach for both discrete and real part of the UC problem. The infeasibility of the solutions is also handled by incorporating some repairing mechanisms in DE, which forcefully satisfy the system constraints and speed up the search process. The experimentation is carried out on various standard and large power systems, starting from the 10-unit base case and then going up to 100 units over a 24 -h time period. The obtained results indicate the effectiveness of the proposed approach as compared to the previous work reported in the literature.

Solution of the mixed integer large scale unit commitment problem by means of a continuous Stochastic linear programming model

Power Systems all around the World faced in the last decade a large increase of penetration of power generation produced by Renewable Energy Sources, a large part of which (in particular wind generation and solar generation) is affected by high levels of uncertainty. Being Renewable Energy Sources only partially controllable all this uncertainty is transferred into Power System operation. Thus, numerical simulation of Power Systems needs to be able to cope with this uncertainty, that is Stochastic Programming techniques have to be considered. Anyway, numerical simulation of Power Systems also involves a very large number of variables, some of which are of integer nature: a large scale mixed integer stochastic problem has thus to be solved, but the requirement in computational power and time could reveal to be far too large. Thus, heuristic procedures must be introduced. In this paper it is introduced the sMTSIM model, based on a Stochastic continuous relaxation of the mixed integer Unit Commitment problem and on an heuristic procedure capable of re-introducing the mixed integer constraints.

Evaluation of Two Lagrangian Dual Optimization Algorithms for Large-Scale Unit Commitment Problems

Lagrangian relaxation is the most widely adopted method for solving unit commitment (UC) problems. It consists of two steps: dual optimization and primal feasible solution construction. The dual optimization step is crucial in determining the overall performance of the solution. This paper intends to evaluate two dual optimization methods - one based on subgradient (SG) and the other based on the cutting plane. Large-scale UC problems with hundreds of thousands of variables and constraints have been generated for evaluation purposes. It is found that the evaluated SG method yields very promising results.

An Advanced Quantum-Inspired Evolutionary Algorithm for Unit Commitment

Based on a quantum-inspired evolutionary algorithm for unit commitment, this paper proposed ways to advance the efficiency and robustness of the algorithm so that its capacity for application in large-scale unit commitment problems can be significantly enhanced. The paper develops an advanced quantum-inspired evolutionary unit commitment algorithm by developing a new initialization method based on unit priority list and a special Q-bit expression for ensuring diversity in the initial search area for improving the efficiency of solution searching. Different techniques such as multi-observation, single-search, and group-search are also proposed for incorporation in the advanced algorithm. The advanced algorithm is tested and compared with the earlier quantum-inspired evolutionary algorithm and a number of known methods through its applications to test systems with up to 100 generator units for a 24-h scheduling horizon.

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.

An Improved Differential Evolution Scheme for the Solution of Large-Scale Unit Commitment Problems

This paper presents an improved differential evolution (IDE) method for the solution of large-scale unit commitment (UC) problems. The objective of the proposed scheme is to determine the generation schedule which minimizes the total operating cost over a given time horizon subject to a variety of constraints. Through its use of enhanced acceleration and migration processes, the IDE method limits the population size required in the search procedure and is therefore an ideal candidate for the solution of large-scale combinatorial optimization problems. The effectiveness of the proposed approach is verified by performing a series of simulations based upon the practical Tai-Power System (TPS) and various other power systems presented in the literature. In general, the results show that the IDE scheme outperforms existing deterministic and stochastic optimization methods both in terms of the quality of the solutions obtained and the computational cost. Furthermore, it is found that the magnitude of the cost savings achieved by the IDE scheme compared to that obtained by the other optimization techniques increases as the number of generating units within the power system increases. Therefore, the proposed scheme represents a particularly effective technique for the solution of large-scale UC problems.

Quantum-Inspired Evolutionary Algorithm Approach for Unit Commitment

This paper presents a novel method for solving the unit commitment (UC) problem based on quantum-inspired evolutionary algorithm (QEA). The proposed method applies QEA to handle the unit-scheduling problem and the Lambda-iteration technique to solve the economic dispatch problem. The QEA method is based on the concept and principles of quantum computing, such as quantum bits, quantum gates and superposition of states. QEA employs quantum bit representation, which has better population diversity compared with other representations used in evolutionary algorithms, and uses quantum gate to drive the population towards the best solution. The mechanism of QEA can inherently treat the balance between exploration and exploitation and also achieve better quality of solutions, even with a small population. The proposed method is applied to systems with the number of generating units in the range of 10 to 100 in a 24-hour scheduling horizon and is compared to conventional methods in the literature. Moreover, the proposed method is extended to solve a large-scale UC problem in which 100 units are scheduled over a seven-day horizon with unit ramp-rate limits considered. The application studies have demonstrated the superior performance and feasibility of the proposed algorithm.

Scalable unit commitment by memory-bounded ant colony optimization with [formula omitted] local search

Ant colony optimization (ACO) is successfully applied in optimization problems. Performance of the basic ACO for small problems with moderate dimension and searching space is satisfactory. As the searching space grows exponentially in the large-scale unit commitment problem, the basic ACO is not applicable for the vast size of pheromone matrix of ACO in practical time and physical computer-memory limit. However, memory-bounded methods prune the least-promising nodes to fit the system in computer memory. Therefore, the authors propose memory-bounded ant colony optimization (MACO) in this paper for the scalable (no restriction for system size) unit commitment problem. This MACO intelligently solves the limitation of computer memory, and does not permit the system to grow beyond a bound on memory. In the memory-bounded ACO implementation, A ∗ heuristic is introduced to increase local searching ability and probabilistic nearest neighbor method is applied to estimate pheromone intensity for the forgotten value. Finally, the benchmark data sets and existing methods are used to show the effectiveness of the proposed method.

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.

A New Lagrangian Multiplier Update Approach for Lagrangian Relaxation Based Unit Commitment

Large scale unit commitment problems are of combinatorial nature and are usually very hard to solve. Among various algorithms, Lagrangian relaxation (LR) based method is one the most promising approaches. LR method typically includes two steps: the dual optimization and feasible solution construction. The dual optimization plays a crucial role in determining the overall computational efficiency and solution quality of the algorithm. The subgradient based method is widely used for dual optimization, but often suffers from slow convergence. This article presents an improved subgradient based method based on the concept of step size scaling factor that may achieve speedy convergence for dual optimization. Case studies have demonstrated the effectiveness of the proposed approach.

Absolutely Stochastic Simulated Annealing Approach to Large Scale Unit Commitment Problem

This paper presents a new approach to the unit commitment problem using the absolutely stochastic simulated annealing method. In each iteration, a solution is taken with a certain probability. Typically, in the simulated annealing minimization method, a higher cost feasible solution is accepted with temperature-dependent probability, but other solutions are accepted deterministically. That may lead to the near optimization slowly. However in this paper, all the solutions, both higher and lower cost, are associated with acceptance probabilities. Besides, the number of bits flipping is decided by an appropriate distribution. Excess units with system-dependent probability distribution handle constraints efficiently. To reduce the economic load dispatch (ELD) overhead recalculations, a sign bit vector is introduced as well. The proposed method is tested using the reported problem data sets. Simulation results for the systems up to 100 units are compared to the previous reported results. Numerical results show an improvement in solution cost and time over to the results obtained from recent powerful algorithms.

Emerging solution of large-scale unit commitment problem by Stochastic Priority List

This paper presents a new approach for unit commitment problem using Stochastic Priority List method. In this method, rapidly some initial unit commitment schedules are generated by Priority List method and priority based stochastic window system. Excess units are added with system dependent probability distribution to avoid overlooking a desired solution during repeated search. Constraints are not considered in this stage. Then schedules are modified gradually using the problem specific heuristics to fulfill constraints. To reduce calculations, heuristics are applied only to the solutions, which can be expected to improve. Besides, sign vector is introduced to reduce economic load dispatch (ELD) overhead recalculations. This process is repeated for optimal solution. The proposed method is tested using the reported problem data set. Simulation results for the systems up to 100-unit are compared to previous reported results. Numerical results show an improvement in solution cost and time compared to the results obtained from Genetic Algorithm and others.

Fast technique for unit commitment by genetic algorithm based on unit clustering

The paper presents a new approach to the large-scale unit-commitment problem. To reduce computation time and to satisfy the minimum up/down-time constraint easily, a group of units having analogous characteristics is clustered. Then, this ‘clustered compress’ problem is solved by means of a genetic algorithm. Besides, problem-oriented powerful tools such as relaxed-pruned ELD, intelligent mutation, shift operator etc. make the proposed approach more effective with respect to both cost and execution time. The proposed algorithm is tested using the reported problem data set. Simulation results for systems of up to 100-unit are compared with previous reported results. Numerical results show an improvement in the solution cost compared with the results obtained from a genetic algorithm with standard operations.

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 Fast Technique for Unit Commitment by Genetic Algorithm Based on Unit Integration

This paper presents a new approach for large scale unit commitment problem. The unit commitment problem is one of most difficult optimization problem in power system, because this problem has many constraints and huge amount of combinations. This cause excessive computation time, making it difficult to solve large scale unit commitment problem. To reduce computation time, a group of units of analogous characteristics are integrated as one generator. This integrated problem is solved by genetic algorithm. The proposed algorithm was tested on a reported problem data. Numerical results for system of up to 100 units are compared to previously reported results. From simulation results, satisfactory schedules are determined in reasonable computation time in comparison with previously reported results.

Fast solution technique for large-scale unit commitment problem using genetic algorithm

An approach for a large-scale unit commitment problem is presented. The unit commitment (UC) problem plays a major role in power systems, because the improvement of commitment schedules results in the reduction of operating costs. However, the unit commitment problem is one of the most difficult optimisation problems in power systems, 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 systems up to 100 units are compared to previously reported results.

Multi-area unit commitment for large-scale power systems

A large-scale multi-area unit commitment method is presented using a Lagrangian relaxation approach. The problem with a transmission network of several thousand buses and lines is equivalently modelled by a system with relatively few areas. Crucial tie-lines between areas are directly modelled. The network within an area is simplified from the application requirements. Based on a DC-flow model, the transmission constraints, as well as system demand and reserve requirements, are relaxed by attaching Lagrange multipliers to form a multi-phase optimisation structure. A large-scale problem based on PG&E's power system with more than 2200 buses and 2500 lines is tested. Small cases are also tested for comparison. The numerical testing results show that the method is able to handle transmission constraints in large-scale unit commitment problems.

Stochastic optimization of unit commitment: a new decomposition framework

This paper presents a new stochastic decomposition method well-suited to deal with large-scale unit commitment problems. In this approach, random disturbances are modeled as scenario trees. Optimization consists in minimizing the average generation cost over this tree-shaped future. An augmented Lagrangian technique is applied to this problem. At each iteration, nonseparable terms introduced by the augmentation are linearized so as to obtain a decomposition algorithm. This algorithm may be considered as a generalization of price decomposition methods, which are now classical in this field, to the stochastic framework. At each iteration, for each unit, a stochastic dynamic subproblem has to be solved. Prices attached to nodes of the scenario trees are updated by the coordination level. This method has been applied to a daily generation scheduling problem. The use of an augmented Lagrangian technique, provides satisfactory convergence properties to the decomposition algorithm. Moreover, numerical simulations show that compared to a classical deterministic optimization with reserve constraints, this new approach achieves substantial savings.

A solution method of unit commitment by artificial neural networks

The authors explore the possibility of applying the Hopfield neural network to combinatorial optimization problems in power systems, in particular to unit commitment. A large number of inequality constraints included in unit commitment can be handled by dedicated neural networks. As an exact mapping of the problem onto the neural network is impossible with the state of the art, a two-step solution method was developed. First, generators to be stored up at each period are determined by the network, and then their outputs are adjusted by a conventional algorithm. The proposed neural network could solve a large-scale unit commitment problem with 30 generators over 24 periods, and results obtained were very encouraging. >