Unit Commitment Solution Research Articles

Fuzzy unit commitment solution—A novel twofold simulated annealing approach

The authors propose a twofold simulated annealing (twofold-SA) method for the optimization of fuzzy unit commitment formulation in this paper. In the proposed method, simulated annealing (SA) and fuzzy logic are combined to obtain SA acceptance probabilities from fuzzy membership degrees. Fuzzy load is calculated from error statistics and an initial solution is generated by a priority list method. The initial solution is decomposed into hourly-schedules and each hourly-schedule is modified by decomposed-SA using a bit flipping operator. Fuzzy membership degrees are the selection attributes of the decomposed-SA. A new solution consists of these hourly-schedules of entire scheduling period after repair, as unit-wise constraints may not be fulfilled at the time of an individual hourly-schedule modification. This helps to detect and modify promising schedules of appropriate hours. In coupling-SA, this new solution is accepted for the next iteration if its cost is less than that of current solution. However, a higher cost new solution is accepted with the temperature dependent total cost membership function. Computation time of the proposed method is also improved by the imprecise tolerance of the fuzzy model. Besides, excess units with the system dependent probability distribution help to handle constraints efficiently and imprecise economic load dispatch (ELD) calculations are modified to save the execution time. The proposed method is tested using standard reported data sets. Numerical results show an improvement in solution cost and time compared to the results obtained from other existing methods.

Reliability Constrained Unit Commitment Using Simulated Annealing

This paper proposes a new method for the incorporation of the unit unavailability and the uncertainty of the load forecast in the solution of the short-term unit commitment problem. The above parameters are taken into account in order to assess the required spinning reserve capacity at each hour of the dispatch period, so as to maintain an acceptable reliability level. The unit commitment problem is solved by a simulated annealing algorithm resulting in near-optimal unit commitment solutions. The evaluation of the required spinning reserve capacity is performed by implementing reliability constraints, based on the expected unserved energy and loss of load probability indexes. In this way, the required spinning reserve capacity is effectively scheduled according to the desired reliability level. Numerical simulations have proven the efficiency of the proposed method

Neural computation using discrete and continuous Hopfield networks for power system economic dispatch and unit commitment

A new method using artificial neural networks for the solution of the unit commitment (UC) and economic dispatch (ED) using Hopfield neural network (HNN) is presented. Discrete and Continuous Hopfield Networks have been used earlier to solve UC and ED problems separately. But these two problems are completely interdependent. Due to their inseparable nature, both the problems must be solved simultaneously. The difficulty in combining these problems is that while the first one requires a discrete neuron model, the latter requires a continuous neuron model. The combined solution of these problems using HNN requires the interconnection of discrete and continuous neural network models and the formulation of a unified energy function, which is quite complicated. The important contribution of this work is the proposal of a new architecture for the discrete HNN for UC and the output of the UC module is used as input to the continuous HNN for ED. The associated advantage of using HNN for the combined solution of UC and ED is the decoupling of their interdependency, i.e., both the UC and ED are iteratively solved using respective HNN for the particular period. The implementation of the proposed method causes a considerable reduction in the HNN size and hence complexity and computation requirements, compared to earlier attempts. The method was successfully tested for different cases (3, 5, 6, 10 and 26 generator units), with varying load pattern of different durations (24 and 168 h) on Matlab on P-IV machine in windows enviroment. Each case study is done with an aim to bring out the important features of the proposed method. The results for the case studies are presented and important observations are discussed.

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.

Long-Term Security-Constrained Unit Commitment: Hybrid Dantzig–Wolfe Decomposition and Subgradient Approach

The solution of a long-term security-constrained unit commitment (SCUC) problem, which often spans several months to a year, may consider multiple long-term fuel and emission constraints in addition to operating constraints embedded in short-term SCUC. The size and the complexity of long-term SCUC are often beyond reasonable computing time and resources. Hence, Lagrangian relaxation is applied in this paper to manage coupling constraints over the entire period. Based on dual relaxation, the large-scale optimization problem is decomposed into many tractable short-term SCUC subproblems without long-term fuel and emission constraints. The resource penalty prices are linking signals for the coordination of subproblems. The short-term SCUC may be solved by any numerical optimization methods, including mixed integer programming and Lagrangian relaxation. A hybrid subgradient and Dantzig-Wolfe decomposition approach is presented for managing Lagrangian multipliers in the large-scale dual optimization of long-term SCUC problem. The proposed hybrid approach is a tradeoff between calculation speed and accuracy of the long-term SCUC solution. A modified IEEE 118-bus system is analyzed to exhibit the effectiveness of the proposed approach.

Security-Constrained Unit Commitment With AC Constraints*

In a restructured power market, the independent system operator (ISO) executes the security-constrained unit commitment (SCUC) program to plan a secure and economical hourly generation schedule for the day-ahead market. This paper introduces an efficient SCUC approach with ac constraints that obtains the minimum system operating cost while maintaining the security of power systems. The proposed approach applies the Benders decomposition for separating the unit commitment (UC) in the master problem from the network security check in subproblems. The master problem applies the augmented Lagrangian relaxation (LR) method and dynamic programming (DP) to solve UC. The subproblem checks ac network security constraints for the UC solution to determine whether a converged and secure ac power flow can be obtained. If any network violations arise, corresponding Benders cuts will be formed and added to the master problem for solving the next iteration of UC. The iterative process will continue until ac violations are eliminated and a converged optimal solution is found. In this paper, a six-bus system and the IEEE 118-bus system with 54 units are analyzed to exhibit the effectiveness of the proposed approach.

Security-Constrained Unit Commitment With AC Constraints

In a restructured power market, the independent system operator (ISO) executes the security-constrained unit commitment (SCUC) program to plan a secure and economical hourly generation schedule for the day-ahead market. This paper introduces an efficient SCUC approach with ac constraints that obtains the minimum system operating cost while maintaining the security of power systems. The proposed approach applies the Benders decomposition for separating the unit commitment (UC) in the master problem from the network security check in subproblems. The master problem applies the augmented Lagrangian relaxation (LR) method and dynamic programming (DP) to solve UC. The subproblem checks ac network security constraints for the UC solution to determine whether a converged and secure ac power flow can be obtained. If any network violations arise, corresponding Benders cuts will be formed and added to the master problem for solving the next iteration of UC. The iterative process will continue until ac violations are eliminated and a converged optimal solution is found. In this paper, a six-bus system and the IEEE 118-bus system with 54 units are analyzed to exhibit the effectiveness of the proposed approach.

A Solution to the Stochastic Unit Commitment Problem Using Chance Constrained Programming

This paper develops a solution method for scheduling units of a power-generating system to produce electricity by taking into consideration the stochasticity of the hourly load and its correlation structure. The unit commitment problem is initially formulated as a chance constrained optimization problem in which we require that the load be met with a specified high probability over the entire time horizon. The solution procedure consists of solving a sequence of deterministic versions of the unit commitment problem that converge to the solution of the chance constrained program. For the deterministic unit commitment problems, Lagrangian relaxation is used to separate the dual problem into its subproblems. Each subproblem is solved by a dynamic program. The initial results indicate that accounting for the correlation structure of the hourly loads reduces the value of the objective function when the optimization problem is formulated as a chance constrained program. Monte Carlo simulation is used to verify the accuracy of the solution provided by the algorithm. The relationship that the unit commitment solution found using the chance constrained optimization approach has with that found using conventional spinning reserves is discussed.

Ant colony optimization algorithm with random perturbation behavior to the problem of optimal unit commitment with probabilistic spinning reserve determination

In this paper, a novel ant colony optimization algorithm with random perturbation behavior (RPACO) based on combination of general ant colony optimization and stochastic mechanism is developed for the solution of optimal unit commitment (UC) with probabilistic spinning reserve determination. In general, the purpose of UC is to enhance the economical efficiency as could as possible while simultaneously satisfying physical and operation constraints of individual unit. Consider the possibility of generating unit failure, the requirement, the sufficient spinning reserve capacity to ensure adequate reliability levels, must be satisfied by the commitment schedule. The security function approach is applied to evaluate the desired level of system security, and the proposed method in this paper, RPACO, is adopted to solve the UC problems. The effectiveness of the proposed method has been demonstrated on the corresponding numerical results. Further, the sensitivity of the desired security level to the optima during optimization is investigated in this paper.

A study of a unit commitment problem with transmission constraints

AbstractUnit commitment problem is an optimization problem to determine the start‐up and shut‐down schedule of thermal units while satisfying various constraints, for example, generation‐demand balance, unit minimum up/down time, system reserve, and so on. Since this problem involves a large number of 0–1 type variables that represent up/down status of the unit and continuous variables expressing generation output, it is a difficult combinatorial optimization problem to solve. The study at present concerns the method for requiring the suboptimum solution efficiently.Unit commitment method widely used solves the problem without consideration of voltage, reactive power, and transmission constraints. In this paper, we will propose a solution of unit commitment with voltage and transmission constraints, based on the unit decommitment procedure (UDP) method, heuristic method, and optimal power flow (OPF). In this method, initial unit status will be determined from random numbers and the feasibility will be checked for minimum start‐up/shut‐down time and demand‐generation balance. If the solution is infeasible, the initial solution will be regenerated until a feasible solution can be found. Next, OPF is applied for each time period with the temporary unit status. Then, the units that have less contribution to the cost are detected and will be shut down based on the unit decommitment rules. This process will be repeated until suboptimal solution is obtained.The proposed method has been applied to the IEEE 118‐bus test system with 36 generating units with successful result. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(3): 36–45, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10187

Unit commitment solution methodology using genetic algorithm

Unit commitment solution methodology using genetic algorithm

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).

An evolving neural network approach in unit commitment solution

In this paper, the Genetic Algorithm (GA) is used to evolve the weight and the interconnection of the neural network to solve the Unit Commitment problem. We will emphasize on the determination of the appropriate GA parameters to evolve the neural network, i.e. the population size and probabilities of crossover and mutation, and the method used for selection amongst generations such as Tournament selection, Roulette Wheel selection and Ranking selection. Performance comparisons are conducted to analyze the learning curve of different parameters, to find out which has a dominant influence on the effectiveness of the algorithm.

Using integer programming to refine Lagrangian-based unit commitment solutions

The authors develop a technique for refining the unit commitment obtained from solving the Lagrangian. Their model is a computer program with nonlinear constraints. It can be solved to optimality using the branch-and-bound technique. Numerical results indicate a significant improvement in the quality of the solution obtained.

99/03743 A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming: Duo, H. et al. Electric Power Systems Research, 1999, 51, (1), 71–77

99/03743 A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming: Duo, H. et al. Electric Power Systems Research, 1999, 51, (1), 71–77

A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming

This paper proposes an approach which combines Lagrangian relaxation principle and evolutionary programming for short-term thermal unit commitment. Unit commitment is a complex combinatorial optimization problem which is difficult to be solved for large-scale power systems. Up to now, the Lagrangian relaxation is considered the best to deal with large-scale unit commitment although it cannot guarantee the optimal solution. In this paper, an evolutionary programming algorithm is used to improve a solution obtained by the Lagrangian relaxation method: Lagrangian relaxation gives the starting point for a evolutionary programming procedure. The proposed algorithm takes the advantages of both methods and therefore it can search a better solution within short computation time. Numerical simulations have been carried out on two test systems of 30 and 90 thermal units power systems over a 24-hour periods.

Optimal scheduling of spinning reserve

Effective control of spinning reserve can provide substantial cost reductions in large power systems. This paper suggests that this goal can he achieved by tightly integrating a probabilistic reserve assessment with the unit commitment (UC) function. This enables the reliability of individual units and the uncertainty of the load forecast to be considered for short-term scheduling. The generation can then be scheduled to meet a given risk index. It is further argued that the optimal value of this risk index should be selected on the basis of a tradeoff between the total schedule cost obtained from the UC solution and the expected cost of energy not served which can be derived from the probabilistic reserve assessment. Finally, the problem of over-commitment of reserve in Lagrangian relaxation based UC is reduced by means of a new unit decommitment technique incorporating a look-ahead feature.

An enhanced simulated annealing approach to unit commitment

Owing to the inability of simulated annealing (SA) to generate solutions that always satisfy all the constraints, the performance of a pure SA-approach established by previous researchers in solving the unit commitment (UC) problem is not so promising. The SA technique is, however, easy to implement, requires little expert knowledge and is not memory intensive. Hence, this article attempts to develop an enhanced SA-approach for solving the UC problem by adopting mechanisms to ensure that the candidate solutions produced are feasible and satisfy all the constraints. The performance of the enhanced SA-based algorithm is demonstrated through two real-life UC problems in power systems. The results of the two studies are also compared with previous reported UC solution methods.

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.