Short-term hydrothermal scheduling using clonal selection algorithm

An efficient optimization procedure based on the clonal selection algorithm (CSA) is proposed for the solution of short-term hydrothermal scheduling problem. CSA, a new algorithm from the family of evolutionary computation, is simple, fast and a robust optimization tool for real complex hydrothermal scheduling problems. Hydrothermal scheduling involves the optimization of non-linear objective function with set of operational and physical constraints. The cascading nature of hydro-plants, water transport delay and scheduling time linkage, power balance constraints, variable hourly water discharge limits, reservoir storage limits, operation limits of thermal and hydro units, hydraulic continuity constraint and initial and final reservoir storage limits are fully taken into account. The results of the proposed approach are compared with those of gradient search (GS), simulated annealing (SA), evolutionary programming (EP), dynamic programming (DP), non-linear programming (NLP), genetic algorithm (GA), improved fast EP (IFEP), differential evolution (DE) and improved particle swarm optimization (IPSO) approaches. From the numerical results, it is found that the CSA-based approach is able to provide better solution at lesser computational effort.     

Short-term hydrothermal generation scheduling model using a genetic algorithm

A new model to deal with the short-term generation scheduling problem for hydrothermal systems is proposed. Using genetic algorithms (GAs), the model handles simultaneously the subproblems of short-term hydrothermal coordination, unit commitment, and economic load dispatch. Considering a scheduling horizon period of a week, hourly generation schedules are obtained for each of both hydro and thermal units. Future cost curves of hydro generation, obtained from long and mid-term models, have been used to optimize the amount of hydro energy to be used during the week. In the genetic algorithm (GA) implementation, a new technique to represent candidate solutions is introduced, and a set of expert operators has been incorporated to improve the behavior of the algorithm. Results for a real system are presented and discussed.     

An improved PSO technique for short-term optimal hydrothermal scheduling

This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using improved particle swarm optimization (IPSO) technique. The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network, water transport delay and scheduling time linkage that make the problem of finding global optimum difficult using standard optimization methods. In this paper an improved PSO technique is suggested that deals with an inequality constraint treatment mechanism called as dynamic search-space squeezing strategy to accelerate the optimization process and simultaneously, the inherent basics of conventional PSO algorithm is preserved. To show its efficiency and robustness, the proposed IPSO is applied on a multi-reservoir cascaded hydro-electric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results are compared with those obtained by dynamic programming (DP), nonlinear programming (NLP), evolutionary programming (EP) and differential evolution (DE) approaches. The simulation results reveal that the proposed IPSO appears to be the best in terms of convergence speed, solution time and minimum cost when compared with established methods like EP and DE.     

Short-term hydrothermal generation scheduling by a modified dynamic neighborhood learning based particle swarm optimization

The main objective of the short-term hydrothermal generation scheduling (SHGS) problem is to determine the optimal strategy for hydro and thermal generation in order to minimize the fuel cost of thermal plants while satisfying various operational and physical constraints. Usually, SHGS is assumed for a 1 day or a 1 week planing time horizon. It is viewed as a complex non-linear, non-convex and non-smooth optimization problem considering valve point loading (VPL) effect related to the thermal power plants, transmission loss and other constraints. In this paper, a modified dynamic neighborhood learning based particle swarm optimization (MDNLPSO) is proposed to solve the SHGS problem. In the proposed approach, the particles in swarm are grouped in a number of neighborhoods and every particle learns from any particle which exists in current neighborhood. The neighborhood memberships are changed with a refreshing operation which occurs at refreshing periods. It causes the information exchange to be made with all particles in the swarm. It is found that mentioned improvement increases both of the exploration and exploitation abilities in comparison with the conventional PSO. The presented approach is applied to three different multi-reservoir cascaded hydrothermal test systems. The results are compared with other recently proposed methods. Simulation results clearly show that the MDNLPSO method is capable of obtaining a better solution.     

Constraint programming for nurse scheduling

Nurse scheduling is a difficult, multifaceted problem. Here, the authors have presented the efficiency of Constraint Programming for solving this problem. The results obtained are very satisfactory for response time and for flexibility. The advantages of implementing this method are multiple: 1) it saves much time for the head nurse in the generation of schedules (the authors met head nurses for whom the task of scheduling takes a full working day); 2) the proposed system is not a rigid tool for schedule generation, but it is designed to help the decision maker in decisions and negotiations; 3) the proposed system is a flexible tool with respect to individual requests and for overcoming unforeseen absences; 4) it is very easy to manage constraints whether, for example, to define new constraints, activating or deactivating particular constraints, or modifying an already defined constraint. Ilog-Solver is a powerful tool for constraint programming. It provides the user with several types of variables, and the possibility of defining a specific constraint for the problem. The integration of object programming provided by Ilog-Solver allows better representation and saves much memory     

Optimization-based sale transactions and hydrothermal scheduling

Selling and purchasing power are important activities for electric utilities because of potential savings. When a selling utility presents an offer including prices, power levels and durations, a purchasing utility selects power levels and durations within the offered range subject to relevant constraints. The decision making process is complicated because transactions are coupled with system demand and reserve, therefore decisions have to be made in conjunction with the commitment and dispatching of units. Furthermore, transaction decisions have to be made in almost real time in view of the competitiveness of the power market caused by deregulation. In this paper, transactions are analyzed from a selling utility's viewpoint for a system consisting of thermal, hydro and pumped-storage units. To effectively solve the problem, linear sale revenues are approximated by nonlinear functions, and nonprofitable options are identified and eliminated from consideration. The multipliers are then updated at the high level by using a modified subgradient method to obtain near optimal solutions quickly. Testing results show that the algorithm produces good sale offers efficiently     

Short-term resource scheduling with ramp constraints [powergeneration scheduling]

This paper describes a Lagrangian relaxation-based method to solve the short-term resource scheduling (STRS) problem with ramp constraints. Instead of discretizing the generation levels, the ramp rate constraints are relaxed with the system demand constraints using Lagrange multipliers. Three kinds of ramp constraints, startup, operating and shutdown ramp constraints are considered. The proposed method has been applied to solve the hydro-thermal generation scheduling problem at PG&E. An example alone with numerical results is also presented     

Generator parameter identification using evolutionary programming

This paper presents a new approach of evolutionary programming (EP) to the parameter identification problem. The EP is used to identify the generator parameters based on the measurements of generator outputs which are highly contaminated by noise. The EP is a very powerful search method and can be used for parameter identification of complex systems, by contrast to the conventional techniques such as the extended Kalman filter (EKF) method. Comparison between the two different methodologies, EP and EKF, is presented in the paper to show the potential of applications of the EP to parameter identification and system modelling.     

Application of evolutionary programming to reactive powerplanning-comparison with nonlinear programming approach

This paper proposes an application of evolutionary programming (EP) to reactive power planning (RPP). Several techniques have been developed to make EP practicable to solve a real power system problem and other practical problems. The proposed approach has been used in the IEEE 30-bus system and a practical power system. For illustration purposes, only results for the IEEE 30-bus system are given. Simulation results, compared with those obtained by using a conventional gradient-based optimization method, Broyden's method, are presented to show that the present method is better for power system planning. In the case of optimization of noncontinuous and nonsmooth functions, EP is much better than nonlinear programming. The comprehensive simulation results show a great potential for applications of EP in power system economical and secure operation, planning and reliability assessment     

Civilized swarm optimization for multiobjective short-term hydrothermal scheduling

This paper presents a solution technique for multiobjective short-term hydrothermal scheduling (MSTHTS) through civilized swarm optimization (CSO) which is the hybrid of society–civilization algorithm (SCA) and particle swarm optimization (PSO). The intra and inter society communication mechanisms of SCA have been embedded into the food-searching strategy of PSO to form CSO. The MSTHTS problem is formulated by considering economic and emission objectives. A new ideal guide method has been proposed to find out the Pareto-optimal front. Multi-reservoir cascaded hydro power plants having nonlinear generation characteristics and thermal power plants with non-smooth cost and emission curves are considered for analysis. Other aspects such as, water transport delay, water availability, storage conformity, power loss and operating limits are fully accounted in the problem formulation. The performance of the proposed CSO is demonstrated through two MSTHTS problems and the results are compared with those presented in the literature. CSO along with the new ideal guide method outperforms all the previous approaches by providing quality Pareto-optimal fronts.     

Optimal reactive power planning using evolutionary algorithms: acomparative study for evolutionary programming, evolutionary strategy,genetic algorithm, and linear programming

This paper presents a comparative study for three evolutionary algorithms (EAs) to the optimal reactive power planning (ORPP) problem: evolutionary programming, evolutionary strategy, and genetic algorithm. The ORPP problem is decomposed into P- and Q-optimization modules, and each module is optimized by the EAs in an iterative manner to obtain the global solution. The EA methods for the ORPP problem are evaluated against the IEEE 30-bus system as a common testbed, and the results are compared against each other and with those of linear programming     

Optimization-based scheduling of hydrothermal power systems withpumped-storage units

This paper presents an optimization-based method for scheduling hydrothermal systems based on the Lagrangian relaxation technique. After system-wide constraints are relaxed by Lagrange multipliers, the problem is converted into the scheduling of individual units. This paper concentrates on the solution methodology for pumped-storage units. There are, many constraints limiting the operation of a pumped-storage unit, such as pond level dynamics and constraints, and discontinuous generation and pumping regions. The most challenging issue in solving pumped-storage subproblems within the Lagrangian relaxation framework is the integrated consideration of these constraints. The basic idea of the method is to relax the pond level dynamics and constraints by using another set of multipliers. The subproblem is then converted into the optimization of generation or pumping; levels for each operating state at individual hours, and the optimization of operating states across hours. The optimal generation or pumping level for a particular operating state at each hour can be obtained by optimizing a single variable function without discretizing pond levels. Dynamic programming is then used to optimize operating states across hours with only a few number of states and transitions. A subgradient algorithm is used to update the pond level Lagrangian multipliers. This method provides an efficient way to solve a class of subproblems involving continuous dynamics and constraints, discontinuous operating regions, and discrete operating states     

Power system operations scheduling using separable programming

The problem of electric power operations scheduling comprises maintenance scheduling, intermediate- and short-term hydro-thermal scheduling, unit commitment and production scheduling. Recognizing the inter-relationship among these subproblems, the effect on one another is analyzed. Computationally efficient formulations and algorithms for maintenance scheduling and intermediate- and short-term hydro-thermal scheduling are presented.A variation of the separable programming technique is presented. This results in a linear programming formulation of the nonlinear scheduling problem. This technique is applied to a hypothetical system containing nuclear, fossil, hydro-electric and pumped-storage units. The large problem of hydro-thermal scheduling due to the inclusion of a nuclear unit is decomposed into two stages. In the first stage, the relatively stable nuclear generation is optimized with respect to the generation from large fossil-steam units. Hourly generation levels for all units in the system are then determined in the second stage.     

Modified cuckoo search algorithm for short-term hydrothermal scheduling

This paper proposes a modified cuckoo search algorithm (MCSA) for solving short-term hydrothermal scheduling (HTS) problem. The considered HTS problem in this paper is to minimize total cost of thermal generators with valve point loading effects satisfying power balance constraint, water availability, and generator operating limits. The MCSA method is based on the conventional CSA method with modifications to enhance its search ability. In the MCSA, the eggs are first sorted in the descending order of their fitness function value and then classified in two groups where the eggs with low fitness function value are put in the top egg group and the other ones are put in the abandoned one. The abandoned group, the step size of the Lévy flight in CSA will change with the number of iterations to promote more localized searching when the eggs are getting closer to the optimal solution. On the other hand, there will be an information exchange between two eggs in the top egg group to speed up the search process of the eggs. The proposed MCSA method has been tested on different systems and the obtained results are compared to those from other methods available in the literature. The result comparison has indicated that the proposed method can obtain higher quality solutions than many other methods. Therefore, the proposed MCSA can be a new efficient method for solving short-term fixed-head hydrothermal scheduling problems.     

Non-uniform composite representation hydroelectric systems forlong-term hydrothermal scheduling

This paper presents a nonuniform composite representation of hydroelectric power systems for use in long-term hydrothermal generation scheduling. This representation was developed from reservoir operational rules based on optimal reservoir trajectories obtained with a deterministic hydrothermal scheduling algorithm. A test system consisting of 7 large hydroelectric power plants of the Southeast Brazilian power system with 12572 MW of installed power capacity was selected for a case study. Operational cost comparisons with the classical uniform composite representation reveal significant savings     

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 second order network flow algorithm for hydrothermal scheduling

This paper presents a second-order network flow algorithm specially designed for hydrothermal scheduling problems. The algorithm is based on the truncated Newton method and takes advantage of the particular layout of the hydro scheduling network. The three-diagonal structure of the Hessian matrix is also exploited. Heuristic strategies for variable partition into basic-superbasic-nonbasic sets are suggested to improve the algorithm's efficiency. Tests with systems of dimensions up to 27 hydro plants in cascade have been performed in order to evaluate the algorithm's performance and compare some variable partition strategies. Results have demonstrated the high efficiency of the code     

A short term hydrothermal scheduling approach for dominantly hydrosystems

A short-term hydrothermal scheduling approach is presented for predominantly hydroelectric systems. The model takes into account both the operating hydroelectric system and the electric transmission network constraints. The model consists of a simulation of the hydraulic system with the discharge decisions given by an optimal DC power flow algorithm. The release targets of the reservoirs, established by long-term operational planning, are enforced by a dual Lagrangean approach that fixes a penalty for the use of water in the reservoirs. Two illustrative examples have been solved in order to evaluate the efficiency of the approach     

基于微分进化算法的水火电短期优化调度的研究

在电力市场机制不断更迭情况下,针对水电发展趋于完善的过渡时期,充分考虑当前环境下水火电协调的新内涵,以电网经营企业利益为核心,提出了适合当前阶段,含阶梯水电站的水火电混合系统发电侧短期购电费用最低的联合调度模型。初次在国内引入微分进化算法到电力系统短期优化调度,以使水火电的出力分配达到最优。实际算例的计算结果表明,该算法能够较好地实现该模型下的经济调度。