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     

A genetic algorithm solution approach to the hydrothermal coordination problem

In this paper, a genetic algorithm solution to the hydrothermal coordination problem is presented. The generation scheduling of the hydro production system is formulated as a mixed-integer, nonlinear optimization problem and solved with an enhanced genetic algorithm featuring a set of problem-specific genetic operators. The thermal subproblem is solved by means of a priority list method, incorporating the majority of thermal unit constraints. The results of the application of the proposed solution approach to the operation scheduling of the Greek Power System, comprising 13 hydroplants and 28 thermal units, demonstrate the effectiveness of the proposed algorithm.     

Scheduling of hydrothermal power systems

The authors present a method for scheduling hydrothermal power systems based on the Lagrangian relaxation technique. By using Lagrange multipliers to relax system-wide demand and reserve requirements, the problem is decomposed and converted into a two-level optimization problem. Given the sets of Lagrange multipliers, a hydro unit subproblem is solved by a merit order allocation method, and a thermal unit subproblem is solved by using dynamic programming without discretizing generation levels. A subgradient algorithm is used to update the Lagrange multipliers. Numerical results based on Northeast Utilities data show that this algorithm is efficient, and near-optimal solutions are obtained. Compared with previous work where thermal units were scheduled by using the Lagrangian relaxation technique and hydro units by heuristics, the new coordinated hydro and thermal scheduling generates lower total costs and requires less computation time     

A new method for unit commitment with ramping constraints

Unit commitment with ramping constraints is a very difficult problem with significant economic impact. A new method is developed in this paper for scheduling units with ramping constraints within Lagrangian relaxation framework based on a novel formulation of the discrete states and the integrated applications of standard dynamic programming for determining the optimal discrete states across hours, and constructive dynamic programming for determining optimal generation levels. A section of consecutive running or idle hours is considered as a commitment state. A constructive dynamic programming (CDP) method is modified to determine the optimal generation levels of a commitment state without discretizing generation levels. The cost-to-go functions, required only for a few corner points with a few continuous state transitions at a particular hour, are constructed in the backward sweep. The optimal generation levels can be obtained in the forward sweep. The optimal commitment states across the scheduling horizon can then be obtained by standard dynamic programming. Numerical testing results show that this method is efficient and the optimal commitment and generation levels are obtained in a systematic way without discretizing or relaxing generation levels.     

Optimal Short Term Operation Planning of a Large Hydrothermal Power System Based on a Nonlinear Network Flow Concept

This paper presents a procedure for solving the short term generation scheduling problem for a large hydrothermal system that includes transmission limitations. The integrated system is divided into a hydro and a thermal subsystem. A reduced gradient algorithm is employed for the solution of the hydro subproblem. This algorithm is specialized to efficiently solve nonlinear network flow problems with additional constraints of non-netwrk type. The thermal subsystem is solved using a fast unit commitment and dispatch algorithm. A case study with the Swedish system is discussed.     

A FAST ALGORITHM FOR OPTIMAL HYDROTHERMAL SCHEDULING WITH CASCADED AND INDEPENDENT HYDRO PLANTS

ABSTRACT

This paper presents a fast algorithm for solving the short-term hydrothermal scheduling problem in a power system consisting of cascaded plants with time delay and independent hydro plants. The operational planning of such problem is concerned with the determination of scheduling for hydro as well as thermal plants to meet the daily system demand with the objective of minimizing the total fuel cost of the thermal plants over the day subject to the relevant operating constraints associated with the thermal and hydro plants.

The algorithm employs a fast and simple alternating solution approach for hydrothermal scheduling in which the hydro subproblem is solved using the method of local variation while the associated thermal subproblem is solved through a judicious combination of Successive Linear Programming (SLP) method and Participation Factor method. Many computational features are incorporated in the solution algorithm exploiting the inherent characteristic of the complex hydrothermal scheduling problem.     

A noise annealing neural network for hydroelectric generationscheduling with pumped-storage units

A new approach based on neural network is proposed for the hydroelectric generation scheduling with pumped-storage units at Taiwan power system. The purpose of hydroelectric generation scheduling is to determine the optimal amounts of generated powers for the hydro units in the system. To achieve an economical dispatching schedule for the hydro units including two large pumped-storage plants, a neural network is employed to reach a schedule in which total fuel cost of the thermal units over the study period is minimized. The neural network model presented can solve nonlinear constrained optimization problems with continuous decision variables. Incorporating the noise annealing concepts, the model is able to produce such a solution which is the global optimum of the original problem with probability close to 1. The proposed approach is applied to hydroelectric generation scheduling of Taiwan power system. It is concluded from the results that the proposed approach is very effective in reaching proper hydro generation schedules     

A genetic algorithm solution to the optimal short-term hydrothermal scheduling

This paper presents an algorithm for solving the hydrothermal scheduling through the application of genetic algorithm (GA). The hydro subproblem is solved using GA and the thermal subproblem is solved using lambda iteration technique. Hydro and thermal subproblems are solved alternatively. GA based optimal power flow (OPF) including line losses and line flow constraints are applied for the best hydrothermal schedule obtained from GA. A 9-bus system with four thermal plants and three hydro plants and a 66-bus system with 12 thermal plants and 11 hydro plants are taken for investigation. This proposed GA reduces the complexity, computation time and also gives near global optimum solution.     

Generation scheduling with thermal stress constraints

This paper describes a scheduling method for representing the thermal stress of turbine shafts as ramp rate constraints in the thermal commitment and dispatch of generating units. The paper uses Lagrangian relaxation for optimal generation scheduling. In applying the unit commitment, thermal stress over the elastic limit is used for calculating the ramping cost. The thermal stress contribution to generation cost requires the calculation of a set that includes thermal stress at the end of each time step; this requirement presents a complicated problem which cannot be solved by an ordinary optimization method such as dynamic programming. The paper uses an improved simulated annealing method to determine the optimal trajectory of each generating unit. Furthermore, the paper uses linear programming for economic dispatch in which thermal stress limits are incorporated in place of fixed ramp rate limits. The paper illustrates the economics of frequently ramping up/down of low cost generating units versus the cost of replacement of their turbine rotors with a shorter life span. The experimental results for a practical system demonstrate the effectiveness of the proposed method in optimizing the power system generation scheduling.     

梯级水电系统组合优化调度方法研究

文章提出两种基于Ｌａｇｒａｎｇｅ松驰技术的梯级水电系统优化调度算法,能够综合处理离散运行区间,最小启停机时间等离散约束、水库间的水力耦合网络约束以及水头影响。基于实际系统数据的数值仿真,表明了该算法的有效性和实用性。     

基于改进离散粒子群算法的电力系统机组组合问题

提出一种新的离散粒子群算法。结合改进的自学习策略优化粒子群算法适用于求解电力系统中的机组组合（unit commitment,UC）问题。算法将UC问题分解为具有整型变量和连续变量的2个优化子问题,采用离散粒子群优化和原对偶内点法相结合的双层嵌套方法对外层机组启、停状态变量和内层机组功率经济分配子问题进行交替迭代优化求...     

Experiences with mixed integer linear programming based approacheson short-term hydro scheduling

This paper describes experiences with mixed integer linear programming (MILP) based approaches on the short-term hydro scheduling (STHS) function. The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hydro units in a hydro-dominant system for a user-definable study period at each time step while respecting all system and hydraulic constraints. The problem can be modeled in detail for a hydro system that contains both conventional and pumped-storage units. Discrete and dynamic constraints such as unit startup/shutdown and minimum-up/minimum-down time limits are also included in the model for hydro unit commitment (HUC). The STHS problem is solved with a state-of-the-art package which includes an algebraic modeling language and a MILP solver. The usefulness of the proposed solution algorithm is illustrated by testing the problem with actual hydraulic system data. Numerical experiences show that the solution technique is computationally efficient, simple, and suitable for decision support of short-term hydro operations planning. In addition, the proposed approaches can be easily extended for scheduling applications in a deregulated environment     

Differential evolution technique-based short-term economic generation scheduling of hydrothermal systems

This paper presents differential evolution (DE)-based optimization technique for solving short-term economic generation scheduling of hydrothermal systems. A multi-reservoir cascaded hydrothermal system with non-linear relationship between water discharge rate, power generation and net head is considered here. The water transport delay between the connected reservoirs is also taken into account. Several equality and non-equality constraints on thermal units as well as hydro units and the effect of valve-point loading are also included in the problem formulation. The effectiveness of the proposed method is demonstrated on two test systems comprising of hydro and thermal units. Convergence characteristic of the proposed technique has been found to be quite satisfactory. The results obtained by the proposed technique are compared with other evolutionary methods. It is seen that the proposed technique is capable of producing encouraging solutions.     

A probabilistic approach to generation maintenance scheduler with network constraints

Most generating unit maintenance scheduling packages consider the preventive maintenance schedule of generating units over a one or two year operational planning period in order to minimize the total operating cost while satisfying system energy requirements and maintenance constraints. In a global maintenance scheduling problem, we propose to consider network constraints and generating unit outages in generation maintenance scheduling. The inclusion of network constraints in generating unit maintenance will increase the complexity of the problem, so we decompose the global generator scheduling problem into a master problem and sub-problems using Benders decomposition. At the first stage, a master problem is solved to determine a solution for maintenance schedule decision variables. In the second stage, sub-problems are solved to minimize operating costs while satisfying network constraints and generators’ forced outages. Benders cuts based on the solution of the sub-problem are introduced to the master problem for improving the existing solution. The iterative procedure continues until an optimal or near optimal solution is found.     

考虑水头影响的梯级水电站群短期优化调度

在梯级水电站群调度模型中恰当表述离散运行区间约束以及水头影响并在求解算法中有效处理这些因素是梯级水电站群调度中面临的挑战。文中通过将水头离散化,设定多维0-1状态变量及相关约束,建立了一个梯级水电系统短期调度的线性混合整数规划模型,能够综合考虑水头影响、不连续运行区间等约束。模型采用CPLEX软件包求解,对一个包含3个梯级水库、12台机组的梯级水电系统进行了测试,结果表明所提出的建模方法是有效的,能灵活处理受水头影响的水库群水电站短期调度中的多种复杂因素。     

Hydrothermal self-scheduling problem in a day-ahead electricity market

This paper addresses the self-scheduling problem of determining the unit commitment status for power generation companies before submitting the hourly bids in a day-ahead market. The hydrothermal model is formulated as a deterministic optimization problem where expected profit is maximized using the 0/1 mixed-integer linear programming technique. This approach allows precise modelling of non-convex variable cost functions and non-linear start-up cost functions of thermal units, non-concave power-discharge characteristics of hydro units, ramp rate limits of thermal units and minimum up and down time constraints for both hydro and thermal units. Model incorporates long-term bilateral contracts with contracted power and price patterns, as well as forecasted market hourly prices for day-ahead auction. Solution is achieved using the homogeneous interior point method for linear programming as state of the art technique, with a branch and bound optimizer for integer programming. The effectiveness of the proposed model in optimizing the generation schedule is demonstrated through the case studies and their analysis.     

Power generation scheduling for multi-area hydro-thermal systemswith tie line constraints, cascaded reservoirs and uncertain data

The authors propose an approach to the short-term generation scheduling of hydro-thermal power systems (GSHT). The objective of GSHT is to minimize the total operation cost of thermal units over the scheduling time horizon. To solve the problem within a reasonable time, the problem is decomposed into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. A probabilistic method is employed in considering load forecasting errors and forced outages of generating units to satisfy system reliability requirements. For the hydro subsystem, network flow concepts are adopted to coordinate water use over the entire study time span and the reduced gradient method is used to overcome the linear characteristic of the network flow method to obtain the optimal solution. Three case studies for the proposed method are presented     

考虑水电厂组合的水电厂短期经济调度

在常规水电厂短期经济调度网流法的基础 ，本文提出了考虑水电厂组合的常规水电厂短期经济调度算法。     

Optimal Long-Range Generation Expansion Planning for Hydro-Thermal System Based on Analytical Production Costing Model

This paper presents a new algorithm for the optimal long-range generation planning for hydro-thermal system. The algorithm is based upon the analytical production costing model developed under the assumption of Gaussian probabilistic distribution of random load fluctuations and plant outages. The optimization problem consists of the master problem to determine the annual investment, and the hydro subproblem to determine the optimal hydro operation. The master problem is formulated as a Hamiltonian minimization problem, and the hydro subproblem is solved using the concept of peak-shaving operation on the original load curve.     

电力市场下发电机组计划检修模型

发电机组的计划检修作为防止机组老化失效的主要方法,在确保电力系统可靠运行方面起着重要作用。文中对市场环境下机组检修策略模型及算法进行了综述,并提出了进一步研究的问题。在市场环境下,制定机组检修计划时应当考虑系统运行的可靠性和发电公司的经济利益2个方面。通常,首先由发电公司确定本公司机组的计划检修时段,然后由独立系统运营商（ISO）考虑系统可靠性充裕度后按一定的原则调整机组检修计划;前者确保了发电公司的经济利益,体现了其独立的经济实体地位,后者保证了系统的安全可靠运行。对于该优化问题,一般采用遗传算法、模拟退火算法等启发式方法或者整数规划法、Benders解耦法等数学规划方法加以求解。