电力市场环境下解决机组组合问题的新方法

机组组合问题是电力市场环境下编制短期发电计划所面临的主要问题,在满足各种约束条件的情况下,如何合理地开、停机组、以及负荷如何在运行的发电机组之间经济地分配是一个比较困难的问题,特别是由于发电机组出力上升、下降速度的限制,使这个问题一直没有很好的解决方法。提出一种组合优化方法解决这一问题,即用启发式方法确定机组组合,用分段线性规划算法分配功率,并满足各种约束条件,特别是可以处理发电机组出力上升、下降速度约束、经实际系统检验是一种非常有效的算法。     

确定机组组合的一种改进的动态规划方法

提出了一种确定机组组合的改进动态规划方法,称为插值动态规划算法。这是一种启发式方法,可以和其他的经济调度算法相结合,用以解决多种约束条件下的机组组合问题,特别是可以处理机组功率上升、下降速度约束,且考虑了机组的开、停机特性、并有效避免了“维数灾”问题,经实践检验是一种简单、有效的实用算法。     

Effects of ramp-rate limits on unit commitment and economicdispatch

The authors propose an algorithm to consider the ramp characteristics in starting up and shutting down the generating units as well as increasing and decreasing power generation. They consider the inclusion of ramping constraints in both unit commitment and economic dispatch. Since implementing ramp-rate constraints is a dynamic process, dynamic programming (DP) is a proper tool to treat this problem. To overcome the computational expense which is the main drawback of DP, this study initially employs artificial intelligence techniques to produce a unit commitment schedule which satisfies all system and unit operation constraints except unit ramp-rate limits. Then, a dynamic procedure is used to consider the ramp properties as units are started up and shut down. According to this adjustment, maximum generating capabilities of units will change the unit operation status instead of following a step function. Finally, a dynamic dispatch procedure is adopted to obtain a suitable power allocation which incorporates the unit generating capability information given by unit commitment and unit ramping constraints, as well as the economical considerations. Two examples are presented to demonstrate the efficiency of the method     

电力市场模拟中的不确定性机组自组合问题

在电力市场环境下,发电商需要在不确定信息下,考虑机组的最小开、停机时间,确定各自机组期望的最优运行状态,并进而优化各自的报价.为了使电力市场模拟中的发电商决策模型更合理,作者基于报价中标概率函数,建立了考虑机组开、停机时间约束的报价决策模型,对机组自组合状态优化和报价决策行为进行研究和模拟.为了求解该不确定性混合整数问题,将其转化成为Markov过程,并提出相应算法.算例表明:考虑机组最小开、停机时间约束后,发电商会为了增加连续开机的可能性而降低在谷荷时段的报价,而这种报价策略会进一步加大市场中的峰谷电价差.该研究为电力市场模拟中发电商的决策提供了新的思路.     

A solution method using neural networks for the generator commitment problem

This paper studies the feasibility of applying the Hopfield-type neural network to unit commitment problems in a large power system. The unit commitment problem is to determine an optimal schedule of what thermal generation units must be started or shut off to meet the anticipated demand; it can be formulated as a complicated mixed integer programming problem with a number of equality and inequality constraints. In our approach, the neural network gives the on/off states of thermal units at each period and then the output power of each unit is adjusted to meet the total demand. Another feature of our approach is that an ad hoc neural network is installed to satisfy inequality constraints which take into account standby reserve constraints and minimum up/down time constraints. The proposed neural network approach has been applied to solve a generator scheduling problem involving 30 units and 24 time periods; results obtained were close to those obtained using the Lagrange relaxation method.     

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.     

基于机组综合状态评价策略的大型水电站?精细化日发电计划编制方法

为减小水电站日发电计划与实际运行的偏差,提出一种基于机组综合状态评价策略的大型水电站精细化日发电计划编制方法.依据机组综合运行状态评价策略,确定机组优先开停次序;考虑水量、水库库容、机组运行限制等多重安全生产约束条件,以发电量最大为目标建立大型水电站日发电计划精细化模型,将其分解为机组组合子问题和开机机组最优流量分配子问题;采用原始量子进化算法和实数差分量子进化算法循环嵌套求解,获得水电站精细化日发电计划最优解.将所提算法应用于葛洲坝水电站并与其他求解方法对比,结果表明所提精细化日发电计划编制方法求解精度高,优化效果好     

含风电的电力系统机组组合问题研究综述

以风电为代表的新能源规模化开发利用,改变了传统电力系统的结构特性,给系统的运行控制方式带来了新的挑战。机组组合是电力系统经济调度的重要环节,通过优化发电周期内各机组的启停计划来降低发电成本,同时满足系统负荷需求和其他约束条件。风电具有随机性、间歇性特点,大规模风电接入电网使传统的机组组合方式难以适应新能源电力系统的要求,研究含风电的机组组合对于应对风电引起的负荷波动、保证电力系统稳定、经济运行具有重要意义。为此,综述了国内外对含风电机组组合问题的研究现状,分析了风电接入电网对电力系统机组组合问题带来的影响,归纳了常用的建模方法和求解算法。并对该领域未来的研究方向进行了探讨,希望为其他学者在该领域的研究提供借鉴。     

Daily integrated generation scheduling for thermal,pumped‐storage,and cascaded hydro units and purchasing power considering network constraints

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 a penalty term to converge the value of those variables to 0 or 1 to the objective function: the sum of the fuel costs and the start‐up costs. This penalty term depends on the 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, that is, load‐power balance, operation reserve, power flow, minimum up/down‐times, and fuel consumption. This result shows that the proposed method is effective. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 175(1): 25–34, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21014     

A Method for Solving the Fuel Constrained Unit Commitment Problem

The unit commitment problem involves finding the hourly commitment schedule for the thermal units of an electrical system, and their associated generation, over a period of up to a week. For some utilities, contractual or other factors limit the amount of fuel available to certain of the units or plants. This paper describes a new method which solves the unit commitment problem in the presence of fuel constraints. The method uses a Lagrangian decomposition and successive approximation technique for solving the unit commitment problem where the generation, reserve and fuel constraints are adjoined onto the cost function using Lagrange multipliers. All important operating constraints have been incorporated including minimum up and down times, standby operation, ramping limits, time-dependent start-up cost, spinning and supplemental reserve. The method is being applied to a production-grade program suitable for Energy Management Systems applications.     

Thermal power generation scheduling by simulated competition

This paper presents a new method for solving the unit commitment problem by simulation of a competitive market where power is traded through a power exchange (PX). Procedures for bidding and market clearing are described. The market clearing process handles the spinning reserve requirements and power balance simultaneously. The method is used on a standard unit commitment problem with minimum up/down times, start-up costs and spinning reserve requirement taken into account. Comparisons with solutions provided by Lagrangian relaxation, genetic algorithms and Chao-an Li's unit decommitment procedure demonstrate the potential benefits of this new method. The motivation for this work was to design a competitive electricity market suitable for thermal generation scheduling. However, performance in simulations of the proposed market has been so good that it is presented here as a solving technique for the unit commitment problem     

考虑多种约束条件的机组组合新算法

提出了考虑系统降出力备用约束、机组出力变化速率、线路潮流约束和断面传输功率约束的机组组合新算法。算法没有引入任何乘子,计算单调收敛,速度快,并且不需要初始可行解。用ＩＥＥＥ ２４母线系统对算法进行了验证,结果表明,算法对各种约束条件的处理正确,解的质量好。     

基于改进的逆序排序法的机组组合优化算法

文章提出了改进的逆序排序法来求解机组组合优化问题.该算法从可用机组全投入运行这一可行解出发,在每次迭代过程中优化一台机组在整个调度周期内的开停状况,以最小化总生产成本或总购电成本,直到连续两次迭代的目标函数值不再减小为止.该方法的显著优点在于计算不会振荡,迭代不会发散,且每次迭代的结果均为可行解.该算法在单机组优化过程中,以机组的最小启停区间而不是单个时段为研究调度对象,缓解了组合爆炸问题,明显地加快了计算速度.     

基于免疫算法的机组组合优化方法

机组组合是改善传统电力系统运行经济性和电力市场出清的重要手段。基于群体进化的智能优化算法存求解过程中存在计算效率低和易于早熟收敛等缺点。提出机组组合的免疫算法，利用免疫算法保持种群多样性的内在机制和免疫记忆特性改进既有的智能优化方法。新算法扩展了约束处理技术，能更好地对可行解空间搜索，采用一种由后向前、由前及后、双向迂回推进的精简程序改善个体可行解的局部最优性，同时利用优先级顺序法产生能较好反映问题先验知识的初始种群。典型算例证实新算法能获得更优的结果，具有更快的收敛速度，且在系统规模扩大时有大致线性的计算复杂性，是一种新的高效的机组组合智能优化算法。     

Unit commitment by genetic algorithm with specialized search operators

An approach for solving the unit commitment problem based on genetic algorithm with new search operators is presented. These operators, specific to the problem, are mutation with a probability of bit change depending on load demand, production and start-up costs of the generating units and transposition. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and units power generation limits. Repair algorithms or penalty factors in the objective function are applied to the infeasible solutions. Numerical results showed an improvement in the solution cost compared to the results obtained from genetic algorithm with standard operators and other techniques.     

A new unit commitment method

This paper introduces a new unit commitment method based on a decommitment procedure for solving the power system resource scheduling problem. From an initial schedule of all available units committed over the study period, a `one-at-a-time' unit decommitment is accomplished by dynamic programming according to some specified economic criteria. The decommitment process continues until no further reduction in total cost is possible, or the unit schedules of two consecutive iterations over the time period remain unchanged without any violation of the spinning reserve constraint. Two criteria for decommiting a unit are introduced and described in detail. Comparisons of the proposed unit commitment method with the Lagrangian relaxation (LR) approach and Fred Lee's sequential unit commitment method (SUC) demonstrate the potential benefits of the proposed approach for power system operations planning     

Optimal Scheduling of Spinning Reserve with Transmission Constraints

An effective method is proposed to schedule spinning reserve optimally. The method considers the transmission constraint in the whole scheduling process. To get the feasible solution faster, transmission line limits are first relaxed using the Lagrangian Relaxation technique. In the economic dispatch, after unit generation and spinning reserve are allocated among the committed units to satisfy the system andunit constraints, the schedule is then modified by a linear programming algorithm to avoid line overloads. The schedule is then updated by a probabilistic reserve assessment to meet a given risk index. The optimal value of the risk index is selected via a cost/benefit analysis based on the tradeoff between the total Unit Commitment (UC) schedule cost and the expected cost of energy not served. Finally, a unit decommitment technique is incorporated to solve the problem of reserve over-commitment in the Lagrangian Relaxation–based UC. The results of reserve scheduling with the transmission constraint are shown by the simulation runs performed on the IEEE reliability test system.     

电力市场中考虑机组启停约束的购电策略

在电力市场环境下,电网以最小化购电费用为目标,而发电公司以最大化售电收益为目标,如何寻找二者之间的市场成交点是一项复杂而重要的工作。制定发电计划时,机组的启停是必须考虑的问题。基于此,文中对电力市场中考虑机组启停约束的购电策略进行了研究,并建立了相应的数学模型,提出了机组报价对电网总购电费用灵敏度的概念,以及考虑机组启停约束的购电算法,得出的结论对制定发电计划有一定的指导意义。     

Multi-Area Power Generation Dispatch in Competitive Markets

In competitive electric energy markets, the power generation dispatch optimization is one of the most important missions among generation companies-how to respond to the markets, dispatch their units, and maximize profits. This paper proposes an approach to incorporate power contracts, which include call and put options, forward contracts, and reliability must-run contracts, into multi-area unit commitment and economic dispatch solutions. The proposed solution algorithm is based on adaptive Lagrangian relaxation, unit decommitment, and lambda-iteration methods. The problem formulation consists of three stages: 1) the incorporation of the power contracts, 2) the multi-area unit commitment, and 3) the multi-area economic dispatch. The proposed algorithm has been successfully implemented, and its testing results on modified IEEE test cases are promising.     

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.