Optimal supply curve bidding using Benders decomposition in competitive electricity markets

This paper describes a new approach for optimal supply curve bidding (OSCB) using Benders decomposition in competitive electricity markets. The inclusion of physical unit constraints and transmission security constraints will assure a subsequent feasible solution for the problem. We decompose the problem into a base-case OSCB (without unit and network constraints) and subproblems for checking the feasibility of unit and network constraints. For a given base-case OSCB schedule, line flow violations are minimized by adjusting units’ generation and phase shifters. In case transmission violations cannot be removed, additional linear constraints are introduced in the master problem in the form of price signals for rescheduling OSCB. An IEEE 24-bus system is used to demonstrate the effectiveness of the proposed approach.     

基于SP/A决策思想的发电公司报价决策模型及求解方法

以安全、潜力和期望(security, potential and aspiration, SP/A)风险决策理论为基础,该文对发电公司面对风险决策时应该考虑的因素进行了分析和数学描述,其中在报价方案潜力性的分析上有效地结合了经济学中机会成本理论。在此基础上,考虑发电公司自身发电计划约束,建立起一种发电公司计及风险因素的竞价决策模型,并结合矩阵实数编码遗传算法(matrix real-coded genetic algorithm, MRCGA)对该模型的优化求解进行了探讨。该文所建的竞价决策模型既考虑了自身发电计划安排,又顾及了在面对风险发电公司竞价决策时应该考虑的一些因素,因此模型比较贴近于实际的发电竞价情况。通过算例的模拟分析表明,文中所提出的基于SP/A的发电公司竞价决策模型是合理的,其求解方法也是切实可行的。     

GENCO's Risk-Based Maintenance Outage Scheduling

This paper presents a stochastic model for the optimal risk-based generation maintenance outage scheduling based on hourly price-based unit commitment in a generation company (GENCO). Such maintenance outage schedules will be submitted by GENCOs to the ISO for approval before implementation. The objective of a GENCO is to consider financial risks when scheduling its midterm maintenance outages. The GENCO also coordinates its proposed outage scheduling with short-term unit commitment for maximizing payoffs. The proposed model is a stochastic mixed integer linear program in which random hourly prices of energy, ancillary services, and fuel are modeled as scenarios in the Monte Carlo method. Financial risks associated with price uncertainty are considered by applying expected downside risks which are incorporated explicitly as constraints. This paper shows that GENCOs could decrease financial risks by adjusting expected payoffs. Illustrative examples show the calculation of GENCO's midterm generation maintenance schedule, risk level, hourly unit commitment, and hourly dispatch for bidding into energy and ancillary services markets.     

静态安全约束下基于Benders分解算法的可用传输容量计算

在电力市场环境下，可用传输容量(ATC)是反映输电线路可用于交易的剩余容量的重要指标。文中以最优潮流为基础，采用Benders分解方法将考虑静态安全约束的ATC计算问题分解为一个基态主问题和一系列与各预想事故有关的子问题。主问题用来处理基态潮流和相应约束以及由子问题所返回的Benders割(cut)约束，而各子问题用来处理各预想事故和形成相应的静态安全约束。文章给出了相应的数学模型，并提出了两种改进的求解策略。4节点和IEEE30节点系统的计算结果表明了该方法和求解策略的有效性。     

Binary fireworks algorithm for profit based unit commitment (PBUC) problem

The deregulation of electricity markets has transformed the unit commitment and economic dispatch problem in power systems from cost minimization approach to profit maximization approach in which generation company (GENCO)/independent power producer (IPP) would schedule the available generators to maximize the profit for the forecasted prices in day ahead market (DAM). The PBUC is a highly complex optimization problem with equal, in equal and bound constraints which allocates scheduling of thermal generators in energy and reserve markets with no obligation to load and reserve satisfaction. The quality of the solution is important in deciding the commitment status and there by affecting profit incurred by GENCO/IPPs. This paper proposes a binary coded fireworks algorithm through mimicking spectacular display of glorious fireworks explosion in sky. In deregulated market GENCO/IPP has the freedom to schedule its generators in one or more market(s) based on the profit. The proposed algorithm is tested on thermal unit system for different participation scenarios namely with and without reserve market participation. Results demonstrate the superiority of the proposed algorithm in solving PBUC compared to some existing benchmark algorithms in terms of profit and number of iterations.     

A new approach to security-constrained generation scheduling of large-scale power systems with a piecewise linear ramping model

This paper presents a new and efficient approach to determine security-constrained generation scheduling (SCGS) in large-scale power systems, taking into account dispatch, network, and security constraints in pre and post-contingency states. A novel ramp rate limit is also modeled as a piecewise linear function in the SCGS problem to reflect more practical characteristics of the generating units. Benders decomposition is applied to this constrained solution process to obtain an optimal SCGS problem based on mixed-integer nonlinear programming (MINLP). The formulation can be embedded in two stages. First, a MIP is formulated in the master problem to solve a unit commitment (UC) problem. This stage determines appropriate on/off states of the units. The second stage, the subproblem, is formulated as a NLP to solve a security-constrained economic dispatch (SCED) problem. This stage is used to determine the feasibility of the master problem solution. It provides information to formulate the benders cuts that connect both problems. The proposed approach is tested in the IEEE 118-bus system to show its effectiveness. The simulation results are more realistic and feasible, whilst assuring an acceptable computation time.     

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.     

Supplier bidding strategy based on non-cooperative game theory concepts in single auction power pools

In single auction power pools, only generators bid several energy price segments depending on the amount of energy supply, at individual generating companies’ (GENCO) own discretion, for every trading interval. Then all selected bidders are paid a uniform Market Clearing Price (MCP). In this paper, it is realized that each GENCO has the complete information on its own payoff as well as the other parties’ payoffs, corresponding to each potential combination of choices of strategies by all the players. Specifically, all the suppliers attempt to estimate the others’ bids using the concept of Nash equilibrium in the general sense of profit maximization. Under some simplified assumptions, this problem can be modeled as a simultaneous-move game confronted by the bidders. Here, the system demand forecast by competitive sellers is captured for the purpose of constructing the optimal bidding strategy. Finally, a numerical example is presented demonstrating the effectiveness of the proposed solution scheme.     

市场环境下基于Benders分解的输电网规划决策

市场条件下,由于不确定因素对市场经济运行的影响,输电网的扩展规划必须考虑发电公司和用户的需求,减缓输电系统阻塞,促进市场的公平竞争。首先以电力联营市场模式为研究背景,针对不确定因素作用下可能的未来场景,基于最优潮流的输电网边际定价模型,提出了以投资成本和运行成本为优化目标的输电网静态规划模型;然后基于奔德斯(B enders)分解算法先求解出各个典型场景下输电网规划优化方案,再根据决策理论中的最小最大悔则进行多场景规划决策;最后在IEEE-24节点系统上进行了仿真计算。与确定性输电网规划方法相比,该模型计及了电网规划与经济运行中不确定因素的影响,从而能更有效地指导市场环境下输电网规划综合决策,提高规划系统经济性能。     

Optimal bidding strategies in oligopoly markets considering bilateral contracts and transmission constraints

In electricity industry with transmission constraints and limited number of producers, Generation Companies (GenCos) are facing an oligopoly market rather than a perfect competition one. Under oligopoly market environment, each GenCo may increase its own profit through a favorable bidding strategy. This paper investigates the problem of developing optimal bidding strategies of GenCos, considering bilateral contracts and transmission constraints. The problem is modeled with a bi-level optimization algorithm, where in the first level each GenCo maximizes its payoff and in the second level a system dispatch will be accomplished through an OPF problem in which transmission constraints are taken into account. It is assumed that each GenCo has information about initial bidding strategies of other competitors. Impacts of exercising market power due to transmission constraints as well as irrational biddings of the some generators are studied and the interactions of different bidding strategies on participants’ corresponding payoffs are presented. Furthermore, a risk management-based method to obtain GenCos’ optimal bilateral contracts is proposed and the impacts of these contracts on GenCos’ optimal biddings and obtained payoffs are investigated. At the end, IEEE 30-bus test system is used for the case study in order to demonstrate the simulation results and support the effectiveness of the proposed model.     

Coordinated preventive maintenance scheduling of GENCO and TRANSCO in restructured power systems

Preventive maintenance of generating units and lines, in a competitive electric energy environment is proposed. Inclusion of transmission constraints and forced outage rates, over a specified operational period is considered. For generator maintenance the objective of the ISO is to maintain adequate level of reliability throughout the operational period, for which Bender’s decomposition technique is used. The objective of the GENCO is to maximize profit or to minimize loss in profit, for which transmission constrained price based unit commitment (TCPBUC), based on Lagrangian relaxation method is used. Bender’s decomposition technique is used for line maintenance, with adequate level of reliability. A coordinating technique using penalty factors is incorporated to obtain convergence of the conflicting objectives. The transmission constraints are modeled using dc sensitivity factors. Detailed case studies of six-bus systems and IEEE RTS system are presented and discussed.     

Development-Scheme Selection for River Valleys

This paper presents a new approach to the problem of selecting a development scheme for a river valley from preliminary surveys on candidate sites. Rather than proceeding by elimination, this approach identifies the scheme which minimizes the investment and operating costs. This minimization problem is decomposed using the Benders technique into a master problem covering the site selection and sizing aspects and a subproblem covering the production aspect. The former is solved by mixed-integer linear programming whereas the latter is transformed by a Lagrangian relaxation into a nonlinear network flow problem which is solved by a variant of the Frank-Wolfe method. Numerical results are reported.     

考虑柔性交流输电系统设备控制的校正型安全约束最优潮流

为提升安全约束最优潮流调度的经济性与安全性,提出一种基于直流潮流的考虑柔性交流输电系统(FACTS)设备控制的校正型安全约束最优潮流模型。在线路故障发生后,通过FACTS设备校正措施,将线路潮流控制在其容许范围内。由于所提模型为大规模的非凸、非线性优化问题,难以直接求解,因此先采用大M法,将原非线性优化模型转换为混合整数线性规化模型,并采用Benders分解算法将转换后的模型分解为基态最优潮流主问题与N-1故障校验子问题。通过固定整数变量的方法,将非凸的混合整数优化子问题转换为线性规划子问题,从而能向主问题返回对应的Benders割。6节点系统与IEEE RTS-79节点系统算例验证了所提模型与算法的有效性。结果表明,考虑FACTS设备校正控制的安全约束最优潮流能有效提升调度运行的经济性。     

Cost minimization in allocation of reactive power sources

A LP-based method for the optimization of the investment and operational costs of the reactive power generation in a large electric power network is presented. The optimal solution is based on the application of decomposition and linear programming approaches. The global problem is decomposed into investment and operation subproblems using the Benders decomposition method. The revised simplex method is proposed for the solution of the investment subproblem. However, the Dantzig-Wolfe decomposition method is used to solve the operation subproblem. The formulation of the operation subproblem has been discussed in our previous studies. The method has been generalized to represent and solve multiple load levels and contingencies simultaneously in the operation subproblem. The results of applying this approach to the IEEE 30-bus system, a 60-bus system and a 180-bus system verify its robustness in solving the operation subproblem and the capability to converge quickly.     

基于可信性理论的输电网短期线路检修计划

传统方法将短期线路检修计划作为单重不确定性优化问题进行建模和求解。但是，架空线路的可靠性指标难以表达现场运行中线路发生故障的可能性，所以需要在短期线路检修计划中对双重不确定性(随机性和模糊性)同时进行建模和求解。可信性理论是基础数学领域最近完成的数学分支， 它提供了随机性与模糊性综合评估的严格数学基础。基于可信性理论可建立短期线路检修计划的混合整数随机模糊双重不确定性优化模型(原始模型)，其目标函数是检修费用与停电损失费用之和的随机模糊期望值最小。文中利用Benders分解法将原始模型分解为主问题和子问题进行求解：主问题是一个多目标整数规划问题，利用改进Balas算法求解；子问题是一个随机模糊双重不确定性模型，利用可信性理论和直流潮流求解。IEEE-RBTS系统和IEEE-RTS系统的算例表明，文中提出的算法可以综合协调全网的风险和经济目标。同时由于支持原始数据的随机模糊性，使得该算法具有较强的实用性。     

Cross decomposition for multi-area optimal reactive power planning

This paper presents a novel decomposition based algorithm to solve the reactive power planning problem in large scale multi-area power systems. Extensive studies on the application of the Benders decomposition method (BDM) have been conducted to solve this complex problem. Nevertheless, these applications are based on the difficult evaluation of the plane cuts from the solution of the master problem. In this paper, the authors introduce the possibility of solving reactive power planning based on an iterative optimization process between the BDM subproblem and the subproblem of a Lagrangean relaxation decomposition method (LRDM). The overall process is referred to as a cross decomposition algorithm (CDA). The merits of the proposed approach are shown by the evaluation of plane cuts based on the solution of easy-to-solve subproblems. Moreover, the proposed approach is extremely efficient in multi-area (zone decomposition) power systems. Test results are demonstrated for the 3-area IEEE 30-bus and the 8-area 180-bus systems     

Security constrained optimal bidding strategy of GenCos in day ahead oligopolistic power markets: a Cournot-based model

Restructured electricity markets may provide opportunities for producers to exercise market power, maintaining prices in excess of competitive levels. In this paper a Cournot equilibrium model is proposed to obtain generation companies’ (GenCos’) optimal bidding strategies in a day ahead oligopoly market, considering elasticity of demand, market power and transmission security constraints. In order to consider network constraints, a multiperiod auction framework is addressed to simulate market clearing mechanism by means of social welfare maximization, in which the behaviors of market participants are modeled through piecewise block curves. Impact of transmission security constraints on participants’ market power is presented. A mixed integer linear programming is employed to solve the problem, resulting supply-demand satisfaction as well as market clearing prices at each hour. A novel methodology is presented for security constrained optimal bidding strategy of GenCos through introducing heuristic effective-supply curves. Subsequently, impact of GenCos’ power exertion on market characteristics and corresponding payoffs is studied. A 9-bus IEEE test system is used to implement the proposed methodology while simulation results demonstrate the effectiveness of the framework.     

计及安全约束的机组最优组合鲁棒优化方法

随着风电出力在电力系统中渗透率的逐步提高,其不确定性给系统安全与经济运行带来了新的问题甚至挑战。在制定电力系统运行方式和调度计划时如何确定计及安全约束的机组最优组合(security constrained unit commitment,SCUC)策略就是一个需要解决的重要课题,也是该文旨在研究的问题。具体地,首先建立基于场景生成的鲁棒优化安全约束的机组最优组合(robust security constrained unit commitment,RSCUC)模型,由此获得的鲁棒机组组合策略满足给定的置信度,对处于置信区间之外的极端场景则采取弃风或切负荷等不得已的措施来维持系统功率平衡,从而在系统运行的经济性和保守性之间合理折衷。之后,采用Benders分解法求解所建模型,将该问题分解为主问题和子问题。其中,主问题为确定性的SCUC问题;子问题则对考虑风电场出力随机变化时的系统状态进行安全性校验,若通过校验则表明所求得的SCUC策略满足鲁棒性约束,否则就生成相应的安全约束即Benders割并反馈给主问题。最后,采用修改的IEEE 39节点系统来说明所提方法的基本特征。     

Optimal security-constrained power scheduling by Benders decomposition

This paper presents a Benders decomposition approach to determine the optimal day-ahead power scheduling in a pool-organized power system, taking into account dispatch, network and security constraints. The study model considers the daily market and the technical constraints resolution as two different and consecutive processes. The daily market is solved in a first stage subject to economical criteria exclusively and then, the constraints solution algorithm is applied to this initial dispatch through the redispatching method. The Benders partitioning algorithm is applied to this constraints solution process to obtain an optimal secure power scheduling.     

基于可信性理论的输电网短期线路检修计划

传统方法将短期线路检修计划作为单重不确定性优化问题进行建模和求解。但是，架空线路的可靠性指标难以表达现场运行中线路发生故障的可能性，所以需要在短期线路检修计划中对双重不确定性(随机性和模糊性)同时进行建模和求解。可信性理论是基础数学领域最近完成的数学分支， 它提供了随机性与模糊性综合评估的严格数学基础。基于可信性理论可建立短期线路检修计划的混合整数随机模糊双重不确定性优化模型(原始模型)，其目标函数是检修费用与停电损失费用之和的随机模糊期望值最小。文中利用Benders分解法将原始模型分解为主问题和子问题进行求解：主问题是一个多目标整数规划问题，利用改进Balas算法求解；子问题是一个随机模糊双重不确定性模型，利用可信性理论和直流潮流求解。IEEE-RBTS系统和IEEE-RTS系统的算例表明，文中提出的算法可以综合协调全网的风险和经济目标。同时由于支持原始数据的随机模糊性，使得该算法具有较强的实用性。