Towards the development of risk-constrained optimal bidding strategies for generation companies in electricity markets

In the competitive electricity market environment, generation dispatching is bid-based, and individual generation companies (Gencos) are required to compete with rivals through bidding to the market. Competition implies the opportunities for Gencos to get more profit and, in the meantime, the risk of not being dispatched. As a result, it has become a major concern for Gencos to build optimal bidding strategies so as to maximize profits while minimizing risks associated. In this paper, a new approach is developed for building optimal bidding strategies with risks taken into account for Gencos participating in a pool-based single-buyer electricity market. It is assumed that each Genco bids a linear supply function and that the system is dispatched to minimize the total purchasing cost of the single-buyer. Each Genco chooses the coefficients in the linear supply function for making tradeoff between two conflicting objectives: profit maximization and risk minimization. A stochastic optimization model is established for the purpose and a novel method for solving this problem is presented. Numerical test results for a simulated electricity market with six Gencos show clearly the essential features of the developed model and method.     

共聚反应机理的发电厂商报价策略的模型

电力市场条件下,发电商报价过程存在着复杂的策略依存关系,以聚合动力学为基础,构建了发电商报价策略的博弈模型,揭示了不同策略选择对市场占有额的影响以及发电商报价策略的调整和变化规律。通过分析发电商报价策略调整和均衡路径的变化,对区域电力市场发电商有效报价策略给出了一般性理论总结。     

Strategic bidding in electricity markets using particle swarm optimization

Profit maximization for power companies is highly related to the bidding strategies used. In order to sell electricity at high prices and maximize profit, power companies need suitable bidding models that consider power operating constraints and price uncertainty within the market. In this paper, we present two particle swarm optimization (PSO) algorithms to determine bid prices and quantities under the rules of a competitive power market. The first method uses a conventional PSO technique to find solutions. The second method uses a decomposition technique in conjunction with the PSO approach. This new decomposition-based PSO dramatically outperforms the conventional form of PSO. We show that for nonlinear cost functions PSO solutions provide higher expected profits than marginal cost-based bidding.     

粒子群优化算法在电力系统中的应用

粒子群优化方法是一种基于群体智能的新型演化计算技术.它在函数优化、神经网络设计、分类、模式识别、信号处理、机器人技术等许多领域已取得了成功应用,但在电力系统中应用的研究起步较晚,关于它实际应用的报道尚不多见.文章较为全面地详述了粒子群优化方法在配电网扩展规划、检修计划、机组组合、负荷经济分配、最优潮流计算与无功优化控制、谐波分析与电容器配置、配电网状态估计、参数辨识、优化设计等方面应用的主要研究成果.随着粒子群优化理论研究的深入,它还将在电力市场竞价交易、投标策略以及电力市场仿真等领域发挥巨大的应用潜力.     

An individual welfare maximization algorithm for electricity markets

An algorithm that allows a market participant to maximize its individual welfare in electricity spot markets is presented. The use of the algorithm in determining market equilibrium points, called Nash equilibria, is demonstrated. The start of the algorithm is a spot market model that uses the optimal power flow (OPF), with a full representation of the transmission system and inclusion of consumer bidding. The algorithm utilizes price and dispatch sensitivities, available from the Hessian matrix and gradient of the OPF, to help determine an optimal change in an individual's bid. The algorithm is shown to be successful in determining local welfare maxima, and the prospects for scaling the algorithm up to realistically sized systems are very good. Nash equilibria are investigated assuming all participants attempt to maximize their individual welfare. This is done by iteratively solving the individual welfare maximization algorithm until all individuals stop modifying their bids.     

基于图形的发电商最优报价决策方法

作者基于供求关系建立了发电商优化报价的数学模型.传统上报价问题以基于博弈论的Nash均衡思想利用最优反应函数来求解,这在报价策略为一维时是有效的.但此文中发电商的行为是报价曲线,策略是其报价曲线的参数矢量,所以传统方法对此已不适用.作者利用图形来模拟交易中心的决策过程和发电商的竞价行为,通过在图形上运用Nash均衡的思想,直观地描述出发电商最优的报价曲线和收益曲线间的关系,得出了求解合理的Nash均衡策略的表达式.与传统方法相比,这种方法更简单易行.另外,对于不完全信息下的重复报价博弈,当各发电商都采用文中给出的报价机制时,通过迭代最终收敛于Nash均衡点.算例结果表明此方法是有效和实用的.     

Influence of feasibility constrains on the bidding strategy selection in a day-ahead electricity market session

Large part of liberalized electricity markets, including the Italian one, features an auction mechanism, called day-ahead energy market, which matches producers’ and buyers’ simple bids, consisting of energy quantity and price pairs. The match is achieved by a merit-order economic dispatch procedure independently applied for each of the hours of the following day. Power plants operation should, however, take into account several technical constraints, such as maximum and minimum production bounds, ramp constraints and minimum up and downs times, as well as no-load and startup costs. The presence of these constraints forces to adjust the scheduling provided by the market in order to obtain a feasible scheduling. The paper presents an analysis of the possibility and the limits of taking into account the power plants technical constraints in the bidding strategy selection procedure of generating companies (Gencos). The analysis is carried out by using a computer procedure based both on a simple static game-theory approach and on a cost-minimization unit-commitment algorithm. For illustrative purposes, we present the results obtained for a system with three Gencos, each owning several power plants, trying to model the bidding behaviour of every generator in the system. This approach, although complex from the computational point of view, allows an analysis of both price and quantity bidding strategies and appears to be applicable to markets having different rules and features.     

Assessing impact of subjective demand beliefs on a dynamic duopoly electricity market game

In the context of liberalized markets, market outcomes generally result from the strategic interactions of all market players. Generation company (Genco), as the distributed players, build their subjective demand evaluations (SDFs) about market for optimal bidding purpose. Due to the differences in terms of data availability and modeling techniques, subjective demand models held by various Gencos are heterogeneous and normally deviate from the real market model as well. The picture of a real electricity market game in Genco’s eye is ‘playing is believing’. Therefore, a question naturally comes to the table: how those SDFs with the heterogeneous manner impact individual player’s decision and game results. To answer this question, this paper relaxes a conventional assumption, commonly used in the classical oligopolistic equilibrium model, that one correct and uniform demand knowledge is shared by all Gencos. The results suggest that the system equilibriums would be influenced by the Gencos’ knowledge about market demand. The economic value of demand information is assessed regarding the system performances.     

Simulation of producers behaviour in the electricity market by evolutionary games

Simulation of the electricity market participant's behaviour is important for producers and consumers to determine their bidding strategies and for regulating the market rules. In literature, for this aim a lot of papers suggest to use the well-known theory of non-cooperative games and the concept of Nash equilibrium. Unfortunately they cannot be applied in an easy way when a multi-players game has to be considered to simulate the operation of the electricity market. In this paper, the authors suggest to use the new theory of evolutionary games and the concept of near Nash equilibrium to simulate the electricity market in the presence of more than two producers. In particular, an opportune genetic algorithm has been developed; from the results reported in the paper, it is clear that this algorithm can be usefully utilised.     

基于多智能体Nash-Q强化学习的综合能源市场交易优化决策

目前求解综合能源市场多参与主体竞价博弈问题普遍采用数学推导法与启发式算法,但两类方法均须以完全信息环境为前提假设,同时前者忽略市场参与者非凸非线性属性,后者易陷入局部最优解.为此,引入多智能体Nash-Q强化学习算法,将市场参与主体构建成智能体,经由智能体在动态市场环境中反复探索与试错寻找博弈均衡点.首先,构建竞价决策-市场出清双层迭代的电-气综合能源市场交易框架.其次,在竞价决策层中通过博弈理论构建市场参与主体间的利益关系模型,采用多智能体Nash-Q强化学习算法优化参与主体竞价策略.然后,在市场出清层中联合博弈竞价策略共同求解得到交易Nash均衡解.最后,通过算例仿真验证了所提方法的有效性和准确性.     

应用动态学习改进对竞争对手微增响应猜测的发电公司投标策略

该文应用微增响应猜测(Conjcctural Variation，CV)方法构造一种在不完全信息情况下的寡头竞争电力现货市场中发电公司通过动态学习改进对竞争对手的微增响应猜测的新投标策略，指出当各发电公司采用该文提出的投标策略进行不断重复的投标竞争后，市场所达到的均衡点为：Nash均衡点。算例计算结果说明各发电公司具有进行动态学习的动力，但是当所有公司进行学习时将会降低市场结清电价从而提高电力市场的社会总效益。算例计算结果还说明了电力需求弹性对学习过程的收敛性具有积极作用。     

碳交易机制下综合能源市场多供能主体均衡竞价策略

为了研究引入碳排放交易机制对综合能源市场(integrated energy market,IEM)运行和多供能主体竞价策略的影响,首先,构建了多供能主体碳交易奖惩规则;其次,基于多供能主体奖惩型碳交易机制建立了多供能主体竞价函数模型;然后,基于纳什均衡建立了碳交易机制下IEM多供能主体均衡竞价模型;鉴于所建模型具有高...     

发电商不同策略的供应函数均衡分析

电力市场是一个接近寡头垄断的市场,因而市场中的发电商往往会采用策略性投标来获得最大收益.根据联营模式下电力市场的特点,利用供应函数模型来模拟发电商的策略行为,给出了各发电商选择改变不同投标参数报价时的反应函数,通过算例比较研究了多个发电商在改变不同投标参数报价时的纳什均衡策略,结果表明选择改变不同投标参数报价会影响均衡结果.此外,还分析了需求弹性等因素对发电商均衡策略的影响.     

基于最优潮流和完全信息的纳什均衡分析

电力市场是一个不完全竞争的市场，发电商可通过策略性投标增加收益.本文利用博弈论研究完全信息条件下发电商投标策略的纳什均衡解.根据实时电价理论利用最优潮流(OPF)计算各发电节点的实时电价．得到不同战略条件下各发电商的收益．进而利用博弈论找出纳什均衡点。通过IEEE-30节点的算例检验了在3种不同负荷水平下3个发电厂商投标策略的纳什均衡．结果表明发电厂商的投标策略会随负荷的变化而改变.     

考虑网络约束的需求侧最优竞价策略

在电力市场环境下,市场竞争带来的潮流运行方式的随机性、多变性和不可预测性与输电网的潮流约束、安全约束相互矛盾而又同时存在,从需求侧角度考虑,针对Pool模式电力市场中需求侧各购电成员之间利润分配的非合作博弈均衡问题,提出了多个需求侧购电成员如何优化自己的购电竞价策略而使所有购电者均达到收益最大化的2层优化模型,考虑了电力网络约束对购电成员收益的影响,针对此均衡约束数学规划问题提出了一种求解多个需求侧购电成员处于纳什均衡点的最优策略解析方法,同时还提供了从备选策略集合中找到纯纳什均衡解的方法,在此基础上,以IEEE 30节点系统为例说明需求侧采用购电策略报价对发电商收益、需求侧各自收益及对电力市场运行的影响.     

Gaming Strategy for Electric Power With Random Demand

Recent work has shown that the profit maximizing problem for a generator in a competitive electricity market can be written as a mathematical program with equilibrium constraints (MPECs). In this paper, the problem of optimal generator bidding when there is a single demand is considered. The simplifications to the MPEC afforded by the assumption on the demand are shown. When the demand is stochastic and assumed to be normally distributed, the optimization that each player undertakes is written as a chance constrained program. It is shown that the solution to this stochastic problem can be found by solving a deterministic MPEC. The problem is considered with and without supply capacity constraints. By considering each of these cases as a game theory problem, the existence and uniqueness of Nash points are analyzed. These properties of the Nash point are then inferred onto the stochastic problem.     

Nash equilibrium bidding strategies in a bilateral electricitymarket

This paper examines bidding strategies in a bilateral market in which generating companies submit bids to loads. A load accepts electricity delivery from the generator with the lowest bid at its bid price as long as this price is not higher than the load's willingness to pay. Necessary and sufficient conditions of Nash equilibrium (NE) bidding strategy are derived based on a generic generating cost matrix and the loads' willingness to pay vector. The study shows that in any NE, efficient allocation is achieved. Furthermore, all Nash equilibria are revenue equivalent for the generators. Based on the necessary and sufficient conditions, this problem is formulated as an optimal assignment problem. Network optimization techniques are applied to calculate NE bid prices for the generators     

电网约束条件下基于古诺博奕的市场力分析

针对不完全信息下的双边竞争市场,研究建立了古诺(Cournot)博奕模型来分析发电商在最大经济利益的驱动下行使市场力的策略竞标行为.考虑输电网络约束后,提出运用两层优化搜索策略计算古诺纳什均衡的方法进行市场力评估.在IEEE30节点的算例分析中,以完全竞争市场下的均衡电价为基准,分析比较了完全信息和不完全信息两种不同条件下寡头竞争市场的市场力,仿真结果表明该市场力分析方法有助于市场监管人员测算与控制市场力,加强市场监督.     

发电市场的失代竞价机制

建立了发电市场迭代竞价模型。该模型在竞价过程中给出了充分的市场信息，发电商可以合理、经济地组织生产，确定竞标策略。电力购买者赋予了议价能力，协调各厂商竞价，促使市场高效地运作。实例模拟表明，在完全竞争的市场环境下，各厂商的发电资源可以得到充分利用，市场处于Nash均衡，出清价收敛于传统的系统边际成本附近，发电系统接近于经济运行状态。比较了迭代竞价机制与单轮投标机制的市场效率。模拟了发电商串通行为的形成，为此有必要制定有效的规则对市场竞价加以约束。     

基于灵敏度分析的机组电价决策及其算法

基于博弈论的机组报价分析算法中，要对所有机组的高中低3种报价组合进行机组功率分配计算。如果系统中机组数较多，计算工作量将会十分巨大。目前的基于Nasb均衡点求解的方法只能竞价一个电价参数，因而很难用于实际系统。该文提出了基于最优解灵敏度的二电价参数的Nasb均衡点求解方法。与已有文献相比，该方法具有数学模型合理可行实用之特点，可用于中长期电量电力市场，日前电力市场，实时电力市场以及辅助服务市场竞价策略的分析。文中给出了实例分析结果，表明所提方法正确合理。