Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market

In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.     

基于多层博弈的智能电网住宅电力实时需求响应机制

通过建立多层博弈模型刻画智能电网系统中电力公司、家庭电力管理中心和家庭内各个电器设备间的电力实时需求响应过程。在此模型中,每个时段电力公司将电价通知各个家庭,每个家庭的电力管理中心接收到实时电价信息后为家庭内各个电器设备分配虚拟电价,各个设备则确定各自最优用电量并将其反馈给家庭电力管理中心,由其确定该家庭总用电量并发送至电力公司,电力公司再计算得到最优电价。证明了所建多层博弈模型的均衡存在唯一性,并得到均衡解。仿真结果验证了模型的有效性,并给出其实际应用价值。     

The emissions trading paradox

This article considers the price history of CO₂ allowances in the EU Emission Trading Scheme. Since European Emissions Trading started in 2005, the prices of allowances have varied between less than one and thirty Euro per ton of CO₂. This previously unpredicted volatility and, more notably, a significant price crash in May 2005 led to the hypothesis that electricity producers might use their market power to influence the prices of allowances. Besides market power, the combination of information asymmetry and price interdependencies (between prices of primary goods – especially electricity – and allowances) plays an important role in explaining the emissions trading paradox. The model presented will show that banking can lead to such a price crash if market participators act rationally. Furthermore, in such a scenario banking can be profitable for sellers at the cost of buyers.     

三角形分布的双方叫价拍卖模型在电力交易中的应用

在完全开放的双边电力市场下,大用户直接购电问题已成为我国电力改革的重大课题.研究发电公司和大用户如何建立有效的报价策略具有十分重要的理论和实践价值.将发电公司看成卖方,将买电代理看成买方,针对卖方的成本和买方的估计是私有信息,并服从区间(0,1)上的三角形分布,建立了基于三角形分布的双方叫价拍卖的贝叶斯博弈模型,并得到了预期的均衡结果.通过一个数值例子与基于均匀分布的经典双方叫价拍卖模型进行比较.结果表明:建立的双方叫价拍卖模型在电力交易拍卖中的应用,能够提供更为准确的理论预期结果,具有更为现实的指导意义.     

基于标杆管理优化算法的供电商购电组合策略

针对开放式电力市场环境下,供电商的购电风险管理问题,结合金融输电权拍卖市场和电能交易市场,构造了一个考虑阻塞风险的供电商最优购电组合模型.由于此模型的非可微性和非凸性,使用了一种新型的智能计算方法——标杆管理优化算法对该模型进行了求解计算.仿真实例表明,提出求解计算方法是切实可行的,具有一定的实用性和灵活性.     

Evaluating the impact of average cost based contracts on the industrial sector in the European emission trading scheme

The inception of the emission trading scheme in Europe has contributed to power price increases. Energy intensive industries have reacted by arguing that this may affect their competitiveness and will induce them to leave Europe. Taking up a proposal of these industrial sectors, we explore the possible application of special contracts, where electricity is sold at average generation cost to mitigate the impact of CO₂ cost on power prices. The model supposes fixed generation capacities. We first consider a reference model representing a perfectly competitive market where all consumers (industries and the rest of the market) are price-takers and buy electricity at short-run marginal cost. We then change the market design by assuming that energy intensive industries pay power either at a regional or at a zonal average cost price. The analysis is conducted with simulation models applied to the Central Western European power market. The models are implemented in GAMS/PATH. This work has been financially supported by the Chair Lhoist Berghmans in Environmental Economics and Management and by the Italian project PRIN 2006, Generalized monotonicity: models and applications, whose national responsible is Prof. Elisabetta Allevi.     

ATLANTIS: techno-economic model of the European electricity sector

Since the nuclear accident in Fukushima the European electricity economy has been in transition. The ongoing shut down of nuclear power plants and the widespread installation of wind power and photovoltaic generation capacities, especially in Germany, has led to a high share of intermittent renewable electricity production. This high amount of generation with very little variable cost has led to a significant decline of the prices at the European energy exchange. This has meant that many thermal power plants are no longer able to work economically and have already been shut down, although they would be needed in times of high demands and as backup capacities. Therefore, a redesign of the European electricity market is needed and in order to find out the right characteristics and effects of such a redesign pre-investigations based on simulation models are reasonable. This paper introduces ATLANTIS, which is a simulation model of the European electricity economy and covers technical as well as economic and environmental issues and allows the calculation of different scenarios up to 2050 and even beyond regarding the specific characteristics of the electricity economy. After a comprehensive introduction of the model some example applications and an outlook are presented.     

Spatial dependencies of wind power and interrelations with spot price dynamics

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. In particular, prices are more volatile due to the stochastic nature of wind, such that more generation of wind energy yields lower prices. Therefore, it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole. In this paper, we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas, incorporated into a supply and demand based model for the electricity spot price. This model is calibrated with German data. We find that the specific location of a turbine – i.e., its spatial dependence with respect to the aggregated wind power in the system – is of high relevance for its value. Many of the locations analyzed show an upper tail dependence that adversely impacts the market value. Therefore, a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases. This effect becomes more important for increasing levels of wind power penetration and may render the large-scale integration into markets more difficult.     

Optimization techniques for Available Transfer Capability (ATC) and market calculations

The recent movement towards an open, competitive market environmentintroduced new optimization problems such as market clearingmechanism, bidding decision and Available Transfer Capability(ATC) calculation. These optimization problems are characterizedby the complexity of power systems and the uncertainties inthe electricity market. Accurate evaluation of the transfercapability of a transmission system is required to maximizethe utilization of the existing transmission systems in a competitivemarket environment. The transfer capability of the transmissionnetworks can be limited by various system constraints such asthermal, voltage and stability limits. The ability to incorporatesuch limits into the optimization problem is a challenge inthe ATC calculation from an engineering point of view. In thecompetitive market environment, a power supplier needs to findan optimal strategy that maximizes its own profits under variousuncertainties such as electricity prices and load. On the otherhand, an efficient market clearing mechanism is needed to increasethe social welfare, i.e. the sum of the consumers’ andproducers’ surplus. The need to maximize the social welfaresubject to system operational constraints is also a major challengefrom a societal point of view. This paper presents new optimizationtechniques motivated by the competitive electricity market environment.Numerical simulation results are presented to demonstrate theperformance of the proposed optimization techniques.     

Market power analysis in electricity markets using supply function equilibrium model

This paper presents a surveillance method based on the gametheory which is used by the ISO to find whether a power supplierin an electricity market has market power. The paper uses thesupply function equilibrium model to analyse the generationsuppliers’ bidding behaviour and models the ISO's marketpower monitoring problem as a bi-level multi-objective problem.The outer sub-problem is a multi-objective problem which maximizessuppliers’ payoffs, while the inner one is the ISO's marketclearing problem based on the locational marginal pricing mechanism.A discrete method is adopted to find ‘good enough’solutions, in a continuous bidding strategy space, which arethe intersection of all suppliers’ optimal response spacesaccording to Nash equilibrium. The paper utilizes the IEEE 118-bussystem to illustrate the application of the proposed methodwith three suppliers as price setters in the energy market andthe other generators as price takers. The numerical resultsshow that the transmission congestion may enhance the suppliers’ability to exercise market power. Likewise, suppliers’gaming behaviour could relieve the transmission congestion.It is shown that applying price caps is an efficient way ofmitigating market power.     

Implicit collusion and individual market power in electricity markets

Wholesale electricity markets may not produce competitive outcomes, either as a result of the exercise of market power, or through problems of implicit collusion. In comparison with the great amount of attention paid to issues of market power, the problems of implicit collusion have not been extensively studied. In this paper, we use a coevolutionary approach to explore the effect of the price elasticity of demand, capacity and forward contracts on implicit collusion in a duopoly. We will demonstrate that implicit collusion has the most importance in market conditions under which there is an intermediate amount of market power. Thus markets which are either highly competitive or in which one or both of the two generators can exercise considerable market power, are also markets in which implicitly collusive outcomes are less likely to arise.     

The model of chaotic sequences based on adaptive particle swarm optimization arithmetic combined with seasonal term

Within a competitive electric power market, electricity price is one of the core elements, which is crucial to all the market participants. Accurately forecasting of electricity price becomes highly desirable. This paper propose a forecasting model of electricity price using chaotic sequences for forecasting of short term electricity price in the Australian power market. One modified model is applies seasonal adjustment and another modified model is employed seasonal adjustment and adaptive particle swarm optimization (APSO) that determines the parameters for the chaotic system. The experimental results show that the proposed methods performs noticeably better than the traditional chaotic algorithm.     

Non-convex power plant modelling in energy optimisation

The European electricity market has been deregulated recently. This means that energy companies must optimise power generation considering the rapidly fluctuating price on the spot market. Optimisation has also become more difficult. New production technologies, such as gas turbines (GT), combined heat and power generation (CHP), and combined steam and gas cycles (CSG) require non-convex models. Risk analysis through stochastic simulation requires solving a large number of models rapidly. These factors have created a need for more versatile and efficient decision-support tools for energy companies.We formulate the decision-problem of a power company as a large mixed integer programming (MIP) model. To make the model manageable we compose the model hierarchically from modular components. To speed up the optimisation procedure, we decompose the problem into hourly sub-problems, and develop a customised Branch-and-Bound algorithm for solving the sub-problems efficiently. We demonstrate the use of the model with a real-life application.     

基于双曲型谱风险度量的大用户购电策略

直购电模式正在推行,大用户与电网公司的风险偏好却各不相同。本文将风险偏好纳入结算策略,建立了基于双曲型谱风险的购电优化模型,并用PJM日前市场的数据进行了实证分析。探讨了风险厌恶因子的敏感范围,将大用户划分为积极、稳健和保守三种类型,分别讨论了其购电策略。结果表明:无论风险偏好如何,大用户总愿意为获得高收益而承担更高的风险;风险偏好是购电策略的重要影响因素;当风险偏好既定时,大用户在远期合同市场和日前市场的购电比例可由谱风险值确定。随着谱风险值的增加,大用户会减少远期合同市场的购电量,更倾向于在日前市场购电。     

电力市场中合同电量与竞争电量交易比例的研究

在单边开放的区域电力市场中,合理的合同电量与竞争电量交易比例是保证电力市场有效运行的一个重要环节。竞争电量所占的比例将主要取决于当前发电公司的市场行为。首先使用BP神经网络对电力需求弹性系数进行了预测,然后以长期电力市场均衡为目标函数,考虑贵州电网发电机组的可用容量与负荷预测的误差,以及贵州输电线路的可靠性诸因素,推导出合同电量与竞争电量交易比例,经过与南方区域电力市场目前运营规则规定的交易比例比较,该比例是合理的,可以规避电力市场价格波动等带来的风险。     

Nash equilibrium in a pay-as-bid electricity market: Part 1 – existence and characterization

We consider a model of a pay-as-bid electricity market based on a multi-leader-common-follower approach where the producers as leaders are at the upper level and the regulator as a common follower is at the lower level. We fully characterize Nash equilibria for this model by describing necessary and sufficient conditions for their existence as well as providing explicit formulas of such equilibria in the market.     

Cyclic behavior in dynamic investment decisions for deregulated energy markets

In the first years after the deregulation of the electricity industry, investment into new generation capacity has not taken place on a large scale in any central european country. Recent increases in prices indicate that investment could be very profitable. However, the fear is that the need for new capacity can be overestimated and that could lead to a decrease in prices and profits and consequently to a reduction/stop of new investments. The aim of this paper is to model and analyze factors that influence the stability of electricity prices. The electricity market is modeled using a Cournot game and the stability of electricity prices is analyzed by simulations. The research was supported by the grant 1/3001/06 of the Grant Agency of Slovak Republic (VEGA) and grant VVGS 36/2006.     

Estimation of Electricity Market Distribution Functions

In an electricity pool market the market distribution function gives the probability that a generator offering a certain quantity of power at a certain price will not be dispatched all of this quantity by the pool. It represents the uncertainty in a pool market associated with the offers of the other agents as well as demand. We present a general Bayesian update scheme for market distribution functions. To illustrate the approach a particular form of this procedure is applied to real data obtained from a New Zealand electricity generator.     

基于鲁棒均值-下半偏差模型的供电公司购电组合策略

电力市场中,日前市场购电电价的随机波动,给供电公司的投资带来了一定的收益风险,因而供电公司需要在不同的市场中合理分配购电电量分散投资,以实现自身收益率尽可能大的同时承受的风险最小.供电公司在多市场中购电电价呈随机波动的特性,本文用均值-下半偏差作为购电风险测度,并用鲁棒优化处理电价的不确定性,建立了供电公司鲁棒均值-下半偏差(Robust Mean Semi-Deviation)购电策略优化模型.最后利用广西电网公司提供的数据进行实证分析,验证了模型的有效性和适用性,表明此模型对供电公司的投资组合决策具有一定的参考价值和指导意义.     

Tacit collusion games in pool-based electricity markets under transmission constraints

Harrington et al. (Math Program Ser B 104:407–435, 2005) introduced a general framework for modeling tacit collusion in which producing firms collectively maximize the Nash bargaining objective function, subject to incentive compatibility constraints. This work extends that collusion model to the setting of a competitive pool-based electricity market operated by an independent system operator. The extension has two features. First, the locationally distinct markets in which firms compete are connected by transmission lines. Capacity limits of the transmission lines, together with the laws of physics that guide the flow of electricity, may alter firms’ strategic behavior. Second, in addition to electricity power producers, other market participants, including system operators and power marketers, play important roles in a competitive electricity market. The new players are included in the model in order to better represent real-world markets, and this inclusion will impact power producers’ strategic behavior as well. The resulting model is a mathematical program with equilibrium constraints (MPEC). Properties of the specific MPEC are discussed and numerical examples illustrating the impacts of transmission congestion in a collusive game are presented.