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.     

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.     

Optimization of transmission network for homogeneous good market

We examine a model of a perfect competitive homogeneous good market with a network structure. Such a structure is typically important for energy resources: natural gas, oil and electricity. Local markets are connected by transmission lines with limited capacities and given cost functions for capacity increments. We consider the total welfare optimization problem and provide a method that determines optimal investments in the transmission system expansion for some types of the networks. In particular, we study the case where the market is divided into two submarkets with binding transmission line flow constraints between the submarkets. We obtain efficient algorithms for determination of the transmission systems optimal expansion. We conclude with the impact of the results and the outlook to future studies.     

An optimization problem in the electricity market

New types of optimization problems are faced by the generating companies that operate on deregulated electricity markets. The characteristics of these problems depend on the various market structures. In the framework of the recently settled Italian electricity market, one of these new problems is the transition from hourly energy programs, defined by the market, to more detailed power generation dispatches, defined for intervals of 15 min. Such a more detailed plan is needed on the one hand by the national system operator (Terna, Rete Elettrica Nazionale) for the assessment of power system stability and security, and on the other hand by the power plant operators for its implementation. The transition procedure should respect the hourly energy constraints and take the main operating constraints of the generating units into account. The paper presents possible solutions of the problem through linear optimization models and reports computational results on real-world instances.      

Solving nonconvex economic load dispatch problem using particle swarm optimization with time varying acceleration coefficients

This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve‐point effects, multi‐fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3‐machines 6‐bus, IEEE 5‐machines 14‐bus, IEEE 6‐machines 30‐bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve‐point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity 21: 299–308, 2016     

安全约束条件下的经济调度优化模型研究

发电侧放开竞争的电力系统需要更加有效、准确的决策工具对有限的资源进行调度规划。短期经济调度优化问题是一个混合整数非线性规划问题,很难得到有效最优解,尤其是对于大规模电力系统。为了提高求解效率,本文提出了一个考虑安全约束的经济调度优化模型(Security-Constrained Economics Dispatch,SCED),主要采用线性化思想处理经济调度优化问题的模型以及各种约束,采用基于校正的交替求解方法,使得调度优化结果在运行成本最小化的前提下满足系统的安全稳定约束。同时,将本文方法运用到IEEE 30节点系统进行测试,从而验证本文方法有效性。     

Two-settlement electricity markets with price caps and Cournot generation firms

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a regulatory intervention. In this paper we explore the implications of these two alternative mechanisms in a two-settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and horizontal market power. As an illustrative test case, we use the 53-bus Belgian electricity network with representative generator costs but hypothetical demand and ownership structure. Compared to a price-uncapped two-settlement system, a forward cap increases firms’ incentives for forward contracting, whereas a spot cap reduces such incentives. Moreover, in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified.     

Hybrid harmony search algorithm and fuzzy mechanism for solving congestion management problem in an electricity market

A hybrid technique for solving the congestion management problem in an electricity market based on harmony search algorithm (HAS) and Fuzzy mechanism is presented in this article. This algorithm does not require initial value setting for the variables and does not require differential gradients, thus it can consider discontinuous functions as well as continuous functions. The HAS is a recently developed powerful evolutionary algorithm, inspired by the improvisation process of musicians, for solving single/multiobjective optimization problems. In the proposed technique, each musician plays a note for finding a best harmony all together. Transmission pricing and congestion management are the key elements of a competitive electricity market based on direct access. They also focus of much of the debate concerning alternative approaches to the market design and the implementation of a common carrier electricity system. This article focuses on the tradeoffs between simplicity and economic efficiency in meeting the objectives of a transmission pricing and congestion management scheme. The effectiveness of the proposed technique is applied on 30 and 118 bus IEEE standard power system in comparison with CPSO, PSO‐TVAC, and PSO‐TVIW. The numerical results demonstrate that the proposed technique is better and superior than other compared methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 90–98, 2016     

有功与无功功率最优实时定价新方法

本文给出了一种基于社会收益最大化的有功与无功功率最优实时定价新方法 .传统的研究仅仅考虑了电力系统运行成本最小这一目标 .本文则把有功运行成本、无功运行成本与消费者的收益结合起来 ,利用把消费者的反映表示为需求函数的逆形式的手段 ,使最大化电力市场参与者的社会收益目标变为可能 ,每条母线上的有功与无功功率定价结果也可相应求出 .     

Some new aspects of the transient analysis of discrete-parameter Markov models with an application to the evaluation of repair events in power transmission

In Markov reliability modelling, a partitioned state space isused to describe the behaviour of a system each state of whichis associated with the system either being functional or underrepair. Such a system alternates between working and repairperiods indefinitely. Recent research results on the distributionof the sequences of the lengths of working and repair periodsafford the reliability analyst a set of system characteristicswhich can be used in addition to the traditional ones (reliability,point availability, etc.) to describe the system‘s transientbehaviour. In this paper, we present a concise derivation ofclosed-form expressions for the probability mass function andthe factorial moments of the total cumulative ’time‘spent in a subset of the state space by an irreducible or absorbingdiscrete-parameter Markov chain during the first n time instances.This result is then applied to analyse the sequence of repairevents categorized as ’minor‘ and ’major‘of a Markov model of a power transmission system. The numericalimplementation using the Macintosh version of MatLab is alsodiscussed.     

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.     

The Deregulated Electricity Market Viewed as a Bilevel Programming Problem

In this paper, we present a bilevel programming formulation of a deregulated electricity market. By examining the electricity market in this format, we achieve two things. First, the relation of the deregulated electricity market to general economic models that can be formulated as bilevel programming problems (e.g. Stackelberg leader-follower games and principal-agency models) becomes clear. Secondly, it provides an explanation of the reason why the so-called “folk theorems” can be proven to be false for electricity networks. The interpretation of the deregulated electricity market as a bilevel program also indicates the magnitude of the error that can be made if the electricity market model studied does not take into account the physical constraints of the electric grid, or oversimplifies the electricity network to a radial network.     

On <Emphasis Type="Italic">M</Emphasis>-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling

Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived. Then the co-derivative formula is used for verifying constraint qualifications and for identifying M-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios. Dedicated to our friend and colleague Jiří V. Outrata on the occasion of his 60th birthday. This work was supported by the DFG Research Center Matheon Mathematics for key technologies in Berlin.     

Evaluating Individual Market Power in Electricity Markets via Agent-Based Simulation

We use agent-based simulation in a coordination game to analyse the possibility of market power abuse in a competitive electricity market. The context of this was a real application to the England and Wales electricity market as part of a Competition Commission Inquiry into whether two particular generators could profitably influence wholesale prices. The research contributions of this paper are both in the areas of market power and market design policy issues for electricity markets, and in the methodological use of large industry-wide evolutionary simulation models.     

Divide to conquer: decomposition methods for energy optimization

Modern electricity systems provide a plethora of challenging issues in optimization. The increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting. The liberalization of the electricity sector brought the need of designing sound markets, ensuring capacity investments while properly reflecting strategic interactions. In all these problems, hedging risk, possibly in a dynamic manner, is also a concern. The fact of representing uncertainty and/or competition of different companies in a multi-settlement power market considerably increases the number of variables and constraints. For this reason, usually a trade-off needs to be found between modeling and numerical tractability: the more details are brought into the model, the harder becomes the optimization problem. For structured optimization and generalized equilibrium problems, we explore some variants of solution methods based on Lagrangian relaxation and on Benders decomposition. Throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems.     

电网安全调度中输电阻塞管理的演化策略

输电阻塞是电力系统运行中的常见问题 .本文建立了用于电网安全调度中输电阻塞管理的数学模型——带线性约束的多目标模糊优化问题模型 ,给出了求解该模型的演化策略 .实际的计算结果表明 ,演化策略解决输电阻塞问题是有效的 .     

一般工商业零售电价套餐适应性评估与优化方法

在电力体制改革的大背景下,合理评估零售电价套餐适应性,对控制电网经营风险和推进售电侧改革有重要意义。针对我国电力市场以及一般工商业的特点,首先从竞争、用户以及市场环境角度出发建立了一般工商业零售电价套餐评估指标体系;其次将层次分析法和改进的灰色白化权函数相结合,对电价套餐进行适应性评估;最后针对该评估方法建立了基于蚁群算法的优化模型,以最小成本得到提高电价套餐适应性等级的优化方案,并验证了该方法具有良好的鲁棒性,具有一定的参考意义。     

Radial Limits of Bloch Functions in the unit Disc

Although a function in the Bloch space may have no radial limits,it is shown that there exist bounded linear functionals whichgive ‘average radial limits’ over an interval onthe boundary. An ‘abelian–tauberian’ theoremis proved, characterizing the existence of a radial limit ata given boundary point in terms of these functionals.     

Deregulation in electricity: understanding strategic and regulatory risk

This paper is motivated by our experiences since 1990 with developing system simulation models to help UK companies in the restructured electricity industry understand the radically different market within which they must become competitive. When public utilities such as electricity have been restructured, deregulated and/or privatised, the process has often been associated with a major change in the competitive environment. As a consequence, the strategic and regulatory uncertainties ahead for these companies are unprecedented. In such a market there has been no historical evolution and all the participants including the regulatory institutions have very little understanding of how it will operate in the short term and evolve in the future. In this situation, the use of system dynamic models appears to offer an attractive way of gaining insights into how aspects of the competitive market might evolve. In the absence of real experience and relevant analogies, learning from models assumes a key role. Such models cannot be validated empirically, but can be developed to represent how the system is designed to operate. From such a prototypical basis, sensitivity analysis can generate insights on the strategic opportunities created by failings in the market design, or its potential instability to shocks and market imperfections.     

A two stage stochastic equilibrium model for electricity markets with two way contracts

This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans et al. (Aust J Manage 23:83–96, 1998) for a duopoly market to an oligopoly market. The main results of the paper concern the structure of a Nash–Cournot equilibrium in the forward-spot market: first, we develop a result on the existence and uniqueness of the equilibrium in the spot market for every demand scenario. Then, we show the monotonicity and convexity of each generator’s dispatch quantity in the spot equilibrium by taking it as a function of the forward contracts. Finally, we establish some sufficient conditions for the existence of a local and global Nash equilibrium in the forward-spot markets. Numerical experiments are carried out to illustrate how the proposed SEPEC model can be used to analyze interactions of the markets.