Impacts of Network Constraints on Electricity Market Equilibrium

Nash equilibrium is usually used as the solution of generator's strategic bidding in electricity markets. The available literature has shown by simulation that multiple market equilibria or no pure equilibrium may be induced after the inclusion of network constraints (transmission constraints). This paper presents a systematical analysis for the impacts of network constraints on the market equilibrium in oligopolistic electricity markets. In our modeling, the independent system operator (ISO) dispatches generation and determines nodal prices via solving an optimal power flow (OPF); and the individual generator optimizes its submitted supply function with Nash-supply function equilibrium (SFE) strategy, after taking into account ISO's decision-making process on dispatched generations and nodal prices. The conditions for the existence of equilibrium are given, and it is shown that there may be multiple equilibria or no pure Nash equilibrium. The equilibrium, if it exists, will be at a point where generators pay no congestion charge     

Electricity market equilibrium of nonlinear power systems with reactive power control

The impact of reactive power control on the electricity market equilibrium is investigated. The effects of limitations on the reactive power generation and absorption, and load power factor adjustments, are examined using a novel electricity market equilibrium model that solves large-scale nonlinear power systems with asymmetric strategic firms. The algorithm implemented employs the linear supply function theory for bid-based pool markets. AC power flow analysis is used to represent the electricity network, incorporating variable price-responsive active and reactive load demands. The significance of the reactive power modeling in the electricity market equilibrium is demonstrated using the IEEE 14-bus and IEEE 118-bus systems. It is shown that variations on the reactive power in the system result in different market outcomes, as incentives are given to the strategic generating firms to alter their bidding strategies. The convergence characteristics of the IEEE 118-bus system are graphically presented and discussed to demonstrate the superior computational performance of the proposed algorithm in producing results under strict binding constraints and heavy transmission congestion conditions.     

Analysis of the effect of voltage level requirements on an electricity market equilibrium model

This paper presents a conjectural-variation-based equilibrium model of a single-price electricity market. The main characteristic of the model is that the market equilibrium equations incorporate the effect of the voltage constraints on the companies’ strategic behavior. A two-stage optimization model is used to solve the market equilibrium. In the first stage, an equivalent optimization problem is used to compute the day-ahead market clearing process. In the second stage, some generation units have to modify their active and reactive power in order to meet the technical constraints of the transmission network. These generation changes are determined by computing an AC optimal power flow.     

求解动态无功优化问题的混合免疫遗传算法

无功优化是电力系统运行中提高经济性和电压安全性的重要措施,为防止静态无功优化可能导致无功控制设备的频繁操作,考虑并联电容器投切组数和有载调压变压器变比档位的调节次数约束,建立了电力系统动态无功优化模型。提出免疫遗传算法与非线性内点法相结合的混合算法进行求解,其中免疫遗传算法处理离散变量,非线性内点法处理连续变量,并在免疫遗传算法中设计独特的编码方式,使抗体能够自动满足动态约束。采用IEEE14系统的24时段无功优化问题进行仿真计算,动态无功优化后离散控制设备的调节次数很少,有功损耗比静态优化结果仅有轻微增加,算例结果验证了混合免疫算法的有效性。     

Bidding strategy of generation companies using PSO combined with SA method in the pay as bid markets

This paper proposes a new method that uses the combination of particle swarm optimization (PSO) and simulated annealing (SA) to predict the bidding strategy of Generating Companies (Gencos) in an electricity market where they have incomplete information about their opponents and market mechanism of payment is pay as bid.In the proposed methodology, Gencos prepare their strategic bids according to Supply Function Equilibrium (SFE) model and they change their bidding strategies until Nash equilibrium points are obtained. Nash equilibrium points constitute a central solution concept in game theory and they are computed with solving a global optimization problem. In this paper a new computational intelligence technique is introduced that can be used to solve the Nash optimization problem. This new procedure, is based on the PSO algorithm, which uses SA method to avoid becoming trapped in local minima or maxima and improve the velocity’s function of particles. The performance of this procedure is compared with results of other computational intelligence techniques such as PSO, Genetic Algorithm (GA), and a mathematical method (GAMS/DICOPT). The IEEE 39-bus test system is employed to illustrate and verify the results of the proposed method.     

考虑输电约束的期权市场与现货市场联合均衡分析

针对实际运营电力市场的需求,研究发电商在期权市场与现货市场的联合竞争问题,建立了一个考虑输电约束的两阶段古诺博弈模型。该模型是一个具有均衡约束的2层数学模型,可使用非线性互补方法和改进的Levenherg-Marquardt算法求解。结果表明,输电阻塞抑制了发电商参与期权交易的积极性,削弱了期权对电力市场的作用,加强了处于阻塞有利位置的发电商的市场力,发电商可通过策略性竞标剥夺用户和网络所有者的部分或全部收益。     

市场指数方法对计及上游燃料市场影响的下游发电企业的博弈策略(英文)

A new index,called the market incentive index is proposed for studying the equilibrium between fuel and electricity markets.Firstly,agame theoretic model with a monopolistic upstream fuel market and an oligopolistic downstream electricity market is introduced.It is a simple model that can represent strategic interactions between the two vertically linked markets.Secondly,the market equilibrium is studied for deriving out the index,in which interaction relationships between the two markets are explained analytically with three lemmas and demonstrated with numerical examples.Based on the three preceding lemmas,the market equilibrium is further studied by the index.The study shows that,even for the very complicated interactions between fuel producers and electricity producers,some insights on the market equilibrium can be developed with the index.The index-based method can be used as a very intuitionistic way to study the impact of fuel price on the market equilibrium.Thus,it is a new useful method for analysis of strategic behaviors in the equilibrium.     

考虑网络约束的区域电力市场交易计划

我国区域性电力市场试点工作率先在华东地区展开，华东区域电力市场 将采用Broker现货市场加双边合同的结构。由于Broker交易匹配法的常规交易计划方法在受网络约束的情况下不能获得最优经济效益，文中提出了直接考虑网络约束的交易计划新方法。通过引入发电贡献因子和负荷汲取因子解决了多级电力市场中存在的协调问题，并针对双边交易的特点，采用交易矩阵的方式建立了区域电力市场中Broker系统制定交易计划的数学模型。在IEEE 30节点系统上的计算结果表明，在不计网络约束的情况下，该模型符合Broker交易模式的特点，而在考虑网络约束的情况下，用该模型可以取得最大的社会福利，从而验证了模型和算法的有效性。     

A study of the homogeneous algorithm for dynamic economic dispatchwith network constraints and transmission losses

This paper presents a study of the homogeneous interior point (HIP) method for the economic dispatch problem that combines both independent blocks of constraints (generation demand balance, network flows) and coupling constraints (ramping) into a single optimization problem. By approximating the network constraints through the DC load flow, and the transmission losses through the B-matrix loss formula, the problem is reduced to a convex optimization problem that possesses nonlinear inequality constraints and free variables. The HIP algorithm is specialized in solving this problem, it yields either an approximate global optimum solution or detects possible infeasibility or unboundedness of the problem. The algorithm is tested on the IEEE 14, 30, 57, and 118 bus test systems dispatched over 10 half-hour intervals. The results show that the algorithm is practically efficient     

一种求解无功优化的支路追加内点法

在传统内点法的基础上,提出了一种求解无功优化的支路追加内点法——将线路和变压器模型整合为统一的支路模型;采用支路追加方式来实现内点法中雅克比矩阵和海森矩阵的求解;将优化模型中目标函数与等式约束的求导过程合并。通过以上改进措施,有效地降低了无功优化的公式推导和编程工作量,提高了算法的效率。最后通过IEEE14、IEEE30和IEEE118等系统的仿真计算,验证了该算法的快速性和有效性。     

Modeling and analysis of strategic forward contracting in transmission constrained power markets

Taking the effects of transmission network into account, strategic forward contracting induced by the interaction of generation firms’ strategies in the spot and forward markets is investigated. A two-stage game model is proposed to describe generation firms’ strategic forward contracting and spot market competition. In the spot market, generation firms behave strategically by submitting bids at their nodes in a form of linear supply function (LSF) and there are arbitrageurs who buy and resell power at different nodes where price differences exceed the costs of transmission. The owner of the grid is assumed to ration limited transmission line capacity to maximize the value of the transmission services in the spot market. The Cournot-type competition is assumed for the strategic forward contract market. This two-stage model is formulated as an equilibrium problem with equilibrium constraints (EPEC); in which each firm's optimization problem in the forward market is a mathematical program with equilibrium constraints (MPEC) and parameter-dependent spot market equilibrium as the inner problem. A nonlinear complementarity method is employed to solve this EPEC model.     

Electricity market equilibrium model with resource constraint and transmission congestion

Electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models and many efforts have been made on it before. However, most past research focused on a single-period, single-market model and did not address the fact that GENCOs hold a portfolio of assets in both electricity and fuel markets. This paper first identifies a proper SFE model, which can be applied to a multiple-period situation. Then the paper develops the equilibrium condition using discrete time optimal control considering fuel resource constraints. Finally, the paper discusses the issues of multiple equilibria caused by transmission network and shows that a transmission constrained equilibrium may exist, however the shadow price may not be zero. Additionally, an advantage from the proposed model for merchant transmission planning is discussed.     

Network constraint impacts on the competitive electricity markets under supply-side strategic bidding

In a competitive electricity market, the oligopoly structure of the market and the network constraints may produce results far from the perfect competition. This paper presents a comprehensive approach to evaluate the performances of the electricity markets with network representation in presence of bidding behavior of the producers in a pool system. A supply function strategic bidding model for the producers is introduced, and then different scenarios in terms of bidding behavior and network constraints are studied and compared on the basis of a set of microeconomic metrics. The aim of the paper is to assess, throughout a set of proper indices, the level of competition in a network-constrained market considering strategic behavior of the producers. The approach proposed gives the possibility to assess the different weight of strategic behavior of the producers and of the network constraints in distorting the market performances from its perfect competition equilibrium. From such an analysis, the worsening of the market efficiency and performances, due to the joint effects of the nonperfect competition and the network constraints, may be assessed and quantified, providing information on the adequacy of the grid considered for accommodating a competitive market. The exploitation of the proposed metrics for the market analysis is shown with reference to the IEEE 30-bus test system with demand elasticity explicitly represented.     

The Demand Elasticity Impacts on the Strategic Bidding Behavior of the Electricity Producers

Due to the oligopoly structure of the electricity markets and to the constraints imposed by the transmission network, the producers may exert market power by strategically bidding higher than their marginal costs. This brings market performance far from the perfect competition equilibrium, with higher market clearing price and extra surpluses obtained by the producers. Demand elasticity can significantly affect the market performance contributing to mitigate the strategic bidding behavior of the producers. Compared to other commodity markets, demand elasticity in the electricity markets is low, but even a small increase can result in appreciable improvement of the market performance. The network constraints of the power system play a specific role in determining the oligopoly equilibrium of the gaming behavior of the electricity producers. The model of supply function equilibrium is first applied to a simple three-bus test system for a conceptual analysis and then to a standard IEEE 30-bus test system. The effects of an increase of demand elasticity are assessed, resorting to a set of proper quantitative indexes     

使用LSFE分析计及输电系统约束的市场势力

基于线性供给函数均衡(LSFE)模型，提出了一种计及输电系统约束的计算发电商Lerner指标的新方法。在竞争性的电力市场中，发电商的发电成本数据并不公开，因此不能使用市场仿真计算发电商的Lerner指标。运用所提出的方法，独立系统运行员(ISO)可以在未知发电商成本信息的情况下计算发电商的Lerner指标。该方法只需要各参与者(发电商和用户)的报价曲线和在市场Nash均衡点的电价、功率信息以及输电网络的运行状态信息就可以计算，计算简便，结果精确。该方法还能表明进行策略报价的发电商的Lerner指标与它的市场份额成正比，与所有其他市场参与者的市场份额、供给(需求)价格弹性和对该发电商的网络影响因子的乘积之和成反比。还定义了一个市场综合指标用来度量整个市场中的发电商市场势力作用的相时程度．     

基于原-对偶内点法和混合整数规划法的机组组合问题研究

电力系统机组组合能带来显著的经济效益,随着电力市场的不断发展,在电力系统优化运行中变得尤为重要。然而电力系统机组组组合问题是一个大规模、非凸、非线性混合整数优化问题,至今仍然没有找到一种理想的优化算法。因此针对其特点,采用了原-对偶内点法和混合整数规划法相结合的算法,首先利用混合整数规划法形成伴随规划来处理离散变量,再通过内点法求解伴随规划子问题和负荷经济分配,充分发挥了两种算法在求解机组组合问题上的优势。文中对标准10机组24时段系统算例进行了仿真测试并与之前的各种优化算法进行了对比,结果表明了本文算法模型解决机组组合问题的有效性和优越性。     

面向能源领域信息物理社会系统的行为仿真建模分析——以现货电力市场为例

信息物理社会系统(CPSS)旨在描述复杂网络系统中信息网络、物理系统和社会因素的特征及其交互影响,以实现对该类系统的建模、推理和决策。CPSS研究中,如何反映社会行为是最大难点之一。依据历史和仿真数据,采用生成对抗网络(GAN)模型对不确定的社会行为建模,并通过混合仿真方法推演了当前广东现货电力市场设计中的实际问题,即燃气机组补贴对市场的潜在影响。     

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。     

基于树木生长算法的含UPFC的最优潮流计算

最优潮流(OPF)计算是一个非凸优化问题,统一潮流控制器(UPFC)的引入增加了OPF问题的非凸程度,使得基于内点法的传统优化算法难以获取全局最优解。文中提出基于树木生长算法(TGA)的计及UPFC的最优潮流计算方法,将发电成本与有功网损、电压偏移加权作为目标函数,并考虑网络与UPFC设备的安全运行约束,优化了OPF模型。最后基于IEEE 30节点系统以及南京西环网116节点实际系统进行算例测试,对比TGA、粒子群与内点法的结果,并使用蒙特卡洛方法对不同的启发式算法分别进行50次计算,验证了TGA具有更好的求解精度与鲁棒性。     

考虑绿色证书交易的寡头电力市场均衡分析

可再生能源配额和可交易绿色证书制度作为一种基于市场机制的新能源扶持政策,得到越来越多的关注。该政策的引入会对电力批发市场的竞争产生重要影响,特别是绿色证书交易市场与电力批发交易市场之间存在复杂的相互影响关系。为了定量研究该影响关系,采用寡头竞争均衡理论,建立了一个考虑绿色证书交易市场和电力批发交易市场的两阶段联合均衡模型。在第1阶段,可再生能源发电商以供应函数模式参与证书市场竞争;在第2阶段,所有发电商以古诺模式参与批发市场竞争。该模型描述的均衡问题可以表示为一个具有均衡约束的均衡问题,可采用非线性互补方法来求解。最后,算例仿真重点研究不同配额要求下发电商在两个市场中的策略性行为及相互影响关系,表明在不同的配额要求下,可再生能源发电商会选择在不同市场中行使市场力,并导致电力批发市场价格与绿色证书市场价格上升。