基于博弈论的考虑输电网络约束电力市场均衡分析
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摘要
世界各地的电力工业在最近几十年正进行或面临着一场规模巨大的重组改革。电力工业引入市场化竞争以提高社会效益及增强运行效率。然而在当前阶段,电力市场具有寡头垄断市场特性,电力公司可以通过策略性报价来影响市场电价。因此研究分析电力市场中的策略行为及市场可能的运行结果显得尤为重要。基于博弈论的纳什均衡相关理论为解决这个课题提供一个科学可行途径。市场纳什均衡不仅可以指导市场监管者监测市场竞争是否充分,而且可以用来分析构建发电厂商的最优竞价策略以获取最大利润。但是由于电力系统具有输电网络约束等鲜明特性,这些特性将市场出清机制变得复杂并使得发电公司的收益函数不再具有凹性与可微性,因此使得求解市场均衡成为一个复杂困难的课题。
本论文主要涉及考虑输电网络约束复杂电力市场的均衡分析,其主要研究内容可概述如下：
1.以线性供给函数均衡模型为基础,建立了考虑输电网络约束、发电容量约束及负荷需求侧策略性竞价的电力市场模型。运用协同进化算法求取市场均衡,两个经典算例被用来说明所建电力市场模型及所提算法的有效性。结果表明：如果纯策略纳什均衡存在的话,协同进化算法能够快速收敛到市场均衡并且能够避免陷入局部最优点能；市场纯策略纳什均衡的存在性不仅仅取决于系统是否存在网络阻塞；负荷需求侧策略性竞价及发电容量约束对市场均衡亦有重要影响。
2.在电力市场不完全竞争模型分析中,求解市场的纳什均衡是个重要任务,其中求解混合策略均衡以及判断是否存在多个均衡均是相当困难的课题。本论文首先建立了考虑网络约束的古诺模型,然后提出属于收益矩阵方法类型的多项式方程系统算法求解市场可能存在的所有均衡。多项式方程系统算法引用支集的特征,将纳什均衡条件转化为多项式方程系统及其不等式约束,而后通过甄别满足不等式条件的解来求取所有均衡。针对三节点测试系统,不同的实验场景被构建用来考察所提出算法的有效性,实验结果表明在一定条件下,多项式方程系统算法能够求解到所有均衡,这表明该方法在实际电力市场分析中有着相当潜力与重要作用。
3.分布式发电与可中断负荷是智能电网的两种重要资源。针对电力用户停电意愿不尽相同,将配电公司的可中断负荷类型建模为离散分布的随机变量,进而建立了具有分布式发电与不完全信息可中断负荷选择的配电公司能量获取模型,综合考虑到发电公司的竞价策略行为,最后建立了完整的不完全信息博弈下的电力市场模型。针对不完全信息博弈的特征,扩展改进了协同进化算法,并用其来求解市场贝叶斯纳什均衡。修正的IEEE 9节点系统验证了模型与求解方法的有效性。结果表明分布式发电与可中断负荷、发电公司策略行为及不完全信息对市场均衡有着重要的影响。
4.电力系统在运行与规划过程中存在负荷不确定性与系统元件故障停运风险等多种不确定性因素,这使得研究考虑这些不确定性因素的电力市场均衡分析显得相当迫切。针对负荷不确定性与随机线路故障停运,建立了考虑系统运行不确定性的电力市场线性供给函数均衡模型。在该模型中,通过枚举不确定性因素而确定系统运行可能的运行状态集合,发电厂商综合考虑各个运行状态下的情况以获取最大期望收益。针对随机博弈的特点,扩展改进了协同进化算法并进一步将其运用于求解随机市场均衡。9节点测试系统作为算例来分析说明所建立电力市场模型与协同进化算法的有效性。
In recent years, the electricity industry throughout the world has been undergoing restructuring. Competition has been introduced in order to improve operational and investment efficiency. However, the electricity market is an oligopoly in that the participants have market power, being able to influence the price by strategic action. The analysis of strategic behaviors and possible operation results in the electricity market seems particularly important. A key concept in analyzing oligopolies is the Nash Equilibrium (NE), which is thought of as a rigorous solution for bidding strategies in electricity markets. This study is important for both regulatory entities and market participants, in that the former have the duty to design and monitor the markets to ensure full competitiveness, and the latter are interested in optimal strategies for maximizing profit. However, it is difficult to solve the market equilibria problem, since the particular characteristics of an electric power system, such as transmission constraints, complicate the market clearing mechanism and make the payoff functions non-differentiable and non-concave.
This dissertation addresses issues of equilibrium analysis of complicated electric power market considering the transmission constraints. The main work and key contribution of this dissertation are as follows:
1. This dissertation proposes a new electricity market equilibrium model based on the Linear Supply Function Equilibrium (LSFE) model. In the proposed model, transmission constraints in addition to generation constraints and consumers bidding behavior are considered. A coevolutionary computation approach is proposed to solve for market equilibrium. Several cases from two sample systems are tested to verify the effectiveness of the proposed method which avoids being trapped in local optimum when searching for Nash Equilibrium. Simulation results indicate that the proposed approach rapidly converges to the pure strategy Nash Equilibrium if it exists. Further, it is observed that the existence of the pure strategy equilibrium is not simply determined by the existence of transmission congestion. The consumer strategic behavior and the generation constraints will also have impacts on the equilibria.
2. It is a key problem to calculate the Nash equilibrium for the deregulated electricity market, and the problem mainly has two difficulties:computation of the mixed strategy Nash equilibrium and determination of whether multiple equilibria exist. Cournot model considering the network constraints is presented in the dissertation, then the solving system of polynomial equations algorithm, which is an algebraic method and belongs to the payoff matrix approach, is proposed to calculate the all Nash equilibrium for the finite-strategy multi-player game in the electricity market. The proposed approach mostly relies on decomposing the game by means of the support sets, and for each support set, the condition of the Nash equilibrium can be characterized by a system of polynomial equation and inequalities, then the all Nash Equilibrium could be found through detecting all the solution. Several examples base on the three-bus text system are used to investigate the effectiveness of the proposed approach, and the results show that the approach is capable of finding all Nash equilibrium under certain condition, which indicate that it has the potential to be used in the study of the real-world electricity markets.
3. Distributed generation and interruptible load are two important resources of the smart grid. Because different kinds of power users have different willingness to curtail their demands, the type of the interruptible loads owned by a distribution company (DISCO) is assumed to be a stochastic variable which meets a discrete distribution. Further an energy acquisition model with the distributed generation and the interruptible load under incomplete information is formulated for the distribution company. Comprehensively taking into consideration of the strategic behavior of a generation company (GENCO), the integrated electricity market model under incomplete information is proposed finally. The coevolutionary approach is improved and further employed to solve the Bayesian Nash equilibrium of the market model. The IEEE 9-bus system appropriately modified is used to illustrate the proposed model and approach. The simulation results show that the market equilibrium is affected greatly by the distributed generation and interruptible load, the strategic behavior of the generation company and the incomplete information.
4. There exist many uncertainty factors in the planning and operation process of electric power system. Therefore it is an urgent task to analyze electricity market taking into account these uncertainties. The paper proposes a supply function equilibrium model considering load uncertainties and random branch outages. The set of possible operational states of power system is determined by enumerating the uncertainties. A generation company pursues the maximum expected revenue comprehensively considering each system operational state. The coevolutionary approach is improved and used to solve the stochastic market equilibrium. Finally the analysis for a 9-bus sample system demonstrates the rationality and validity of the proposed market model and approach.
本论文主要涉及考虑输电网络约束复杂电力市场的均衡分析,其主要研究内容可概述如下：
1.以线性供给函数均衡模型为基础,建立了考虑输电网络约束、发电容量约束及负荷需求侧策略性竞价的电力市场模型。运用协同进化算法求取市场均衡,两个经典算例被用来说明所建电力市场模型及所提算法的有效性。结果表明：如果纯策略纳什均衡存在的话,协同进化算法能够快速收敛到市场均衡并且能够避免陷入局部最优点能；市场纯策略纳什均衡的存在性不仅仅取决于系统是否存在网络阻塞；负荷需求侧策略性竞价及发电容量约束对市场均衡亦有重要影响。
2.在电力市场不完全竞争模型分析中,求解市场的纳什均衡是个重要任务,其中求解混合策略均衡以及判断是否存在多个均衡均是相当困难的课题。本论文首先建立了考虑网络约束的古诺模型,然后提出属于收益矩阵方法类型的多项式方程系统算法求解市场可能存在的所有均衡。多项式方程系统算法引用支集的特征,将纳什均衡条件转化为多项式方程系统及其不等式约束,而后通过甄别满足不等式条件的解来求取所有均衡。针对三节点测试系统,不同的实验场景被构建用来考察所提出算法的有效性,实验结果表明在一定条件下,多项式方程系统算法能够求解到所有均衡,这表明该方法在实际电力市场分析中有着相当潜力与重要作用。
3.分布式发电与可中断负荷是智能电网的两种重要资源。针对电力用户停电意愿不尽相同,将配电公司的可中断负荷类型建模为离散分布的随机变量,进而建立了具有分布式发电与不完全信息可中断负荷选择的配电公司能量获取模型,综合考虑到发电公司的竞价策略行为,最后建立了完整的不完全信息博弈下的电力市场模型。针对不完全信息博弈的特征,扩展改进了协同进化算法,并用其来求解市场贝叶斯纳什均衡。修正的IEEE 9节点系统验证了模型与求解方法的有效性。结果表明分布式发电与可中断负荷、发电公司策略行为及不完全信息对市场均衡有着重要的影响。
4.电力系统在运行与规划过程中存在负荷不确定性与系统元件故障停运风险等多种不确定性因素,这使得研究考虑这些不确定性因素的电力市场均衡分析显得相当迫切。针对负荷不确定性与随机线路故障停运,建立了考虑系统运行不确定性的电力市场线性供给函数均衡模型。在该模型中,通过枚举不确定性因素而确定系统运行可能的运行状态集合,发电厂商综合考虑各个运行状态下的情况以获取最大期望收益。针对随机博弈的特点,扩展改进了协同进化算法并进一步将其运用于求解随机市场均衡。9节点测试系统作为算例来分析说明所建立电力市场模型与协同进化算法的有效性。
In recent years, the electricity industry throughout the world has been undergoing restructuring. Competition has been introduced in order to improve operational and investment efficiency. However, the electricity market is an oligopoly in that the participants have market power, being able to influence the price by strategic action. The analysis of strategic behaviors and possible operation results in the electricity market seems particularly important. A key concept in analyzing oligopolies is the Nash Equilibrium (NE), which is thought of as a rigorous solution for bidding strategies in electricity markets. This study is important for both regulatory entities and market participants, in that the former have the duty to design and monitor the markets to ensure full competitiveness, and the latter are interested in optimal strategies for maximizing profit. However, it is difficult to solve the market equilibria problem, since the particular characteristics of an electric power system, such as transmission constraints, complicate the market clearing mechanism and make the payoff functions non-differentiable and non-concave.
This dissertation addresses issues of equilibrium analysis of complicated electric power market considering the transmission constraints. The main work and key contribution of this dissertation are as follows:
1. This dissertation proposes a new electricity market equilibrium model based on the Linear Supply Function Equilibrium (LSFE) model. In the proposed model, transmission constraints in addition to generation constraints and consumers bidding behavior are considered. A coevolutionary computation approach is proposed to solve for market equilibrium. Several cases from two sample systems are tested to verify the effectiveness of the proposed method which avoids being trapped in local optimum when searching for Nash Equilibrium. Simulation results indicate that the proposed approach rapidly converges to the pure strategy Nash Equilibrium if it exists. Further, it is observed that the existence of the pure strategy equilibrium is not simply determined by the existence of transmission congestion. The consumer strategic behavior and the generation constraints will also have impacts on the equilibria.
2. It is a key problem to calculate the Nash equilibrium for the deregulated electricity market, and the problem mainly has two difficulties:computation of the mixed strategy Nash equilibrium and determination of whether multiple equilibria exist. Cournot model considering the network constraints is presented in the dissertation, then the solving system of polynomial equations algorithm, which is an algebraic method and belongs to the payoff matrix approach, is proposed to calculate the all Nash equilibrium for the finite-strategy multi-player game in the electricity market. The proposed approach mostly relies on decomposing the game by means of the support sets, and for each support set, the condition of the Nash equilibrium can be characterized by a system of polynomial equation and inequalities, then the all Nash Equilibrium could be found through detecting all the solution. Several examples base on the three-bus text system are used to investigate the effectiveness of the proposed approach, and the results show that the approach is capable of finding all Nash equilibrium under certain condition, which indicate that it has the potential to be used in the study of the real-world electricity markets.
3. Distributed generation and interruptible load are two important resources of the smart grid. Because different kinds of power users have different willingness to curtail their demands, the type of the interruptible loads owned by a distribution company (DISCO) is assumed to be a stochastic variable which meets a discrete distribution. Further an energy acquisition model with the distributed generation and the interruptible load under incomplete information is formulated for the distribution company. Comprehensively taking into consideration of the strategic behavior of a generation company (GENCO), the integrated electricity market model under incomplete information is proposed finally. The coevolutionary approach is improved and further employed to solve the Bayesian Nash equilibrium of the market model. The IEEE 9-bus system appropriately modified is used to illustrate the proposed model and approach. The simulation results show that the market equilibrium is affected greatly by the distributed generation and interruptible load, the strategic behavior of the generation company and the incomplete information.
4. There exist many uncertainty factors in the planning and operation process of electric power system. Therefore it is an urgent task to analyze electricity market taking into account these uncertainties. The paper proposes a supply function equilibrium model considering load uncertainties and random branch outages. The set of possible operational states of power system is determined by enumerating the uncertainties. A generation company pursues the maximum expected revenue comprehensively considering each system operational state. The coevolutionary approach is improved and used to solve the stochastic market equilibrium. Finally the analysis for a 9-bus sample system demonstrates the rationality and validity of the proposed market model and approach.
引文
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