Methods and Models for Stochastic Energy Market Equilibria

该项目将开发带有概率分量的能源市场均衡模型，并分析确保解的存在和唯一性的条件。将考虑两种模式，第一种模式将审查天然气等特定部门，第二种模式对应于总体能源市场，其中部门(例如煤炭市场)将从高层次的角度进行建模。在具体部门的方法中，个别市场参与者(如天然气生产商、发电商)将被描述为解决受运营限制以及不确定需求或其他随机因素制约的利润最大化问题。这些市场参与者要么被建模为纳什-古诺参与者，从而有可能主张市场力量，要么被视为完全竞争的参与者，认为市场价格是给定的。这些最优化问题中的每一个问题的同时解以及市场出清条件都将导致一个非线性互补或变分不等问题的求解。在所考虑的第二种模式中，将对整个能源部门进行建模，以允许某些关键因素(例如，管道容量)因人为或自然事件而不确定。还将研究基于非线性互补/变分不等方法的相关市场均衡的存在性和唯一性问题。该项目还将开发和分析有效的算法，以利用分解、矩阵分解或追索权方法来解决这些随机市场均衡问题。因此，该项目将加入随机优化和均衡建模这两个重要学科。最后，该项目将使用这些模型分析关键的能源政策情景。现代社会严重依赖于多种类型的基础设施才能有效运行。这些基础设施有多种形式，如电网、交通网络、水处理设施等。然而，这些基础设施中的许多要素都面临着严重降低社会效益的风险。例如，最近的能源市场放松管制和结构调整在某些情况下造成了能源价格的大幅波动，对社会产生了不利影响。能源部门某些方面的不稳定是麻烦的，因为能源对经济的许多部分至关重要。因此，能源领域的风险管理可以使许多领域受益。为了应对这些能源基础设施问题，人们可以开发数学模型，预测能源部门在各种情况下将如何运作，然后通过建立冗余系统、使用金融工具或其他措施进行相应的规划。该项目将开发和分析能源市场均衡模型，并建立和分析解决此类问题的有效算法。这些模型将直接考虑不确定的需求或其他概率因素，以更准确地反映市场参与者在面临不确定性时的行为。然后，这些模型将被用来分析某些关键的能源政策情景，并酌情与美国和其他国家的能源官员进行磋商。

The project will develop energy market equilibrium models with probabilistic components and analyze conditions that ensure existence and uniqueness of solutions. Two modes will be considered, the first one in which a specific sector such as natural gas will be examined and the second one corresponding to the overall energy market where sectors (e.g., the coal market) will be modeled from a high-level perspective. In the sector-specific approach, individual market players (e.g., natural gas producers, electric power generators) will be depicted as solving profit maximization problems subject to operational constraints as well as uncertain demand or other stochastic elements. These market participants will either be modeled as Nash-Cournot players and thereby have the potential to assert market power, or perfectly competitive players that take market prices as given. The simultaneous solution of each of these optimization problems along with market clearing conditions will lead to a nonlinear complementarity or variational inequality problem whose solution will be sought. In the second mode considered, the overall energy sector will be modeled allowing for certain key elements (e.g., pipeline capacity) to be uncertain due to man-made or natural occurrences. Existence and uniqueness issues for the related market equilibria also based on a nonlinear complementarity/variational inequality approach will be examined. The project will also develop and analyze efficient algorithms to solve these stochastic market equilibrium problems making use of decomposition, matrix factorizations, or recourse approaches. As such, the project will join the two important disciplines of stochastic optimization and equilibrium modeling. Lastly, the project will analyze key energy policy scenarios using these models. Modern society depends heavily on many types of infrastructure to operate efficiently. This infrastructure is in many forms such as the electric power grid, transportation networks, water treatment facilities, etc. However, many of these infrastructure elements face risks that threaten to seriously degrade the societal benefits. For example, recent energy market deregulation and restructuring have in some cases contributed to large volatility in energy prices which have adversely affected society. The instability in certain aspects of the energy sector is troublesome since energy is vital to many parts of the economy. Thus, risk management in energy can benefit many areas. To combat these energy infrastructure problems, one can develop mathematical models to predict how the energy sector will function under a wide range of scenarios and then plan accordingly by building redundant systems, using financial instruments or other measures. This project will both develop and analyze energy market equilibrium models as well as build and analyze efficient algorithms to solve such problems. These models will directly take into account uncertain demand or other probabilistic elements to more accurately reflect the market players' actions when faced with uncertainty. These models will then be used to analyze certain key energy policy scenarios in consultation with U.S. energy officials as well as those of other countries as appropriate.