COLLABORATIVE RESEARCH: Commitment, Expansion, and Pricing in Uncertain Power Markets: Discrete Hierarchical Models and Scalable Algorithms

不确定电力市场中的承诺、扩展和定价：离散分层模型和可扩展算法我们的研究是基于不确定性、非线性和分层结构对电力系统和市场中的关键长期规划(例如输电扩展)和运行问题(例如机组组合问题(UCP)和输电切换)的影响。这类问题的最佳解决具有重大意义。例如，UCP的算法每年节省数十亿美元，而传输切换的类似方案可能具有类似的潜力。然而，许多可用的技术只能处理确定性的线性问题。但是，通过交流潮流将无功和电压管理结合在一起，产生了越来越多的非线性概括，而需求和可用性等问题数据的不确定性导致了问题复杂性的大幅增长。同样具有挑战性的是分层问题，这些问题是在认识到长期监管、经济和技术不确定性的情况下，根据后续能源市场行为优化输电资产的扩张而产生的。计划和操作问题都导致了极具挑战性的优化问题，并且没有可扩展的通用算法来解决这类问题，这促使了拟议的研究。通过与两个美国市场的独立系统运营商的关系，我们的研究将有助于为利益相关者提供有关电力和容量市场设计的讨论。更有效率的短期和长期市场降低了电力部门的成本，提高了环境的可持续性。特别是，我们与PJM InterConnection的合作将审查不确定性下的承诺、切换和扩展问题，确保发电充分性的可靠性定价模型，以及在整合可再生能源的背景下可靠性溢价的设计。我们的目标有两个：(A)随机优化模型：我们考虑开发：(I)强调无功管理、输电切换和随机性的随机机组组合问题的运行模型；(Ii)不确定环境下输电扩展以及可靠性定价的规划模型，特别是发电和输电资源的充分性。(B)可扩展算法：这些模型导致可能因非线性而复杂的混合二进制随机优化问题。不幸的是，现有的分解方案不足以解决这些问题，我们考虑了两个大的方向。(I)利用内点方法、割平面技术和Schur补方法的组合来开发可伸缩内点方法的随机障碍切割方案，用于竞争混合二进制随机非线性规划；以及(Ii)随机混合整数二次规划，包括在开发割平面方案和近似解方面潜在地使用半定规划松弛。如果成功，这项研究将带来可扩展的计算工具，用于解决一系列由层级、离散性和非线性组成的复杂的随机优化问题。

Commitment, Expansion, and Pricing in Uncertain Power Markets: Discrete Hierarchical Models and Scalable AlgorithmsOur study is motivated by the impact of uncertainty, nonlinearity, and hierarchy on critical long-term planning (such as transmission expansion) and operational problems (such as unit commitment problems (UCPs) and transmission switching) in power systems and markets. The optimal resolution of such problems is of significant relevance. For instance, algorithms for UCPs have saved billions of dollars annually while analogous schemes for transmission switching may have similar potential. Yet, much of the available technology can only cope with deterministic linear problems. But nonlinear generalizations are assuming increasing relevance and emerge from incorporating reactive power and voltage management through AC load flows, while uncertainty in problem data, such as demand and availability, leads to a massive growth in problem complexity. Equally challenging are the hierarchical problems, arising from optimizing the expansion of transmission assets subject to subsequent energy market behavior, recognizing long run regulatory, economic, and technology uncertainties. Both the planning and operational problems lead to inordinately challenging optimization problems and no general purpose algorithms exist for the scalable resolution of such problems, motivating the proposed research. Through relationships with independent system operators for two US markets, our research will help inform stakeholder discussions concerning the design of markets for electric energy and capacity. More efficient short-run and long-run markets lower the cost and enhance the environmental sustainability of the power sector. In particular, our collaboration with PJM Interconnection will examine commitment, switching, and expansion problems under uncertainty, reliability pricing models for ensuring generation adequacy, and the design of reliability premiums in the context of integrating renewables. The proposal is equipped with an educational plan that includes the organization of research workshops and professional course development.Our goals are twofold: (a) Stochastic optimization models: We consider development of: (i) Operating models for stochastic unit commitment problems emphasizing reactive power management, transmission switching, and stochasticity; and (ii) Planning models for transmission expansion in uncertain settings as well as the pricing of reliability, in particular the adequacy of generation and transmission resources. (b) Scalable algorithms: These models lead to mixed-binary stochastic optimization problems possibly complicated by nonlinearity. Unfortunately, existing decomposition schemes are ill-equipped to address such problems and we consider two broad directions. (i) A stochastic barrier-cut scheme that utilizes a combination of interior point methods, cutting plane techniques, and Schur-complement methods to develop scalable interior-point methods for contending with mixed-binary stochastic nonlinear programs; and (ii) Stochastic mixed-integer quadratic programs, including potential use of semidefinite programming relaxations, both in terms of developing cutting-plane schemes as well as approximate solutions. If successful, this research will lead to scalable computational tools for resolving a range of stochastic optimization problems, complicated by hierarchy, discreteness, and nonlinearity.