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：离散层次模型和可扩展算法我们研究的动机是不确定性、非线性和层次对电力系统和市场中关键的长期规划（如输电扩展）和运营问题（如机组承诺问题（ucp）和输电交换）的影响。这类问题的最佳解决方案具有重要的相关性。例如，ucp的算法每年节省了数十亿美元，而传输交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线性问题。但是，非线性泛化假设越来越重要，并且通过交流负载流整合无功功率和电压管理，而问题数据（如需求和可用性）的不确定性导致问题复杂性的大幅增长。同样具有挑战性的是等级问题，这是由于输电资产的优化扩张受制于随后的能源市场行为，认识到长期的监管、经济和技术不确定性而产生的。规划和操作问题都导致了极具挑战性的优化问题，并且没有通用的算法来解决这些问题，这激发了本文的研究。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告知利益相关者关于电力能源和容量市场设计的讨论。更有效的短期和长期市场可以降低成本，增强电力部门的环境可持续性。特别是，我们与PJM互联的合作将研究不确定性下的承诺、转换和扩展问题，确保发电充足的可靠性定价模型，以及整合可再生能源背景下的可靠性溢价设计。该提案附有一项教育计划，其中包括组织研究讲习班和专业课程开发。我们的目标是双重的：(a)随机优化模型：我们考虑发展：(i)强调无功管理、传输切换和随机性的随机机组承诺问题的运行模型；（二）不确定环境下输电扩展的规划模式以及可靠性定价，特别是发电和输电资源的充足性。(b)可扩展算法：这些模型导致可能因非线性而复杂化的混合二元随机优化问题。不幸的是，现有的分解方案不足以解决这些问题，我们考虑两个广泛的方向。(i)一种随机障碍切割方案，该方案结合了内点法、切割平面技术和schur -互补方法，开发了可扩展的内点法，用于处理混合二进制随机非线性程序；（ii）随机混合整数二次规划，包括半定规划松弛的潜在用途，无论是在开发切割平面方案方面还是在近似解方面。如果成功，这项研究将导致可扩展的计算工具来解决一系列随机优化问题，复杂的层次，离散性和非线性。

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.