Equilibrium models and algorithms, with applications to energy market design, operation and policy analysis

在竞争激烈的电力市场的运作中，复杂的基于计算机的模型决定了哪些发电机将每小时供电，以及将支付的发电价格。这些模型结合了经济思想和对发电和输电技术的现实描述，以及关于优化的现代数学知识，即从有限的资源中获得最大利益。相关的优化模型也被用来探索政策对能源和环境的影响。*本研究的目的是在建立这些模型、电力市场的相应运作以及使用这些模型来分析能源-环境政策方面提高技术水平。*许多模型从一个主体(如公司)的角度超出了优化的范围，而是考虑了几个相互作用的主体的“均衡”，每个主体都试图进行优化。研究工作的一部分还将致力于提高计算速度，以便足够快地获得解决方案，用于电力市场的运营。加速策略是一种称为“分解”的“分而治之”的方法。*在创建和使用均衡模型方面的另一个技术挑战是，需要表示二元决策，例如启动或关闭发电机，或建造新的发电设施。与现在广为人知的决定发电机发电量或新设施规模的数学表示相比，二元决策的纳入使均衡模型变得极其复杂。本研究旨在改善二元决策变量均衡模型的研究现状。

In the operation of a competitive market for electricity, complex computer-based models determine which generators will supply electricity each hour, and the prices that will be paid for electricity generation. These models combine economic ideas, and realistic descriptions of generation and transmission technology, with modern mathematical knowledge about optimization, i.e., getting the greatest benefit from limited resources. Related optimization models are also used to explore the implications of policies on energy and the environment.****This research aims to improve the state of the art in building these models, in the corresponding operation of electricity markets, and in the use of such models for analysis of energy-environment policies.****Many of the models to be studied go beyond optimization from the point of view of one agent, such as a company, and consider instead the "equilibrium" of several interacting agents who each try to optimize. Part of the research effort will also be devoted to improving the speed of the computations, so that solutions are available quickly enough to be used in the operation of electricity markets. The speedup strategy is a "divide and conquer" approach called "decomposition." ****Another technical challenge in creation and use of equilibrium models is due to the need to represent binary decisions such as turning a generator on or off, or building a new generation facility or not. Compared with the mathematical representation of deciding on the amount of power from a generator, or the size of a new facility, which is well known now, the inclusion of binary decisions tremendously complicates the equilibrium models. The research aims to improve the state of the art in equilibrium models with binary decision variables.********