Decentralized Power Flow Optimization on Electricity Grids via Distributed Consensus Methods

许多与能源相关的问题本质上是具有不确定参数的动态问题，例如未来时段需求不确定的多时段发电和配电控制。该项目的重点是设计对能源需求不确定性具有健壮性的智能电网，并在尊重每个电网节点的数据隐私要求的同时，以分散的方式有效地控制这些电网。为了实现这些目标，首席研究员将开发分布式计算方法，这些方法利用现有的网格硬件，这些硬件只能进行简单的本地计算和与邻近设备的通信。在分布式方法的帮助下，电网将作为一个分散的系统运行，利用计算资源，例如智能电表和智能恒温器，以优化整个网络的功率流。与昂贵且缺乏可扩展性的传统中央计算基础设施相比，这些目标将更经济地实现。这项研究将通过开发可扩展的优化计算工具，为稳定电网的可靠、稳健和隐私运行做出贡献。这项研究具有多学科性质：需要最优化理论、计算数学和电气工程的技术。PI将从事这项研究的本科生和研究生来自代表不足的群体工程和数学。PI将研究电容器组在配电系统上的最优位置，以使其对不确定负荷分布的变化具有稳健性，通过将潜在问题描述为(分布上)稳健的离线优化问题。接下来，在给定电容器组的位置和短期需求预测引擎的情况下，PI将考虑电容器组向电网注入的最优无功功率，以最小化发电成本。这是一个大规模的动态问题，可以通过分布式优化算法来解决，这些算法将在尊重隐私的同时监管发电和配电，并与动态不确定负载竞争。此外，为了解决需求预测中的误差，将开发一种分散的样本平均近似方案。由于通信、内存和计算开销的原因，这些分布式优化方法实际上仅限于使用一阶信息。利用最优潮流问题的特殊结构，该研究有望为开发新的一阶原始-对偶方法做出贡献，以解决存在特定节点私有约束的计算节点网络上的共识优化问题。如果成功，该项目将导致创建新的数学模型、分析和算法，用于与能源生产和分配相关的决策。

Many energy-related problems are dynamic in nature with uncertain parameters, e.g., multi-period power generation and distribution control with uncertain demand in future periods. The focus of this project is on designing smart power grids that are robust to uncertainty in energy demand, and efficiently controlling these grids in a decentralized manner while respecting data privacy requirements of each grid node. To achieve these goals, the principal investigator will develop distributed computational methods that leverage existing grid hardware capable of only simple local computation and communication with neighboring devices. With the help of distributed methods, the grid will operate as a decentralized system exploiting computational resources, e.g., smart-meters and smart-thermostats, to optimize power flow throughout the network. These goals will be realized more economically as compared to traditional central computing infrastructure that is expensive and lacks scalability. The research will contribute to reliable, robust, and privacy-enabled operation of a stable grid through the development of scalable computational tools for optimization. This research has multi-disciplinary nature: requiring techniques from optimization theory, computational mathematics, and electrical engineering. The PI will engage in this research undergraduate and graduate students from underrepresented groups in engineering and mathematics.The PI will investigate the optimal placement of capacitor banks on the distribution system to make it robust to changes in the uncertain load-profile by formulating the underlying problem as a (distributionally) robust offline optimization problem. Next, given the locations of capacitor banks and a short-term demand forecast engine, the PI will consider the optimal reactive power injection from capacitor banks into the grid to minimize the generation cost. This is a large-scale dynamic problem, and can be addressed through distributed optimization algorithms that will regulate power generation and distribution while respecting privacy, and contending with dynamic uncertain load. Moreover, to account for errors in demand forecasts, a decentralized sample average approximation scheme will be developed. Due to communication, memory, and computational overhead, these distributed optimization methods are practically limited to use first-order information only. Exploiting the specific structure in optimal power flow problems, the research is expected to make contributions to the development of new first-order primal-dual methods to solve consensus optimization problems over a network of computing nodes when there are node-specific private constraints. If successful, this project will result in the creation of new mathematical models, analyses, and algorithms for decision-making related to energy production and distribution.