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动态的，具有不确定的参数，例如，未来时段需求不确定的多时段发电与配电控制。该项目的重点是设计对能源需求不确定性具有鲁棒性的智能电网，并以分散的方式有效地控制这些电网，同时尊重每个电网节点的数据隐私要求。为了实现这些目标，首席研究员将开发分布式计算方法，利用现有的网格硬件，只能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，网格将作为利用计算资源的分散系统运行，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，这些目标的实现将更加经济。这项研究将有助于通过开发可扩展的计算工具进行优化，从而实现稳定网格的可靠，健壮和隐私操作。这项研究具有多学科性质：需要从优化理论，计算数学和电气工程的技术。PI将参与这项研究的本科生和研究生，来自工程和数学领域的代表性不足的群体。PI将研究配电系统上电容器组的最佳布置，通过将底层问题制定为（分布）鲁棒离线优化问题，使其对不确定负载分布的变化具有鲁棒性。接下来，给定电容器组的位置和短期需求预测引擎，PI将考虑从电容器组到电网的最佳无功功率注入，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调节发电和配电，并与动态不确定负载竞争。此外，考虑到需求预测中的误差，将制定一个分散的样本平均近似方案。 由于通信、存储器和计算开销，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，该研究有望为发展新的一阶原始-对偶方法以解决具有节点特定私有约束的计算节点网络上的一致性优化问题做出贡献。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.