[论文解读] On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators

Christian Moya, Guang Lin+2 more|arXiv (Cornell University)|Jan 29, 2023

Model Reduction and Neural Networks被引用 6

一句话总结

本论文提出了一种基于深度算子网络（DeepONet）的框架，用于近似电力系统中同步发电机的动态响应，通过算子学习实现快速、精确的仿真。该方法实现了高保真度的暂态响应预测并提供误差估计，同时通过基于DAgger的微调策略实现交互式仿真，在真实世界两区域系统基准测试中表现出色。

ABSTRACT

This paper designs an Operator Learning framework to approximate the dynamic response of synchronous generators. One can use such a framework to (i) design a neural-based generator model that can interact with a numerical simulator of the rest of the power grid or (ii) shadow the generator's transient response. To this end, we design a data-driven Deep Operator Network~(DeepONet) that approximates the generators' infinite-dimensional solution operator. Then, we develop a DeepONet-based numerical scheme to simulate a given generator's dynamic response over a short/medium-term horizon. The proposed numerical scheme recursively employs the trained DeepONet to simulate the response for a given multi-dimensional input, which describes the interaction between the generator and the rest of the system. Furthermore, we develop a residual DeepONet numerical scheme that incorporates information from mathematical models of synchronous generators. We accompany this residual DeepONet scheme with an estimate for the prediction's cumulative error. We also design a data aggregation (DAgger) strategy that allows (i) employing supervised learning to train the proposed DeepONets and (ii) fine-tuning the DeepONet using aggregated training data that the DeepONet is likely to encounter during interactive simulations with other grid components. Finally, as a proof of concept, we demonstrate that the proposed DeepONet frameworks can effectively approximate the transient model of a synchronous generator.

研究动机与目标

• 开发一种数据驱动框架，用于近似同步发电机的无限维解算子，以实现快速的电力系统仿真。
• 实现所学习的发电机模型与电力系统其余部分数值仿真器的无缝集成，避免引入延迟误差。
• 相比传统的DAE-based时域仿真，降低计算成本，同时保持精度。
• 通过残差DeepONet架构，将数学模型中的物理知识融入神经网络。
• 设计基于DAgger的训练策略，提升在与其他电网元件交互仿真中的泛化能力。

提出的方法

• 设计DeepONet以学习发电机的解算子，将输入轨迹（如电流、励磁）映射为状态轨迹（如功角、频率）。
• 开发基于训练后DeepONet的递归数值格式，用于在短至中等时间范围内仿真动态响应。
• 提出残差DeepONet，结合数据驱动学习与发电机微分代数方程的物理信息约束。
• 推导残差DeepONet格式的累积误差界，以量化预测的可靠性。
• 采用基于DAgger的数据聚合策略，从交互式仿真中收集并优化训练数据，提升对未见输入的鲁棒性。
• 通过插值方式在每个时间步内对输入在多个时间点进行离散化，提升输入表征的时间分辨率。

Figure 1 : A block diagram description of the differential-algebraic model ( 2 ) introduced in [ 41 ] . The model describes the Network equations ( 2c ), the stator ( i.e., generator interface) algebraic equations ( 2b ), and the SGs’ differential equations ( 2a ).

实验结果

研究问题

• RQ1 DeepONet能否在多种故障场景下准确近似同步发电机的动态响应？
• RQ2 将物理模型融入DeepONet架构对预测精度和泛化能力有何影响？
• RQ3 所提出的框架能否在长时间时间范围内实现稳定、递归仿真，而不会出现显著的误差累积？
• RQ4 基于DAgger的数据采集策略在多大程度上提升了模型在交互式电网仿真中的性能？
• RQ5 残差DeepONet的累积误差界是多少，与真实解相比如何？

主要发现

• 数据驱动的DeepONet与电力系统工具箱（PST）的真值结果高度一致，如四维状态轨迹δ(t)、ω(t)、E′d(t)和E′q(t)的对比所示。
• 残差DeepONet框架融合了物理约束，并提供可量化的累积误差估计，增强了在安全关键应用中的可靠性。
• 递归DeepONet方案在5秒时间范围内成功模拟了发电机动态，保持一致的精度，证明了其在中长期仿真中的可行性。
• 基于DAgger的训练策略有效提升了模型泛化能力，使DeepONet能够处理初始训练中未遇到的输入。
• 采用多传感器输入离散化（m=2）提升了输入表征质量，相比单点采样，显著提高了预测保真度。
• 该框架成功复现了连接无穷大母线的同步发电机的暂态响应，验证了其作为数字孪生组件的潜力。

Figure 2 : The DeepONet for learning the solution operator describing the dynamic response of an SG. The Branch Net takes as input a vector resulting from concatenating (i) the current state $\tilde{x}(t_{n})\in\mathbb{R}^{n_{x}}$ , (ii) the discretized interacting variables $\tilde{y}_{m}^{n}\in\ma