Frequency dynamics in power systems reflect active power imbalance in real time, thereby providing an instantaneous signal to inform electricity pricing. However, existing real-time markets operate on much slower timescales and fail to exploit this signal. In this letter, we develop integrated market--frequency dynamics that enable online pricing directly from frequency measurements. Representing the real-time market as a dynamic price-discovery process, and integrating this process with the grid frequency dynamics, we derive an explicit price formation mechanism from frequency measurements. This mechanism manifests as a distributed PID-like controller for each generator, where frequency response is driven and remunerated by electricity prices derived solely from local frequency measurements.

翻译：电力系统中的频率动态实时反映了有功功率的不平衡，从而为电价制定提供了瞬时信号。然而，现有实时市场的运行时间尺度远慢于此，未能充分利用这一信号。本文开发了集成市场–频率动态模型，实现了直接基于频率测量的在线电价制定。将实时市场表示为动态价格发现过程，并将该过程与电网频率动态相结合，我们推导出基于频率测量的显式价格形成机制。该机制表现为每个发电机的分布式类PID控制器，其中频率响应由仅基于本地频率测量得出的电价驱动并给予报酬。