Network constraints play a key role in the price finding mechanism for European Power Markets, but historical data is very sparse and usually insufficient for many quantitative applications. We reconstruct the constraints data, known as the Power Transmission Distribution Factors (PTDFs) and Remaining Available Margins (RAMs), by first recovering the underlying time dependent signals known as the Generation Shift Keys (GSKs) and Phase Angles (PAs), and the electricity grid characteristics, via a mathematical optimisation problem. This is solved by exploiting marginal convexity in certain subspaces via alternating minimisation. The GSKs and PAs are then mapped to the PTDFs and RAMs, using the grid structure. Our reconstruction achieves good in-sample and out-of-sample relative errors for the PTDFs and RAMs. We further show that our model outperforms the naive approach, and that the reconstructed GSKs and PAs recover specific structure.

中文翻译：

---

电力市场日前拍卖网络约束的原理数据完成

网络约束在欧洲电力市场的价格发现机制中起着关键作用，但历史数据非常稀少，通常不足以用于许多定量应用。我们重建约束数据，称为电力传输分配因子 (PTDF) 和剩余可用裕度 (RAM)，首先恢复称为生成转换键 (GSK) 和相角 (PA) 的基础时间相关信号，以及电网特性，通过数学优化问题。这是通过交替最小化利用某些子空间中的边缘凸性来解决的。然后使用网格结构将 GSK 和 PA 映射到 PTDF 和 RAM。我们的重建为 PTDF 和 RAM 实现了良好的样本内和样本外相对误差。