Principled Data Completion of Network Constraints for Day Ahead Auctions in Power Markets

TL;DR

This paper introduces a mathematical optimization method to reconstruct network constraints in European power markets from sparse data, improving the accuracy of key parameters like PTDFs and RAMs for better market analysis.

Contribution

It presents a novel approach to reconstruct power grid constraints and signals using convex optimization, outperforming naive methods and capturing underlying structures.

Findings

Achieves low in-sample and out-of-sample errors in reconstructing PTDFs and RAMs.

Outperforms naive reconstruction approaches.

Recovers meaningful structure in GSKs and PAs.

Abstract

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.