  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.
