Reliable time series of installed wind power capacity are critical for reproducing past production and for normalizing historical data when training forecasting models. Databases of wind power installations can be used to create time series of installed capacity, but are incomplete or lack fine-grained temporal resolution for many countries or regions. Any inaccuracies in magnitude or timing of installed capacity propagate into downstream analyses.

We demonstrate that the Combined Power curve and Quadratic optimization (CPQ) method effectively reconstructs historical capacity time series. It is also shown that CPQ-derived capacity time series can be used to normalize the training data for a forecasting model to improve forecast accuracy. Requiring only aggregated production and publicly available wind data, the CPQ method can fill information gaps in regions with poor data coverage or during crises when energy systems evolve faster than databases can be updated.

The CPQ method iteratively (i) fits a generic power‑curve model to derive a capacity factor time series, and (ii) solves a constrained quadratic program that identifies the capacity time series most consistent with observed production. The updated capacity series can be re‑inserted into the power‑curve model until convergence. The inputs to the model are aggregated measured production for the region and wind speeds, here taken from the ERA5 dataset. Optionally, a database of wind power installations can be used for initialization.

To evaluate the accuracy of the CPQ method, it is here applied to the Danish onshore wind energy system. Monthly installed capacity per municipality from Energinet (the Danish Transmission System Operator) served as ground truth. The period from 2017 through 2024 has been studied, during which the capacity of onshore wind power increased from around 4 to 5 GW. The installed capacity time series based on the Master data registry of wind power plants from Energistyrelsen and the Cumulative Maximum method (a persistence-based approach where capacity is assumed constant until a new production maximum is observed) were included as references. The CPQ method reduced both the Mean Absolute Error and the Root Mean Squared Error fell by >50% relative to using the capacity time series from the database and by >10% relative to using the CM method.

A second evaluation was designed to assess the capacity time series without having a known target. A day-ahead forecasting model based on gradient-boosted regression trees was trained on meteorological reanalysis data and historical production data that had been normalized using different sources of capacity time series. In this evaluation, the capacity time series from the CPQ model resulted in smaller forecast errors than both the CM-method, the database from Energistyrelsen and, interestingly, even the capacities from Energinet.