The day-ahead trading of electricity necessitates that cross-border capacities limit inter-zonal exchanges. To construct trading domains, two-day-ahead congestion forecasts for the electricity grid are needed. These comprise nodal predictions for load as well as renewable and conventional power generation, from which line flows can be derived. Trading domains limit deviations from the predicted line flows to respect physical grid constraints, requiring an accurate prediction of unit-specific power outputs. This analysis explores various statistical and statistical learning methods, with the goal of adequately predicting the on/off status and power output levels of all power plants within a control zone. The methods are tested for 205 conventional generating units in Germany using forecast values of fundamental variables, namely, load, renewable energy generation and the unavailabilities of power plants. For most units, the extra trees classifier achieves classification accuracy values of over 90% and a second-step extra trees regressor results in average errors of below 10% in relation to the installed capacities. Flexible units, especially hard coal, gas and pumped-storage hydropower plants, exhibit the largest errors. An analysis of errors suggests that load and solar generation are the main drivers of prediction deviations.