With the share of renewable energy sources in the energy system increasing,accurate wind power forecasts are required to ensure a balanced supply anddemand. Wind power is, however, highly dependent on the chaotic weathersystem and other stochastic features. Therefore, probabilistic wind powerforecasts are essential to capture uncertainty in the model parameters and inputfeatures. The weather and wind power forecasts are generally post-processedto eliminate some of the systematic biases in the model and calibrate it topast observations. While this is successfully done for wind power forecasts,the approaches used often ignore the inherent correlations among the weathervariables. The present paper, therefore, extends the previous post-processingstrategies by including Ensemble Copula Coupling (ECC) to restore the de-pendency structures between variables and investigates, whether including thedependency structures changes the optimal post-processing strategy. We findthat the optimal post-processing strategy does not change when including ECCand ECC does not improve the forecast accuracy when the dependency struc-tures are weak. ... mehrWe, therefore, suggest investigating the dependency structuresbefore choosing a post-processing strategy.