Models are frequently used for decision support in modern-day decision making. This approach is referred to as model-based decision support and it is mostly at least implicitly used for predictive purposes. However, predictions are almost always wrong and can be dramatically misleading for policy making. Another shortcoming related to predictive model use is the lack of proper consideration of deep uncertainty. Deep uncertainty refers to the lack of knowledge or agreement related to the correct representation of a system and the evaluation of (model-based) outcomes. This paper proposes to embrace deep uncertainty by using models in an exploratory way in order to improve model-based decision support under deep uncertainty. For this purpose, a new research methodology for analyzing complex and deeply uncertain systems, Exploratory Modeling and Analysis, is combined with System Dynamics modeling to capture deep uncertainties and dynamic complexities related to energy transitions. In this paper, we illustrate this methodological approach by using three different versions of a world wind power model (to introduce structural uncertainties) and by introducing some parametric uncertainties. This case clearly illustrates the need to consider both structural and parametric uncertainties for technology management under deep uncertainty.