The Smart Grid is the vision underlying the evolution the power grid is currently undergoing. Its pillars are increased efficiency, self-healing, operation automation, and renewable energy integration obtained through real-time control and digitalization of the infrastructure. Thus, an important ingredient-if not the main one-is information technology support for power transmission and distribution. Given the size of the power grid, its pervasiveness, and the need for its availability, it is easy to imagine that any serious ICT infrastructure dealing with it will have to manage a great deal of rapidly forming data. Now the question is whether the amount, diversity, and uses of such data put the smart grid in the category of Big Data applications, followed by the natural question of what is the value of such data. To provide an initial answer to this question, we analyze the current state of data generation of the Dutch grid, its evolution towards a smart grid, and a future realistic scenario. The scenario considered shows that the amount of data generated is comparable to some of today's social media and 'classic' Big Data examples.