The Smart Grid approach enhances the power grid with information technology. Smart Meters are an important part of the Smart Grid. They record the energy consumption of households with a high-resolution and transfer consumption records to the energy provider in real time. Since they allow to infer personal information like the daily routine of the household members, Smart Meters are also a promising source for lifelogging. However, in liberalized energy markets, many different parties have access to these data. This puts the privacy of consumers at risk. In this paper, we analyze to which degree Smart Meter data, as collected by our industry partner, can be linked to its producer, using simple statistical measures. We devise features of the energy consumption, for example, the first peak of demand in the morning, and we describe an analytical framework that quantifies how well these features can identify households. Finally, we conduct a study with 60,480 energy-consumption records from 180 households. Our study shows that 68 % of the records can be re-identified with simple means already. This insight is important for Smart Grids, as it emphasizes the need for research and use of anonymization techniques for the Smart Grid.