In smart power grids it is possible to match supply and demand by applying control mechanisms that are based on fine- grained load prediction. A crucial component of every control mechanism is monitoring, that is, executing queries over the network of smart meters. However, smart meters can learn so much about our lives that if we are to use such methods, it becomes imperative to protect privacy. Recent proposals recommend restricting the provider to differentially private queries, however the practicality of such approaches has not been settled. Here, we tackle an important problem with such approaches: Even if queries at different points in time over statistically independent data are implemented in a differentially private way, the parameters of the distribution of the query might still reveal sensitive personal information. Protecting these parameters is hard if we allow for continuous monitoring, a natural requirement in the smart grid. We propose novel differentially private mechanisms that solve this problem for sum queries. We evaluate our methods and assumptions using a theoretical analysis as well as publicly available measurement data and show that the extra noise needed to protect distribution parameters is small.