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Power consumption data is very useful as it allows to optimize power grids, detect anomalies and prevent failures, on top of being useful for diverse research purposes. However, the use of power consumption data raises significant privacy concerns, as this data usually belongs to clients of a power company. As a solution, we propose a method to generate synthetic power consumption samples that faithfully imitate the originals, but are detached from the clients and their identities. Our method is based on Generative Adversarial Networks (GANs). Our contribution is twofold. First, we focus on the quality of the generated data, which is not a trivial task as no standard evaluation methods are available. Then, we study the privacy guarantees provided to members of the training set of our neural network. As a minimum requirement for privacy, we demand our neural network to be robust to membership inference attacks, as these provide a gateway for further attacks in addition to presenting a privacy threat on their own. We find that there is a compromise to be made between the privacy and the performance provided by the algorithm.