Battery electric vehicles (BEV) are envisioned to play a significant role in the future of personal mobility. A key challenge in the transition from internal combustion engine (ICE) powered vehicles to BEV is the limited driving range of the latter, which makes an energy-efficient operation essential. In this work, we analyze how vehicle-to-x (V2X) communication, in particular traffic-light-to-vehicle communication (TLVC), can help the drivers of BEVs save energy and thus increase driving range. Furthermore, we analyze factors impacting energy consumption which are relevant to the design of V2X applications for BEV. Our results indicate that TLVC can significantly reduce the energy consumption of BEV, up to 20% in our setup. The actual result, however, is highly dependent on a combination of traffic situation, communication range, auxiliary consumer power demand, road gradient and minimum speed requirement.