Machine learning (ML) applications to time series energy utilization forecasting problems are a challenging assignment due to a variety of factors. Chief among these is the non-homogeneity of the energy utilization datasets and the geographical dispersion of energy consumers. Furthermore, these ML models require vast amounts of training data and communications overhead in order to develop an effective model. In this paper, we propose a communication-efficient time series forecasting model combining the most recent advancements in transformer architectures implemented across a geographically dispersed series of EV charging stations and an efficient variant of federated learning (FL) to enable distributed training. The time series prediction performance and communication overhead cost of our FL are compared against their counterpart models and shown to have parity in performance while consuming significantly lower data rates during training. Additionally, the comparison is made across EV charging as well as other time series datasets to demonstrate the flexibility of our proposed model in generalized time series prediction beyond energy demand. The source code for this work is available at https://github.com/XuJiacong/LoGTST_PSGF