This work presents a wireless communication network (WCN) infrastructure for the smart grid based on the technology of Worldwide Interoperability for Microwave Access (WiMAX) to address the main real-time applications of the smart grid such as Wide Area Monitoring and Control (WAMC), video surveillance, and distributed energy resources (DER) to provide low cost, flexibility, and expansion. Such wireless networks suffer from two significant impairments. On one hand, the data of real- time applications should deliver to the control center under robust conditions in terms of reliability and latency where the packet loss is increased with the increment of the number of industrial clients and transmission frequency rate under the limited capacity of WiMAX base station (BS). This research suggests wireless edge computing using WiMAX servers to address reliability and availability. On the other hand, BSs and servers consume affected energy from the power grid. Therefore, the suggested WCN is enhanced by green self-powered based on solar energy to compensate for the expected consumption of energy. The model of the system is built using an analytical approach and OPNET modeler. The results indicated that the suggested WCN based on green WiMAX BS and green edge computing can handle the latency and data reliability of the smart grid applications successfully and with a self-powered supply. For instance, WCN offered latency below 20 msec and received data reliability up to 99.99% in the case of the heaviest application in terms of data.