A microgrid (MG) represents an outstanding possibility to transform the power sector into a more reliable, efficient, and accessible set of services for economic growth and environmental protection. The use of renewable energy resources contributes to the greening of the environment and the reduction of power costs. This article shows that a MG can likewise benefit from cloud/fog computing when it comes to computing-intensive tasks. By employing an artificial neural network with a modified gray wolf optimizer, a fog-driven energy management problem can be solved by an economical method. An area of several smart homes is considered in this study. Every house has a microgrid for generating energy. Meanwhile, it connects to the fog server so that data can be shared and stored. A fog server allows smart power users to exchange information about surplus power. Simulations are conducted to validate the suggested method for reducing costs and reduction of electricity imports considering the digital twin of smart homes.