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Microgrids (MGs) are a growing energy industry segment and represent a paradigm shift from remote central power plants to more localized distributed generation. Controlling MGs represents a challenge mainly due to their complexity and the different properties each asset in the MG has. Various methods have been proposed to address this challenging problem of MG control. Some of these methods are considered the optimal operation of MG assets. Other works are based on a systems approach and address the scalability and simplicity of synthesizing a MG&#x2019;s energy management system (EMS). <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-variables based logical control strategies, which are practical methods to model control strategies in MGs, can make the control structure more scalable. However, this method is not optimal. On the other hand, Switched Model Predictive Control (S-MPC) is an advanced method utilized to control power systems while satisfying several constraints to achieve an optimal solution based on various criteria. Nevertheless, its implementation is not straightforward. Therefore, to overcome these existing problems, this paper proposes a novel systems approach method called an extended optimal <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-variable method developed by combining the <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-variable based control method with the S-MPC method. This unique method has demonstrated a significant improvement in optimizing an MG&#x2019;s energy management and enhanced the adaptation and scalability of a control structure of the MG. Our results show that the proposed extended optimal <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-variable method: (i) reduces the operational cost of MG by nearly 35&#x0025;; (ii) reduces the usage of the battery energy storage system by 42&#x0025;, and (iii) enhances the practicality of photovoltaic (PV) usage by 28&#x0025;. Our novel extended optimal <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-variable technique also increases the adaptation and scalability of the control structure of the MG significantly by translating the results of S-MPC to the <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-variable method.

Energy Management of Grid-Connected Microgrids Using an Optimal Systems Approach