Distributed robust Lasso-MPC based on Nash optimization for smart grid: Guaranteed robustness and stability

The integration of variable renewable energy supplies into smart grid energy management poses several obstacles to system operation. An efficient solution for resource management is essential to ensuring reliable operation. This research presents distributed robust $L$asso-model predictive control ($\mathrm{D\; -\; RLMPC}$) as a way to handle energy problems in a multi-layer and multi-time frame optimization method. The $\mathrm{D\; -\; RLMPC}$ is a hierarchical system that integrates a centralized supervisory management ($\mathrm{SM}$) layer for long-term optimization with a distributed coordination management ($\mathrm{CM}$) layer for short-term adaptation to high power fluctuations. The higher layer, known as the $\mathrm{SM}$, is responsible for providing the grid operator with specific operating plans and offering guidance to the bottom layer, known as the $\mathrm{CM}$. The $\mathrm{CM}$ is responsible for coordinating the interaction between the centralized optimization goals and the physical power system layer. Furthermore, a distributed extended Kalman filter ($\mathrm{DEKF}$) is used to ascertain the inter-dependencies among subsystems. Next, an iterative approach based on $N$ash optimization is proposed to get the globally optimum solution of the whole system in a partly distributed manner. The simulation results demonstrate the effectiveness of the proposed control approach, which combines the advantages of centralized and distributed control to provide a comprehensive solution for the grid operating issue. To verify and assess the effectiveness of the suggested approach, the acquired outcomes are compared to those of the centralized robust, distributed robust, and distributed $\mathrm{MPC}$ approaches. The simulation findings confirm the practicality of using the suggested system to manage future smart grid assets.