# Stochastic Predictive Energy Management of Multi-Microgrid Systems
## 1 Introduction
In [22], a hierarchical MPC methodology is proposed for energy management of MG clusters while taking into account different sources of uncertainties. In [23], an EMS based on chance-constrained MPC is proposed in which the cooperation of different MGs is modeled using a joint probabilistic constraint. In [24], the energy exchange of MMG systems with the main grid is studied from the perspective of the DSO. Reducing the demand-side peak-to-average ratio (PAR) and maximizing the profit from selling energy to the MMGs is the main goal of the DSO. Authors in [25] present a decentralized-distributed adaptive robust optimization method to address the distributed scheduling of AC/DC hybrid MMG systems considering accidental communication failures. An approximate reinforcement learning (RL) methodology is used in [26] for bi-level power management of networked MGs considering the limited knowledge of MGs behavior. The RL-based learning method is used to discover the relationship between the retail price and the exchanged power of MGs. Recent review studies on energy management and control of MMG networks can be found in [10; 27; 28]. According to the current literature, the majority of the studies in this area concern development of the high-level controllers. The common assumption is the existence of efficient local controllers that are capable of appropriately following the scheduled set points. In other words, no analysis is conducted to indicate the applicability of the developed controllers to be incorporated in the full control hierarchy, which can guarantee power system technical requirements. Moreover, there are only a few experimental results in the context of multiple IMGs [29; 30]. Besides, the potential of the two-stage stochastic MPC in operation management of MMG systems has not been considered. Finally, considering the significant role of the MMG system in the next-generation power systems,designing systematic and fair cost allocation methodologies to motivate MGs participation in the cooperative energy management strategies is of vital importance. In this regard, a hierarchical EMS is developed to tackle complexities in the integrated operation management of interconnected RE-based MGs in this paper. MGs in a neighborhood area desire to keep the power exchange level of the MMG system with the main grid around a reference trajectory. Considering the hierarchical structure of MGs control [31], the proposed methodology includes three control levels. The central energy management system (CEMS) at the system-level, is responsible for coordinating the operation of MGs and determining day-ahead optimal trajectory for power transactions with the main grid considering system technical requirements. During the operation day, in a 60-min scheduling cycle, local EMSs (LEMSs) at the MG-level are responsible for managing the charging/discharging process of storage devices based on the power references received from CEMS. Two-stage stochastic programming with recourse variables is adopted to mitigate the uncertainty of non-controllable generators production including wind turbine (WT) and PVs as well as the variability of loads. Finally, local controllers (LCs) are designed to follow the provided set points through LEMS of each MG. To distribute any penalty cost resulted from real-time power deviation systematically and fairly, a new method based on the line flow sensitivity factors is proposed in which penalty cost is allocated by following the MGs contribution in the power deviation. The effectiveness of the proposed approach is verified by hardware-in-the-loop (HIL) simulation study. The main contributions of this paper can be summarized as follows:  
1. Modeling integrated energy management of an MMG system in a hierarchical framework;
2. Proposing an efficient control strategy using MPC and two-stage stochastic programming with recourse;
3. Developing a novel methodology for cost allocation among MGs using the line flow sensitivity factors. The rest of this paper is organized as follows.