The volatility and uncertainty associated with the high proportion of wind and PV output in the new power system significantly impact power and energy balance, making it challenging to accurately assess the risks related to renewable energy abandonment and supply guarante. Therefore, a probabilistic power and energy balance risk analysis method based on distributed robust optimization is proposed. Firstly, the affine factor and the flexible ramp reserve capacity of thermal power are combined to establish a probabilistic index, which serves to characterize the risk associated with power and energy balance. Drawing upon the principles of conditional value at risk theory, the risk indexes of load shedding power and curtailment power under a certain confidence probability are proposed. Secondly, the probability distribution fuzzy sets of uncertain variables are constructed using the distributionally robust method to measure the Wasserstein distance between different probability distributions. Finally, aiming at minimizing the operation cost of thermal power, the risk cost of power abandonment and the risk cost of load shedding, a distributed robust optimal scheduling model based on flexible ramp reserve of thermal power is established.

As an emerging network paradigm, Space-Air-Ground integrated networks (SAGIN) has attracted the attentions from academia and industry. That is because SAGIN can implement seamless global coverage and connections among electronic devices in space, air, and ground spaces. Additionally, the shortages of computing and storage resources in mobile devices greatly affect the quality of experiences for intelligent applications. Hence, we devise to integrate SAGIN as an abundant resource pool into mobile edge computing environments (MEC). To facilitate efficient processing, we need to solve the optimal task offloading decisions. Different from the existing MEC task offloading solutions, we have to face some new challenges, such as the fluctuation of processing capability for an edge computing node, the uncertainty of the transmission latency caused by the heterogeneous network protocols, the uncertain amount of uploaded tasks during a period, and so on. In this paper, we firstly describe a task offloading decision problem in new challenge environments. But, we cannot use the standard robust optimization and stochastic optimization methods to obtain the optimal result under the uncertain network environments. In this paper, we propose the condition value at risk-aware distributionally robust optimization algorithm, named as CVAR-DRO, to solve the task offloading decision problem. The proposed CVAR-DRO method combines the distributionally robust optimization and the condition value at risk model for solving the optimal result. And then, We have evaluated our approach in simulation SAGIN environments with the confidence interval, the number of mobile task-offloading and the various parameters. We compare our proposed CVAR-DRO algorithm with the state-of-the-art algorithms, such as the standard robust optimization algorithm, the stochastic optimization algorithm, the DRO algorithm, and the brute algorithm. The experimental results show that CVAR-DRO can get a sub-optimal mobile task-offloading decision. Overall, CVAR-DRO is more robust than others to the new challenges mentioned above in SAGIN.

Smart Transformer (ST)-based Meshed Hybrid AC/DC Microgrids (MHM) are a feasible alternative to increase the performance of conventional microgrids (MG) and to increase the penetration of Distributed Energy Resource (DER) at the same time, active and reactive power dispatch on the system. Despite this, MHMs present challenges in managing resources under uncertainties and controlling electronic converters associated with the ST and DER, making it complex to achieve optimal system performance. In this paper, a Data-Driven Distributionally Robust Optimization (DDDRO) for Day-Ahead Operation Planning of an ST-based MHM considering the reactive power dispatch of the DER that minimizes network losses, voltage deviations, and operation cost simultaneously, considering uncertainties of Photovoltaic Generators (PVG) and demand, is proposed. The Column and Constraint Generation (C&CG) algorithm and Duality-Free Decomposition (DFD) method are adopted. Besides, the original mixed-integer non-linear planning problem is converted into a Mixed-Integer (MI) Second-Order Cone Programming (SOCP) problem through second-order cone relaxation and positive octagonal constraint method. Simulation experiments and results with a connected MHM system demonstrate the effectiveness and performance of the proposed model. Finally, we observe the effect of the meshed structure of MG and the positive impact of integrating the ST to form MHM, taking advantage of the degrees of freedom of this multi-stage converter for optimal energy management under uncertain conditions.