Caixia Tan

This study develops a tri-level adversarial robust optimization framework for cyber–physical scheduling in smart grids, addressing the intertwined challenges of coordinated cyberattacks, defensive resource allocation, and stochastic operational uncertainties. The upper level represents the attacker’s objective to maximize system disruption and conceal detection, the middle level models the defender’s optimization of detection and redundancy deployment under budgetary constraints, and the lower level performs economic dispatch given tampered data and uncertain renewable generation. The model integrates Distributionally Robust Optimization (DRO) based on a Wasserstein ambiguity set to safeguard against worst-case probability distributions, ensuring operational stability even under unobserved adversarial scenarios. A hierarchical reformulation using Karush–Kuhn–Tucker (KKT) conditions and Mixed-Integer Second-Order Cone Programming (MISOCP) transformation converts the nonconvex tri-level problem into a tractable bilevel surrogate solvable through alternating direction optimization. Numerical case studies on multi-node systems demonstrate that the proposed method reduces system loss by up to 36% compared to conventional stochastic scheduling, while maintaining 92% dispatch efficiency under high-severity attack scenarios. The results further reveal that adaptive defense allocation accelerates robustness convergence by over 50%, and that the risk–reward frontier stabilizes near a Pareto-optimal equilibrium between cost and resilience. This work provides a unified theoretical and computational foundation for adversarially resilient smart grid operation, bridging cyber-defense strategy, uncertainty quantification, and real-time economic scheduling into one coherent optimization paradigm.

The impact of decarbonization on regional coal-fired power generation is investigated using a weighted control method with panel data for China from 2001 to 2020. Five provinces, Guangdong Province, Liaoning Province, Hubei Province, Shaanxi Province and Yunnan Province, were used as the experimental group, and the remaining provinces were used as the control group. The robustness of the experimental results was verified by multidimensional tests such as dynamic test, counterfactual test, change window period test and ranking test. The empirical test results show that the low-carbon policy has a restraining effect on the carbon emissions, coal consumption and coal-fired power generation caused by regional coal-fired power generation. At the same time, Hansen test results show that low-carbon policy has no significant impact on regional coal-fired power generation through technology effect, but it has significant impact on regional coal-fired power generation through structure effect and regulation effect.

To push forward the development of electric vehicles while improving the economy and environment of virtual power plants (VPPs), research on the optimization of VPP capacity considering electric vehicles is carried out. In this paper, based on this, this paper first analyzes the framework of the VPP with electric vehicles and models each unit of the VPP. Secondly, the typical scenarios of wind power, photovoltaic, electric vehicle charging and discharging, and load are formed by the Monte Carlo method to reduce the output deviation of each unit. Then, taking the maximization of the net income and clean energy consumption of the VPP as the objective function, the capacity optimal allocation model of the VPP considering multiobjective is constructed, and the conditional value-at-risk (CVaR) is introduced to represent the investment uncertainty faced by the VPP. Finally, a VPP in a certain area of Shanxi Province is used to analyze a calculation example and solve it with CPLEX. The results of the calculation example show that, on the one hand, reasonable selection of the optimal scale of EV connected to the VPP is able to improve the economy and environment of the VPP. On the other hand, the introduction of CVaR is available for the improvement of the scientific nature of VPP capacity allocation decisions.