In the context of the “Carbon peak, Carbon neutral” target, the introduction of carbon trading and the connection of new energy generation such as wind power and photovoltaics to the power grid have become important means to achieve a reduction to low carbon emissions. To this end, a virtual optimization model is established to take into account both low-carbon and economic aspects. Firstly, based on the basic concept of a virtual power plant, a virtual power plant model containing wind power, photovoltaic power, a gas turbine, and energy storage is established. Then, considering the uncertainty factors of wind power and PV power generation, Latin hypercube sampling (LHS) is used to simulate wind power and PV output scenarios, combined with the improved CLARA clustering algorithm to reduce the scenarios to form a classical scenario set to reduce the influence of wind power and PV output volatility. Finally, a carbon-trading mechanism and time-sharing tariff are introduced, and the model is solved with the objective function of maximizing the net benefit and minimizing the carbon emission of the Virtual Power Plant. Using arithmetic examples for verification, the results show that the introduction of carbon-trading mechanism can improve the net benefits of the Virtual Power Plant while promoting energy saving and emission reduction.

A combined approach of Latin hypercube sampling and K-means clustering is proposed in this study to address the uncertainty issue in wind and solar power output. Furthermore, the loads are categorized into three levels: primary load, secondary load, and tertiary load, each with distinct characteristics in terms of demand. Additionally, a load demand response characteristic model is developed by incorporating the dissatisfaction coefficient of electric and thermal loads, which is then integrated into the system’s operational costs. Moreover, an electricity–hydrogen–thermal power system is introduced, and a source-load coordination response mechanism is proposed based on the different levels of demand response characteristics. This mechanism enhances the interaction capability between the power sources and loads, thereby further improving the economic performance of the virtual power plant. Furthermore, the operation economy of the virtual power plant is enhanced by considering the participation of renewable energy sources in carbon capture devices and employing a tiered carbon-trading mechanism. Finally, the CPLEX algorithm is employed to solve the optimization model of the virtual power plant, thereby validating the effectiveness of the proposed models and algorithms.

To address the challenge of inaccurate fault location of variational mode decomposition (VMD) in practical engineering, due to poor choice of mode decomposition number K and quadratic penalty factor α, a traveling wave fault location method using Northern Goshawk optimization algorithm (NGO) to optimize VMD was proposed. First, the NGO algorithm is used to optimize VMD, and the optimal K and α are obtained. Secondly, the optimal parameters are inputted into VMD for fault signal decomposition, and the eigenmode components are obtained. Due to the difficulty of identification of the traveling wave head in the process of traveling wave propagation, Hilbert transform is used to determine the time of initial arrival of the traveling wave head at both ends of the line, and the fault location is precisely calculated by using the two-ended traveling wave fault detection formula. Finally, simulation experiments are carried out to verify the accuracy of the proposed location method, which shows that the proposed location method can locate the fault more accurately and has good engineering application value.

Aiming to address the defects of the arithmetic optimization algorithm (AOA), such as easy fall into local optimums and slow convergence speed during the search process, an improved arithmetic optimization algorithm (IAOA) is proposed and applied to the study of distribution network reconfiguration. Firstly, a reconfiguration model is established to reduce network loss, and a cosine control factor is introduced to reconfigure the math optimization accelerated (MOA) function to coordinate the algorithm’s global exploration and local exploitation capabilities. Subsequently, a reverse differential evolution strategy is introduced to improve the overall diversity of the population and Weibull mutation is performed on the better-adapted individuals generated in each iteration to ensure the quality of the optimal individuals generated in each iteration and strengthen the algorithm’s ability to approach the optimal solution. The performance of the improved algorithm is also tested using eight basis functions. Finally, simulation analysis is carried out by taking the IEEE33 and IEEE69 node systems and a real power distribution system as examples; the results show that the proposed algorithm can help to reconfigure the system quickly, and the system node voltages and network losses were significantly improved after the reconfiguration.

A new fault location method based on the three-terminal travelling wave method is proposed for the fault location problem of multi-branch overhead line–cable transmission lines. Firstly, the process of fault travelling wave propagation in overhead transmission lines and the phenomenon of refraction are analysed, and an improved phase-mode transformation is introduced to decouple the electromagnetic coupling and perform fault phase selection. Secondly, the Pearson correlation coefficient is introduced to compare the similarity of the current travelling waveforms at different measurement points in order to implement fault segmentation. To solve the problems of the complexity of the fault travelling wave propagation process and the difficulty of identifying the travelling wavehead, the Hilbert–Huang transform is used to extract the fault signal characteristics, and the travelling wave arrival moment is accurately calculated by the sampling error correction method to determine the fault location. Finally, the accuracy and stability of the method are verified via a simulation test on the MATLAB/Simulink platform. The results show that the proposed positioning method combining the three-terminal travelling wave method with HHT and sampling error correction can locate the fault location more accurately, and it has good potential for application in the engineering field. It provides a new technical means for fault location in overhead transmission lines, which is expected to become one of the most important technologies in the future power system.

An improved fault localization method combining total aggregate empirical modal decomposition (MEEMD) and Teager energy operator (TEO) is proposed to address the fault localization issue of three-terminal multi-segment overhead line–cable hybrid transmission lines. This method solves the fault localization problem caused by wave impedance discontinuity in hybrid lines. First, the MEEMD algorithm, which improves modal aliasing, and the Teager energy operator, which reflects transient energy changes, are combined for the accurate detection of faulty traveling wave heads. The fault line section determination condition within the fault branch is used to determine the overhead line section or cable section where the fault is located after determining the faulty branch line. This condition is based on the time difference between the initial traveling wave of the fault arriving at each end measurement point and the T-node. Ultimately, the fault distance is determined using the double-ended traveling wave technique. By combining PSCAD and MATLAB for simulation verification, the accuracy of the ranging method is compared and analyzed, and the results show that the method is able to ensure the accuracy of ranging at different fault locations and transition resistances. Additionally, the localization error is basically kept within 30 m, which significantly improves the accuracy of fault localization.