The increased penetration of electric vehicles (EVs) and distributed generator (DG) units has led to uncertainty in distribution systems. These uncertainties—which have not been adequately considered in the literature—can entail risks in the optimal sizing of EV charging stations (EVCSs) and DG units in active distribution network planning. This paper proposes a method for obtaining the optimal sizing of DG units and EVCSs (considering uncertainty), to achieve exact power system analysis and ensure EV driver satisfaction. To model uncertainties in optimal sizing planning, this study first generates scenarios for each system asset using a probability distribution that considers the asset characteristics. In this step, the wind-turbine (WT), PV, and EVCS are modeled applying the Weibull, exponential, and kernel density estimation (KDE), and scenarios for each asset are generated using random sampling. Then, the k-means clustering is carried out for scenario reduction and the representative scenario The probability of occurrence for each representative scenario is assigned depending on the number of observations within each cluster. The representative scenarios for each asset are integrated into the scenario for all assets through the joint probability. The integrated scenarios are applied in the optimization problem for optimal sizing of the system asset framework. The optimal sizing of the system assets problem is proposed (to minimize the line loss and voltage deviation) and formulated via stochastic second-order conic programming, to reflect the uncertainty under an AC power flow; this is a convex problem that can be solved in polynomial time. The proposed method is tested on a modified IEEE 15 bus system, and the simulation is performed with various objective functions. The simulation results demonstrate the effectiveness of the proposed method.

The rapid integration of renewable energy sources and the increasing complexity of modern power systems urge the development of advanced methods for ensuring power system stability. This paper presents a novel continuation power flow (CPF) method that combines two well-known parameterization techniques: natural parameterization and arc-length parameterization. The proposed hybrid approach significantly improves computational efficiency, reducing processing time by 32.76% compared to conventional methods while maintaining high accuracy. The method enables faster and more reliable stability assessments by efficiently managing the complexities and uncertainties, particularly in grids with high penetration of renewable energy.

When power system equipment fails due to disasters, resulting in the isolation of parts of the network, the loads within the isolated system cannot be guaranteed a continuous power supply. However, for critical loads—such as hospitals or data centers—continuous power supply is of utmost importance. While distributed energy resources (DERs) within the network can supply power to some loads, outages may lead to compensation and fairness issues regarding the unsupplied loads. In response, this study proposes a methodology to determine the appropriate power contract price for key customers by estimating the unsupplied power demand for critical loads in isolated networks and incorporating both outage compensation costs and voltage stability penalties. The microgrid under consideration comprises DERs—including electric vehicles (EVs), fuel cell electric vehicles (FCEVs), photovoltaic (PV) plants, and wind turbine (WT) plants—as well as controllable resources such as battery energy storage systems (BESS) and hydrogen energy storage systems (HESS). It serves both residential load clusters and critical loads associated with social infrastructure. The proposed methodology is structured in two stages. In normal operating conditions, optimal scheduling is simulated using second-order conic programming (SOCP). In the event of a fault, mixed-integer SOCP (MISOCP) is employed to determine the optimal load shedding strategy. A case study is conducted using the IEEE 123 bus test node system to simulate the outage compensation cost calculation and voltage penalty assessment processes. Based on this analysis, a contract price for key customers that considers both disaster-induced outages and voltage impacts is presented.

Stable operating conditions in electrolyzers are crucial for preserving system durability, ensuring highly pure hydrogen production, and enabling the sustainable utilization of surplus renewable electricity. However, in active distribution networks, the output uncertainty of distributed energy resources, such as renewable energy sources (RES) on the generation side and load demand side, can lead to voltage fluctuations that threaten the operational stability of electrolyzers and limit their contribution to a low-carbon energy transition. This paper proposes a novel framework for optimal electrolyzer placement, tailored to their operational requirements and to the planning of sustainable renewable-integrated distribution systems. First, probabilistic scenario generation is carried out for RES and load to capture the characteristics of their inherent uncertainties. Second, based on these scenarios, continuous power-flow-based P–V (power–voltage) curve analysis is conducted to evaluate voltage stability and identify the loadability and load margin for each bus. Finally, the optimal siting of electrolyzers is determined by analyzing the load margins obtained from the voltage stability assessment and deriving a probabilistic electrolyzer hosting capacity. A case study under various uncertainty scenarios examines how applying this method influences the ability to maintain acceptable voltage levels at each bus in the grid. The results indicate that the method can significantly improve the likelihood of stable electrolyzer operation, support the reliable integration of green hydrogen production into distribution networks, and contribute to the sustainable planning of other voltage-sensitive equipment.