Search Results (122)

To address the increased operational risk in distribution network caused by the grid integration of distributed wind power, a distribution network risk assessment method that combines a Dirichlet process mixture model (DPMM) with the cumulant method (CM) is proposed, to achieve effective quantification of operational risk. Firstly, a DPMM is employed to cluster wind power output data, and adaptive kernel density estimation is introduced to construct a probabilistic model of wind power output, thereby improving local fitting accuracy. Secondly, uncertainties arising from wind generation and load are considered, and a probabilistic power flow model for the distribution network is established based on the CM and the Gram–Charlier series expansion, in order to obtain the probability distributions of state variables and branch power flows. Then, distribution entropy theory is introduced to quantify the severity of limit violations for state variables such as voltage and power, so that operational risk assessment is enabled. Finally, simulations are conducted on a modified IEEE 34-bus distribution test system, and the results demonstrate the effectiveness of the proposed method. Full article

The transition toward sustainable and low-carbon power systems increasingly depends on the efficient accommodation of high shares of renewable energy while maintaining secure and reliable grid operation. In interconnected power systems, this challenge is intensified by strong cross-regional coupling, tie-line flow violation risks, and the high computational burden of fully coupled probabilistic assessments. To support the sustainable operation of renewable-rich interconnected systems, this paper proposes a probabilistic production simulation method that incorporates risk-aware tie-line exchange optimization. Sequential random sample paths are constructed by considering load fluctuations, renewable energy output uncertainty, and random outages of conventional units. Using cross-regional exchange power as coupling variables, a conditional value-at-risk (CVaR)-based pre-scheduling model is established to control tie-line and interface flow tail risks. Given the scheduled exchange power, cross-regional exchanges are transformed into regional boundary power injections, enabling decoupled sequential probabilistic production simulation for each region. The exchange schedule is then iteratively updated through marginal-value feedback. A four-region interconnected system is used for case-study validation. Results show that the proposed method improves renewable energy accommodation, reduces renewable curtailment, suppresses tie-line flow violation risk, and maintains high reliability assessment accuracy. Compared with the region-decoupled benchmark with fixed exchange power, the proposed method increases the renewable energy accommodation rate from 93.82% to 95.41% and reduces renewable curtailment from 312,162 MWh to 231,284 MWh, while also lowering expected energy not served and loss of load expectation. In addition, under the reported case-study setting, the proposed RC-IEF-PPS reduces the computation time from 5216.24 s for Full-PPS to 4074.63 s, i.e., by 21.9%, while maintaining comparable reliability assessment accuracy. These results indicate that the proposed framework can support the sustainable integration of high-penetration renewable energy by improving clean-energy utilization, operational reliability, and computational tractability in interconnected power systems. Full article

This paper develops a probabilistic Available Transfer Capability (ATC) framework that quantifies export headroom for renewables across transmission-distribution interfaces under time-varying uncertainty. Static transmission reliability margins can unnecessarily curtail exports. A dynamic transmission reliability margin (TRM) is embedded within ATC using rolling window statistics and adaptive confidence factor scheduling to release capacity in calm periods and tighten margins during volatile transitions. Uncertainty is modeled as net nodal power imbalance variability from load and renewable deviations, together with stochastic thermal limit fluctuations. Correlated multivariate scenarios are generated via Latin Hypercube Sampling with Iman-Conover correlation preservation and propagated through full AC power flow analysis. Validation on the IEEE 39-bus system and New Zealand’s HVDC inter-island corridor recovers 93.31 MW of usable transfer capacity on the IEEE system relative to the pooled Monte Carlo P95 constant-margin baseline, with 78.11 MW attributable to rolling window volatility tracking and 15.20 MW to adaptive confidence factor scheduling, and 59.51 MW (+7.6%) on the New Zealand corridor relative to the corresponding pooled Monte Carlo P95 baseline, with the gain arising primarily from rolling window volatility tracking. Relative to a 95% one-sided reliability target, achieved coverage is 93.9% for IEEE and 91.8% for New Zealand, translating into increased export headroom and reduced curtailment. Full article

This study presents an integrated simulation framework that combines agent-based transport modeling with probabilistic load-flow analysis to quantify power system loading of long-haul heavy-duty electrification. The approach is applied to a case study considering fully electrified road freight in the Skåne region in Sweden, using high-resolution transport demand data and the actual power grid model used by the grid owner in the study area. The synthetic freight population covers the full long-haul truck segment intersecting Skåne. Both public en-route fast charging and end-of-trip depot charging are considered. The analysis reveals two fundamentally different charging demand profiles: a heavily fluctuating profile for public en-route charging, accounting on average for 82% of the total daily charging energy, and a stable profile for end-of-trip depot charging, covering on average the remaining 18%. The latter is achieved through a Linear Programming (LP) optimization model that flattens the load by scheduling charging across depot stay windows. These profiles serve as inputs to a probabilistic load-flow simulation that computes loading distributions for substation transformers. The simulation results show that in 4 of the 43 primary substations studied, the maximum transformer loading exceeds 100% following the introduction of truck charging, with peak loading at the most affected substation rising from 99% to 159%. This stress is primarily caused by the public charging demand, which peaks from late morning to noon, aligning with the early stages of logistics operations. However, there is no clear correlation between the magnitude of the truck charging load and the impact on transformer loading, since this is also highly dependent on local grid conditions. These findings highlight the value of integrated transport-energy simulations for planning resilient infrastructure and guiding targeted grid reinforcements. Full article

Unlike traditional power systems, the heterogeneous energy support of electric–gas regional distribution networks brings new challenges to resilience assessment. On the basis of identifying N-k fault uncertainty risks, establishing a resilience assessment methodology is one of the important issues in resilience research. Existing reliability assessment methods cannot accurately quantify resilience under N-k extreme fault scenarios. To address this limitation, we propose a non-simulation resilience assessment method. The approach can simultaneously quantify the dynamic interactions of heterogeneous energy flows and the impact of repair process time uncertainty on system resilience under extreme fault scenarios. Specifically, the resilience indexes are established by combining the load outage and mathematical expectation during/after the extreme fault and applying probabilistic knowledge to express the N-k load outage event, so as to effectively offset the data scarcity due to the limited N-k fault data samples. The internal consistency and parametric responsiveness of the proposed non-simulation method are demonstrated through systematic case comparisons under varying failure rates, repair times, and coupling conditions. Full article

The large-scale integration of wind turbine generators (WTGs) and photovoltaic (PV) generation increases operational uncertainty and can exacerbate stability limitations in weak transmission networks, motivating the use of green hydrogen energy storage systems (HESS). This paper presents a probabilistic planning framework for the joint siting and sizing of HESS to support hybrid WTG–PV integration under stochastic wind, solar irradiance, and load conditions. The proposed framework explicitly couples Monte Carlo-based probabilistic power flow with weak-grid security constraints by enforcing FVSI-based voltage-stability limits and an SSI-based system-strength requirement within the optimization loop, rather than treating these indices as post-analysis checks. The planning problem is formulated using a weighted-sum scalarization to minimize life-cycle carbon footprint and active power losses, subject to security constraints based on the Fast Voltage Stability Index (FVSI) and a system-strength constraint expressed through a System Strength Index (SSI). To solve the resulting constrained, nonlinear optimization problem, a sequential hybrid metaheuristic that couples Whale Optimization (exploration) with Osprey Optimization (exploitation) is developed. The framework is implemented in MATLAB using MATPOWER and evaluated on a modified IEEE 39-bus system. Simulation results report an annual carbon footprint of 22.16 Mt CO₂eq/yr, an improvement of 9.2% and 5.3% relative to PSO and GA/PSO baselines, respectively, while increasing the weakest-bus SSI to 4.68 (bus 7). The resulting HESS design comprises a 296.9 MW electrolyzer, a 262.7 MW fuel cell, and 28,012 kg of hydrogen storage. Full article

Voltage security assessment is increasingly challenged by stochastic demand growth and localized stress patterns that are not well represented by deterministic, single-snapshot analyses. This paper proposes a fully steady-state probabilistic stress-testing framework based on Monte Carlo simulation and Newton–Raphson AC power flow, jointly evaluating the minimum bus voltage magnitude $V_{min}$ (voltage-floor adequacy) and the scenario maximum Fast Voltage Stability Index $FVS{I}_{max}$ (worst-case line stress). Stress is injected selectively on screened weak buses by sampling a random stress footprint and intensity across three progressive levels (L1–L3), while preserving the local power factor. The approach is demonstrated on IEEE 14-, 30-, and 118-bus benchmark systems using $N=2000$ realizations per level, with 100% convergence across all cases. Across all systems, results show a consistent, monotone degradation of the voltage floor and a systematic increase in violation risk as stress intensifies. For the IEEE 14 system, the voltage-risk profile escalates rapidly, with $\mathbb{P}(V_{min}<0.90)$ rising from 0.16 (L1) to 0.54 (L3), while the worst-case FVSI tail strengthens markedly (p95 increasing from 0.1455 to 0.2081), indicating a growing likelihood of severe voltage-stress events. In contrast, the IEEE 30 and IEEE 118 systems exhibit milder shifts in central voltage levels but maintain substantial exposure relative to the 0.95 pu planning threshold, with $\mathbb{P}(V_{min}<0.95)$ reaching 0.79 and 0.74 at L3, respectively. Beyond risk magnitudes, the framework reveals a nontrivial structural phenomenon in worst-case line stress: as system size increases, stochastic stress outcomes become increasingly concentrated into a small number of dominant transmission corridors. Recurrence analysis at the highest stress level shows fragmented criticality in IEEE 14 (Top-3 lines sharing criticality), near-total dominance by a single corridor in IEEE 30 (>92% of cases), and complete dominance collapse in IEEE 118 (one corridor governing 100% of $FVS{I}_{max}$ events). These results demonstrate that probabilistic stress-testing can simultaneously quantify voltage-risk escalation and expose hidden structural bottlenecks that remain invisible under deterministic screening, providing a scalable diagnostic tool for planning-stage monitoring and reinforcement prioritization. Full article

Probabilistic streamflow models play a pivotal role in quantifying hydrological uncertainty and form the backbone of modern risk management strategies for flood and drought forecasting, water allocation planning, and the design of resilient infrastructure. Unlike deterministic approaches that yield single-point estimates, these models provide a spectrum of possible outcomes, enabling a more realistic assessment of extreme events and supporting informed, sustainable water resource decisions. By explicitly accounting for natural variability and uncertainty, probabilistic models promote transparent, robust, and equitable risk evaluations, helping decision-makers balance economic costs, societal benefits, and environmental protection for long-term sustainability. In this study, we introduce the bounded half-logistic distribution (BHLD), a novel heavy-tailed probability model constructed using the T–Y method for distribution generation, where T denotes a transformer distribution and Y represents a baseline generator. Although the BHLD is conceptually related to the Pareto and log-logistic families, it offers several distinctive advantages for streamflow modeling, including a flexible hazard rate that can be unimodal or monotonically decreasing, a finite lower bound, and closed-form expressions for key risk measures such as Value at Risk (VaR) and Tail Value at Risk (TVaR). The proposed distribution is defined on a lower-bounded domain, allowing it to realistically capture physical constraints inherent in flood processes, while a log-logistic-based tail structure provides the flexibility needed to model extreme hydrological events. Moreover, the BHLD is analytically characterized through a governing differential equation and further examined via its characteristic function and the maximum entropy principle, ensuring stable and efficient parameter estimation. It integrates a half-logistic generator with a log-logistic baseline, yielding a power-law tail decay governed by the parameter $\beta$, which is particularly effective for representing extreme flows. Fundamental properties, including the hazard rate function, moments, and entropy measures, are derived in closed form, and model parameters are estimated using the maximum likelihood method. Applied to four real streamflow data sets, the BHLD demonstrates superior performance over nine competing distributions in goodness-of-fit analyses, with notable improvements in tail representation. The model facilitates accurate computation of hydrological risk metrics such as VaR, TVaR, and tail variance, uncovering pronounced temporal variations in flood risk and establishing the BHLD as a powerful and reliable tool for streamflow modeling under changing environmental conditions. Full article

The variability of renewable energy sources, coupled with the decentralised configuration of distributed generation (DG), significantly complicates grid management, necessitating sophisticated visual analytics to enhance power system performance and energy distribution. This paper presents a probabilistic visualisation technique based on polar histograms to identify the dynamic influence zones of DG units by analysing line current flows. The proposed framework explicitly accounts for the probabilistic representation of reverse power flows, which provides an overall view of DG impacts on distribution networks. Quasi-dynamic simulations are conducted on a 33-bus distribution system using DIgSILENT PowerFactory 2020, MATLAB R2020, and Python 3.8. The results demonstrate that the polar histogram approach provides intuitive insights into DG influence, revealing zones of grid-dominated, DG-dominated, and shared interactions. These findings act as a potential practical tool for voltage management, demand balancing, and secure integration of renewable DG units into modern power grids. Full article

To address active power fluctuations in power grids induced by high renewable energy penetration and overcome the limitations of existing probabilistic power flow (PPF) methods that ignore generator frequency regulation constraints, this paper proposes a segmented stochastic power flow modeling method and an efficient analytical framework that incorporates the actions and capacity constraints of regulation units. Firstly, a dual dynamic piecewise linear power injection model is established based on “frequency deviation interval stratification and unit limit-reaching sequence ordering,” clarifying the hierarchical activation sequence of “loads first, followed by conventional units, and finally automatic generation control (AGC) units” along with the coupled adjustment logic upon reaching limits, thereby accurately reflecting the actual frequency regulation process. Subsequently, this model is integrated with the State-Independent Linearized Power Flow (DLPF) model to develop a segmented stochastic power flow framework. For the first time, a deep integration of unscented transformation (UT) and regulation-aware power allocation is achieved, coupled with the Nataf transformation to handle correlations among random variables, forming an analytical framework that balances accuracy and computational efficiency. Case studies on the New England 39-bus system demonstrate that the proposed method yields results highly consistent with those of Monte Carlo simulations while significantly enhancing computational efficiency. The DLPF model is validated to be applicable under scenarios where voltage remains within 0.95–1.05 p.u., and line transmission power does not exceed 85% of rated capacity, exhibiting strong robustness against parameter fluctuations and capacity variations. Furthermore, the method reveals voltage distribution patterns in wind-integrated power systems, providing reliable support for operational risk assessment in grids with high shares of renewable energy. Full article

This paper quantifies the steady-state voltage-compliance impact of ultra-fast electric vehicle (EV) charging on the IEEE 33-bus radial distribution feeder. Four practical scenarios are examined by combining two penetration levels (6 and 12 charging points, i.e., ≈20% and ≈40% of PQ buses) with two charger ratings (1 MW and 350 kW per point). Candidate buses for EV station integration are selected through a nodal voltage–reactive sensitivity ranking ($\partial V/\partial Q$), prioritizing electrically robust locations. To capture realistic operating uncertainty, a 24-hour quasi-static time-series power-flow assessment is performed using Monte Carlo sampling ($N=100$), jointly modeling residential-demand variability and stochastic EV charging activation. Across the four cases, the worst-hour minimum voltage (uncompensated) ranges from 0.803 to 0.902 p.u., indicating a persistent under-voltage risk under dense and/or high-power charging. When the expected minimum-hourly voltage violates the 0.95 p.u. limit, a closed-form, sensitivity-guided reactive compensation is computed at the critical bus, and the power flow is re-solved. The proposed mitigation increases the minimum-voltage trajectory by approximately 0.03–0.12 p.u. (about 3.0–12.0% relative to 1 p.u.), substantially reducing the depth and duration of violations. The maximum required reactive support reaches 6.35 Mvar in the most stressed case (12 chargers at 1 MW), whereas limiting the unit charger power to 350 kW lowers both the severity of under-voltage and the compensation requirement. Overall, the Monte Carlo V–Q sensitivity framework provides a lightweight and reproducible tool for probabilistic voltage-compliance assessment and targeted steady-state mitigation in EV-rich radial distribution networks. Full article

The sustained growth of electricity demand and the global transition toward low-carbon energy systems have intensified the need for efficient, flexible, and reliable operation of electrical distribution networks. In this context, the coordinated integration of distributed renewable energy resources and demand-side flexibility has emerged as a key strategy to improve technical performance and economic efficiency. This work proposes an integrated optimization framework for active power supply in a radial, distribution-like network through the optimal siting and sizing of photovoltaic (PV) units and wind turbines (WTs), combined with a real-time pricing (RTP)-based demand-side response (DSR) program. The problem is formulated using the branch-flow (DistFlow) model, which explicitly represents voltage drops, branch power flows, and thermal limits in radial feeders. A multiobjective function is defined to jointly minimize annual operating costs, active power losses, and voltage deviations, subject to network operating constraints and inverter capability limits. Uncertainty associated with solar irradiance, wind speed, ambient temperature, load demand, and electricity prices is captured through probabilistic modeling and scenario-based analysis. To solve the resulting nonlinear and constrained optimization problem, an Improved Whale Optimization Algorithm (I-WaOA) is employed. The proposed algorithm enhances the classical Whale Optimization Algorithm by incorporating diversification and feasibility-oriented mechanisms, including Cauchy mutation, Fitness–Distance Balance (FDB), quasi-oppositional-based learning (QOBL), and quadratic penalty functions for constraint handling. These features promote robust convergence toward admissible solutions under stochastic operating conditions. The methodology is validated on a large-scale radialized network derived from the IEEE 118-bus benchmark, enabling a DistFlow-consistent assessment of technical and economic performance under realistic operating scenarios. The results demonstrate that the coordinated integration of PV, WT, and RTP-driven demand response leads to a reduction in feeder losses, an improvement in voltage profiles, and an enhanced voltage stability margin, as quantified through standard voltage deviation and fast voltage stability indices. Overall, the proposed framework provides a practical and scalable tool for supporting planning and operational decisions in modern power distribution networks with high renewable penetration and demand flexibility. Full article

The integration of cyber and physical networks in modern power system introduces complex interdependencies that necessitate effective robustness assessment frameworks. In this paper, we propose a novel robustness assessment method for cyber-physical power systems (CPPS), which integrates structural and functional robustness. Firstly, an interdependent dynamic hierarchical network model that accounts for static topological structure, functional attributes and dynamic operational characteristics of cyber-physical power system is established. Based on the model, a probabilistic cascading failure model considering topological connectivity loss, power flow overload, cyber functional failures, and cyber-physical dependence is proposed. The proposed model quantifies the cross-layer impact of cyber-layer impairments (such as communication delay and data loss) on physical-layer operation. Finally, the impacts of cyber network performance and initial failure modes on the robustness of the coupled system are analyzed. The results show that an excellent processing performance and topological connectivity of cyber network can enhance the robustness of the coupled system, and the failure of high-degree nodes is more likely to trigger more severe cascading failure results than the failure of high-betweenness nodes. Full article

As renewable energy penetration increases, the volatility and uncertainty of photovoltaic generation and load demand pose significant challenges to power-system stability. This paper proposes a data-driven probabilistic load-flow method that employs a Gaussian mixture model (GMM) to model uncertainties in photovoltaic generation and load demand. Cumulative quantity analysis is then applied to conduct probabilistic load-flow studies, quantifying the impact of these uncertainties on the power system. Building upon this foundation, a two-layer optimization model is constructed to optimize the siting, capacity, and operational strategies of energy storage systems. Experimental results demonstrate that this method effectively reduces the probability of voltage-limit violations, ensures the reliability of supply–demand balance, and enhances system stability and reliability even under fluctuating PV generation and load-demand conditions. Full article

This paper presents a comprehensive framework for real-time energy management in microgrids integrating distributed renewable energy sources and demand response (DR) programs. To address the inherent uncertainties in key operational variables—such as load demand, wind speed, solar irradiance, and electricity market prices—this study employs a probabilistic modeling approach. A two-stage stochastic optimization method, combining mixed-integer linear programming and optimal power flow (OPF), is developed to minimize operational costs while ensuring efficient system operation. Real-time dynamic pricing mechanisms are incorporated to incentivize consumer load shifting and promote energy-efficient consumption patterns. Three microgrid scenarios are analyzed using one year of real historical data: (i) a grid-connected microgrid without DR, (ii) a grid-connected microgrid with 10% and 20% DR-based load shifting, and (iii) an islanded microgrid operating under incentive-based DR contracts. Results demonstrate that incorporating DR strategies significantly reduces both operating costs and reliance on grid imports, especially during peak demand periods. The islanded scenario, while autonomous, incurs higher costs and highlights the challenges of self-sufficiency under uncertainty. Overall, the proposed model illustrates how the integration of real-time pricing with stochastic optimization enhances the flexibility, resilience, and cost-effectiveness of smart microgrid operations, offering actionable insights for the development of future grid-interactive energy systems. Full article