Search Results (736)

Understanding intra-urban spatial interaction is essential for context-sensitive urban planning. While classical spatial interaction theories provide strong conceptual foundations, systematically translating these theoretical concepts into quantifiable indicators remains a significant methodological challenge. Furthermore, capturing the complex, non-linear dynamics driving urban mobility requires analytical approaches that balance predictive power with interpretability. To address this gap, this study develops a feasible, theory-informed analytical framework that bridges classical spatial interaction theory with interpretable machine learning to quantify the predictive patterns underlying intra-urban mobility. In a case study of Changchun, China, Ullman’s three core concepts, together with fundamental measures of urban scale, were systematically operationalized as a set of quantitative proxy variables based on multi-source geospatial big data. XGBoost was then used to model grid-level origin-destination flows at multiple spatial resolutions, and the SHapley Additive exPlanations (SHAP) was used to assess the contributions and dependence patterns of the theory-driven indicators. The results demonstrate the framework’s predictive robustness, with the XGBoost model consistently outperforms the traditional parametric benchmark across all evaluated spatial resolutions. The 1000 m resolution provided the best balance between predictive performance and spatial detail, yielding an R² of 0.696, compared with 0.611 for the benchmark. The explanatory analysis indicates that functional complementarity is the most critical predictive dimension overall. It also identifies distinct nonlinear patterns, including negative associations between transfer impedance and predicted mobility flows beyond critical thresholds, positive associations between built-environment scale indicators and predicted flows only above minimum intensity thresholds, and diminishing marginal associations between intervening opportunities and predicted flows. This study provides a scalable and transferable approach for diagnosing spatial interactions in data-rich urban contexts, providing an empirical basis for calibrating future micro-level urban simulations. Full article

Extreme weather couples spatially correlated component damage with photovoltaic (PV) derating, changing electric-vehicle (EV) demand, repair delay, and time-varying network topology. This paper develops a coordinated restoration architecture for multi-area feeders containing PV, battery energy storage, and charging stations. Its weather-facing layer constructs joint outage-risk, renewable-error, charging-demand, and voltage-vulnerability descriptors. Those descriptors parameterize a two-stage mixed-integer second-order-cone program with a finite-support optimal-transport ambiguity set that remains well defined for discontinuous mixed-integer recourse. Regional actor–critic agents propose five-minute corrections around the hourly robust schedule; constrained projection, non-linear AC power-flow screening, emergency fallback, and margin-tightened re-optimization retain the authority to accept or reject each proposal. The evaluation uses public 33-node and 123-node feeders together with synthetic 240-node and 850-node stress networks. A pre-fit manifest allocates 240 records to training, 80 to validation, and 320 to final testing, while aggregate operational outcomes cover 50 random streams. Within this controlled benchmark, accepted schedules restore 93.6% of critical-load energy (SD 2.1 percentage points), serve 96.7% of total demand (SD 1.8 percentage points), retain 82–86% of EV service across hazard classes, and reduce the modeled 24 h objective by 25.8% relative to deterministic dispatch. The full pipeline records two to four candidate-stage voltage-limit events by hazard, and 4.9% of candidates undergo tightened re-optimization before accepted schedules reach zero reported AC voltage-limit violations. Between-method comparisons are descriptive and unpaired; the larger synthetic cases are structural stress tests rather than feeder-transfer tests. Full article

Power Flow (PF) analysis is a fundamental tool in distribution systems since it determines the steady-state operating point for specified input conditions. Modern distribution networks face high distributed energy resource (DER) penetration and variable operating conditions, requiring repeated PF evaluations in time-series and scenario-based studies. Their unbalanced operation and high $R/X$ ratios can challenge conventional PF solvers, thereby requiring accurate, robust, and scalable methods. Prior studies have examined nonlinear distribution PF solvers and uncertainty-based formulations, but the review literature remains limited to specific categories and lacks a unified discussion of linearized models, numerical robustness, and acceleration techniques. Therefore, this paper presents a state-of-the-art review of PF methods for modern distribution networks, covering 205 studies published between 2000 and 2026. It summarizes conventional nonlinear PF formulations, reviews linearized models with their assumptions and applicability, and surveys numerical robustness strategies for improved convergence. The methods are compared according to their applicability to radial, weakly meshed, and unbalanced networks, while practical selection criteria are provided based on accuracy, convergence reliability, and computational requirements. Probabilistic, interval, and fuzzy approaches are also reviewed under renewable and load uncertainty. Finally, acceleration strategies for repeated PF evaluation are discussed, emphasizing sparse numerical implementations, topology-based schemes, and physics-informed surrogate models. Full article

This paper studies a risk-averse stochastic unit commitment framework for an energy aggregator, operating a portfolio of conventional generators, renewable units, and battery energy storage in a network-constrained environment. Renewable generation and demand uncertainty are represented through a scenario-based extensive-form mixed-integer linear program. To avoid exposure to rare but high cost events, the model incorporates conditional value-at-risk as part of the objective function. The approach captures key market interactions, including day-ahead commitments, imbalance penalties, and power exchange with a neighboring network, while respecting generator constraints, storage dynamics, line flow limits, and bus voltage security. A comprehensive parametric study is conducted to quantify the influence of two risk parameters: the conditional value-at-risk confidence level $\alpha$ and the risk-aversion weight $\lambda$. Using a 300-scenario test set on a modified IEEE 9-bus system, the results show that risk-neutral scheduling exposes the aggregator to larger operational costs in extreme scenarios. Minor levels of risk aversion (0.1–0.5) reduce CVaR and tighten the distribution of costs. Increasing $\lambda$ further yields diminishing returns, while higher $\alpha$ values focus risk mitigation on the most severe outcomes. The results demonstrate how CVaR-based stochastic scheduling can support aggregator decision-making by quantifying downside risk under renewable uncertainty. Full article

The formation pressure system of ultra-deep wells is complex, and managed pressure cementing (MPC) is a commonly used technical means of safety control and cementing quality improvement. During the MPC process, pump switching operations can induce substantial annular back-pressure. The attenuation of annular back-pressure within the wellbore serves as a pivotal foundation for the precise determination of back-pressure compensation values in ultra-deep wells. Building upon the one-dimensional transient flow model of the wellbore, we developed a transient transmission model for annular back-pressure and solved it using the finite difference method. The computational results were validated against experimental data, thereby elucidating the attenuation pattern of annular pressure waves in ultra-deep wells. The findings reveal that the primary controlling factors for the attenuation of pressure waves encompass well depth, the elastic modulus of the wellbore rock, and the rheological model of the drilling fluid. As well depth increases, the pressure wave exhibits a linear decrease, with discontinuities occurring at the casing and open-hole sections. The rate of pressure wave attenuation accelerates within the open-hole interval. The lower the elastic modulus of the open-hole segment, the more rapid the attenuation rate of the pressure wave becomes. The attenuation laws of annular fluids with different rheological models are ranked as follows: Power-law model > Herschel–Bulkley model > Bingham model. Under the computed well conditions, the pressure of the power-law fluid decreases to 85% of its initial back-pressure value. This research provides theoretical underpinnings for the design and execution of on-site MPC operations. Full article

Power system state estimation (PSSE) requires accurate and timely inference from noisy measurements, but large labeled operational datasets are often unavailable and deployment data may differ from offline training data. This paper presents Deep Transfer Learning for State Estimation (DeepTL4SE), which combines Physics-Informed Data Generation (PIDG) with supervised transfer learning. PIDG evaluates the AC power-flow relations for selected voltage states and constructs paired measurements and state labels directly from the network equations. DeepTL4SE produces a point estimate of the current electrical state. A prox-linear network is pretrained on the physics-derived pairs, selected early layers are frozen, and the remaining layers are fine-tuned on target-domain samples. Tests on the IEEE 14- and 118-bus systems show the lowest average RMSE among the reported prox-linear and feed-forward baselines. The best average RMSE values are $0.01266\%$ for the IEEE 14-bus system with MSE loss and $0.00452\%$ for the IEEE 118-bus system with Huber loss. Full article

Following extreme disasters, hybrid wind farms comprising grid-following (GFL) and grid-forming (GFM) turbines can serve as black-start resources for power system restoration. However, wind power uncertainty, wake effects, and collection-grid restoration constraints complicate the startup sequence planning of GFL turbines within hybrid wind farms. To address these challenges, this paper proposes a multi-objective mixed-integer linear programming (MILP) model that jointly considers electrical impedance paths, wind uncertainty, and spatial wake effects. Information Gap Decision Theory (IGDT) is incorporated into active power support constraints to account for wind uncertainty through a robust adjustment of available generation capacity, while the Dijkstra algorithm is employed to convert collection-cable parameters into impedance-based cost factors for identifying minimum-impedance restoration paths and mitigating transient overvoltage risks. In addition, dynamic wake losses under non-uniform turbine layouts are quantified to capture the influence of startup sequences on local flow fields, and the resulting nonlinear terms are reformulated using the big-M linearization technique. Case studies considering different wind directions, time-varying wind speed conditions, and cable-impedance sensitivities demonstrate the effectiveness of the proposed framework. The results show that the proposed strategy provides a favorable balance between impedance-cost minimization, wake-effect mitigation, and robustness enhancement, while maintaining reliable restoration performance under diverse operating conditions. Full article

Active distribution grids require analysis methods that combine physical fidelity with low computational cost for repeated screening, optimization workflows, and operational decision support. Local linearized power-flow models can support these tasks, but their accuracy depends strongly on the operating point around which they are derived and on how the relevant operating range is represented. This paper benchmarks operating-point-dependent linearized power-flow models for active distribution grids across five SimBench networks. We compare operating-point selection strategies, library sizes, and targeted library extensions for three separate target quantities: voltage magnitude, line loading, and transformer loading. The evaluation combines equal-budget accuracy, critical- and near-limit operating states, post-action AC validation, and controlled runtime measurements. At an equal budget of 36 linearization points, k-medoids provides the most consistent general-purpose accuracy and achieves the first target-specific rank for all three quantities. Increasing the library size yields diminishing gains, with the largest improvement between 10 and 22 points. A k-medoids/k-center hybrid improves all six primary accuracy metrics relative to a common 28-point basis and provides the best upper-tail voltage accuracy in critical states. In post-action validation, nominal linear actions are AC-feasible in 31 of 35 cases, while adding a safety margin yields successful AC results in all 35 cases without new violations. Online evaluation requires about 3.5 ms per state and achieves a median speed-up of about 26–28 relative to AC power flow. The results show that operating-point libraries can provide a practical accuracy–runtime compromise when representative coverage, critical-state validation, and residual decision margins are considered jointly. Full article

The rheological behaviour of complex fluids such as blood and polymer melts is governed by viscosities that are inherently subject to epistemic uncertainty arising from incomplete knowledge of evolving small scales rather than intrinsic randomness. Classical continuum models assume precisely known viscosity functions, an assumption that is physically unjustifiable in such systems, while existing fuzzy approaches have failed to integrate rigorously with the full conservation laws of continuum mechanics. To address this gap, we introduce Fuzzy–Viscous Fluid Dynamics (FVFD), a novel framework in which dynamic viscosity is governed by Dynamic Interval-Valued Intuitionistic Fuzzy Sets (DIVIFS), with membership functions grounded in Coleman–Gurtin internal-variable thermodynamics and evolution equations derived from a Lyapunov dissipation postulate. Employing the parabolic comparison principle together with Galerkin–Leray–Hopf theory, we establish that intuitionistic ordering constraints are preserved over time and prove the existence of global weak solutions to the coupled fuzzy Navier–Stokes equations (FNSEs). An exact analytical solution for fuzzy Couette flow is derived, recovering the classical Newtonian limit and shown, via a structural argument, to be non-linear precisely because and only because FVFD departs from the purely local generalised-Newtonian closure shared by the Power-law, Carreau–Yasuda, and Cross models. Three governing dimensionless parameters, the Reynolds number ($Re$), Damköhler number ($Da$), and fuzzy number ($Fz$), are identified and justified to characterise distinct flow regimes. This framework provides a rigorous, physically grounded alternative to stochastic and data-driven methods for explicitly tracking epistemic uncertainty through interval-valued hesitancy parameters, enabling more accurate modelling of complex fluids whose internal aggregation states remain inaccessible to direct observation. Full article

To improve the transient operating stability of Francis turbines under flexible regulation conditions, this study investigates the effects of different speed-change modes on the internal flow structure and pressure pulsation characteristics of a high-head Francis-99 model turbine during variable-speed transients. Three representative acceleration strategies, namely linear, quartic, and fourth-root speed-change modes, are designed. In all cases, the rotational speed increases from 333 r/min to 346.2 r/min within 4 s, corresponding to a speed increase of approximately 3.96%, thereby eliminating the influence of differences in speed-change amplitude and duration on the flow response. During this process, the main frequency induced by runner blade passing at the guide vane outlet increases from approximately 166.5 Hz to 173.1 Hz, while the main frequency induced by guide vane passing at the runner inlet increases from approximately 155.4 Hz to 161.6 Hz. Comparative analyses of the pressure distribution in the runner and guide vane regions, runner streamline evolution, time-domain pressure pulsation, and time–frequency characteristics obtained using the Hilbert–Huang transform show that the temporal distribution of the speed-change rate significantly affects pressure-field uniformity, flow-separation development, and spectral-energy distribution. The linear speed-change mode produces a continuous and relatively predictable migration of pressure and frequency. The quartic mode, characterized by a “slow-first and fast-later” strategy, delays the development of initial disturbances, yields a more balanced pressure-gradient distribution and more localized flow separation, and produces a more concentrated time–frequency energy distribution with shorter-lasting high-frequency pulsation regions. By contrast, the fourth-root mode induces excessive initial acceleration, leading to a polarized pressure distribution with high pressure at the inlet and low pressure at the outlet, large-scale separation vortices, persistent low-frequency modes, and nonlinear frequency coupling. The results indicate that, while satisfying rapid power-response requirements, avoiding excessive acceleration at the initial stage and adopting nonlinear acceleration strategies with an initial-buffering feature are effective approaches for improving the stability of variable-speed turbine transients. Full article

High-frequency traffic data from remote sensors often suffer from severe gaps and multi-day blackouts. Traditional deterministic imputation fails during these extended failures, artificially destroying natural traffic variance. To resolve this, this study develops an adaptive Multiple Imputation (MI) framework to reconstruct missing 2-min volumes. A novel multi-tier historical median predictor with adaptive expansion (up to ±30 min) serves as a variance-protected anchor for two stochastic engines: Stochastic Linear Regression and Predictive Mean Matching with Approximate Bayesian Bootstrap (PMM-ABB). PMM-ABB features dynamic $K$-neighbor autotuning, with simulation convergence governed by a dual-metric algorithm. Performance was evaluated against a Historical Average (HA) baseline via multi-domain validation, strictly assessing the models’ ability to recover hidden, real-world ground-truth counts rather than replicating the engineered input features. Under severe block-missingness, the stochastic models prevented collapse, reducing Temporal Cross-Validation MAE from 33.7 (HA) to 22.7 (Cohen’s $d$ = −0.4). Power Spectral Density matching confirmed that both models preserved macro-periodic traffic waves, keeping spectral tracking errors under 4.8 dB. Ultimately, PMM-ABB slightly outperformed Stochastic Regression in sequential time dependency and point accuracy, confirming that the framework provides a highly reliable structural proxy for continuous highway flow modeling. Full article

High photovoltaic penetration increases reserve needs in active distribution networks, while PEDF microgrid flexibility is seldom coordinated as a reserve product. This study develops a complete-information Stackelberg framework in which a distribution system operator posts bounded prices for energy exchange, reactive support, and directional reserve. A Wasserstein ambiguity set centered on the empirical source–load error distribution supports a worst-case conditional value-at-risk calculation of hourly requirements. PEDF reserve offers are constrained by available battery energy, flexible-load headroom, recoverable photovoltaic curtailment, shared converter capacity, and activated feeder states. KKT conditions and Big-M linearization yield a mixed-integer second-order cone program. On a modified IEEE 33-bus feeder, joint PEDF and external reserve procurement reduces system cost by 2.455% and aggregate PEDF net cost by 10.402%, with zero reserve shortages and a minimum voltage of 0.951284 p.u. Fixed-ratio, SAA-CVaR, Box-RO, and WDRO-CVaR comparisons reveal an economy–reliability tradeoff. Rolling out-of-sample tests identify 0.1 as the smallest tested radius multiplier meeting a 5% violation target in all three training windows. An IEEE 69-bus extension reduces system cost by 4.233%, and all 144 nonlinear AC power-flow states converge. The results support one-interval steady-state reserve coordination under the tested assumptions. Full article

Escalating energy demand and the evolving landscape of power transmission have intensified the operational pressures on electrical grids, specifically during N-1 contingency events. The unexpected loss of a single transmission circuit often precipitates critical system instabilities, including power flow congestion, voltage degradation, and heightened transmission losses. While conventional grid expansion remains the standard for maintaining reliability, its implementation is frequently hindered by lengthy permitting processes, significant capital investment, and regulatory complexities. This research offers an alternative by presenting a robust optimization-based framework for the strategic placement and sizing of a battery energy storage system (BESS) within the Electricity Generating Authority of Thailand (EGAT) transmission network. Focusing on the N-1 contingency resulting from the 115 kV Thatako Substation (TTKS)–Bueng Sam Phan Substation (BGSS) circuit outage during peak load hours, this study introduces the musk ox optimizer (MOO) to solve the complex, non-linear allocation problem. The objective function is formulated to minimize cumulative system costs while enforcing strict network operational envelopes. Simulation results indicate that the optimized BESS configuration achieves compliant grid performance, successfully restoring the post-fault bus voltage, enhancing voltage profile, reducing transmission losses, and mitigating peak line loading. These findings demonstrate that the proposed MOO-based strategy provides a physically compliant, flexible, and robust non-wire alternative for transmission constraint management, confirming its viability as a sustainable, low-environmental-impact framework for enhancing modern grid resilience and utility development. Full article

Conventional small-signal security assessment requires repeated power flow calculations, system linearization, and eigenvalue analysis, resulting in considerable computational burden for online applications. Moreover, existing data-driven methods generally provide insufficient representation of branch power flows, line operating states, and incomplete PMU measurements. To address these limitations, this paper proposes an edge-enhanced graph attention network (EE-GAT) for real-time small-signal security assessment. The model takes bus voltage magnitude, phase angle, active and reactive power injections, and PMU availability masks as node features, while branch active and reactive power flows and line operating states are incorporated as edge features. An edge-enhanced multi-head attention mechanism is employed to jointly learn node state and branch coupling information, and a global attention readout mechanism is used to construct the system-level representation for secure/insecure classification. Tests on the New England 39-bus and NPCC 140-bus systems show that EE-GAT achieves accuracies of 97.75% and 96.47%, respectively, outperforming XGBoost, LSTM, CNN, GCN, and conventional GAT. The proposed model also maintains superior performance under incomplete PMU measurements and requires only 0.0034 s and 0.0051 s for the corresponding test batches, demonstrating its potential for online small-signal security screening. Full article

This paper proposes a network-constrained multi-step optimization approach for robust flexibility provision from distributed energy resources (DERs) under photovoltaic (PV) generation uncertainty. The proposed method optimally schedules day-ahead battery operations based on PV output predictions and confidence intervals, while strictly satisfying network constraints. To ensure operational feasibility, the AC power flow is modeled using DistFlow equations. To bridge the gap between computational tractability and exact AC feasibility, a multi-step solution strategy is introduced. First, a linearized DistFlow (LinDistFlow) model is employed within a column-and-constraint generation algorithm to efficiently identify the worst-case scenario. Subsequently, the robust day-ahead battery schedule is determined by solving a second-order cone (SOC)-relaxed DistFlow model under the identified scenario. Finally, a post-processing exact recovery step is executed by solving the original non-convex DistFlow equations under the fixed battery schedule and the worst-case scenario. This crucial step compensates for approximation errors introduced by the LinDistFlow and SOC models, significantly enhancing practical operational AC feasibility under the identified critical condition. Extensive case studies on the IEEE 33-bus test system verify the effectiveness of the proposed multi-step approach in balancing computational efficiency and robust flexibility provision. Full article