Search Results (220)

Against the backdrop of the global low-carbon transition, power-to-ammonia (PtA) has emerged as a pivotal direction for large-scale energy storage. Distributionally robust optimization can effectively address uncertainties in energy systems; however, traditional distributionally robust dispatch models generally suffer from over-conservatism that leads to increased operational costs, and existing PtA studies mostly focus on scenario-based adaptations of established optimization tools, lacking mechanistic and methodological innovations tailored to the electricity–hydrogen–ammonia coupling characteristics. To address these issues, this paper proposes a distributionally robust chance-constrained economic dispatch model (WMDRCC) based on the Wasserstein metric and first-order moment information, and introduces a logical mapping relationship that links hydrogen storage capacity with the operating modes of ammonia synthesis. This mechanism enables real-time optimization of the H₂/N₂ feed ratio, mitigates hydrogen source fluctuations, and avoids reactor instability and cost-ineffective shutdowns. Furthermore, by integrating Conditional Value at Risk (CVaR), duality theory, and big-M linearization, the complex robust chance-constrained problem is reformulated into a computationally tractable mixed-integer linear programming (MILP) model. Numerical results on the IEEE 33-bus system demonstrate that, compared with a distributionally robust model based solely on the Wasserstein distance, the proposed method effectively reduces system operating costs under the tested 24 h daily scenarios, while simultaneously improving renewable energy accommodation and reducing network losses, thereby providing a novel dispatch scheme for PtA systems that balances both economic efficiency and robustness. Full article

Traditional risk parity approaches rely largely on volatility measures, which may not fully capture asymmetric risk profiles. This study examines a dynamic allocation approach that minimizes portfolio-level Conditional Value-at-Risk (CVaR). The CVaR-Minimizing Dynamic Allocation (CVaR-DA) approach is intended to manage tail-risk events more effectively than traditional variance-based methods. We conducted an out-of-sample rolling-window simulation for the dynamically re-estimated strategies, covering different market conditions from 2015 to early 2025. Two investment universes were examined: a concentrated equity–gold portfolio and a multi-asset portfolio comprising global equities, sovereign bonds, commodities, and gold. Variance-based DRP generated higher Sharpe ratios than Static Risk Parity in both universes while maintaining low portfolio turnover. The CVaR-DA approach provided better downside protection, particularly in the multi-asset universe, but produced higher turnover. Bootstrap inference yielded positive mean differences in Sharpe ratios between DRP and Static Risk Parity. However, the confidence intervals included zero, indicating that the differences were not statistically significant at conventional levels. The favorable drawdown results nevertheless suggest that dynamic risk allocation may improve portfolio resilience when risk conditions change. Moving from static, volatility-based allocation toward adaptive strategies that account for tail risk may therefore support capital preservation for institutional investors and fund managers. Full article

Cryptocurrency holdings in conventional portfolios challenge the empirical adequacy of standard tail-risk estimators. This study identifies a calibration mechanism that brings feature-based machine learning to supervisory-grade value at risk (VaR) coverage, improves its joint VaR and expected shortfall (ES) record relative to volatility filtering, and measures the value of tail-oriented allocation. Ten risk models are evaluated on equity, cryptocurrency and mixed portfolios across 1397 out-of-sample trading days, covering several distinct market phases. Three of these models are variants of a single learner, sharing the same feature set and estimation protocol, and differing only in how the predicted quantile is placed. Uncalibrated gradient boosting understates the tail in every portfolio, yielding violation rates as high as 10.81% against a 5% nominal level, and volatility filtering does not correct the shortfall. Split-conformal calibration keeps forecasts in the green zone of the generalised traffic-light criterion throughout and under every initialisation, yet 47 of the 49 significant loss comparisons still favour a classical benchmark. Separation is only modestly stronger on the cryptocurrency book, at 19 significant comparisons against 15 for each of the other two portfolios. Minimum conditional value at risk (CVaR) allocation reduces realised tail loss by 65% and maximum drawdown by 64% without improving risk-adjusted return. Thus, the evaluated machine learning models require calibration to achieve adequate coverage, whereas the econometric benchmarks retain an advantage in predictive accuracy. Full article

Facing price volatility risks and multi-agent strategic interactions in two-level electricity markets, this paper proposes a bi-level decision framework integrating Conditional Value at Risk (CVaR) and Mean Field Game (MFG). The upper level minimizes purchasing costs and CVaR risk for inter-provincial traders, while the lower level models market clearing based on generation cost minimization in sending provinces. An MFG model with homogeneous traders is then introduced, coupling individual optimal control (HJB equation) with population distribution evolution (FPK equation) to capture collective behavior feedback on prices. An adaptive regularization Deep Q-Network algorithm is designed to improve computational efficiency. Multi-scenario simulations using grid data analyze the effects of risk aversion, uncertainty, and network congestion on costs and price volatility. Results show that the model effectively characterizes the interplay between risk attitudes and market equilibrium, offering theoretical and practical support for risk management and market design in inter-provincial trading. Full article

Financial risk along the China–Pakistan Economic Corridor may combine fast firm-level scaling changes with slower joint-tail exposure. This study evaluates a leakage-controlled two-speed architecture for seven Pakistani equities during July 2021–June 2026. Causally timed, bounded-influence wavelet p-leader states feed quantile learners, while 13 prespecified directed hyperedges define a structural map. Evidence comprises 999 iterative amplitude-adjusted Fourier-transform (IAAFT) surrogates per node, 999 matched random edge sets, a 249-origin locked Value-at-Risk–Expected Shortfall test, learner-by-feature ablations, moving-block inference, and cost-adjusted portfolios. Robustification removes the legacy KEL spectrum anomaly; only LUCK rejects the IAAFT null after false-discovery-rate control (q = 0.009). No hyperedge has a confirmed increment beyond singleton conditionals and the pairwise-only benchmark. The map’s mean lift is 0.951 versus a placebo median of 0.989 (p = 0.834). The reservoir is competitive in point loss but indistinguishable from the conditional autoregressive Value-at-Risk benchmark (p = 0.420); its p-leader gain does not transfer across learners or survive KEL-block exclusion. The 0.606-percentage-point drawdown difference relative to historical conditional Value-at-Risk (CVaR) is imprecisely estimated (95% interval: [−7.652, 5.648]; p = 0.626). The framework supports robust multiscale measurement and transparent structural mapping, not general forecasting superiority, unique hyperedge information, or reliable portfolio protection. Full article

Co-phase traction power supply system (CTPSS) integrated with photovoltaic (PV) and hybrid energy storage system (HESS) can enhance power supply capacity while facilitating the on-site consumption of renewable energy. This integration provides a pathway toward green development and the achievement of the “carbon peaking and carbon neutrality” goal. However, the stochastic nature of PV poses challenges to safe and economical operation of the system. Existing energy management methods remain limited in simultaneously balancing operational economy and extreme risks caused by PV uncertainty, making it difficult to achieve an effective trade-off between operating cost and constraint violation risk. To address this issue, a risk-sensitive optimal scheduling framework integrating probabilistic PV forecasting, correlated scenario generation, and risk-aware optimization is developed. First, a PV probabilistic prediction model based on parallel TCN-BiLSTM-Attention is proposed, which extracts multiscale local features and long-range temporal features from PV for accurate uncertainty quantification. Second, a t-Copula PV scenario generation method driven by weather classification and temporal correlation is proposed. On this basis, a day-ahead optimal scheduling strategy integrating chance constraints programming (CCP) and conditional value at risk (CVaR) is established to simultaneously control constraint violation risk and extreme economic risk. The proposed prediction model can accurately quantify uncertainty, achieving an R² value of 0.9979. When the allowable power supply loss probability is 0.5%, the proposed scheme’s operating cost is reduced by 1.36% compared with the baseline scheme. The results demonstrate that the proposed framework can effectively coordinate operating economy and extreme-risk control, thereby improving the risk-sensitive operational performance of CTPSS with PV and HESS. The proposed strategy balances economy and extreme risk, providing a reference for safe, low-carbon and economical operation of CTPSS with PV and HESS. Full article

With the increasing scale of centralized photovoltaic-plus-storage power stations, they are required not only to supply local load demands but also to provide power support to the upstream grid. The coupled interactions among renewable energy output, sharp fluctuations in local loads, and limited tie-line support capacity cause conventional dispatching methods to face issues in rare extreme scenarios, such as shortfalls in scheduled power delivery, increased imported power during peak support periods, load shedding, and voltage violations. To address these issues, this paper proposes a Wasserstein distributionally robust dispatch strategy for active distribution networks (ADNs) tailored for Upstream Power Support (UPS) tasks, incorporating tail risk assessment. An ADN operation model is established that integrates PV, energy storage, interruptible loads, and a bidirectional interface with the main grid, where the scheduled power delivery during UPS periods characterizes the support demand to the upper grid. A comprehensive risk loss function, encompassing load shedding, power shortfalls, peak-period power import, PV curtailment, and voltage violations, is constructed, and Conditional Value-at-Risk (CVaR) is employed to capture the tail risk caused by extreme scenarios. A Wasserstein ambiguity set is built around the empirical distribution of finite historical samples, and via dual reformulation, the worst-case distribution conditional risk model is transformed into a tractable mixed-integer second-order cone programming problem. Case studies on modified IEEE 33-bus and 69-bus ADN test systems demonstrate that the proposed method achieves a trade-off between routine operational costs and extreme-scenario security. By optimizing day-ahead charging/discharging schedules of energy storage, it reduces scheduled power shortfalls under low-PV and high-load conditions, as well as peak-period power import dependence, thereby enhancing the power support capability and supply resilience of the active distribution network. Full article

This paper examined whether portfolio-objective choice or forecasting complexity was more consequential in heavy-tailed commodity ETF allocation. Using daily Bloomberg data for 30 U.S.-listed commodity ETFs from 12 December 2018 to 16 December 2024, we compared historical and dynamic mean–variance and conditional value-at-risk (CVaR) portfolios under long-only and long–short constraints. The dynamic framework combined ARMA–GARCH marginals, Student-t innovations, and copula dependence. Minimum-variance and minimum-CVaR portfolios generally produced higher Sharpe, Calmar, and STARR ratios than tangent portfolios across the baseline and robustness analyses. Dynamic estimation produced higher Sharpe, Calmar, and ${\mathrm{STARR}}_{0.95}$ point estimates for C99 and the tangent portfolios, but none of the historical–dynamic differences remained significant after max-t adjustment. Hill estimates indicated heavy downside tails, while VaR and Expected Shortfall backtests showed no calibration rejections for the minimum-risk portfolios and revealed 95% VaR failures for dynamic tangent portfolios. The long-only minimum-variance and 95% minimum-CVaR portfolios recorded higher Sharpe, Calmar, and ${\mathrm{STARR}}_{0.95}$ ratios than the 60/40 SPY–AGG benchmark, whereas the benchmark had a smaller maximum drawdown and lower VaR and Expected Shortfall. Overall, portfolio-objective choice was more consistently associated with realized performance than additional forecasting complexity. Full article

Integrated electricity–gas–heat systems underpin sustainable energy provision by coupling renewable, gas, and thermal resources across carriers. Sustainable operation of such systems must limit service loss caused by cross-carrier contingencies while maintaining economic efficiency and tracking carbon performance. This paper develops a 6 h rolling linear dispatch framework in which a security-margin floor, a scenario-weighted unserved-energy limit, and a conditional value-at-risk (CVaR) limit jointly define the admissible operating domain. The two risk limits adapt to the evolving load, forecast uncertainty, and gas-supply state, and future forecasts use only the error observed at the current dispatch instant. Across 30 paired forecast-error realizations, the adaptive method reduces the weighted unserved-energy index and the maximum hourly CVaR by 4.88% and 4.38%, respectively, relative to a fixed-cap rolling method under identical inputs, at a 2.14% cost increase. The equal-mean-budget comparison shows that temporal allocation adds a smaller, operationally modest improvement, with a paired CVaR difference of −0.094 MWh (95% CI: −0.108 to −0.079 MWh). A transfer case on the linear IEEE 39-bus–Belgian 20-node–DHS 6-node model keeps the network flexibility equivalent within its calibrated 0–65 MW domain, and all three rolling schedules pass 24 h full-topology linear routing checks without additional shedding at nominal capacities. These results establish implementability within the tested linear models; all reported risk indices are comparative scenario-risk measures rather than annual reliability statistics. By jointly safeguarding service continuity, economic efficiency, and carbon performance, the proposed framework supports the environmental, economic, and social dimensions of sustainable integrated-energy operation. Full article

This paper examines portfolio optimization and tail-risk analytics for a heterogeneous universe of 30 actively managed investment funds using daily Bloomberg data from 2020 to 2025. The study compares buy-and-hold, mean–variance, conditional value-at-risk (CVaR)-based, and tangency-type portfolio strategies under long-only and long–short constraints. The sample consists predominantly of actively managed exchange-traded funds, with PTTRX retained as an actively managed fixed-income mutual-fund comparator. The results show substantial heterogeneity across thematic equity, fixed-income, income-oriented, multi-asset, and alternative strategies, creating both diversification opportunities and meaningful differences in volatility, drawdown behavior, downside exposure, and tail risk. Historical results indicate that tangency-type portfolios are generally the strongest competitors to the buy-and-hold benchmark, while minimum-variance and CVaR-minimizing portfolios provide more conservative downside control. Dynamic allocation improves performance selectively: TVP records the strongest risk-adjusted performance, followed by TC95 and TC99, but these strategies are more sensitive to turnover, transaction costs, and implementation frictions, especially under long–short constraints. Tail-risk diagnostics based on empirical VaR, Expected Shortfall, maximum drawdown, left-tail Hill estimators, and peak-over-threshold generalized Pareto distribution (POT–GPD) methods show that downside tail exposure remains meaningful after portfolio aggregation. Overall, the findings suggest that actively managed ETFs are best evaluated as components of a joint investment opportunity set in which dependence structure, portfolio design, dynamic allocation, implementation frictions, and tail-risk exposure jointly shape performance. Full article

Renewable-driven operation exposes proton-exchange membrane (PEM) electrolyzers to ramps, starts, and partial-load conditions that accelerate degradation and weaken scheduling reliability. This paper develops a health-aware scheduling framework for an integrated electro-hydrogen system. It represents operating stress, delayed response, irreversible degradation, recoverable performance loss, and efficiency feedback. Scheduled rest partially relaxes the recoverable state, while per-unit health budgets yield degradation shadow prices that redirect load from health-scarce stacks. A Wasserstein distributionally robust model implements a health-conditioned risk-aversion policy by adjusting the protection radius with pre-horizon fleet health and filtered stress. The tractable finite-support formulation is evaluated through progressive ablations and five uncertainty treatments using chronological Liaoning wind, solar, and load data. Rotational recovery provides the main degradation mitigation, whereas shadow prices primarily improve allocation among heterogeneous stacks. Compared with fixed-radius DRO, the health-conditioned policy reduced the point estimates of ${\mathrm{CVaR}}_{95}$, energy-violation rate, and severe health-budget exceedance by 3.91%, 1.68 percentage points, and 3.36 percentage points, respectively. These results indicate the value of coordinating equipment health and uncertainty protection in short-term electro-hydrogen scheduling. Full article

Capacity planning for air-cargo hub terminals is still performed stage by stage against deterministic mean-value forecasts, which conceals both the coupling of the six-stage handling chain and the pronounced upper-tail variability of cargo demand. This study proposes a risk-averse configuration framework that jointly decides line deployment, cargo-class assignment, and capacity tier across receiving, screening, sortation, storage, ULD build-up, and loading. The model is a two-stage stochastic program optimizing four criteria simultaneously—time-weighted service level, life-cycle cost, a Pollaczek–Khinchine congestion penalty, and a CVaR-augmented unmet-demand measure—with chance constraints handled by sample-average approximation and 5000 Monte Carlo scenarios compressed to 30 by forward Kantorovich reduction. An improved NSGA-II with hierarchical function–class–tier encoding, sequence-aware repair, time-priority mutation, and scenario-recursive fitness evaluation solves the resulting mixed-integer problem. On a calibrated super-hub instance (2800 t outbound per day), the knee-point design attains 96.4% of the service-maximal service level at 88.0% of its cost and cuts the conditional value-at-risk of unmet demand at the 0.90 confidence level by about 42% versus a deterministic-equivalent plan; the value of the stochastic solution reaches 9.9%. The algorithm outperforms NSGA-II, NSGA-III, MOEA/D-DE, SPEA2, and MOPSO on hypervolume and inverted generational distance. Compositional volatility, not aggregate volume, emerges as the dominant driver of service collapse. Full article

In remote regions with abundant hydropower resources, upstream and downstream river basin virtual power plants (RBVPPs) operated by different entities are hydraulically coupled. Independent scheduling may therefore lead to inefficient water allocation and profit losses because downstream inflow depends on upstream reservoir releases. This study proposes a multi-RBVPP scheduling strategy based on a bidirectional water compensation contract. The independent-operation outflow schedule serves as the contractual baseline, and both increases and decreases in upstream releases are compensated according to their time-dependent effects on the downstream inflow. These effects are quantified using matrices for hydraulic connectivity, flow distribution coefficients, and water travel time. In the Stackelberg framework, the downstream RBVPP determines the time-varying compensation prices and electricity sales plan, whereas the upstream RBVPP adjusts reservoir releases and generation schedules subject to its own operational constraints. Only boundary outflow information is exchanged, preserving the privacy of internal operations. Conditional value-at-risk (CVaR) and scenario-based stochastic optimization are used to address uncertainties in renewable generation and hydrological conditions. The results for wet, normal, and dry conditions show that the proposed framework increases the profits of both RBVPPs and improves the coordinated use of basin water resources. Full article

High levels of photovoltaic (PV) generation in distribution networks create substantial uncertainty and voltage variability, which limits the effectiveness of conventional deterministic distribution network reconfiguration (DNR) strategies. In PV-dominated feeders, rare but severe operating conditions may considerably influence active power losses and voltage stability. To address this challenge, this paper proposes a risk-informed optimization framework for DNR that combines reinforcement learning with probabilistic performance assessment. A Deep Q-Network (DQN) agent is designed to support the selection of feasible radial switching configurations by interacting with the distribution network environment. Throughout the learning process, candidate network topologies are evaluated through radial load flow calculations, while a composite objective function incorporating active power losses and voltage deviation steers the agent toward improved configurations. The training stage is based on deterministic performance indices; however, the final reconfiguration solution is assessed under uncertainty to examine its operational robustness. For this purpose, extensive Monte Carlo simulations are performed to capture the stochastic behavior of PV generation and load demand. Tail-based risk metrics, including Value at Risk (VaR) and Conditional Value at Risk (CVaR), are computed for both loss and voltage deviation indices, providing insight into the performance of the selected configuration under unfavorable operating scenarios. The proposed framework is first validated on the IEEE 33-bus distribution system and then further investigated on the IEEE 69-bus network. The obtained results demonstrate that the proposed DQN-based reconfiguration approach can enhance voltage profiles and reduce power losses under high PV penetration. In addition, the probabilistic analysis identifies meaningful trade-offs between efficiency and voltage robustness, highlighting the importance of considering uncertainty-driven risk assessment in computational decision-making for modern active distribution networks. 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