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Summary Economic load dispatch (ELD) is a key issue for the economic and eco‐friendly operation of smart grids. With the increasing prevalence of renewable energy generation (REG), the stochastic properties of REG are drawing increased attention in the field of microgrid ELD. In this paper, the microgrid ELD problem considering uncertain REG, namely stochastic ELD (SELD), is formulated based on the wait‐and‐see approach. SELD is an optimization problem constrained by stochastic variables, and the optimal solutions are also random. The model incorporates many important factors, such as the detailed generation cost characteristics of microsources that make it difficult to obtain closed‐form solutions. Therefore, the efficient two‐point estimate method is applied to determine means and standard deviations of optimal solutions. To solve the cost‐minimization subproblem of microgrid SELD, an improved particle swarm optimization (IPSO) is also proposed. The simulation results show that the new mechanism in IPSO contributes to the optimization ability. Results also show that combined heat and power‐based microsources and the electricity tariff between the upstream grid and the microgrid have a significant influence on the expected total cost. Copyright © 2014 John Wiley & Sons, Ltd.

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.

Abstract Physically based landslide susceptibility analysis is widely used for landslide prediction owing to its high predictive capability. However, due to limited information and the spatial variability of slope materials, this approach involves uncertainty. To quantify the uncertainty, probabilistic analysis has been adopted. However, for accurate implementation of probabilistic analysis, it is important to have sufficient data for an evaluation of statistical parameters of random variables. Probabilistic landslide analysis for a regional area is associated with difficulties because of limited data. The bootstrap method, which was adopted in this study, is known to be effective in dealing with uncertainty caused by insufficient data. The bootstrap method combined with the point estimate method (PEM) was proposed to overcome the limitations of previous bootstrap methods, the results of which did not provide a single value of failure probability. The proposed method was applied to a practical case, and the probabilistic approach using Monte Carlo (MC) simulation was also applied for comparison. The analysis showed that the performance of the bootstrap–PEM method was superior to that of the MC simulation. In addition, by comparing analysis results obtained with and without correlated variables, this study found that the cross-correlation between cohesion and the friction angle affects the analysis results. Therefore, the proposed approach based on the bootstrap sampling method that can readily evaluate and handle the cross-correlation presents an advantage over probabilistic analysis in that cross-correlation between input parameters can be involved in physically based susceptibility analysis.

The scope of this study is the optimal siting and sizing of distributed generation within a power distribution network considering uncertainties. A probabilistic power flow (PPF)-embedded genetic algorithm (GA)-based approach is proposed in order to solve the optimisation problem that is modelled mathematically under a chance constrained programming framework. Point estimate method (PEM) is proposed for the solution of the involved PPF problem. The uncertainties considered include: (i) the future load growth in the power distribution system, (ii) the wind generation, (iii) the output power of photovoltaics, (iv) the fuel costs and (v) the electricity prices. Based on some candidate schemes of different distributed generation types and sizes, placed on specific candidate buses of the network, GA is applied in order to find the optimal plan. The proposed GA with embedded PEM (GA–PEM) is applied on the IEEE 33-bus network by considering several scenarios and is compared with the method of GA with embedded Monte Carlo simulation (GA–MCS). The main conclusions of this comparison are: (i) the proposed GA–PEM is seven times faster than GA–MCS, and (ii) both methods provide almost identical results.

The increasing penetration of photovoltaic distributed generation (PV-DG) in Radial Distribution Systems (RDSs) plays a vital role in achieving sustainable energy transition objectives; however, the inherent uncertainty associated with solar irradiance and load demand poses significant challenges to optimal planning and operation. This paper presents a stochastic optimization framework for PV-DG allocation in RDSs using the Barrel Theory-Based Optimizer (BTO). Uncertainties in solar irradiance and load demand are explicitly modeled using appropriate probability density functions and efficiently represented through a higher-order Point Estimate Method (PEM), which captures the essential statistical characteristics with a limited number of representative scenarios. The proposed framework simultaneously optimizes the location and capacity of PV-DG units to minimize real power losses and enhance voltage profile performance while ensuring system operational constraints are satisfied. The effectiveness of the proposed approach is validated on the 85-bus and the IEEE 118-bus RDSs, where the BTO exhibits superior convergence characteristics and enhanced solution robustness when compared with several benchmark optimization techniques, including the well-established Differential Evolution Algorithm (DEA), the recent Crocodile Ambush Optimization (CAO, 2025), and the Schrödinger Optimizer Algorithm (SOA, 2025). For the 85-bus RDS, the impact of integrating different numbers of PV units is systematically investigated. Simulation results confirm that the proposed BTO-based stochastic planning strategy significantly improves energy efficiency, voltage regulation, and loss reduction, thereby enhancing the overall sustainability of the RDS. For the 85-node RDS, the BTO achieves a noticeable reduction in average real power losses, outperforming DEA, CAO, and SOA by 2.55%, 4.10%, and 6.74%, respectively, when three PV units are installed. Additionally, for the case of four PV units, the proposed BTO yields even greater improvements, with loss reductions of 5.12%, 7.50%, and 14.12%, respectively, compared with the same benchmark algorithms. Furthermore, for five PV units, the BTO achieves much greater reduction, outperforming DEA, CAO, and SOA by 13.05%, 6.45%, and 32.31%, respectively, when three PV units are installed.

Country participation in one-state, one-vote forums like the United Nations General Assembly often reflects underlying power asymmetries and endogenous political processes. Voting alignment is undoubtedly an important preference indicator. However, this paper contends that it is incomplete; silence is politically significant as well. Weak states use absence as a form of institutional power that shields them from geopolitical pressure and competing-principals problems. While abstention is a public signal of neutrality that undercuts voting unanimity, the ambiguous intent of absence makes it a distinct form of political expression. We examine the politics of absences at the General Assembly, highlighting how states may be strategically absent from select votes for political reasons. Building on the Bailey et al. Journal of Conflict Resolution, 61(2), 430–456, 2017 roll-call voting data, we distinguish strategic absences from other types of absence and provide evidence that such behavior is linked to US interests and competing-principals problems. Taking these non-random reasons for missingness into account provides a fuller picture of how weak states engage with international institutions and highlights how silence can be a consequence of larger political processes.

We use data from the Survey of Professional Forecasters (SPF) to compare point predictions of gross domestic product (GDP) growth and inflation with the subjective probability distributions held by forecasters. We find that most SPF point predictions are quite close to the central tendencies of forecasters subjective distributions tend to be asymmetric, with SPF forecasters tending to report point predictions that give a more favorable view of the economy than do their subjective means/medians/modes.

Large-scale integration of inverter-based renewables is displacing synchronous machine generation, causing a reduction in the inertia of electrical power systems. This reduction is reflected in an increase in the rate of change of frequency (RoCoF). Additionally, the variation of the RoCoF will depend on the uncertainty associated with the generation of non-conventional renewable energy sources. For the planning of the operation of the system, it is essential to know the range of variation of the RoCoF when there are disturbances in the system and uncertainties in the generation of non-conventional sources of renewable energy. This paper proposes to establish the calculation of a confidence interval of the RoCoF variation that considers these uncertainties. So, this paper proposes a method to consider these uncertainties based on the probabilistic point estimate method (PEM); considering multiple renewable non-conventional sources with correlated or uncorrelated behavior in their powers injected into the system. On the other hand, as there are different proposals to calculate the RoCoF, this paper presents the application of the uncertainty model with three different RoCoF proposed calculation methods.

A microgrid energy management system (EMS) with several generation and storage units is crucial in attaining stable and reliable operation. Optimal scheduling of energy resources in EMS becomes arduous due to uncertainty in the forecasting of intermittent renewable sources, electricity pricing, and load demand. However, with the demand response (DR) approaches the operational benefits in the EMS framework can be maximized. In order to improve the cost-effectiveness of the microgrid, a novel day-ahead energy management strategy is proposed for optimal energy allocation of the distributed generators with environmental consideration. An incentive load control-based demand response program is developed to improve the operational results. The forecasting uncertainties are handled using probability-based Hong’s 2 m approximation method. The suggested approach uses a metaheuristic genetic algorithm (GA) to solve the constrained convex problem in determining optimal load shifting. Incentive pricing is developed to adapt to the demand shifting for the benefit of the customers and utility operators. Two case studies with grid-connected and islanded modes are studied to assess the strategy. Results indicate that the proposed technique reduces the overall cost fitness by 12.28% and 18.91% in the two cases, respectively. The consistency in operational parameters with popular methods confirms the effectiveness and robustness of the method for day-ahead energy management.

Extensive high-speed railway (HSR) network resembled the intricate vascular system of the human body, crisscrossing mainlands. Seismic events, known for their unpredictability, pose a significant threat to both trains and bridges, given the HSR’s extended operational duration. Therefore, ensuring the running safety of train-bridge coupled (TBC) system, primarily composed of simply supported beam bridges, is paramount. Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently. Instead, efficient algorithm like the new point estimate method combined with moment expansion approximation (NPEM-MEA) is applied to study random responses of numerical simulation TBC systems. Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method. Comparative analysis confirms the accuracy and efficiency of the method, with a recommended truncation order of four to six for the NPEM-MEA. Additionally, the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system. This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.