Flexible Distribution Research Articles

A novel extension of generalized Rayleigh model with engineering applications

In this study, we introduce a new flexible distribution constructed by a modification to the Rayleigh distribution and we referred it as unit generalized Rayleigh distribution (UGRD). Varied statistical properties were established, such as reliability, hazard rate, survival rate, moments, quantiles, ordered statistics, etc. The maximum likelihood estimation method is applied to estimate the parameters of the proposed model and different entropy measures including: Rényi entropy, Shannon entropy, Havrda and Charvat entropy, Tsallis entropy, Arimoto entropy, and Mathai–Haubold entropy are provided. The effectiveness of the proposed entropy estimators have been conducted through Monte Carlo (MC) simulation experiments regarding average estimate, average bias, mean square error, and mean relative errors compared to the simple random sample. Finally, we illustrated two real engineering data sets to assess the potential of the proposed UGRD among some existing models.

Multi-objective teaching–learning-based optimization algorithm for carbon-efficient integrated scheduling of distributed production and distribution considering shared transportation resource

Being “carbon efficient” is always one of the missions for suppliers to stay competitive. Production and distribution are the core sections of the supply chain, and integrated scheduling of production and distribution has received increasing research interest because of its great potential to enhance operational performance. Distributed production has gained popularity in recent years. However, distribution strategies compatible with distributed production have not been considered. In this paper, we investigated carbon-efficient integrated scheduling of distributed production and distribution considering shared transportation resource. Particularly, the shared transportation resource strategy, which allows vehicles to serve customers from various depots, enables a more flexible distribution than the traditional method. A bi-objective model is constructed to minimize total carbon emission and completion time simultaneously. To address the computational challenge, an enhanced multi-objective teaching–learning-based optimization (EMTLBO) algorithm is proposed. In EMTLBO, several heuristic rules are introduced to obtain high-quality initial solutions and neighborhood structures are designed for efficient neighborhood search. The comprehensive experiments have demonstrated that (1) the proposed enhancement strategies are effective, (2) the overall performance of EMTLBO is superior to seven well-known algorithms in solving this problem, and (3) the shared transportation resource strategy considerably reduces carbon emission during distribution stage, leading to average decreasing of 41.0 %, 70.6 %, and 41.5% for the instance sets. This work presents significance in promoting a clean and efficient modern supply chain.

Two-Stage Robust Optimal Scheduling of Flexible Distribution Networks Based on Pairwise Convex Hull

With distributed generation (DG) being continuously connected into distribution networks, the stochastic and fluctuating nature of its power generation brings ever more problems than before, such as increasing operating costs and frequent voltage violations. However, existing robust scheduling methods of flexible resources tend to make rather conservative decisions, resulting in high operation costs. In view of this, a two-stage robust optimal scheduling method for flexible distribution networks is proposed in this paper, based on the pairwise convex hull (PWCH) uncertainty set. A two-stage robust scheduling model is first formulated considering coordination among on-load tap changers, energy storage systems and flexible distribution switches. In the first stage, the temporal correlated OLTCs and energy storage systems are globally scheduled using day-ahead forecasted DG outputs. In the second stage, FDSs are scheduled in real time in each time period based on the first-stage decisions and accurate short-term forecasted DG outputs. The spatial correlation and uncertainties of the outputs of multiple DGs are modeled based on the PWCH, such that the decision conservativeness can be reduced by cutting regions in the box with low probability of occurrence. The improved column-and-constraint generation algorithm is then used to solve the robust optimization model. Through alternating iterations of auxiliary variables and dual variables, the nonconvex bilinear terms induced by the PWCH are eliminated, and the subproblem is significantly accelerated. Test results on the 33-bus distribution system and a realistic 104-bus distribution system validate that the proposed PWCH-based method can obtain much less conservative scheduling schemes than using the box uncertainty set.

Consumption inequality between farm and non-farm households in rural Vietnam

PurposeThis study aims to analyse the consumption inequality between farm and non-farm households in rural Vietnam, using the data from the 2016 Vietnam household living standards survey.Design/methodology/approachThe present paper applies the “recentered influence functions (RIF)” in “Oaxaca-Blinder (OB)” type decomposition as proposed by Firpo et al. (2018) to allow for the flexible distribution of the outcome variables and the non-randomness of non-farm employment that violates the classical linearity assumption.FindingsNon-farm households have significantly higher per capita consumption expenditure than farm households for the entire distribution. The gap in expenditure is large at low percentiles and narrowing with higher percentiles. At 10th percentile, the gap is estimated at 27.1%, but it is decreasing to 11.1% at 90th percentile. Most of the gaps are explained by the differences in the observed characteristics between farm and non-farm households such as ethnicity, education, income, internal transmittances and household composition. Non-farm households are endowed with more productive factors that result in higher per capita consumption expenditure.Originality/valueGaps in ethnicity and education are found to be key predictors of the inequality in consumption expenditures between farm and non-farm households, then, government policies that are aimed at increasing access to non-farm employment and education for ethnic minorities and for rural poor households are pathways to improve rural household welfare and hence reduce inequality.

Modelling the Wind Speed Using Exponentiated Weibull Distribution: Case Study of Poprad-Tatry, Slovakia

In the paper, we statistically analysed data on the average hourly wind speed obtained from the meteorological station Poprad (located at the Poprad-Tatry airport, the Prešov region, Northern Slovakia) for the period 2005–2021. High altitude and rough mountainous terrain influence the weather conditions considerably and are a source of occasional weather risks. Finding an appropriate wind speed distribution for modelling the wind speed data is therefore important to determine the wind profile at this particular location. In addition to the commonly used two- and three-parameter Weibull distribution, a more flexible exponentiated Weibull (EW) distribution was applied to model the wind speed. Based on the results of the goodness-of-fit criteria (the Kolmogorov–Smirnov test, the Anderson–Darling test, Akaike’s and Bayesian information criteria, the root mean square error, and the coefficient of determination), the EW distribution obtained a significantly better fit to seasonal and monthly wind speed data, especially around the peaks of the data. The EW distribution also proved to be a good model for data with high positive skewness. Therefore, we can recommend the EW distribution as a flexible distribution for modelling a dataset with extremely strong winds or outliers in the direction of the right tail. Alongside the wind speed analysis, we also provided the wind direction analysis, finding out that the most prevailing direction was west (W)—with an occurrence rate of 34.99%, and a mean wind speed of 3.91 m/s, whereas the northern (N) direction featured the lowest occurrence rate of only 4.45% and the mean wind speed of 1.99 m/s.

Analysis of Pre- and during COVID-19 Mixed Load Models on Unbalanced Radial Distribution System Using a New Metaphor-Less Rao Optimization

An unbalanced electrical distribution system (DS) with radial construction and passive nature suffers from significant power loss. The unstable load demand and poor voltage profile resulted from insufficient reactive power in the DS. This research implements a unique Rao algorithm without metaphors for the optimal allocation of multiple distributed generation (DG) and distribution static compensators (DSTATCOM). For the appropriate sizing and placement of the device, the active power loss, reactive power loss, minimum value of voltage, and voltage stability index are evaluated as a multiobjective optimization to assess the device’s impact on the 25-bus unbalanced radial distribution system. Various load models, including residential, commercial, industrial, battery charging, and other dispersed loads, were integrated to develop a mixed load model for examining electrical distribution systems. The impact of unpredictable loading conditions resulting from the COVID-19 pandemic lockdown on DS is examined. The investigation studied the role of DG and DSTATCOM (DGDST) penetration in the electrical distribution system for variations in different load types and demand oscillations under the critical emergency conditions of COVID-19. The simulation results produced for the mixed load model during the COVID-19 scenario demonstrate the proposed method’s efficacy with distinct cases of DG and DSTATCOM allocation by lowering power loss with an enhanced voltage profile to create a robust and flexible distribution network.

A new flexible distribution with applications to engineering data

In this work, we presented a new model called the alpha power inverse power Burr-Hatke distribution (APIPBHD). It provides several greater advantages in fitting a variety of different types of data. Estimates of the model parameters are provided and based on traditional research methods. We established the superiority of the proposed distribution by utilizing the importance and adaptability of the APIPBHD compared to other well-known distributions. The real data set includes 63 observations, all of which were manufactured to approximate the strengths of glass fibers to highlight the relevance and flexibility of the provided technique. We proved our superiority using one set of real data. Finally, major findings and conclusions are recorded at the end of the paper. Also, we added future work on the upcoming research depending on the proposed model.

Feasibility analysis of PV and energy storage system integration for flexible distribution networks: A moment-based distributionally robust approach

With the requirements of carbon neutrality and scientific and technological progress, massive distributed renewable energy resources have been integrated in distribution networks. The flexible interconnected distribution networks (FDNs) provide an effective way to avoid the negative effects of power quality, network loss and relay protection. This paper proposes a feasibility analysis model of distributed photovoltaic power generations (PVs) integration for FDNs based on distributionally robust. It uses moment-based ambiguity sets to model the uncertainty of PV outputs. Based on the circular constraint linearization method and duality theory, the solution method of the above model is designed. In this paper, two typical FDN structures are considered, namely, the closed-loop flexible interconnected structure between feeders and the flexible interconnected structure between feeder loops. The hosting capacity of the PV and energy storage system of the two structures is analyzed in case study, and the effectiveness of the proposed model and method is verified.

Ensemble Multi-Quantiles: Adaptively Flexible Distribution Prediction for Uncertainty Quantification.

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of [Formula: see text] in regression tasks. This conditional distribution's quantiles of probability levels spreading the interval (0,1) are boosted by additive models which are designed by us with intuitions and interpretability. We seek an adaptive balance between the structural integrity and the flexibility for [Formula: see text], while Gaussian assumption results in a lack of flexibility for real data and highly flexible approaches (e.g., estimating the quantiles separately without a distribution structure) inevitably have drawbacks and may not lead to good generalization. This ensemble multi-quantiles approach called EMQ proposed by us is totally data-driven, and can gradually depart from Gaussian and discover the optimal conditional distribution in the boosting. On extensive regression tasks from UCI datasets, we show that EMQ achieves state-of-the-art performance comparing to many recent uncertainty quantification methods. Visualization results further illustrate the necessity and the merits of such an ensemble model.

Financing Russia's transport infrastructure using public-private partnership facilities: Current challenges and prospects

Subject. This article examines the main ways and legal forms of implementation of transport infrastructure projects in the Russian Federation, the challenges associated with financing, and the prospects for the development of the public-private partnership (PPP) mechanism when implementing transport projects. Objectives. The article aims to substantiate the effectiveness of the use of PPP mechanisms when implementing transport infrastructure projects in Russia to ensure the long-term development of the country. Methods. For the study, I used analysis and synthesis, deduction and induction, statistical and graphical analyses, and comparison. Results. The article assesses the role of PPP facilities in project financing to encourage the inflow of investments in the field of transport infrastructure and determines the main organizational and legal framework for the implementation of transport projects. Conclusions. The State's participation in project financing through PPP mechanisms when implementing transport infrastructure projects in Russia can help improve the attractiveness of long-term projects with high capital expenditures due to a more efficient and flexible distribution of risks and responsibilities among the key partners, and it also contributes to the achievement of national transport objectives significantly.

Air pollution and coronary heart disease-related hospital visits in Beijing, China: time-series analysis using a generalized additive model.

To investigate correlations between environmental and meteorological factors and frequency of presentation for coronary heart disease (CHD) in Beijing. Daily measurements of levels of six atmospheric pollutants were made, data relating to meteorological conditions collected, and CHD-related outpatient visits recorded from January 2015 to December 2019 in Beijing. A time-series analysis was made, using a generalized additive model with Poisson distribution, and R 3.6.3 software was used to estimate relationships among levels of atmospheric pollutants, ambient temperature, and visits occasioned by CHD. Results were controlled for time-dependent trend, other weather variables, day of the week, and holiday effects. Lag-response curves were plotted for specific and incremental cumulative effects of relative risk (RR). The aim was to correlate meteorological-environmental factors and the daily number of CHD-related hospital visits and to quantify the degree of correlation to identify any pathological associations. Response diagrams and three-dimensional diagrams of predicted exposure lag effects were constructed in order to evaluate relationships among the parameters of air pollution, temperature, and daily CHD visits. The fitted model was employed to predict the lag RR and 95% confidence interval (95% CI) for specific and incremental cumulative effects of random air pollutants at random concentrations. This model may then be used to predict effects on the outcome variable at any concentration of any defined pollutant, giving flexibility for public health purposes. The overall lag-response RR curves for the specific cumulative effects of the pollutants, particulate matter (PM)2.5, PM10, SO2, CO, and NO2, were statistically significant and for PM2.5, PM10, CO, and NO2, the overall lag-response RR curves for the incremental cumulative effect were statistically significant. When PM2.5, PM10, SO2, CO, and NO2 concentrations were above threshold values and the temperature was below 45 °F (reference value 70 °F), the number of CHD-related hospital visits increased with a time lag effect. The outpatient volume of CHD was predicted by the model to guide the flexible distribution of medical resources. Elevated PM2.5, PM10, SO2, CO, and NO2 concentrations in the atmosphere combined and low ambient temperature increased the risk of CHD with a time lag effect.

Modeling and analysis of recovery time for the COVID-19 patients: a Bayesian approach

The ongoing pandemic of COVID-19 has changed every aspect of life. Most of the people who become a victim of COVID-19 experience mild to moderate symptoms, but some people may become seriously ill. This illness, sometimes, may lead to a very painful death. The Fréchet distribution is one of the flexible distribution for survival time. Hence, in this article, the recovery time of COVID-19 patients is modeled by a new Fréchet-exponential (FE) distribution, and the parameters of the distribution are estimated in the classical and Bayesian paradigms. Since the Bayes estimators using informative priors are not in the closed form, the Lindley and Tierney–Kadane approximation methods are used for their evaluation. The results obtained through simulation studies and the COVID-19 data set assess the superiority of the Bayes estimators over the classical estimators in terms of minimum risks. Mathematically and graphically, it is shown that our proposed model appropriately fits the data set. The minimum values of Akaike information criterion, Bayesian information criterion, corrected Akaike information criterion, and Hannan-Quinn information criterion proves that the FE distribution better fit than the competitors’ distribution for the data set about the recovery time of COVID-19 patients.

Risk-based joint flexible distribution network expansion planning and allocation of EV parking lots

Risk-based joint flexible distribution network expansion planning and allocation of EV parking lots

A New Extension of Generalized Extreme Value Distribution: Extreme Value Analysis and Return Level Estimation of the Rainfall Data

This paper presents an extension of the generalized extreme value (GEV) distribution, based on the T-X family of distributions: Gompertz-generated family of distributions that make the existing distribution more flexible called the Gompertz-general extreme value (Go-GEV) distribution. Some properties of the proposed distribution are introduced, and a new distribution is applied to actual data, namely rainfall in Lopburi Province, by comparing the proposed model with the traditional GEV distribution and estimating the return levels of the rainfall in Lopburi Province. Results showed that the Go-GEV was an alternative flexible distribution for extreme values that fitted with actual data and described the maximum rainfall better than the traditional GEV distribution. The probability density functions of the Go-GEV distribution had various shapes including left-skewed, right-skewed and close to symmetric. Estimation of the return levels of rainfall values in Lopburi Province by the Go-GEV distribution indicated that Buachum Station should be monitored because it had higher precipitation and return levels than Lopburi Station at 2, 5, 10 and 15 years. HIGHLIGHTS The analysis of data with extreme values is complex but ignoring an observation just because it is unacceptable is not best practice. One of the widely used tools in such situations is “Extreme Value Theory” The Gompertz-generalized extreme value (Go-GEV) distribution is a new extension of GEV distribution using deffinition of Gompertz-generalized family of distributions The developed Go-GEV model described the maximum rainfall data better than the GEV distribution because the new extension distribution was more flexible and its probability density function had a more diverse shape, such as both left-skewed, right-skewed and close to symmetrical The developed Go-GEV model is a flexible alternative for applying the model to extreme value data GRAPHICAL ABSTRACT

Updates in SASfit for fitting analytical expressions and numerical models to small-angle scattering patterns.

Small-angle scattering is an increasingly common method for characterizing particle ensembles in a wide variety of sample types and for diverse areas of application. SASfit has been one of the most comprehensive and flexible curve-fitting programs for decades, with many specialized tools for various fields. Here, a selection of enhancements and additions to the SASfit program are presented that may be of great benefit to interested and advanced users alike: (a) further development of the technical basis of the program, such as new numerical algorithms currently in use, a continuous integration practice for automated building and packaging of the software, and upgrades on the plug-in system for easier adoption by third-party developers; (b) a selection of new form factors for anisotropic scattering patterns and updates to existing form factors to account for multiple scattering effects; (c) a new type of a very flexible distribution called metalog [Keelin (2016). Decis. Anal. 13, 243-277], and regularization techniques such as the expectation-maximization method [Dempster et al. (1977). J. R. Stat. Soc. Ser. B (Methodological), 39, 1-22; Richardson (1972) J. Opt. Soc. Am. 62, 55; Lucy (1974). Astron. J. 79, 745; Lucy (1994). Astron. Astrophys. 289, 983-994], which is compared with fits of analytical size distributions via the non-linear least-squares method; and (d) new structure factors, especially for ordered nano- and meso-scaled material systems, as well as the Ornstein-Zernike solver for numerical determination of particle interactions and the resulting structure factor when no analytical solution is available, with the aim of incorporating its effects into the small-angle scattering intensity model used for fitting with SASfit.

A Bayesian-Weighted Inverse Gaussian Regression Model with Application to Seismological Data

Developing an efficient model for analyzing right-skewed positive observations has a long history, and many authors have attempt in this direction. This is because the common analytic modeling procedures such as linear regression are often inappropriate for such data and leads to inadequate results. In this article, we proposed a new model for regression analysis of the right-skewed data by assuming the weighted inverse Gaussian, as a great flexible distribution, for response observations. In the proposed model, the complementary reciprocal of the location parameter of response variable is considered to be a linear function of the explanatory variables. We developed a fully Bayesian framework to infer about the model parameters based on a general noninformative prior structure and employed a Gibbs sampler to derive the posterior inferences by using the Markov chain Monte Carlo methods. A comparative simulation study is worked out to assess and compare the proposed model with other usual competitor models, and it is observed that efficiency is quite satisfactory. A real seismological data set is also analyzed to explain the applicability of the proposed Bayesian model and to access its performance. The results indicate to the more accuracy of proposed regression model in estimation of model parameters and prediction of future observations in comparison to its usual competitors in literature. Particularly, the relative prediction efficiency of the proposed regression model to the inverse Gaussian and log-normal regression models has been obtained to be 1.16 and 64, respectively, for the real-world example discussed in this paper.

Dynamic modeling and coupling characteristics analysis of biomass power plant integrated with carbon capture process

Biomass direct-fired circulating fluidized bed boiler has distinguished advantages of strong fuel adaptability, high combustion efficiency and low NOX emission, thus has been regarded as one of the important pathways for biomass utilization. Retrofitting the biomass direct-fired circulating fluidized bed boiler power plant (BCFBP) with carbon capture can strongly support the goal of carbon neutrality, because negative CO2 emission is achieved during the power generation. Nevertheless, the biomass direct-fired circulating fluidized bed boiler is sensitive to the combustion condition, high in operating costs, slow in dynamic response and poor in regulating capability. The integration of carbon capture may pose significant changes on the operating safety, efficiency and flexibility. A comprehensive analysis is thus required to understand the interactions between the BCFBP and carbon capture under various operating conditions. To this end, this paper develops a plant-wide dynamic model for a 130 ton/h BCFBP integrated with solvent-based post-combustion carbon capture (PCC) system. Multi-stage models of biomass combustion, steam generation and steam turbine-feedwater heater systems are developed to represent the dynamic interactions among biomass, heat, electricity and carbon, so that the impacts of BCFBP operation on the PCC process can be evaluated. Detailed BCFBP-PCC connecting system model are also developed to reflect the dynamic changes of steam/water flowrate, pressure and temperature in the steam turbine system caused by the integration of PCC. The developed model is then used to analyze the system interactions, operating costs, negative carbon capability and load ramping flexibility of the integrated BCFBP-PCC. Results show that the integration of PCC 1) causes significant impacts on the water/steam parameters of the steam turbine-feedwater heaters behind the reboiler steam extraction point; 2) reduces the power output of BCFBP by 26.12 % under 95 % CO2 capture level condition; 3) expands the power output variation range of the BCFBP from 22.3 to 36.6 MWe and provides the negative CO2 emission capacity from 2.2 to 6.9 kg CO2/s; 4) offers a feasible way to improve the power ramping performance through flexible distribution of the water/steam in the steam turbine-feedwater heater system. This paper provides specific guidance for the design, retrofit and operation of the BCFBP-PCC plant.

A New Modified Exponent Power Alpha Family of Distributions with Applications in Reliability Engineering

Probability distributions perform a very significant role in the field of applied sciences, particularly in the field of reliability engineering. Engineering data sets are either negatively or positively skewed and/or symmetrical. Therefore, a flexible distribution is required that can handle such data sets. In this paper, we propose a new family of lifetime distributions to model the aforementioned data sets. This proposed family is known as a “New Modified Exponent Power Alpha Family of distributions” or in short NMEPA. The proposed family is obtained by applying the well-known T-X approach together with the exponential distribution. A three-parameter-specific sub-model of the proposed method termed a “new Modified Exponent Power Alpha Weibull distribution” (NMEPA-Wei for short), is discussed in detail. The various mathematical properties including hazard rate function, ordinary moments, moment generating function, and order statistics are also discussed. In addition, we adopted the method of maximum likelihood estimation (MLE) for estimating the unknown model parameters. A brief Monte Carlo simulation study is conducted to evaluate the performance of the MLE based on bias and mean square errors. A comprehensive study is also provided to assess the proposed family of distributions by analyzing two real-life data sets from reliability engineering. The analytical goodness of fit measures of the proposed distribution are compared with well-known distributions including (i) APT-Wei (alpha power transformed Weibull), (ii) Ex-Wei (exponentiated-Weibull), (iii) classical two-parameter Weibull, (iv) Mod-Wei (modified Weibull), and (v) Kumar-Wei (Kumaraswamy–Weibull) distributions. The proposed class of distributions is expected to produce many more new distributions for fitting monotonic and non-monotonic data in the field of reliability analysis and survival analysis.

DLMP-Based Quantification and Analysis Method of Operational Flexibility in Flexible Distribution Networks

With high penetration of flexible resources, operational flexibility of flexible distribution networks (FDNs) is important to ensure high-quality electricity services. This paper proposes a value quantification and analysis method for operational flexibility in FDNs based on distribution locational marginal pricing (DLMP). First, flexibility constraints are formulated from the perspective of node integration, branch transfer, and network aggregation of flexibility. Then, a unified analytical framework for quantifying the operational flexibility is established, in which spatial-temporal transfer of flexibility is modeled with the derivation of flexibility sensitivity factors. Further, a DLMP-based flexibility value quantification model is proposed with nodal net power as the unit for flexibility pricing. The obtained flexibility price can not only quantify flexibility value but also be used to guide the flexible resources. Finally, the effectiveness of the proposed method is validated on a modified IEEE 33-node distribution system and a modified IEEE 123-node distribution system. Results verify that the proposed method can quantify the impact of nodal net power on operational flexibility and effectively improve the overall flexibility performance through the guide of flexibility price.

Sine-Exponential Distribution: Its Mathematical Properties and Application to Real Dataset

To increase flexibility or to develop covariate models in various ways, new parameters can be added to existing families of distributions or a new family of distributions can be compounded with well-known standard normal distribution. In this paper, a trigonometric-type distribution was developed in order to come up with flexible distribution without adding parameters, considering Exponential distribution as the baseline distribution and Sine-G as the generator. The proposed distribution is referred to as Sine Exponential Distribution. Statistical features, including the moment, moment generating function, entropy, and order statistics were obtained. The proposed distribution's parameters were estimated using the Maximum Likelihood method. Using real datasets, the model's importance was demonstrated. The newly developed model was proven to be better than its competitors.