Point Estimate Method Research Articles

Probability assessments of identified parameters for stochastic structures using point estimation method

In this paper, a kind of inverse problem for assessing the probabilities of identified parameters with uncertainties in structural parameters and limited experimental results is investigated. The point estimation method and maximum entropy principle are adopted to efficiently evaluate the effect of uncertain parameters on the identified parameters. First, the probability distribution function of each uncertain parameter can be approximately represented by several nodes. Thus, the uncertain inverse problem can be transformed into several deterministic inverse problems through multivariate Taylor expansion and point estimation method. Then, to obtain the moments of identified parameters, the deterministic inverse process for each selected node with concentrated probability are conducted by the genetic algorithm. Finally, the probability distribution functions of the identified parameters can be assessed by the obtained moments based on the maximum entropy principle. The proposed method effectively avoids the low efficiency of uncertain inverse problem, which commonly involves a double-loop procedure with uncertainty propagation and inverse calculation. Numerical examples and the engineering application demonstrate the feasibility and effectiveness of the proposed method.

Two-layer optimization methodology for wind distributed generation planning considering plug-in electric vehicles uncertainty: A flexible active-reactive power approach

With increasing the penetration of wind power, the voltage regulation becomes a more important problem in active distribution networks. In addition, as an uncertain load Plug-in Electric Vehicles (PEVs) will introduce a new concern in voltage adjustment of future distribution networks. Hence, this paper presents a flexible active-reactive power based Wind Distributed Generation (WDG) planning procedure to address the mentioned challenges. The uncertainties related to WDGs, load demand as well as PEVs load have been handled using the Point Estimate Method (PEM). The distribution network under study is equipped to on-load tap-changer and, as a conventional voltage control component, the Capacitor Banks (CBs) will be planned simultaneously with WDGs. The planning procedure has been considered as a two-loop optimization problem that is solved using Particle Swarm Optimization (PSO) and Tabu Search (TS) algorithms. The tap position and power factor of WDGs are taken into account as stochastic variables with practical limitations. The proposed methodology is applied to a typical distribution network and several scenarios are considered and analyzed. Simulation results show that the standard deviation of power factor depends on PEVs penetration that highlights the capability curve of WDGs. The optimal penetration of wind power increases nonlinearly versus increasing of PEVs connected to the distribution network, however the fixed CBs are required to increase the optimal penetration of WDGs. The proposed Modified PSO (MPSO) is compared with the conventional PSO in numerical studies that show MPSO is more efficient than the conventional algorithm for this analysis.

Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems

We perform a comparative analysis using three reduced-order strategies–Missing Point Estimation (MPE) method, Gappy POD method, and Discrete Empirical Interpolation Method (DEIM)–applied to a biological model describing the spatio-temporal dynamics of a predator–prey community. The comparative study is focused on the efficiency of the reduced-order approximations and the complexity reduction of the nonlinear terms. Different variants are discussed related to the projection-based model reduction framework combined with selective spatial sampling to efficiently perform the online computations. Numerical results are presented.

Study of Network Reconfiguration in Distribution Systems Using an Adaptive Modified Firefly Algorithm

This paper suggests a new method based on the probabilistic load flow and Adaptive Modified Firefly Algorithm (AMFA) in order to evaluate the optimal management of the Distribution Feeder Reconfiguration (DFR) operation problems by considering a few Wind Turbines (WTs) in system and performance satisfaction of the proposed method is examined on the IEEE 32-bus standard test system. The significant objective functions in this paper includes: 1) Minimizing the total cost of active power losses in the network, 2) voltage profile improvement, 3) decreasing the present network total costs such as power production cost by the main network and distributed generations. Furthermore, a new stochastic solution based on Point Estimate Method (PEM) is proposed to effectively deal with the uncertainty related to the important random parameters such as active and reactive loads in addition to the wind speed variations. Thus, the suggested probabilistic framework must be considered in order to solve the reconfiguration problem with regard to uncertainties which caused by the wind turbines.

Parzen Window Density Estimator-Based Probabilistic Power Flow With Correlated Uncertainties

This paper presents a numerical-based algorithm to solve the probabilistic power flow problem. Parzen window density estimator is used to efficiently estimate probabilistic characteristics of power flow outputs. Correlations between wind generation, load, and plug-in hybrid electric vehicle charging stations are taken into account. The proposed algorithm works properly for random variables with various probability distribution functions and is very useful when limited information is available for each random variable. The algorithm is tested on the IEEE 14-bus and IEEE 118-bus systems considering correlated and uncorrelated conditions. Comparison between the proposed algorithm with 2n, $\text{2n} + 1$ point estimation methods as well as Monte Carlo simulation and linear diffusion method are provided. In addition, probability density and cumulative distribution functions are determined using the proposed algorithm, diffusion method, and the combined Cumulants and Gram-Charlier for $\text{2n} + 1$ point estimation method. Error indices are introduced to evaluate all random variables in a single benchmark. Simulation results show the effectiveness of the proposed algorithm to provide complete statistical information for probabilistic power flow outputs.

Probabilistic Decision Making for the Bulk Power System Optimal Topology Control

Power system topology control through transmission line switching for economic gains and reliability benefits has been recently considered in day to day operations. This paper introduces a probabilistic formulation for a more efficient application of topology control strategies in real world scenarios with anticipated increase in the presence of highly variable renewable generation and uncertain loads. Such uncertainties are modeled via the point estimation method embedded into the dc optimal power flow-based formulations for optimal switching solutions. Hourly and daily advantages of the proposed probabilistic framework, compared with the conventional operations and deterministic formulations, are discussed. As the anticipated economic gains would increase through sequential implementation of several switching actions, a new probabilistic decision making approach to identify the optimal number of switching actions at each hour is also proposed. This decision support tool uses the probabilistic reliability cost/value analytics in which not only the financial benefits, but also the costs of reliability risks, are taken into account. The approach is tested through various scenarios on the modified IEEE 118-bus test system, with and without renewables integration, and the results revealed its applicability and efficiency.

Pedestrian lane detection in unstructured scenes for assistive navigation

Automatic detection of the pedestrian lane in a scene is an important task in assistive and autonomous navigation. This paper presents a vision-based algorithm for pedestrian lane detection in unstructured scenes, where lanes vary significantly in color, texture, and shape and are not indicated by any painted markers. In the proposed method, a lane appearance model is constructed adaptively from a sample image region, which is identified automatically from the image vanishing point. This paper also introduces a fast and robust vanishing point estimation method based on the color tensor and dominant orientations of color edge pixels. The proposed pedestrian lane detection method is evaluated on a new benchmark dataset that contains images from various indoor and outdoor scenes with different types of unmarked lanes. Experimental results are presented which demonstrate its efficiency and robustness in comparison with several existing methods.

Inference for Type II bivariate Pólya–Aeppli distribution

ABSTRACTIn this article, we discuss the estimation of model parameters of the Type II bivariate Pólya–Aeppli distribution using the method of moments and the maximum likelihood method. We also compare some interval estimation methods. We then carry out a Monte Carlo simulation study to evaluate the performance of the proposed point and interval estimation methods. Finally, we present an example to illustrate all the inferential methods developed here.

Switch and recloser placement in distribution system considering uncertainties in loads, failure rates and repair rates

For maximizing the customer satisfaction and retention, improvement of service reliability is a major concern for electric utilities. Service reliability can be improved by placing switches and reclosers at appropriate locations in the distribution system so that supply from the main substation to the healthy load points can be maintained after isolating the faulted section. This paper presents a formulation for an optimal placement of switches and reclosers in a distribution system for maximizing system reliability while minimizing the associated investment and outage costs considering uncertainties in load data, system failure and repair rates. The uncertainties have been incorporated in the formulation using point estimate method (PEM). The proposed formulation has been tested on 13, 58 and IEEE 123-bus test systems using differential evolution (DE) and mixed integer nonlinear programming (MINLP) method. The obtained results establish the effectiveness of the consideration of data uncertainties in improving the distribution system reliability and maximizing utilities’ profits.

Probabilistic geotechnical analysis of energy piles in granular soils

Energy piles provide clean energy in lieu of non-renewable energy resources such as petroleum and coal. The current geotechnical design of energy piles is merely realized through enlarging the factor of safety. The factor of safety used for energy piles is at least twice that used for traditional piles, which can lead to considerable additional costs and inconsistent levels of safety. Although the performance of existing energy pile technology is satisfactory and recent investigators have significantly advanced the understanding of the load-transfer mechanisms of energy piles, it is still necessary to quantify the uncertainty in the thermal–mechanical analysis and to develop reliability-based designs for energy piles. This paper presents a pioneering probabilistic study on the geotechnical design of energy piles. The critical soil parameters for ultimate limit state (ULS) and serviceability limit state (SLS) are identified through sensitivity study. The point estimate method is adopted to understand the uncertainty propagation and to estimate the probability of ULS failure and the probability of SLS failure. The adverse effects of thermal loading in the geotechnical design of energy piles are explicitly demonstrated through a case study.

Stochastic LMP (Locational marginal price) calculation method in distribution systems to minimize loss and emission based on Shapley value and two-point estimate method

LMP (Locational marginal price) calculation is a serious impediment in distribution operation when private DG (distributed generation) units are connected to the network. A novel policy is developed in this study to guide distribution company (DISCO) to exert its control over the private units when power loss and green-house gases emissions are minimized. LMP at each DG bus is calculated according to the contribution of the DG to the reduced amount of loss and emission. An iterative algorithm which is based on the Shapley value method is proposed to allocate loss and emission reduction. The proposed algorithm will provide a robust state estimation tool for DISCOs in the next step of operation. The state estimation tool provides the decision maker with the ability to exert its control over private DG units when loss and emission are minimized. Also, a stochastic approach based on the PEM (point estimate method) is employed to capture uncertainty in the market price and load demand. The proposed methodology is applied to a realistic distribution network, and efficiency and accuracy of the method are verified.

Probabilistic Power Flow Analysis Based on the Stochastic Response Surface Method

This paper proposes a probabilistic power flow analysis technique based on the stochastic response surface method. The probability distributions and statistics of power flow responses can be accurately and efficiently estimated by the proposed method without using series expansions such as the Gram-Charlier, Cornish-Fisher, or Edgeworth series. The stochastic continuous input variables following normal distributions such as loads or non-normal distributions such as photovoltaic generation and wind power and their multiple correlations can be easily modeled. The correctness, effectiveness and adaptability of the proposed method are demonstrated by comparing the probabilistic power flow analysis results of the IEEE 14-bus and 57-bus standard test systems obtained from the proposed method, the point estimate method, and the Monte Carlo simulation method.

Probabilistic load flow calculation using cumulants and multiple integrals

Probabilistic load flow (PLF) is a powerful and widely used tool to address the random nature of renewable energy resources for the planning and operation of power systems. In this study, a new approach using a combination of the multiple integral method (MIM) and the cumulant method (CM) is proposed for PLF studies. The PLF problem with high dimensionality is decomposed into a bi-level problem and solved by MIM and CM to reduce the computational burden significantly while achieving satisfactory accuracy. The proposed method is applied to the IEEE 118-bus system and is compared with CM and point estimate method. Simulation results show that the proposed method achieves great computational efficiency and accuracy.

A variance change point estimation method based on intelligent ensemble model for quality fluctuation analysis

For multivariable production process, knowing the first time of process really changes (change point) will help to accelerate the location of assignable causes and make measures for process adjustment. So effective estimating the change point is an important way to analyse the quality fluctuation of process. In the present study, an intelligent ensemble model for quality fluctuation analysis is proposed to estimate the variance change point in multivariable process. With the method, the process is decomposed based on moving window analysis, then different types of kernel functions are combined together to form the multi-kernel support vector machine model, which has combined the feature mapping capability of each basic kernel in the new feature space. The particle swarm optimisation is considered to search the optimised multi-kernel parameters. After that, each sub-characteristic is regarded as a pattern to be recognised to determine the change point by using the optimised intelligent ensemble model. Finally, a case study is conducted to evaluate the performance of proposed approach. It reveals that the method could estimate the time of variance change point in continuous production process accurately.

Probabilistic congestion management using EVs in a smart grid with intermittent renewable generation

This paper presents a probabilistic model to reduce the probability of line congestions and voltage violations in a smart grid located in a radial distribution network. Renewable distributed resources and a high penetration of Electric Vehicles (EVs) are considered. The uncertain parameters taken into account are: power demand, power generated by wind and solar photovoltaic generators, and the behavior of the EVs that do not participate in the congestion procedure. A probabilistic power flow based on the point estimate method is firstly used to compute the distribution functions of the line flows and node voltages. Next, a congestion management strategy is proposed in order to keep the line flows and node voltages within the appropriate range at a given confidence level. The strategy is based on the sensitivity distribution factors: Power Transfer Distribution Factors (PTDFs) and Voltage Distribution Factors (VDFs). The control variables to carry out the corrective actions are the active and reactive power injections from a subset of EVs or their charging points. It is assumed that these controlled EVs are able to inject power into the network using Vehicle to Grid (V2G) capabilities. To illustrate the method, a distribution grid based on a modified version of the IEEE-37 Node Test Feeder is tested.

Method for Calculating Point Estimates and Standard Errors for Meta‐Analysis from Reported Point Estimates, 95% Confidence Intervals, and P‐Values

BackgroundThe quality of a meta‐analysis depends on accurate estimates from original publications. Existing back‐calculation methods for point estimates [e.g., odds ratios (ORs), log(ORs), or means] and standard errors (SEs) from reported point estimates and 95% confidence intervals (CIs) can create estimates that, when forward‐calculated, do not round to the originally reported values. This can be particularly true for ORs. A new method is proposed that incorporates information from the upper and lower CIs and point estimates, with examples of data encountered in a meta‐analysis of the associations between quick service restaurant foods and obesity.MethodsLog(ORs) and SEs are calculated using one of four methods: using the lower CI and the OR; the upper CI and the OR; the average SE from SEs calculated from the lower and upper CIs; and a new method that proposes to use the centroid of a region of values that satisfies the originally reported, rounded OR and CI (herein referred to as the Centroid Method). The methods are compared by simulating 10,000 2×2 tables, rounding the true OR and CI to 1 or 2 decimal places, and calculating the residuals between the log(OR) and SE determined through the four methods compared to the true log(OR) and SE. Extensions of the method are demonstrated for continuous data and under different distributional assumptions. The methods are compared using real examples from data extracted for a meta‐analysis of the associations between quick service restaurants and obesity.ResultsAll methods appear unbiased, but the proposed Centroid Method results in log(ORs) and SEs that deviate less from the simulated true log(ORs) and SEs. The improvement in estimates drops precipitously as the number of decimal places reported for ORs and CIs increases. The method can successfully restrict the region of possible values based on z or t distributional assumptions for the back‐calculation of CIs, and can further restrict the legal region by including reported p‐values. The Centroid Method allows for valid estimates of point estimates where the other methods failed, such as the case where a study reported an OR and 95% CI of 1.3 [1.1,1.7].ConclusionsThe proposed Centroid Method provides tighter estimates of log ORs and SEs for meta‐analyzing data reported as odds ratios with 95% confidence intervals; provides valid estimates where other methods fail; and can be used with different distributional assumptions and data types.Support or Funding InformationAWB was supported in part by NIDDK grant P30 DK056336. JAD was supported by startup funds provided by Texas Tech University through his department (Nutritional Sciences, College of Human Sciences) and the President Cluster Hire in Biostatistics and Bioinformatics (Center for Biotechnology and Genomics). The content is solely the responsibility of the authors and does not necessarily represent the official views of any organization.

Probabilistic load flow with detailed wind generator models considering correlated wind generation and correlated loads

The enhancement in the penetration of intermittent generation necessitates the need to include uncertain behaviour in the conventional power flow programs. In this paper, four different wind generation models have been incorporated in probabilistic load flow for calculating the probability distribution of the reactive power consumed by the wind generators for three different scenarios; i) uncorrelated wind and uncorrelated loads ii) uncorrelated wind and correlated loads and iii) correlated wind and correlated loads The above mentioned scenarios have been implemented in probabilistic load flow using point estimate method in the IEEE-118 bus test system and accuracy of the results have been validated by comparing these results with those obtained by Monte Carlo simulation studies.

Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties

Increasing penetration of wind power in power systems causes difficulties in system planning due to the uncertainty and non dispatchability of the wind power. The important issue, in addition to uncertain nature of the wind speed, is that the wind speeds in neighbor locations are not independent and are in contrast, highly correlated. For accurate planning, it is necessary to consider this correlation in optimization planning of the power system. With respect to this point, this paper presents a probabilistic multi-objective optimal power flow (MO-OPF) considering the correlation in wind speed and the load. This paper utilizes a point estimate method (PEM) which uses Nataf transformation. In reality, the joint probability density function (PDF) of wind speed related to different places is not available but marginal PDF and the correlation matrix is available in most cases, which satisfy the service condition of Nataf transformation. In this paper biogeography based optimization (BBO) algorithm, which is a powerful optimization algorithm in solving problems including both continuous and discrete variables, is utilized in order to solve probabilistic MO-OPF problem. In order to demonstrate performance of the method, IEEE 30-bus standard test case with integration of two wind farms is examined. Then the obtained results are compared with the Monte Carlo simulation (MCS) results. The comparison indicates high accuracy of the proposed method.

Day-ahead resource scheduling of a renewable energy based virtual power plant

The evolution of energy markets is accelerating in the direction of a greater reliance upon distributed energy resources (DERs). To manage this increasing two-way complexity, virtual power plants (VPPs) are being deployed today all over the world. In this paper, a probabilistic model for optimal day ahead scheduling of electrical and thermal energy resources in a VPP is proposed where participation of energy storage systems and demand response programs (DRPs) are also taken into account. In the proposed model, energy and reserve is simultaneously scheduled considering the uncertainties of market prices, electrical demand and intermittent renewable power generation. The Point Estimate Method (PEM) is applied in order to model the uncertainties of VPP’s scheduling problem. Moreover, the optimal reserve scheduling of VPP is presented which efficiently decreases VPP’s risk facing the unexpected fluctuations of uncertain parameters at the power delivery time. The results demonstrated that implementation of demand response programs (DRPs) would decrease total operation costs of VPP as well as its dependency on the upstream network.

Discussion on “Assessment of the application of point estimate methods in the probabilistic stability analysis of slopes” by A. Morteza and P. Rainer [Comput. Geotech. 69 (2015) 540–550

Discussion on “Assessment of the application of point estimate methods in the probabilistic stability analysis of slopes” by A. Morteza and P. Rainer [Comput. Geotech. 69 (2015) 540–550