Point Estimate Method Research Articles

Surrogate-Assisted Multi-Objective Probabilistic Optimal Power Flow for Distribution Network With Photovoltaic Generation and Electric Vehicles

The uncertainties of solar photovoltaics generation, electric vehicle charging demand, and home appliances load are the major challenge of energy management planning in the residential areas. Optimal allocation of battery energy storage systems for distribution networks based on probabilistic power flow (PPF) is an effective solution to deal with these uncertainties. However, the high computational burden is the main obstacle of this method. Therefore, this paper proposes a surrogate-assisted multi-objective probabilistic optimal power flow (POPF) to reduce the expensive computational time. The surrogate model is developed by using a machine learning method namely deep learning which is used for bypassing the deterministic load flow calculation. Zhao’s point estimation method combined with Nataf transformation is selected to handle the PPF analysis considering correlated uncertain input variables. The multi-objective POPF problem is solved using the multi-objective differential evolution. The historical data including solar irradiation, ambient temperature, residential load, and electric vehicle (EV) travel distance is calculated in the low voltage distribution system to demonstrate the potential advantages of the proposed method. Numerical results show that the proposed surrogate assisted multi-objective POPF method provides the optimal solution for operating cost, helps to prolong transformer life and reducing environmental impact. Moreover, the results show that the proposed surrogate-assisted optimization framework gives a better solution when comparing with the conventional surrogate-assisted method.

A Review of Change Point Estimation Methods for Process Monitoring

When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for the different types of changes in the literature. they are: Maximum Likelihood Estimator (MLE), the Cumulative Sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) approaches. This paper gives a synopsis of change point estimation, specifies, categorizes, and evaluates many of the methods that have been recommended for detecting change points in process monitoring. The change points articles in the literature were categorized broadly under five categories, namely: types of process, types of data, types of change, types of phase and methods of estimation. Aside the five broad categories, we also included the parameter involved. Furthermore, the use of control charts and other monitoring tools used to detect abrupt changes in processes were reviewed and the gaps for process monitoring/controlling were examined. A combination of different methods of estimation will be a valuable approach to finding the best estimates of change point models. Further research studies would include assessing the sensitivity of the various change point estimators to deviations in the underlying distributional assumptions.

Probabilistic Load Flow Based on Parameterized Probability-Boxes for Systems With Insufficient Information

The increased penetration of intermittent renewable energy sources and random loads has caused many uncertainties in the power system. It is essential to analyze the effect of these uncertain factors on the behavior of the power system. This study presents a new powerful approach called probability-boxes (p-boxes) to consider these uncertainties by combining interval and probability simultaneously. The proposed method is appropriate for problems with insufficient information. In this paper, the uncertainty of distribution functions is modeled according to the influence of natural factors such as light intensity and wind speed. First, the p-boxes load flow problem is studied using an appropriate point estimation method to calculate statistical moments of probabilistic load flow (PLF) outputs. Then, the Cornish–Fisher expansion series is used to obtain the probability bounds. The proposed approach is analyzed on the IEEE 14-bus, and IEEE 118-bus test systems consist of loads, solar farms, and wind farms as p-boxes input variables. The obtained results are compared with the double-loop sampling (DLS) approach to show the proposed method’s precision and efficiency.

The Polish Practice of Probabilistic Approach in Power System Development Planning

Power systems can be analyzed using either a deterministic or a probabilistic approach. The deterministic analysis centers on studying the quantities and indicators that characterize the operating states of the power system under strictly defined conditions. However, the long-term horizon of planning analyses, the changes of marketing mechanisms, the development of renewable electricity sources, the leaving from large-scale generation, the growth of smart technology and the increase in consumer awareness make the development of transmission networks a non-deterministic problem. In this article, we propose a planning procedure that takes the probabilistic elements into account. This procedure was developed to take into account the high variability of power flows caused by the generation of renewable sources and international exchange. Such conditions of the power system operation forced a departure from deterministic planning. The new probabilistic approach uses the existing tools and experience gained during subsequent development projects. As part of the probabilistic approach, simulations were carried out using the Latin Hypercube Sampling and Two Point Estimation Method algorithms. These methods effectively reduce the computation time and, at the same time, give satisfactory results. The verification was carried out on a test grid model developed in accordance with the technical standards used in the Polish Power System. Effects were assessed using a deterministic and probabilistic approach. This analysis confirmed the practical possibility of using the probabilistic approach in planning the development of transmission network in Poland. When using a probabilistic approach to predict power flow, the criteria of technical acceptability for a given development variant and the manner in which the strategy is determined are of particular importance.

Application of KLE-PEM for Random Dynamic Analysis of Nonlinear Train-Track-Bridge System

A nonlinear train-track-bridge system (TTBS) considering the random track irregularity and mass of train is discussed. Based on the Karhunen–Loéve theory, the track irregularity is expressed and input into the TTBS, and the result of random response is calculated using the point estimation method. Two cases are used to compare and validate the applicability of the proposed method, which show that the proposed method has a high precision and efficiency. Then, taking a 7-span bridge and a high-speed train as an example, the calculation results of random response of the nonlinear and linear wheel-rail model are compared, and the results show that for the bridge and rail response, the nonlinear and linear models are almost the same. Finally, comparing the calculated probability distribution results with the test results, it shows that the method can be applied to the prediction of actual response range.

Allocation of electric vehicle charging station considering uncertainties

Abstract Electric vehicle (EV) is essential to reduce the emission caused by conventional vehicle. Placement of electric vehicle charging station (EVCS) is crucial to fulfilling the charging demand at different locations maintaining the minimum negative impact on the power system network. In this article, placement of EVCS has been planned in a radial distribution network superimposed with a road network. The weightage for different places have been considered as per charging demand which depends on the supermarket, road junctions, residences etc. The objectives are minimization of the energy loss, voltage deviation of the power system network and minimization of the land cost with maximum weightage to serve maximum EV with minimum establishment cost. The area has been divided into three zones to establish an EVCS at each zone to make it distributed. Uncertainties related to EV have been considered in this work using 2m Point Estimation method (2m PEM). The optimization problem has been solved using Differential Evolution (DE) and Harris Hawks Optimization (HHO) techniques.

Distributed generation hosting capacity in electric distribution network in the presence of correlated uncertainties

High penetration of renewable distributed generations is one of the most current challenges of electric distribution networks due to resources uncertainties, and hosting capacity limitation of the networks. The challenges may be more critical when uncertainties are highly correlated. The effect of correlated uncertainties of wind speed and load on the distributed generation hosting capacity of distribution networks is evaluated. A combination of point estimation method, and inverse Nataf transformation is proposed for correlated uncertainties modelling. The efficiency of some ANM schemes on the hosting capacity improvement is also studied in the presence of correlated uncertainties. To do so, an optimisation framework with the objective of maximising the installed capacity of distributed generation subject to network operational constraints such as voltage deviation is proposed. The proposed optimisation problem is formulated in a mixed-integer quadratically constrained program form, and is solved via CPLEX solver. The proposed method is implemented on the 33-bus standard test system. The results demonstrate the significant effect of the correlation between uncertainties on the distributed generation hosting capacity of network.

Probabilistic Steady State Voltage Stability Assessment Method for Correlated Wind Energy and Solar Photovoltaic Integrated Power Systems

Herein, a novel method for the assessment of steady state probabilistic voltage stability margins (PVSMs) in power systems considering generation and load demand uncertainty is investigated. The steady state VSM in an uncertain environment is jointly analyzed through continuous power flow (CPF) and the three point estimation method (3PEM). The statistical distribution of the VSM is obtained using Cornish–Fisher (CF) expansion series. Results are compared with the benchmark Monte Carlo simulation method. Probabilistic models of grid‐connected wind and solar photovoltaic energy sources are utilized in this study. For identification of weak/strong buses and contingency ranking of transmission lines, a steady state voltage stability index, the L‐index, is utilized. The validation of the proposed method is analyzed through IEEE 24 bus and 118 bus test systems. For a realistic study of the system, correlations among wind speeds, solar power outputs, and load demands are considered with various static load models, i.e., constant impedance (CZ), constant current (CI), constant power (CP), and ZIP. Moreover, the concept of relative electrical distance (RED) is applied for selecting the conventional generators for power balancing. The results reveal that factors such as load characteristics and correlations have significant effects on PVSM.

Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew

In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ , hazard rate h(t) and the two measures of reliability, namely R(t) = P(X > t), where X denotes the lifetime of an item and P = P(X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew . We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average confiddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.

Charging Scheduling of Electric Vehicle Incorporating Grid-to-Vehicle and Vehicle-to-Grid Technology Considering in Smart Grid

In recent days, the deployment of electric vehicles (EVs) in automobile sector is increasing the load demand in the distribution system. To deal with this load demand, the charging management needs to be improved. Nevertheless, an EV needs several hours to complete charge. Reducing the charging time, energy consumption is a huge contest to deal with the promotion of EV over conventional vehicles. The condition of the itineraries may affect the energy consumption of the EV, which needs to be considered before fulfilling the energy demand. In this article, these are considered assigning suitable charging stations (CS) to individual EVs and their scheduling is taken as an optimization problem. The first part deals with the proper assignment of CS, which is a linear optimization problem and the second deals with the charging scheduling problem. An “intelligent charging scheduling algorithm (ICSA)” is proposed with the integration of Henry gas solubility optimization to minimize total daily price incurred by the CS operator. Later, ICSA is clubbed with other standard optimization techniques considering practical constraints. A 2 m point estimation method has been utilized to tackle the uncertainty and its performance has been compared with the Monte-Carlo simulation technique. The robustness of ICSA is evaluated and confirmed using the Wilcoxon signed rank test and Quade test.

Intelligent energy management in hybrid microgrids considering tidal, wind, solar and battery

This article addresses the optimal management of hybrid microgrids considering varied types of renewables such as wind, tidal and solar units. The proposed model considers an AC formulation for the AC part and a DC formulation for DC part which can cooperate with each other to reduce the costs and supply the loads in a high-quality and safe zone. Also, a stochastic structure based on a new point estimate method is developed to capture the uncertainties rooting from the forecasting of tidal unit, wind unit and solar unit, market price and total load demand. In contrast to the conventional methods, only a few concentration points of the probability density function fitting uncertain parameters are needed to make a comprehensive modeling of the problem randomness. Due to the nonlinear and complex nature of the problem, an innovative optimization algorithm based on bat algorithm is proposed to solve the problem. Moreover, a modification approach is devised to let the method increase its population variety and make a better search. The fitting performance and high efficacy of the proposed model is inspected on an IEEE test system.

A Practical Method for Rapid Assessment of Reliability in Deep Excavation Projects

Many reliability analysis methods require complicated mathematical process or access to comprehensive datasets. Such shortcomings limit their application to solve the geotechnical problems. It is of advantage to develop simpler reliability analysis methods that can be employed in the design of geotechnical structures. The current study suggests a simple framework for quick reliability analysis of deep excavation projects in urban areas, which is a common geotechnical problem. To investigate the feasibility of the presented method, five case studies were considered. It is worth mentioning that the horizontal displacement at the crest of excavation was set to be the main system response. For verification purposes, the results were compared to the random set, point estimate and Monte Carlo methods results, which are also used for reliability analysis of geotechnical problems. All case studies were recognized as projects of high importance and monitored during the excavation process. The field observations confirmed that the estimated probabilities of excessive deformations were reasonable for all cases. Comparing the modeling results and field measurements suggests the feasibility of the presented method for evaluating the reliability of deep urban excavations and estimating the horizontal displacement at the crest of excavations.

Water Cycle Algorithm for Probabilistic Planning of Renewable Energy Resource, Considering Different Load Models

This work introduces multi-objective water cycle algorithm (MOWCA) to find the accurate location and size of distributed energy resource (DERs) considering different load models for two seasons (winter, and summer). The impact of uncertainties produced from load and renewable energy resource (RES) such as wind turbine (WT) and photovoltaic (PV) on the performance of the radial distribution system (RDS) are covered as this is closer to the real operation condition. The point estimate method (PEM) is applied for modeling the RES uncertainties. An optimization technique is implemented to find the multi-objective optimal allocation of RESs in RDSs considering uncertainty effect. The main objectives of the work are to maximize the technical, economic and environmental benefits by minimizing different objective functions such as the dissipated power, the voltage deviation, DG cost and total emissions. The proposed multi-objective model is solved by using multi-objective water cycle algorithm (MOWCA), considering the Pareto criterion with nonlinear sorting based on fuzzy mechanism. The proposed algorithm is carried out on different IEEE power systems with various cases.

Global Sensitivity Analysis applied to Model Inversion Problems: A Contribution to Rail Condition Monitoring

Rising demands on railroad infrastructure operator by means of profitability and punctuality call for advanced concepts of Prognostics and Health Management. Condition based preventive maintenance aims at strengthening the rail mode of transport through an optimized scheduling of maintenance actions based on the actual and prognosticated infrastructure condition, respectively. When applying model-based algorithms within the framework of Prognostics and Health Management unknown model parameters have to be identified first. Which of these parameters should be known as precisely as possible can be figured out systematically by a sensitivity analysis. A comprehensive global sensitivity analysis, however, might be prohibitive by means of computation load when standard algorithms are implemented. In this study, it is shown how global parameter sensitivities can be calculated efficiently by combining Polynomial Chaos Expansion and Point Estimate Method principles. The proposed framework is demonstrated by a model inversion problem which aims to recalculate the track quality by measurements of the vehicle acceleration, i.e. analyzing the dynamic railway track-vehicle interaction.

Quantification of probabilistic concentrations for mixed-size sediment particles in open channel flow

The Rouse equation is a well-known deterministic model for suspended concentrations. However, the transport of sediment particles is influenced by several random variables, such as non-uniform sediment size and turbulence structure. Experiments have demonstrated that the stochastic characteristics of turbulence structure, such as ejections and sweeps, can cause fluctuations in sediment concentrations. A new method is proposed to quantify the probabilistic sediment concentrations. In this study, the multiple-state discrete-time Markov chain and stochastic particle tracking model were used to simulate sediment transport with spatially and temporally varying probabilistic concentrations under the stochastic turbulence structure. Point estimate methods were adopted to estimate the variability of non-uniform sediment sizes. The proposed model was implemented for three cases. In the first case, the proposed model was validated against the experimental data. In the second case, spatial and temporal concentrations at high and low Rouse numbers with mean and non-uniform sediment sizes were compared. The result demonstrates that in the prediction with mean sediment sizes, the sediment concentration is overestimated near the bed, and the advection of the sediment concentration in the x-direction is underestimated. In the last case, higher-order statistical moments of the fluctuating concentrations were estimated through simulations using the proposed model. Simulation results conducted using the proposed method were compared with experimental data. The results revealed that the prediction results based on the proposed model are in good agreement with experimental data.

Probabilistic Source Localization Based on Time-of-Arrival Measurements

This article was motivated by the need to localize a sensor (signal source) in an Internet-of-Things (IoT) network to an area with a predetermined probability (credibility). The source is assumed to transmit a short time duration (burst) signal in a homogeneous line-of-sight environment. The source's signal is known to an array of spatially separated receivers, which can measure the times of arrival of the source's signal subject to Gaussian measurement errors. The time that the signal leaves the source (i.e., the transmit time) is, however, unknown. The authors develop a method for computing the exact a posteriori probability density functions (pdfs) of the coordinates of the source's in both 2-D and 3-D spaces. The obtained a posteriori pdfs incorporate arbitrary a priori densities, which makes them very useful in many practical scenarios. Unlike existing point-estimate methods, the probabilistic method does not simultaneously solve a set of equations so there is neither a lower nor upper limit on the number of receivers. Various examples are provided to demonstrate the superiority and usefulness of the proposed method. In particular, it is shown that the joint a posteriori pdf of the target's location is not always approximately jointly Gaussian, especially when the target is in close proximity to one of the gateways, or when the gateways are located in close proximity to each other.

Branching on the Bench: Quantifying Division in the Supreme Court with Trees

The popular method of ideal point estimation provides empirical legal scholars with spatial representations of the Supreme Court justices that help elucidate ideological inclinations and voting behavior. This is done primarily in one dimension, where politics dominates, though recent work details a second dimension capturing differing attitudes on the authority of various legal actors. This paper introduces and explores a new network-theoretic tree-based method for visualizing the relationships between the justices, based on their voting records, that allows scholars to study the intricate branching structure of the Court. It is shown how this tool can be used to uncover periods in the Court's history where the balance on the bench fractured in unusual and interesting ways. Moreover, by defining several tree-based measures and charting their evolution over time, a picture emerges that throughout the past fifty years the Court became increasingly one-dimensional and bipolar, dividing along political lines.

Markerless Rat Behavior Quantification With Cascade Neural Network.

Quantifying rat behavior through video surveillance is crucial for medicine, neuroscience, and other fields. In this paper, we focus on the challenging problem of estimating landmark points, such as the rat's eyes and joints, only with image processing and quantify the motion behavior of the rat. Firstly, we placed the rat on a special running machine and used a high frame rate camera to capture its motion. Secondly, we designed the cascade convolution network (CCN) and cascade hourglass network (CHN), which are two structures to extract features of the images. Three coordinate calculation methods—fully connected regression (FCR), heatmap maximum position (HMP), and heatmap integral regression (HIR)—were used to locate the coordinates of the landmark points. Thirdly, through a strict normalized evaluation criterion, we analyzed the accuracy of the different structures and coordinate calculation methods for rat landmark point estimation in various feature map sizes. The results demonstrated that the CCN structure with the HIR method achieved the highest estimation accuracy of 75%, which is sufficient to accurately track and quantify rat joint motion.

Visual SLAM With Drift-Free Rotation Estimation in Manhattan World

This letter presents an efficient and accurate simultaneous localization and mapping (SLAM) system in man-made environments. The Manhattan world assumption is imposed, with which the global orientation is obtained. The drift-free rotational motion estimation is derived from the structural regularities using line features. In particular, a two-stage vanishing points (VPs) estimation method is developed, which consists of a short-term tracking module to track the clustered line features and a long-term searching module to generate abundant sets of VPs candidates and retrieve the optimal one. A least square problem is constructed and solved to provide refined VPs with the clusters of structural line features every frame. We make full use of the absolute orientation estimation to benefit the whole SLAM process. In particular, we utilize the absolute orientation estimation to increase the localization accuracy in the front end, and formulate a linear batch camera pose refinement problem with the known rotations to improve the real time performance in the back end. Experiments on both synthesized and real-world scenes reveal results with high-precision in the real time camera pose estimation process and high-speed in pose graph optimization process compared with the existing state-of-the-art methods.

Considering the uncertainty of hydrothermal wind and solar-based DG

Lately, researchers have widely centered around renewable energy assets, for example, wind control and solar units to decrease the utilization of fossil fuels as the fundamental wellspring of ecological natural contaminations. One of the fundamental difficulties for the generation of wind and solar energies is that they frequently including the uncertainty because of the stochastic natures of wind speeds and solar radiation. Along these lines, the current uncertainty to assets the wind and solar units and necessary to assess the arranging strategy of distribution systems for having a dependable execution. To display the uncertainty related along with the wind and solar power, the point estimate method (PEM) is utilized. Weibull and Beta distributions are utilized to deal with uncertain information factors. These fundamental goals present work is to minimize the generation cost of the framework is enhanced dependent on the butterfly optimization algorithm (BOA). Four case test frameworks viewed as it is discovered that the proposed strategy gives better arrangement as far as execution time and normal cost viability. The recreation results demonstrate that the entrance of sustainable energy source builds, the generation cost diminishes. The outcomes acquired along with the butterfly optimization algorithm contrasted and another one understood strategy. Also, the precise distribution of generation cost.