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probabilistic load flow calculation and power system security analysis based on improved CGC-CM

ELECTRIC POWER SYSTEMS RESEARCH 2024年 237卷

作者： Huang, Jingwen Du, Zhiye Cai, Hongwei He, Jingxuan Yue, Guohua Li, Gen Zhao, Huashi Chen, Yiping Wuhan Univ Sch Elect Engn & Automat Wuhan 430072 Peoples R China China Southern Power Grid Power Dispatching Control Ctr Guangzhou 510663 Peoples R China

The increasing permeability of renewable energy render the traditional static security analysis method based on deterministic load flow no longer applicable. In power systems with uncertain renewable energy sources, probabilistic load flow (PLF) analysis must be conducted to achieve static security analysis of the power system by examining voltage and branch load flow during the operation. This paper proposes a PLF calculation method based on C-type Gram-Charlier series expansion and cumulant (CGC-CM), which can determine the distribution characteristics of bus voltage and branch transmission power. The proposed method solves the problem of negative values in the calculation of PLF for the results of the traditional A-type Gram-Charlier series expansion (AGC) method. Additionally, three typical wind and photovoltaic power generation output scenarios are created using k-means clustering, followed by an assessment of the static security of the power system. In this paper, the accuracy and efficiency of the algorithm is verified using the IEEE30 test system. Besides, it is observed that the static stability of the power system decreases with an increase in wind and photovoltaic power output. Subsequently, a real power system model was established and demonstrated that the branch capacity increase can improve the stability of the system operation.

关键词： Wind and photovoltaic power Static security analysis probabilistic load flow Gram-Charlier series

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probabilistic load flow for Wind Integrated Power System Considering Node Power Uncertainties and Random Branch Outages

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2023年第1期14卷 482-489页

作者： Singh, Vikas Moger, Tukaram Jena, Debashisha Natl Inst Technol Karnataka Dept Elect & Elect Engn Mangalore 575025 India

This paper proposes an analytical probabilistic load flow (PLF) approach that considers conventional generator outages, load variability, and random branch outages. The branch outages are modeled as 0-1 distributions of fictitious power injections at the appropriate nodes. The distribution of state variables and line power flows is then obtained using a combined Cumulant and Gram-Charlier series expansion approach. The proposed PLF performs contingency sequencing with fuzzy logic to eliminate random line checking and avoid masking mistakes faced by performance index-based algorithms. The Jacobian inverse calculation in the traditional Cumulant method is eliminated to conserve storage space and speed up the computation using the Gauss-Jordan method. The correlations among loads and wind power generations has been modeled using the Nataf transformation process. Results of 24-bus and 259-bus equivalent systems of the Indian southern and western power grids are analyzed and validated with those obtained using the Monte Carlo simulation method. The suggested method's efficacy is justified by its accuracy and low computational burden.

关键词： Branch outage correlation cumulant method gram-charlier expansion nataf transformation probabilistic load flow

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probabilistic load flow analysis for evaluation of photovoltaic grid connection applications

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ELEKTROTECHNIK UND INFORMATIONSTECHNIK 2024年第7-8期141卷 468-475页

作者： Wohlfart, Peter Renner, Herwig Graz Univ Technol Inst Elect Power Syst Inffeldgasse 18 A-8010 Graz Austria

Uncertainty in power system analysis is increasing, mainly due to decentralized generation and the related spatial distribution of power plants, as well as the inherent volatility of renewable energy sources. In Austria, this development is reflected in a high number of photovoltaic grid connection applications in recent years. On the consumption side, there are changes in grid loads due to the increasing electrification of society, which is reflected, for example, in a rising number of electric vehicles. These aspects of uncertainty in generation and consumption must be considered in the planning process of distribution grids. A proper way to include uncertainty in the hosting capacity analysis of power grids are probabilistic load flow calculation methods. This paper provides an introductory overview of probabilistic load flow analysis, available calculation methods, required input parameters and the interpretation of results. This paper focuses on photovoltaics, so a correlation analysis of historical power generation measurements of spatially distributed photovoltaic power plants in Austria is presented. Furthermore, an insight into the development of Austrian photovoltaic grid connection applications from recent years is given. Die Unsicherheit bei der Berechnung von Energiesystemen nimmt zu, insbesondere aufgrund von dezentraler Erzeugung und der damit verbundenen r & auml;umlichen Verteilung der Kraftwerke sowie der inh & auml;renten Volatilit & auml;t erneuerbarer Energietr & auml;ger. In & Ouml;sterreich spiegelt sich diese Entwicklung in einer hohen Zahl von Antr & auml;gen auf Netzanschluss durch Photovoltaikanlagen in den letzten Jahren wider. Auch auf der Verbrauchsseite gibt es Ver & auml;nderungen durch die zunehmende Elektrifizierung der Gesellschaft, die sich beispielsweise in einer steigenden Anzahl von Elektrofahrzeugen niederschl & auml;gt. Dieser Aspekt der Unsicherheit von Erzeugung und Verbrauch muss bei der Planung von Verteilernetzen ber & u

关键词： Hosting capacity analysis probabilistic load flow Photovoltaics Decentralized generation Aufnahmekapazit & auml t von Netzen Probabilistischer Lastfluss Photovoltaik Dezentrale Erzeugung

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Maximum entropy based probabilistic load flow for assessing input uncertainties and line outages in wind-integrated power systems

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ELECTRIC POWER SYSTEMS RESEARCH 2025年 244卷

作者： Singh, Vikas Moger, Tukaram Jena, Debashisha Natl Inst Technol Karnataka Surathkal India

The swift expansion of distributed generation, particularly from photovoltaics and wind turbines, poses a formidable challenge to conventional probabilistic load flow (PLF) methods. This paper addresses the urgent need fora robust and efficient PLF approach by investigating a maximum entropy (ME) based probabilistic density function (PDF) approximation, utilizing advanced cumulant arithmetic from linearized power flow formulation. The ME-PLF method notably enhances the accuracy of output PDFs under extensive uncertainties, such as load demand fluctuations and disturbances in network branches. Unlike the Gram-Charlier expansion (GCE) reconstruction method, ME-PLF effectively eliminates the issue of erroneously obtaining negative values in the tail regions of the PDFs. Additionally, the fundamental cumulant method (CM) is refined to better model dependencies between wind power generators (WPGs) and loads. The simulations are conducted using the MATLAB programming software. Results from practical test systems have been validated against those obtained using the Monte Carlo simulation method. The suggested method has been proven to be highly effective due to its preciseness and reduced computational effort.

关键词： Correlation Gram-Charlier expansion Maximum entropy Network uncertainty probabilistic load flow

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Multi-Scenario probabilistic load flow Calculation Considering Wind Speed Correlation

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Energy Engineering 2025年第2期122卷 667-680页

作者： Xueqian Wang Hongsheng Su School of Automation and Electrical Engineering Lanzhou Jiaotong UniversityLanzhou730070China

As the proportion of newenergy increases,the traditional cumulant method(CM)produces significant errorswhen performing probabilistic load flow(PLF)calculations with large-scale wind power *** the wind speed correlation,a multi-scenario PLF calculation method that combines random sampling and segmented discrete wind farm power was ***,based on constructing discrete scenes of wind farms,the Nataf transform is used to handle the correlation between wind ***,the random sampling method determines the output probability of discrete wind power scenarios when wind speed exhibits ***,the PLF calculation results of each scenario areweighted and superimposed following the total probability formula to obtain the final power flow calculation *** in the IEEE standard node system,the absolute percent error(APE)for the mean and standard deviation(SD)of the node voltages and branch active power are all within 1%,and the average root mean square(AMSR)values of the probability curves are all less than 1%.

关键词： Wind speed correlation probabilistic load flow multi-scenario piecewise cumulant method

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Advanced probabilistic load flow methodology for voltage unbalance assessment in PV penetrated distribution grids

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 155卷

作者： Gruosso, Giambattista Londono, Cesar Diaz Daniel, Luca Maffezzoni, Paolo Politecn Milan DEIB Piazza Leonardo Vinci 32 I-20135 Milan Italy MIT 77 Massachusetts Ave Cambridge MA 02139 USA

The balancing of three-phase node voltages in modern power distribution grids can be significantly deteriorated by the penetration of single-phase PV renewable sources. For a given grid topology and prescribed loads, voltage unbalance critically depends on the nodes where power is injected. Its amount can vary substantially at different observations Buses in the grid. In this paper, we present a methodology that can inform network operators about the critical Buses in the grid and critical injection scenarios. The method is based on a numerically efficient but accurate probabilistic load flow that can handle the case of many PV sources and provides detailed information on the probability distribution of voltage unbalance. The proposed methodology relies on the complex-domain modeling of voltage unbalance sensitivity and on accelerating Monte Carlo simulations via parameter space partitioning.

关键词： Data clustering Multi-variate function approximation Photovoltaics probabilistic load flow Sensitivity analysis voltage unbalance factor

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Nataf-KernelDensity-Spline-based point estimate method for handling wind power correlation in probabilistic load flow

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 245卷

作者： Shaik, Mahmmadsufiyan Gaonkar, Dattatraya N. Nuvvula, Ramakrishna S. S. Muyeen, S. M. Shezan, Sk. A. Shafiullah, G. M. Natl Inst Technol Karnataka Dept Elect & Elect Engn Mangalore 575025 Karnataka India NITTE Deemed Univ NMAM Inst Technol Dept Elect & Elect Engn Mangaluru 574110 Karnataka India Qatar Univ Dept Elect Engn Doha Qatar Engn Inst Technol Dept Elect Engn & Ind Automat Melbourne 3008 Australia Murdoch Univ Sch Engn & Energy Perth WA Australia

Modern power systems integrated with renewable energies (REs) contain many uncertainties. The proposed method introduces a novel approach to address the challenges associated with wind power generation uncertainty in probabilistic load flow (PLF) studies. Unlike conventional methods that use wind speed as an input, the paper advocates for utilizing wind generator output power (WGOP) as an input to the point estimate method (PEM) in solving PLF. The uniqueness lies in recognizing the distinct behavior of wind power uncertainty, where not all random samples of wind speed contribute to actual wind power production. The paper suggests a NatafKernelDensity-Spline-based PEM, combining the Nataf transformation, Kernel density estimation (KDE), and cubic spline interpolation. This innovative integration effectively manages wind power correlation within the analytical framework. By incorporating spline interpolation and kernel density estimation into the traditional PEM, the proposed method significantly enhances accuracy. To validate the effectiveness of the proposed approach, the method is applied to IEEE-9 and IEEE-57 bus test systems, considering uncertainties related to load, wind power generation (WPG), solar power generation (SPG), and conventional generator (CoG) outages. Comparative analysis with Monte Carlo simulation (MCS) results demonstrates that the proposed method outperforms the conventional PEM in terms of accuracy. Overall, the paper contributes a pioneering solution that not only highlights the importance of using WGOP as an input in PLF but also introduces a sophisticated method that surpasses traditional approaches, improving accuracy in power system studies involving renewable energy integration. The accuracy of the proposed method is validated by comparing its results with those obtained through Monte Carlo simulation (MCS), where the proposed method yields more accurate results than the conventional PEM.

关键词： Correlation Cubic spline interpolation Kernel density estimation Nataf transformation Point estimate method probabilistic load flow

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An innovative real-time framework for probabilistic load flow computation in renewable-based microgrids considering correlation: Integrating automatic data clustering with an enhanced arithmetic optimization algorithm

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APPLIED ENERGY 2025年 382卷

作者： Javidan, Aghil Ara, Afshin Lashkar Tolabi, Hajar Bagheri Islamic Azad Univ Dept Elect Engn Dezful Branch Dezful Iran Islamic Azad Univ Dept Elect Engn Khorramabad Branch Khorramabad Iran

This paper suggests a new approach, called automatic data clustering, using an enhanced arithmetic optimization algorithm (ADC-EAOA), for improving the probabilistic load flow (PLF) in microgrids (MGs) integrated with distributed generation resources (DGR). The proposed ADC-EAOA method aims to address real-time solution of the PLF in MGs based on DGR with output large fluctuations, across various states of MG operation. The ADCEAOA approach achieves more robust clustering compared to traditional data clustering methods by optimizing two objectives: a) maximizing cohesion within clusters, and b) enhancing separation between clusters. The correlation modeling between input random variables (IRVs) comprehensively has been considered. Five strategies have been introduced to improve the arithmetic optimization algorithm (AOA) to stop the algorithm from being extremely greedy and avoid trapping in local optima. The effectiveness of the EAOA is firstly assessed utilizing the test functions CEC2005 and CEC2019 in comparison to well-known optimization algorithms. Subsequently, the EAOA and the suggested ADC-EAOA hybrid approach are applied on 69-node, 33-node, and 123node MGs to optimize the cost function used in the PLF which is equal to the mismatch among computation power with scheduled power in each node. The outcomes of solving the PLF problem were contrasted with those of the Monte-Carlo Simulation (MCS), the AOA, the PSO, the K-means, and as well as the Fuzzy C-means in terms of precision and run-time. The simulation outcomes demonstrate that the suggested ADC-EAOA approach dramatically increases the processing speed while simultaneously maintaining a high degree of accuracy so that it can provide various advantages and facilities for real-time power system studies.

关键词： Enhanced arithmetic optimization algorithm Automatic data clustering Uncertainty Microgrid probabilistic load flow Correlation

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Frequency-Control-Aware probabilistic load flow: An Analytical Method

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IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第6期38卷 5170-5187页

作者： Jia, Mengshuo Cao, Qianni Shen, Chen Hug, Gabriela ETH Dept Informat Technol & Elect Engn CH-8092 Zurich Switzerland Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account. However, system control, as an automatic buffer between the fluctuations in random variables and the variations in system variables (e.g., nodal voltages), has a significant impact on the final PLF result. To consider control actions' influence, this paper proposes the first analytical PLF method for the transmission grid that takes into account primary and secondary frequency controls. This method is based on a high-precision linear power flow model, whose precision is even further improved in this paper by an original correction approach. This paper also proves that if the joint probability distribution (JPD) of random variables is expressed by a Gaussian mixture model (GMM), then the JPD of system variables is an infinite GMM. By leveraging this proposition, the proposed method generates the joint PLF of the whole system at the quasi-steady and steady states. The high accuracy and satisfactory efficiency of this method are verified on multiple test systems with different percentages of renewables.

关键词： Random variables load flow Frequency control Renewable energy sources Probability distribution Analytical models Gaussian mixture model probabilistic load flow control frequency regulation analytical method transmission system

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probabilistic load flow Based on Parameterized Probability-Boxes for Systems With Insufficient Information

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IEEE ACCESS 2021年 9卷 161038-161045页

作者： Amiri, Hafez Mohammadi, Mohammad Karimi, Mazaher Rastegar, Mohammad Rostami, Amir Shiraz Univ Sch Elect & Comp Engn Dept Power & Control Shiraz *** Iran Univ Vaasa Sch Technol & Innovat Vaasa 65200 Finland

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 in 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.

关键词： Uncertainty probabilistic logic Mathematical models Estimation Distribution functions Random variables load modeling Cornish-Fisher expansion series double-loop sampling parameterized p-boxes probabilistic load flow probability bounds

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