Faculty Publications
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Item Probabilistic Load Flow Considering Load and Wind Power Uncertainties using Modified Point Estimation Method(Institute of Electrical and Electronics Engineers Inc., 2022) Singh, V.; Moger, T.; Jena, D.Nowadays, renewable energy sources (REs) are increasingly integrated into electrical power networks. Among many REs, wind energy has emerged as a prominent source of electricity. However, rising wind power penetration has increased the system's net generation variability. Consequently, the ability to monitor and simulate the behavior of wind power generation (WPG) in detail is critical. Furthermore, the wind speed or wind power output of different wind farms can be highly interdependent and may not follow Normal distribution. This study proposes a probabilistic load flow (PLF) technique for modeling normally distributed loads and non-normally distributed WPG based on the modified point estimation method (PEM). This modification allows modeling dependent input random variables as a function of many independent ones using the Nataf transformation. By utilizing the findings of the Monte-Carlo method as a reference, the usefulness of the suggested technique is tested by conducting case studies on a 24-bus equivalent system of the Indian Southern region power grid. Simulation results indicate that the modified PEM can easily handle the correlation and have high processing efficiency. © 2022 IEEE.Item Modified Cumulant based Probabilistic Load Flow Considering Correlation between Loads and Wind Power Generations(Institute of Electrical and Electronics Engineers Inc., 2022) Singh, V.; Moger, T.; Jena, D.With the growing use of wind sources, power system analysis should consider the variation of wind power and the correlation among wind farms. In this paper, the Cumulant method (CM) for performing probabilistic load flow (PLF) analysis is modified to account for the correlation between random input variables. Considering the dependence between loads and wind power generations (WPGs), the modified CM models the dependent variables as a function of many independent ones using the Nataf transformation. The effectiveness of the suggested method is verified by performing case studies on a 24-bus equivalent system of the Indian southern region power grid. Furthermore, relative error values in reference with the Monte-Carlo simulation (MCS) method are analyzed. © 2022 IEEE.Item A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach(Elsevier Ltd, 2017) Prusty, B.R.; Jena, D.A power system with large integration of renewable energy based generations is inherently associated with different types of uncertainties. In such cases, probabilistic load flow is a vital tool for delivering comprehensive information for power system planning and operation. Efforts have been made in this paper to perform a critical review on different probabilistic load flow models, uncertainty characterization and uncertainty handling methods, since from its inspection in 1974. An efficient analytical method named multivariate-Gaussian mixture approximation is proposed for precise estimation of probabilistic load flow results. The proposed method considers the uncertainties pertaining to photovoltaic generations and load demands. At the same time, it effectively incorporates multiple input correlations. In order to examine the performance of the proposed method, modified IEEE 118-bus test system is taken into consideration and results are compared with univariate-Gaussian mixture approximation, series expansion based cumulant methods and Monte Carlo simulation. Effect of various correlation cases on distribution of result variables is also studied. The effectiveness of the proposed method is justified in terms of accuracy and execution time. © 2016 Elsevier LtdItem Uncertainty handling techniques in power systems: A critical review(Elsevier Ltd, 2022) Singh, V.; Moger, T.; Jena, D.Integration of renewable generations with electrical power systems has gained considerable attention in recent years due to environmental and economic benefits. However, this integration introduces additional uncertainties into the existing system and requires appropriate uncertainty modeling for power systems. Typically the uncertainties in power systems are modeled using probabilistic or possibilistic approaches. A combined probabilistic-possibilistic approach is necessary when some uncertain variables are probabilistic and others are possibilistic. This paper presents a complete review of uncertainty categorization and several techniques to address the uncertainty in power systems, along with the merits and weaknesses of each technique. The challenges have been highlighted for future research directions. Analytical and approximate methods are reviewed in this paper when wind power generations are integrated into the existing power grid. Considering the uncertainties of wind power generation and system load demands, the basic probabilistic methods such as Monte-Carlo simulation, cumulant, and 2n+1 point estimation methods are implemented. To explore the capability and shortcoming of these basic methods, a 72-bus equivalent system of Indian southern region power grid is taken into consideration. The results obtained using Monte-Carlo simulation method are treated as a benchmark to analyze the performance of the cumulant and 2n+1 point estimation methods. © 2021 Elsevier B.V.Item Probabilistic Load Flow for Wind Integrated Power System Considering Node Power Uncertainties and Random Branch Outages(Institute of Electrical and Electronics Engineers Inc., 2023) Singh, V.; Moger, T.; Jena, D.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. © 2010-2012 IEEE.Item Probabilistic Load Flow Approach Combining Cumulant Method and K-Means Clustering to Handle Large Fluctuations of Stochastic Variables(Institute of Electrical and Electronics Engineers Inc., 2023) Singh, V.; Moger, T.; Jena, D.The modern electrical power system faces various uncertainties, including load fluctuations, forced outages of conventional generators, network branches. Furthermore, the rising penetration of wind power generation introduces additional uncertainty, causing difficulties in power system planning, operation. This paper uses an analytical probabilistic load flow approach to account for all such uncertainties. The random branch outages are simulated using the fictional powers injections into the relevant nodes. A fuzzy method is used to perform contingency sequencing to avoid masking mistakes that might occur when utilizing performance index-based sequencing methods. The sparse Jacobian inverse is eliminated to preserve storage space, accelerate the computation. A modified Cumulant method is used in conjunction with the K-means clustering process to deal with the substantial fluctuations of the input variables. In the proposed approach, the correlated samples are generated using inverse Nataf transformation. These correlated samples are clustered using K-means clustering. The Cumulant method is applied within each cluster, total probability law is used to integrate each cluster's findings. The proposed PLF is tested on 24-bus, 259-bus wind integrated equivalent systems. Compared with the Monte-Carlo simulation, the proposed PLF yields computationally efficient, more accurate findings. © 1972-2012 IEEE.Item Maximum entropy based probabilistic load flow for assessing input uncertainties and line outages in wind-integrated power systems(Elsevier Ltd, 2025) Singh, V.; Moger, T.; Jena, D.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 for a 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. © 2025 Elsevier B.V.Item A modified point estimate-based probabilistic load flow approach for improving tail accuracy in wind-integrated power systems(Elsevier Ltd, 2025) Singh, V.; Moger, T.; Jena, D.Modern power systems confront risks, including demand variations and forced outages of traditional generators. Moreover, the extensive grid integration of new energy generation has exacerbated the uncertainty because of its intermittent nature. The Hong's three-point estimation method (3PEM) for performing probabilistic load flow (PLF) is commonly used to cope with power system uncertainties; however, it has poor tail accuracy. To overcome this issue, the basic 3PEM is modified by adding a new pair of tail points. This modified 3PEM (MH3PEM) is equivalent to 5PEM but utilize reduced order moments. Also, a hybrid Hong-Harr PEM approach is proposed to efficiently deal with a mixture of independent and correlated input variables. The input variables’ correlation is modeled using the Nataf transformation. The proposed approaches are tested on wind farm-integrated 24-bus and 72-bus equivalent systems, and their findings are compared with the fundamental PEM schemes. Utilizing the Monte-Carlo simulation as a reference, the MH3PEM provides the most accurate results with a low computational burden. © 2025 Elsevier B.V.