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Showing 3 results for Probability Density Function

M. E. Haji Abadi, H. Rajabi Mashhadi,
Volume 9, Issue 3 (9-2013)
Abstract

In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the Pdf estimation problem can be reformulated as the optimal control problem. Finally, the proposed method is applied to estimate the Pdf of the hourly electricity prices of New England and Ontario electricity markets. Obtained results show the efficiency of the proposed method.
H. Kiani Rad, Z. Moravej,
Volume 15, Issue 3 (9-2019)
Abstract

In this paper, a new method is conducted for incorporating the forecasted load uncertainty into the Substation Expansion Planning (SEP) problem. This method is based on the fuzzy clustering, where the location and value of each forecasted load center is modeled by employing the probability density function according to the percentage of uncertainty. After discretization of these functions, the location and value of each of the new load centers are determined based on the presented fuzzy clustering based algorithm. A Genetic Algorithm (GA) is used to solve the presented optimization problem in which the allocations and capacities of new substations as well as the expansion requirements for the existing ones are determined. With the innovative presented method, the impact of uncertainty of the power and location of the predicted loads on the results of SEP is measured, and finally, it is possible to make a proper decision for the SEP. The significant features of this method can be outlined as its applicability to large-scale networks, robustness to load changes, the comprehensiveness and also, the simplicity of applying this method to various problems. The effectiveness of proposed method is demonstrated by application on a real sub-transmission system.

I. K. Okakwu, O. E. Olabode, D. O. Akinyele, T. O. Ajewole,
Volume 19, Issue 2 (6-2023)
Abstract

This paper evaluates the wind potential of some specified locations in Nigeria, and then examines the response of wind energy conversion systems (WECSs) to this potential. The study employs eight probability distribution (PD) functions such as Weibull (Wbl), Rayleigh (Ryh), Lognormal (Lgl), Gamma (Gma), Inverse Gaussian (IG), Normal (Nl), Maxwell (Mwl) and Gumbel (Gbl) distributions to fit the wind data for nine locations in Nigeria viz. Kano, Maiduguri, Jos, Abuja, Akure, Abeokuta, Uyo, Warri and Ikeja. The paper then uses the maximum likelihood (ML) method to obtain the parameters of the distributions and then evaluates the goodness of fit for the PD models to characterize the locations’ wind speeds using the minimum Root Mean Square Error (RMSE). The paper analyses the techno-economic aspect of the WECSs based on the daily average wind speed; it evaluates the performance of ten 25 kW pitch-controlled wind turbines (WT1 – WT10) with dissimilar characteristics for each location, including the cost/kWh of energy (COE) and the sensitivity analyses of the WECSs. Results reveal that Ryh distribution shows the best fit for Kano, Jos, Abeokuta, Uyo, Warri and Ikeja, while the Lgl distribution shows the best fit for Maiduguri, Abuja and Akure due to their minimum RMSE. WT7 achieves the least COE ranging from $0.0328 in Jos to $4.4922 in Uyo and WT5 has the highest COE ranging from $0.1380 in Ikeja to $53.371 in Uyo. The paper also details the sensitivity analysis for the technical and economic aspects.


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© 2022 by the authors. Licensee IUST, Tehran, Iran. This is an open access journal distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license.