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Wind energy is considered one of the most important alternative energy sources for generating electricity. But the stochastic nature of wind, leads to use the distribution function to present the wind system. The two-parameter Weibull distribution is often used in the wind speed presentation. The two-parameter Weibull distribution has scale and shape parameters that are important in wind energy applications, thus selecting the optimum method for estimation them is important. The unpredictability in wind speed leads to uncertainty in devolved power which leads to difficult system operation. In this study, two novel artificial intelligence (AI) methods called Mayfly algorithm (MA) and Aquila Optimizer (AO) are used for calculating the Weibull distribution parameters. Results are compared with four classical numerical methods called the Maximum likelihood approach, Energy pattern factor method, Graphical method, and Empirical method. The two AI methods prove superiority and robustness for evaluating two-parameter of Weibull distribution as they give lower errors and higher correlation coefficients. Moreover, to prove the accuracy of the MA method in solving the optimal power flow (OPF) problem, single and multi-objective OPF is applied on a standard IEEE-30 bus system to minimize fuel cost, power loss, thermal unit emissions, and voltage security index (VSI), and results are compared with other metaheuristic methods. The results prove the validity and robustness of the MA method in solving the OPF problem. Then, single and multi-objective stochastic optimal power flow (SCOPF) is applied to modified IEEE-30 which contains two wind farms to minimize total generation cost, power loss, thermal unit emission, and VSI. The fuzzy-based Pareto front technique is utilized in multi-objective optimization (MOO) to obtain the best compromise point solution. The objective function of SCOPF considers reserve cost for overestimation and penalty cost for underestimation of wind energy. Finally, this paper studies the effect of changing Weibull parameters, penalty cost coefficient, and reverse cost coefficient in wind energy generation cost. The proposed MA method could be valuable to system operators as a decision-making aid when dealing with hybrid power systems.

Global warming and depletion of fossil fuels have urged the world to control their impacts and find clean and green energy sources. Due to this paradigm shift, renewable energy resources (RESs) have received tremendous attention around the globe and amongst other RESs, wind energy has been proving itself a promising renewable resource. However, still, the proper selection of wind turbines (WTs) and their installation is considered a major challenge. Presently, due to the economic boom of Pakistan as a regional power under the China Pakistan Economic Corridor (CPEC) and increasing energy demand, it needs to meet the energy shortage. This paper aims to conduct a pre-feasibility ainvestigation of wind farm exploitation at Gwadar and Quetta, major cities of Baluchistan province in Pakistan by harnessing the wind energy potential and electricity generation cost through different WT models. The wind speed (WS) data is recorded by a professional wind mast at different measurement heights during F.Y 2016 and analyzed using Five approaches, Modified Maximum Likelihood Method (MMLM), Graphical Method (GM), Empirical Method of Lysen (EML), Empirical Method of Jestus (EMJ) and Energy Pattern Factor Method (EPF) at the proposed site and EPF shows the best performance than other approaches. Different WTs models are also evaluated and out of them, the GW121 WT gives the lowest cost in dollars and lowest payback period at each site so it can be recommended as one of the most feasible WT for electricity generation for powering local communities at the proposed sites.

This paper: (1) examines the results of Yong-Ming Li (see ibid., vol.43, p.255-63, 1994) and points out its errors and shortcomings; and (2) proposes a new graphical method for estimating the parameters of a 3-parameter Weibull distribution.

A variety of shapes of two-Weibull mixtures on Weibull probability paper are explored and classified into six types of Cdf curves (A-F). Types B-D represent Cdf's composed of two well-mixed subpopulations. Type F represents the Cdf composed of two very well-separated subpopulations. Types A and E are in between types B-D and type F. The Kao-Cran graphical parameter estimation method cannot be applied to type A-C, E, and F curves. It is recommended that it not be applied to the type D curve. The theoretical basis is developed for the Jensen-Petersen graphical method for mixtures with well-separated subpopulations, viz, the type F curve. For type A and E curves, the method can be applied. However, for type B-D curves, there is no theoretical basis for the method. >

Under strong assumptions associated with Weibull distributions for normal and accelerated test conditions, a statistical hypothesis-testing procedure is developed that permits the life of cable insulation material under normal stress conditions to be inferred from accelerated life-test data in which few, if any, breakdown owns occur. The procedure also yields an approximate relation between the number of tests required for testing under normal stress conditions and the number of tests required under accelerated test conditions. This relation, in turn, provides a graphical method for judging the feasibility of proposed accelerated life tests. Subject to the validity of the assumptions these procedures may have application to a broad range of materials, components, and systems.

The time to electric breakdown, and the electric field necessary to result in breakdown of solid insulation, seem to be best represented by a Weibull probability distribution. This tutorial paper reviews the graphical method of estimating the parameters of the Weibull distribution. It also presents the method of Maximum Likelihood as an objective technique, developed by statisticians for improving the estimates of the Weibull parameters, especially for censored experiments. Procedures for calculating confidence intervals are also given. It is shown in an example that the confidence intervals can be very wide for sample sizes commonly used in dielectric life tests.