الفهرس 
Chapter 1Only 14 pages are availabe for public view
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Abstract
Wind and solar energy are very important nowadays in the power system because they are cheap and environmentally friendly, and they have played a critical part in the modern electric power system. Wind energy has a complicated system operation due to uncertainty in wind speed which leads to uncertainty in devolved power. Photovoltaic (PV) power generation uncertainty is influenced by global solar irradiance, weather temperature, and PV power losses owing to overheating, particularly in hot regimes. This thesis presents stochastic modeling of wind and solar energy and a stochastic optimal power flow (SCOPF) to obtain the optimal scheduled power by the wind and solar sources. Since the SCOPF problem is highly nonconvex and nonlinear, two novel heuristic optimization methods are used in this work to solve it called Aquila Optimizer (AO) and Mayfly algorithm (MA).
First, this work presents modifications in the original probability distribution functions (PDF) where the original PDF functions are insufficient for wind speed and solar irradiance modeling because they have a significant error between the real data frequency distribution and the estimated distribution curve. This modification is using mixture probability distributions which can improve the fitting of data and reduce this error. The main aim of this work is to model wind speed and solar irradiation behaviors using two components mixture distribution (TCMD) and three components mixture distribution (THCMD) generated from integration of the original Weibull, Lognormal, Gamma, and Inverse Gaussian PDFs. The optimal parameters of original PDFs are obtained using numerical methods and artificial intelligence (AI) methods, the numerical methods are the maximum likelihood approach, Energy pattern factor method, graphical method, and Empirical method. The AI techniques are AO and MA. The PDFs used in this work are compared using actual reading obtained from a site located in the USA for five years and data obtained from the distribution curve by correlation coefficient (R2), root means square error (RMSE), and Chi-square (X2). The parameters of the mixture PDFs are calculated using MA and AO methods
Moreover, a single-objective SCOPF is carried by the AO method with six scenarios for the penalty and reverse cost coefficients to obtain optimal scheduled wind power on the three IEEE systems (30, 57, and 118). This study applies two stochastic models of solar and wind energy to electrical power systems to study the SCOPF using the MA method with single and multi-objective optimal power flow (OPF) problems and the results are compared to those of other metaheuristic approaches in the standard IEEE-30 bus system, The results demonstrate the MA method’s validity and robustness in solving this complex problem.
Finally, stochastic optimal power flow (SCOPF) is carried out again in a modified IEEE-30 bus system but with adding two wind farms and one solar farm rather than fuel generators with the same objective functions.