Fractional Differential Equations

Power System Economics

In this paper, the design of stochastic computational intelligent solver is presented for the solution of mathematical model representing the dynamics of mosquito dispersal in a heterogeneous environment by feedforward artificial neural networks (FFANNs) trained with genetic algorithms (GAs) aided with sequential quadratic programming (SQP), i.e., FFANN-GASQP. In the scheme FFANN-GASQP, the formulation of fitness function in mean square error sense with continuous mapping-based differential equation models of FFANNs for the mosquito dispersal system and training of these networks are accomplished by integrated competency of GA and SQP. The exactness, reliability and stability of the designed FFANN-GASQP approach are established through comparative studies with Adams numerical results for both single and multiple runs. Outcomes of statistical assessments are used to validate the accuracy and convergence of the designed FFANN-GASQP scheme.

A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment

The present study aims to design stochastic intelligent computational heuristics for the numerical treatment of a nonlinear SITR system representing the dynamics of novel coronavirus disease 2019 (COVID-19). The mathematical SITR system using fractal parameters for COVID-19 dynamics is divided into four classes; that is, susceptible (S), infected (I), treatment (T), and recovered (R). The comprehensive details of each class along with the explanation of every parameter are provided, and the dynamics of novel COVID-19 are represented by calculating the solution of the mathematical SITR system using feed-forward artificial neural networks (FF-ANNs) trained with global search genetic algorithms (GAs) and speedy fine tuning by sequential quadratic programming (SQP)—that is, an FF-ANN-GASQP scheme. In the proposed FF-ANN-GASQP method, the objective function is formulated in the mean squared error sense using the approximate differential mapping of FF-ANNs for the SITR model, and learning of the networks is proficiently conducted with the integrated capabilities of GA and SQP. The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials. The results of statistical evaluations further authenticate the convergence and prospective accuracy of the FF-ANN-GASQP method.

https://www.mdpi.com/2073-8994/12/10/1628/pdf

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane–Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNEICS for DSMF-LES is presented after derivation from standard Lane–Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the mean-squared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

In this paper, a novel nature inspired meta heuristic optimization approach of Grey Wolf Optimization (GWO) algorithm is employed to solved the optimal reactive power dispatch (ORPD) problems. Essentially, it is the sub and non-linear optimization problem of optimal power flow (OPF) in which the control parameters of the power networks are optimized. The Grey wolf optimizer (GWO) which is inspired from grey wolves’ leadership and hunting behaviors to solve the ORPD problems. For which, the optimizer is tested on two test cases of IEEE30 standards specially, for 13 and 19 variables in order to get three fitness objectives for instance; transmission line losses ( $\text{P}_{\mathrm {losses}}$ , MW), voltage deviation (VD), voltage stability index (VSI) and cost of energy in ($). During computing all fitness objectives, the minimum fitness values are possibly achieved by the finest settings of control variables. The simulation results are compared with other artificial intelligence methods in previous literature to ensure the superior performance of the GWO for ORPD problem. The consistency of GWO will further be validated through detailed statistical analysis including histogram illustrations, boxplots, empirical CDF plot, probability plot and plot of minimum fitness during each independent trial.

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A Novel Nature Inspired Meta-Heuristic Optimization Approach of GWO Optimizer for Optimal Reactive Power Dispatch Problems

In this research work, bio-inspired computational heuristic algorithms (BCHAs) integrated with active-set algorithms (ASA) were designed to study integrated economics load dispatch problems with valve point effects involving stochastic wind power. These BCHAs are developed through variants of genetic algorithms based on a different set of routines for reproduction operators in order to make exploration and exploitation in the entire search space for finding the global optima, while the ASA is used for rapid local refinements of the results. The designed schemes are estimated on different load dispatch systems consisting of a combination of thermal generating units and wind power plants with and without valve point loading effects. The accuracy, convergence, robustness and complexity of the proposed schemes has been examined through comparative studies based on a sufficiently large number of independent trails and their statistical observations in terms of different performance indices.

https://www.mdpi.com/1996-1073/12/13/2568/pdf

Hybrid Bio-Inspired Computational Heuristic Paradigm for Integrated Load Dispatch Problems involving Stochastic Wind

In fact, optimal RPD is one of the most critical optimization matters related to electrical power stability and operation. The minimization of overall real power losses is obtained by adjusting the power systems control variables, for instance; generator voltage, compensated reactive power and tap changing of the transformer. In this search, a new heuristic computing method named as fractional particle swarm optimization gravitational search algorithm (FPSOGSA) is presented by introducing fractional derivative of velocity term in standard optimization mechanism. The designed FPSOGSA is implemented for the optimal RPD problems with IEEE-30 and IEEE-57 standards by attaining the near finest outcome sets of control variables along with minimization of two fitness objectives; active power transmission line losses ($P_{loss,}$ MW) and voltage deviation ($\text{V}_{\mathrm {D}}$ ). The superior performance of the proposed FPSOGSA is verified for both single and multiple runs through comparative study with state of art counterparts for each scenario of optimal RPD problems.

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Design of Fractional Particle Swarm Optimization Gravitational Search Algorithm for Optimal Reactive Power Dispatch Problems

The Flexible alternating current transmission systems (FACTS) is considered one of the most developed technologies applied for enhancing the performance of system due to their ability of adjusting different parameters in the transmission systems such as the buses voltage, the transmission line impedance, the active and reactive powers flow in transmission lines. The static synchronous series compensator (SSSC) is an effective member of the FACTS which is connected in series with the transmission lines and it consists of a solid-state voltage source inverter coupled with a transformer which aims to control and secure the operation of the power system. The main function of SSSC is inserting a controllable voltage in series with the transmission line to control the active and reactive powers flow in transmission lines. Solving the optimal reactive power dispatch (ORPD) problem is nonlinear, non-convex and it becomes a complex problem with integration of the SSSC. The contributions of article include, 1) an efficient and reliable optimization algorithm is developed to solve the ORPD problem and identify the optimal location and ratings of the SSSC, 2) The proposed algorithm is based on modifying the salp swarm algorithm (SSSA) using Levy Flight Distribution and spiral movement of particles to enhance the searching capabilities of the SSA, 3) an efficient model of SSSC based on power injection approach is used for representation the SSSC in ORPD. The ORPD is solved with and without the SSSC controller to minimize power losses and voltage deviations as well as improve the voltage stability. The proposed algorithm for ORPD is tested on the standards IEEE 30-bus and 57-bus systems. The simulation results demonstrate that MSSA is more effective and superior for solving the ORPD compared with some other reported meta-heuristic techniques. Moreover, the system performance is enhanced considerably with optimal inclusion the SSSC.

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Optimal Siting and Sizing of SSSC Using Modified Salp Swarm Algorithm Considering Optimal Reactive Power Dispatch Problem

The optimal reactive power dispatch (ORPD) is a major tool, and it plays a vital role for enhancement of the power system performance. ORPD is one multimodal, non-convex, and non-linear problem. Many elegant benefits can be obtained by using the renewable energy resources (RERs), but many technical issues related to the RERs including the stochastic characteristics of these resources due to continuous variations of solar irradiance and the wind speed lead to increasing the uncertainties of system. Thus, solving the ORPD problem with RERs is a crucial task. The contribution of the paper includes application a modified hybrid algorithm for solving the ORPD considering the uncertainties of the RERs and the load demand. The proposed algorithm is based on Fractional Calculus with Particle Swarm Optimization Gravitational Search Algorithm (FPSOGSA) which aims to enhance the searching capabilities of the conventional PSOGSA algorithm and overcome its tendency to stagnation. The proposed algorithm is tested on IEEE 30-bus system for reducing power losses and voltage deviation as well as enhancing voltage stability. The scenario-based method is employed to produce a set of scenarios from the uncertainties of load, wind speed and solar irradiance. The simulation results verify the effectiveness of the proposed algorithm for solving the ORPD problem with and without considering the uncertainties in the system. Furthermore, the proposed algorithm is superior compared with the state-of-the-art techniques in terms of the reduction of power losses and voltage deviations as well as the stability enhancement.

/pdf/fractional-psogsa-algorithm-approach-to-solve-optimal-2x2thj8uyc.pdf

Raheela Jamal

Papers

A Novel Nature Inspired Meta-Heuristic Optimization Approach of GWO Optimizer for Optimal Reactive Power Dispatch Problems

Hybrid Bio-Inspired Computational Heuristic Paradigm for Integrated Load Dispatch Problems involving Stochastic Wind

Design of Fractional Particle Swarm Optimization Gravitational Search Algorithm for Optimal Reactive Power Dispatch Problems

Optimal Siting and Sizing of SSSC Using Modified Salp Swarm Algorithm Considering Optimal Reactive Power Dispatch Problem

Fractional PSOGSA Algorithm Approach to Solve Optimal Reactive Power Dispatch Problems With Uncertainty of Renewable Energy Resources