Fractional order of rational Jacobi functions for solving the non-linear singular Thomas-Fermi equation

2017 ◽  
Vol 132 (2) ◽  
Author(s):  
Kourosh Parand ◽  
Pooria Mazaheri ◽  
Hossein Yousefi ◽  
Mehdi Delkhosh
Keyword(s):  
Fractional Order ◽  
Thomas Fermi ◽  
Non Linear ◽  
Jacobi Functions

scholarly journals Central Tunicate Swarm NFOPID-Based Load Frequency Control of the Egyptian Power System Considering New Uncontrolled Wind and Photovoltaic Farms

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3604
Author(s):  
Hady H. Fayek ◽  
Panos Kotsampopoulos
Keyword(s):  
Power System ◽  
Fractional Order ◽  
Frequency Control ◽  
Optimization Techniques ◽  
Load Frequency Control ◽  
The Novel ◽  
Operating Condition ◽  
Load Frequency ◽  
Non Linear ◽  
Fractional Order Pid

This paper presents load frequency control of the 2021 Egyptian power system, which consists of multi-source electrical power generation, namely, a gas and steam combined cycle, and hydro, wind and photovoltaic power stations. The simulation model includes five generating units considering physical constraints such as generation rate constraints (GRC) and the speed governor dead band. It is assumed that a centralized controller is located at the national control center to regulate the frequency of the grid. Four controllers are applied in this research: PID, fractional-order PID (FOPID), non-linear PID (NPID) and non-linear fractional-order PID (NFOPID), to control the system frequency. The design of each controller is conducted based on the novel tunicate swarm algorithm at each operating condition. The novel method is compared to other widely used optimization techniques. The results show that the tunicate swarm NFOPID controller leads the Egyptian power system to a better performance than the other control schemes. This research also presents a comparison between four methods to self-tune the NFOPID controller at each operating condition.

scholarly journals 5G Poor and Rich Novel Control Scheme Based Load Frequency Regulation of a Two-Area System with 100% Renewables in Africa

2020 ◽  
Vol 5 (1) ◽  
pp. 2
Author(s):  
Hady H. Fayek
Keyword(s):  
Power System ◽  
Fractional Order ◽  
Packet Loss ◽  
Pid Controller ◽  
Frequency Control ◽  
Operating Conditions ◽  
Load Frequency Control ◽  
Load Frequency ◽  
Control Scheme ◽  
Non Linear

Remote farms in Africa are cultivated lands planned for 100% sustainable energy and organic agriculture in the future. This paper presents the load frequency control of a two-area power system feeding those farms. The power system is supplied by renewable technologies and storage facilities only which are photovoltaics, biogas, biodiesel, solar thermal, battery storage and flywheel storage systems. Each of those facilities has 150-kW capacity. This paper presents a model for each renewable energy technology and energy storage facility. The frequency is controlled by using a novel non-linear fractional order proportional integral derivative control scheme (NFOPID). The novel scheme is compared to a non-linear PID controller (NPID), fractional order PID controller (FOPID), and conventional PID. The effect of the different degradation factors related to the communication infrastructure, such as the time delay and packet loss, are modeled and simulated to assess the controlled system performance. A new cost function is presented in this research. The four controllers are tuned by novel poor and rich optimization (PRO) algorithm at different operating conditions. PRO controller design is compared to other state of the art techniques in this paper. The results show that the PRO design for a novel NFOPID controller has a promising future in load frequency control considering communication delays and packet loss. The simulation and optimization are applied on MATLAB/SIMULINK 2017a environment.

scholarly journals Iterative analysis of non-linear Swift-Hohenberg equations under nonsingular fractional order derivative

2021 ◽  
pp. 104080
Author(s):  
Israr Ahmad ◽  
Thabet Abdeljawad ◽  
Ibrahim Mahariq ◽  
Kamal Shah ◽  
Nabil Mlaiki ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order Derivative ◽  
Fractional Order Derivative ◽  
Iterative Analysis ◽  
Non Linear

scholarly journals Fuzzy generalised predictive control for a class of fractional-order non-linear systems

2018 ◽  
Vol 12 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Bin Wang ◽  
Ke Shi ◽  
Lan Yang ◽  
Fengjiao Wu ◽  
Diyi Chen
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Predictive Control ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems

2021 ◽  
Vol 13 (19) ◽  
pp. 3819
Author(s):  
Anhong Tian ◽  
Chengbiao Fu ◽  
Her-Terng Yau ◽  
Xiao-Yi Su ◽  
Heigang Xiong
Keyword(s):  
Chemical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Classification Accuracy ◽  
Chaotic Dynamic ◽  
Soil Salinization ◽  
Extension Theory ◽  
Non Linear Circuit ◽  
Non Linear ◽  
Dynamic Errors

Soil salinization process is a complex non-linear dynamic evolution. To classify a system with this type of non-linear characteristic, this study proposed a mixed master/slave chaotic system based on Chua’s circuit and a fractional-order Chen-Lee chaotic system to classify soil salinization level. The subject is the soil in Xinjiang with different levels of human interference. A fractional-order Chen-Lee chaotic system was constructed, and the spectral signal processed by the Chua’s non-linear circuit was substituted into the master/slave chaotic system. The chaotic dynamic errors with different fractional orders were calculated. The comparative analysis showed that 0.1-order has the largest chaotic dynamic error change, which produced two distinct and divergent results. Thus, this study converted the chaotic dynamic errors of fractional 0.1-order into chaotic attractors to build an extension matter-element model. Finally, we compared the soil salt contents (SSC) from the laboratory chemical analysis with the results of the extension theory classification. The comparison showed that the combination of fractional order mixed master/slave chaotic system and extension theory has high classification accuracy for soil salinization level. The results of this system match the result of the chemical analysis. The classification accuracy of the calibration set data was 100%, and the classification accuracy of the validation set data was 90%. This method is the first use of the mixed master/slave chaotic system in this field and can satisfy certain soil salinization monitoring needs as well as promote the application of the chaotic system in soil salinization monitoring.

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