Optimal tuning of controller parameters for a magnetic levitation system using radial basis based neural network metamodeling approach

Abstract

The world is facing global warming due to the burning of fossil fuels to generate electricity. Therefore, Renewable Energy Sources (RES) such as wind turbines are integrated into the power system to reduce global warming. But the largescale integration of the wind turbines into the power system can cause instability in the system due to intermittency in their outputs. Therefore, the wind turbine Proportional Integral (PI) based pitch controls are typically applied to enhance the generated power and the dynamic stability of the outputs. But, the PI controller’s gains in the pitch controls have to be tuned to further enhance the generated power and dynamic stability of the outputs. In this study, the Grey Wolf Optimizer (GWO) is proposed to tune the PI gains of the pitch controls as a better tuning technique than the Particle Swarm Optimization (PSO) which has slow convergence speed, the Genetic Algorithm (GA) which has premature convergence and the Zeigler Nichols (ZN) tuning technique which has high overshoot. Also, the modification of the updating mechanism of the GWO is proposed to improve the GWO convergence speed and provide better PI gains of the pitch controls. The implementation of the PI gains of pitch controls obtained using the GWO in the pitch controls of the fixed speed and DFIG wind turbines is to show the GWO can enhance the generated power and the dynamic stability of the wind turbines. The tuning model for the PI pitch control was developed based on the Integral Time multiplied Square Error (ITSE) objective function with the PI gains as constraints. The tuning of the PI gains of the pitch control was conducted by minimizing the objective function using the GWO, the modified GWO, the PSO and the GA. The proposed modified GWO was validated through a comparison of its tuning result with the tuning results of the GWO, PSO and GA. The GWO and the modified GWO provided the least value of the objective function than the PSO and the GA. Additionally, the modified GWO exhibited faster convergence speed and provided better PI pitch control gains than the GWO, PSO and GA. Furthermore, the GWO, PSO, GA and ZN tuned gains were implemented in the PI pitch controls of fixed speed and DFIG wind turbines connected to the distribution system in four case studies. In the first case study, a 3MW fixed speed wind turbine connected to a 22.9 kV distribution line, and a 12.5 m/s average wind speed was used to run the wind turbine aimed to test the tuned PI controllers in the pitch control. In the second case study, a unit step increase above rated wind speed was applied to test the tuned PI pitch controllers in the 8x3MW fixed speed wind turbines connected as a wind farm with a 9 Bus IEEE stability test feeder. For the third and fourth case studies, a unit-step decrease in the pitch control nominal power and consecutive unit-step increases above rated wind speed respectively were applied, to test the tuned PI pitch controllers of DFIG wind turbines connected to a 9 Bus IEEE stability test feeder. The result from the first case study shows the GWO tuning of pitch control enhanced the generated power generation of the 3MW fixed speed wind turbine by 3.04 % compared to PSO, GA and ZN tuning techniques. For case studies, two to four, the GWO tuning of pitch controls enhanced the dynamic stability of fixed speed and the DFIG wind turbine outputs compared to the PSO, GA and ZN tuning techniques. The dynamic stability of the wind turbine outputs provided by the GWO tuning of PI pitch controls can reduce the stress on the pitch systems of the wind turbines.