Some Hermite-Hadamard type inequalities for the fractional integrals are established and these results have some relationship with the obtained results of [11,12].

The hybrid power system is a combination of renewable energy power plants and conventional energy power plants. This integration causes power quality issues including poor settling times and higher transient contents. The main issue of such interconnection is the frequency variations caused in the hybrid power system. Load Frequency Controller (LFC) design ensures the reliable and efficient operation of the power system. The main function of LFC is to maintain the system frequency within safe limits, hence keeping power at a specific range. An LFC should be supported with modern and intelligent control structures for providing the adequate power to the system. This paper presents a comprehensive review of several LFC structures in a diverse configuration of a power system. First of all, an overview of a renewable energy-based power system is provided with a need for the development of LFC. The basic operation was studied in single-area, multi-area and multi-stage power system configurations. Types of controllers developed on different techniques studied with an overview of different control techniques were utilized. The comparative analysis of various controllers and strategies was performed graphically. The future scope of work provided lists the potential areas for conducting further research. Finally, the paper concludes by emphasizing the need for better LFC design in complex power system environments.

In this research article, authors have established a general integral identity for Riemann-Liouville fractional integrals. Some new results related to the left-hand side of Hermite-Hadamard type integral inequalities utilizing this integral identity for the class of functions whose second derivatives at some power are P-convex are obtained.The presented results have some closely connection with [M. E.Özdemir, C. Yıldız, A. O. Akdemir, E. Set, On some inequalities for s-convex functions and applications, Jounal of Inequalities and Applications, 2013:333] Mathematics subject classification (2010): 26A15, 26A51, 26D10.

This paper presents a load frequency control (LFC) design using the variable structure model predictive controller (VSMPC) for gain scheduling (GS) of PI controller in PV connected thermal for multi-area system. Due to the increasing impact of renewable energy sources into the grid system, the system frequency deteriorates. The proposed PV connected thermal system is evaluated under varying load conditions under increased penetration of the PV source.The combination of renewable energy into the thermal power system aggravates the frequency and it is indispensable to mitigate such a problem by introducing an optimal controller. Perturbation in load greatly affects the system frequency and this problem is addressed by using VSMPC based gain scheduling knowing the effect of proportional and integral in transient and steadystate conditions. The oscillations in frequency are controlled by a proposed controller and the impact of frequency under penetration of PV is monitored.Further verification of the proposed technique is accomplished through communication delay in the governor and turbine. The Hardware in the loop (HIL) which validates the accuracy and real time performance of the controller. Finally, the validation of the proposed controller is compared with MPC to tune PI controller and renowned evolutionary tuned techniques like particle swarm optimization (PSO), genetic algorithm (GA) and firefly algorithm (FA) to optimize PI controller. The VSMPC with GS of PI controller shows promising results.

The advancement in technology has proceeded exceptionally that the stability of the power system becomes a major challenge. The mismatch of generation and demand creates frequency perturbation that need to be curbed under the limits to avoid power breakdown. Owing to this, the paper focuses to counter the ever-increasing challenges to the power system much like load and fault disruption that causes frequency deterioration and breakdown. A novel master-slave (MS) control design is formulated for a hybrid interconnected power system in which fractional-order-proportional-integral-derivative (FOPID) controller act as a master and model predictive controller (MPC) act as a slave controller. The gain parameters of the master controller are tuned by salp swarm algorithm (SSA) which act as a secondary loop controller, while slave act as a primary loop controller. The MS formation has resultantly removed the steady-state error associated with MPC and help to mitigate the LFC problem. Furthermore, the superiority of the controller is tested under load and fault disruption in a multi-area power system. The designed controller is tested under four states (1) abrupt load variation, (2) sinusoidal load deviation, (3) sensitivity analysis and (4) IEEE 39-bus test system analysis. The disclosed simulation results depicts that the proposed control scheme has a dynamic performance as compared to other controllers.