The utilization of renewable energy expanded significantly everywhere throughout the world, soon after the primary huge oil crisis in the late seventies. Besides, with the worldwide ecological contamination and energy crisis, sustainable power sources, for example, photovoltaic (PV) and wind [1–7] have assumed an influential role in electricity generation. In any case, the yield of PV and wind power generation is normally oscillating because of the discontinuity and haphazardness of sun-powered and wind vitality, and results in a vigorous effect on the grid in case of grid-connected mode. As of late, the integration of energy storage (ES) into renewable energy sources (RES) has turned out to be a standout amongst the most pragmatic solutions for taking care of this issue [8–17]. The principal roles of ES are to level the variance and increment the infiltration of RES, update the transmission line capability, increment the power quality, keep up the system dependability and soundness [18]. With the integration of RES, the complexity of the power system operation is increasing. Moreover, the system operating point varies instantaneously, and subsequently the system encounter deviation in frequency [19]. This deviation leads to bothersome impacts. Load frequency control (LFC) is one of the essential auxiliary administrations which assume a critical role in keeping up the frequency of the system at its ostensible value [20]. Due to the viral role of LFC, optimal control-based controllers have been studied in many research. Parmar et al. [21] have studied the two-area LFC system with diverse power generation sources. The optimal feedback controller gains have been calculated to minimize the quadratic performance index. They have realized better dynamic performance for the system considering shunt DC/AC tie-line in the presence of parameter changes. The controller to the hybrid RES with Fuel Cell (FC) system has been introduced by Rawat et al. [22]. The system consists of a Micro-hydropower system (MHP), PV, Diesel Generator (DG) and (FC). They have proved the efficiency of the tuned proportional integral derivative (PID) rather than the proportional-integral (PI) controller over system stability and performance. Kabiri et al. [23] have proposed a controller to regulate thermal units and determine the amount of their generated power to compensate PV system and regulate frequency oscillations to improve the frequency in the smart grid. The authors in Liu et al. [24] have introduced PID and fuzzy logic controllers to the modeled hybrid hydro systems with the synthesis of wind, thermal, solar, and diesel plants. Satisfied performance and robustness were achieved for both controllers. Lotfy et al. [25] proposed a Polar Fuzzy (PF) control strategy for a multi-unit energy system. In this study, the authors have utilized the electric vehicle (EV) battery as an enormous energy storage unit to promote the system frequency stability. They have considered the error control signal of the power supply and frequency deviation. In Zeng et al. [26] have presented an adaptive model predictive load frequency control (MPC) method for the multi-area power system (MAPS) in discrete time form with PV generation. They have considered a dead band for governor and generation rate constraint for the steam turbine. They have ensured the priority of the proposed MPC method on the conventional PI control methods over dynamic and steady-state performance for the nominal condition, parameters uncertainties cases, load disturbance. In Mohamed et al. [27] have proposed several frequency control techniques for variable speed wind turbines and solar PV generators. These techniques have allowed renewable energy sources to keep a certain amount of reserve powers and then release the reserved power according to frequency events. Mu et al. [28] have investigated the LFC problem of a standalone microgrid with PV power and (EVs) which are used as large-scale energy storage units. An observer-based integral sliding mode (OISM) controller has succeeded to regulate the deviated frequency of the power system. Pandey et al. [29–31] have studied the LFC of MAPS with multi-power generation sources utilizing HVDC link parallel to AC two areas interconnection tie-line. They have applied differential evolution for tuning the controller parameters to their best values to realize a satisfying system performance. Other control schemes for LFC in power systems with or without integration of RES based on artificial intelligence and optimization algorithms have been introduced in Golpira et al. [32,33].

In this paper, a novel optimized controller based-Multi-Verse Optimization algorithm (MVO) has been presented to regulate the LFC. The proposed controller is applied for a single area and interconnected multi-area MSPS. MATLAB/SIMULINK has been utilized to simulate the control system with diverse operating conditions.

The proposed system includes hydro, thermal with reheat turbine, gas, PV, and wind power plants. Each unit has been modeled linearly for simulation as shown in Fig. 1. The symbols of the system have been presented in Appendix I. The following are the controller design for multi-source single area power system (SAPS) and MAPS:

MVO algorithm has been inspired by the theory of multi-verse as presented in Mirjalili et al. [34,35]. The mathematical model of the MVO algorithm can be described as: firstly, the universes have to be sorted based on their rise rates and the roulette wheel select one universe to be the white holes in every sample, based on the following expressions:

(4) U=[x11x12…x1dx21x22…x1d........xz1xz2…xzd]

(5) xij={xkj,r1<Nl(Ui)xij,r1>Nl(Ui)

where, d and z are the number of variables and universes, respectively. xkj specifies the j-th parameter of i-th universe, Ui is the normalized inflation rate of the i-th universe, r1 is a random number in [0,1], Ui displays the i-th universe, and xij designates the j-th parameter of k-th universe nominated by a roulette wheel.

The procedure described in Fig. 6 can be described as pursues:

(6) xij={Xj+TDR.((ubj−lbj).r4+lbj)r3<0.5,r2<WEPXj−TDR.((ubj−lbj).r4+lbj)r3≥0.5,r2<WEPxij,r2≥WEP

where, Xj demonstrates the j-th parameter of best universe so-far, lbj displays the lower bound of j-th variable, ubj is the upper bound of j-th variable, xij demonstrates the j-th parameter of i-th universe, and r2, r3, r4 are random numbers in [0,1]. TDR, and WEP are the rate of traveling distance and the existence probability of wormholes, respectively and can be calculated as the following:

(7) WEP=min+l.(max−minL)

(8) TDR=1−l1/pL1/p

where, L expresses the maximum iterations, and l specifies the recent iteration. p is the exploitation accuracy over the iterations. Fig. 7 presents the flowchart of MVO.

The MVO algorithm has been utilized for the simulation and validation of the proposed control scheme. The simulation has been carried out using Core™ i5-4210U CPU, 1.7 GHz, and 8 GB RAM computer. The MVO has been simulated with 10 independent runs to validate the proposed procedure for each case. The obtained results by MVO are compared with PSO. The standard deviation values are 0.0565 and 0.1119 respectively for MVO and PSO methods. Also, the minimum cost values are 3.1626e^-04 and 3.3e^-03 respectively for MVO and PSO methods. A comparison between the convergence curves of MVO and PSO for several runs is presented in Fig. 5. The results confirmed the robustness of the MVO algorithm. The values of the best solution of the optimized PI controllers based on MVO and PSO have been recorded in Tab. 1.

To test the performance of the proposed controller with parameters variation, the wind power, and PV power variations have been assumed as shown in Fig. 7. To achieve this target, 5 cases of study have been introduced against load disturbance, frequency variation as the following:

An MVO algorithm has been utilized in this paper to optimize the control parameters of the LFC of a predefined power system. This system comprises thermal, gas and hydro power plants as the conventional sources of power generation and PV, and wind power plants as RES. The algorithm has been applied to a single area and a two-area power system. The system performance has been observed on the basis of dynamic parameters and frequency overshoot. The Examination of dynamic responses revealed that the application of MVO improves the transient responses extraordinarily and enhances the frequency overshoot.