Within the power system network, frequency control is one of the challenges that must be addressed properly. It is becoming more important because of uncertainties and the complexity of the electrical network [1]. The early aim of LFC is to maintain the scheduled system frequency and interarea tieline power within predetermined limits to cope with the load variations and system disturbances [2, 3]. Control strategies that are robust, easy to implement, and take into account the growing complexity and variation in the power system are required to achieve desirable performance.
Over the last decades, control system designers have applied several research and design strategies to the LFC problem to find the best solutions. In LFC problems, proportional–integral–derivative (PID) is still a suitable controller. Conventional techniques for determining PID parameters need a linearized mathematical model of the system under study. Recently, heuristic and metaheuristic optimization techniques like genetic [4], cuckoo search [5], bacterial foraging [6], imperialist competitive [7], whale optimization algorithm [8], and chaotic optimization [9] have been discussed to overcome these issues. In Ref [10], load frequency control for the power system with uncertainties such as GDB and GRC has been investigated. Control systems that employ fixed parameters, such as PID controllers, are incapable of handling uncertainties and load perturbations due to their design at specific nominal operating points. Therefore, robust and adaptive control strategies in the papers address this problem since these traditional control strategies may no longer perform well in all operating conditions.
Fuzzy logic is one of these control approaches to solve the LFC problem. Unlike conventional methods that rely primarily on a mathematical model for analysis, fuzzy logic control is based on experience and knowledge of experts about a system [11]. The success of fuzzy logic controllers is also presented in Ref. [12,13,14,15]. In these papers, several optimizations techniques have been carried out to find the gains of the fuzzy controllers. Reference [12] uses a sine cosine algorithm, and Ref. [13] presents a fuzzy tuning PI controller using a selfmodified bat algorithm (SAMBA) for tuning the parameters. Also, type2 fuzzy controller [14] and fractionalorder fuzzy PID [15,16,17] have been introduced to enhance the performance of the fuzzy approach in the LFC.
Other techniques such as neural network in Ref. [18, 19], H∞ controller, sliding mode controller, and predictive control in Ref. [20,21,22,23,24] have been applied for the LFC problem. By implementing these strategies, the performance of dynamic controllers is improved when dealing with nonlinearities and uncertainties compared to conventional methods. However, complex calculations to obtain parameters and difficulties in physical implementation continue to obstruct their use in power system grids. Considering these concerns, and with the power system structure becoming more complex day by day, new intelligence techniques are essential to provide desirable performance for power systems.
Recently, a new method of load control has been introduced based on coefficient diagrams. The method uses an algebraic approach to indirectly determine the poles and settle time by using a polynomial overall closed loop [25]. While CDM has a relatively recent application in LFC, its primary principle has been investigated in other fields. Servo motors, steel mill drives, gas turbines, and spacecraft attitude control are examples of these applications. CDM is a polynomial technique that has been developed to guarantee the robustness of the solution. From the shape of the diagram, the designer can see the response, stability, and robustness. Therefore, the design procedure is easier to understand and less complicated [25].
In Ref. [26], a LFC method using CDM is proposed. In this paper, comparing this CDM controller with integrators and model predictive controllers, its superiority has been demonstrated. However, the coefficient and parameters to tune the controller have not been optimized. In Ref. [27], state feedback gains and Kalman filters were used to improve the CDM controller performance. Despite the fact that this article presents a superior control technique, state feedbackbased controllers are not practical because they are too complex and are not available in real power systems. In Ref. [28], rather than merely using the classical technique of decentralizing algebraic CDM, the suggested control scheme in this research work takes into account an optimization technique to illustrate the best performance of this controller. Despite the fact that this paper presents a new approach to finding the best coefficients for CDM controllers, it has a lot of tunable parameters, making it complicated, while the CDM has the potential to demonstrate proper performance with much fewer variables.
Along with all the many benefits of the CDM controller, which have already been presented in the mentioned research works, this paper introduces a new design approach to find the best performance of this controller with respect to its algebraic equations. Moreover, to make the controller practical for industrial applications, the proposed CDM controller’s tuning parameters have been decreased compared to previous papers. The key parameters of the proposed controller have been determined using an optimization algorithm called the water cycle algorithm (WCA). The WCA is a new optimization algorithm that has been proposed by the observation of the water cycle process and the movements of rivers and streams toward the sea [29]. The performance of WCA in tuning CDM parameters compared to GA and PSO has also been investigated in the present work. A variety of cases, including large steps and uncertainty in dynamic parameters, were used to illustrate the superiority of the proposed method. In this study, comparing the results of using a classical integral, a CDM alone, a fuzzy strategy, an optimized PID, and the proposed controller, the superiority of the suggested controller has been confirmed. The objectives of this work are:

(a)
Optimize the parameters of CDM with respect to its algebraic equations.

(b)
Using an optimization technique called WCA with better performance to find the coefficients of CDM controller.

(c)
Making the CDM Controller more practical by minimizing the number of tunable parameters.

(d)
Comparing the proposed control strategy with existing ones to demonstrate its superiority.

(e)
Show the robustness of the suggested controller against uncertainties and large disturbances.
This paper is organized as follows: “Dynamic response of power system” provides an overview of the power system structure and its essential control loops. In the “coefficient diagram method” section, a general explanation of this method is described. The “Water Cycle Algorithm” section discussed a new optimization technique used in this paper. In “proposed control strategy,” the CDMOPT method is introduced. Several simulations for studying the performance of the control strategy and the results are in section “Results and simulations.” The paper ends with the “conclusion” section, followed by the references.