## 1 Introduction  
With the rapid development of new energy generation technologies such as photovoltaic power generation, wind power generation, et cetera, as well as user's growing requirement of power quality and power supply reliability, power system has changed from the traditional centralized large power grid to the multi-area interconnected power system [1]. The reliability, flexibility and economy of power grid can be greatly improved by the coordinated and optimal operation of regional interconnected power system. Moreover, it should not be ignored that the interconnection of regional power systems will increase the uncertainties and bring problems about the frequency stability in the power network [1; 2; 3]. A high-quality power system requires the power frequency rate and voltage of system to be kept within a certain range around the set value. This requirement can be reached by adjusting the active power and reactive power of the system. The load frequency control (LFC) is an important part of the automatic power generation control (AGC) in power system and the function of the LFC is to ensure the stability of power system load frequency [4; 5]. In other words, the LFC is used to keep the balance between the generating power and user load. Specific assignments of the LFC are as follows: (1) Make sure that the deviation of load frequency can be maintained at zero. (2) The switching power between tie-lines can return to the set value quickly under any load variation disturbance [6]. The study of load frequency stability control in power system began around the 1970s [7; 8]. In pace with the development of LFC, the control mode has developed from only considering the load frequency stability into combining the load frequency with the tie-line exchanged power together [8; 9; 10]. The control object has also changed from a single generator to the whole power plant area, and from a single-area system to the multi-area interconnected power system [10]. Many scholars have been looking for methods to improve the control effect of the LFC, such as applying neural network theory, adaptive control, fuzzy control, predictive control and other optimal control theories. The chaos optimization algorithm is used to adjust the multi-area load frequency control PID controller in [11]. In [12], it is proposed to combine the adaptive modified bat algorithm with the fuzzy logic (FL) to set the parameters of the proportional controller on line to improve the control effect of the LFC. The particle swarm optimization (PSO) algorithm is applied to adjust parameters of the proposed PI controller in [13]. The uncertainty caused by the variation of governor and turbine parameters is considered in [14], and an adaptive model predictive control (AMPC) method is applied to the LFC controller for multi-area power systems which can change the object model in MPC structure online. However, the research on LFC optimization is not only reflected in the improvement of controller and algorithm. In [15], multiple controllable thyristors or synchronous series compensators are installed in multi-area power systems, improving the dynamic control effect of the LFC by the coordinated control of phase shifter. The main contributions of this paper are as follows: (1) We propose a new diagram of four-area interconnected power system and establish the dynamic mathematical model of power system in each control area. (2) The HESS is introduced to provide the power flow in purpose of regulating the frequency and tie-line exchanged power of system. (3) We apply the generic mode control method in [16] to realize the charging and discharging of the HESS. (4) We design the H\({}_{\infty}\) robust controller based on the LMI and state-feedback method to calculate how much power the HESS should provide to the power system.