## 2 Multi-Area Interconnected Power System with the HESS
### Hybrid Energy Storage System  
To guarantee the balance between the user power requirement and the active power generated by power grid, it is necessary to install the energy storage equipment with a certain capacity to adjust the power fluctuation of the power system. In the power system, the energy storage system is mainly used to calm down the fluctuating power of the system, reduce the sharp oscillation of system and cut down the peak and valley difference of the load power rate curve in purpose of enhancing the power quality [21; 22; 23]. We introduce the HESS into the inter-connected power system. The HESS aims to stabilize the load frequency of the power grid and eliminate a series of negative effects caused by the fluctuating power. HESS is a kind of energy storage equipment composed of super capacitor (SC) and battery (B). The HESS has been proved theoretically that the structure can give full play to the characteristics of these two kinds of energy storage equipment by [PERSON] et al. in 2002 [24; 25]. The SC has the characteristics of high power density, short charge and discharge time, high reliability and long cycle life. It is suitable for situations require high power, frequent electric charge and discharge instead of the battery with low energy density [22; 25]. Nevertheless, the combination of SCs and batteries can not only meet the qualification of high power density and high energy density, but also can reduce the rated capacity of batteries and prolong its service life. Currently, the HESS has been widely regarded as an effective way to calm down the grid power fluctuation due to its technical and economic advantages [26; 27]. The hybrid energy storage system (HESS) can be mainly divided into two categories: the passive HESS and the active HESS. In this paper, we choose an active parallel HESS comprised of super capacitors and Lithium-ion batteries. The basic structure of HESS is shown in Figure 3.  
In Figure 3, the battery is connected with a boost converter and the supercapacitor is connected with a bi-directional DC-DC converter (buck-boost) [28]. Two converters share the same DC link which is connected to the power system through a DC-AC converter. As shown in Figure 3, the Lithium-ion battery part is composed of a inductance with high frequency \(L_{B}\), an IGBT (Insulated-Gate Bipolar Transistor) \(K_{1}\), a diode \(D_{1}\) and an output filter capacitor \(C_{B}\) which plays a role in protecting the battery [29]. \(U_{Bat}\) is the voltage of the Lithium-ion battery. \(i_{Bc}\) is the inductor input current. \(i_{Bat}\) denotes the boost converter output current. \(U_{dc}\) represents the voltage of DC bus. The super capacitor part consists of a high frequency inductance \(L_{Sc}\) and two IGBTs \(K_{2}\) and \(K_{3}\); \(R_{s}\) and \(L_{s}\) represent the equivalent resistance and equivalent capacitance value of the super capacitor. \(U_{Sc}\) is the voltage of the SC. \(i_{Sc}\) is the inductor input current and it can be positive or negative. \(i_{Sc}\) is positive when the SC is in discharging mode. IGBT \(K_{1}\), \(K_{2}\) and \(K_{3}\) respectively controlled by binary signal \(q_{1}\), \(q_{2}\) and \(q_{2}\). The PWM signals for Lithium-ion battery and super capacitor are generated according to the energy-management strategy [16]. The power exchange between the HESS and power system can be seen in Figure 4.  
Figure 4: Power exchange between the HESS and power system. Figure 3: Basic structure of the hybrid energy storage system. \(P_{ci}\) represents the power requirement from power system corresponding to the output power instruction from the H\({}_{\infty}\) state feedback controller designed in this paper. \(P_{Bat}\) and \(P_{Sc}\) are the power should be provided to power system by the battery and super-capacitor. Moreover, \(P_{Sc}\) is positive when the SC is in discharging mode and negative in charging mode. There are two working modes, namely, the voltage-reduction or charging mode and the boosting or discharge mode [30].