## 1 Introduction  
Wind power generation is spotlighted because of global warming and the depletion of fossil fuels, etc. [1]. If a large number of wind farms (WFs) are introduced to the power systems, it leads to a solution to the above issues, since thermal power generation in the power system is reduced. However, the power quality, such as frequency and voltage in the power system, is degraded because WF output constantly fluctuates with wind speed [2; 3; 4]. In the worst case, the power system may get unstable. Therefore, it is essential to smooth the WF output to maintain the power quality. In fact, technical requirements that are related to WF power fluctuation are issued in many countries [5; 6; 7]. To this end, three main approaches: energy storage system (ESS) (battery, superconducting magnetic energy storage system, or flywheel, etc.) [4; 6; 7; 8; 9; 10; 11; 12; 13; 14], pitch angle control [15; 16; 17], and kinetic energy (KE) [18; 19; 20; 21] control have been studied. The ESS is the most widely used in these approaches. However, its cost is very high. Some control schemes that reduce the rated power (the rated capacity) of the ESS have been proposed. A first-order low-pass filter (FLF) is usually used in ESS control systems [8; 9; 10]. Although the FLF is simple, a large rated ESS power is required. To improve the FLF, complex methods (optimal FLF [6; 7], high-order filter [4], Kalman filter [13], fuzzy control [11], and machine learning method [12], etc.) have been proposed. Nevertheless, it is difficult to reduce the rated power (the rated capacity) of the ESS sufficiently. A simple controller composed of a gain and a second-order high-pass filter was proposed in [14]. This controller can reduce the rated power of the ESS more than the FLF. However, further cost reduction is desired in order to smooth the output of large-scale WFs. The pitch angle control can smooth wind generator (WG) output without an ESS [15; 16; 17]. The implementation of the pitch angle control is easy and its installation cost is inexpensive. However, the WG output significantly decreases, since blades of the WG are operated in order to release the wind. It implies that the profit significantly decreases. In addition, the increase of mechanical stress and fatigue of the WG is inevitable. Therefore, it is impractical for the WG output to be smoothed by the pitch angle control. The KE control has been proposed in order to smooth the WG output without releasing the wind [18; 19; 20; 21]. The KE stored in the rotor of the WG can be used to smooth the WG output. When the smoothing command is received, the rotating mass releases or absorbs energy via rotor speed deceleration/ acceleration. The control system is simple and easy to implement, as is the case of pitch angle control. Nevertheless, the operating point of the WG is shifted from the maximum power point. It implies that there is a trade-off between the WG output smoothing and the generating efficiency. Therefore, the reduction of the generating efficiency is inevitable in the KE control, although the efficiency of WG with KE control is higher than that with pitch angle control [18; 19; 20]. In addition, the available KE of the WG is much less than the energy of ESS. As a result, it is hard to satisfy the technical requirement (see Section 2.4) with only the KE control. Table 1 summarizes the characteristics of standard smoothing methods. Because these methods have both advantages and disadvantages, it is difficult to achieve both cost reduction and WF output smoothing by a single method. Methods that coordinate these systems may achieve a good trade-off between these two objection. Although the system without ESS is attractive, there is no better way to replace the ESS completely, as discussed above. This paper proposes a system that is composed of ESS and WF operated by the KE control. In addition, we present a coordination method for the ESS and WF via the optimization of the KE control.