## 1 Introduction  
Over the last several decades, environmental problems such as global warming have been becoming serious, and renewable energies such as solar and wind energies have attracted much attention as a countermeasure against the issues. Among renewable energy sources, wind power generation has been installed throughout the world because of its low environmental influence. Wind power generation has various strong points, including that the cost is relatively less, and the efficiency of the energy conversion is higher, in general, than other electricity generation systems that are based on renewable energy. However, when a network fault such as a grounding fault occurs in the vicinity of a wind farm (WF) in a power system with a large-scale WF, the WF can become unstable and then trip from the grid according to the fault ride-through (FRT) grid code [1,2] after the fault. As a result, grid frequency decreases significantly, and the power system can be unstable because the generated power from the WF is lost. To solve such problems, stabilizing control by using a storage battery has been proposed [3, 4, 5, 6, 7]. Since storage batteries have a fast response speed and high controllability, they can be used effectively for enhancing power system frequency stability, as well as power system transient stability. However, the cost of storage batteries is, in general, very expensive. Therefore, it is often difficult to solve problems of system frequency stability and transient stability by using only a large-scale storage battery in the power system. On the other hand, adjustable-speed pumping generators (ASGs) [8; 9; 10; 11; 12; 13; 14; 15], which are used as pumping generators in pumping hydropower plants, can be a powerful countermeasure against power system instability. ASGs were first put into practical use in Japan [8], and several ASGs are presently in operation in Japan. Additionally, ASGs have been widely adopted in pumping hydropower plants around the world [14]. Therefore, if there is an ASG in a power system, it should be utilized effectively for enhancing the power system stabilities cooperatively with batteries, and as a result the number of batteries can be reduced. Although an ASG has a large stored energy capacity, its response speed is not as fast when compared with a storage battery, and it is not so easy for it to respond quickly to an event, such as a trip accident of the WF. In contrast, although storage batteries have a high response speed, their rated power and energy storage capacity are, in general, not as large, and they cannot supply sufficient power to the grid, such as in the case of an accident with large generation power loss due to a network fault. Considering this background, this paper presents a new control system in which an ASG and battery supply and compensate power coordinately to a power system to enhance the frequency stability and the transient stability of the system during disconnection from a large WF. In the proposed control strategy, the ASG ensures the amount of compensatory power, and the battery ensures the control speed of the compensatory power. Therefore, the battery first responds quickly to the system frequency deviation due to a grid fault and improves the frequency nadir, and then the ASG starts to supply the compensatory power to recover the system frequency to the rated frequency. Although it is almost impossible for a usual fixed-rotor-speed pumping generator (FSG) to achieve such control for grid system stabilization, the proposed coordinated control between an ASG and storage battery can enhance grid system stability. Although there have been many reports so far discussing several characteristics of ASGs [8; 9; 10; 11; 12; 13; 14; 15], few have proposed a coordinated and effective control system between an ASG and battery for enhancing power system frequency stability, as well as transient stability. Both the ASG and the battery have an ability to enhance power system stability; however, each of them has weak points, respectively, as stated above.