## 1 Introduction
A wind-battery optimization model is established for a storage system and wind farm to conduct scheduling in the same manner as a traditional plant does. Other literature is available on real-time scheduling involving fuzzy logic control and dynamic programming. [PERSON] _et al._ presented a two-level dynamic programming to manage a wind farm and a storage system [33], in which the upper level is implemented over the whole period to obtain the reference trajectory and the lower level is implemented for real-time operation. In [28], a combination of the MPC method with fuzzy logic control was proposed, in which MPC is used for real-time control to achieve the optimization objective, and a fuzzy logic controller adjusts the power reference to increase the lifetime of the storage system. In [24], the author took advantage of two-time-scale property of the dynamics of the integrated system to improve the computational efficiency of the control problem formulation. This merit has reduced the computation burden of the method, and now it can be implemented in real time system. However, we think this method could exist a demerit in running stability. In extreme condition, the prediction error could lead to the optimal mode failure in finding feasible solution. In [25], the merit of the paper is presented with a third-order battery model and a state space is used to describe the battery model. Additionally, author has also found that the prediction horizon of MPC is an important parameter that contributes to the scheduling performance. The demerit of this paper could be that the battery energy storage system (BESS) charge/discharge frequency is relatively high. Thus, the limit constrain of charge/discharge frequency should be added in this model. In [28], the merit of the method is that MPC method is combined with fuzzy logic control (FLC) method to control the wind farm and energy storage. The combination of the two methods is a novel way, and the results have demonstrated that the wind farm revenue has been improved by 3%. The demerit of this paper is that authors adopt single storage rather than two types of storage. The hybrid storage has more advantages than single type energy storage, and these advantages can assist the wind farm in following scheduling. In [33], the author has succeeded in overcoming the dilemma of the conflict between long horizon and prediction accuracy. The method is very useful in controlling sophisticated system consisted by wind farm and energy storage. However, we think there was a minor unreasonable description in the battery model. We believe that the battery ought is to occupy only one of the three states at any given time: charge, discharge, or shut-down, while according to the battery mode (Equation (5)) a battery can be in charge and discharge state simultaneously, therefore we think the author may have neglected this minor point in his model. Although many researchers have investigated the management of a wind farm with a single type of storage based on MPC, few researchers have studied a wind farm with a hybrid storage system based on MPC, especially when the hybrid storage system includes pumped hydro storage. A battery storage system may be more practical than a pumped hydro storage system; however, there are some special cases in which a battery storage system cannot replace a pumped hydro storage system. For example, on an isolated island, pumped hydro storage serves as not only energy storage but also a reservoir for local citizens. Moreover, the pumped hydro storage system has some advantages such as large storage capacity, high efficiency, mature construction technology, relatively low capital cost per unit of energy and time-shifting between wind generation and demand profiles. The purpose of this paper is to present two MPC models to be implemented in wind farms with hybrid storage systems including a pumped hydro storage system and a fly wheel system.