## 1 Introduction  
With the increasing demand on energy resources, human society is confronted with significant issues including fossil resource exhaustion, climate change and pollutant emission. In recent decades, renewable energy resources (RER) such as wind and solar energy attracted world-wide attention for their merits in energy conservation as well as in reducing pollutant emission. It is highly recognized that utilization of RER will be one of the most promising methods to solve the global energy problem and achieve sustainable development [1; 2]. The distributed integration of wind and solar power helps to reduce loss from long-distance transmission and is a significant method of RER utilization, but the intermittency and fluctuation of wind and solar energy will inevitably influence power supply reliability. Besides, the imbalance between the amount of generation and the load demand may result in power system instability [3]. Hence energy storage (ES) devices, including lead-acid batteries, Li-ion batteries, super capacitor (SC), flywheel storage and superconducting magnetic energy storage (SMES) can be utilized for output power smoothing. A small power system consisting of power converter-based generation, ES devices, small classic synchronous generation, and various types of loads forms a microgrid (MG) [4]. While a number of research works on MG have been done on various aspects, includingcontrol strategy [5; 6; 7; 8; 9; 10], energy management systems [11; 12; 13; 14; 15; 16; 17], marketing policies [18; 19; 20; 21] and system design [22; 23; 24; 25; 26; 27], this paper mainly focuses on the optimal sizing of Distributed Energy Resources (DERs), especially the capacity of ES devices in MG.  
Power source optimization of MG is basically done by minimizing economic cost while the reliability is guaranteed [28; 29]. A number of existing works are done with consideration of complementarity among various power sources as well as source-load coordination. In [25], both reserve sizing problem and loss of load probability (LOLP) index are integrated into the existing storage sizing problem and a probabilistic model is established to strive for a trade-off between reserve cost, storage cost and selling profit. The relationship between storage capacity, reserve capacity and LOLP index is obtained for decision-making on balancing financial cost and reliability. The planning framework proposed in [26] takes into consideration the various characteristics of ES as well as the availability of different renewable energies. The case illustrated in that work adopts hour-level data and emphasized the influence on optimization result caused by variation of diesel generation capacities. The authors of [27] propose a method for coordinated sizing of energy storage (ES) and diesel generators in an isolated microgrid based on discrete Fourier transform. The power fluctuation is decomposed into high-frequency component and low-frequency component, then ES and diesel generators are assigned to these two parts of power correspondingly for power smoothing according to their respond characteristics. The authors of [30] proposed an optimal sizing method of a Vanadium Redox battery in MG and the cost-effective solution is obtained based on the optimal ratings for the battery in both short-term (one-day) and long-term (entire year) scenarios proposed in the paper. ES devices in the above papers basically involve battery energy storage, while other types of ESs, as well as hybrid energy storage systems (HESS), are discussed in some other works. In [31], the authors proposed a super capacitor energy controller (SCEC) and presented a method for selection of the SCEC and filter parameters as well as precise sizing of the super capacitor for a given application. Battery lifetime is extended by diverging the high-frequency power variations to the super capacitor, and the size of the super capacitor is significantly lower than the one estimated for the traditional super capacitor voltage controller.