# Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines
## 1 Introduction  
Wind energy is the most mature and promising renewable energy source in the world at present. The doubly-fed induction generator (DFIG) based and direct-drive permanent magnet synchronous generator (PMSG) based systems are the most popular wind energy conversion systems (WECS), which are widely used in wind farms [1]. Though both of the two WECSs have their own advantages and disadvantages, the direct-drive PMSG based WECSs are preferred in high power applications owing to the simple structure, high efficiency, and high reliability due to the absence of gearboxes [1; 2; 3]. However, due to the stochastic nature of wind, the output power of the wind farm is fluctuating, which brings negative influences to the stability and economy of the grid operation. Specifically, the problems caused by the wind power fluctuations are listed as: frequency deviation, voltage flicker, low power quality, and harm to sensitive loads [3; 4; 5]. To solve these problems, several methods are proposed to smooth the output power of the wind farm, which can be basically divided into two major categories: direct power control and indirect power control. The direct power control usually depends on using the wind turbine (WT) itself without energy storage devices, such as through the DC bus voltage control, rotor inertia control, and the pitch angle control [6; 7; 8; 9; 10; 11]. However, the DC bus voltage control may cause the excessive voltage ripple, thus affecting normal operation of the WECS [5]. For the rotor inertia control, the rotor speed is always controlled to exceed the rated value to store the kinetic energy. According to the research [5],the efficiency of the kinetic energy control relying on the generator inertia is close to the maximum power point tracking (MPPT) control. The trade-off between the maximum power tracking and power smoothing is explored through the optimal control of WTs based on the rotating kinetic energy reserves in references [7; 8]. The pitch angle control has to operate at a fast rate, thus mechanical stress accrues in the wind turbine blade. Besides, the direct power control methods always focus on the output power smoothing of a single WT, which may lead to the poor effect for the entire wind farm. In addition, all the smoothing capability of the direct power control method is constrained by the rated power of the WTs. The indirect power control is realized by using energy storage systems (ESS), such as the battery, the supercapacitor, the superconductor magnetic energy storage (SMES), the flywheel, and so on [12; 13; 14; 15; 16; 17; 18; 19]. But all existing ESSs have certain problems in practical application. The charge-discharge cycles of the battery are limited, although many types of batteries are quite mature at present [12; 13]. The supercapacitor has the much longer life of charge-discharge processing than that of batteries, but it cost too much to be used on a large scale [14]. SMES is a large superconducting coil that can store electric energy in the magnetic field produced by the flow of a DC current through it. The effectiveness of the SMES is demonstrated by many studies, but it is still too costly [15; 16]. The flywheel ESS utilizes the kinetic energy of a rotating disc, which depends on the square of the rotational speed. It has the advantages of long cycling life, large energy storage capacity, and high reliability [17; 18]. However, the drawbacks of immature technology, large size, and high standing losses cannot be ignored in practical use at present. Then hybrid ESSs for smoothing out wind power fluctuations are proposed in literatures to overcome the disadvantages of the single ESS, but the control strategies are more complicated [19]. As above, all the existing power smoothing control strategies have both advantages and disadvantages, which result in difficulties for practical application.