Dispersed wind power connected to the weak grid may cause the frequency instability. In this paper, a hierarchical controller applied to a microgrid (MG), including wind turbines (WT) and battery units (BU), is proposed to provide in a coordinated frequency support to a weak grid by adjusting the tieline active power flow according to the frequency-grid requirements. The coordination between MG local and central controllers provides the following features. (i) In case of required grid-frequency, the MG tie-line power flow will be controlled to be constant in each dispatching time interval. (ii) In case of underfrequency, the coordination between WT virtual inertia and BU controllers will be used to participate in primary frequency regulation (PFR). Then, BU supplies power according to the secondary frequency regulation (SFR) commanded by the maingrid dispatch center. (iii) In case of over-frequency, BU absorbs power to reduce the tie-line active power for PFR purposes. After that, the SFR uses pitch control coordinated with the battery charge control. A stability analysis model is established to deal with several transitions among different operation modes and the interaction between the weak grid impedance and the MG output impedance. Simulation results are presented to validate the proposed approach. Index Terms-Wind/battery microgrids, primary frequency regulation (PFR), secondary frequency regulation (SFR), hierarchical control, central controller, local controller NOMENCLATURE Parameter DescriptionWW Generated wind energy [J] T Scheduling period [min] PWf Forecast output power of WT [W] PT Average wind power [W] B * Reference power of the BU inverter [W] PWT Actual WT output power [W] PWT * WT expected output power [W] Pinertia WT virtual power inertia [W] f Difference between the grid frequency and the rated one [Hz] k PFR factor [-] kd Differential coefficient of the frequency deviation [-] PAGC_MG AGC power scheduling of MG [W] PAGC_g AGC power scheduling of grid[W] CMG Frequency-regulation capacity of the MG [W] are with Tianjin Key Laboratory of Advanced Electrical Engineering and Energy Technology, Tianjin Cg Frequency-regulation capacity of the grid [W] fmin Minimum value of the normal frequency [Hz] fmax Maximum value of the normal frequency[Hz]  WT rotor angle speed [rad/s] rated WT rotor rated angle speed [rad/s]  PMSG rotor position angle[] p Pole pairs number of PMSG[-] Psloss PMSG stator losses[W] isabc PMSG stator current[A] Udc Back-to-back converter dc bus voltage[V] Air density [kg/m 3 ] WT radius[m] Wind energy utilization factor [W‧s 3 /kg‧m 2 ] β * Pitch angle reference of the WT [] β Pitch angle of the WT [] λ Tip speed ratio[-] maximum wind energy utilization factor [W‧s 3 /kg‧m 2 ] Popt WT maximum power [W] sd , sq d-q stator inductances [mH] s Stator resistance [Ω] sd , sq d-q stator voltages [V] Synchronous angular velocity[rad/s] φ Permanent magnet flux of the PMSG [Wb] Te Electromagnetic torque of the PMSG [N‧m] E Kinetic energy stored in the WT [J] J Inertia of the WT and i...