Due to the high volatility and uncertainty of wind power

the integration of the energy storage system(ESS)in wind farms is required to mitigate the wind power fluctuations so that the requirements of wind power integration can be satisfied. To solve this problem

a multi-scale multi-index ESS sizing model applied to wind power fluctuation mitigation is proposed

which considers the penalty costs. Firstly

a piecewise linearized evaluation method for wind power fluctuations is proposed

which considers the penalty costs. Secondly

a multi-index ESS sizing model is proposed. It minimizes the sum of penalty costs

ESS investment and wind curtailment costs. Also

the fluctuation limits of 1 min time-scale and 10 min time-scale are considered in the model. Thirdly

the large M method is introduced to solve the model accurately. The original nonlinear model is transformed into a mixed integer linear programming model

which is solved by Gurobi. Finally

the effectiveness of the proposed model is validated based on one-week actual wind farm data.