## 1 Introduction  
In light of increasing of energy crises and environmental pollution, the utilization of renewable energies is attracting more and more attention. Wind power has been rapidly exploited worldwide due to its low environmental impact and technical development, and expects to reach 2000 GW by the year 2030 [1]. Based on the statistics of the Global Wind Energy Council, the global installed capacity of wind power from 1997-2017 is shown in Figure 1[2]. The global wind capacity has expanded from 7.6 GW to 539.58 GW in the past two decades, and wind power has experienced a rapid growth trend since 2008. The top 10 countries for total wind power capacity in 2017 can be found in Figure 2[2]. China, with a total wind power capacity of 188.39 GW, accounts for the largest proportion, with 35%. The United States (89.07 GW, 17%) and Germany (56.13 GW, 10%) take the second and the third place, respectively. Figure 3 shows the prediction of wind power capacity in different areas [2]. Asia is expected to have the fastest development regarding both capacity and developing speed, while Europe and North America are ranked second and third, respectively. Wind energy is a major part of the smart grid. In the past decades, there are many engineering applications of wind power generation in smart grids [3; 4; 5; 6; 7; 8; 9; 10; 11], which promotes the progress of related technologies, such as wind farm planning, grid-connected system protection, wind power forecasting and monitoring, and wind farm modeling and simulation. Modeling plays an important role during development. In the early phases, the modeling of a single wind turbine has received more attention, due to the application of small-scale wind power. In recent years, with the advent of new types of wind generators as well as the high penetration of wind power, the modeling and simulation of wind farms has become a research direction in smart grids [12; 13; 14; 15; 16; 17; 18; 19]. At present, there are two categories of modeling methods, respectively, (a) detailed modeling, and (b) equivalent modeling. In detailed modeling, all of the components, such as generators, step-up transformers, and a large number of collector circuits, are modeled comprehensively. However, equivalent modeling starts from the influence of wind farms on smart grids, and regards wind farms as a whole to aggregate or reduce the order of wind turbines. Compared with detailing modeling, equivalent modeling is used widely, since its computational complexity is drastically  
Figure 1: The global installed capacity of wind power during 1997–2017. Figure 3: Wind power capacity from 2017 to 2022. Figure 2: The top 10 global countries for total wind power capacity in 2017.  
reduced, while legitimate precision is maintained. Figure 4 shows the framework of the wind farm modeling with the aggregating method. The wind farm aggregation modeling mainly consists of the following three stages. (1) Modeling of wind speed. Randomness, volatility, and uncontrollability are the main aspects of wind speed that affect the operation and grid-integration of wind farms. Based on the features and emphasis, wind speed models include three groups: probability distribution models, time-series models, and component models. Probability distribution models and data-based black box models are established by the large amounts of data, including measured wind speed, historical data, wind speed prediction, and environment data. In the component model, wind speed is decomposed into different wind speed components focusing on different wind speed variety characteristics and different time lengths. Then, the probability distribution model or time-series wind speed model for each wind speed component can be established. (2) Modeling of wind turbine generator. The wind turbine generator (WTG) model is the key part of the aggregation modeling of a wind farm.