# Key Issues on the Design of an Offshore Wind Farm Layout and Its Equivalent Model
## 9 Equivalent Model for a Wind Farm  
A large wind farm comprises hundreds or thousands of wind turbines. Therefore, works on the development of a simulation platform and power system analyses are increasing, and much time will be consumed in simulations that involve correspondingly many data. If each wind turbine were modeled in detail, then data preparation and model calculations would involve substantial amounts of time and effort. The most efficient method for simulating a large wind farm uses an equivalent wind farm to reduce complexity and simulation time [56; 57]. Equivalent methods for simulating wind farms typically involve a single-machine model or a multi-machine model; however, to reflect actual operating conditions, most equivalent methods use multi-machine models [58; 59; 60]. Based on the variation of wind speed among turbines, the single-machine representation method can be further classified as using a \"1+1\" model (one wind turbine with one generator) or an \"n+1\" model (n wind turbines with one generator). This method is suited to dynamic equivalent modeling when wind-speed is uniformly distributed throughout the wind farm. However, the distribution of wind speeds in a large wind farm is frequently non-uniform as a result of topography, the wake effect, and the time-lag of wind speeds. Therefore, the single-machine representation method cannot easily capture comprehensively the dynamic characteristics of the entire wind farm. The multi-machine representation method is used to construct an \"n+n\" model (n wind turbines with n generators), which is based on the principle that wind turbines in the same clustering generate similar amounts of power.  
Most of the wind farms are irregularly arranged, thus different wind turbines have different operating conditions. To increase the efficiency of simulation of a wind farm, in multi-machine models, wind turbines have been grouped by wind speed using various clustering methods [60; 61; 62; 63; 64].  
As an example of the above, reference [64] developed a system cluster algorithm that combines four types of statistics in a standard to the wind farm equivalent. Reference [60] used the growing spanning tree (GST) clustering method for the wind farm equivalent. The advantage of GST is that it captures the operating conditions of different wind turbines. Reference [62] used the Fuzzy C-Mean algorithm and the Xie-Beni exponent to cluster wind turbines in a wind farm. Reference [63] used the annual forecasting of wind speed and wind direction to build the probability distribution of wind. Next, wind speeds and wind directions with high probabilities were selected to evaluate a clustering index and then an equivalent model of a wind farm was established using the support vector clustering (SVC) algorithm. Every equivalent method has advantages and disadvantages. Therefore, equivalent methods must be carefully selected to ensure accuracy of simulation and provide a favorable computation speed.  
The single-machine equivalent model has a simple structure but provides low simulation accuracy, while the multi-machine equivalent model provides a higher simulation accuracy. A multi-machine equivalent model of a wind farm must consider the wake effect. However, traditional linear wake models cannot accurately reflect the actual wake effect, reducing the usefulness of wind turbine clustering. Therefore, a more accurate nonlinear wake model should be used to evaluate wake loss in wind farms.