**2. Simulation Methodology**

Gusts modelled in this study are created through the use of IEC standardised descriptions of gusts available in IEC 61400-3-1:2019 [26]. This offshore wind turbine standard in section 6.4.3.1 directly refers back to IEC 61400-1:2019 [27], an onshore wind turbine standard that describes the mean wind speed based wind gust profiles. In this standard, five extreme wind conditions are proposed: Extreme Operating Gusts (EOG), Extreme Direction Change (EDC), Extreme Coherent Gusts (ECG), Extreme Coherent Gusts with direction change (ECD) and Extreme Wind Shear (EWS). This study focuses on EOG and ECG. ECGs are considered as the increase in wind speed is sustained once the maximum gust speed is reached. This gust profile is useful for identifying any saturation limits of the system whereas the Mexican hat shape of EOGs present the greatest rate of change during the gust and therefore challenge the system due to the maximum rate of change of pitch angle. This worst-case analysis approach does not consider direction change of the wind, as the greatest amount of energy and therefore the most challenging input for the directly interconnected bus, occurs when the wind is directly incident on the turbine blades [28]. All gusts are applied with the hub facing directly into the wind with no yaw control considered. Future work may include an analysis of the other conditions. EOG and ECG profiles are generated using Equations (1) and (2).

$$u(z,t) = \begin{cases} \bar{\mathcal{U}}(z) - 0.37 \mathcal{U}\_{\text{gust}} \sin(\frac{3\pi t}{T}) (1 - \cos(\frac{2\pi t}{T})) & 0 \le t \le T\\ \bar{\mathcal{U}}(z) & \text{otherwise} \end{cases} \tag{1}$$

As defined in IEC 61400-1, *Ugust* is the hub height magnitude defined by extreme wind speed recurrences for a particular site along with other physical factors such as rotor diameter. This *Ugust* factor is varied along with the period *T* to peak gust speed and settling time. *U*¯ (*z*) is the average wind speed upon which the wind gust is superimposed.

$$u(z,t) = \begin{cases} \bar{\mathcal{U}}(z) & t < 0\\ \bar{\mathcal{U}}(z) + 0.5\mathcal{U}\_{\mathbb{C}\mathbb{X}}(1 - \cos(\frac{\pi t}{T})) & 0 \le t \le T\\ \bar{\mathcal{U}}(z) + \mathcal{U}\_{\mathbb{C}\mathbb{X}} & t > T \end{cases} \tag{2}$$

In Equation (2), *U*¯ (*z*) is the average wind speed, *Ucg* is the magnitude of the coherent gust and T represents the rise time of the gust. Once the gust is complete the wind speed remains at this new value of *U*¯ (*z*) + *Ucg*. A sample of each gust type with the same rise time of five seconds is shown in Figure 3.

**Figure 3.** EOG and ECG profiles with rise times of 5 s.

The characteristic time for ECGs/EDCs stated in IEC 61400-1:2019 6.3.3.6 is 10 s [27]. This represents a rise time of 10 s between the base wind speed and the maximum wind speed value. However, in the case of EOGs in section 6.3.3.3, the characteristic time is 10.5 s. This time represents the length of the entire gust. Therefore the corresponding rise time would be 5.25 s. For this study, we round down this rise time to 5 s and consider rise times of 3 s, 5 s and 10 s to investigate these gusts on a like for like basis. These values are representative of the gust profiles as described in the standard, but also push beyond the values to investigate system limits.

Each turbine utilises a Permanent Magnet Synchronous Generator (PMSG) with a rated power of 800 kVA and is based on a real-world turbine characterisation [29]. The rated speed was selected at 14 m/s. The simulation begins with all wind turbines interconnected as per the direct interconnection algorithm described in [13]. Turbine 5 is selected as the pilot generator responsible for the maintenance of the frequency and voltage of the interconnected bus. This turbine in the real world would be selected as a turbine towards the centre of the wind park, thus minimising the risk of this turbine being the first to experience a wind disturbance. Each turbine has its own local dump load for spin up and disconnection from the main bus. A simulation diagram is shown in Figure 4. Disconnection could be required for dispatching down, in line with Transmission System Operator (TSO) instructions [30] or during times when the wind speed is outside of cut in and cut out speeds.

**Figure 4.** Simulation Diagram Showing the five turbines with their respective dump loads, the directly interconnected bus and the main load for the farm.
