*2.2. Simulation Parameters*

The simulation parameters utilised in this study are provided by the company JSPM, a subsidiary of the Areva group, and represent a real-world PMSG turbine [33]. These values are applied to each PMSG model in the simulation. This characterisation is employed to provide a consistent simulation analysis approach for DIT. These parameters displayed in Table 1 as used by Pican and Ebrahimi Salari [24,29], provide a basis for comparison of DIT in varying configurations and conditions. The farm size selection of 5 turbines is presented as the base number of turbines which would realistically be deployed in the field. Larger farms could be made up of a single directly interconnected bus or multiple strings of directly interconnected buses, each consisting of varying numbers of turbines due to transmission, resource availability or geographical constraints [34–36]. A larger number of interconnected generators, similar to the traditional AC power gird, will facilitate better sharing of disturbances and simplify the frequency and power response of the system.


**Table 1.** Simulation Parameters [33].

#### *2.3. Gust Factor and Variation Limits*

Gust Factor is a representation of the peak average *τ* second wind speed as a fraction of the *T* seconds moving average wind speed [37]. This is shown in Equation (6), where *Umax*,*<sup>τ</sup>* is the maximum *τ* second moving average wind speed in a *T*-second averaging period and *UT* is the *T*-second average wind speed. Typical values for *τ* are 1–10 s with common values for *T* are 10 min to 1 h [37]. The gust factors of all test gusts applied are calculated and analysed.

$$G\_{T,\tau} = \frac{\mathcal{U}\_{\text{max},\tau}}{\overline{\mathcal{U}\_T}} \tag{6}$$

The tolerance threshold for both measured parameters of the simulation is selected as 5% (±2.5%). This threshold is selected to closely follow current grid connection codes on the farm side of the power converter [38]. This paper shows the differing gird requirements that the power conversion system of wind turbines are required to comply with. By limiting variation of frequency and active power to 5%, the power conversion system will be able to ensure grid interconnection compliance [30].

#### **3. Results**

#### *3.1. Baseline System Response*

The baseline system response is generated applying the reference wind gust to the leading turbine while all pitch controllers on turbines 1–5 are disabled. This shows the reaction of the interconnected system of wind turbines in the absence of controllers assisting in dealing with gust disturbances. As shown in Figure 8 without any pitch control the system behaves similar to a single synchronous machine causing the collective bus frequency to increase while active power is inserted at the lead turbine. This relatively small disturbance causes both the bus active power and bus frequency responses to vary outside the 5% (±2.5%) tolerance threshold.

**Figure 8.** Baseline system test for both ECG and EOG. Δ*T* = 3 s *Vgust* max = 15 m/s.

#### *3.2. Extreme Coherent Gust Responses*

The following section displays simulations results for Extreme Coherent Gusts (ECG) as described in the IEC Standard [27]. The test gust is applied to generator one with the system at a steady state at time zero. All generators are synchronised and interconnected to the main bus before time zero and have reached a steady state. Extreme coherent gust simulations are preformed at Δ*T* values of 3 s, 5 s and 10 s respectively. Example test gusts for Δ*T* = 3 s are displayed in Figure 9.

**Figure 9.** 3 s ECG test gusts applied.

For each rise time *Vgust* max is varied from 15 m/s to 30 m/s in 1 m/s increments. The corresponding gust factors of these gusts can be calculated by Formula (6), where *Umax*,*τ* is the maximum *τ* second moving average wind speed in a *T*-second averaging period and *UT* is the *T*-second average wind speed [37]. The gust factors for the input ECG test gusts applied are displayed in Table 2 assuming a ten minute moving average base wind speed *UT* = 14 m/s and *τ* = 1 s.


**Table 2.** ECG Input Gust Factors.

Figure 10 displays the frequency responses of each gust measured at the offshore bus. As can be clearly seen the 28 m/s gust response exceeds the limit of 5% (±2.5%) variation. This is due to the rate of change limitation of pitch angle variation of turbines. With an 8 degree per second maximum rate the pitch control is not capable of maintaining the 5% maximum variation. However, it can be seen that the system can damp the variation and return to steady state in all of the input gust cases. The 27 m/s gust also approaches the negative 2.5% limit but does not exceed it and therefore can be taken to be the maximum boundary limit with regard to our frequency response criteria.

**Figure 10.** System frequency response to 3 s ECG gusts.

As can be seen in Figures 10 and 11, the active power and the frequency response are directly linked. As the 28 m/s ECG is rejected due to the frequency response criteria it can already be discounted. The 26 m/s, 27m/s and 28 m/s responses all fall outside the negative boundary leaving the 25 m/s as the maximum boundary within the limit with regard to the active power criteria. It can therefore be said that for the system modelled any ECG with Δ*T* of 3 s and magnitude up to and including 25 m/s can be tolerated.

**Figure 11.** Bus active power response to 3 s ECG gusts.

The remaining simulations for ECGs with Δ = 5 s and Δ = 10 s all show performance within the 5% tolerance level. The 8 degrees/s of pitch angle control is capable of damping response without becoming saturated. The results of all the simulations are tabulated in Table 3. The light blue segments denote the respective criteria are satisfied while dark blue denotes that one or both of the ±2.5% threshold levels have been exceeded. Considering the 5 s and 10 s rise time simulations, it can be observed that ECGs up to 30 m/s can be tolerated by the system. The maximum gust factors for these events of 1.64 through 2.14 are well beyond the gust factors measures at the coastal wind site in Frøya [37]. The 3 s ECG is within limits up to and including a *VGust* max of 25 m/s. With a gust factor of 1.79 from Table 2, this 25 m/s gust is well above the measured gust factors at this site with a mode value of 1.20.

**Table 3.** This table displays the results of all ECG simulations completed. Light Blue demonstrates the respective responses remain within the ±2.5% boundary limitations with dark blue showing the criteria has not been met. The minimum and maximum values of both frequency and active power reached during each gust are displayed.


#### *3.3. Extreme Operating Gust Responses*

This section outlines the Extreme Operating Gust responses for Δ*T* values of 3 s, 5 s and 10 s. The same initial conditions of synchronisation and steady state are utilised with the gust being applied to turbine 1 at time t = 0. The *VGust* max values are incremented by 1 m/s from 15 m/s to 30 m/s. Example 3 s EOG input gusts can be seen in Figure 12.

**Figure 12.** 3 s EOG test gusts applied.

The corresponding gust factors for the 3 s, 5 s and 10 s rise time EOGs are calculated by integrating (1) with limits of ±0.5 s of the peak gust time giving the sliding window of *τ* = 1 s and are displayed in Table 4. The 10 min moving average wind speed *UT* = 14 m/s.


**Table 4.** EOG Input Gust Factors.

Considering Figure 13, it can clearly be seen that the wind farm struggles to maintain electrical frequency through EOGs, when compared with ECGs of the same magnitude displayed in the previous section. This is to be expected as now the leading turbine first experiences a dip in wind speed prior to the sharp rise to *Vgust* max. It can be observed that EOGs with magnitudes greater than 18 m/s lead to a violation of the 5% pk-pk limitation on bus frequency. The initial negative dip in wind speed preceding the rise causes a greater *dVGust*/*dt* which saturates the 8 degree per second rate of change limitation on the pitch controller.

**Figure 13.** System frequency response to 3 s EOG gusts.

Figure 14 displays the active power variation on the main bus through the event. It can be seen that the 18 m/s gust displayed in purple, while within tolerance levels for frequency variation, fails to remain within 5% limitation on active power. However, as the active power only exceeds this limitation by 100 kW, it is possible that it could be considered tolerable in some electrical power conversion systems, particularly those which incorporate storage. This simulation assumes that all wind turbines remain connected to the bus throughout the transience however in the higher cases of *Vgust* max, it is likely that the turbine would be forced to disconnect from the main bus. This case however is outside the scope of this study and may be explored in future work.

**Figure 14.** Bus active power response to 3 s EOG gusts.

The system frequency responses as shown in Figure 15 display a similar trend to that of the three second EOG tests. We can see however that the 19 m/s is within tolerable limits with the 20 m/s forming the boundary condition with regard to system frequency.

**Figure 15.** EOG Bus Frequency Responses Δ*T* = 5 s.

Figure 16 displays the bus active power variation for the 5 s EOG tests. It can be observed that the 19 m/s EOG trace shown in green falls outside the negative 2.5% variation limit for a short period of time. For the purposes of this study, this will be declared outside the tolerance range.

**Figure 16.** EOG Bus Active Power Responses Δ*T* = 5 s.

All test runs are displayed in Table 5. The light blue denotes the output remains within the respective boundary condition with dark blue showing that one or both of the ±2.5% boundaries have been exceeded.


**Table 5.** This table displays the results of all EOG simulations completed. Light Blue demonstrates the respective responses remain within the ±2.5% boundary limitations with dark blue showing the criteria has not been met.

Analysing Table 5, it can be observed that the EOG gusts present a much greater challenge to the DIT bus parameters than ECGs. The 10 s rise time EOGs are the most effectively controlled which is to be expected as they have the lowest rate of change of *Vgust* max. The gust factors for these gusts are higher than the gust factors for shorter rise time gusts of the same magnitude. This is due to the wind speed cresting the maximum point for a greater time on either side of the maximum, therefore increasing the 1 s sliding average value. For a rise time of 10 s, the maximum gust factor which was successfully controlled by blade pitch angle control is 1.424. This gust factor is significantly below the 10 s for ECGs of 2.14 and above. Comparing this to the findings of Bardal et al., it can be observed that gust factors of 1.4 and above at the 100 m hub height are very rare [37]. As the average hub heights of modern offshore turbines are greater than 100 m, the 100 m data is the most relevant to this study.

If we consider the 3 and 5 s EOG data the corresponding boundary gust factors of 1.189 and 1.273 are within the range of values experienced offshore [37], however, the majority of gusts in the study fall below these values. This study also includes gust factors of gusts which may have occurred during times when the average wind speed may have been above the typical cut out speed of the turbine of 25 m/s and therefore the farm would not have been operating [39]. Gusts of this nature that do occur during the operation of a DIT wind farm would require further mitigation techniques outside of pitch angle control to maintain the 2.5% variation parameter studied.

#### **4. Discussions & Conclusions**

Extreme Operating and Coherent wind gust responses for directly interconnected systems have been investigated and discussed. It has been shown that through the use of pitch control on individual turbines the majority of wind gusts can be tolerated and the boundaries of this tolerance have been identified. The respective gust factors for these gust events have been calculated and compared to real coastal wind data [37]. These boundaries as presented in Tables 3 and 5 form the basis for further study on DITs interconnection to the grid. Power converter design and location can be investigated to further improve the gust tolerance of DIT systems. Additional analysis of large wind data sets will provide estimates of the frequency of gusts with gust factors greater than the tolerance levels described, facilitating comparison of DIT and traditionally interconnected wind systems in terms of capacity factor, capital expenditure (CapEx) and operational expenditure (OpEx).

Extreme operating gusts pose a greater challenge when compared to the extreme coherent gust conditions due to the higher rate of change in wind speed occurring throughout the gust. This study has not used B2BC which ordinarily provide a means on an individual turbine by turbine basis, of dealing with variations on the wind side while maintaining power on the grid side within specified limits of frequency and voltage. In the proposed DIT topology it is still intended to use B2BCs for a number of turbines as shown in Figure 2. Employing the farm level B2BC control and the pitch control as analysed in this paper

will facilitate a greater tolerance range of gusts for DIT systems and will be the subject of future work. It is possible that with wind prediction methods such as LiDAR and more sophisticated machine learning-based control systems, that the boundaries could be further improved thereby reducing the load on the pitch control system and the power conversion systems down steam of the interconnected bus.

In conclusion, the Direct Interconnection Technique has been shown to be capable of tolerating wind gust conditions. The boundary of tolerance has been established and methods for further improvement have been proposed.

**Author Contributions:** C.W.O. carried out the reported research work, writing the paper and revisions. M.E.S. and D.J.T. supervised the research work, revisions and editing. The content of this paper is discussed by the authors and they all contributed to the final article. All authors have read and agreed to the published version of the manuscript.

**Funding:** This publication has emanated from research supported by the Science Foundation Ireland under the MaREI Centre research programme (Grant No. 12/RC/2302, and 14/SP/2740) and LERO Science Foundation Ireland grant 13/RC/2094. It is also co-funded under the European Regional Development Fund through the Southern and Eastern Regional Operational Programme to MaREI (www.marei.ie (accessed on 20 December 2021)) and Lero (www.lero.ie (accessed on 20 December 2021)) centres.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data Available on request.

**Conflicts of Interest:** The authors declare that the publication of this article has no conflict of interest.
