## 5 Optimisation of a Wind Farm--Kinetic Energy Storage System
### Discussion  
Following a thorough analysis of the results it was concluded that the applied optimisation methods, the parameters of the control algorithm of the energy flow between a wind farm, energy storage system and the power grid, and the system model were correct for the characteristics of the analysed task. Its solution had high reproducibility in minimising the capacity of the kinetic storage \(A_{FESSmit}\) (Figure 6a) and fast computation times (Figure 6b). In the analysed examples, the tasks were solved between the 30 th and 40 th generations. Based on the completed studies, it was established that the relationship between the minimum capacity of the energy storage system \(A_{FESSmit}\) meeting the required criteria of a wind farm--kinetic energy storage system and time \(\mathrm{T_{max}}\) was non-linear (Figures 7 and 8). It was demonstrated that the dependence points \(A_{FESSmit}=\)_f_(\(T_{max}\)) could be approximated by polynomial functions of order 3. The values of the determination coefficients identified for the functions amount to over 0.97,  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & \multirow{2}{*}{\(P_{\mathrm{Smit}}\)} & \multirow{2}{*}{\(T_{max}\)} & \multirow{2}{*}{\(T_{max}\)Tmax} & \multicolumn{2}{c}{\(T_{max}\)Tmax} & \multirow{2}{*}{\(T_{max}\)Tmax} & \multirow{2}{*}{\(A_{FESSmit}\)} & \multirow{2}{*}{\(A_{FESSmit}\)} & \multirow{2}{*}{\(P_{\mathrm{WThr}}\)} & \multirow{2}{*}{\(\Delta A\)} \\  & & & & (H) & & (H) & & (\%) & & Power(\(-\))/(MW) & (MW) \\ \hline \hline \multicolumn{10}{c}{\(T_{max(2)}=  
confirming the good fit of a polynomial model for the calculation points. A non-linear character was also observed for changes in the capacity \(A_{FESSmin}\) as a function of the optimisation time constraint \(T_{sumTmax}-A_{FESSmin}=f\) (\(T_{sumTmax}\)) (Figure 9). The application of higher constraints (lower values of \(T_{sumTmax}\)) amounting to 150, 125, 100, and 75 h/year contributed to an increase in the required capacity of energy storage \(A_{FESSmin}\). The increase was diversified for different values of time \(T_{max}\) and power \(P_{3 min}\), but between subsequent values of \(T_{sumTmax}\) it usually ranged from 1.5 to 3.0 times (Figure 8). In the case of optimising calculations made for time \(T_{max}\) = 30 minutes and the strongest constraint \(T_{sumTmax}\) = 75 h, the task was not solved (Figure 8) for neufrepower \(P_{3 min}\) = 10%\(P_{WFn}\) nor for \(P_{3 min}\) = 20%\(P_{WFn}\). Tests were repeated many times and an additional detailed analysis of the system operation with optimised parameters (type and number of turbines) was performed with a simultaneous increase in the power storage capacity. It was demonstrated that \(T_{sumTmax}\) could not be limited at the level of 75 h/year by further increasing storage capacity. This was caused by the characteristics of the annual changes in wind speed for the reference geographical location (especially for the mean annual wind speed, which amounts to 4.1 m/s at an altitude of 1 m AGL, and to 6.2 m/s at 100 m AGL), and the nominal parameters of the analysed turbines and energy storages systems. Depending on the geographical location of the farm and the parameters of the turbines and storage systems, it is possible that no solutions can occur for different values of time \(T_{max}\). Therefore, it is important to identify the maximum value of time for the assumed wind farm power \(P_{WFn}\), location and basic parameters of the system for which elimination of power generation periods with power values below \(P_{3 min}\) is possible on the \(T_{sumTmax}\) level. Still, the developed algorithm and application require significant modifications, alongside additional studies. The authors plan to address this in future works on the cooperation between wind farms and kinetic energy storages. The level of the guaranteed output power \(P_{3 min}\) (Figures 7 and 8) in periods lasting up to \(T_{max}\) greatly affects the minimum energy storage capacity \(A_{FESSmin}\).