## 2 Characteristics of a Wind Farm--Kinetic Energy Storage System  
### Description of the System, Power Flow Algorithm  
A wind farm is an unstable source with random values of the instantaneous power \(P_{1}(t)\) in the range [0, \(P_{\text{WFn}}\)], where \(P_{\text{WFn}}\) stands for the total of the rated power values of all turbines. The annual and multi-annual deterministic components add to the stochastic nature of the wind speed changes, which means that a period of one year should be taken as the minimum period of analysis for such systems. In relation to the above, even high rated power wind farms, where turbines are located at a certain distance from one another, do not guarantee stable power released to the power grid in either short (minutes) or long (hours, days) time intervals [16]. The stability and predictability of power generation by the sources within the power grid are essential in order to guarantee an adequate level of power supply reliability and determine the energy safety of a country. In the case of wind sources, the best results of the output power stability (power released to the power grid) are achieved by using energy storage devices with a capacity suited to the power plant efficiency, its geographical location and assumed period of continuous operation. The capacity of the storage not only depends on the farm's efficiency and the mean annual wind speed \(v_{\text{wAvg}}\), but also on the dynamics of wind speed changes specific for the local conditions, and on the statistical parameters of breaks in power generation: their mean duration, the number of subsequent intervals between the periods when the energy storage can be charged, etc. The author has presented detailed results of such studies in Reference [24]. Figure 1 presents a schematic diagram of a wind farm cooperating with a global (common for all turbines) storage of kinetic type. The power generated in each turbine \(P_{1(i)}(t)\) (for \(i=1,\,2,\,\ldots,\,N_{WT}\), where \(N_{WT}\) is the number of turbines in the farm) is supplied to a node and then--depending on the instantaneous power of farm \(P_{1}\) and the state of charge (SOC) of the ESS--to storage \(P_{2}\) and/or power grid \(P_{3}\). The storage can also operate with power \(P_{2}\) when discharged, and then the stored energy is supplied to the power grid. The (+) sign of power \(P_{2}\) means that the storage is discharged, while (\(-\)) stands for its charged conditions. Power \(P_{3}\) is supplied to the power grid. The power is the sum of the power of the turbines and the storage, reduced by the \(\Delta P\) power loss in the transformer and the line supplying power to the grid:  
\[P_{3}(t)=P_{1}(t)+P_{2}(t,\,\,\text{SOC})-\Delta P \tag{1}\]  
The CFEM (_control flow of energy module_) is responsible for controlling the flow of energy between the wind farm, storage, and power grid. It is possible to improve the reliability of electrical energy supplies to the power grid from a wind farm-kinetic energy storage system when an appropriate control algorithm is implemented that stores the flow of energy between the turbines, storage and power grid. This assumes that the minimum set power \(P_{3 min}\) on the system outlet is maintained at all times with the maximum duration \(T_{max}\), even when the wind speed drops below the turbine cut-in speed \(v_{\text{cut-in}}\) (then \(P_{1}\) = 0). At an appropriately selected energy storage capacity \(A_{FESSn}\)[24], it is possible to recover power in the periods when the power generated by the farm is lower than the assumed minimum value \(P_{3 min}\). In this way, the system guarantees the maintenance of power supplied to the power grid regardless of weather conditions in a period not longer than \(T_{max}\) and with power not lower than \(P_{3 min}\). The implementation of energy storage results in an increase in the predictability of the source generation related to the partial stabilisation of its output power \(P_{3}\).