## 1 Introduction
The combined wind-battery system can estimate the active power mismatch that results from a contingency or trip, determine the ensuing frequency variations, and then deliver a fast-frequency response robustly and reliably to arrest the aforementioned frequency distortions thanks to the proposed fuzzy-logic-based controller and a wash-out filter. The frequency support of a WPG with the ROCOF was enhanced by employing model-free control and rotor speed control and envisaging synthetic inertia and primary frequency response support from WPGs to overcome the demerits of the conventional ROCOF loop [17; 21; 22]. The supplementary power generated by the frequency deviation loop is proportional to the difference between the standard and current frequency of the system; thus, after the frequency nadir, additional generated power adds to the undesirable influence of the ROCOF loop. However, the performance of the ROCOF loop is affected by noise components. Consequently, in [23], the frequency control technique utilizes the frequency deviation loop. The performance of the frequency control technique can be enhanced by increasing the gain; however, the WPG then becomes susceptible to operational instability outside of the rotor speed operating region. Thus, a relatively small value for the fixed gain is chosen. To increase the minimum point of the frequency, a frequency deviation loop with an adjustable gain was suggested while the operation stability of the WPG is maintained [14]. The rotor speed of the WPG determines the variable gain in this technique, thus ensuring stable operation when a large generator fault is experienced. Since in the low-rotor-speed region the stored kinetic energy of the WPG is insufficient and cannot perform frequency control, the conventional schemes show low performance to maintain the frequency at the above condition. An additional device, such as a supercapacitor, flywheel, or battery, is thus required to assist in the frequency response of a WPG. As seen from the above related studies, further research is required combining battery model systems and WPGs, and to improve the minimum point of the frequency during a frequency drop, this paper suggests the following contributions:  
* A frequency control support technique based on an adaptable power reference comprising a WPG and a battery is implemented. The battery and WPG are assigned different rules in the frequency control service to accomplish this control. * The suggested frequency control technique incorporates a supplementary control loop used in combination with the MPPT control loop which relies on the frequency difference. The speed of the rotor and the frequency determine the gain to increase the minimum frequency and ensure that the WPG operates in a stable condition. * In the low-rotor-speed region, the battery improves the operational stability of the WPG. This is accomplished by determining that the power of the battery operates depending on its state-of-charge (SOC) and the WPG's rotor speed. * An IEEE 14-bus system with two wind power plants (WPPs), doubly fed induction generators (DFIGs), a battery with a 5 MWh capacity, five synchronous generators, and specified loads using the EMTP-RV simulator are used for the analysis of the suggested technique. The remainder of this study is organized as follows: The control systems of the DFIG and battery system are presented in Section 2. The conventional frequency control support techniques and suggested frequency control support techniques in the wind power generator-battery system are presented in Sections 3 and 4, respectively. The model system employed in this study is presented in Section 5. In Section 6, scenario studies are presented with their respective results for the suggested technique compared with the conventional approach. Additionally, a qualitative feasibility analysis of the wake effect in the wind farm is presented considering the [PERSON] wake model.