## 2 Related Work
This method remains simple and allows for a fast response of tracking the MPP, but defining an accurate relationship for a real WT system is still difficult. Concerning MPPT-P&O, this technique is the most used for power extraction. It is a simple technique that allows for reaching the MPP without knowledge of the WT system parameters. It consists of perturbing the system, observing and analyzing the output electrical power and then deciding the direction of the next perturbation based on that outcome. Several variables could be perturbed in this method, such as the DC bus voltage, the DC current and the rotational speed, or the duty cycle of the boost converter could be adjusted [12; 13]. However, it is not preferable to perturb the rotor speed in order to avoid the use of a mechanical sensor. Moreover, the choice of the appropriate perturbation step size is not obvious. Indeed, according to the chosen step size, the performances of the WT (response time, oscillation around the MPP and high mechanical vibration) change. For this reason, many authors suggested an adaptive P&O method with a variable step size. [PERSON] et al. [26] suggested an adaptive P&O method where the variable step size was calculated by multiplying the fixed step size by a variable gain. [PERSON] et al. [27] proposed an adaptive duty cycle step using proportional-integral-derivative controller based on a genetic algorithm. In [28], an ANN approach is proposed to provide the power converter duty cycle under different atmospheric conditions. Besides the MPPT method presented above, other control strategies, such as pitch control, could be added to increase the performances of the WT system. These control strategies are mostly used to protect WTs, especially when the rated power is reached while the wind speed is still increasing. SSWTs are not concerned by this type of control since their pitch angle is always set at 0\({}^{\circ}\). Even though small-scale wind energy production should ideally operate to extract the maximum power, its exploitation can require the use of an additional strategy to limit the generated power. Only a few studies have been interested in limiting the generated power of SSWTs. [PERSON] et al. [29] proposed an intelligent power management controller for a small standalone off-grid wind energy system equipped with a PMSG. It consists of two methods: a slope-assisted MPPT algorithm, which tracks the MPP and minimizes the logical errors by identifying the changes in atmospheric conditions, and a power limited search (PLS) algorithm which minimizes the surplus generated power and avoids energy dissipation. In this paper, three LPPT-P&O algorithms for the SWECS are proposed. The SSWT used in this work will be integrated in a DC MG. It should respect the MG constraints and requirements. In this case, the SSWT should not always extract the maximum power but rather provide the power depending on the needs of the MG. The proposed algorithms are P&O with fixed step size, P&O based on [PERSON]'s method, and P&O based on the fuzzy logic (FL) technique. All proposed methods should have the ability to perform at two operating points. They ensure an easy transition from one point to another depending on the user's requirements and the turbine's characteristics (less power loss, low generator speed, etc. ).