# Small Magnus Wind Turbine: Modeling Approaches
## 1 Introduction
In [11], this comparison research is expanded and  
Figure 1: Render drawing (**a**) and laboratory prototype (**b**) of Magnus effect-based wind turbine used in current research (**c**) drivetrain of the MWT. shows the benefits of MWT in wind speed of less than 8 m/s. The research conclusion takes into account constructive calculations, and power coefficients were given in [12]. The second project was under the lead of [PERSON] [13,14]. Based on experimental results in [12], he has led an algorithm for the development of MWT and has resulted in cylindrical blades' lift and drag forces experimental measurements being within the recommendation for calculations of power coefficients, with a discussion of power density. Another paper [13] focused on aerodynamic characteristics of MTW and design calculations. This paper discussed the possibility of maximum power-tracking algorithms for better control of the MWT based on power coefficient. The MWT prototype from [PERSON]'s team is similar to [PERSON]'s team's MWT. The third scientific group managed by [PERSON] focused its efforts on developing control systems of MWT [15,16]. They concluded that the most efficient approach is the maximum power point tracking (MPPT), based on the hill-climbing control algorithm (HIL) [15]. Based on the background, the authors designed an algorithm and method to realize the fixed-step HIL algorithm for MWT. The expanded description of the HIL algorithm was described in [16]. That paper focused on algorithm practical realization. The construction of their MWT was similar to the previous one, including a boost converter and DC motors for cylindrical blades. The last team, led by [PERSON] [17], reported a practical realization of MWT with vertical axis blades. Nowadays, they have undertaken an active promotional campaign at energy markets in various countries. The main publication in their research is [18], where the principal scheme was shown, and the MPPT algorithm was described. All these projects have tried to find the optimum solution for the control system and design the modern MWT. The main idea in all teams is to find the maximum power point for MWT. All commands try to find such a point using experimental results. Another study in synthesizing the MPPT algorithm for MWT is given in [19]. Here was given an algorithm to control four cylindrical blades of an MWT using the hill-climbing algorithm with divided steps. Simulation results confirmed the correctness of this method. In [20], momentum theory and symbolic regression found the optimum number of cylinders for MWT. It was shown that the optimum number of cylindrical blades is two. This two-cylinder blade configuration allows for the generation of maximum energy. Increasing the number of cylindrical blades decreases the MWT output power. In this research, the construction of the two-cylinder blades was considered. As seen from the literature review, there is little attention paid to MWT development nowadays. However, promising MPPT algorithms may have potential application in distribution grids, where energy balancing is critical. This paper presents a comparative analysis of MWT simulation models, and the development of a numerical model proposed to be used in the MPPT algorithm. From a sustainability point of view, this work provides a systematic analysis method that may help optimize the overall efficiency of novel renewable energy sources. Furthermore, the presented model (s) may be used to improve life cycle assessment and power management. Full experimental and methodical details are provided so that the research work results can be reproduced using the code published together with an article (see Data Availability Statement). The structure of the research paper is as follows: Section 2 presents the analysis of three available models and power coefficient calculation for studied MWT; Section 3 presents model adaptation for the MPPT algorithm; the implications of main findings and future research directions are discussed in Section 4.