# Small Magnus Wind Turbine: Modeling Approaches
## 1 Introduction  
According to the Global Wind Report 2021 of GWEC [1], the wind industry in 2020 was growing by 13% when compared to the previous year. Nowadays, 743 GW of installed wind power helps avoid over 1.1 billion tons of CO\({}_{2}\) produced by fossils. This is happening because climate change requires increased wind energy exploitation for decarbonization procedures, and wind energy is still one of the most popular renewable energy systems, despite the increasing usage of solar energy. However, traditional wind generators are not suitable for places with an annual average wind speed lower than 5 m/s, and the studies show [2] that in such cases, the needed power of the wind generator will grow too high, which makes the generator economically not feasible. Notwithstanding the previous, Russia already has ambitious projects [3] to design wind power plants in areas with low wind speed, such as in Saint Petersburg. Furthermore, similar solutions may be implemented in neighboring Estonia, where the annual average wind speed further, away from the coast and islands, is not reaching the required levels [4]. Furthermore, the rapid development and massive implementation of distributed energy solutions are based on an alternative paradigm, which offers the closeness of generators to the consumers, changesin consumer roles, and the development of new types of generators in power systems, making small wind turbines a popular choice. However, the traditional blades of small wind turbines have not proven to be energy efficient enough, especially in areas with low wind speeds. That is why developing a new type of small wind turbine with maximum energy efficiency at low wind speed is a crucial challenge for modern technology. Magnus effect-based Wind Turbines (MWT) described in [5] could be energy efficient in a wide wind speed range of 2-40 m/s, in comparison with 5-25 m/s for conventional bladed small wind turbines [6]. The Magnus effect is a sideways force that influences the rotating cylinder, immersed in the surrounding motion between the rotation cylinder and the environment. As a whole, MWT is a complex device needing an extra subsystem that rotates the turbine's cylinders. The structure scheme of MWT is presented in Figure 1. It consists of two cylindrical blades with diameters 575 \(\times\) 125 mm, with a maximum power density of 2 kW. Cylinder blades are installed on an aluminum rack connected to the shaft of MWT via the hub. The shaft rotates inside the nacelle, supported by two bearings. The cylinders are caused to rotate by two motors, and connected to the shaft of the MWT via the hub. Rotating cylinders provide lift force. The shaft rotates inside the nacelle and rotates all the nacelle, leading to the rotation of the generator. As a generator in this realization of MWT, we used a Permanent Magnet Synchronous Generator (PMSMG). However, it could be also be built using a Flux-Switching Permanent Magnet Synchronous Generator as described in [7]. This prototype of MWT is designed to operate at a 100 rpm external wheel that satisfies low wind speed (2-8 m/s). A research survey in this area revealed that four investigators' teams were developing different types of MWTs. However, only three of them achieved the fifth technology readiness level. The first project, headed by [PERSON] [8; 9; 10; 11; 12], aimed to develop a six cylinder MWT. The MWT working principle is based on lift force, posed by six cylindrical blades [8]. Overall dimensions were 3.6 \(\times\) 3.6 m, and aerodynamic simulation showed the effectiveness of such a wind turbine at 4.5 m/s wind. His team also provided research in construction limitations, and, in [9], a MWT simulation with various types of cylindrical blades diameters, from 0.05 to 0.09 m, was presented. DC motors rotated the cylindrical blades with speeds of up to 8000 rpm. Other research in constructive simulation, speed, and power density simulations is featured in [10]. This research demonstrated a comparison between a traditional bladed wind turbine and a cylindrical MWT.