## 1 Introduction
Since then, several floating support platform configurations have been developed, and the performance of these concepts has been tested both experimentally and numerically. FOWTs can be divided into three categories: spar type [13; 14; 15], semi-submersible type [16; 17; 18; 19; 20], and tension leg platform type [21; 22]. The Hywind concept developed by Statoil [13] is based on a slender deep draft substructure and is a typical spar type FOWT. Numerical studies [23; 24; 25; 26], experiments, as well as long-term prototype tests [9] were carried out for the proportional models [27; 28; 29]. Due to the excellent stability of the spar buoys, after continuous theoretical research and on-site monitoring, the Hywind concept was finally commercialized in the world's first floating wind farm, Hywind Scotland [30] in 2017, which is a milestone in the history of offshore wind turbines. The semi-submersible foundation has unique advantages compared to the foundation of the spar and tension leg platform (TLP) type, because the semi-submersible foundation is simple in construction, regular in shape, simple in assembly, small in size, modular, and easy to assemble and debug [17]. These steps can be carried out at the dock site, and the structure after installation can be transported to the designated location by tugboat. On the other hand, the installation cost of the mooring system is also significantly lower than that of the other two types of foundations. In addition, due to the large draft of the semi-submersible foundation, the natural period of the heavy motion response is longer, so the hydrodynamic characteristics caused by the wind load are better [31]. According to the relevant research results, the semi-submersible foundation's motion response shows an interesting law. The surge response is similar to the spar type, but the pitch motion is smaller [32]. In recent years, scholars have conducted a lot of researches and proposed many concepts on FOWT. The National Renewable Energy Laboratory (NREL) has developed a 5 MW baseline wind turbine [33]. In the Offshore Code Comparison Collaboration (OC3) phase, a spar floating platform called OC3-Hywind was designed [34]. In one phase of the Offshore Code Comparison Collaboration Continuation (OC4), a semi-submersible type platform (DeepCwind)was designed [20], which is another concept of FOWT. It relies on large columns linked by braces to maintain stability, showing good wave-resistance ability. In this paper, a modification based on the original DeepCwind semi-submersible FOWT is carried out, in which the number of the floating columns is changed but the total weight remains unchanged. The calculations are performed using fully coupled in-house codes, and the results are analyzed to reveal the effects of the number of the floating columns to the dynamic response of the DeepCwind semi-submersible FOWT. Section 2 introduces the quasi-static theory of the mooring system and the calculation of the dynamics of the platform structure using the potential flow theory. Section 3 describes the details about the wind turbine, floating platforms, and mooring systems. In Section 4, the dynamic response of the FOWT is studied, and the effects from the number of the floating columns is obtained.