# Research and Development of a Large-Scale Axial-Flux Generator for Hydrokinetic Power System
## 3 Results  
### Preliminary Design Simulation Results  
Dynamic simulations were performed using the virtual prototype, which is shown in Figure 2b. The simulation model presents complete generator functionality, including the rotor's relative motion to the stator, using a model of the entire structure. Three-dimensional low-frequency electromagnetic transient simulation software (ANSYS Maxwell v.19) was used; it solves electromagnetic field problems by solving [PERSON]'s equations in a finite region of space with time-varying or moving electrical sources. It uses the differential equations for Faraday (5), Gauss (6), and Ampere (7) laws, involving the electric field strength, E, the magnetic flux density, B, the magnetic field strength, \(H\), and the electric current density, \(J\), together with the constitutive material equations (B = f (\(H\)) for the magnetic field). \[\
abla\times E=-\frac{\partial B}{\partial t} \tag{5}\]  
Figure 3: Scheme of planned design study stages and variants. \[\
abla\times B=0 \tag{6}\]  
\[\
abla\times H=\text{J} \tag{7}\]  
The numerical solution of such equations is based on T-\(\Omega\) formulation (a single connected solution domain) in which \(\Omega\) is the nodal-based magnetic scalar potential, defined in the entire solution domain, and T is the edge-based electrical vector potential, defined only in the conducting eddy-current region. Three simulations are run for the model at various input mechanical power values--10 MW, 14 MW, and 18 MW. These simulations were performed using a workstation with actual configuration (corresponding to 2\(\times\) Intel Xeon Gold 5318Y @ 2.1 GHz 24 cores CPU and 1 TB DDR4 RAM) that resulted in an adequate computational time. The simulation results show the losses and allow for calculating the generator efficiency. The software (ANSYS Maxwell v.19) calculates the core loss (eddy current, calculated using the Steinmetz formula, and hysteresis losses in a transient solution) and conductor loss (solid or stranded conductor). The conductor loss is dominant because of the type of electrical machine examined--coreless, and the conductor loss is determined from the current density and the material conductivity (volume-integral value). The results obtained from all three simulations are briefly presented in Figure 4. Torque variations over time are shown, demonstrating some fluctuations, partially due to the specifics of the design and partially due to simulation accuracy (a nonlinear model of a rotating electromagnetic field). Magnetic field intensity is also presented--in Figure 4**b**--to visualize its distribution in the structure during the rotation of the moving parts. The major output of the simulation is the averaged value of the torque (used to adjust simulation parameters to the required input mechanical power values) and the losses, which are indicators of the efficiency, as well as further requirements for the thermal management of the entire system. A summary of three performed simulations is shown in Figure 5. The graphs present the changes in power loss and, respectively, the efficiency by changing the input mechanical power. This is an essential indicator for generator design, and it was used in further considerations. Figure 4: Results for 10 MW load case: (**a**) torque variations over time, *10\({}^{6}\) Nm; (**b**) total magnetic field intensity distribution field, A/m. Several conclusions could be identified, based on the reported results:  
* The examined preliminary design reaches a 2.4 A/m\({}^{2}\) current density per winding at a 10 MW input mechanical power. This case also shows the best efficiency--75%. * The 14 MW input mechanical power reflects in nearly a 3.5 A/m\({}^{2}\) current density per winding. The efficiency for this case is much lower--66%. * The design shows a high rate of loss in windings, and it is not efficient. * Several reasons for this low efficiency were found after detailed results' analysis. * A large air gap between the magnet and the winding--140 mm. A similar design [27] has an air gap of 40 mm.