## 4 Case Study
### System Parameters  
The HKT system in this work is derived from the work presented by [PERSON] et al., which is a three-bladed horizontal axis turbine with a rotor diameter of 0.88 m [42]. For this example HKT system, the rotor dimensions have been linearly scaled from the dimensions presented in [42] to reach 6 kW at a flow velocity of 2.25 m/s, resulting in a blade radius of 0.8538 m. The \(C_{p}\) versus \(\lambda\) curve derived from the results presented by [PERSON] et al. is presented in Figure 7. A summary of all HKT parameters is shown in Table 1.  
The PMSG for this case study was modeled off the custom-made PMSG used in [34]. This PMSG was designed specifically for direct-drive HKT applications operating at similar rated flow velocity conditions. A list of all the utilized PMSG parameters can be found in Table 2.  
All pertinent information for the power electronic converter is shown in Table 3. For this case study, a Wolfspeed E3M0160120J2 1.2 kV rated SiC MOSFET (Wolfspeed, Durham, NC, USA) has been selected as the example device. It should be noted that details on the internal control loops have been omitted as it is assumed that the dynamics of the power electronic converter are significantly faster than the dynamics of the HKT response. Also, all thermal parameters required for the simplified Cauer thermal model shown in Figure 4 are included in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Rated flow velocity \(u_{0,rated}\) & 2.25 m/s \\ Rotor Length \(R\) & 0.8538 m \\ Maximum \(C_{p}\) & 0.46 \\ Optimal Tip Speed Ratio \(\lambda^{*}\) & 6.1 \\ Coefficient of Friction \(C_{fric}\) & 1.667 Nm-s/rad \\ Moment of Inertia \(J_{turbine}\) & 2.1816 kg-m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for example HKT. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Rated Power \(P_{rated}\) & 6 kW \\ Rated Speed \(\omega_{rated}\) & 15.7 rad/s \\ Number of Poles \(p\) & 24 \\ Moment of Inertia \(J_{gen}\) & 0.26 kg-m\({}^{2}\) \\ Stator Resistance \(R_{s}\) & 3.7110 \(\Omega\) \\ d-/q-Axis Inductance \(L_{d}/L_{q}\) & 45.25 mH/64.88 mH \\ Rotor Flux Linkage \(\lambda_{r}\) & 1.9059 Wb \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PMSG parameters derived from [34]. Figure 7: C\({}_{p}\) versus \(\lambda\) curve derived from the results presented in [42]. The RL parameters used to define the SARSA agent, the RBF approximation method, and the monetary-based reward function are shown in Table 4. The values of the SARSA parameters (\(\alpha_{0}\), \(\gamma\), \(\varepsilon\), and \(\varepsilon_{d}\)) shown in Table 4 were chosen through a heuristic search. However, some insight can be drawn from [37] on how setting these parameters' values may affect the RL agent's performance. For example, reducing the value of \(\alpha_{0}\) may make learning more stable but will also extend the required amount of time to converge to the final policy. The values used for the RBF approximation method were determined as follows. The value of \(n_{c}\) was chosen heuristically, converging on a value that enables sufficient mapping of Q-values in each dimension without causing a significant strain on memory. With the final value of \(n_{c}\) (5) and the four states and one action the agent must consider, the feature vector is constructed of 3125 different RBF center points. The value of \(\sigma\) was chosen to be one-half the distance between the evenly spaced RBF center points in each dimension. The base value \(k_{b}\) was designated to be the value that would ensure the turbine system would track the optimal value of \(\lambda\) and maximize \(C_{p}\) for all flow conditions. The base values \(u_{b}\), \(T_{b}\), and \(c_{b}\) were designated to be the maximum values the agent could expect for flow velocity, water temperature, and cost of energy, respectively. Finally, the values used for the variables that comprise the reward function were determined as follows.