## 5 Simulation and Discussion
### Simulation Results
#### 5.2.1 Step Changes of Wind Speed and Rotor Speed Input  
The change curves of the wind and rotor speed input are shown in Figure 8. The wind speed changes suddenly from 8 m/s to 9 m/s and the rotor speed input increases from 24 r/min to 26 r/min, which both occur at 50 s. The displacement factors of the variable pump in two cases are shown in Figure 9. As shown, the pump displacement factor rises from 0.35 to 0.43 when the wind speed suddenly increases. The variation trend of the pump displacement factor is the opposite when the rotor speed input has a sudden increase, which decreases rapidly from 0.35 to 0.17 and gets back to the begin value 0.35. It can be seen that the displacement factor gradually decreases in both cases as time goes on.  
Figure 10 shows that the pump speed will increase faster to 24.6 r/min owing to the wind speed step. The hydraulic counter-torque acting on the variable pump becomes big for the increase of the pump displacement. The variable pump begins to decelerate when the hydraulic counter-torque is greater than the wind torque. Finally, the pump speed returns to 24 r/min. When the rotor speed input step occurs, the pump accelerates on account of the decrease of the pump displacement. It reaches finally at 26 r/min after a small overshoot.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Accumulator volume & \(V_{0}\) & 6000 & L \\ Gas precharge pressure & \(P_{0}\) & 120 & bar \\ Accumulator pressure & \(P_{a}\) & 210 & bar \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main parameters of energy storage system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Motor maximum displacement & \(V_{m}\) & 500 & cm\({}^{3}\)/rev \\ Number of pole pairs & \(P\) & 2 & \\ Stator winding resistance & \(R_{a}\) & 0.006 & \(\Omega\) \\ Synchronous speed & \(R_{g}\) & 1500 & r/min \\ Moment of inertia & \(I_{m}\) & 60 & kg\(\cdot\)m\({}^{2}\) \\ Coefficient of viscosity & \(B_{m}\) & 0.05 & Nm/(r/min) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Main parameters of hydraulic motor and synchronous generator.  
From Figures 11-13, it can be shown that the flow curves of the pump and the accumulator show the same trends as that of the pump displacement. The pump flow with the wind speed step is greater than that with the rotor speed step at 75 L/min. The discharge flow of the accumulator has the maximal value 130 L/min when the rotor speed arises. The accumulator pressure in both cases rises gradually because the accumulator is in the state of charge in most of the time. The accumulator pressure in the wind speed step increases much more rapidly as a result of more charge flow.  
Figure 8: Wind speed step and rotor speed input step.  
Figure 10: Pump speed.  
Figure 9: Pump displacement factor.  
Figure 14 shows that the power coefficient and tip speed ratio in both cases. As shown, the tip speed ratio increases from 6.8 to 7.5 when the rotor speed changes from 24 r/min to 26 r/min. Corresponding, the power coefficient increases from 0.37 to 0.42. It can be seen that the tip speed ratio reduces from 6.8 to 6.1 as the wind speed arises. The power coefficient decreases to 0.33 accordingly.  
As shown in Figure 15, the wind power changes from 470 kW to 675 kW as the wind speed varies from 8 m/s to 9 m/s. The turbine power captured by the rotor blades is 185 kW when the wind speed  
Figure 11: Pump flow rate.  
Figure 12: Accumulator flow rate.  
Figure 13: Accumulator pressure.  
and the rotor speed are 8 m/s and 24 r/min. As the wind speed increases to 9 m/s, the turbine power is equal to 223 kW. As the wind turbine speed accelerates to 26 r/min, the turbine power reaches 199 kW.