## 7 Results Analysis
### Simulated Results
#### 7.2.4 Discussion  
The simulated results indicate the response of the FESS model for charging, discharging, and standby states. The flywheel system stores 5 kWh of energy within a speed range of 10,000-20,000 rpm, and an accelerating torque of 6.7 N\(\cdot\)m. During the standby state, when no torque is applied on the system, the calculated self-discharge energy losses are about 1.25% of the total stored energy. This is due to the system losses, and especially mechanical losses, which create friction torque, and hence, loss of stored kinetic energy. The total standby energy losses during 30 min has been approximately 70 Wh. For the same period and considering a fully charged flywheel with a maximum speed of 20,000 rpm, the friction torque will reduce its speed to 19,600 rpm. This gives 5% loss of energy per  
Figure 14: FESS in step-charging mode: Torque, power, and three-phase current (top left, top right, and bottom left); PMSM no load speed (bottom right).  
Figure 15: FESS in step-charging mode: Inverter output voltage and DC-bus voltage at (\(t=2\) s) (top left); Inverter output voltage and DC-bus voltage at (\(t=8\) s) (top left); FESS state-of-charge (bottom left); DC-bus voltage at (\(t=2,\ 8,\&\ 10\,\mathrm{s}\)) (bottom right).  
hour, and adding copper and stray losses will give an overall roundtrip efficiency of 88%. To reduce the run-down losses of the system, use of a passive magnetic bearing has been used to levitate most of the weight, and the axial load on the ball bearing system will be very light, leading to low friction and high life. Rotor drag loss can be mitigated by enclosing the flywheel in a vacuum chamber with only occasional re-pumping requirements due to the lower speed of the system. Electromagnetic drag on the rotor is another area of concern, but this can be kept low by use of low iron loss materials.  
The analysis of simulations was also performed for a short duration of 12 s, to indicate the most important effects and dynamic response of the system for real life scenarios. It is shown that sudden step changes in load torque renders corresponding variations in charging characteristics and stored energy of the flywheel system. By contrast, the bidirectional converters at the machine side and the grid side control the operation of the PMSM-Flywheel and, regardless of the mode of operation, a stable DC-bus voltage is maintained. The fluctuation of the DC-bus voltage due to load instabilities is limited to 3%, which is recovered within 40-45 ms. Conformation of the flywheel speed and power with respect to torque variations indicates a favourable system responsiveness and dynamic performance for each state.  
Compliance of the simulated results imply that the model can be further explored to analyse performance a PMSM-Flywheel integrated to a power system providing energy backup. This is an area with very limited experimental data available, since the majority of grid connected flywheel systems are used for high power applications providing power quality and ride through services. Another widely unexplored scenario would be operation of a flywheel system providing longer duration energy storage backup in an isolated power system in the presence of renewables such as solar photovoltaic system. Application of FESS providing frequency improvement services for wind and solar PV systems is previously addressed in the literature, but its operation as a stand-alone energy storage option still remains unexplored. The software tool explored in this work can be modified accordingly to test and analyse numerous real-life scenarios for such systems. For example, this can be a grid connected FESS charged once or two times daily for energy saving purposes, or a hybrid flywheel and diesel generator in a solar PV system with the flywheel providing energy backup to reduce diesel generator involvement.