Rotor Dynamic Analysis and Experiment of 5kWh Class Flywheel Energy Storage System

Transcription

1 Rotor Dynamic Analysis and Experiment of 5kWh Class Flywheel Energy Storage System Cheol Hoon PARK Sang-Kyu CHOI Sang Yong HAM Nano Convergence and Manufacturing Systems Research Division, Korea Institute of Machinery and Materials, Yuseong-gu, Daejeon , Korea ABSTRACT FESS(flywheel energy storage system) is a kind of mechanical energy battery which can collaborate with various electric energy sources such as wind power generator, regenerative brake system and so on. Generally, flywheel rotor of FESS is mounted on the magnetic bearings so as to minimize the air friction loss. The magnetic bearings should have enough stiffness and damping to suppress the imbalance response of flywheel rotor, and the rotor should be designed to have as high first bending critical speed and small unbalance response as possible to minimize the use of electric energy by magnetic bearings. The critical speed analysis of the rotor mounted on the magnetic bearings should include the magnetic bearings, its controller and FEM model of rotor. This paper presents the design procedure and rotor dynamics analysis of flywheel rotor for 5kWh class FESS mounted on the magnetic bearings. The designed flywheel rotor has succeeded to run stably up to 15,rpm with small unbalance response. The experimental results such as open loop FRF, rigid body critical speeds are presented and compared with the analysis results as well. Keywords: Flywheel Energy Storage System, Rotor Dynamics, Critical Speed, Magnetic Bearings and Finite Element Method. 1. INTRODUCTION FESS(Flywheel Energy Storage System) is a kind of mechanical energy storage system which can store electric energy in the form of kinetic energy and convert kinetic energy to electric energy again when necessary. Recently the application of FESS becomes various and wide in the area of, for example, uninterrupted power supplies (UPS), voltage regulator of wind power plant, vehicles and railways and so on [1]. Especially, the exhaustion of fossil fuels is accelerating the development of FESS for the wind power plant as an alternative energy. In order to stabilize the output and maximize the operating efficiency of the wind power plant, it needs to be connected to the energy storage system [2][3]. 5kWh class FESS has been developed to meet this kind of needs. FESS is an electro-mechanical battery having a great deal of advantages of high energy density, long life and affinity for the environment compared to other forms of energy storage systems such as the chemical battery [4]. The developed FESS here has been designed to output 5kW power at 15,rpm and the operating test has been done successfully. FESS mainly consists of non-contacting active magnetic bearings(amb) that provide very lower frictional losses and smaller maintenance costs compared to the mechanical bearings, a composite flywheel rotor of high energy density and high mechanical strength, a motor/ generator that converts mechanical energy to electric form, and vice versa, and a vacuum chamber that minimizes windage losses. Since AMB is open-loop unstable, the feedback controller is absolutely required for the stable operation. AMB controller for 5kWh FESS was developed by using MATLAB/xPC Target which is the PC-based real time control system of The MathWorks, Inc[3]. This paper presents the design concept of 5kWh class FESS and the experimental results for the operational test for the flywheel mounted on AMB up to 15,rpm. 2. SYSTEM DESCRIPTION Figure 1 is the schematic diagram of FESS. The electric energy is converted to the kinetic energy and stored into the flywheel by the motoring operation of 2kw class motor/generator located at the lower shaft

2 area. If the motor/generator stops the motoring operation and changes its operating mode to the generating mode, the kinetic energy of the flywheel is converted to the electric energy. The axial and radial displacements of flywheel shaft are measured by the axial and radial gap sensors and controlled by the forces from the thrust and radial AMB actuators. The axial weight of the flywheel is mainly supported by the attractive force of the permanent magnet which is located at the upper thrust AMB actuator. Upper Radial AMB Thrust collar Motor/Generator Lower Radial AMB Permanent Magnet for Supporting Weight Flywheel Upper Thrust AMB Lower Thrust AMB Permanent Magnet for Motor/Generator Figure 1. Schematic diagram of FESS In order to minimize the energy losses by the control input to the AMB actuators, the control input for the unbalance response of the flywheel should be minimized. The selection of I p /I t is very critical to the unbalance response of the flywheel. Because the rotational kinetic energy stored to the flywheel is linearly proportional to the polar moment of inertia, I p and the thick disk shaped flywheel is preferred to minimize the mass of the flywheel relative to the stored kinetic energy, I p /I t of the flywheel for FESS is generally designed to be more than 1. When I p /I t of the flywheel rotor here is designed to be more than 1, the conical critical speed was placed at around 19,rpm. Consequently, the unbalance response increases continuously in proportional to the rotational speed until it reaches to the target speed 15,rpm and the control input to the radial AMB actuator must be increased continuously and the bandwidth of the AMB controller must be over 25Hz. It s very difficult to realize the AMB actuators and controller having this kind of performance. It s not the best choice to increase the bandwidth of the AMB actuators and controller recklessly. Instead of that, if the conical critical speed can be passed through at the low rotational speed where the AMB actuators can produce the enough forces, the rotational speed of the flywheel can be increased to the target speed keeping the displacement of the flywheel shaft due to the unbalance response minimized[6]. This is sort of easy method to realize. From this kind of reason, I p /I t of the flywheel here is designed to be around.5 so that the conical critical speed could be passed through at the rotational speed less than 3~4,rpm. The thrust AMB is designed to be the hybrid double acting type which has the permanent magnet inserted in the upper thrust AMB actuator and attracts the flywheel upward. The flywheel shaft is designed to have its 1 st bending mode frequency above 45 Hz so that the freedom to design the AMB controller could be ensured even for the frequency area over 25Hz corresponding to the target speed, 15,rpm. In order to achieve this, the heavy thrust collar is located as near to the center area of the flywheel shaft as possible so that the additional mass effect could be minimized. The permanent magnet for the motor/generator is located at the lower shaft area. By this way, the burden due to the additional mass can be uniformly distributed to the upper and lower shaft. The material for the flywheel shaft is SUS34 which is relatively cheap and easy to manufacture. The composite material is used for the flywheel rims to resist the tension due to the centrifugal force. Figure 2 shows the detailed configuration of the designed flywheel and Table 1 shows the specification of the flywheel. Thrust Collar Titanium (shrink fit) Si-steel Laminated core Composite Material SUS34 Shaft Aluminum Hub Figure 2. Detailed configuration of flywheel Table 1 Specification of flywheel Item Value Material SUS34 Mass[kg] 47 Length[mm] 1119 Diameter[mm] 58 I p /I t.51 Permanent Magnet for Motor Si-steel Laminated core Titanium (shrink fit)

3 in free-free condition would be 518Hz and 1143Hz respectively. Figure 5 shows the rotor dynamic model for full flywheel. It was predicted that first and second bending mode frequencies of flywheel would be 612Hz and 1184Hz respectively. Aluminum hub strengthened the stiffness of shaft and increased bending frequencies. 612Hz is sufficiently high first bending frequency considering the operating speed of 3Hz. Imbalance response was predicted as figure 6. After passing through the rigid body mode with the peak response of less than 2μm, it would be possible to increase the rotational speed without the additional effect of imbalance. Figure 3. FESS in vacuum chamber The casing of FESS must be designed to have the strong structure so that the radial AMB actuators, thrust AMB actuator and motor stator could be supported strongly and the flywheel rotor could rotate stably about the rotational center. Moreover, after assembling the upper and lower radial AMB actuators, the misalignment of them should be minimized. The casing of FESS must have the stiffness so that the 1 st bending mode frequency of the casing could be placed above 3Hz which is above the target speed 15,rpm, that is, 25Hz. Figure 3 shows the draft of the assembled FESS in the vacuum chamber. Figure 4-5 shows the manufactured AMB actuators, flywheel and the assembled FESS. 3. ROTOR DYNAMIC ANALYSIS Figure 5. Rotor dynamic model for flywheel Response [μm] Rotational Speed [rpm] Figure 6. Prediction of imbalance response Figure 4. Rotor dynamic model for shaft only Composite material and aluminum hub are removed from flywheel in figure 2 and flywheel shaft are modeled by using xlrotor as shown in figure 4. Titanium and Si-steel part, thrust collar and permanent magnet for motor are modeled as added masses which do not help for the stiffness of shaft. It was predicted that first and second bending mode frequencies of shaft Impact test was performed after fabricating the shaft only and full flywheel as shown in figure 7 and 8. First and second bending frequencies of shaft in figure 7 are measured to be 549Hz and 118Hz in the upper shaft and 518Hz and 12Hz in the lower shaft respectively. The impact test results are very similar to the analytical results, which means that the shaft was fabricated well and meet the design requirement. First bending frequencies of flywheel in figure 8 are measured to be 62Hz (figure 9) and 762Hz for the upper and lower part, respectively.

4 x = A( Ω) x + Bu y = Cx + Du (1) Figure 7. Impact test for shaft only (a) Block diagram of AMB controller Ethernet Host PC mag[db] phase[deg] (a) Flywheel (b) FESS Figure 8. Fabricated flywheel and FESS Hz Hz Figure 9. Impact test result of flywheel (Upper part) (a) Thrust Actuator (b) Radial Actuator Figure 1. Fabricated actuators Power Amp DC Power Supply Target PC (b) Each component of AMB controller Figure 11. Hardware of AMB controller using xpc Target 4. SYSTEM IDENTIFICATION Bias linearization method is employed to get the linearized model of the radial AMB dynamics and a state-space equation is arranged as equation(1)[7]. By using the state-space model described above, the initial PD controller can be designed and FRF (Frequency response function) of AMB can be measured. The control system for AMB is implemented by using xpc Target of MathWorks, Inc which is the real time digital control system [5]. Figure 11 shows the configuration of control system using xpc Target. The control block diagram is written by using MATLAB/Simulink in Host PC and it is downloaded into Target PC. During the control code is running in Target PC, Host PC can change the control variables in Target PC and get the each signal data easily from Target PC through Ethernet. Target PC reads the value of the position sensor through A/D and calculates the control input and sends it to Power Amp through D/A. Power Amp transfers the current corresponding to the control input to the coil of AMB actuators.

5 Figure 8 shows the Simulink block diagram for the AMB controller. Because 1kHz sampling rate is selected for the AMB controller, FRF can be measured up to 5kHz using swept sine method as shown in figure 13 and equation(2)[4][8]. are added right after PD controller so that the first bending mode is not excited by the control input. The depth of the notch filters are designed so that the magnitude of the first bending mode is attenuated below -15dB on the open loop bode of the radial AMB control system. After applying the selected gains and the notch filters, the stability of the AMB system was verified by measuring the open loop bode and plotting the nyquist plot. 2 Plant Bode(Amp + Acuator + ) Magnitude[dB] Figure 12. Simulink block diagram for AMB controller Phase[deg] 1-1 Out( S) FRF ( S) = In( S) (2) Frequency[Hz] (a) Upper AMB r + - e Controller Swept Sine + + In Amplifier +AMB y Magnitude[dB] Plant Bode(Amp + Acuator + ) Out Figure 13 Block diagram to measure FRF of AMB The FRFs of upper and lower AMB measured in standstill are given in Figure 14. These FRFs include the dynamics of flywheel rotor, AMB actuator, power amp and sensor. 1 st bending mode at 61Hz is noticeable from the FRFs and 25Hz corresponding to the target speed 15,rpm is far enough from the 1 st bending frequency. Therefore, there is no problem to consider the rigid body motion only for controller design. 5. CONTROLLER DESIGN Based on the measured FRFs, PD controller and cross feedback controller for AMB were designed and PD-gain are selected to be 16.7 and.2 each for the stable AMB operation[9]. Moreover, the notch filters Phase[deg] Frequency[Hz] (b) Lower AMB Figure 14. Frequency response function of AMB 6. EXPERIMENTAL RESULTS The operating test has been done for the assembled FESS and the AMB controller by increasing the rotational speed up to 15,rpm. Figure 15 shows the orbit plot for the runout of the upper and lower flywheel shaft at 15,rpm. It can be observed that there is almost no other runout frequency components except for 1x component and AMB runs stably with the orbit of the diameter of less than 2 μm. It is

6 confirmed that the performance of AMB is satisfactory and there is enough radial margin between the flywheel shaft and the touchdown bearings which is located from the flywheel shaft with the gap of 3 μm. 1x runout component which is most of the overall runout is due to the imbalance response of the flywheel rotor. The magnitude of the imbalance response changes depending on the rotational speed reflecting the rotor vibration mode. Figure 16 shows the magnitude change of 1x component in the upper AMB from standstill to 15,rpm. It can be clearly observed that the cylindrical and conical mode exist at 1,2rpm and 3,rpm each. Zero-to-peak runout is less than 17 μm even when the rotational speed passes through the cylindrical critical speed. It can be also seen that after the rotational speed passes through the conical critical speed, AMB runs stably with the runout less than 1 μm. Mag[um] (a) Upper AMB (b) Lower AMB Figure 15 Orbit plot of AMB at 15,rpm Cylindrical Conical Rotational Speed[RPM] Figure 16 Magnitude of 1x component versus the rotational speed in upper AMB respectively and it was verified that the analytical results were sufficiently similar to the impact test results. The validity of the analytical results was confirmed by the measured FRF as well. It was also shown that the flywheel design to make its Ip/It.5 was effective to minimize the unbalance response of the flywheel and reduce the control input to the AMB actuators. The controller design and implementation procedure using Matlab /Simulink and xpc Target was very simple and straightforward. In the experiment, FRFs were measured easily and the monitoring signal was gathered handily by using xpc Target, too. REFERENCES [1] R. Okow, A.B Sebitosi, A. Khan and P. Pillay, The Potential Impact of Small-scale Flywheel Energy Storage Technology on Uganda s Energy Sector, Journal of Energy in Southern Africa, Vol. 2, No. 1, 29, pp [2] P. Gyuk and S. Eckroad, EPRI-DOE Handbook Supplement of Energy Storage for Grid Conneted Wind Generation Applications, EPRI, Palo Alto, CA, USA, 24. [3] I. Hadjipaschalis, A. Paullikkas and V. Efthimiou, Overview of Current and Future Energy Storage Technologies for Electric Power Applications, Renewable and Sustainable Energy Reviews, Vol. 13, 29, pp [4] C.H. Park, S.K. Choi, J.P. Lee and Y.H. Han, On the Dynamic Behavior of a 5kWh FESS Mounted on AMBs, the 11 th International Conference on Mechatronics Technology, Ulsan, Korea, 27, pp [5] xpc Target TM User s Guide, The MATLAB Works, Inc., Natick, MA, USA, 27. [6] J. M. Vance, RotorDynamics of TurboMachinery, A Wiley-Interscience Publication, USA, 1988, pp [7] S.Sivrioglu and K. Nonami, Active permanent magnet support for a superconducting magnetic-bearing flywheel rotor, IEEE Transactions on Applied Superconductivity, Vol. 1, 2, pp [8] D. Clark, Developing improved servos for the multiple mirror telescope, American Control Conference, Proceedings of the 25, Vol, 6, 25, pp [9] M. Ahrens, L. Kucera and R. Larsonneur, Performance of a magnetically suspended flywheel energy storage device, IEEE Transactions on control systems technology, Vol. 4, 1996, pp CONCLUSION In this paper, the design procedure including rotor dynamic analysis of the 5kWh class FESS mounted on AMB were introduced and it was shown that AMB have run stably up to target speed, 15,rpm by using simple PD controller and notch filters. Rotor dynamic analysis was performed for the shaft and full flywheel