Stability analysis and control of a flywheel energy storage rotor with rotational damping and nonsynchronous damping

Based on the principle of Lagrange mechanics, especially considering the effects of rotation damping and nonsynchronous damping, a radial 4-dimensional dynamic model of the flywheel bearing rotor system is proposed. Applying the Laplace eigenvalue method, the stability effects of rotational damping, nonsynchronous damping, and their coupling effects are investigated by means of root locus method. Under the control of the linear quadratic regulator, dynamical characteristics of the flywheel bearing rotor system with varied rotational damping and nonsynchronous damping are also studied. The results show that the rotation damping, nonsynchronous damping, and their coupling effects have vast and complex instability effects on high-speed flywheel bearing rotor system. However, there are three exceptions. The tiny proportional rotational damping, remaining below 12%, and the minuscule proportional co-nonsynchronous damping; the product of the nonsynchronous damping and the speed ratio below 5% both can enhance the stability of the system. Furthermore, in the situation that the counter-nonsynchronous damping is coupled with the large proportion of rotational damping, the stability of the system can also be boosted distinctly. On the other hand, the numerical experimental results show that the rotational damping and nonsynchronous damping have a beneficial effect on the flywheel system controlled by linear quadratic regulator. In addition, under the control of linear quadratic regulator, the transient dynamical behavior of the flywheel rotor system with rotational damping or co-nonsynchronous damping performed better than the flywheel rotor system with the coupled damping. The numerical simulations of the transient response of the flywheel rotor system under active control are consistent with some of the derived stability analysis results. The results about the stability analysis and the performance in vibration control give the suggestions for the instability control and fault detection of the system.

Analysis of Standby Losses and Charging Cycles in Flywheel Energy Storage Systems

Aerodynamic drag and bearing friction are the main sources of standby losses in the flywheel rotor part of a flywheel energy storage system (FESS). Although these losses are typically small in a well-designed system, the energy losses can become significant due to the continuous operation of the flywheel over time. For aerodynamic drag, commonly known as windage, there is scarcity of information available for loss estimation since most of the publications do not cover the partial vacuum conditions as required in the design of low loss energy storage flywheels. These conditions cause the flow regime to fall between continuum and molecular flow. Bearings may be of mechanical or magnetic type and in this paper the former is considered, typically hybridized with a passive magnetic thrust bearing. Mechanical bearing loss calculations have been extensively addressed in the open literature, including technical information from manufacturers but this has not previously been presented clearly and simply with reference to this application. The purpose of this paper is therefore to provide a loss assessment methodology for flywheel windage losses and bearing friction losses using the latest available information. An assessment of windage losses based on various flow regimes is presented with two different methods for calculation of windage losses in FESS under rarefied vacuum conditions discussed and compared. The findings of the research show that both methods closely correlate with each other for vacuum conditions typically required for flywheels. The effect of the air gap between the flywheel rotor and containment is also considered and justified for both calculation methods. Estimation of the bearing losses and considerations for selection of a low maintenance, soft mounted, bearing system is also discussed and analysed for a flywheel of realistic dimensions. The effect of the number of charging cycles on the relative importance of flywheel standby losses has also been investigated and the system total losses and efficiency have been calculated accordingly.

Improving the Energy Capacity and Cost Effectiveness of Flywheel Rotors in Grid-Scale Energy Storage Systems by Varying Their Shape, Speed and Size

Flywheel energy storage systems (FESS) are an excellent short duration grid energy storage solution; however, their cost and energy storage capacity are typical barriers to their widespread commercialization. FESS can be designed by optimizing the shape of the flywheel rotor, choice of rotor material, operating speed and rotor radius. This study optimizes the flywheel rotor shape at various operating speeds and outer radii. It is found that the energy capacity of the rotor can be improved by choosing an ideal combination of operating speed and rotor radius. Our earlier work showed that including the cost of the FESS as an optimization objective could significantly alter the FESS design [1]. Therefore, the cost effectiveness of the FESS is also studied by comparing rotors made from different materials on an energy-per-cost basis, while the cost ratio of the materials is varied.

Optimal control for hybrid magnetically suspended flywheel rotor based on state feedback exact linearization model

For a hybrid magnetically suspended flywheel (MSFW) rotor suspended by permanent magnet biased active magnetic bearing (AMB) and passive magnetic bearing (PMB), the dynamic functions are nonlinear and coupling among different degrees of freedom (DOFs). In this article, the nonlinear dynamic functions in two controllable DOFs of the hybrid MSFW rotor are developed based on the equivalent magnetic circuit, and then the nonlinear dynamic function is linearized by using the state feedback exact linearization (SFEL) in order to minimize the coupling in two controllable DOFs. Furthermore, an optimal control based on the SFEL model is designed to reduce displacement runout and coupling among two controllable DOFs of the hybrid MSFW rotor at the rated speed. Finally, the simulation and experimental results validate the effectiveness of the optimal control based on SFEL model, and the stability of the hybrid MSFW rotor with an impulse-type disturbance is improved.