A control algorithm for a simple flywheel energy storage system to be used in space applications

Flywheels have been under consideration to be used for energy storage purposes in space applications to replace electrochemical batteries. An electrical machine is used as a motor to store kinetic energy when the solar energy is available, and then the stored energy is converted back to electrical energy by running the machine as a generator when the solar energy is no longer available. A control algorithm for these systems is proposed in this paper. The proposed method uses a current reference rather than a speed reference in the motor mode. A method is also suggested to properly determine the current reference to overcome the losses and to create constant acceleration. The proposed algorithm is tested on an experimental set-up and the results are given.

A control algorithm for a simple flywheel energy storage system to be used in space applications

Flywheels have been under consideration to be used for energy storage purposes in space applications to replace electrochemical batteries. An electrical machine is used as a motor to store kinetic energy when the solar energy is available, and then the stored energy is converted back to electrical energy by running the machine as a generator when the solar energy is no longer available. A control algorithm for these systems is proposed in this paper. The proposed method uses a current reference rather than a speed reference in the motor mode. A method is also suggested to properly determine the current reference to overcome the losses and to create constant acceleration. The proposed algorithm is tested on an experimental set-up and the results are given.

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  • Current Generation Back-EMF Estimation Wm_ref Im_ref SW-ON RESET PI Controller (Spd. Ctrl.) _ _ Ha Hb Hc Figure 3. Flywheel control architecture. PWM Inverter Voltage Commutation PI Controller (Current Ctrl.) M MOTOR/GENERATOR Current Commutation Speed Estimation Reference Current Generation Back-EMF Estimation SW-ON PI Controller (Spd. Ctrl.) _ _ Ha Hb Hc Figure 4. System during the charging (motor) mode. A speed loop in the motor controller is used only for over-speed protection. When the speed reaches a predetermined speed limit, this loop is activated and the motor speed is regulated at this level. As long as the speed is below this limit, the motor is driven by the current reference that is defined in Eq. (3). The friction power loss has been calculated for the steel ball bearings and is included in the algorithm. The back EMF constant (K V ) of the BLDC machine is used to calculate the peak value of the back EMF voltage. E m = ϖ m /K V (4) Hall sensor pulses are used to calculate the speed. The output of a counter that is activated at the half-period of each Hall sensor pulse is used for this purpose. The current commutation block computes a phase C current using phase A and phase B current measurements. Next, a DC control current ( I m ) is obtained using the peak values of these currents. The current controller is a PI regulator, and the voltage reference is obtained at its output. This voltage reference is multiplied by the Hall-effect sensor signals in the voltage commutation block to obtain the voltage references for each phase. These phase voltage references are compared to 20-kHz triangular carrier signals to generate the PWM switching signals. Discharge mode When the solar energy is no longer sufficient, the DC bus voltage drops below the predefined threshold level and the SW switch is turned off by the controller, initiating the discharge mode. The load, which is just a resistor here, is supplied by the generator. The active sections of the system in this mode are shown in Figure 5. P WM Inve rte r Volta ge Commuta tion M MOTOR/GENERATOR Curre nt Commuta tion S pe e d Es tima tion Re fe re nce Curre nt Ge ne ra tion Ba ck-EMF Es tima tion Ha Hb Hc Wm Im_re f Figure 5. System during the discharge (generator) mode. The DC bus voltage is regulated at a predetermined level in this mode. The PWM inverter is used as a PWM boost rectifier in this mode for this purpose. The DC bus voltage is first compared to the reference voltage to generate a current reference that is then compared to the real current ( I m ) . A different control algorithm, the boost algorithm, is used inside the voltage commutation block in this mode. The phase voltage reference signals are obtained by the boost algorithm, and these signals are compared to the 20-kHz triangular carrier signals to generate the PWM switching signals. The current reference and speed estimate algorithms continue to run during the discharge mode since their outputs should be available when the next charging mode starts. The accumulated output of the integrator may cause the voltage references to reach very high values in the generator mode. This, in turn, may result in very high instantaneous motor currents, leading to the activation of the over-current control during the transition from the generator mode to the motor mode. The current controller needs to be reset before initiating the generator mode to prevent this problem. Experimental results The experimental set-up seen in Figure 6 was used to test the system. A DC power supply was used instead of solar panels, and the switch on the DC bus was controlled manually. A Maxon EC22 BLDC was used as the motor/generator unit. A Technosoft MCK2812 was chosen as the flywheel driver. The control algorithm was developed in a DMC28x Developer Pro software environment. A 500- µ H external inductor was placed in series with the phase windings to reduce the current ripple and for the boost operation in the generator mode. Figure 6. Experimental set-up. It should be noted that these systems are normally designed for space applications and, therefore, either magnetic or ceramic bearings are used to minimize the mechanical losses. There are no windage losses either, since the system operates in a vacuum. However, the experimental set-up is not operated in a vacuum, and standard steel ball bearings are used. Therefore, the losses are high. As a result, the speed is limited to 9500 rpm and the stored energy is not very high. The charging and discharging intervals have been kept short to demonstrate the concept. For the same purpose, high-resistance loads (5 k Ω and 310 Ω) have been used to prevent fast speed reductions. In light of this information, Eq. (3) needs to be modified if the power loss due to the windage effects ( P wnd ) is added. I m = P acc + P f r + P wnd E m (5) Power loss due to windage and mechanical friction is usually defined by empirical equations. The following equations have been used in this work [17]. The shaft diameter has been ignored in the calculations of the windage losses. P f r = 1 2 m ∗ K f r ∗ F ∗ D b watt (6) P wnd = 1 64 M ∗ ρ ∗ ϖ 3 m r watt (7) Here, K f r is the friction coefficient (0.001–0.005), F is the force acting on the bearings (N), D b is the inner diameter of the bearing (m), ω m is the flywheel angular speed (rad/s), C M is the torque constant, ρ is the density of the air (kg/m 3 ) , and D r is the flywheel diameter (m). The Reynold number needs to be determined first to calculate the torque constant: R e = ρϖ m D 2 r 4µ (8) The variable µ in this equation represents the dynamic viscosity and it is 1.8 10 −5 kg/m s for 1 atm at 20 ◦ C. The air density is 1.2 kg/m 3 for the same conditions. A flywheel with a diameter of 0.135 m is used. If the Reynold number is calculated for the flywheel speeds below 10,000 rpm (1047 rad/s) it is found to be less than 230,7 In this case, the torque constant can be calculated as follows [12]: C M = R 0.5 e
  • In order to determine the losses caused by the bearing, the friction forces acting on the bearings need to be known. In the system under consideration, these forces are the force due to the flywheel weight ( F G ) and the imbalance forces ( F B ) . F = F G + F B (10) The imbalance force can be calculated as follows: F B = meϖ 2 m , (11) where m is the residual mass (kg), e is the eccentricity between the rotational axis of the flywheel and the center of gravity (m), and me is the residual unbalance (kg m). The total force acting on the flywheel is then: F = F G + F B = M g + meϖ 2 m , (12) where g is the gravity (10 m/s 2 ) and M is the flywheel mass (0.233 kg). The manufacturer of the bearings defines the friction coefficient ( K f r ) as approximately 0.003. The only unknown left then is the residual unbalance (me). This value can be determined experimentally. The motor is accelerated to a certain speed by the constant current reference. Afterwards, the acceleration power is zero ( P acc = 0) and the motor is driven by the current reference that is calculated using the windage and friction loss values. It is expected that the motor will keep the final speed reached by the constant current reference if the reference value is calculated correctly. A residual unbalance value of 1175 g mm has met this condition for the experimental set-up. The acceleration power defined in Eq. (3) is written in a different way in Eq. (13). P acc = (J dϖ m dt )ϖ m watt (13) The parameters used in the power equations are finally obtained as follows: K f r = 0.003 F = (0.235 10 + 1.175 10 −3 ω 2 m ) N D r = 0.135 m D b = 0.010 m J = 8 × 10 −4 kg m 2 dω m = 30,000 RPM (3141.6 rad/s) dt = (65 × 60) s As a result, aside from the acceleration power, the friction and windage losses can be defined as a function of the flywheel speed: P acc = 870e −4 ϖ m P f r = (35 + 1.175e-3ϖ 2 m ) ∗ ϖ m P wnd = 67e −8 ϖ 3 m ϖ 0.5 m
  • In the experiments, the motor has been driven by a constant current reference of 386 mA ( I m ref ) for 60 s. Next, the calculated reference value has been used to drive the motor at a constant speed ( P acc = 0). The result is given in Figure 7. In the second stage, the P acc given in Eq. (14) is applied at t = 60 s and an acceleration test is conducted. The results are given in Figure 8. The expected acceleration is 7.7 rpm/s. The acceleration is calculated as 8 rpm/s from the test results given in Figure 8. The error is caused by the difficulty of calculating the real values of the friction and windage losses. 25 5 0.75 S pe 20 40 60 80 100 Time (s) S pe 20 40 60 80 100 Time (s) Figure 7. Result of the test to calculate the friction coefficient experimentally by driving the motor with a calculated current reference. Once the necessary adjustments are done, subsequent motor-generator operation tests can be performed. In the motor operation, a high value of acceleration of 143 rpm/s (15 rad/s 2 ) is used to drive the motor to the maximum speed (9500 rpm) in a short time (75 s). At this instant, the 32-V bus voltage is disconnected and the generator mode is initiated. In the generator mode, first a 5 k Ω resistance was used as the load. In this mode, the bus regulation is performed by the flywheel system and it was designed to regulate the voltage at 9 V. This value was chosen due to the practical limitations arising from the low back EMF voltage value of the available motor (around a 7.8-V peak) at this speed. The speed variation in the generator mode is given in Figure 9 and the bus voltage variation is shown in Figure 10. Figure 9. Flywheel speed variation during the generator’s operation (load resistance is 5 k Ω) . Figure 10. Bus voltage variation during the generator’s operation (load resistance is 5 k Ω) . As seen from Figure 10, the bus voltage can be regulated at 13.7 V. Following the generator mode, 32 V of bus voltage is reapplied and the motor starts acceleration again as expected. The operation stability at varying load conditions in the generator mode is also an important performance parameter. To test the system for this concept, the load was changed from 5 k Ω to 310 Ω and then back to 5 k Ω during operation. The speed and bus voltage variations for this operation are given in Figures 11 and 12, respectively.
  • Figure 11. Flywheel speed variation during the generator’s operation (load resistance is changed from 310 Ω to 5 k Ω) . Figure 12. Bus voltage variation during the generator’s operation (load resistance is changed from 310 Ω to 5 k Ω) . In this operation, the generator mode is started with 5 k Ω . About 4 s later, the load is changed to 310 Ω . After 3 s of operation at this condition, the load is brought back to 5 k Ω . As seen in Figure 12, the bus regulation is not dramatically affected by this load variation. Conclusion A simple flywheel energy storage system for space applications was investigated in this paper. A control algorithm was presented and the experimental results were given. The current reference instead of the speed reference was proposed to drive the machine in the charging mode to avoid instantaneous current variations. This requires a good estimation of the mechanical losses, and a method was proposed for this purpose. A bus voltage regulation algorithm was successfully applied during the generator (discharging) mode. The transition between the operation modes was realized without any problems. Due to the physical limitations, the operation speed was limited to below 9500 rpm. The application of the algorithm presented in this paper to flywheel systems with magnetic and ceramic bearings is planned. This will provide a good chance to compare the results. Moreover, the effects of the energy storage function on the attitude control may be investigated if this system is utilized in an integrated power and attitude control system for spacecrafts. References B.H. Kenny, P.E. Kascak, R. Jansen, T.P. Dever, W. Santiago, “Control of a high-speed flywheel system for energy storage in space applications”, IEEE Transactions on Industry Applications, Vol. 41, pp. 1029–1038, 2005. M.R. Patel, Spacecraft Power Systems, CRC Press, Boca Raton, FL, USA, 2005. B.H. Kenny, P.E. Kascak, H. Hofmann, M. Mackin, W. Santiago, R. Jansen, “Advanced motor control test facility for NASA GRC flywheel energy storage system technology development unit”, 36th Intersociety Energy Conversion Engineering Conference, 2001. A.S. Nagorny, N.V. Dravid, R.H. Jansen, B.H. Kenny, “Design aspects of a high speed permanent magnet synchronous motor/generator for flywheel applications”, IEEE International Conference on Electric Machines and Drives, pp. 635–641, 2005. B.H. Kenny, P.E. Kascak, “Sensorless control of permanent magnet machine for NASA flywheel technology development”, NASA TM 2002-211726, 2002. P.E. Kascak, B.H. Kenny, T.P. Dever, W. Santiago, R.H. Jansen, “International space station bus regulation with NASA GRC flywheel energy storage system development unit”, NASA TM 2001-211138, 36th Intersociety Energy Conversion Engineering Conference, 2001. B.H. Kenny, P.E. Kascak, “DC bus regulation with a flywheel energy storage system”, SAE Power Systems Conference, 2002. P.E. Kascak, R.H. Jansen, B.H. Kenny, T.P. Dever, “Single axis attitude control and DC bus regulation with two flywheels”, 37th Intersociety Energy Conversion Engineering Conference, pp. 214–221, 2002. B.H. Kenny, R.H. Jansen, P.E. Kascak, T.P. Dever, W. Santiago, “Demonstration of single axis combined attitude control and energy storage using two flywheels”, Proceedings of the IEEE Aerospace Conference, Vol. 4, pp. 2801– 2819, 2004.
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