Experimental Validation of a Dynamic model of a SRM used in superconducting bearing flywheel energy storage system

J.L. SILVA NETO1, R. DE ANDRADE Jr1,2,

L.G.B. ROLIM1,2, A.C. FERREIRA1,2, G. G. SOTELO2, W. SUEMITSU1,2 1Department of Electrical Engineering, 2COPPE/Electrical Engineering Program

Federal University of Rio de Janeiro P.O.Box 68504, CEP 21941-972

BRAZIL luizneto@dee.ufrj.br, ferreira@ufrj.br, rolim@dee.ufrj.br

Abstract: - This paper presents a dynamic model of a flywheel energy storage system with superconducting magnetic axial thrust bearing (SMB) and a permanent magnet radial bearing (PMB), which uses a switched reluctance machine (SRM) as motor/generator. The SMB was built with Nd-Fe-B magnet and YBCO superconducting blocks, refrigerated with liquid nitrogen. The developed model can take SRM non-linearities into account, by including the inductances as a function of the angular position and phase current. Simulations of the power electronics and SRM show that the system can work up to 30,000 rpm supplying the required energy during disturbances. The control and power circuitry are described. An experimental validation of the model is performed. Key-Words: - flywheel, superconducting magnetic bearings, switched reluctance machine, energy storage.

1. Introduction In modern production plants, momentaneous voltage

disturbances, such as voltage sags, can cause slow output, production interruption or damage to machines. Energy customers with continuous process involving fragile materials, like paper forming, food processing, etc, are likely to avoid prejudices with interruptions due to the energy quality problems. In order to mitigate voltage sags dynamic voltage restorers can regulate the voltage at the load bar avoiding the prejudices, but some of these devices draw the energy necessary to compensate the voltage sags from the same grid that they will compensate. This strategy can cause a system failure in some cases. In order to avoid this failure, these equipments may employ energy storage devices as electrochemical batteries and flywheels [1].

The above reasons have motivated the launch of a joint project between the Federal University of Rio de Janeiro (UFRJ) and a local energy distribution company, concerning the development of a flywheel-based energy storage device for custom power equipments. Two major potential applications are under consideration for further development: the compensation of voltage sags and a short-term uninterruptible power supply, to provide ride-through capability to critical loads under momentary fault conditions.

The performance degradation of the electrochemical batteries is directly related to the number of charges and discharges cycles. Furthermore, they are expensive and not environmental safe [7]. On the other hand, flywheel energy storage systems (FESS) coupled to an electrical machine can be used to store mechanical energy, which can be used in a dynamic voltage restorer, for example. FESS are environmental safe and do not degrade the performance with charges and discharges cycles. To surpass the electrochemical batteries, FESS need to have better energy volume density, life-cycle cost and FESS monitoring require less effort than for batteries [7]. The FESS has the burst risk in case of bearing failure.

The energy stored in a flywheel is proportional to the moment of inertia and the square of angular velocity. Then increasing the flywheel angular velocity may increase the energy density of FESS [3]. When the flywheel velocity is increased the idling losses are increased too, due to the aerodynamic drag and the losses in the bearings. The aerodynamic drag can be reduced with a partial vacuum in the flywheel container, and the bearing losses with magnetic bearings [2-4]. Active magnetic bearings (AMB) are expensive and demand an energy consumption that have to be computed as a loss. Superconducting magnetic bearings (SMB) are one alternative to AMB, they are entirely passive and do not suffer from catastrophic failure as the AMB does. The SMB will fail if its cooling system fails and the superconductors warm up, but this will be a gradual process [4]. As the price of superconductors is still high, the overall system cost may be reduced if the SMB is used together with a permanent magnetic bearing (PMB) in an Evershed arrangement. In this case the PMB does the most of efforts to bear the flywheel and motor and the SMB gives stability to the whole set.

Other significant aspect of the energy storage device is concerned to the electromechanical energy conversion between the flywheel and the electrical system. In order to use the most of the stored kinetic energy in the flywheel, the electrical machine has to be electronically controlled. It is usual to use a permanent magnet synchronous machine in flywheel projects [2,4], but the permanent magnet machines always have idling losses related to the eddy currents induced by the magnetic field on the stator. This can be avoided using a switched reluctance machine (SRM), which has a null idle magnetic field [5]. The SRM can work at very wide

speed ranges: from zero up to several ten thousand rpm; it is fault tolerant and has null idle losses. Its robustness leads to achieve a high reliability.

This paper describes a FESS with an Evershed type bearing and a switched reluctance machine. First a dynamic model of the system is presented which takes magnetic non-linearities into account. The required data can be either measured or calculated from finite-element simulations. Then, preliminary results of low speed tests carried out in a prototype will be presented and compared with simulation model.

2. Flywheel Energy Storage System A. Design

Fig. 1 shows the FESS prototype that is being in development. It is composed of an Evershed type bearing in order to minimize the bearing losses, a SRM as the motor/generator and a flywheel to store kinetic energy. The system will be placed in a vacuum chamber, with pressure of about 1 µbar, to reduce the aerodynamic drag. The Evershed bearing system is composed of a SMB and a PMB.

(a)

(b)

Fig. 1. Experimental test rig used in the low speed SRM tests. a) In the figure: 1) the vacuum enclosure, 2) the motor support, 3) the SRM, 4) the SMB rotor, 5) the YBCO blocks and 6) the superconductors’ chiller. b) The prototype in the vacuum enclosure

B. Superconducting Magnetic Bearing The superconducting magnetic bearing was

constructed with Nd-Fe-B magnets and YBa2Cu3O7-δ (YBCO) superconducting blocks. There are two SMB under test: SMB-A and SMB-B. Both of them are

assembled with 16 square blocks of YBCO, 36 mm x 36 mm and 20 mm high, mounted in 4x4 array and cooled with liquid nitrogen (LN2). The permanent magnets rotors, Fig. 2, are assembled with magnetic flux shapers, in order to increase the levitation force and the stiffness [5]. SMB-A uses a set of brick shaped magnets, 20.0 mm x 14.0 mm x 2.8 mm, assembled in a ring arrangement, Fig 2a. SMB-B uses 3 rings of Nd-Fe-B, magnetized axially, and 4 rings of steel as flux shapers, Fig. 2b. It is difficult to get Nd-Fe-B rings magnetized axially; the rings were fabricated and magnetized in sections. The steel rings smooth the magnetic field enough to avoid magnetic drag in the bearing.

The levitation forces measurements of the SMB are shown in Fig. 3. The SMB-B has about the same levitation force that SMB-A for gaps smaller than 10 mm, but SMB-B rotor is smaller (130 mm outer diameter against 175 mm of SMB-A) and lighter (1.4 kg against 4.9 kg of SMB-A) than SMB-A rotor. This is due to the greater intensity and radial gradient of magnetic field in the design of SMB-B rotor.

The stiffness, axial and radial, and damping of SMB-A was measured in a previous work [5]. The stiffness, axial and radial, increases strongly when the superconductors are cooled in the magnetic field of the bearing, reaching 74.5 N/mm for a cooling distance of 3 mm, which results in a gap of 1.9 mm. From these measurements the bearing damping was also obtained and it is a low damping (~0.01) in all cases. Dynamic measurements of linear bearings with flux shapers showed similar results [8].

Fig. 2. The SMB permanent magnets rotors: (a) SMB-A and (b) SMB-B.

Fig. 3. Levitation force measurements for both SMB rotors for zero field cooling.

C. Permanent Magnetic Bearing The PMB plays two roles in the FESS: radial

positioning and reduction of the load over the SMB. This PMB will act in attraction in concert with the SMB. PMB by itself cannot provide stability for bearing system, as predicted by Earnshaw’s theorem [8].

Finite element simulation of the designed PMB shows that it will produce a levitation force of about 200 N at 5 mm gap and a radial stiffness of about 24 N/mm.

3. Switched Reluctance Machine Model The operation of a switched reluctance machine

(SRM) is based on the principle of minimal reluctance. When the coil of some phase is excited, forces are developed over the magnetic circuit that tend to bring it to the position where the reluctance reaches a minimum, as seen from the energized coil. At this position coil inductance reaches a maximum. If this phase is switched off and the next phase is switched on slightly before this position is reached, continuous movement of the rotor can be achieved.

The symmetry of the magnetic circuit allows for nearly null mutual flux linkage, even under saturated conditions. As a result, the contribution of each phase for torque production is mainly defined by the self-inductance profile of that phase. So, one can calculate a family of inductance profile curves for one phase, as a function of rotor position for different values of phase current. The calculations have been carried out with the ANSYS® package, which uses the finite element method (FEM).

The electromagnetic torque produced by one single coil is given by equation (1), where Te is the electromagnetic torque, θr is the rotor angular position, λ is the total flux linked to the coil and i is the coil current.

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂= ∫

i

rr

re ,i)diλ(θθ

,i)(θT0

(1)

Both relationships Te (θr , i) and λ(θr , i) are strongly non-linear, a fact that makes it difficult to develop an analytical mathematical model for the SRM. Thus instead of trying to obtain such an analytical model, the methodology adopted in this work was to use tabulated data for Te (θr , i) and λ(θr , i), which may have been obtained off-line by means of static measurements or FEM computations with the ANSYS® package, over a range of values wide enough to cover any situation that may occur within given simulation/real limits.

The electromagnetic torque produced by one single coil is given by the following equation:

⎥⎦

⎤⎢⎣

⎡

∂∂= ∫

i

Lrr

Lre )di,iλ(θθ

)i(T0

,θ (2)

The tabulated data is then used, with linear interpolation, directly in the solution of the electrical and mechanical dynamic equations (3) and (4).

dtidir Lr

Ls),(V θλ+⋅=

(3)

meTr TT

dtdJ −=⋅ 2

2θ

(4)

where V is the coil terminal voltage, rs is the coil resistance and i is the current flowing through the coil. In equation (4), J is the combined moment of inertia (SRM rotor plus flywheel), Te is the electromagnetic torque and Tm is the load opposing torque and mechanical losses.

Unfortunately equation (3) cannot be properly digitally solved in this form. It suggests the use of λ(θr , i) as a state variable. One must remember that the relation between λ and i expresses the non-linear magnetic characteristics of the machine along the rotor position. In order to simulate the electrical phase equations of the SRM, they must be put in an appropriate form, suitable to be applied in most circuit simulation software. The second term on the right side of (3) represents a voltage drop on a non-linear multi-variable dependent inductance, not available as a fundamental circuit element in these programs.

Modeling inductive non-linear relations involving rotating magnetic circuits is not apparent. With the purpose of addressing this problem, let us consider the fundamental v-i relationship in an inductance:

dttdiLtv L

L)()( =

(5)

)0()(1)( LLL idttvL

ti += ∫

(6)

Equation (6) is obtained by solving (5) for iL(t). It suggests that an inductance can be modeled as a current source controlled by the integral of the voltage between its terminals, or equivalently, by the total magnetic flux λ linked to the coil. Note that iL(λ) is obtained from the magnetization characteristics of the inductor, and can be linear or non-linear.

The elements involved in this modeling are common in most circuit simulation programs. The modeled inductance is inserted on the simulated circuit between two nodes (current source terminals). The control blocks perform the intrinsic feedback exposed by (6), and the tabulated data representing the non-linear magnetic characteristics can be incorporated in a look-up table type block.

For the SRM the data λ(θr,iL) must be resampled in order to produce the inverse relation iL(θr,λ). This operation involves interpolation of the tabulated values considering the chosen discrete values for λ. The electrical torque Te (θr , iL) can also be obtained from tabulated data. Fig. 4 illustrates the implementation for the SRM of the discussed per-phase model of the inductance. For the 6/4 machine used in this work, Fig. 4 shows the variation of torque and flux linkage of one phase with current and rotor angular position.

s1

vL

vL

iL

θ

T

λiL(θ,λ)

T(θ,iL) Fig. 4. Model of one phase inductance of the SRM

The mechanical dynamics of the SRM can be modeled directly from (4). The total instantaneous electrical torque is calculated by adding the per-phase torque (Te1, Te2 e Te3) extracted from the tabulated data as a function of the currents and the rotor angular position, and then equation (4) is applied.

4. Power and control circuits In this work an asymmetrical bridge is used as the

power circuit responsible for the current control. The main feature of this topology is the two-quadrant operation, allowing for reversibility of the applied voltage with unidirectional current. Since the direction of the magnetic flux does not influence the inductance profile along the angular position, the polarity of the circulating current is not important. However, a bipolar voltage circuit is crucial for fast current extinction in motoring operation, and for the correct current control in the regenerating mode.

For the current synthesis the strategy adopted is the PWM control with hysteresis band. The phase current tracks its reference inside a tolerance band, in a closed-loop operation. According to the required energy flow direction, the switching sequence determines three different states (Fig. 5) for the power circuit.

STATE 1 is characterized by the IGBTs T1 and T2

conducting and the DC voltage been applied forcing the current to circulate in the positive sense. Therefore, the energy flows from the DC link to the machine. When T2 and D2 conduct (STATE 2) the current falls freely if the angular interval of conduction determines a positive torque for positive angular speed. Otherwise, for positive speed and negative torque, the phase current will tend to

grow due to the negative sign of the factor dtdθ

θλ

∂∂ . This

term can be viewed as a “speed voltage” obtained from

the expansion of dt

id Lr ),(θλ (equation (3)).

Finally, for STATE 3 only the diodes D1 e D2 conduct applying a negative voltage (-Vdc) over the stator phase, forcing the current to decrease. Under this condition, the converter injects current into the DC link regenerating energy. In all three states the current flows through the stator phase in the same direction.

Since each state ultimately define the voltage applied to the stator phases, the behavior of the power converter can be modeled by switching functions. This approach is particularly interesting to be employed in some simulation software having convergence problems or inherently slow execution rate, like MATLAB/SIMULINK. Modeling static switches involves determining the zero-crossing instants, which can be very time-consuming, depending on the algorithm for solving non-linear differential equations. Therefore, it is possible to model the converter using voltage sources controlled by switching functions. For the SRM drive one can define the function p that can assume values 1, 0 or –1 according to states 1, 2 and 3 respectively. The voltage VL applied to one stator phase is then calculated by (7), where VF and VCEsat are the voltages across the diodes and transistors respectively. The dc link total current is simply calculated by (8), where IL1, IL2 and IL3 are the stator phases currents.

VL = pVdc + (p – 1)VF – (1 + p) VCEsat (7) Idc = p1IL1 + p2IL2 + p3IL3 (8)

5. System simulation Future developments of the proposed FESS rely

heavily in a possibility of working with virtual prototypes, which will allow for testing several design optimizations without actually building them. Therefore there is a need for models that correctly represent all the system components. In this section a model developed to analyze the interaction between the energy storage system and the electric power system to which it is connected is presented. This model was implemented in PSCAD/EMTDC software and is able to represent the main components affecting this interaction, namely: the SRM, the power electronics circuit, the control circuit and the mechanical system. The model is first validated against test results carried out in a prototyped running at low speed and later is used to predict the system operation at speed levels close to the envisaged.

The logic for determining the operation as motor or generator and the PWM control for a 6/4 SRM is presented by the abstract code in Fig. 6. Each stator phase conducts for approximately 30 mechanical degrees on either motoring or regenerating modes. In Fig. 12: θON, θOFF are the angles for, respectively, the triggering and blocking the current circulation; iL , ref

Li are respectively the mesured and the reference current; ∆i is the hysteresis current band; and ω is the angular speed.

Estado 1

V dc

i L

i L

T 1

T 2

D 1

D 2

Estado 3

V dc

i L

iL

T 1

T2

D1

D2

Estado 2

V dc i L

T 1

T 2

D 1

D 2

State 1 State 2 State 3

Fig. 5 Operating states of the power circuit

Fig. 6. Control logic of the SRM drive: a) mode of

operation decisions; b) PWM current control. The power electronics circuit consists of two

converters. To drive the SR machine a half-bridge IGBT-based converter is used, allowing operation as motor or generator. The dc link is connected to the network by a bridge PWM converter, which is controlled according to Akagi’s pq theory [9]. The objective of the control operation is to determine the direction of the power flow. This is achieved by regulating the dc link voltage. The flywheel shaft speed must be controlled according to the instantaneous active power demanded by the grid. In this work, the implementation of a two-stage control strategy for the flywheel shaft speed is proposed. Both stages are coupled through a common state variable: the voltage across the dc link capacitor. The main idea is to control the acceleration of the SRM in proportion to the mismatch between the dc link capacitor voltage and a given reference value. If no power flows between the flywheel and the grid, then the dc link capacitor voltage remains regulated at its nominal value. However, if the grid demands active power, the command will act directly upon the network side converter, adjusting its current. It causes variations of the dc link capacitor voltage, which is compensated by the dc link voltage PI regulator, which ultimately defines the operation of the machine as motor or generator. There is however another speed PI regulator, with the main purpose of adding a small offset to grid converter average real power ( p∆ ), in order to bring the flywheel back to the rated maximum speed after any transients. Its output signal should be limited to values that do not cause excessive power consumption from the grid.

In order to demonstrate the flywheel operation with the developed PSCAD/EMTDC model, a simulation was carried out where, for simplicity but without loss of generality, the connection to the power grid was modeled by a current source connected directly to the dc link. The SRM drive was modeled based on the real 1.5 kW prototype. The intention was to study the performance of the control loop when energy is injected or drawn from

the link. Fig. 7 shows the simplified circuit. The simulation results are shown in Fig. 8. At t=0s a 10A current is solicited from the dc link by the grid, imposing that the SRM operates as a generator. The situation is reversed at t=6s when the grid injects energy into the capacitor at small rate in order to restore the reference speed.

MG

Converter SRM

Vgrid dci

Fig. 7. Flywheel energy storage system simplified Circuit.

6. Experimental validation

In order to validate the model, tests were carried out in the prototype presented in Fig. 1. The main components are: 1.5 kW 6/4 SRM, bi-directional converter with a dc link capacitor and a Superconductor Magnetic Thrust Bearing, which also works as a flywheel increasing the system inertia. The coupling between the SRM rotor shaft and the bearing is assumed to be rigid so they were represented as a single inertia. The agreement between measurements and simulated results can be better verified when the system is operating in the single pulse mode illustrated in Fig. 9, which shows the current in one stator phase. The machine was running in open-loop at 1000 rpm with 9 V in the dc link, opposing to the normal closed-loop operating voltage (>400V). The parameters used in the SRM model were obtained from Finite Element

Fig. 8. Results of the power electronics simulation showing the system response.

simulations. The small differences observed in Fig. 9 are due, mainly, to the low dc voltage. Normally the forward voltage drop in the power electronic devices is not significant when compared to the dc link voltage, and then do not need to be precisely modeled.

By showing the uncontrolled dc link voltage, Fig. 10 reveals the direction of the energy flow when the machine operates as a generator (0.2s – 1.0s) and as a motor (1.0s – 2.0s).

7. Conclusions This paper has presented a dynamic model of a

flywheel based energy storage system which can take non-linearities into account. The system uses a switched reluctance machine. The machine and control models were described and validated with simulations and experimental tests.

8. Acknowledgement The authors are grateful to CNPq, CAPES, Light and

FUJB for the financial support.

9. References: [1] G. Tanneau e D. Boudou, “Custom Power

Interface”, Proceedings da CIRED2001, pp. 2.48, June 2001.

[1] A. M. Wolsky, “An overview of flywheel energy systems with HTS bearings”, Supercond. Sci. Technol., Vol. 15, pp.836-837, 2002.

[2] R. Hebner, J. Beno and A. Walls, “Flywheel Batteries Come Around Again”, IEEE Spectrum, pp. 46-51, April 2002.

[3] T. A. Combs, A. Cansiz, and A. M. Campbell, “A superconducting thrust-bearing system for an energy storage flywheel”, Supercond. Sci. Technol., Vol. 15, pp.831-835, 2002.

[4] R. de Andrade, et al. “A superconducting high-speed flywheel energy storage system”, Physica C, Vol. 408-410, pp. 930-931, 2004.

[5] R. de Andrade et al. , “Performance of Nd-Fe-B and Ferrite Magnets in Superconducting Linear Bearings with Bulk YBCO”, IEEE Trans. on Applied Superconductivity, Vol. 13, pp. 2271-2274, June 2003.

[6] R. Arnold, “Solutions to the Power Quality Problem”, IEE Power Engineering Journal, pp. 65-73, April 2001.

[7] A. V. Radun, C. A. Ferreira and E. Richter, “Two-Channel Switched Reluctance Starter/Generator Results”, IEEE Transactions on Industry Applications 34, 1026-1034 (1998)

[8] M. E. Elbuluk, M. D. Kankam, “Potential Starter/Generator Technologies for Future Aerospace Application”, IEEE AES Systems Magazine, October 1996, pp. 17-24.

[9] [8] Akagi, H., Kanazawa, Y. e Nabae, A. (1983). "Generalized Theory of the Instantaneous Reactive Power in Three-Phase Circuits," Proceedings of the IPEC'83 – Int. Power Electronics Conf., Tokyo, pp. 1375-1386.

Fig. 9. Current in one stator phase in the single pulse

mode.. The tables were obtained from the static simulation on FEM and used in the dynamic model.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 280

90

100

110

120

130

140

150

160

T (s)

DC

link

Vol

tage

(V)

Fig. 10. Uncontrolled DC link voltage increases for generating (0.2s – 1.0s) and decreases for motoring

operation (1.0s – 2.0s).