0306-epe2014-full-21091806

Homo-Heteropolar Synchronous Machine for Low Power Variable Speed Wind or Hydro Applications: Design, 3D FEM Validation and Control

Marcel Topor, Sorin Ioan Deaconu, Lucian Nicolae Tutelea POLITEHNICA UNIVERSITY OF TIMISOARA

Revolutiei str., no. 5, Hunedoara, Romania

Tel.: +0040 / (254) 207.529. Fax: +0040 / (254) 207.501.

E-Mail: [email protected] URL: http://www.fih.upt.ro

Acknowledgements This paper was supported by the project "ATRACTING" POSDRU/159/1.5/S/137070.

Keywords Hybrid electric vehicle, Control of drive, Design, Permanent magnet motor.

Abstract In an effort to introduce a low cost (PM less), low power electric wind or hydro generators, this paper reports on preliminary design aspects, 3D FEM analysis and control of a 2.5 KVA, 250-1000 rpm, reactive homo-heteropolar synchronous machine (RHHSM).

Introduction A direct connection between the prime mover and the generator has many advantages, such as low noise, high efficiency, and high power density. Recently the price increase of the permanent magnets forces the designers to reconsider the available solutions to electrically excited generators i.e. synchronous generators or induction generators [1, 2]. Still, most electric generators are synchronous machines that need tight (rigid) speed control to provide constant frequency output voltage. To connect such generators in parallel, the speed controllers (governors) have to allow for a speed droop in order to produce balanced output of all generators. Of course, frequency also varies with load but this variation is limited to less than 0.5Hz. Variable speed constant voltage and frequency generators with decoupled active and reactive power control would make the power grids naturally more stable and more flexible. With the development of power electronics, many approaches have been proposed to solve these problems. One of the main disadvantages of the classic synchronous machines is the armatures excitation winding which determines a great rotor weight and inertia and involves the sliding contacts existence (brushes and slips rings) [1]. The RHHSM removes all these disadvantages, being destined to equip hydro-electric or wind power stations of low and middle power. This machine can be used also as servomotor due to the armatures reduced inertia [2, 3]. In present paper we introduce a new topology of variable reluctance synchronous generator for low power applications. The new topology is characterized by an electrical excitation winding placed in stator. Placing both the DC excitation coils and the three-phase AC winding on the stator characterizes this topology of homopolar (figure 1) [2, 3], or homo-heteropolar synchronous machine (figure 2) [4-6]. The attractive advantages of this kind of machine are its better controllability in the very large speed range and the flexibility of the output generator characteristics [8, 9]. Since the air-gap flux linkages created by the two stator windings and the induced rotor currents, the main air gap flux saturation phenomenon is more complicated than that of the normal synchronous machine [10]. Because of this complexity, a reconsideration of the main flux linkage saturation effect is called for in the design of the machine and in the development and practical implementation of speed/torque control algorithms. To

Homo-Heteropolar Synchronous Machine for Low Power Variable Speed Wind orHydro Applications: Design, 3D FEM Validation and Control

TOPOR MARCEL

EPE'14 ECCE Europe ISBN: 978-1-4799-3014-2 and 978-9-0758-1520-7 P.1

avoid deep magnetic saturation in the stator core and teeth and rotor poles, magnetic design methodologies have been suggested both for the brushless homo-heteropolar synchronous machine [9], [10-12]. An approach to include the influence of magnetic saturation and iron loss using finite-element analysis in the performance prediction of the brushless homo-heteropolar synchronous machine was set. The proposed finite-element model provides very good steady-state predictions and can be used for the sizing and design optimization of the machine.

Field coil

Rotor pole

x v Induced coil

Stator core

Fig. 1: Magnetic circuit cross section in homopolar synchronous machine Stator core

(laminations stack)

Excitation coil

Airgap

Rotor pole

Fig. 2: Longitudinal magnetic circuit section in homo-heteropolar synchronous machine

Constructive elements and design The constructive elements of the novel RHHSM, are presented in fig. 3 in a 3D view.

Laminations stack

Excitation coil

Armatures winding

b) Fig. 3: a) 3D representation of stator magnetic circuit with excitation and phase winding coils. b) 3D representation of the rotor The excitation coils has a ring shape and are placed in the windows of the E-shaped laminations stack. The armature AC winding is placed in the open slots, formed between the pockets of lamination stack.


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To design the three dimensional magnetic structure of the RHHSME is necessary to identify the flux distribution of the machine. The geometry of the RHHSMES poses a challenging problem because of the various cross-couplings between the rotor and stator. The flux distribution caused by the AC winding and by the DC excitation is investigated separately. The parameters of the prototype design are given in Table I.

Table I: Parameters and design dimensions of the prototype

Frequency (f) 50 Hz Outer stator diameter (Dso) 462 mm

Number of poles - p 6 poles Inner stator diameter (Dsi ) 270 mm

Air-gap length (hag) 0.5 mm Stator slot width (hss) 11.5 mm

Ideal core length (li) 190 mm Rotor poles high (hrs) 31.5 mm

Stator slot number (Nss) 36 Inner rotor diameter (Dri) 207 mm

Rotor poles number (pr) 6 Rated DC supply voltage (UDC) 250 V

Rated apparent power (Pn) 2.5 KVA Rated line voltage (Un) 400 V

Number of ring excitation coils 2 Number of main winding layers 3

Rated speed (n) 1000 rpm Phase connections Y

Phase rated current (IN) 5.5 A Excitation rated current (IEN) 6 A Experimental model was build (figure 5 the stator and figure 6 the rotor) and parameters were tested (figure 4 show the test bench).

Fig. 4: Experimental test bench Fig. 5: Stator assembly before introducing the

armatures winding

Fig. 6: Prototype rotor assembly without damping cage


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3D FEM validation The finite element method is used in order to obtain key parameters of the RHSMSE. Since the topology of the machine has is a purely 3 dimensional flux paths one the complete transient characteristics and parameters can not be obtained without an extensive computation effort. Finite element analysis of the machine was done a commercial software platform. When applied to electrical machines, the described problem is usually reduced to cover only one pole or one pole pair with the help of boundary and symmetry conditions in order to reduce the computation time. The windings are in star connections and thus the excitation current shares among phases are IA= I, IB=IC = -I/2. From the 3D finite element we will consider only some key values or verification values which can not be obtained from other means. In figure 7 the 3D flux density repartition and flux density in the air-gap for homopolar case and in figure 8 3D flux density and torque variation are presented.

Axial length [mm]

Bn

airg

ap [T

]

Flux density airgap

0 20 40 60 80 100 120 140

-1,5

-1

-0,5

0

0,5

1

1,5

Bn [T]

Bt [T]

a) b) Fig. 7: Finite element results for homopolar case: a) 3D field; b) airgap flux density for Ie=6A at no load.

a) b) Fig. 8 Finite element results for heteropolar case: a) 3D field; b) torque versus angle at different currents. In fig. 9a the no load voltage U = f(IE) of the RHHSM is presented. From the 3D FEM field results the inductance variation curve with position is obtained (figure 9b). The synchronous inductances on phase were calculated by relating the magnetic linkage of the respective phase to the effective current though the phase, to a certain load angle. From 3D simulation results the values Ld = 26.53 (mH) and Lq = 16.54 (mH). From based design equations we obtained Ld = 22.14 (mH) and Lq = 13.74 (mH).


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5 10

Vol

tage

Ue0 (V

)

Excitation current IE (A)

experimental

simulation

450

400

350

300

250

200

150

100

50

0 0

Angle (rad)

Indu

ctiv

ity L

s (m

H)

a) b) Fig. 9: a) No load voltage characteristics; b) inductance characteristic function of rotor angle

Generator control strategy Orthogonal model of RHHBSM In order to evaluate the dynamic performance of the machine in generator mode it is necessary to identify the orthogonal d-q model of the generator. Using a twophase stator model, we have two orthogonal armature windings whose orientations are denoted as axes d and q. A field winding along the rotor axis f has mutual inductance with the armature; this inductance varies with the angle between the d and q axes. Thus in a stationary reference frame we have the twoaxis model. Using the Park transformation for fluxes and currents, the expressions of the fluxes by axes d and q are obtained, d and q where Ls is the own dispersion inductance, L0 the inductances constant component, L2 the inductance dependent on the rotors position, M0 the coupling constant inductance, ME, MD, MQ the coupling maximum inductances between a stator phase and the excitation respectively damping winding D and Q [9], [10]:

DDEEddSd iMiMiLMLiL ++

++=

23

23

200 , (1)

QQqqSq iMiLMLiL +

+=

23

23

200 . (2)

If its neglected the dispersion coupling inductance between the stator and cage D (LdD = 0), are obtained the synchronous inductances, longitudinal Ld and transversal Lq [11]:

200 23 LMLLd = , (3)

200 23 LMLLq += , (4)

20

0LM = . (5)

Angle has the expression, where r is the rotors angular speed and 0 the initial value:

+= 0 dtr . (6) The binding relation between the orthogonal models currents id, iq and i0 and the real machines currents ia, ib and ic is [9]:


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[ ]

=

cba

abcdqqd

iii

Piii

00

, (7)

where:

[ ]( )( )

+

+

=

21

21

21

32

32

32

32

32

0

sinsinsin

coscoscos

Pabcdq , (8)

the same relation being valid also for fluxes,

[ ]

=

cba

abcdqqd

P

00

. (9)

From the previous relations and taking into account the relation:

[ ]

=

00

iii

Piii

qdT

abcdqcba

, (10)

is obtained:

( ) DDEEdSd iMiMiLLL ++

++=

23

23

20 , (11)

( ) QQqSq iMiLLL +

+=

23

23

20 , (12)

[ ] 00000 2 iLiMLL SS ++= . (13)

Considering a single rotor cage by each axis, the voltages UD = UQ = 0 and the brushes speed b = r, there are obtained the general equations of the orthogonal model of the homo-heteropolar synchronous machine, where RS is the stator resistance, RE the excitations resistance, RD and RQ the rotor cages resistances, Me the electromagnetic torque and p the number of pole pairs:

qrd

dSd tURi +

= , (14)

drq

qSq tURi

+

= , (15)

qrE

EEE tURi +

= , (16)


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tRi DDD

=

, (17)

tRi QQQ

=

, (18)

( )dqqde iipM = . (19)

Full scale converter control of the RHHBSM In this analysis we have considered to use the RHHBSM synchronous generator controlled with a diode rectifier and a boost converter, which is similar to the solution initially proposed in [1]. The RHHBSM generator is connected to a diode rectifier, a DC-DC PWM controlled boost converter and a DC/AC PWM inverter which is connected to the main grid. This solution allows extracting maximum energy from the wind for low wind speeds by optimizing the turbine speed, while minimizing mechanical stresses on the turbine during gusts of wind or the variation of the water flow as it is presented in [13].

Inverter DC-DC Boost Converter

g

A

B

C

+

-

A

B

C

+

-

Vf_

Pm

g 1

2

[Iabc_grid_conv]

[Vabc_grid]

[Pm_gen]

[wr]

[Boost_Pulse]

[Tm]

C_DClink ``RHHBSM

A

B

C

A

B

C

Choke

Iabc

B_grid

Rectifier

Omega[Boost_Pulse]

Fig. 10: Simulation model of the RHHSM for controlled generator operation

The objectives of this controller is to control the response of the system when is subjected to variations in active and reactive load. It is desirable to have nearly constant or limited variations in frequency and voltage during steady state. Active power flow is related to a prime movers energy input and, thus, to the speed of the RHHSM in generator mode operation. On the other hand, reactive power control is related to terminal voltage. Large active power load would leads to collapse in speed, while large reactive power loads cause voltage to collapse. The main scope in this proposed solution is to control the reactive power generated or absorbed by the VSC connected to the grid. This reactive power is controlled by the magnitude of the converter AC voltage. The control block diagram of the grid side converter is presented in fig. 10. It consists in two controller loops one is the Vdc regulator and the second is the VAR regulator.

Voltage regulator

Current regulator

Id ref

Iq ref

Reset Value

Out

Discrete-Time(Trapezoidal)

Integrator

[id_ref]

[iq_ref]

[Vq]

[Vd]

[id_ref]

[w_pu]

[iq_ref]

[iq_ref]

[id_ref]

[w_pu]

PI

R_RL

R_RL

L_RL

L_RL

Idq_gc

Iq

Id

Id

vd'

vq'

Vd inverter Vq inverter

var regulator

Vdc regulator

Iq_ref limit

Vdc_nom Vdc_ref (V)

1/z

sqrt u 2 -C-

Imax^2

Max

Min

In

Ki

Hold

Reset

[Vdc]

-K- K Ts z-1 x o

PI

boolean

Ki_volt_reg 0

-K- ->pu

Vmeas Qmeas

Qref

Vdc

Vref

Fig. 11: Grid side inverter control of the RHHSM for generator operation


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For generator excitation operation we consider a controlled rectifier directly supplying the field winding of the synchronous generator (SG) figure 10. Static power electronics exciters are characterized by fast voltage response, but cannot eliminate the effect of the doT time constant on the delay the field current response. A reasonable model of a modern exciter is a linearized model [11,12], which takes into account the major time constant and ignores the saturation or other nonlinearities.

Fig. 12: Potential-source, controlled-rectifier exciter model [11]

Excitation control In order to model the controlled rectifier excitation system, we have used the ST1A IEEE model [11] with the excitation power coming from the generator terminals via a transformer and regulated with a controlled rectifier. Fig. 12 shows a simplified representation of the excitation system. The main goal in synchronous generator excitation control is to prevent electromechanical oscillations in the generator and to secure the generator and the power system stability during the load transients. The main difficulties in the excitation feedback control are the nonlinear character of a RHHBSM generator and the parameter variations due to saturation [12]. The parameters of the excitation simulation model are given in table II.

Table II: Parameters and design dimensions of the prototype

Parameter Value Unit Parameter Value Unit

Ka 210.0 pu Vrmin -6.0 pu

Ta 0.0 sec Kc 0.038 pu

Tb 1.0 sec Kf 0.0 pu

Tc 1.0 sec Tf 0.0 sec

Tc1 0.0 sec Klr 4.54 pu

Tb1 0.0 sec Ilr 4.4 pu

Vrmax 6.46 pu

In our case the control loop of the excitation is based on the use of a flux controller based on a simple PI regulator [10] figure 12. The flux controller is used to determine the voltage fV command which is necessary for the control of the static excitation. The flux is obtained from a flux estimator which used the stator equation as in [11]. For low speeds the flux reference is kept constant in an open loop controller. With the increase of the speed the controller changes in a closed loop control.


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The excitation controller computes the active and reactive power which is imposed to be delivered to the grid based on input values obtained from the turbine model ( *P ) and from the reactive controller (

*Q ). The reactive power *Q can either come from a separate controller called VAR controller. This

controller monitors the generator reactive power, genQ , and the grid voltage, gridV to compute the voltage and current commands. The control of active and reactive power is handled by fast, high bandwidth regulators within the converter controls.

1Vf

avoid divisionby 0

Switch

1

Flux_ref

1

Flux_ref

PI2wr

1Flux

Vf

Flux

Fig. 13: Simulink model of the flux controller

Flux

Resistance

Resistance f(u)

Magnitude of flux

-1

Omega

phi_q

Id

Vd

Rs*Id

Iq

Vq

Rs*Iq

phi_d

Fig. 14: Simulink model of the flux estimator

SIMULATION RESULTS

Fig. 11: RHHSM generator operation Due to technical difficulties we can only provide simulation results for the RHHBSM generator operation. In this paper we have considered a simple scenario in order to observe the steady-state


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operation of the RHHBSM generator and its dynamic response to voltage sag resulting from a remote fault. The voltage drop is occurs at t=0.03 s. Initially the system produces 2 KW of active power. The corresponding turbine speed is equal to the generator synchronous speed. The DC voltage is regulated at 560 V and reactive power is kept at 0 var. At t=0.03 s the voltage suddenly drops to 0.75 rated value causing an increase on the DC bus voltage and a drop on the generator output power. During the voltage sag the control systems try to regulate DC voltage and reactive power at their set points (560V, 0 VAR). The system recovers after fault elimination.

Conclusion The paper presents a design model of the reactive homo-heteropolar synchronous brushless machine (RHHBSM) (2.5 KVA rated apparent power, 82% efficiency, specific mass ratio cooper/iron 0.3, specific power 0.066 KVA/kg, inductances ratio Ld/Lq=1.612), by means of the equivalent magnetic circuit. The main advantage of the RHHSM is its improved capability to operate at variable speed for wind or hydro power plants. The design method was validated also by means of 3D FEM model. General performance characteristics of ampere-turns, inductor flux, resulting flux and inductances variation are presented. Based on designed parameters a d-q equivalent model was presented and evaluated based on which dynamic performance will be simulated as generator. These preliminary results prove the concept quantitatively but further studies, which are already under way, in relation to experimental tests, are needed to fully prove the practicality of the proposed system.

References [1] Balchim M.J. and Eastham J.F.: Characteristics of heteropolar linear synchronous machine with passive secondary, Electric Power Application, vol. 2, no. 8, December 1979, pp. 213-218. [2] Deaconu S.I., Tutelea L., Popa G. N., Popa I. and Abrudean C.: Optimizing the Designing of a Reactive Homopolar Synchronous Machine with Stator Excitation, IECON 2008, 34th Annual Conference of the IEEE Industrial Electronics Society, Orlando, Florida, USA, 10-12 November, 2008, pp. 1311-1318. [3] Deaconu S.I., Topor M., Tutelea L.N., Popa G.N. and AbrudeanC.: Mathematical Model of a Reactive Homopolar Synchronous Machine with Stator Excitation, EPE-PEMC 2009, Barcelona, Spain, 8-10 September, 2009, pp. 2269-2277. [4] Deaconu S.I., Topor M., Tutelea L.N., Popa G.N. and AbrudeanC.: Modeling and Experimental Investigations of a Reactive Homo-Heteropolar Brushless Synchronous Machine, IECON 2009, 35th Annual Conference of the IEEE Industrial Electronics Society, Porto, Portugal, 3-5 November, 2009, pp. 1209-1216. [5] Nobuyuki I., Shigeo M., Sanada M., and Takeda Y.: Influence of magnetic saturation on Sensorless Control for Interior Magnet Synchronous Motors with Concentrated Windings, IEEE Transaction on Industry Applications, vol. 42, no. 5, sept./oct. 2006, pp. 1193-1200. [6] Aliprantis D.C., Sudhoff S.D., and Kuhn B.T.: A synchronous machine model with saturation and arbitrary rotor network representation, IEEE Transaction on Energy Conversion, vol. 2, no.3, September 2005, pp. 584-594. [7]Mademlis C.: Compensation of magnetic saturation in maximum torque to current vector controlled synchronous reluctance motor drives, IEEE Transaction on Energy Conversion, vol. 18, no. 3, september 2003, pp.379-385. [8] Boldea I.: The electrical machines parameters. Identification estimation and validation, Romanian Academy House, Bucharest, Romania, 1991. [9] Cannistra G., Negro G., and Laleini M.: Automatic generation of grids for studying electrical machines by finite element method, Int. Aegean Conf. on Electrical Machines and Power Electronics, vol. 2/2, Husadasi, Turkey, 1992, pp. 80-88. [10] Ostovic V.: Dynamics of saturated electric machines, Springer Verlag, New-York, 1989. [11] Kanniah Jagannathan, Malik O.P., Hope G.S.: Excitation Control of Synchronous Generators Using Adaptive Regulators Part I-Theory and Simulation Results, Power Apparatus and Systems, IEEE Transactions on, Volume: PAS-103, Issue: 5, May 1984, On page(s): 897 - 903 [12] IEEE Guide for Identification, Testing, and Evaluation of the Dynamic Performance of Excitation Control Systems, ANSI/IEEE Std 421A-1978. [13] Nicholas W., Miller William W., Price Juan J. Sanchez-Gasca: Dynamic Modeling of GE 1.5 and 3.6 Wind Turbine-Generators, GE WTG Modeling-v3-0.doc, 10/27/03 General Electric Company, U.S.A.


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0306-epe2014-full-21091806

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