Stand-alone Double-excited Synchronous Generator Operating On A Variable Load

STAND-ALONE DOUBLE-EXCITED SYNCHRONOUS GENERATOR OPERATING ON A VARIABLE LOAD I.A. VIOREL – D. FODOREAN – A. VIOREL – L. SZABÓ Technical University of Cluj, Department of Electrical Machines RO-400020 CLUJ, Daicoviciu 15, Romania Phone: +40-264-401-232 / Fax: +40-264-594-921 e-mail: [email protected] Abstract: The double-excited or hybrid synchronous generator (HSG), has the excitation field produced by permanent magnets and auxiliary excitation winding. It can be employed in small-scale distributed or autonomous power systems. In the paper, the steady-state equation for a HSG with excitation fields on both axes are developed and particularized for different possible variants. A HSG prototype is presented and test results are compared with the calculated one, evincing a quite large output voltage and power factor control. Keywords: hybrid synchronous generator; standalone operating

Different ways of modelling the PMSG, or its companion motor, were developed, based on the circuit-field analysis [8, 9] or on the time-stepping coupled field-circuit method [7, 10]. A general approach to compare different electric machines based on sizing and power density equations was presented in [11]. The hybrid synchronous machine was presented in quite many papers too, such as [12, 13, 14] and a basic construction of such a machine is given in Fig. 1.

1. INTRODUCTION The large synchronous wound-field generators, with controllable field current, are the most representative electric power generators. Due to the field control flexibility these generators may assure an adequate bus voltage and reactive power control. Recently, mostly due to the environmental concerns and to the lowering the cost purpose, the number of smallscale distributed or autonomous power system were increased. For such applications, the permanent-magnet synchronous generator (PMSG) is used more often despite his inherent drawbacks caused by its almost constant and difficult to control rotor field. Distributed or autonomous generation systems cover a very large scale of systems, from small electric mill to automobile and electric vehicle generators. The PMSG might find its place there, but also some other constructions, such as the double-excited or hybrid synchronous generator (DESG or HSG) should be studied since their price to performance ratio can be a competitive one. There are a large number of books and papers which deal with the construction, technology, design and characteristics of permanent magnet synchronous machines [1, 2, 3, 4, 5, 6, 7], therefore the PMSG can be considered as well known and perfectly defined.

Figure 1. HSG basic structure

The HSG has a conventional stator with slots and a distributed or concentrated winding; in Fig. 1 is not given the stator winding. The rotor has surface, like in Fig. 1, or inset permanent magnets and an auxiliary field winding placed in rotor slots. The rotor structure might differ, from the basic one given in Fig. 1, containing for instance inset permanent magnets oriented on the q-axis and an important saliency [6]. In the first case the auxiliary winding excitation current and the permanent magnets produce a field oriented on the d-axis direction, while in the second the fields are in quadrate. In the paper, the steady-state equations are developed for a general machine construction, with excitation fields on both axes. They are particularized for the construction similar to that

given in Fig. 1, the calculated results being compared with the ones obtained by tests. Since, as previously stated, the stand-alone systems cover a large area, the generator should operate at constant or large variable speed, and its load may be of variable or unity power factor. All these variants are discussed through a theoretical development, the tests being conducted quite in the same manner.

Neglecting the stator phase resistance the dand q-axis projections in the phasors’ diagram, Fig. 2, lead to the scalar equations: E0d = Vs cos γ 0 + X d Id E0q = Vs sin γ 0 − X q Iq X d = ωLd X q = ωLq

γ 0 = α 0 + θ0 Id = Is sin(γ 0 + ϕ ) Iq = Is cos(γ 0 + ϕ )

2. MATHEMATICAL MODEL The HSG mathematical model, considering on the rotor excitation fields on both d- and q-axis, is given by the dq0 generator equations: v d + Ri d = ωλq v q + Ri q = −ωλd

(4)

The HSG symmetrical load and an electronically controlled LC block on each phase is considered, Fig. 3.

(1)

λd = Ld i d + λfd λq = Lq i q + λfq By introducing the state phasors results: v s + R i s = − jω λs

λs = λd + jλq =

(2)

= Ld i d + jLq i q + λfd + jλfq

The phasors’ diagram is given in Fig. 2, where the induced emfs are:

E0 d = − jωλ fd

(3)

E0 q = − jω ( jλ fq ) q E0q jXdid E0d

vS≈-jωλS

γ0 jλfq Ldid

Lqjiq λfd

λS

RiS

E0

θ0 φ iS id

The phase synchronous generator current is: Is = IB + IL ⎛ 1 1 ⎞ ⎟ + I s = V s ⎜⎜ ⎟ ⎝ ZB ZL ⎠ Z Is = Vs ZL ZB ⎛R Z R Z Z = ⎜⎜ B L + L B ZL ⎝ ZB

jXq(jiq) α0

Figure 3. HSG load and EC block on one phase

jiq

d

The notations are the usual ones, − vd, vq; id, iq; λd, λq; Ld; Lq; are d and q-axis voltages, currents, flux linkages and synchronous inductances respectively. − ω is rotor speed, equal with the stator emf pulsation for one pole pair machine.

2

⎞ ⎛X Z X Z ⎟⎟ + ⎜⎜ L B + B L ZB ⎠ ⎝ ZL

⎞ ⎟⎟ ⎠

2

where RL, RB, XL, XB, ZL, ZB are load, respectively LC block, resistances, reactances and impedances. After some simple mathematical calculations results:

cos ϕ = Figure 2. Phasors’ diagram, HSG steady-state regime

(5)

Vs (1 − X q / X d ) sin γ 0 cos γ + Z Vs Xq Z L ⋅ ZB E0d X q / X d sin γ 0 − E0q cos γ 0 + Z Vs Xq ZL ⋅ ZB

(6)

The HSG steady state regime implies that the rotor speed n is constant and so are the load and LC block impedances. All of them can be different at different times, but the steady state regime has to be maintained. Let look now to some particularly cases. 1. Consider that, due to an intermediary electronic converter placed between HSG and the load [3, 6] the power factor is equal to unity. Then the stator output voltage comes as: Vs =

2.

E0d X q X d sin γ 0 − E0q cos γ 0 Z X q − (1 − X q X d ) sin γ 0 cos γ 0 ZL ZB

(7)

Consider that the HSG has a reduced saliency, which consequently means:

Xd ≅ Xq = Xs Vs =

E0d sin γ 0 − E0q cos γ 0 Z Xs ZL ZB

E0d sin γ 0 Z Xs ZL ZB

Figure 4. HSG prototype

The HSG, Fig. 4, has surface NdFeB permanent magnets on the rotor d-axis and an auxiliary excitation winding placed in special slots; the cross section of the machine is given in Fig. 5.

(8)

In all the cases, the q-axis field should have an opposite direction to the q-axis stator current in order to obtain a power factor, or output voltage increase, as for BEGA generator [6]. It is also clear that the d-axis excitation field acts in the same manner as the q-axis excitation field does. In the case of the built HSG prototype, Figs. 1 and 4, the q-axis excitation field does not exist and due to the fact that the rotor has surface permanent magnets the d- and q-axis synchronous inductances differ slightly. Consequently the product between output HSG phase voltage and power factor comes as: Vs cos ϕ =

3. HYBRID SYNCHRONOUS GENERATOR

Figure 5. HSG prototype cross section

The stator core sheets were taken from an induction motor while the rotor was adapted to the requirements, Fig. 6.

(9)

If there is no electronically controlled LC block, which means no voltage and power factor control through this block, than the voltage can be controlled only via d-axis variable field, the usual simplified formulae: Vs cos ϕ =

E0d sin γ 0 ZL Xs

(10)

The product between output voltage and power factor can be controlled by induced emf which varies due to auxiliary excitation winding mmf, (10).

Figure 6. HSG prototype rotor

The stator winding is a single layer three phase one with 3 slots per pole and per phase, placed in 36 slots.

The machine was designed analytically and checked by using a two dimensions finite element method (2D-FEM) calculation. The HSG prototype is far of the best one since the stator iron core was imposed and only the winding and stack length could be changed, The main geometrical data of the HSG are: outer stator diameter Des = 0.2 m; inner stator air-gap length diameter Dis = 0.124 m; g = 0.001 m; permanent magnet thickness hm = 0.0035 m; motor’s stack length l = 0.1 m; rotor slot height / width hrs / wrs = 0.017 / 0.022 m Since the d-axis field should be controlled via the auxiliary excitation current the auxiliary excitation winding was designed very carefully. By using a 2D-FEM calculation the air-gap flux density was computed to evince the excitation winding mmf influence. In Fig. 6 the air-gap flux density variation corresponding to four values of the excitation current, 0, 12.7, 19.2 and 24 A is presented showing the important flux weakening.

Figure 7. No load air-gap flux density at different excitation currents, 2D-FEM calculation

A comparison between phase emf values, 2D-FEM calculated, respectively test obtained, at no load is given in Fig. 8.

Figure 8. 2D-FEM and tests values, induced stator phase emf

To emphasize the existing differences in Fig. 8 the error between the two sets of data was computed and plotted, Fig. 9.

Figure 9. Errors between 2D-FEM and tests values, induced stator phase emf

As it can be seen from Fig. 9 the differences are quite unimportant in the flux weakening domain (in special for the excitation currents situated in the interval of -15 A ÷ -5 A), but they increase due to the iron core saturation. Anyway, at constant speed, n = 1500 rpm, the variation of the induced emf can be considered linear for excitation current variation between -15 A and +15 A, the sign signification being related with the flux direction, which is opposite to the permanent magnet one for the current negative values. The HSG parameters, obtained by tests or by 2D-FEM calculation are: − Stator phase resistance R = 1.7745 Ω, − Stator phase leakage inductance Lσ = 0.004975 H, − d-axis synchronous inductance Ld = 0.02028 H, − q-axis synchronous inductance Lq = 0.01586 H. The rated output power is 5.16 kW at rated phase voltage Vs = 200 V and rated phase current Is = 8.6 A for unity power factor.

4. RESULTS The behaviour of a stand-alone synchronous generator (SG) operating on a load together with a static VAR compensator was discussed in [5] where only the inductance could be varied through a thyristor ignition angle. In the present paper an electronically controlled LC block, quite similar to a VAR compensator, was considered within the model only for the sake of generality, since the HSG has, as proved before, quite large voltage control due to the auxiliary excitation mmf. Therefore the tests are conducted on HSG with various loads and the results are compared with the calculated values. The induced emf

variation function of auxiliary excitation winding current is considered linear accordingly to the tests and 2D-FEM calculations. For the given HSG the characteristics can be calculated based on the equations: tgγ 0 =

The test set-up was built up in the Electrical Machines Laboratory of the Technical University of Cluj (Romania), Fig. 11.

X q cos ϕ ZL + X q sin ϕ

E0d cos γ 0 Vs = 1 + X d (tgγ 0 cos ϕ + sin ϕ ) ZL

(11)

Once given the load the power factor is known and the load angle γ0 can be calculated. It will result a relation between the output voltage and the induced emf, respectively auxiliary excitation winding current. A general equation where the phase terminal voltage is given in function of load current IS and power factor, induced phase emf and HSG parameters comes after some mathematical developments as:

(VS + I S X q sin ϕ )2 + (I S X q cos ϕ )2 E 0 = VS 2 + VS I S ( X d + X q ) sin ϕ + X d X q I S 2

(12)

For a particular case when the load is the rated one with unity power factor and excitation current varies from -15 A to +15 A results: Vs = 0.966E0d = 0.966(3.88Iex + 197.2) (13)

The computed values and the estimation given in equation (13) are shown in Fig. 10.

Figure 11. The laboratory set-up

The HSG prototype terminal voltages were measured at different excitation currents and variable loads. In all the cases the HSG speed was maintained at its rated value (1500 rpm). Hence the terminal characteristics were plotted for excitation currents varying from -15 A to +15 A, the designed excitation current range. The calculated terminal characteristics were plotted, too. In order to make a correct comparison between the characteristics obtained via the two ways the terminal voltage of the generator was computed exactly for the measured current values. From the numerous terminal characteristics plotted based upon the computed, respectively measured results, here only two sets will be presented: those obtained at unitary power factor and Iex = 0 A, respectively Iex = 2.5 A (Fig. 12).

Figure 10. The estimation against to computed values

For any type of generator the terminal characteristics (the plots of the terminal voltages versus the line currents) are of maximum importance. These characteristics were plotted based both of measured and computed data.

Figure 12. The terminal characteristics plotted upon measured and computed data

As it can be seen at low line currents the two plots are closed and at higher currents the

difference begins to be quite important. Neglecting of the stator phase resistances in the HSG analytical equations is a reason for this increasing difference, another one being the iron core saturation. The terminal voltage can be maintained constant for a quite large load domain by varying the auxiliary excitation current, and consequently the induced emf. As example one can see the plot given in Fig. 12 where the terminal voltage of 190 V is kept constant for an important load variation at unity power factor on the test bench.

permanent magnet excitation as can be seen from the good agreement between the computed and test obtained values.

6. ACKNOWLEDGMENTS The work was possible due to the support given by the Romanian National Council of Scientific Research in Higher Education through a grant offered.

7. REFERENCES [1] [2] [3]

[4]

[5]

Figure 13. HSG prototype excitation current vs. load current, phase voltage 190V, unity power factor

This is an important advantage of HSG over the conventional PMSG and it makes HSG a competitor in the low power stand-alone generators’ market.

5. CONCLUSIONS The most important conclusions are: − The d- and q-axis excitation acts in the same manner concerning the output voltage and power factor control of a HSG. Consequently the permanent magnets and the auxiliary excitation can be placed together on the d-axis in a more compact and simpler rotor structure. − The auxiliary winding excitation mmf can assure, within an adequate design, a quite good control of the output voltage for a large load variation. To extend this control domain an EC LC block can be employed too. − The developed steady-state model is adequate considering the fact that the saturation is reduced due to the

[6]

[7]

[8] [9] [10]

[11]

[12]

[13] [14]

J.F. Gieras and M. Wing "Permanent magnet motor technology, design and applications," New York Marcel Dekker, 1997. D.C. Hanselmann, "Brushless permanent magnet motor design," New York McGraw-Hill, 1994. M. Comanescu, A. Keyhani, M. Dai, "Design and analysis of 42-V permanent-magnet generator for automotive applications," IEEE Trans EC, vol. 18, no. 1, pp. 107-112, 2003. T.F. Chan, L.L. Lai, L-T Yan "Performance of a threephase ac generator with inset NdFeB permanentmagnet rotor" IEEE Trans. EC, vol. 19, no. 1, pp.88-94, 2004. M.A. Rahman, A.M. Osheiba, T.S. Radwan, E.S. Abdin "Modelling and controller design of an isolated diesel engine permanent magnet synchronous generator," IEEE Trans. EC, vol. 11, no. 2, pp.324-330, 1996. S. Scridon, I. Boldea, L. Tutelea, F. Blaabjerg, A.E. Ritchie "BEGA – a biaxial excitation generator for automobiles: comprehensive characterization and test results," IEEE Trans. IA, vol. 41, no. 4, pp. 935-944, 2005. T-F Chan, L.L. Lai, L-T Yan "Analysis of a stand-alone permanent magnet synchronous generator using a timestepping coupled field-circuit method," IEE Proc. – Electr. Power Appl., vol. 152, no. 6, pp. 1459-1467, 2005. G. Henneberger and I.-A. Viorel, "Variable reluctance electrical machines," Aachen, Germany, Shaker Verlag, 2001. P. Zhou, M.A. Rahman, M.A. Jabar "Field circuit analysis of permanent magnet synchronous motors," IEEE Trans. Magn., vol. 30, no. 4, pp.1350-1359, 1994. S.I. Nabeta, A. Foggia, J-L, Coulomb "A time-stepped finite-element simulation of a symmetrical short-circuit in a synchronous machine" IEEE Trans. Magn., Vol. 30, no. 5, pp.3683-3686, 1994. S. Huang, J. Luo, F. Leonardi, T. Lipo "A general approach to sizing and power density equations for comparison of electrical machines" IEEE Trans. EC, vol. 34, no. 1, pp. 92-97, 1998. G. Henneberger, J. R. Hadji-Minaglou, R.C. Ciorba "Design and test of permanent magnet synchronous motor with auxiliary excitation winding for electric vehicle application" Proc. of EPE Chapter Symposium, pp. 645649, Lausanne, 1994. X. Luo, T.A. Lipo "A synchronous permanent magnet hybrid ac machine" Proc. of IEEE IEMDC, Seattle, pp. 19-21, 1999. D. Fodorean, A. Djerdir, A. Miraoui, I.-A. Viorel "Flux weakening performances for a double-excited machine" Proc. of ICEM '04, Krakow, Poland, paper no. 434 on CD-ROM.