Direct Active and Reactive Power Control of Variable-Speed Doubly

Direct Active and Reactive Power Control of Variable-Speed Doubly-Fed Induction Generator on Micro-Hydro Energy Conversion System Stefan BREBAN1,2, Mircea M. RADULESCU1, Benoît ROBYNS2

Abstract – This paper proposes a direct power control technique applied to a variable-speed doubly-fed induction generator (DFIG) of a micro-hydro energy conversion system. This assembly consists of a permanent-magnet synchronous machine (PMSM) linked mechanically and electrically (through back-toback power electronic converters) to the DFIG (on the rotor side). The PMSM has the role to recover or supply the slip power of the DFIG. The main advantages related to this system are that the energy conversion system is completely autonomous (can supply isolated load or can be connected to power grid) and also, the PMSM and the power converters are designed for only about 25 % of the hydro-plant rated power. Index Terms – Direct power control; variable-speed doubly-fed induction generator; micro-hydro plant; distributed generation with renewable energy sources

I. INTRODUCTION The decision taken by the European Union to increase the production of electrical energy from renewable sources by 2020 presumes to increase the production of energy from renewable sources (wind, hydro, photovoltaic, bio-fuels) and reduce the usage of fossil carbon based fuels like coal, oil or natural gas. Hydroelectricity is the most expanded renewable energy source over the world. It represents almost 94% of the renewable energy production and 20 % of worldwide power needs. In fact, this is due to high power hydroelectric stations, which have been built for approximately one century, each of them producing several hundreds of megawatts. Nowadays, it is no more possible to set up such a plant in most European and North-American countries because of suitable site rareness and environmental concerns. Nonetheless substantial capacities remain in Africa, Asia and South America. Micro-hydropower has a quite large potential of development because of the increasing interest in renewable energies and dispersed electrical generation. ___________________________ This work was supported in part by the Romanian Ministry of Education and Research (Grant CNCSIS No. 421/2007) and HEI de Lille. (1) Special Electric Machines and Light Electric Traction (SEMLET) Group Technical University of Cluj-Napoca, P.O. Box 345, RO-400110 ClujNapoca 1, Romania; Email : [email protected] (2) Laboratoire d’Electrotechnique et d’Electronique de Puissance de Lille (L2EP),Ecole des Hautes Etudes d’Ingénieur (HEI) 13, rue de Toul, F-59046 Lille Cedex, France; Email : [email protected]

This type of hydroelectricity ranges from 0 to 10 MW in Europe where, without accounting for newly integrated countries, the micro-hydro capacity is over 11500 MW, representing 1.7 % in electricity production capacity and 10% of hydroelectric power. The European growth potential reaches about 6000 MW [1]. Micro-hydropower stations are nowadays based on a fixed-speed synchronous machine or a squirrel-cage induction generator. In both configurations, no use is made of power electronic devices. In the first case, speed is necessarily fixed; in the second one, speed may vary in a small range according to active power demand changes, if the station is gridconnected, or the additional capacitor and load equivalent impedance variations, if the asynchronous machine supplies a passive network, i.e. the station is islanded. For both generators, the turbine rate of flow regulation allows supplying the necessary active power, and to controlling the frequency when the station is connected to isolated loads. II. SYSTEM UNDER STUDY The scheme of the proposed micro-hydropower station is represented in Fig.1. Like most of such plants, the studied one is considered as run-of-river leading to the use of a Kaplan hydraulic turbine well suited for low water heads. The turbine is associated with a gear box because of its small rotating speed. It drives a doubly-fed induction generator (DFIG), whose excitation is supplied on its rotor by a permanent magnet synchronous machine (PMSM) mounted on the same shaft. Two back-to-back PWM power electronic converters, connected by means of a DC bus, achieve the electric link between the machines. Converter 1 controls the DC-link voltage leading to the balance between the DFIG rotor active power and the PMSM one. Converter 2 is dedicated to the control of the DFIG in order to operate this generator on isolated loads and/or on power grid ([2], [3]). It is worthy to notice that the presented structure is also considered in the field of aeronautics for aircraft embedded network supply [4], the hydro-power turbine being then replaced by a jet engine. It may be emphasized that the considered configuration is different from the most common doubly-fed induction machine, whose rotor windings are connected, even with the help of power electronic converters, to stator ones.

Fig.1. Micro-hydro power system under study

As mentioned above, a Kaplan turbine is considered in this paper. It is referred to a fixed head and a constant water flow. It is assumed that water flow variations are very slow compared to the drive dynamics. The turbine model is a simplified one, i.e. it includes neither blade pitch control nor upstream guide vane one. According to these assumptions, hydro-power turbine behaviour may be taken into account by means of the static mechanical characteristics represented in Fig.2, for a fixed rate of flow. Turbine torque (Tt) vs. speed (Ω) characteristic is assumed to be a straight line. Torque becomes null for a rotating speed value Ωe, which is the runaway speed, i.e. speed when noload torque is applied on the shaft. Ωe is a turbine parameter, and a value of 1.8 times the turbine rated speed Ωn is assumed [5]. Torque vs. speed characteristic equation, under rated water flow and head, may be expressed as

⎛ Ω Tt = Tn ⎜⎜1.8 − Ωn ⎝

⎞ ⎟⎟ , ⎠

(1)

where subscript "n" is used for rated values. Mechanical power (Pmec) simplified characteristic is, consequently, a parabola. Taking into account the water wheel efficiency depending on the rate of flow and on the rotating speed, this power results from the hydro power (Phyd) which is given by Torque

Mechanical power

Phyd = ρgHq ,

where ρ is the water density, g, the gravity acceleration, H, the water head and q, the water rate of flow. III. DIRECT POWER CONTROL (DPC) FOR DFIG The principle of the DPC is developed after the Direct Torque Control (DTC) strategy introduced by Takahashi [6] and Depenbrok [7]. In the case of DTC, the flux and the torque are regulated with the help of the hysteresis controllers. This control technique is more robust and more simple than the Field-Oriented Control (FOC) strategy due to small dependency on machine’s variables. Only stator resistance is needed, in the case of DTC, in order to compute the amplitude and position of the stator-flux space-vector. DTC strategy for induction machines is based on the appropriate stator-voltage vector selection in order to reduce the errors between the reference and estimated values of the torque and stator flux. In our case, the active and reactive powers are the control variables, which are estimated by means of PWM Converter 2 connected to the rotor-side of the DFIG. DPC for DFIG is based on the appropriate rotor voltage vector selection. The reference frame is rotating synchronously with the DFIG rotor [8]. The DFIG active and reactive powers are controlled by means of two independent hysteresis controllers, and the feedback signals (Pmes and Qmes) are computed from DFIG stator voltages and currents: Pmes = v sα ⋅ i sα + v sβ ⋅ i sβ (3)

Qmes = v sβ ⋅ i sα − v sα ⋅ i sβ 0

Ωn

Ωe

Rotating speed

Fig.2. Hydro power turbine torque and mechanical power vs.rotating speed, for given water flow.

(2)

(4)

where vsα, vsβ are the stator voltages and isα, isβ, the stator currents in α – β stationary reference frame. In order to select the optimum rotor voltage spacevectors, the stator-flux position related to one of the six sectors (sextants) in Fig. 3 must be known.

Ψs

Fig. 4. Hysteresis controllers

TABLE II SELECTION OF THE ROTOR VOLTAGE VECTORS Fig. 3. DFIG stator-flux variations in Sector 1.

Sector

TABLE I DETERMINATION OF THE STATOR FLUX VECTORS

Sector

Ψ sαr

1

>0

2

>0

3

ψs 2 − 3 r 3 r ψ s < ψ sβ r < ψs 2 2 − 3 r ψ sβ r < ψs 2 − 3 r ψ sβ r < ψs 2

The stator-flux components Ψ sα , Ψ sβ and its amplitude are computed according to the following relations:

ψ sα = ∫ (v sα − rs i sα )dt

(5)

ψ sβ = ∫ (v sβ − rs i sβ )dt

(6)

ψ s = ψ sα 2 + ψ sβ 2

(7)

where rs is the stator resistance. Because the control of DFIG is made on the rotor side, the voltage vectors applied are rotating with the slip speed related to the stator ones, thus, stator flux must be expressed in the rotor α r – βr reference frame (8).

⎡ψ sα r ⎤ ⎡sin θ r − cos θ r ⎤ ⎡ψ sα s ⎤ ⎢ r⎥=⎢ ⎥⋅⎢ s⎥ ⎢⎣ψ sβ ⎥⎦ ⎣cos θ r sin θ r ⎦ ⎢⎣ψ sβ ⎥⎦

SQ

(8)

In Table I, the proposed solution to determine the stator flux space-vectors related to each of the six sectors is presented. As mentioned before, the active and reactive powers are controlled be means of hysteresis regulators both comprising two-level comparators (Fig. 4).

-1

1

2

3

4

5

6

+1

Vr5

Vr6

Vr1

Vr2

Vr3

Vr4

-1

Vr3

Vr4

Vr5

Vr6

Vr1

Vr2

+1

Vr6

Vr1

Vr2

Vr3

Vr4

Vr5

-1

Vr2

Vr3

Vr4

Vr5

Vr6

Vr1

SP

The analog hysteresis controllers have a well-known disadvantage: variable switching frequency. Nevertheless, this disadvantage can be eliminated by using discrete hysteresis controllers. In contrast with the analog controllers, when using a discrete controller the ripples are not kept exactly within the hysteresis band, but the discrete system operates at fixed sampling time Ts and involves a constant switching frequency. The power converter can deliver eight voltage vectors, six active (V1, V2, V3, V4 V5, V6) and two null (V0, V7). In the proposed control strategy, only the active vectors were chosen for sake of simplicity. Using zero vectors complicates the control procedure because of different behaviours of DFIG operating in hyper-synchronism or under-synchronism. Table II shows the rotor voltage selection according to the state of the hysteresis controllers (1 or -1). Knowing the applied voltage vector and DC-link voltage, one can calculate the rotor tri-phase voltages as follows:

V dc (2 S a − S b − S c ) 3 V v b = dc ( − S a + 2 S b − S c ) 3 V dc vc = (− S a − S b + 2 S c ) 3 va =

(9) (10) (11)

where Sa, Sb and Sc are the commutation states of the power converter and Vdc the DC-link voltage. In Fig. 5, the detailed control scheme proposed for the DFIG is presented. As already shown in Table I, the rotor voltages applied by Converter 2 are selected considering stator-flux vector position. It is to be noticed, that Manel et. al [9] differently propose the identification of rotor flux sector position instead, for the selection of rotor voltages, hence the necessity to measure the rotor currents.

PMSM

Ia Parameters Estimation

Ua,b,c

VDCref

PI

–

Ib Ic VDC

Control and Command

PWM Converter 1

Switching table

PWM Converter 2

VDC Hysteresis controllers

Qref –

Pref –

Sector Determination

Ur(αβ) Ur(abc)

Active Power and Reactive Power Estimator

Ir(αβ) Ir(abc)

Sa,b,c VDC Ira Irb Irc

Power grid DFIG

Fig.5. DPC scheme for DFIG.

IV. SIMULATION RESULTS The micro-hydropower plant is connected to power grid, whose line-to-line reference voltage is 225 V rms. The DClink nominal value is 100 V. The water rate of flow is considered constant for this time interval, because its variability has a time-scale of hours or days. The simulations are performed over an interval of 15 s, as follows: -

-

at t = 0 s the small hydro-power plant is connected to power grid with the references Pref = 0 W and Qref = 0 VAR; at t = 0.1 s the reference for the active power Pref = -1000 W and Qref = 0 VAR; at t = 3 s, Pref = -1500 W and Qref = -500 VAR; at t = 6 s, Pref = -1000 W and Qref = -1000 VAR; at t = 9 s, Pref = -1000 W and Qref = 0 VAR; at t = 12 s, Pref = -2000 W and Qref = 0 VAR.

Reactive Power

Active Power

Fig. 6. Simulated DFIG active and reactive powers.

The parameters of the machines are given in Appendix, and characterize the machines used for experimental validation on the test bench.

Fig. 7. Simulated DFIG stator currents.

a PMSM and a 3 kW (4 poles) DFIG, mechanically coupled to the DC machine and the PMSM (Fig.11). Two converters make the link between the DFIG rotor and the PMSM. Power converters components switches are controlled by dSPACETM cards. As DFIG stator coils are star-connected with neutral point isolated, measuring two stator currents is enough. Rotor currents are no longer measured because rotor fluxes are not needed. Stator instantaneous voltage value is also measured to calculate the active and reactive powers transmitted by the generator to power grid [10].

Fig. 8. Simulated DFIG rotor currents.

Power Converters

PMSM

DFIG DC Machine

Fig. 9. Simulated DC-link voltage. Fig. 11. Photograph of the test bench.

Reactive Power

Fig. 10. Simulated mechanical speed of the micro-hydropower system.

The results are presented in Fig. 6 to Fig. 10. In this simulation a 50 μs sampling period was considered. Also, the DC-link voltage reference was set to 100 V. The ripples of the generated power (Fig. 6) are directly dependent on these two parameters. A minimum DC-link voltage and a maximum switching frequency will greatly reduce the generated power ripples. In Figs. 7 and 8, DFIG stator currents and rotor currents are presented on a time-interval of 40ms and 500ms, respectively. Fig. 9 shows that the DC-link voltage is well regulated. The mechanical speed of the microhydropower plant (Fig. 10) proves that the DFIG is working properly in hyper-synchronism (over 1500 rot/min) and in hypo-synchronism (under 1500 rot/min) as well.

Active Power

Fig. 12. Experimental DFIG active and reactive powers.

V. EXPERIMENTAL RESULTS The micro-hydropower system consists of a hydraulic turbine emulator, based on a torque-controlled DC machine,

Fig. 13. Experimental mechanical speed of the micro-hydropower system.

Fig. 14. Experimental DC-link voltage.

The experimental results presented in Figs. 12 to 14 validate the proposed control scheme. The active and reactive powers are regulated around the reference ones. The power ripples are suggesting the necessity to decrease sampling time or to use a Space Vector Modulation technique (Fig. 12). The mechanical speed (Fig. 13) has a wide spectrum variation in hyper-synchronism and in hypo-synchronism. This allows the micro-hydro power station to function on any point of the turbine mechanical characteristic. Unfortunately, the PMSM used on the test bench has the same power as the DFIG (normally should be 25% of DFIG power), and the magnetisation field generated by the permanent magnet is far too big, at normal operation speed, to maintain the DC-link voltage to 100V or less. Thus, a separate unregulated bidirectional power source was used instead of the PMSM. DC-link voltage variations are shown in Fig. 14. VI. CONCLUSIONS A direct active and reactive power control method, submitted to a DFIG from a variable speed micro-hydro power system, was presented. The method consists on selecting appropriate voltage vectors based on the stator flux position and active and reactive power errors. The validation is made with the help of simulations (Figs. 6-10) and experimental tests (Figs. 12-14). Future work will stress on generalisation of direct controls for the entire power system and optimisation of this control techniques. REFERENCES [1] [2] [3]

[4]

[5] [6]

Renewable energy barometer Eurobserv'ER ; www.energiesrenouvelables.org A. Ansel, B. Robyns, “Modelling and simulation of an autonomous variable speed micro hydropower station,” Mathematics and Computers in Simulation, vol. 71, n°. 4-6, pp. 320-332, june 2006. S. Breban, M. Nasser, A. Ansel, C. Saudemont, B. Robyns, M. Radulescu, “Variable Speed Small Hydro Power Plant Connected to AC Grid or Isolated Loads”, EPE Journal, Vol. 17, No. 4, Octomber – November – December 2007, pp. 29 – 36. F. Khatounian et al “Control of a Doubly-Fed Induction Generator for Aircraft Application”, Industrial Electronics Society, 2003. IECON '03. The 29th Annual Conference of the IEEE, 2-6 Nov. 2003, Volume 3, Page(s):2711 – 2716. “Petites centrales hydrauliques – Turbines hydrauliques,” Report of PACER Program, Switzerland. Takahashi, I.; Noguchi, T., “A new quick response and high efficiency control strategy of an induction motor”, IEEE – Transactions on

Industry Application, Vol. 22, No. 5, September - October 1986, pp. 820-827. [7] Depenbrock, M.; 1985, “Direct self control of inverter fed induction machines”, IEEE Transactions on Power Electronics, Vol. 3, No. 5, October 1989, pp.420-429. [8] L. Xu, Ph. Cartwright, “Direct Active and Reactive Power Control of DFIG for Wind Energy Generation”, IEEE Transactions on Energy Conversion, Vol. 21, No. 3, September 2006, pp. 750-758. [9] J.-B. Manel, A. Jihen, S.-B. Ilhem, “A novel approach of Direct Active and Reactive Power Control Allowing the connection of the DFIG to the Grid”, EPE 2009, 13th International European Power Electronics Conference and Exhibition, Sept. 2009, Barcelona, Spain, CD-ROM. [10] S. Breban, M. Nasser, V. Courtecuisse, A. Vergnol , B. Robyns, Mircea M. Radulescu, „Study of a grid-connected hybrid wind/microhydro power system”, OPTIM 2008, 22-24 mai Braşov, România.

APPENDIX a) DFIG Parameters Rated power: 3kW (220/380 V, 50 Hz); Number of poles: 2p=4; Stator resistance: RS = 1.6 Ω; Rotor resistance: RR = 0.4 Ω; Magnetizing inductance: M = 55 mH; Stator inductance: LS = 150 mH; Rotor inductance: LR = 23 mH; Inertia: J= 0.01 kgm2. b) PMSM Parameters Rated power: 2.87kW (3000 rpm); Number of poles: 2p=6; Stator resistance: RS = 0.94 Ω; Direct-axis inductance: Ld = 14.4 mH; Quadrature-axis inductance: Lq = 25 mH; Back-emf coefficient: Ke= 0.78Vsrad-1; Inertia: J= 0.0014 kgm2

BIOGRAPHIES Stefan Breban received the M.S. degree from the Technical University of Cluj-Napoca, Cluj-Napoca, Romania, in 2005, and the Ph.D. degree jointly from the Technical University of Cluj-Napoca and the Ecole Nationale Supérieure d’Arts et Métiers (ENSAM) de Lille, Lille, France, in 2008, both in electrical engineering. He is currently with the Department of Electric Machines, Technical University of Cluj-Napoca, as an Assistant Lecturer, and also with the Special Electric Machines and Light Electric Traction (SEMLET) Group, Technical University of Cluj-Napoca, as a Researcher. Mircea M. Radulescu received the Dipl.-Ing. degree with honors from the Technical University of Cluj-Napoca, Cluj-Napoca, Romania, in 1978 and the Ph.D. degree from the Polytechnic University of Timisoara, Timisoara, Romania, in 1993, both in electrical engineering. Since 1983, he has been with the Faculty of Electrical Engineering, Technical University of ClujNapoca, where he is currently a Full Professor in the Department of Electric Machines and the Head of the Special Electric Machines and Light Electric Traction (SEMLET) Group. He is author or co-author of more than hundred published scientific papers in refereed technical journals and international conference and symposium proceedings. Benoit Robyns received the Ingénieur Civil Electricien and Docteur en Sciences Appliquées degrees from the Université Catholique de Louvain, Louvain-la-Neuve, Belgium, in 1987 and 1993, respectively. He received the Habilitation à Diriger des Recherches degree from the Université des Sciences et Technologies de Lille, Lille, France, in 2000. He is the author or co-author of more than 120 papers and one book in the fields of digital control of electric machines, renewable energies and distributed generation. Prof. Robyns is a member of the Société Française des Electriciens et des Electroniciens (SEE), of the Société Royale Belge des Electriciens (SRBE), and of the European Power Electronics Association (EPE).