Modeling and analysis of parallel connected permanent magnet synchronous generators in a small hydropower plant

Transcription

1 Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) Moeling an analysis of parallel connecte permanent magnet synchronous generators in a small hyropower plant N. GAUTAM *, A. RENTSCHLER **, T. SCHNEIER **, A. BINER ** * AHEC, Inian Institute of Technology Roorkee, Inia ** armstat University of Technology, Germany Abstract- The simulation of parallel operation of gri connecte permanent magnet synchronous hyro generators with amper using MATLAB/Simulink is presente. The mathematical moel of the synchronous generator in terms of two axes - variables is use. The hyro turbines connecte to each PM generator in a so-calle matrix arrangement give input shaft torue to the rotor of each PM generator. Matrix like arrangement of these small turbine generator units allows generation of electric power from waste water in river barrages, but nees parallel operation of the machines. The influence of changing operating conitions like suen loa change, blocking of rotor of a generator an three phase short circuit are investigate for parallel operation of 4 machines. Investigations are one for 300 kva, three phase, 24 poles, 1.9 kv permanent magnet synchronous generators. All stationary results obtaine are verifie by analytical calculations. Keywors- ynamic Simulation, PMSM, amper cage, HyroMatrix, Parallel-Operation, Gri-Connecte 1 INTROUCTION In existing hyropower plants, the energy of water at the overflow of the am is waste. A new concept for hyropower plants is propose by the VA Tech Hyro, Austria [1], [2]. Small water turbines (e.g. 300 kw) integrate with generators are arrange in matrix structure calle HyroMatrix. For example 2 8, 3 3 or 4 4 turbines (meaning 2 rows of 8 units one above the other (Fig.1)) are integrate in the am to transform the water energy into electric energy. So far the generators use for these matrix turbines are inuction machines (Fig. 1). To get a higher efficiency, the inuction machines shoul be substitute in the future by permanent magnet synchronous machines. This paper eals with the uestion of the mutual influence of the generators that are use in parallel in the matrix structure. A ynamic simulation moel of the permanent magnet synchronous machine with amper is evelope in MATLAB/Simulink. The influence of loa changes, isconnection of machines from the gri, ifferent fault conitions like 3-phase short circuit an blocking of the rotor is investigate for the parallel generator operation. Simulink supports the simulation of continuous, isperse or mixe linear an non linear ifferential euations systems graphically an is use to investigate continuous an asymmetric working conitions in parallel connection. Fig. 1. Jebel Aulia power plant, Suan (Source: VA Tech, Austria) 2 PMSM with rotor amper Permanent magnet synchronous machine (PMSM) is a class of synchronous machine which uses high uality magnet material in the rotor to prouce the excitation fiel. It has the characteristics of high efficiency, simple structure an easy to control. The investigate machines have been built as prototypes in small power plant Agonitz, Austria. They consist of a slotte stator with the three phase istribute AC wining an the rotor containing not only the permanent magnets, but also a copper amper cyliner [2] for amping the

2 Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) oscillations of the rotor. Small PM synchronous machines operating with stiff gri (fixe voltage an freuency) may start asynchronously via the rotor cage an are pulle into the synchronism by the rotor permanent magnets. The PM generators in matrix are starte via the turbine, so the amper cyliner can be reuce in size. Loa steps at such PM synchronous machines will cause them to oscillate, but the oscillations will be ampe by rotor amper. A 24 pole, 3 phase, cylinrical rotor permanent magnet synchronous machine with amper cyliner (Fig. 2) is constructe as straight flow turbine arrangement. The rotor is fixe to the turbine blaes, being operate in water. The stator is seale an arrange aroun the turbine rotor. Stator core Stator wining Permanent magnet 3) The influence of stator slotting on air gap fiel is neglecte 4) Magnetic saturation an hysteresis of iron is neglecte. The following set of euations represents the mathematical moel for the PM synchronous machine with amper in rotor reference frame: A) Voltage euations ψ U = Rs Ω L ψ t (1) ψ U = Rs Ω L ψ t (2) 0 = ψ R t (3) 0 = ψ R t (4) B) Flux linkage euations ψ = L M Ψ (5) ψ = L M (6) PM ψ = L M ψ (7) PM Turbine blae Fig. 2 PM Generator by VA-Tech Hyro, Austria 3 Mathematical moel of PMSM with amper The two axis (-) moel is evelope for the PM synchronous machine with rotor amper by moifying the mathematical moel for the permanent magnet synchronous machine an the synchronous machine with amper cage given in [3]. The coorinate frame is the two-axes or - coorinate frame which orientates the euations to the rotor reference frame. The transformation from the stator to the rotor reference frame is the PARK-transformation. The following assumptions are mae for the moelling: ψ = L M (8) C) Torue euation 3 M e = p ( ψ ψ 2 ) Mechanical angular spee euation Ω L = p Ω m (10) E) PARK s transformation euation The PARK s transformation euations [4] are use to transform the uantities like voltages, currents etc. from 3-phase system (U, V, W) into the system in rotor reference frame (,, 0). The following transformation matrix (T) eu. is use: ) (9) 1) The stator m.m.f. is sinusoially istribute along the air gap, 2) The cylinrical rotor permanent magnets burie below the amper cyliner are consiere to generate constant flux linkage with stator wining,

3 Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) 2 2 2π cosγ cos γ U 2 2 2π U = sinγ sin γ U o π cos γ 3 3 U 2 4π (11) sin γ U V 3 3 U 1 W 3 Transformation form (,, 0) to (U, V, W): sin γ cos γ 0 U U U 2π 2π UV = sin γ cos γ 0 U (12) 3 3 UW 2π 2π Uo sin γ sin γ Base on the above mathematical euations, a moel for PM synchronous machine with amper cyliner connecte to a stiff gri is evelope using MATLAB/Simulink. The machine is operate as a generator with input as rate shaft torue applie in the form of water flowing over the turbine an permanent magnet flux linkage ψ PM of the magnets emboie in the rotor. ue to high PM flux linkage ψ PM an the weak amper cyliner, asynchronous starting torue is not sufficient to overcome PM flux linkage braking. So it is not possible to start the machine from gri without any aitional accelerating torue (Fig. 3). For simulation the synchronous machine is starte with an accelerating torue eual to 75% rate shaft torue. This may be physically realize by water flowing on the blaes of hyromatrix turbine. This accelerating shaft torue is applie for first 3 secons an then rate shaft torue is applie. Torue(Nm) IM As an alternative, a turbine P controller can be use. The turbine is accelerate by the water flow, with open generator terminals. After reaching the machine synchronous spee the machine is connecte to gri. Fig. 4 shows the schematic for such turbine P controller. Ref. spee activator switch (0,1) ERROR electric torue - Kp s J * Integrator Inertia Fig. 4 Schematic for the turbine P controller 4 MOEL VERIFICATION Actual spee The accuracy of the evelope moel is verifie in two steps by comparing with stationary analytical calculations. A) Machine as an inuction machine (ψ PM = 0), consiering only rotor amper cyliner. Following stationary parameters are verifie by comparing the simulation result with the analytically calculate s. Table. 1 Verification as an inuction machine ata verifie Analytical Simulation iff. % Static 8616 Nm 8609 Nm 0.08 breakown torue No loa A A 0.05 current Slip at loa of 5000 Nm Current at loa of 5000 Nm A A PM IM amper Rotor Spee(rpm) Fig. 3 Calculate spee vs torue characteristics for inuction machine IM an PMSM

4 Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) B) As a synchronous machine Table. 2 Verification as synchronous machine ata verifie Analytical Simulation iff. % Rate A 73.3 A 0.2 current Rotor 250 rpm 250 rpm 0.00 spee Torue knm knm 0.00 The simulation results an the analytically calculate s show a goo accorance for a single machine. The moel is now extene to simulate the parallel operation of 4 permanent magnet synchronous generators. The generators are connecte to the stiff gri via a 100 m cable as shown in Fig. 5. Fig. 6 Calculate spee of machine M1 (Cable resistance (100 m) R C = Ohm; Cable inuctance (100 m) L C = mH ) Fig. 7 Spee of machine M2, M3, M4 Fig. 5 Schematic for parallel operation of gri connecte PM synchronous generators. 5 SIMULATION RESULTS AN ANALYSIS A) Suen loa change on generator M1 Fig. 6 shows the ynamic curve for rotor spee of machine M1. After start up with 75% rate torue, the machine M1 is loae with twice the rate loa at instant t = 10s. Fig. 7 an Fig. 8 show the influence in rotor spee of this suen loa increase on other machines M2, M3 an M4 in parallel an zoome spee view respectively. It is observe that fluctuation in spee of M1 is maximum an that of the other machines is negligible. Fig. 8 Zoome view of Fig. 7 B) Blocking of rotor of generator M1 Fig. 9 shows the calculate spee of machine M1, when rotor of machine is blocke for example ue to some woo piece strucking to the turbine blaes, reucing its spee immeiately to zero at instant t =

5 Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) 15s. Here the machines are starte with turbine P controller. Fig. 10 an 11 show the spee for the other machines M2, M3 an M4 in parallel an the zoome spee view respectively. Rotor spee for these machines stabilizes to rate spee of 250 rpm after few transients. Fig. 11 Zoome view for Fig. 8 Fig. 12 shows the torue for machine M1. It is clear that ue to blocking, the machine M1 is esynchronize an its torue oscillates with very high aroun the rate torue of knm. Fig. 13 an Fig. 14 show the corresponing transient torue curves for machines M2, M3 an M4 in parallel. The torue for these machines unergoes the electrical transients of gri freuency just after the blocking with very short time constant, which are superimpose on the long time constant mechanical transients. Fig. 9 Calculate spee of machine M1 Fig. 12 Calculate torue for machine M1 Fig. 10 Spee of machine M2, M3, M4 Fig. 13 Torue for machines M2, M3, M4 Fig. 14 Zoome view of Fig. 13

6 Proceeings of the 2006 IASME/WSEAS International Conference on Energy & Environmental Systems, Chalkia, Greece, May 8-10, 2006 (pp83-88) 6 CONCLUSIONS This paper aresses the metho of moeling an simulation of parallel operation of PM synchronous generators with amper cyliner being employe as hyro generators. For transient simulations MATLAB/Simulink is use. The parallel operate generators are of rather small power (300kW per unit), being arrange as a so calle hyro matrix turbine in river barrages. The influence of isturbances in operating conitions like blocking of rotor an suen loa change of one machine, an its effect on the other parallel generators is simulate. The fluctuations cause in spee an torue of these parallel generators ue to these isturbances are well within the tolerable limits. Thus parallel operate PM synchronous generators can be consiere as a suitable replacement for inuction generators in hyromatrix turbine arrangement for future projects. 7 Nomenclature I [A] electric current L [H] self inuctance M [H] mutual inuctance M [Nm] torue p [-] number of pole pairs t [s] time U [V] electric voltage ψ [Vs] magnetic flux linkage Ω L [1/s] rotor reference angular freuency Ω m [1/s] mechanical angular spee γ [ra] circumference angle e m s PM SUBSCRIPTS irect axis uantity amper wining in irect axis electric mechanical uarature axis uantity amper wining in uarature axis stator uantities permanent magnet rotor 8 SIMULATION ATA Stator voltage U s 1905 V Rate current I s 52.5 A Synchronous voltage U p 1917 V Freuency f 50 Hz Number of poles 2p = 24 Power factor cosϕ 0.98 Rotor inertia J kgm 2 Main reactance X h 7.25 Ohm Synchronous reactance X s Ohm Stator resistance R s Ohm Rotor resistance R r 2.03 Ohm Rotor reactance X r 0.49 Ohm Permanent magnet flux Ψ PM Wb Rate torue M N knm Rate power P N 294 kw 9 REFERENCES [1] Schneeberger, M.; Schmi, H.; StrafloMatrix further refinement to the HYROMATRIX technology. VA TECH HYRO Gmbh & co, Austria, ( [2] Biner, A.; Schneier, T.; Permanent magnet synchronous generators for regenerative energy conversion a survey, 11 th European Conf. on Power Electronics an Applications (EPE), , resen, Germany, C-Rom, 10 pages, to appear [3] Schröer,.; Elektrische Antriebe Grunlagen. 2. e., Springer, Berlin [4] Ong, C. M.; ynamic simulation of electric machinery Prentice Hall PTR, [5] Pillay, P.; Krishnan, R.; Moelling, simulation an analysis of permanent magnet motor rives, part-i : The permanent magnet synchronous motor rive. IEEE Trans. on In. Appl. Vol. 25, No.2, pp March/April, [6] Xiaoyuan, W.; Na, R.; Simulation of asynchronous starting process of synchronous motors base on MATLAB/Simulink. 6 th Int. Conf. on Electrical Machines an Systems-2003, Beijing, pp [7] Cui, X.; Funieru, B.; Biner, A.; PM Generator No-Loa Aitional Loss Calculation Using FE Moels with an Euivalent Current Layer, Proc. Sixth Int. Conf. on Computational Electromagnetics (CEM2006), VE Verlag, Aachen, Germany, April 4-6, [8] Cui, X.; Funieru, B.; Biner, A.: Calculation of No- Loa Aitional Losses in the Rotor of StrafloMatrix Synchronous Turbine-Generators, Int. Symposium on Power Electronics, Electrical rives, Automation an Motion (SPEEAM 2006), Taormina, Italy, May 23-26, (to appear)