Analysis of voltage control for a self-excited induction generator using a three-phase four-wire electronic converter

Transcription

1 Analysis of voltage control for a selfexcited induction generator using a threephase fourwire electronic converter José Antonio Barrado 1, Robert Griñó 2 1 Departaento de Ingeniería Eléctrica, Electrónica y Autoática ETSE, Universitat Rovira i Virgili Avinguda Països Catalans, Tarragona (España) Tel.: , fax: , eail: joseantonio.barrado@urv.net 2 Instituto de Organización y Control de Sisteas Industriales (IOC) ETSEIB, Universitat Politècnica de Catalunya Avinguda Diagonal, Barcelona (España) Tel.: , fax: , eail: roberto.grino@upc.edu Abstract. This paper shows the effect of agnetic uration during selfexcitation process in an isolated threephase induction generator, for a given capacitance and rotor speed value. After the steady state condition of a selfexcited induction generator (SEIG) is attained, an increase of load causes a decrease in the agnitude of generated voltage and its frequency. Moreover, when a threephase fourwire generator work under unbalanced and/or nonlinear loading conditions, the voltage and stator currents are also unbalanced, flows a current in the neutral conductor and appears haronics. Therefore, a threephase fourwire active filter is used to copene the haronics and asyetries in the stator currents caused by the previous type of loads. The control strategy of this electronic converter is based in a fundaental positivesequence detector. Finally, for sall hydro plants applications, the converter incorporate too a chopper to keeps the load constant on the SEIG, so the generator aintain the rated voltage and frequency. The siulation results show a good perforance of the SEIG and the electronic converter under different loading conditions. Key words Selfexcited induction generator, static copenor, shunt active filter, electronic load controller. 1. Introduction An externally driven induction achine with an appropriate value of capacitor bank can be used as a generator [1]. This syste is called selfexcited induction generator (SEIG). The SEIG has any advantages over the synchronous generator: brushless (squirrel cage rotor), reduced size, rugged and low cost. But the induction generator offers poor voltage regulation and its value depends on the prie over speed, capacitor bank and load. The cagetype induction generators have eerged in these recent years as a suitable candidate in reote areas where this achine can be driven using a wind turbine, a diesel engine or sall hydro plants. Norally, in this last application, the SEIG generates constant voltage and frequency because it is operating at constant load power. When an isolated SEIG feeds unbalanced and/or nonlinear loads, the threephase terinal voltage and stator currents are also unbalanced and ay appear haronics. These increase the power losses, create unequal heating and cause torque pulion on the shaft of the generator. Also, the unbalanced threephase currents yield a current in the neutral conductor that involves ore power losses and heating. 2. Syste configuration The proposed syste consists of a SEIG driven by an unregulated hydraulic turbine. The generator supplies an isolated threephase fourwire load. The voltage and frequency control of the syste is achieved by an electronic converter connected to the generator terinals (Fig. 1). This converter is ade up of a shunt active filter and an electronic load controller. Load i L i C i S AF / ELC Fig. 1. Scheatic diagra of proposed syste a b c n Capacitor Bank V Induction Generator Prie Mover i R

2 The SEIG is a threephase induction achine with a wyeconnected stator winding. Its iddle point is connected to the neutral conductor. The capacitor bank is connected to the other three external terinals. Finally, a prie over rotates the squirrel cage rotor at a speed higher than the synchronous speed. The electronic converter is a static copenor (STATCOM). It consists of a fourwire shunt active filter (AF) ade up of a threeleg splitcapacitor boost converter [2] and an electronic load controller (ELC) ade up of a chopper connected to a resistor [3,4]. 3. Modeling of the syste A. Induction generator odel The dynaic odel of the squirrel cage induction generator in the stationary dq reference frae is described by the following equations []: Flux linkages per second with uration effect rs v xls = ω qs b qs q qs rs v xls = ω ds b ds d ds (1) (2) The agnetic uration is the ain factor for voltage buildup and its stabilization on SEIG. For achines with unifor air gap, the urated value of the utual flux linkage per second in qdaxes is given by where q ' = xm xls x' x qs qr q (1) (11) (12) Assuing a proportional reduction in the utual flux linkages of the qdaxes (Fig. 2), the value of Ψ q and Ψ d is deterined fro the following relationships q = x ' ds dr d d M xls x' x = x x x' x M ls q = q d = d (13) (14) ωr r' r ωb x' ' = ω ' ' qr b dr q qr (3) Ψ q Ψ q Ψ q Ψ Ψ Ψ ωr r' r ωb x' ' = ω ' ' dr b qr d dr (4) Ψ d Ψ d Ψ d d The stator qd currents can be calculated as The electroagnetic torque equation is 3 P T = i i The otion of the rotor is given by i i qs ds qs = xls ds = x q d ω i = = v ri ( ) e ds qs qs ds 22ωb 2 dω T = J T T P r e dap ec ls ( ) s b s s s s xls xls () (6) (7) (8) (9) Fig. 2. Saturation in dq coponents While the value of Ψ and Ψ is obtained fro the terinal voltage versus noload stator current test (Fig.3). Ψ Ψ Ψ Ψ Fig. 3. Saturation curve of the induction achine Another way of consider the effect of uration on SEIG is trough the nonlinear relationship between agnetizing reactance and agnetizing current in the induction achine [6]. i

3 The odel of induction generator, with urated utual flux linkage per second, is ipleented with Siulink [7]. It is divided in blocks that consider the transforations: abcqd of the stator voltages and qd abc of the stator currents and solve the previous equations (1) to (14): stator currents, flux linkages, agnetic uration, torque and rotor speed (Fig. 4). The differential equations of the inverter are as follow v = R i L di e a an La a a an v = R i L di e b bn Lb b b bn v = R i L di e c cn Lc c c cn (1) (16) (17) The voltage of the bus can be calculated fro the inductor currents at the VSI and the chopper current. 1 v = vc1 vc2 S S S S v vc1= Aia Bib Cic D C1 R (18) (19) a b c N Fig. 4. Induction generator odel ipleented in Siulink B. Electronic converter odel Fig. shows the electrical schee of the electronic converter. This syste is ade up of a threephase fourwire current controlled voltage source inverter (CCVSI) [8] and a chopper connected to its bus. The threeleg converter topology with the neutral wire connected directly to the idpoint of the capacitors (splitcapacitor) is preferred due to its lower nuber of power seiconductor devices respected the four switchleg topology. i (a,b,c) RL, L S Ap SBp SCp e a e b S An SBn SCn e c Fig.. Electronic converter i i R The CCVSI is odeled by three switching functions (S A, S B, and S C ) to deterinate the state of the IGBTs (S Ap to S Cn ) in each branch of the bridge. Considering the coutation basic rules of converters, the switches of a branch ust change of copleentary for (Table 1). As far as the chopper is concerned, S D is the switching function to deterinate the state of its IGBT. VC1 VC2 Table 1. Switching functions of CCVSI S A 1 S Ap =1 S An = S Ap = S An =1 S B 1 S Bp =1 S Bn = S Bp = S Bn =1 S C 1 S Cp =1 S Cn = S Cp = S Cn =1 S D R 1 S S S S v vc2 = i A a i B b i C c D C2 R The voltages on the ac side of inverter are described by e = S v S A v an A C1 C2 e = S v S B v bn B C1 C2 e = S v S C v cn C C1 C2 (2) (21) (22) (23) The set point of V ust be greater than the peak value of ac phase voltages in order to generate the desired ac line currents. The side currents of VSI and its relationships with the ac side currents are expressed by i = ic1 ir ic2 = ic1 in ia ib ic in = (24) (2) (26) The currents can flow in both directions through the switches and capacitors. But the splitcapacitor inverter topology has a proble with the voltage in the capacitors C1 and C2. The total side voltage (V ) and the voltage difference (V C1 V C2 ) will oscillate not only at the switching frequency of power seiconductor devices, but also at the corresponding frequency of the zero sequence coponent current that flow by the neutral wire. The ac side currents of CCVSI ust to follow its reference current. For this purpose the switching patterns are generated, by the current controller, according to the copared results between the easured ac side currents and the reference currents with a sall hysteresis band.

4 4. Control schee The block diagra of the proposed control schee is shown in Fig. 6. This controller forces the electronic converter to copene the load current and to absorb a deterinate value of power fro induction generator. Thus the current supply fro SEIG becoes sinusoidal, balanced and its active value is aintained constant. Therefore, the induction generator provides the active power of load and also other active power coponent to regulate the voltage in the capacitors. This last additional coponent deterines a current value to cover the losses in the power converter (switching losses of IGBTs, leakage current of capacitors, etc), to supply the current of controlled load and to follow the new conditions iposed to the syste. All this power changes cause voltage variation on bus [9], the slower feedback control loop of the voltage regulator will change the signal i loss to ake the active filter absorb/supply a fundaental positivesequence current to copene the above voltage variation. For the purpose explained above, a PLL block is used to deterine the agnitude and phase of fundaental positivesequence of the voltage line and the load current [1]. Fro this two agnitudes and its phase difference, another block generates the threephase balanced active coponent of the load current, i Ld (a,b,c)*. The difference between this value and the easured load current, i L (a,b,c), yields the reference current to copene the reactive power, the unbalanced currents and load haronics of fourwire electric syste [11]. The total reference currents of electronic converter, i C (a,b,c)*, are the su of previous copened current (active filter part) and other current to absorb by a controlled load (chopper part). This last coponent value is the result of the difference between active fundaental coponent of the load current, i Ld (a,b,c)*, and active fundaental rated current to supplies fro SEIG, i Sd (a,b,c)*. Moreover, this rated current value is copened through a regulator according to voltage value in the generator terinals. The threephase fourwire currents of VSI are deterined by a hysteresis band current control. It copares the easured ac side currents, i C (a,b,c), and the reference currents of the converter, i C (a,b,c)*. The difference between the active current value that SEIG supplies, the active fundaental current of the load with and another coponent fro the voltage regulator i loss are coputed to generate the reference current i R * of PWM current controller. Finally, this reference current of PWM controller, a triangular carrier wavefor and the current through R deterine the gating signal to switch the IGBT (S D ) of chopper. i L (a,b,c) v S (a,b,c) PLL circuit & Positive sequence calculation v S i L θ Active coponent reference current i Ld (a,b,c)* i C (a,b,c)* v S* i S act* Vs regulator Magnitude to abc i Sd (a,b,c)* i C (a,b,c) v v * V regulator i loss i R * Hysteresis band Current controller i R PWM Current Controller Gating signals Active Filter Gating signal Load Controller STATCOM Fig.6. Block diagra of the electronic converter control

5 . Siulation results The SEIG starts its operation with constant rotor speed, the capacitor bank connected to its terinals, without load and the STATCOM disabled. Fig. 7 represents the transient selfexcitation process of the induction generator. Vabc (V) freq (Hz) 6 9 Vabc (V) Iabc.load (A) In.IM (A) Iabc.IM (A) Fig. 7. Growth and stabilization of generated voltage and stator current of the induction achine. Whereas Fig. 8 shows de behavior of SEIG under a sudden unbalanced load switched at 1. seconds and electronic converter disabled. In this case, the generated voltage and its frequency decrease. Moreover, the threephase terinal voltage and stator currents are also unbalanced. As a result of this unbalanced currents yield a current that flow by the neutral conductor. When the syste reaches the steady state, the electronic converter begins its operation before the connection of the load to the syste terinals. In this way the electronic converter, together with its control loops, is Fig. 8. Transient responses of SEIG supplying an unbalanced load able to react to the disturbing characteristics of the load keeping the right average value, the frequency and the shape of the voltage on SEIG terinals. Fig. 9 shows the response of the syste under various loading conditions through the plot of next transient wavefors: induction generator currents, load currents, terinal voltage on SEIG, threephase currents of electronic converter, neutral current of electronic converter and average current of chopper. First SEIG supplies its rated power, but it works without load, so the converter consues all this generated power. The left side of Fig. 9 depicts the respective values of threephase fourwire currents in electronic converter and average current of chopper. At.27 seconds, a threephase balanced inductive load is connected to generator. This involves a decrease of ac Iabc.SEIG 1 1 Iabc.CS (A) 1 1 Iabc.load (A) In.CS (A) Vabc (V) I.ELC (A) Fig. 9. Transient responses of SEIG and electronic converter under different loading condition

6 and currents on electronic converter. But de voltages and currents on SEIG are the sae. Finally, at.39 seconds, a variable singlephase nonlinear load is connected to the SEIG that is feeding the previous threephase balanced load. The ac line currents of converter are unbalanced, so a current flows by its neutral conductor. However, the SEIG currents are balanced and the linetoneutral terinal voltages have the sae value for the three phases. The results of the siulation are obtained with the following paraeter values of syste: Induction achine P = 3 HP, V s = 127/22 V ( /Y), f = 6 Hz, 4 poles, R s =.43 Ω, R r =.816 Ω, X ls = X =.829 Ω, X = Ω. Electronic converter R =.6 Ω, L = 1.2 H, C 1 = C 2 = 4 µf. [7] CheeMun Ong, Dynaic siulation of electric achinery using MATLAB/Siulink, New Jersey: Prentice Hall PTR, ISBN: [8] A. Cavini, F. Ronchi and A. Tilli, Fourwires shunt active filters: optiized design ethodology, IEEE Annual Conference of the Industrial Electronic Society, Vol. 3, pp , 26 Noveber 23. [9] R. Rodríguez, R. Pindado and J. Pou, Energy control of threephase fourwire shunt active power filter, IEEE Annual Conference of the Industrial Electronic Society, Vol. 2, pp , 26 Noveber 23. [1] M. Aredes and L.F.C. Monteiro, A control strategy for shunt active filter, International Conference on Haronics and Quality of Power, Vol. 2, pp , 69 October 22. [11] B. Singh, K. AlHaddad and A. Chandra, "Haronic eliination, reactive power copenion and load balancing in threephase fourwire electric distribution systes supplying nonlinear loads", Electric Power Systes Research, Vol. 44, pp. 931, Threephase inductive balanced load V ac = 22 V, P = 9 W, Q = 3 var 6. Conclusions This paper proposed a controller of a static copenor to regulate and to balance the generated voltage of a standalone SEIG with hydraulic turbine. The converter is ade up of an active filter and a controlled load. It copenes haronics, reactive power and eliinates neutral current. The tested odel of threephase fourwire SEIGSTATCOM is a powerful tool for study the transient and steady state responses of this syste at different types of loads. The siulated results show a good perforance and efficiency of the whole syste under different loading conditions. References [1] E.D. Bassett and F.M. Potter, Capacitive excitation for induction generators, AIEE Transactions on Electrical Engineering, Vol. 4, pp. 44, May 193. [2] C.A. Quinn and N. Mohan, Active filtering of haronic currents in treephase fourwire systes with threephase and singlephase nonlinear loads, Applied Power Electronics Conference, pp , [3] R. Bonert and G. Hoops, Stand alone induction generator with terinal ipedance controller and no turbine controls, IEEE Trans. Energy Conversion, Vol., Issue 1, pp. 2831, March 199. [4] B. Singh, S.S. Murthy and S. Gupta, An iproved electronic load controller for selfexcited induction generator in icrohydel applications, IEEE Annual Conference of the Industrial Electronic Society, Vol. 3, pp , 26 Noveber 23. [] P.C. Krause, "Analysis of electric achinery", New York: McGrawHill, ISBN: [6] D. Seyou, C. Grantha and M.F. Rahan, The dynaic characteristics of an isolated selfexcited induction generator driven by a wind turbine, IEEE Transactions on Industry Applications, Vol. 39, Issue 4, pp , JulyAugust 23.