Characteristics of a Stand-Alone Induction Generator in Small Hydroelectric Plants

Transcription

1 Characteristics of a Stand-Alone nduction Generator in Sall Hydroelectric Plants M. H. Haque School of Electrical and Electronic Engineering Nanyang Technological University Singapore Abstract-This paper proposes a siple ethod of evaluating the steady state characteristics of a stand-alone induction generator driven by a sall hydro-turbine. The steady state operation of the generator is first described by a set of nonlinear equations using the conventional loop ipedance approach. The torque-speed characteristic of the hydro-turbine is then carefully incorporated into the generator equations. The ultiate set of equations is solved using a nuerical based routine fsolve given in the optiization toolbox of MATAB. The effectiveness of the proposed ethod is then evaluated on a.5-kw, -V, three-phase induction generator. Siulation results obtained by the proposed ethod are copared with the corresponding actual values found through an experiental setup. The steady state characteristics of the generator for regulated (constant speed) and unregulated (variable speed) operations are also copared.. NTODUCTON The rapid depletion of conventional energy sources and the increasing concern of greenhouse effects have otivated the world towards exploring the use of non-conventional and renewable energy sources. Soe of the renewable energy sources such as wind and ini-hydro are usually located in reote areas where grid supply ay or ay not be available. Such energy sources can easily be used to drive prie overs of sall power plants. The generated electrical power of such plants can be injected into a grid, if it is available. Otherwise, the plants can operate in stand-alone ode and supply power to local counities. nduction generators are increasing being used in reote areas to generate electrical power fro wind or ini-hydro turbines because of their any advantageous features over the synchronous generators [], []. These features are low cost, brushless and rugged construction, aintenance and operational siplicity, self-protection against fault and overload, lack of dc power supply requireent, etc. The steady state and dynaic perforances of induction generators are investigated by a nuber of researchers and a vast aount of literature on the above topics is listed in []-[4]. When an induction generator is connected to a grid (without using a converter), the terinal voltage and frequency of the generator are fixed and deterined by the grid. The reactive power required for the generator excitation can also be obtained fro the grid. Thus, the analysis of a grid connected induction generator becoes straightforward [5]. However, for stand-alone operation of an induction generator, an appropriate size of capacitor bank need to be connected across the generator terinals to obtain the reactive power needed for its excitation. Such a generator is also called self-excited induction generator (SEG). The voltage and frequency of a SEG are not fixed but depend on any factors such as generator paraeters, excitation capacitor, speed and load [], [6]. These ake the analysis of a stand-alone or self-excited induction generator uch ore difficult than that of a grid connected generator. The steady state perforance of a SEG is usually deterined fro its equivalent circuit. The loop ipedance approach [7]-[] or the nodal adittance approach []-[] is coonly used in analyzing the circuit. n both approaches, two nonlinear equations are first derived in ters of frequency () and agnetizing reactance (X ) of the generator. The equations are then solved by soe suitable iterative ethods. Once the values of and X are know, the steady state perforance of the generator can easily be evaluated through its equivalent circuit. Most of the previous ethods of analyzing a SEG assued constant speed operation [6]-[] by considering that the generator operates with soe fors of speed control turbine or prie over to regulate the speed. Such a sophisticated speed controller or regulator ay not be used in a sall standalone power plant in a reote area. The speed of a ini-hydro turbine, with constant water head, is not constant but load dependent. n fact, the speed of the turbine decreases linearly with load torque [4]. Thus, when the generator is driven by a ini-hydro turbine, it is necessary to incorporate the torquespeed characteristic of the turbine into the generator equations to get the correct characteristics. eference [5] incorporated the torque-speed characteristic of a ini-hydro turbine into the generator equations. The final equations are then solved using the Newton-aphson ethod that requires lengthy and tedious derivations of the equations (in ters of actual unknowns) as well as their partial derivatives. eference [6] used a two-level iterative ethod to solve the syste of equations and is also found to be very coplicated. This paper proposes a siple ethod of forulating the proble of a stand-alone or self excited induction generator 8 Australasian Universities Power Engineering Conference (AUPEC'8) Paper P-4 Page

2 with torque-speed characteristic of the prie over. The forulated proble is then solved using a nuerical based routine fsolve given in MATAB. The effectiveness of the proposed ethod is then evaluated on a three-phase induction generator and the siulation results obtained are also copared with the corresponding experiental values.. GENEATO MODE The per-phase equivalent circuit [] of a three-phase induction generator with an excitation capacitor C and an - load is shown in ig. where, X,, X, c and X represent the stator resistance, stator leakage reactance, rotor resistance, rotor leakage reactance, core loss resistance and agnetizing reactance, respectively, of the generator. and v represent the per unit (pu) frequency and speed, respectively. The load ipedance is represented by ( +jx ) Z θ and the reactance of the excitation capacitor is represented by X C. Note that the circuit of ig. is noralized to the based frequency by dividing all paraeters and voltages by the pu frequency. jx v jx sh c V g jx ig. Per-phase equivalent circuit of a three-phase induction generator. V t C jx jx C The circuit of ig. can be represented by three series ipedances as shown in ig.. The ipedances are given by Z ( / + jx ) Z Z / c + jx jx C / + + The loop equation in ig. is /( v) + jx / + jx ( Z + Z + Z) () Under noral operating condition, the stator current is not zero and thus, ( Z + Z + Z ) ust be zero. By separating the real and iaginary parts of the loop ipedance, the following two scalar equations can be obtained g real( Z + Z + Z ) () g iag( Z + Z + Z ) Note that () and (4) represent the basic equations and are to be satisfied for all operating conditions of the generator. The rotor circuit power P in ig. can be written as (4) (5) v P Here is the rotor current and its expression is given in Section V. The rotor copper loss P cu is given by Z P cu (6) Thus, the input power P i to the rotor of the generator (or the output power of the prie over) can be written as Z V g V t Z P P + P (7) i cu The input torque T i to the generator is associated with P i and is given by ig. Siplified representation of ig. T P i i (8) vωs All paraeters of the generator, except the agnetizing reactance X, are considered as constant. The value of X depends on agnetic saturation and hence the ratio of air-gap voltage to frequency (V g /). The relationship between V g / ratio and X can be considered as [7] Vg k + kx + k X + k X () The procedure of finding the coefficients of the above equation is described in [8]. Here ω s is the synchronous angular velocity (in radian/sec) of the generator at the base frequency. Note that the input torque to the generator and the output torque of the prie over are the sae.. PME MOVE TOQUE-SPEED CHAACTESTC The input power or torque to the generator ust be supplied by the prie over. n this study, it is considered that the generator is driven by a ini-hydro turbine at a constant water 8 Australasian Universities Power Engineering Conference (AUPEC'8) Paper P-4 Page

3 head. or such a case, the torque-speed (T d -ω ) characteristic of the turbine is linear and can be expressed as [4]-[6] ω a (9) bt d Here a and b are constant. The above equation can also represent the torque-speed characteristic of a separately excited dc otor. Thus, in a laboratory, the characteristic of the ini-hydro turbine can be eulated by a separately excited dc otor. The developed torque T d of the otor can be written as a ω Td () b Note that the developed torque is the su of output (or shaft) torque T o and rotational loss torque T rot. Thus, the output torque of the otor can be expressed as a ω To Trot () b Values of a, b and T rot can be deterined for the no-load test data of the otor [9]. When the dc otor and the induction generator are coupled to the sae shaft, both the otor and the generator ust run at the sae speed (i.e. ω vω s ). Also, under steady state condition, the output torque of the otor ust be the sae as the input torque to the generator. Using (8) and (), the torque balance equation can be written as a vωs Pi g Trot () b vω s Thus, when the torque-speed characteristic of the prie over is considered, equations (), (4) and () ust be satisfied for all steady state operating conditions. V. POBEM OMUATON Deterination of steady state perforance of a SEG driven by a ini-hydro turbine involves siultaneous solutions of (), (4) and (). Note that the circuit of ig. has five unknown or adjustable paraeters: agnetizing reactance X, speed v, frequency, excitation capacitor reactance X C and load ipedance Z (for a given power factor). However, the solution of the above equations can provide the values of only three unknowns. Thus, it is necessary to assign soe feasible values to other two unknowns and consider the as fixed paraeters. n this study, (), (4) and () are solved to find the values of X, and v for given or assued values of X C and Z. The above equations, in general for, can be written as G(X) () Here G [g g g ] T and X [X v] T. n this study, () is solved using a nuerical based routine fsolve given in the optiization toolbox of MATAB [] and it does not require to express the equation explicitly in ters of the actual unknowns. The sae routine is successfully used in [] to deterine the paraeters of induction otors fro a set of nonlinear equations. eference [7] used a constraint optiization routine to deterine the perforance of a SEG without considering the torque-speed characteristic of the prie over. When the generator is driven at a constant speed by a regulated prie ove, it is not necessary to incorporate the torque-speed characteristic of the prie over into the generator of equations. n this case, the coefficient b of (9) is zero and thus, ω a vωs. or such an operation, only () and (4) are to be solved to find the values of X and for given values of X C, Z and v. Once the values of X and are known in either case (regulated or unregulated), the steady state perforance of the generator can be evaluated fro its equivalent circuit. V. PEOMANCE EVAUATON By knowing the values of X and, the air-gap voltage V g of the generator can be evaluated fro (). The stator current (in ig. ) and the rotor current (in ig. ) can be written as Vg / (4) Z + Z Vg / /( v) + jx (5) Here V g is considered as reference. ro the equivalent circuits, the terinal (or load) voltage V t and the load current can be written as Z Vt Vg Z + Z (6) Vt + jx (7) The active power P and the reactive power Q absorbed by the load are given by P (8) Q X (9) The reactive power Q C supplied by the excitation capacitor is Q C Vt X / C () 8 Australasian Universities Power Engineering Conference (AUPEC'8) Paper P-4 Page

4 The various characteristics of the generator can be obtained fro the above equations with repeated solutions of () for various values of load ipedance Z. V. ESUTS AND DSCUSSONS The proposed ethod of evaluating the perforance characteristics of a stand-alone induction generator is tested on a three-phase,.5-kw, -V, 5-Hz, 4-pole, delta-connected, induction otor operated as a generator. The fixed paraeters of the generator are 5. Ω, Ω, c 5.47 kω and X X 5.66 Ω. Using the synchronous speed test data, the coefficients of () are found as k 596., k -.5, k.74 and k A brief description of siulation and experiental results obtained for the above generator is described in the following. both load voltage and power. The experiental results found for this case are also shown in ig. by a sybol o and are observed to be in very good agreeent with the corresponding siulation results. Current, A 5 4 C oad voltage, V oad power, W ig. 4 Variation of stator, load and capacitor currents against load power. P ax oad power, W Speed, rp 4 5 ig. Variation of load voltage against load power. The generator is first driven by a separately excited dc otor (to eulate the ini-hydro turbine) and the no-load speed of the otor-generator set is adjusted to. pu (or,5 rp). The corresponding rotational loss is found as 7.4 W (or T rot. N). t is assued that the rotational torque T rot reains constant. The excitation capacitor C of the generator is then turned on to generate voltage. or C 7 μ, the noload voltage is found as.4 V. The generator is then gradually loaded by decreasing the load ipedance fro infinity. igure shows the variation of load voltage against load power (at unity power factor) and it indicates that the terinal voltage decreases with load. n this case, the generator can deliver a axiu power P ax of 57.6 W at which the voltage drops to 64.8 V and the speed reduces to 4. rp. Note that the speed deviation depends on the slope b of the torque-speed characteristic of the prie over. urther reduction of load ipedance (beyond P ax ) decreases oad power, W ig. 5 Variation of generator speed against power. The variation of stator current, capacitor current C, and load current against load power is shown in ig. 4. t can be observed in ig. 4 that the generator has a stator current of 4.6 A at no-load and it decreases slightly with load. This happened because of the reduction of capacitor current due to lower voltage. The variation of otor speed and generator frequency against load power is shown in igs. 5 and 6, respectively, and the figures indicate that both the speed and the frequency decrease with load, as expected. igures Australasian Universities Power Engineering Conference (AUPEC'8) Paper P-4 Page 4

5 also indicate that the siulation results are very close to the corresponding experiental results. Only a slight deviation in speed and frequency is observed around the axiu power point. requency, Hz oad power, W ig. 6 Variation of generator frequency against power. entioned here that even though the no-load speed of the generator, for unregulated case, was initially adjusted to,5 rp but it decreased to 48 rp when the excitation capacitor was turned on. This happened because of the additional losses (core and copper losses) in the generator associated with the generated voltage. That is why the no-load voltage for the unregulated case is slightly lower than that for the regulated case (see ig. 7). t can also be noticed in ig. 7 that, for regulated case, the generator can deliver a axiu power P ax of W and is uch higher than that for the unregulated case (57.6 W). The voltage in the regulated case is also found higher than that of the unregulated case. Note that, for a given load, the voltage depends not only on the speed but also on the aount of reactive power Q C supplied by the excitation capacitor. A coparison of Q C, for regulated and unregulated cases, is shown in ig. 8. The experiental values of Q C are obtained fro the easured values of terinal voltage and capacitor current. apid reduction of Q C in ig. 8, for unregulated case, is ainly due to the lower voltage. ower frequency in unregulated case is also contributes to the rapid reduction of Q C. A coparison of stator current and load current, for regulated and unregulated cases, is shown in ig. 9. igures 7-9 again indicate that the experiental values are very close to the corresponding siulation results. 5 oad voltage, V 5 egulated Capacitive reactive power, VAr 5 5 Unregulated egulated Unregulated oad power, W ig. 7 Coparison of load voltage for regulated and unregulated cases oad power, W ig. 8 Coparison of Q C for regulated and unregulated cases. The characteristics of the generator are then evaluated for constant speed operation (or regulated case) and copared with that of the unregulated case (when driven by the dc otor). n this case, the generator is driven at a constant speed of. pu (or,5 rp) by a 4-pole, 5-Hz synchronous otor. igure 7 shows the coparison of voltage versus power characteristic (regulated and unregulated cases) of the generator for an excitation capacitor of 7 μ. t ay be V. CONCUSONS A siple ethod of evaluating the steady state characteristics of a stand-alone induction generator driven by a ini-hydro turbine is described in this paper. The torquespeed characteristic of the turbine, with a constant water head, is carefully incorporated into the generator equations to describe the steady state operation. The ultiate set of equations is then solved using a nuerical based routine given 8 Australasian Universities Power Engineering Conference (AUPEC'8) Paper P-4 Page 5

6 in MATAB. The perforance characteristics of the generator are also evaluated for constant speed operation (regulated case) and copared with that of the unregulated case (when driven by a ini-hydro turbine). The siulation results obtained by the proposed ethod are also copared with the corresponding experiental values and are observed to be in excellent agreeent. n the laboratory, the generator is driven by a dc otor and a synchronous otor to eulate the unregulated and the regulated operations, respectively, of the generator. or the unregulated case, the perforance of the generator (in ters of voltage and power) deteriorates significantly copared to the regulated case even though the speed reduction is not so significant. Current, A 5 4 Stator current oad current Unregulated egulated oad power, W ig. 9 Coparison of currents for regulated and unregulated cases. EEENCES [] M.G. Sioes and.a. arret, enewable energy systes Design and analysis with induction generators, CC Press, New York, USA, 4. [] G.K. Singh, Self-excited induction generator research a survey, Electric Power Systes esearch, Vol. 69, 4, pp [].C. Bansal, Three-phase self-excited induction generators: An overview, EEE Trans. on Energy Conversion, Vol., No., 5, pp [4].C. Bansal, T.S Bhatti and D.P. Kothari, Bibliography on the application of induction generators in nonconventional energy systes, EEE Trans. on Energy Conversion, Vol. 8, No.,, pp [5] M.G. Say, Alternating current achines, Wiley, 976. [6] A.K. Tandon, S.S. Murthy and G.J. Berg, Steady state analysis of capacitor self-excited induction generators, EEE Trans. on Power Apparatus and Systes, Vol., No., 984, pp [7] A. Kh. Al-Jabri ad A.. Alolah, iits on the perforance of the three-phase self-excited induction generators, EEE Trans. on. Energy Conversion, Vol. 5, No., 99, pp [8]. Shridhar, B. Shing and C.S. Jha, A step towards iproveents in the characteristics of self-excited induction generator, EEE Trans. on Energy Conversion, Vol. 8, No., 99, pp [9] S.P. Singh, B. Singh and M.P. Jain, Perforance characteristics and optial utilization of a cage achine as capacitor excited induction generator, EEE Trans. on Energy Conversion, Vol. 5, No. 4, 99, pp [] S.S. Murthy, B.P. Singh, C. Nagaani and K.V.V. Satyanarayana, Studies on the use of conventional induction otors as self-excited induction generators, EEE Trans. on Energy Conversion, Vol., No. 4, 988, pp [] T.. Chan, Capacitance requireents of self-excited induction generators, EEE Trans. on Energy Conversion, Vol. 8, No., 99, pp. 4-. []. Quazene and G. McPherson, Analysis of the isolated induction generator, EEE Trans. on Power Apparatus and Systes, Vol., No. 8, 98, pp [] T.. Chan, Analysis of self-excited induction generators using an iterative ethod, EEE Trans. on Energy Conversion, Vol., No., 995, pp [4] J.A. ule Jr., A strategy for odeling hydroelectric plants and iproving their perforance, PhD Thesis, Virginia Polytechnic nstitute and State University, 988. [5] S.M. Alghuwaine, Steady-state analysis of an isolated self-excited induction generator driven by regulated and unregulated turbine, EEE Trans. on Energy Conversion, Vol. 4, No., 999, pp [6] T.. Chan, Self-excited induction generator driven by regulated and unregulated turbines, EEE Trans. on Energy Conversion, Vol., No., 996, pp [7] A.. Alolah and M.A. Alkanhal, Optiization-based steady state analysis of three phase self-excited induction generators, EEE Trans. on Energy Conversion, Vol. 5, No.,, pp [8] B. Singh, S.S. Murthy and S. Gupta, Analysis and design of STATCOM-based voltage regulator for self-excited induction generators, EEE Trans. on Energy Conversion, Vol. 9, No. 4, 4, pp [9] G.B. Shrestha and M.H. Haque, AC circuits and achines, Prentice Hall, Pearson Education South East Asia, Singapore, 6. [] Matlab 7a and Siulink, 7. [] M.H. Haque, Deterination of NEMA design induction otor paraeters fro anufacturer data, EEE Trans. on Energy Conversion, n press. 8 Australasian Universities Power Engineering Conference (AUPEC'8) Paper P-4 Page 6