Analysis of Prevention of Induction Motors Stalling by Capacitor Switching

Transcription

1 16th NTIONL POWER SYSTEMS CONFERENCE, 15th-17th DECEMER, nalyi of Prevention of Induction Motor Stalling by Capacitor Switching S.Maheh and P.S Nagendra rao Department of Electrical Engineering Indian Intitute of Science, angalore, India , btract Switching capacitor i one of the way by which voltage intability due to large increment in induction motor load can be prevented. new analyi technique i propoed that help to relate the capacitance and the lip at the intant of witching with the rotor dynamic following the witching and conequently voltage tability. Thi approach can be ued to chooe appropriate capacitance to be witched at the induction motor terminal to prevent it talling following a udden load increment. Thi approach ha been extended to a general power ytem where the induction motor i connected at one of the load bue of the ytem. I. INTRODUCTION In thi paper, we invetigate the iue in the context of voltage tability improvement in ytem having large induction machine. The talling of induction motor could lead to voltage collape. Thi i a fat voltage intability problem and the conventional method of voltage tabilization cannot be applied [3]. The 1987 Tokyo blackout ha been attributed partly to the characteritic of the new electronically controlled air conditioner (load commutated inverter) [5]. The prevention of voltage intability due to induction motor i an important concern. The prevention of induction motor talling by witching a capacitor at the induction motor bu i tudied in [1], [2], [4], [6] and [7]. It ha been mentioned in [2] that if a capacitance of a particular value ha to be witched, it ha to be done before the machine lip croe the lip at the interection point of the load characteritic and the compenated network characteritic in the untable region of the compenated network characteritic. aed on the imulation reult, [2] alo retate what i referred to a the minimum voltage criterion which wa originally mentioned in [7]. ccording to thi criterion after the inertion of a reactive upport, the immediate operating voltage mut be higher than a minimum voltage determined by the interection of the teady tate motor(load) characteritic and the modified network curve. However, how to ue thi criterion to deign the capacitance value to be witched i not obviou from [2] or [7] a no uch procedure i given. The capacitor ued for the imulation tudy in [2] ha been choen arbitrarily and i not determined baed on thi criterion. cheme i propoed in thi paper to determine the capacitance value to be inerted at the induction motor terminal at any lip to prevent the voltage collape of the ytem following a very large diturbance that can potentially reult in talling. Several apect of thi way of preventing induction motor talling have been tudied in detail. II. CLCULTION OF CPCITNCE The criterion propoed here that facilitate the deign of the witching capacitance i the following. When the mechanical power output, of an induction motor i uddenly increaed to final, it lip tart increaing monotonically. If final i of uch a value that could make the motor tall, then to prevent the talling, the voltage immediately after the witching of the capacitor hould enure that the electromechanical power output of the motor i greater than final. In the limiting cae, it will be equal. For the eae of dicuing the critical iue, conider the ytem in Fig 1 a in [1] that how an induction motor upplied from a contant voltage ource through a line. The ytem equation are given by (1) to (6). E 0 Fig. 1. Line flow equation jx e jx c V θ n induction machine ytem F 1 : P k = R r jx r EV in( θ) X e (1) Department of Electrical Engineering, Univ. College of Engg., Omania Univerity, Hyderabad,.P, INDI.

2 16th NTIONL POWER SYSTEMS CONFERENCE, 15th-17th DECEMER, F 2 : Q k = E2 EV co θ (2) X e X e where P k and Q k are the real and the reactive power injected by the ource at the bu where the induction motor i connected. Induction machine equation Rotor dynamic where X e R r X r P e Q e I ω θ F 3 : P e = R rv 2 R 2 r + 2 X 2 r F 4 : Q e = 2 X r V 2 R 2 r + 2 X 2 r (3) (4) F 5 : P e (1 ) = 0 (5) F 6 : d dt = 1 Iω 2 θ [ ] Pm 1 P e -: line reactance -: rotor reitance of the motor -: rotor reactance of the motor -: lip of the motor -: mechanical power output of the motor -: electrical power input to the motor/torque in p.u -: reactive power input to the motor -: moment of inertia of the motor -: nominal frequency of the motor. The principle ued for determining the capacitance to be inerted at the induction motor terminal i that the pot witching terminal voltage mut enure the development of a motor output power(at that lip) greater than the final (load) being driven by the induction motor. Conidering the lip at the intant of the capacitor witching to be given, it i required to enure that after capacitor witching the electrical torque mut be greater than mechanical torque. In the limit R r V 2 R 2 r + 2 X 2 r = final 1 The voltage at the intant of capacitor witching V can be calculated baed on the circuit in the Fig 1. Let R r1 = R r / and X r1 = X r. It i eay to ee that V = EX r1 X c jer r1 X c X c (X r1 + X e ) X e X r1 + j(x e R r1 X c R r1 ) Rewriting the above a a quadratic equation in X c Xc 2 (Xr1V Xe 2 V 2 + 2X e X r1 V 2 + Rr1V 2 2 E 2 Xr1 2 E 2 Rr1) 2 + X c ( 2X e Xr1V 2 2 2Xe 2 X r1 V 2 2Rr1X 2 e V 2 ) + Xe 2 Rr1V 2 2 (9) +Xe 2 Xr1V 2 2 = 0 Solving (9), we get two value for X c (ay ωc 1 and ωc 2 ) when the root are real. For a particular pot diturbance final, if the witching intant witch i varied(tarting from the initial operating lip initial ) ωc 1 and ωc 2 can be calculated for each of (6) (7) (8) uch witch uing (9). In Fig 2 ωc 1 and ωc 2 are plotted with repect to witch. For a particular diturbance final that can make the motor tall, when the lip at which the capacitance i witched, witch i increaed from initial, ωc 1 decreae till a lip of min (correponding to point D) and then tart increaing. Similarly, ωc 2 increae till a lip of max (correponding to point ) and then tart decreaing a can be een in the Fig 2. t a lip critical, ωc 1 = ωc 2. Thi, we refer to a critical lip. For a given pot diturbance final which can make the motor tall, it i not poible to prevent talling by witching any value of capacitor beyond = critical. The critical i independent of the initial load on the motor. The critical will be lower for greater value of the pot diturbance final than for the maller value of the pot diturbance final a can be een in the Fig 4, wherein the ωc 1, ωc 2 contour are drawn for different value of final. Conidering the region beyond initial, in the ωc- plane hown in Fig 3, we ee that thi contour(variation of ωc 1 and ωc 2 ) form a cloed contour. Thi divide the plane into two ditinct region. Note that every point in thi plane correpond to witching a particular value of capacitance at a particular value of lip. If the witching choice correpond to any point within the region formed by the contour CDE, the electrical power output of the motor(p eout ) immediately after witching would be greater than final. t all the point on the contour, P eout of the motor would be exactly equal to final and outide the contour, it will be alway le than final. In order to undertand the implication of variou witching choice, we draw two line, HD and I parallel to the axi a hown in the Fig 3. Thee line will be tangential to the contour at point (ωc 2max ) and D(ωC 1min ) repectively. In addition, we alo include two line, DF and G that atify the following. If we deignate any point on thee line a P, correponding to a lip p and a capacitance C p the line DF and G are uch that p repreent the lip at which C p mut be witched o a to get the maximum power output(due to the witching of C p ). The repone of a induction motor which ha experienced a load change from P initial to final at initial for all poible choice of the witching intant and the witching capacitor value can be undertood from thi augmented diagram hown in Fig 3. If the witching choice i uch that the correponding point lie outide the region HDCIEH, it i impoible to retore the tability of the machine. If we witch correponding to any point within the region CDF G, at the intant of witching the motor output will be greater than the load and the lip will be in the untable region of the motor characteritic. (We refer to the region with lip from 0 to maxpm of the pot witching characteritic a the table region and the lip greater than maxpm a the untable region). The rotor will accelerate and ultimately ettle in the table region a dictated by the final. If we chooe any point on the egment CD of the contour, then theoretically the rotor could ettle at the lip at the intant of witching without any additional dynamic. Since thi i an untable equilibrium point, if the Department of Electrical Engineering, Univ. College of Engg., Omania Univerity, Hyderabad,.P, INDI.

3 16th NTIONL POWER SYSTEMS CONFERENCE, 15th-17th DECEMER, capacitor i choen o that the witching point come inide the region, it will ultimately accelerate and ettle at it table equilibrium point. If the witching choice i uch that it fall either in the region DEF or G at the intant of witching, the machine will be in the table region with P eout >. Hence, it will accelerate for a hort time and ettle at the table equilibrium point. If the witching choice i uch that it fall within the region DEH or I, then at the intant of witching, the motor torque output will be le than the load and the machine being in the table region continue to decelerate and ultimately ettle at the table operating point(at a higher lip). Note that thee two region are outide the region determined by the relation (7). Hence the condition given by (7)(motor power load power at the intant of witching) i only a ufficient condition and not a neceary condition. Thi condition become a neceary condition if the lip at the intant of witching i greater than maxpm correponding to the pot witched condition. Hence, we ee that the condition for determining the magnitude of the capacitance turn out to be different depending on whether the lip at the intant of capacitor witching i leer than maxpm or otherwie. If the witching choice i uch that the correponding point lie either on egment DE or, then the witching lip will be the final lip at which the rotor will ettle and therefore there will be no additional dynamic due to the capacitor witching. For a particular pot diturbance final the following can be noted. ω C initial ω C 2 ( max,ω C 2max ) C ( critical,ω C critical ) E ( min,ω C 1min ) ω C 1 D 0 1 witch Fig. 2. Variation of ωc 1 and ωc 2 with witch for a particular pot diturbance ω C I G F C 1) If initial < witch < min, the value of ωc witch ha to be within the boundary ωc 1min ωc witch ωc 2max. Note that thi value i different from that obtained from (9). 2) If min < witch < max, then ωc witch hould be trictly greater than ωc 1 at witch and leer than or equal to ωc 2max (not the ωc 2 computed from (9)). 3) If max < witch < critical, then ωc witch hould be trictly greater than ωc 1 and trictly leer than ωc 2 at witch. 4) For witch > critical the talling of induction motor cannot be prevented by inertion of any value of capacitance. Fig. 3. E H D lip ωc V contour divided into different witching region For different value of final, contour imilar to that hown in the Fig 2/Fig 3 can be obtained. family of ωc V characteritic ha been obtained and hown in Fig 4. It can be oberved from the Fig 4 that for higher value of final, the region within the contour hrink. The lip critical occur at a lower value for higher value of final. Thi tudy of witching capacitance at variou lip, baed on the reult in Fig 2, 3 and 4 i extremely ueful in getting an inight into the proce of tabilization. Thi alo provide u the theoretical limit for the poible witching option, the bai for uch limit, a well a the nature of the pot witching tabilization proce. Fig. 4. ωc witch V witch contour for variou value of final Department of Electrical Engineering, Univ. College of Engg., Omania Univerity, Hyderabad,.P, INDI.

4 16th NTIONL POWER SYSTEMS CONFERENCE, 15th-17th DECEMER, III. NUMERICL RESULTS The actual choice of the witching trategy in a particular ituation ha to be made baed on the theoretical conideration dicued earlier; in addition, iue uch a the practical availability of the deigned capacitor ize, acceptable over voltage, limit on rate of acceleration/deceleration mut alo be taken into account. In thi ection, we illutrate the concept preented above conidering the ytem hown in the Fig 1. We chooe a particular value of final and obtain the ωc V contour imilar to that given in the Fig 3. Then we chooe variou witching option o a to have point from all the region of the C plane and obtain the dynamic behavior of the ytem and how how the general nature of thi dynamic behavior can be predicted baed on the location of the witching point in Fig 3. The initial operating condition of the ytem in the Fig 1 are given a follow. P e = , Q e = , V = , θ = , = The ytem parameter are given a follow [1]. E = 1.0, X e = 0.3, R r = 0.01 and X r = i uddenly increaed to 1.47 p.u. The ωc V contour CDE for final = 1.47 i obtained olving (9) for variou value of and i hown in the Fig 5. The value of critical, min, max, ωc 1min and ωc 2max are identified for thi final and marked in the diagram. The line DH and I are drawn parallel to the axi. The line G and F D are determined by finding the lip at which the maximum power occur conidering variou value of the witching capacitance between ωc 1min and ωc 2max. Thee line/contour divide the C plane to a number of region. One value of capacitance and lip from each of thee region i choen to undertand the dynamic due to thee capacitance-lip witching option. The capacitance value and the lip at which the capacitance are witched( witch ) are given in the Table I. Conider the witching capacitance and the witching lip correponding to the point 38 given in the Table I. The induction motor i increaed to 1.47 p.u at t = The witching capacitance correponding to the point 38 i 7.2 and the lip i The capacitor i inerted when the lip of the motor reache at t = The pre witching and pot witching V characteritic are given in the Fig 6. It can be een from the Fig 5 that the point 38 lie in the region CDF G of the contour. It can be een from the Fig 6 that at the intant of witching, = which i greater than 1.47 at witch = 0.075, and it lie in the untable region of the motor V characteritic. Since the at witch i greater than 1.47, the motor will accelerate. The final ettling point i at a lip of which i the interecting point of the motor V characteritic and the load V characteritic correponding to = 1.47 in the table region of the motor characteritic a evident from the Fig 6. ll thee feature can be qualitatively predicted by oberving that the point 38 lie inide the contour. To tudy the dynamic of the rotor due to capacitor witching, the variation of the lip of the induction motor with time for thi witching option ha been obtained and i given in Fig 7. It can be oberved from the Fig 7 that a oon a the initial load i increaed, the lip tart increaing. When the capacitor i witched, at t = , the lip tart decreaing at a lower rate. However, after t = 0.45, the lip tart decreaing at a fater rate, croe = , which i the lip at the maximum for thi value of witched capacitance and ettle down at a lip of at t = We have tudied the impact of witching the capacitance for each of the 25 point marked in the C plane in Fig 5 in the imilar manner. The ummary of the impact of witching each of the capacitance value at their repective witching lip i given in the Table I. For each cae, mot of the qualitative and quantitative apect of the pot witching behavior are tabulated in Table I. From the reult in Table I, it i eay to ee that the predicted pot witching behavior baed on Fig 3 in the ection II i actually realized. ω C 9 8 I G 3 F 2 E min = ω C 1min = max = ω C 2max = critical = ω C 1 =ω C 2 = D H lip Fig. 5. ωc V characteritic for final = 1.47p.u at t = (0.0457,1.6978) (0.0266,1.47) (0.0278,1.3883) = lip (0.075,1.4952) (0.075,0.8792) pre witching characteritic 36 C = 1.47 Fig. 6. Induction motor V characteritic for ωc = 7.2 IV. EXTENSION TO PRCTICL SITUTIONS The procedure preented in the lat ection to determine the capacitance to be inerted conidering a imple equivalent Department of Electrical Engineering, Univ. College of Engg., Omania Univerity, Hyderabad,.P, INDI.

5 16th NTIONL POWER SYSTEMS CONFERENCE, 15th-17th DECEMER, TLE I SUMMRY OF CPCITOR SWITCHING FOR THE POINTS ON THE CONTOUR IN THE FIG 5 Point ωc witch Contour region witch Pm at witch Pmmax maxpm witch po final Rotor dyn On the egment Leer 0.02 NC I Leer Dec On the egment DE Leer 0.02 NC outide the contour Leer untable 15 4 CDF G Greater cc DEF Leer cc 17 6 G Leer cc outide the contour Leer untable On the egment Leer 0.04 NC outide the contour Leer untable On the egment CD Greater 0.04/ cc outide the contour Greater untable 25 4 CDF G Greater cc G Leer cc outide the contour Greater untable I Leer Dec On the egment CD Greater 0.075/ cc 32 8 outide the contour Greater untable On the egment CD Greater 0.075/ cc outide the contour Greater untable 35 5 CDF G Greater cc outide the contour Greater untable outide the contour Greater untable CDF G Greater cc DEH Leer Dec -:For 23, 31 and 33 ideally final = witch. ut the motor will accelerate and ettle in the table region due to mall diturbance witch po-: witch poition, whether witch i greater than or equal to or leer than maxpm final -: final ettling lip(if it exit) Rotor dyn-: rotor dynamic, cc-:ccelerate, Dec-:Decelerate, NC-:No change lip time() Fig. 7. Variation of lip with time for witching ωc = 7.2 at t = circuit of the induction motor can be extended to a more general etting. Conider the Fig 8(), which i a chematic of a large ytem. n induction motor connected to one of the bue a hown in the Fig 8() i conidered here. The induction motor in the Fig 8() i repreented by it complete equivalent circuit hown in Fig 8(C) which can be replaced by an exact equivalent a hown in the Fig 8(D) which i determined a the impedance of the motor een from. In Fig 8(D), R e + jx e = jx m lel( R r + jx r) = jr rx m X m X r R r + jx m + jx r (10) The ret of the ytem in Fig 8() i replaced by it Thevenin equivalent circuit a hown in the Fig 8() where E th -:repreent the Thevenin voltage at the induction motor bu without the motor. Z th -:equivalent impedance of the ytem een from the induction motor bu including all the load(treated a impedance) Z IM -:induction motor equivalent impedance. Z IM = R + R e () + j(x + X e ()). It i eay to ee that at any lip 1 (R e ) V 2 = 1 1 (R + R e ) 2 + (X + X e ) 2 (11) The lip at the intant of capacitor witching i aumed to be known and hence V can be calculated from (11). The circuit in the Fig 8() i imilar to that in the Fig 1. So an equation imilar to (9) can be ued to determine the range of capacitance by making the appropriate change. Thi approach ha an implicit aumption that the power ytem load are linear. The accuracy of the computed range of capacitance depend on the validity of thi aumption. If the ytem load are highly nonlinear, the computed range could be conidered a only a reaonable approximation. V. CONCLUSIONS Switching the capacitor at the induction motor terminal i a known method of preventing the talling of induction motor following a udden load increae. Reult in thi paper help u to undertand all apect of thi phenomenon. In addition to providing inight into the bai of capacitor election, it alo can be ued a a practical method to chooe the value of the capacitor a well a it intant of witching. Even though mot of the concept are developed conidering a mall ample ytem, it i demontrated in thi paper that thee can be extended to induction motor working a a part of a large ytem. REFERENCES [1] Yauji Sekine and Hirohi Ohtuki, Cacaded Voltage Collape, IEEE tranaction on Power Sytem, Vol 5, No 1, February 1990, pp Department of Electrical Engineering, Univ. College of Engg., Omania Univerity, Hyderabad,.P, INDI.

6 16th NTIONL POWER SYSTEMS CONFERENCE, 15th-17th DECEMER, V R I (C) SYSTEM () jx jx m jx r IM R r I r ( ) R j X + X e( ) + R () e V I E th X th (D) () Z im Fig. 8. () general power ytem containing an induction motor load ()Thevenin equivalent of the circuit in the Fig () een from into the ytem (C)The actual equivalent circuit of the induction motor(d)the equivalent circuit of the induction motor een from. [2] D. H. Popovic, I.. Hiken and D. J. Hill, Stability nalyi of Induction Motor Network, Electric Power and Energy Sytem, Vol 20, No 7, 1998, pp [3]. E. Hammad and M. Z. El-Sadek, Prevention of Tranient Voltage Intabilitie due to Induction Motor Load by Static VR Compenator, IEEE Tranaction on Power Sytem, Vol 4, No 3, ugut 1989, pp [4] C. W. Taylor, Power Sytem Voltage Stability, McGraw-Hill, [5]. Kurita and T. Sakurai, The Power Sytem Failure on July 23, 1987 in Tokyo, Proceeding of the 27th IEEE conference on Deciion and Control, utin, Texa, December 1988, pp [6] M. K. Pal, ement of Corrective Meaure for Voltage Stability Conidering Load Dynamic, Electric Power and Energy Sytem, Vol 17, No 5, 1995, pp [7] W. Xu, Y. Manour and P. G. Harrington. Planning Methodologie for Voltage Stability Limited Power Sytem, International Journal of Electrical Power and Energy Sytem, Vol 15(4), 1993, pp Department of Electrical Engineering, Univ. College of Engg., Omania Univerity, Hyderabad,.P, INDI.