CONSTRUCTION OF GENERATOR CAPABILITY CURVES USING THE NEW METHOD FOR DETERMINATION OF POTIER REACTANCE M.M. Kostić *, M. Ivanović *, B. Kostić *, S. Ilić** and D. Ćirić** Electrical Engineering Institute Nikola Tesla, Belgrade, SERBIA* TPPs-OCMs "Kostolac", Kostolac, SERBIA ** Abstract: The most important objective of this paper is the fact that it enables the capability curve (P-Q curve) of generator to be determined only on the base of the results of the no-load and reactive load examinations held in the power plant. First, the values (dependences) of the Potier reactance (X P ) in the area of the relevant values of reactive loads are determined, and then according to those results the capability curve (P G -Q G curve) of the generator is being constructed. This method is verified for experimental modes of active and reactive power around the nominal values, on the example of turbogenerator 348 MW in power plant "Kostolac B". It is important that the significant discrepancies in relation to the P-Q curve of the drive manufacturer's documentation generator were established, and thereby the recommendations for defining (or testing) the P-Q curve in the period of times, every 5-6 years or after major repairs. Similar discrepancies were obtained during the extensive testing and research for newer generators in U.S. Key words: capability curve of generator, Potier reactance, inductive load test (at zero power factor), no-load test, short circuit test. 1. INTRODUCTION Capability curvess, P G -Q G curve, Figure 1, are necessary to the operating stuff for the proper selection of the generator's load. These curves define the limits of reactive power modes Q G Q G,N (Mvar) during operation of generators with a nominal or reduced the active power P G P G,N (MW), while at the same temperature and excitation currents do not exceed allowable limits. Thus, the elevated reactive power for 1% brings to the rotor winding overheating by 2% when it comes to new generators with saturated magnetic circuit. Therefore, it is important to dispose of as accurate P G -Q G curves, both for operation and planning. The most important part of the curve is the part with coordinates (Q G Q G,N, P G P G,N ), because it defines the modes when the generator is running with increased reactive power.
It is not unknown that, with certainty, the drive charts (P G -Q G curves), which are found in the manufacturer, can not be accepted. An additional difficulty is that, during the years of work, it comes inevitably to minor or major changes in the parameters of generators that are relevant for the definition of P-Q curves. Therefore, it is common in the period of exploitation to define or test P-Q curves periodically, every 6-7 years or after major repairs. Significant discrepancies of capability curves, compared to those given by manufacturers, were obtained during the extensive testing and research for newer generators in U.S., [1, 2], Figure 1. Figure 1: Comparison chart of actual capability curves (P-Q curves) with the manufacturer's generator capability curves 2. BASIC PRINCIPLES FOR THE DESIGN OF CAPABILITY CURVE 2.1. Capability curve of generator with unsaturated magnetic circuit The basis for designing the capability curve (P-Q curve) is a vector diagram of generator electromotive forces, Figure 2. When constructing a vector diagram, Figure 2, resistance of the generator inductor winding is ignored and the saturation of magnetic circuits is being neglected as well. For the unsaturated machine, vector diagram of generator electromotive forces represents also (with corresponding scaling ratio) the vector diagram of generator excitation currents. When the generator is connected to a strong network (unlimited power), the voltage on the generator connections remains constant (u = u n = 1 = Const.). It is further assumed that the generator is loaded with a nominal current (i = i n = 1 = Const.) while the current phase position (φ) changes
and thus change the corresponding values of active (p) and reactive (q) power, in relative units of apparent power (s n = u n, i = 1 ). Figure 2: Vector diagram of generator electromotive forces (and the excitation currents) Generator is sized in a way to reach the nominal temperature at the rated values of active (p n ) and reactive (q n ) powers, the point R on Figure 2. Although the stator winding retains the nominal value of temperature for all induct currents, i a = i an = 1 = Const., the generator will not be able to work with rated induct current when the current phase increases (φ > φ n ) so that the active power decreases and reactive power increases. Namely, the excitation current then begins to exceed the nominal excitation current, i.e. i a = Const. curve is above the curve i f = Const., Figure 2. As the value of excitation current in the nominal mode, as a rule, is also the maximal allowed value of the current (i fmax = i fn = Const.), allowable values of reactive power increase more slowly than in the case when there are no limitations on excitation current. Curve i f = Const., from the point (R), defines the limits of reactive power modes, q q R (), in work of the generator with a nominal or reduced active power p p R (), while not allowing to current (and temperature) of excitation winding to exceed the allowable value. The neglect of saturation of magnetic circuit enters an error, which is even greater when the mentioned generator is more saturated. When it comes to modern large power generators (300-800 MW), its magnetic circuit is so saturated that the construction of more accurate vector diagrams, such as one on Figure 2, and the corresponding chart drive requires extensive testing with measurements and (or) complicated calculations of electric forces, Figure 2. 2.2. Capability curve of generator with saturated magnetic circuit When it comes to vector diagrams of excitation currents of generator with saturated magnetic circuit, it is necessary:
- to use the curve of saturated machine, which is derived from no-load test, but also - to include additional magnetic circuit saturation on the part of the rotor of loaded machine. It is particularly difficult to quantify the second impact. Some authors do this by using data on values of longitudinal synchronous reactance in saturated mode (x d,sat < x d ), while others introduce Potier reactance (x P > x l ) instead of the stator leakage reactance (x l ). By Potier method, reffered influence of additional saturation of the rotor magnetic circuit is counted by an increase of stator leakage reactance (x l ), so as x P > x l and the corresponding electromotive force behind Potier reactance e P = u+x P i>u+x l i = e l, i.e. it is greater than electromotive force behind the leakage reactance, Figure 3. Figure 3: Magnetization curves, in no-load mode i f0 (e) = i f0 (e P ) and at loaded machine i fl (e l ); vector diagrams of electromotive forces behind Potier reactance (e P ) and behind the leakage reactance (e l ); vector diagrams of excitation currents: i fp i fl, i fa,n = x d - x P and i fr = i fp + i fa,n ; saturation components Δi f (e P ) = Δi fu + Δi fs + Δi fr Qualitative view of the impact (increase) component of saturation current Δi f (e P ) = Δi fu + Δi fs + Δi fr (Figure 3) is presented on Figure 4. Component of saturation excitation current is counted in a way that starting point of a vector diagram moves down the value of Δi f (e P ). Since the length of the excitation current vector is constant (i fi = Const.), and the mentioned starting point is changed (points C R, C 1, C 2 and C M ), the corresponding arches i fi = Const. are moved down as well. Thus, for purely reactive load (p = 0), instead of point q' M, point q M with less reactive power q M < q' M is obtained (q' M - corresponding reactive for power generator with saturated magnetic circuit).
Figure 4: Diagrams of electromotive forces and excitation currents for generator with saturated magnetic circuit 3. DETERMINATION OF POTIER REACTANCE FOR TURBOGENERATORS The results of numerous investigations [5-10] confirm the fact that Potier reactance, considered as a constant parameter values, is not suitable for calculations and analysis of synchronous machines in a wider range of generator voltage, and even in the range of real change of generator electromotive forces (E p or E l ). This means that for accurate calculations and capability curve construction, values of Potier reactance (x P ) for examined regimes should be obtained (or defined). This means that it is necessary to determine the dependence of this reactance for the required regimes, for example x P (u,q). 3.1. Determination of Potier reactance for turbogenerators in relevant regimes At equal values of reactive power (Q G ) in any operating mode and inductive load mode of generator (Q G = Q Gi,cosφ = 0 ), the corresponding values of generator voltage are also practically equal U Gi = U G,cosφ=0. On this basis, as has been shown [12, 13], the conclusion about approximate equality of the appropriate values of Potier reactances (x p,i = x p,cosφ=0 ): x p,i = x p,cosφ=0, for Q Gi = Q G,cosφ=0
Hereby, for a particular generator and the corresponding regime of generator voltage U Gi = f u (Q G ), dependence of Potier reactance x p = f(q G,U G ) is reduced to uniform dependence x p = f(q G ), for the (approximately) constant voltage at the point of connection to the electric power system. U EES = Const. It provides that, instead of family P-Q curves, the appropriate (unambiguous) P/Q dependence, for the voltage at the point of connection to the electric power system, should be used. By this way defined value of Potier reactance for nominal mode, is approximately equal to x P90, fot the reactive load mode with current i = i an sinφ n (u = u n, i = i an sinφ n and φ = 90 0 ), i.e.: x P,n x P90, for i 90 = i an sinφ n (1) This means that the obtained values (dependences) of Potier reactance from the inductive load tests could be used to design the appropriate capability chart for the very same generator [13, 14]. The specified rule was tested on the example of mentioned generator GTHW 360 (360 MW) in the nominal regime, i.e. by comparison of [13]: - measured values for the generator excitation current regimes around the nominal (P G P Gn, and Q G Q Gn ), and - calculated values based on the same value of Potier reactances (x P ), defined for Q G Q Gn. Calculated values of excitation current (I F ) differ by about 0.4% which is within the limits of accuracy of the measured values of excitation current (I F ). It is expected that the accuracy is higher in the area of higher values of reactive power, as appropriate (allowed) active power is less, so those regimes are less different from referent regimes for reactive loads for which the valuse of Potier reactances are determined. Based on this and equality (1), it comes to the more general equality [13]: x P x P90, for i 90 = i a sinφ n (2) 3.2. Determination of values (dependences) of Potier reactance from the induction load tests Values (dependances) of Potier reactance are determined from the induction load test for relevant values of the load. The entire process is automated and conducted on the computer (the "Excel"), by a new method for determining the value of Potier reactance [11]. Sometimes manufacturer's parameters of the machine are not reliable data. In order to verify this, no-load and short circuit tests were carried out. From no-load test the corresponding dependence i 0 (e 0 ) was obtained, and it was found that the values of excitation current in no-load regime (I f0 ) and excitation in air-gap (I fg ), are somewhat different from those obtained from the manufacture. Thus: - measured values are I f0 =807 A and I fg = 677 A, while - values from manufacturer's data are I f0 =818 A and I fg = 703 A. In the short circuit test the value of direct-axis synchronous reactance was determined, x d,mer = 2.535, which significantly differs from the value provided by manufacturer, x d,manuf = 2.347.
The functin of Potier reactance x p = f(q G, U G ), for tested generator GTHW 360, 348 MW [14], is given in the Table 1 for wider range of reactive powers. Besides the relative values of reactive powers (Q G /Q G,N ) i voltages (U G /U G,N ), there are presented their absolute values as well (Q G, U G ). Namely, the calculation of specific valuse of Potier reactance (x p ), for this generator, the absolute values of reactive power (Q G ) and voltage (U G ) are competent, i.e. the corresponding pair of values Q Gi, U Gi. The aforementioned calculations were conducted for the nominal apparent power generator S G,N = 410 MVA and cosφ GN = 0.85, and for the most active power P G,N = 348.5 MW and the corresponding reactive power Q G,N = 216 Mvar. Table 1: Values of Potier reactance x p, i.e. x p,i (Q G ) = x p,cosφ=0 (Q G ), for given values Q G [Mvar], U G [kv] and S G,N = 410 MVA QG QG U G U G Q G x p QG, N SG, N U G, N kv Mvar 0.6 0.3161 1.0242 22.532 129.6 0.297 0.8 0.4215 1.0390 22.858 172.2 0.284 1.00 0.5268 1.0538 23.184 216.0 0.273 1.05 0.5531 1.0574 23.263 226.8 0.270 1.10 0.5795 1.0611 23.344 237.6 0.268 1.15 0.6058 1.0648 23.426 248.4 0.266 1.20 0.6321 1.0685 23.507 259.2 0.264 1.25 0.6585 1.0722 23.588 270.0 0.262 1.30 0.6848 1.0759 23.670 280.8 0.260 1.35 0.7112 1.0796 23.751 291.6 0.259 1.40 0.7375 1.0833 23.833 302.4 0.258 1.45 0.7638 1.0870 23.914 313.2 0.257 In Figure 5 is given a graphical representation of dependence of Potier reactance, x p,i (Q G ). The Potier reactance values (x p ), for generator GTH-360 are changing in the wider limits when reactive power changes. These values decrease with increase in load, but Potier reactance value can not become equal to the leakage reactance (x l = 0.188) as it is stated in the literature - it is rather x p,min x l 1.1 1.15, Figure 5.
x [r.j.] 0.40 0.36 0.32 x P 0.28 0.24 0.20 x l 0.16 0.12 0.08 0.04 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Q G /Q G,N [r.j.] Figure 5: Dependance of Potier reactance for generator GTH-360 from reactive power, x p,i (Q G ), and comparative illustration with leakage reactance values (x l = 0.188) 4. CONSTRUCTION OF GENERATOR CAPABILITY CURVE If one has the exact Potier reactance values for all investigated regimes, it would be possible to construct more accurate vector diagram and the corresponding capability curve, Figure 4. The point is to calculate, for given characteristics of the regime and the corresponding value of Potier reactance, the value of excitation current, i.e. to calculate, for given (nominal) value of excitation current (i fn ) and given value of active power (p i ), the appropriate value of allowable reactive power (q i ). Corresponding values of actve power (P Gi ) are determined by calculations, whereby the independent ariable takes the value of reactive load Q Gi Q Gi,cosφ 0. The calculations are carried out for the relevant (and changing) value of Potier reactance for the corresponding (given) value of generator reactive load (Q Gi ). 4.1. Determination of P-Q curve by a new mathod The values of excitation current, for previously determined values of Potier reactance (x p ), Table 1, ' can be calculated using the following expression which is derived from a right triangle OF R F R (Figure 3): i fr i ( x x )(s / u )(sin cos cos sin ) 2 ( x x ) (cos cos sin sin ) 2 fp d P (3) d P
Values cosδ, sinδ and i fp are calculated for the parameters in given regimes s = S/S n = 1, p = P n /S n = cosφ, q = Q/S n = sinφ and u = U/U n = 1. Values i fl (e p ) are determined by the observed dependence i f0 (e), for e = e p. The stated dependence i f0 (e) is given in analytical form, so the complete procedure for calculating the value of i f (or i f,n ) is automated and operated by PC. Table 2 gives a tabulation of the proceedings and results of calculations according to P-Q curve of the generator GTH-360, TE "Kostolac B" (Block B1), for currently defined maximal allowed value of excitation current I f,max = 2550 A. The calculation is carried out for given values x p = f(q G ), Table 1. The calculation procedure performed in the following way: - the values of reactive loads Q Gi Q Gi,cosφ 0 were taken as independent variables, and - the corresponding values of active power (P Gi ) were determined by calculation (3). This way, as the active power changes for given reactive power (Q G ), values cosδ and sinδ (3) are also changed (and automatically calculated). The target value of maximum active power P Gi,max = P Gi is the one for which the value of excitation current is I f,max = 2550 A. The stated equation (3) is solved numerically by PC: more precisely, the increase (or variation of assumed) values of active power (P Gi ) causes the change of the excitation current value (I f ), so the calculatin can be considered to be finished in iteration in which it becomes I f I f,max. It is obvious that this is a new procedure for determining the capability diagram (P-Q dependence). The above calculations of P-Q curve are carried out for generator nominal apparent power S G,N = 410 MVA and cosφ GN = 0.85, as for the most active power P G,N = 348.5 MW and the corresponding value of reactive power Q G,N = 216 Mvar, for which the value of excitation current I fn 2550 A is determined by measurements. Afterwards, values of reactive power were increased, in steps of ΔQ G = 0.05Q G,N, i.e. a range of values of generator reactive power was formed: Q G,i = 1.00Q G,N ; 1.05Q G,N ; 1.10Q G,N ; 1.15Q G,N ; 1.20Q G,N ; 1.25Q G,N ; 1.30Q G,N ; 1.35Q G,N. The corresponding (reduced) values of the active power were established by calculations, for a given value of excitation current I f1,max = 2550A. The series of corresponding values of reactive and active power were obtained, in absolute values, and they were given in Table 2. With further increase of reactive power, for example to the value Q G,i = 1.40Q G,N, the value of excitation current would be I f1,max > 2550 A also for P G,i = 0, so the (computational) test was conducted for a small increase in reactive power, the last three rows in Table 2. Table 2: Tabulation of the proceedings and results of calculations P-Q dependence for the generator GTH- 360, for the values of excitation current I f1,max = 2550 A. x p U kv u=j δo j o P MW Q Mvar S MVA p q s i f,calc I f,calc A 0.273 23.183 1.05376 1.3221 348.5 216 410.01 0.85 0.5268 1.00002 3.7696 2552 0.27 23.264 1.05744 1.3332 328 226.8 398.78 0.8 0.5532 0.97262 3.7691 2551.7 0.268 23.345 1.06113 1.3445 305 237.6 386.62 0.7439 0.5795 0.94299 3.7708 2552.8 0.266 23.426 1.06482 1.3559 278 248.4 372.81 0.678 0.6059 0.90929 3.769 2551.6 0.264 23.507 1.06851 1.3675 248 259.2 358.73 0.6049 0.6322 0.87496 3.7704 2552.6
0.262 23.588 1.0722 1.3793 212 270 343.28 0.5171 0.6585 0.83728 3.7708 2552.9 0.26 23.669 1.07588 1.3912 166 280.8 326.2 0.4049 0.6849 0.7956 3.7699 2552.2 0.259 23.751 1.07957 1.4033 95 291.6 306.68 0.2317 0.7112 0.74801 3.7698 2552.2 0.259 23.77 1.08046 1.4062 66 294.2 301.51 0.161 0.7176 0.7354 3.7701 2552.3 0.259 23.782 1.081 1.4081 33 295.8 297.64 0.0805 0.7215 0.72594 3.7681 2551 0.2585 23.788 1.08128 1.409 0 296.6 296.6 0 0.7234 0.72341 3.7683 2551.2 4.2. Capability curve (P-Q curve) of the generator The above dependence in Table 2 is presented in a format that is used as an capability diagram of the generator, in the form of tabular P-Q dependences. Thus, based on data obtained from Table 2 the corresponding P-Q dependence is obtained, Table 3. Table 3: Capability diagram generator for GTH - 360, P-Q spreadsheet dependency, for i f1,max = 2550 A Q G,i /Q G,N () 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.362 1.369 1.373 Q G,i (Mvar) 216.0 226.8 237.6 248.4 259.2 270.0 280.8 291.6 294.2 295.8 296.6 P G,i (MW) 348.0 328.0 305.0 278.0 248.0 212.0 166.0 95.0 66.0 33.0 0.0 It has been established that manufacturer's P-Q curve for generator GTH 360, for a reduced active power: 250 MW (or P G = 0.71P G,N ), 200 MW (P G = 0.581P G,N ) and 50 MW (or P G 0.20P G,N ), gives, respectively, overestimated the value of reactive power by 2%, 4% and 6%. Therefore, it is usual in the period of exploitation, every 6-7 years or after major repairs, to test (or check) the generator P-Q curves. Similar discrepancies were obtained during the extensive testing and research for newer generators in the U.S. [3, 4]. On Figure 6, in addition to the capability diagram of the manufacturer's documentation (-), the capability diagram for generator GTHW-360 is drawn, based on data obtained from the results of the corresponding calculations (- - -). Figure 6: Capability diagrams for generator GTHW-360: curve from manufacturer's documentation ( ) significantly deviates from the curve obtained during tests (- - -)
5. CONCLUSION The most important conclusion in this paper is that it allows to determine the P-Q curve generator according to a new method - more precisely on the basis of test results at no load and reactive load tests carried out in the plant. First, the values (dependences) of Potier reactance within the limits of the relevant values of reactive loads are determined, and then on the base of those, the P-Q curve of the generator can be constructed. This method is verified experimentally, on the example of turbogenerator with nominal power of 348 MW, in the power plant "Kostolac B" [14], for the two modes with the active and reactive power around nominal values. It is significant that noticeable deviations were established, comparing the P-Q curves from manufacturer's documentation and those which are obtained during experiments. This confirms the justification for the recommendation to experimentally test (or check) the generator P-Q curves from time to time, every 5-6 years or after major repairs. Similar discrepancies were obtained during the extensive testing and research for newer generators in the U.S. [1, 2]. 6. LITERATURE [1] N. E. Nilsson, J. Mersurio, "Synchronous Generator Capability Curve Testing and Evolution", IEEE Tran. Power Deliv. and Systems, V. No. 2 January 1994, pp. 414-424. [2] M.M.Adibi, D.P.Milanovic, "Reactive Capability Limitation of Synchronous Machines", IEEE Tran. Power Delivery and Systems, Vol. 9, No. 1 January 1994, pp. 29-40. [3] Standard IEC 34-4/1985, "ROTATION ELECTRICAL MACHINES", Part 4: Methods for determining synchronous machine quantities from tests". [4] Al, "Transmission and distribution "- Manual, Chapter "Characteristics of Machine" pp. 149-198, Translation, Građevinska knjiga Beograd, 1964.. [5] M. P. Kostenko, L. M. Piotrobskij,, "Električeskie mašini", str. 648, "Energija", Leningrad 1973 (in Russian). [6] A. M. El-Serafi, J.Wu, "A New Method For Determining The Armature Leakage Reactance of Synchronous Machines", IEEE Transc. on Energy Conversion,Vol. 6, No. 1, March 1991, pp. 120-125. [7] Ion Boldea, "Synchronous Generators - The Electric Generator Handbook", pp. 512, 2006 by Taylor &Francis Group, Boca Raton London New York, 2006. [8] A.E. Fitzgerald, Charles Kingsley, "Electrical machines", Naučna knjiga Beograd, 1962. god, page 560. (Serbian translation). [9] A. Ivanov-Smolensky, "Electrical Machines, Vol. 2", pp. 464, 1988, Publishers Moscow. [10] S. H. Minnich, SM; R. P. Schulz, SM; D. H. Baker, SM; "Saturation Functions for Synchronous Generators From Finite Elements", IEEE Transc. on Energy Conversion, Vol. EC-2, No. 4, December 1987, pp. 680-692. [11] M.M.Kostić, "A new method for determining the Potier reactance of synchronous turbogenerator", "Elektroprivreda", No 4, 2009, pp. 59-68. (in Serbian) [12] M.M.Kostić, "A new rule for determining the Potier reactance for synchronous turbogenerators relevant loads", "Elektroprivreda", No 3, 2010, (in Serbian) [13] M.M.Kostic, "Proposal for addition of IEC 34-4 Standard in part for determination of Potier reactance", "Power Plant 2010", Proceeding [14] The study "Determination of regulation, power losses and the actual diagram of active and reactive power (PQ curve generator) of blocks B1 and B2 in the power plant Kostolac B", Electrical Engineering Institute Nikola Tesla, Belgrade 2008, page 58, in Serbian
[15] The parameters and results of the generator Block 1 in the power plant "Kostolac B" KONSTRUISANJE POGONSKIH DIJAGRAMA GENERATORA POMOĆU NOVE METODE ZA ODREĐIVANJE POTJEOVE REAKTANSE M.M. Kostić *, M. Ivanović *, B. Kostić *, S. Ilić** i D. Ćirić** Elektrotehnički institut Nikola Tesla, Beograd, Srbija* PD Termoelektrane i kopovi Kostolac, Kostolac, Srbija ** Kratak sadržaj: Najvažniji rezultat rada je u tome da omogućava da se pogonski dijagram (P-Q kriva) generatora odredi samo na osnovu rezultata ispitivanja u praznom hodu i ogleda reaktivnog opterećenja koji se sprovode u elektrani. Prvo se utvrde vrednosti (zavisnosti) Potjeove reaktanse (x P ) u području relevantnih vrednosti reaktivnih opterećenja, pa se na osnovu istih konstruiše pogonski dijagram (P G -Q G kriva) generatora. Taj metod je, na primeru turbogeneratora snage 348 MW u Termoelektrani "Kostolac B", proveren eksperimentalnim putem za režime rada sa aktivnim i reaktivnim snagama oko nominalnih vrednosti. Značajno je da su utvrđena i značajnija odstupanja, u odnosu na P-Q krivu iz pogonske dokumentacuje proizvođača generatora, pa je time potvrđena opravdanost preporuke da se u periodu eksploatacije povremeno, na svakih 5-6 godina ili posle većih remonata, ispitivanjima određuju (ili proveravaju) P-Q krive generatora. Slična odstupanja su dobijena i tokom opsežnih ispitivanja i istraživanja za novije generatore u SAD. Ključne reči: pogonski dijagram generatora, Potjeova reaktansa, ogled reaktivnog opterećenja, ogled praznog hoda, ogled kratkog spoja.