PROPOSAL FOR ADDITION OF IEC 34-4 STANDARD IN PART FOR DETERMINATION OF POTIER REACTANCE

PROPOSAL FOR ADDITION OF IEC 34-4 STANDARD IN PART FOR DETERMINATION OF POTIER REACTANCE M. M. Kostic * Electrical Engeneering Institute Nikola Tesla, Belgrade, SERBIA* Abstract: On the base of ones investigations results author comes to new conclusion: that the Potier reactance values depend almost only from of turbogenerators reactive currents (i aq = i an sinφ), for given voltage values. This new rule is prove by general qualitative analysis, and then it is checking for the region about rated values active and reactive power, on the example of the considering turbogenerator GTHW 360 (360 MW). Potier reactance values (x P ) are determined with sufficiently accuracy by new method which is published recently by this author. It proposes change of corresponding standard IEC 34-4/1985: ROTATION ELECTRICAL MACHINES, Part 4: Methods for determining synchronous machine quantities from tests, in the part for determination of the Potier reactance. It is proposed that it determined by of the excitation current corresponding to the rated voltage and armature current value i = i an sinφ n, at zero-power factor (overexcitation), and for some characteristic values which would be convenient for construction of turbogenerator capable curve (P-Q curve). Key words: turbogenerator, rotor saturation, leakage reactance, Potier reactance, excitation current, reactive load test, capable curve. 1. INTRODUCTION The excitation (field) current required operating the SG at rated steady-state active power, power factor, and voltage is a paramount factor in the thermal design of a machine. To determine the excitation current under specified load conditions, the Potier reactance X p (or leakage reactance X l ), the unsaturated d and q reactance X du and X qu, armature resistance R a, and the open-circuit saturation curve e 0 (i f ) are needed. Methods for determining the Potier reactance is especially important. It takes into account the additional of the field winding on load and in the overexcited region and is greater than real value of the armature leakage reactance (X p > X l ). The accurate determination of the armature leakage reactance of synchronous machines is essential for the analysis of these machines [l-5]. Although numerical techniques for calculating this

reactance have been suggested in the literature, there has not been a practical method for determining its accurate value experimentally owing to the fact that it is difficult to measure the armature leakage flux directly [6, 7]. For experimental machines, search coils inserted in the air gaps of the machines have been used to detect this leakage flux [5]. In general, the armature leakage reactance is usually approximated by the Potier reactance measured at rated terminal voltage [8, 9]. However, the values of the Potier reactance of synchronous machines measured at rated terminal voltage could be much larger than those of the armature leakage reactances [1, 10]. By ours investigation [11] it is confirmed that the discrepancies between the values of the Potier reactance and the armature leakage reactance of four synchronous machines could be as high as 50%. Recent investigations on experimental synchronous machines have also resulted in the same observation [l2]. Instead of measuring the Potier reactance at rated terminal voltage, March and Crary proposed [l] that measuring the Potier reactance at a higher value of the terminal voltage could result in a more accurate value of the armature leakage reactance. However, the application of this method is difficult since the machine under test may not be able to stand the high values of the field current at which the armature leakage reactance is well approximated by the Potier reactance. In order to obtain more accurate values of the armature leakage reactance without any risk to the machines under test, an alternative method is proposed [l]. However, that it is more important to establish the Potier reactance real values then the accurate values of the armature leakage reactance, one can to be shown on the base of the following facts: 1. Leakage reactance X l is nearly independent of the saturation of the magnetic circuit and is therefore assumed to be a constant. 2. The saturation curve of the synchronous generator under load conditions is assumed to be the same as the open-circuit characteristics. According to this assumption, the field leakage flux is assumed to have the same effect under load conditions as it has at no-load. Any error introduced by the use of the open-circuit characteristic is empirically compensated for by use of the Potier reactance (X p >X l ). 3. The field MMF equivalent to the armature MMF and component corresponding of field current (I af ) can be found from unsaturated armature reactance (X a ). 4. The air gap is assumed to be uniform so that the direct-axis synchronous reactance X d is equal to the quadrature axis synchronous reactance X q. For nonsalient-pole synchronous machine (turbogenerator), practically X d = X q. The unsaturated direct-axis synchronous reactance is calculated by equation X du = X a + X l. In numerous investigations [1, 6, 10, l5] one is shown that Potier reactance values depends from of the terminal voltage values. In addition to, on the base ours investigations [l2, 13] it is shown that the Potier reactance depends essentially and from reactive load values, for the given voltage value.

It have been reason that, in this paper, is proposed change and addition of the Standard IEC 34-4/1985, in part for determination of Potier reactance [9], which is presented in Appendix 1. 2. THE POTIER REACTANCE DEPENDENCE FROM (REACTIVE) LOADS An equivalent reactance used in place of the armature leakage reactance to calculate the excitation on load by means of the Potier methods. It takes into account the additional of the field winding on load and in the overexcited region and is greater than real value of the armature leakage reactance. At rated voltage tests, the Potier reactance X p may be larger than the actual leakage reactance by as much as 20 to 30% [l5]. By ours investigation [l2] it is confirmed that the discrepancies between the values of the Potier reactance and the armature leakage reactance of four synchronous machines could be as high as 50%. About a half mentioned increasing origins from (reactive) load values, for the given voltage value. Namely, the additional leakage flux of the field winding on load, in the overexcited region, leads additionally increasing Potier reactance X p. It have been reason that, in this paper, is proposed change and addition of the Standard IEC 34-4/1985, "ROTATION ELECTRICAL MACHINES, Part 4: Methods for determining synchronous machine quantities from tests" in part for determination of Potier reactance [9]. One is proposed that X p it determines by of the excitation current corresponding to the rated voltage and armature current value i = i an sinφ n, at zero-power factor (overexcitation), and for some characteristic values which would be convenient for construction of turbogenerator capable curve (P-Q curve). Namely, on the base of ones investigations results [13] author comes to new conclusion: that the Potier reactance values depend practically only from of turbogenerator reactive currents (i aq = i an sinφ), for given voltage values. This new rule is proved: a) first, by qualitative analysis, and b) then it is checking on the example of the considering turbogenerator GTHW 360 (360 MW), for the region of active and reactive loads relevant values [12, 13]. Potier reactance values (x p ) are determined with sufficiently accuracy by new method which is published recently by this author [14]. Standard graphical method is used for determination of Potier reactance [9], which is presented in Appendix 1 (Figures A1 and A2), by the following data: a) from the no-load saturation and sustained three-phase short-circuit characteristics, and b) of the excitation current corresponding to the rated voltage and rated armature current at zero power-factor (overexcitation). If, during overexcitation test at zero power-factor, the voltage and current differs from rated value by not more then ± 0.15 per unit, a graphical method is used for the determination of the excitation current corresponding to the rated voltage and current [1]. On the contrary, author this paper

proposes that overexcitation test at zero power-factor be performed for three (four) values armature current (I a ) and corresponding generator voltages, i.e.: - I a1 = I a,max > I an sinφ N (i.e. Q G1 = Q Gmax > Q GN ), which is corresponding to excitation rated current (I f = I fn ) and U G1 = U G at Q G1 = Q Gmax > Q GN (approximately: point C 1, Figure 1); - I a2 = I an sinφ N (i.e. Q G2 = Q GN ) and U G2 = U G at Q 2 = Q N (approximately: point C 2, Figure 1); - I a3 = 0.8I an sinφ N (i.e. Q G3 0.8Q N ) and U G3 = U G at Q G3 (approximately: point C 3, Figure 1), and - I a4 = (I a1 + I a2 )/2, i.e. Q G4 = (Q Gmax + Q GN )/2 and U G4 = U G4 at Q G4. For different reduced excitation current values (for rated voltage and armature current), Figure 1: i f (A1) < i f (A2) < i f (A3) different values of Potier reactance are obtaining, Figure 2, i.e.: x P (A1) < x P (A2) < x P (A3) On the base of these characteristic values of Potier reactance one would be constructed the corresponding capability curve (P-Q curve) of the test generator. Figure 1: Determination of the excitation current corresponding to the rated voltage and rated current at zero power-factor i f (A1) < i f (A2) < i f (A3) [9] for three experimental point i (C1) > i (C2 > i (C3)

Fig. 2: Potier reactance values, X P (A1) <X P (A2) < X P (A3) for three different field current corresponding to the rated voltage and rated current at zero power-factor, i f (A1) < i f (A2) < i f (A3) 3. ANALYSIS OF THE POTIER REACTANCE DEPENDENCE ON THE GENERATOR LOAD AND THE NEW RULE FOR THE DETERMINING THEREOF Based on the results of own investigations [12, 13, 14], the author came to a conclusion: that the value of the Potier reactance, for the given voltage value, depends almost exclusively on the reactive load values (i aq = i a sinφ). The above new rule shall be proved, firstly by qualitative analysis, and then based on the Potier reactance dependence (x P ) on the specific generator s active and reactive load [12]. The values (x P ) shall be determined with high accuracy by means of the new method [14]. In Fig. 3, in addition to the graphic procedure for determination of the Potier reactance (x Pn ) for the rated generator region (u u n,, i i n i φ φ n ), has also been included a part of the graphic determining the Potier reactance value (x Pn,90 ) for the reactive load region with the rated load (u u n,, i i n i φ 90 0 ). The procedure for determination of the Potier reactance (x Pn,90 ) has been running in due orders marked by numbers 7 and 8, and is identical to the procedure applied in determining the value (x Pn ). The reactance values x Pn and x Pn,90 were set by means of the new method [14], by the procedure illustrated in Fig. 3. The magnetization curve of the machine under load i fl (e l ) is given for the specific turbogenerator and also determined by the new method [14]. The Potier reactance value for the rated region (x pn ) set in such manner, as a rule exceeded the same for the reactive load region with the rated current (x Pn,90 ), i.e. x Pn > x Pn,90 (Fig. 3). The explanation lies in the fact that the electromotive forces behind the Potier reactance (e P ) and the dissipation

reactance behind the dissipation reactance (e l ) have a larger value in the reactive load region with rated current (u u n,, i i n i φ 90 0 ), i.e e P90 = 0F > OC = e Pn,90 (Fig. 3), so that in such region the turbogenerator magnetic circuit saturation is larger and the corresponding reactances are therefore smaller. In the case of the concrete turbogenerator [12], the Potier reactance value for the rated region (x Pn ) is as much as by around 20% larger. That the Potier reactance value, for the given voltage value, depends almost exclusively on the reactive current load value (i aq = i an sinφ), is shown in Fig. 4. In Fig. 4 is, apart from the Potier reactance value (x Pn ) for the rated generator s generator region (u u n,, i i n i φ φ n ) (i an ), additionally was included a part of the graphic determining the Potier reactance value (x Pn,90 ) for the reactive load region, i i aq = i an sinφ n, i.e. For the region where: u u n,, i i an sinφ n and φ 90 0. The procedure for determining the Potier reactance value (x Pn,90 ) is running in due order marked by numbers 7 and 8, and is identical to the procedure applied when determining the value (x Pn ). The described procedure was conducted for the same turbogenerator as in Fig.3. Fig. 3: Vector diagrams of electromotive forces behind the Potier reactance (e P ) and electromotive forces behind the dissipation reactance (e l ), and procedure for determining the Potier reactance - for the rated generator region (u u n,, i i n and φ φ n ), from 1-6; - for the reactive load with rated current region (u u n, i i n and φ 90 0 ), from 7-8. That the Potier reactance value, for the given voltage value, depends almost exclusively on the reactive current load value (i aq = i an sinφ), is shown in Fig. 4. In Fig. 4 is, apart from the Potier reactance value (x Pn ) for the rated generator s generator region (u u n,, i i n and φ φ n ) (i an ), additionally was included a part of the graphic determining the Potier reactance value (x Pn,90 ) for the reactive load region i i aq = i an sinφ n, i.e. For the region where: u u n,, i i an sinφ n and φ 90 0.

The procedure for determining the Potier reactance value (x Pn,90 ) is running in due order marked by numbers 7 and 8, and is identical to the procedure applied when determining the value (x Pn ). The described procedure was conducted for the same turbogenerator as in Fig.3. Fig. 4: Vector diagrams of electromotive forces behind the Potier reactance (e P ) and electromotive forces behind the dissipation reactance (e l ), and procedure for determining the Potier reactance - for the rated generator region (u u n,, i i n and φ φ n ), from 1-6; -for the reactive load with rated current region i = i an sinφ n (u u n, i i an sinφ n and φ 90 0 ), from 7-8. The Potier reactance value for the rated region (x Pn ) determined in such a way is, as a rule, approximately equal to the value (x P90), of the reactive load region i = i an sinφ n (u u n, i i an sinφ n i φ 90 0 ), i.e. (Fig. 4): x x, for i 90 = i an sinφ n (1), P, n P,90 Based on the equivalence (1) and illustrations in Fig.4, it is possible to write a general equivalence x, for i 90 = i a sinφ n (2), P x P,90 The explanation lies in the two following facts: (1) The electromotive force behind the Potier reactance (e P ) and the electromotive force behind the dissipation reactance (e l ), have approximately the same values in the a) reactive load region i = i an sinφ n and b) in the nominal generator region, i.e. e l90 e ln =0B and e P90 e Pn =0C (Fig. 4), so that the corresponding main turbogenerator s magnetic fluxes are also equivalent. (2) The corresponding components of the longitudinal magnetic dissipation of the excitation coil (of the rotor) are also equivalent as they, just as the components of the longitudinal magnetic dissipation of the stator coil, depend almost exclusively on the reactive load.

From (1) and (2) follows that corresponding longitudinal magnetic on the stator and rotor parts are equivalent. The consequence thereof is that the turbogenertor s magnetic circuit dissipation are approximately equivalent. For that reason the Potier reactance values for the rated region and the reactive load region i = i an sinφ n, i.e. x Pn x P90 (Fig. 4) are also approximately equivalent. The above proofs are sufficient for the conclusion: a) that the Potier reactance values, for the given voltage value, depend almost exclusively on the reactive load component (i aq = i an sinφ), and b) to propose a change of standard [9] in the part referring to the determination of the Potier reactance, i.e. in order that it be determined based on the reactive load test i = i an sinφ n, as well as concerning several additional characteristic values, which would be appropriate for the construction of the capability curve ( P-Q curve) of the turbogenerator. The above rule is tested on the example of the considered turbogenerator GTHW 360 (360 MW), by comparing - the measured values of the generator s excitation current for the regions around the rated region (P G P Gn, and Q G Q Gn ), and - the calculated values thereof based on the Potier reactance values (x P ), determined for Q G Q Gn. 4. EXAMPLE OF PROCEDURE APPLICATION AND TEST FOR RATED GENERATOR REGION As an example, the Potier reactance values were determined by the method [14], based on the data from the reactive load test and given generators magnetization characteristics (no-load), I F0 (U 0 ). The results of the Potier reactance calculation are given in Table 1, for four turbogenerator reactive load values GTHW 360, as follows: 1. For values Q G1 =Q Gmax > Q GN, corresponding to the rated excitation current I f = I fn ; 2. For values Q G2 = Q GN, at voltage U G2 = U G for Q G2 = Q N ; 3. For values Q G3 = (Q Gmax + Q GN )/2, at voltage U G3 = U G for Q G3 ; i 4. For values Q G4 0.8Q N, at voltage U G = U G4 for Q G4. It is emphasized that the reactive load test is done with the generator connected to the rigid power network (i.e. at the power plant), and that the generator voltage changes only due to change of drop of voltage at the block transformer, at change of reactive loads. This enables the Potier reactance change to take place in real regions at the change of reactive loads, as only the change thereof leads to perceptible voltage changes at connections of a generator operating in a rigid grid. The required Potier reactance values were determined by the new method [14], and are given in Table 1. From the results in Table 1, it can be seen that the Potier reactance value is significantly

reduced (increased) when the reactive load is increased (reduced). Those changes could be larger (up to 30-40%), when turbogenerators of 500-800 MW in capacity are concerned, and whose magnetic circuit at the stator and rotor part is not even more saturated. This justifies the proposal to determine the value of this reactance by the reactive load test, for the relevant values thereof. Table 1. The data from reactive load test of the turbogenerator GTHW 360, procedure and results of the Potier reactance (x P ) calculation x s =x d p.u. P MW Q Mvar U G kv U G /U Gn / I F A x P p.u. Region with the maximally permitted reactive power(q G,max ), for Cosφ 0 1. 2.535 33.1 296.0 23.77 1.080 2549.5 0.258 Region with the rated reactive power (Q Gn ), for Cosφ 0 2. 2.535 33.5 216.0 23.22 1.055 2048.0 0.273 Region with reactive power Q G =(Q Gn + Q G,max )/2, for Cosφ 0 3 2.535 32.0 256.0 23.66 1.075 2296.0 0.265 Region with reactive power Q G =0.80Q Gn, for Cosφ 0 4 2.535 33.7 173.0 22.92 1.042 1788.0 0.285 For the purpose of testing this position: that the Potier reactance value (virtually) does not change with the active generator power, if the change if the reactive load value stays constant, two regions were considered where the load thereof deviate little from the rated ones in terms of the active and reactive power. In addition to that, for every such region (Table 2), the generator excitation current values (I F ) are as follows: - the excitation current values obtained by measurement (Table 2, type 1a and 2a); and - the excitation current value calculated (Table 2, type 1b and 2b), for the Potier reactance value determined by reactive load test for the above values thereof. The calculated excitation current values of the generator (I F ) differ, in turn, by +0.79% and-0.39%, which is within the accuracy limits of the measured excitation current (I F ) values. The accuracy is expected to be even higher in the region of larger reactive power values, as the corresponding (permitted) active power is smaller and the regions therefore differ less from the referent reactive load regions for which the Potier reactance values are determined. The results of more complete application of this procedure, for the purpose of determining the dependence of the Potier reactance on the (reactive) load values are given in the paper [16].

Table 2: Values of excitation currents, for generator voltages and currents about the rated values. Data from the reactive load test, procedure and results of the Potier reactance (x P ) calculation x s =x d P Q U G U G /U Gn x P I F p.u. MW Mvar kv / p.u. A Region 1: 1a. Measured values 2.535 321.0 216.0 23.0 1.055 / 2499 1b. Calculated values 2.535 321.0 216.0 23.2 1.055 0.273 2480 Region 1: 1a. Measured values 2.535 321.0 231.0 23.3 1.059 / 2579 1b. Calculated values 2.535 321.0 231.0 23.3 1.059 0.275 2569 5. CONCLUSION Based on the results of own research, the author reached an important conclusion: that the Potier reactance values, for the given voltage value, almost exclusively depend on the reactive load (i aq = i a sinφ) component. The above hypothesis was proved, a) firstly by a general qualitative analysis, and b) was then tested on the example of the considered turbogenerator GTHW 360 (360 MW), for two operating regions with active and reactive power around the rated values. The Potier reactance (x P ) values were determined with sufficient accuracy by means of the new method of the author thereof [12]. APPENDIX 1: METHOD FOR DETERMINATION OF POTIER REACTANCE [9] When the synchronous machine is operated as a generator on full load, given methods to calculate X p from measurements are applicable [9]. An equivalent reactance used in place of the armature leakage reactance to calculate the excitation on load by means of the Potier methods. It takes into account the additional of the field winding on load and in the overexcited region and is greater than real value of the armature leakage reactance. The Potier reactance is determined graphically from the no-load and three-phase short-circuit characteristics and the excitation current corresponding to the rated voltage and rated armature current at zero power-factor. The no-load and three-phase short-circuit characteristics are plotted on a diagram (Figure A1) as well as a point (A), the ordinate of which is the rated voltage (u=1) and

abscissa is the excitation current (i fb ) measured at rated armature current (i=1) and zero powerfactor (cos φ=0) at overexcitation. To the left from the point A, parallel to the abscissa, a length AF equal to the excitation current (i fk ) for the rated armature short-circuit current is laid off. A line parallel to the initial lower portion of the no-load characteristic is drawn through the point F up to the intersection with the upper part of the no-load characteristic (point H). The length of perpendicular from point H to point G (intersection with AF line) represents the voltage drop on reactance x p at rated armature current. In per unit values x p =HG. u i e (i ) fg i k (i ) f e 0 (i ) H f K F G A 1.0 0 K' F' D 1.0 2.0 i fk i fa B i f Fig. A1: Determination of Potier reactance from no-load, e 0 (i f ), and short-circuit, i k (i f ), characteristics and the point A(i f, u) corresponding to the rated voltage and current at zero power-factor If, during the excitation test at zero power-factor, the voltage differs from rated value by not more than ±0.15 per unit, a graphical method is used for the determination of the excitation current corresponding to the rated voltage and current, using the data of the test and the no-load and short circuit characteristics, fig. 1. An experimental point (point C, Figure 2) is plotted on a diagram with the no-load curve of the test machines. This point corresponds to zero power-factor and the measured values of armature current (i), voltage (u) and excitation current (i f ). Vector OD equal to the excitation current, corresponding to the armature current (i) on the short-circuit curve, is laid of along the abscissa axis. From the point C, a length CF equal to OD is laid off towards the no-load saturation characteristic and parallel to the abscissa axis. A the line FH is drawn parallel to the extended straight line portion of the no-load saturation characteristic intersecting the latter at H. Line HC is extended to a point N such that HN/HC=1/i, where is i the current corresponding to point C. The no-load curve is then transferred to the right and downwards parallel to itself and by distance HN. Point A is found on this curve which corresponds to the rated voltage and armature current at zero power-factor.

Fig. A2: Graphical method for the determination of the excitation current corresponding to the rated voltage and rated current at zero power-factor [9] REFERENCES [1] A.M. El-Serafi, J. Wu, A new Method for Determining the Armature Leakage Reactance of Synchronous Machines, IEEE Transactions on Energy Conversion, Vol.6, No 1, March 1991, pp.120/125. [2] A. B. J.Reece, and A. Pramanik, Calculation of the End Region Field of A.C. Machines, Proc. IEE, Vol. 112, 1965, pp. 1355-1368. [3] Slemon, R G., Analytic Models for Saturated Synchronous Machines, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-90, 1971, pp. 409-417. [4] E.A. Abdel-halim, C.D. Manning, Modelling Saturation of Laminated Salient-Pole Synchronous Machines, Proc. IEE, Vol. 134, Pt. B, 1987. pp. 215-223. [5] Joseph O. and Thomas, A., An Improved Model far Saturated Salient Pole Synchronous Motors, IEEE Transactions on Energy Conversion, Vol. EC-4, 1989, pp.135-142. [6] Liwschitz-Garik, M., Electric Machinery, D. Van Nostrand Company Inc., New York, 1946. [7] J. C. Flores, Buckley. G. W. and Mc Phtrson Jr. G., The Effects of Saturation on the Armature Leakage Reactance of Large Synchronous Machines, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-103, 1984, pp. 593-600. [8] R. Bourne, Electrical Rotating Machine Testing, Iliffe Books Ltd, London, 1969. [9] Standard IEC 34-4/1985, "ROTATION ELECTRICAL MACHINES, Part 4: Methods for determining synchronous machine quantities from tests". [10] J. Wu, Theoretical and Experimental Investigations of the Cross-Magnetizing Phenomenon in Saturated Synchronous Machines, Master s thesis, University of Saskatchewan, 1989. [11] Studija, Zavisnost pobudne struje i gubitaka snage u sinhronim generatorima Termoelektrana Nikola Tesla A i B od nivoa reaktivnih opterećenja, Elektrotehnički institut Nikola Tesla, 2008.godine, str.54 (on Serbian). [12] Studija: Određivanje stvarnih dijagrama aktivnih i reaktivnih snaga (P-Q krivih) generatora blokova B1 i B2 u Termoelektani "Kostolac" B, Institut Nikola Tesla Beograd, 2009, str.59 (on Serbian). [13] M.M.Kostić, "Novo pravilo za određivanje Potjeove reaktanse za relevantna opterećenja turbogeneratora", "Elektroprivreda", No 3 2010, str. XX-XX (on Serbian). [14] M.M.Kostić, "Nova metode za određivanje Potjeove reaktanse sinhronih turbogeneratora", "Elektroprivreda", No 4, 2009, str. 59-68 (on Serbian). [15] Ion Boldea, Synchronous Generators - The Electric Generator Handbook, pp. 512, 2006 by Taylor &Francis Group, Boca Raton London New York, 2006. [16] M.M.Kostic, "Construction generator capable curves by of new method for determining of Potier reactance, International Conference Power Plants 2010, Serbia.