Transfer functions of loaded synchronous machine

were selected for analysis. The cylinder data take an intermediate position be­ tween the needle and sphere data. Above 150,000 feet and even somewhat below, electrode shape has little effect on the breakdown voltage. For the 1/2-inch- electrode spacing used, this voltage is approximately 500 volts. Analysis of the data also shows that spacing is not highly significant above 150,000 feet. At 4 inches, for example, the comparable voltage values range from 700 volts for needle electrodes to 1,200 volts for sphere electrodes. Extrapola­ tion of the data indicates that this latter value would become 700 volts at approxi­ mately 170,000 feet. Conclusions The data reported in this paper should form a basis for the designer to establish safe voltage breakdown distances between terminals and between terminals and ground for transformer applications that require 100,000 feet altitude and 500 C THE GENERAL STUDY of the tran­sient performance of the synchronous machine is based on Park's1·2 theory. Various authors have presented useful methods for the study of this subject, and a complete bibliography is contained in reference 3. Problems related to the transient operation of the synchronous machine have been treated as well, aiming at the representation of the synchronous machine for analog studies.1011 Any change in the operating conditions of the synchronous machine causes corre­ sponding changes in electrical quantities. In the case of sudden short-circuiting of an unloaded synchronous machine the current decreases steadily from a maxi­ mum to its steady-state value. The vari­ ation of the armature current is ad­ mittedly related to an apparently variable reactance. Although the value of this re­ actance is continuously changing,7 for practical purposes it is taken to be equal to a definite value according to the prob­ lem considered. For example, in stabil- temperature ratings. The data show that terminal spacings under these conditions must be severely derated from their normal ambient values. Air dielectric strength data were ob­ tained for the simple electrode shapes such as needle points and spheres and corre­ lated with those taken on a specific termi­ nal type representative of more complex shapes. I t was found that: 1. the ter­ minal dielectric system behaves more nearly as sphere electrodes above 70,000 feet and somewhat less ideally below that altitude; 2. electrode separation and elec­ trode shape become less significant as alti­ tudes of 150,000 feet and higher are ap­ proached; and 3. the nature of the dis­ charge at breakdown for the electrode shapes evaluated changed from a spark to a glow at approximately 70,000 feet alti­ tude at room temperature. References 1. I N V E S T I G A T I O N OP P O R C B L A I N I N S U L A T O R S A T H I G H A L T I T U D E S , C. V. F i e l d s , C. L. Cadwel l . AIEE Transactions, vol . 65 , Oct. 1946, pp . 6 5 6 - 6 0 . ity problems the synchronous machine is represented by the transient reactance, just as it is represented by the synchro­ nous reactance in steady-state operation problems. The transient performance of the syn­ chronous machine can be analyzed di­ rectly with the aid of circuit equations, without reference to a variable reactance. Although the theoretical results obtained are readily applicable to other problems, this paper will be concerned with varia­ tions of the excitation conditions only, assuming constant torque acting on the shaft of the machine, the speed of rotation corresponding to the nominal frequency. It will be further assumed that the varia­ tion of the excitation voltage is relatively small, such as 10% to 20% of its initial value. This limitation is necessary for the approximation admitted in the evalua­ tion of certain terms. The general case of the transients in the synchronous machine, involving further consideration of torque equations relating 2. A P P L I C A T I O N OF I D E A L G A S T H E O R Y TO T B B G A S E O U S E X P A N S I O N FROM A N E L E C T R I C S P A R K , R. B . E d m o n s o n , H . L. Ol son , £ . L. Gayhart . Journal of Applied Physics, N e w York, N . Y . , vol . 25 , Aug. 1954. 3. E F F E C T OF A L T I T U D E ON E L E C T R I C B R E A K ­ D O W N AND F L A S H O V E R OF AIRCRAFT INSULATION, L. J. B e i b e r i c h , G. L. M o s e s , A. M . St i l e s , C. G. Veinott . AIEE Transactions, vol . 6 3 , 1944, pp . 3 4 5 - 5 4 . 4. S P A C E C H A R G E F O R M A T I O N A N D T H E T O W N S E N D M E C H A N I S M O F S P A R K B R E A K D O W N I N G A S E S , R. W . Crowe , J . K. Bragg, V. G. T h o m a s . Physical Review, N e w York, N . Y . , vol . 96 , no. 1, Oct . 1, 1954. 5. A S M A L L H I G H - V O L T A G E B U S H I N G D E S I G N FOR H I G H A L T I T U D E S , F . J. Voge l , H . A. Hart . AIEE Transactions, vol . 68 , pt . I , 1949, pp . 7 6 1 - 6 4 . 6. B A S I C P R O C E S S E S OF G A S E O U S E L E C T R O N I C S (book) , L. B . Loeb . Univers i ty of California Press, Berkeley, Calif., 1955. 7. G A S E O U S C O N D U C T O R S (book) , J . D . Cobine- McGraw-Hi l l B o o k C o m p a n y , Inc . , N e w York»· N . Y . , 1941 . 8. M E A S U R E M E N T OF V O L T A G E I N D I E L E C T R I C T E S T S . AIEE Standard no. 4, Sept . 1953. 9. I C A O S T A N D A R D A T M O S P H E R E . NACA TN 3182, Nat iona l Advisory Commit tee for Aero­ nautics , Washington, D . C , 1956. 10. N A C A T E N T A T I V E U P P E R A T M O S P H E R E . NACA TN 1200, Nat iona l Advisory C o m m i t t e e for Aeronautics , 1956. 11. V O L T A G E B R E A K D O W N AT L O W G A S P R E S ­ S U R E S ( H I G H A L T I T U D E S ) , J. W . B aliar d, C. B . G e e s n e r . WADC Technical Note 56-304, Wright Air D e v e l o p m e n t Center, D a y t o n , Ohio, July 1956. to angular position of the rotor, is not within the scope of this paper. In the experimental results reported here, the power-angle variation is deduced from oscillographic records. In order to arrive at rather simple ex­ pressions the amortisseur has not been considered. This affects only slightly the results obtained as response to step varia­ tions of the excitation voltage and, in the study of the behavior of the voltage-reg­ ulating system given as an example, sufficient approximation is obtained. The general case of the salient pole ma­ chine will be treated. I t has been found Paper 58-796 , recommended b y the A I E E Feed­ back Control S y s t e m s and approved b y the A I E E Technical Operations Depar tment for presentat ion at the A I E E S u m m e r General Meet ing and Air Transportat ion Conference, Buffalo, N . Y . , June 2 2 - 2 7 , 1958 and re-presented at the A I E E Winter General Meet ing , N e w York, N . Y. , February 1-6, 1959. Manuscr ipt submit ted June 5, 1957; made avai lable for printing December 15, 1958. D . H A M D I - S E P E N is with the Technical Univers i ty of Istanbul , Istanbul , Turkey . T h e author wishes to acknowledge the use of the facilities of the D e p a r t m e n t of Electrical Engi­ neering, Massachuse t t s Ins t i tute of Techno logy , Cambridge, Mass . , and the suggest ions of Profs. A. E . Fitzgerald and K. L. Wildes; also those of Dr. E . Mishkin , now with the Polytechnic Ins t i tute of Brooklyn , Brooklyn , N . Y . T h a n k s are also due to G. Belfils, Technical Manager of Société A L S T H O M , Paris, France, for the opportuni ty of working in t h e research laboratories of this com­ pany at Belfort, France, where the experimental results wi th ampl idyne exciter were obta ined; and to his staff for i ts help. T h e other experi-' mental results were obtained in the laboratories of the Technical Univers i ty of Istanbul , Istanbul , T u r k e y . Transfer Functions of Loaded Synchronous Machine D. HAMDI-SEPEN ASSOCIATE MEMBER AIEE M A R C H 1959 Hamdi-Sepen—Transfer Functions of Loaded Synchronous Machine 19 Ef(s)+ M/rf Ld + sTf+ 1 ojLd(sTfd + |) XsSL Tf(0+) f 1 coLq Viä{s) Id (s) Iq(S) that in round-rotor machines saliency can Fig. 1 (above). Block dia- be of the same order of importance as sat- S«m of the synchronous n j l i^ f i uration.12·13 machine Theoretical Considerations % 2.4 v 16 v v 63v !jjt|!!!|jp»i? LU Id Od o LU û (2>< cd UJ 1 current is dependent upon the following: 1. The voltage Ef{s) applied to the field terminals. If this voltage is varied in the form of a step function to a constant value Ë/, this term is (Ëf/s)KiG/(s) and evaluated as a function of time. If the variation of e/ can not be represented as a simple Laplace transform to be introduced in equation 21 it is possible to replace its variation in a step-by-step calculation by elementary step functions replacing the actual variation of e/. 2. The voltage vq in general is not a known function of time, and is dependent upon δ; the evaluation of the term Vq(s)K2G2(s) is possible just in the form of Duhamel's in­ tegral in a step-by-step calculation. If the machine is entirely reactive loaded, neglect­ ing the armature resistance Va would be zero, and Vq constant and equal to v; this term will be (V/s)K2G2(s) and evaluated. This can still be approximately admitted in opera­ tion with lagging power-factor angle about 40 to 30 degrees, for example, according to machine characteristics. The variation of δ and consequently of vq remains small so that the hypothesis of its constancy is not much in error. 3. The term ^ / ( O + ^ i d M represents the initial conditions. As no amortisseur winding in g-axis is considered, neglecting the armature tran­ sients, the g-component of the current is directly iq = Vd/ a. K57V mitìittmMiìi i itHmiinitit i i i i i 8 v MÌMflfM !«f»!JJ»M""f|'fi|«!lff?!|f!||i|l ■Ili' SlltuHlilìiiililiiiì-.Ì.; , , η , η Μ Η Μ η Μ Μ Μ Η Μ η Μ , Ι Ι , Π ΐ , π , Μ , Μ Μ ΐ Μ η , Μ Ι , , Π , , η Ν Μ ΐ , Ι , Ι Ι ΐ η ϋ t 12.7 a m p , , , Μ Μ Μ Μ ' ί Μ Ι ΐ Γ Μ Μ Μ Ι ί Μ Μ Η Ι Μ Ι Μ Η Ι Μ Π Ι Μ - η ΐ Ι Μ Τ ΐ Ρ ΐ ΐ , , Π , < ί η Ι Η ΐ ί Η ΐ Ι Ι Ι Π Η ΐ | | | Π Μ π Η Μ ί ΐ Μ Π ΐ Η ] ΐ Μ Η Μ Ι Η Ν Π ΐ Η ί Ι Η Μ ί ΐ Μ Ν π π Lf-2.53amp , 3.05amp f 22.1 v 26>6V Fig. 3. Results for operation % 2 9 V A ( left )—ψ=47.5 B Siri=47 i i ì i i t i i i i i iÉie degrees lead JWWHMJJJMW« 16 co u a: OJ a. < I I - z a: 3 O 12 δ ^ \ — * ! co 16 12 ω O LÜ Û 0.68 amp ι 8 H < en 005 0.10 OIS 0 2 0 0.25 0.30 T IME - SECONDS Transfer Functions of Loaded Synchronous Machine Equations 18(A) and 23 are the basic equations determining the transient opera­ tion of the synchronous machine and can be represented in the form of block dia­ grams as in Fig. 1. Ef(s), Vtq(s), and Vtd(s) are input functions, while ψ/(0+) represents the initial conditions. Id(s) and Ig(s) are the output quantities. The block diagram as given in Fig. 1 can be introduced as representing the synchronous machine in any closed-loop system such as the example treated in Appendix II . Experimental Results The accompanying oscillograms have been obtained on a 7-kva 110-190-volt 1,500-rpm 50-cycle 3-phase machine. The unsaturated value of Xa is 8.5 ohms and the transient reactance X& is 1.7 ohms. We neglect the armature resist­ ance which is 0.279 ohm. M is 0.284 henry; L/ is found equal to 5.59 henrys. ft is 8.57 ohms, but is larger for currents about 0.5 amp (ampere). Its value is calculated from ef and if as measured. Tf is equal to 0.65 second, and T/d = 0.131 second. The machine was directly connected to the infinite bus. Tests have been made with terminal BSV LO 16 S 12 Σ < « 8 h- au ce z> o 0 -Δ « flD · i O O voltage about 0.5 per unit, in unsaturated conditions, for quantities related to the c?-axis. I t is known that the case is different for quantities related to the g-axis.14 The variation of the power angle during transients is obtained with the aid of the following arrangement: An auxiliary alter­ nator is mounted on the shaft of the main synchronous machine, with the same num­ ber of poles with movable stator. The power angle δ is calculated from phasorial difference voltage eò between the voltage of this auxiliary alternator and a voltage taken over a resistor connected between phase and neutral of the infinite bus. These two voltages are regulated to have the same amplitude, and the stator of the auxiliary alternator is rotated so that the phasorial difference between these two voltages is zero when the synchronous machine connected to the infinite bus is running at no load. The stator of the auxiliary alternator remains in this posi­ tion. During tests these voltages were regulated to 44 volts. With the foregoing values of the con­ stants, the solution of equations 20 and 23 for the transient current components 40 30 20 10 0.10 020 0.30 0 4 0 050 0.60 T IME - SECONDS co LU LJ CL O LJ Û I LJ _l o < ce 1 * AMPLIDYNE GENERATOR INFINITE BUS -c=D RECTIFIER Fig. 4. Voltage-regulating system with amplidyne exciter reading of the oscillograms which cannot be as precise as the reading of an instru­ ment. The small variation of δ has no effect on the value of the current. In Fig. 3(A) are given the results ob­ tained during operation with lagging power-factor angle 0 = 47.5 degrees, in response to a sudden increase of ef from 22.1 volts to 26.6 volts. The initial con­ ditions were i/ = 65 volts, i=12.7 amp, f/=2.53 amp. From the curves of Fig. 3(A) it will be seen that nearly the entire variation of the current has occurred before any relatively important variation of the power angle. Subsequently, the further variation of the power angle has no effect on the value of the current. The variation of the arma­ ture current is dependent practically upon the variation of its ^-component. The value of φ at the end of the transients is 62.5 degrees lag. The iq component of the current used in the calculation is deduced from δ as recorded. The case is entirely different for opera­ tion with leading power-factor angle, as seen in Fig. 3(B). The machine was operating with 0 = 47 degrees lead, when the voltage at the field terminals was in­ creased from 5.5 volts to 6.5 volts, and the initial conditions were v = 58 volts, i= 9.3 amp, and *7=0.55 amp. The variation of the armature current is entirely dependent upon the variation of its quadrature component and related to the power angle as seen from the curves of Fig. 3(B), though the variation of δ remains related to the variation of ψα- Steady-state value of φ is 42 degrees lead. The performance of the voltage reg­ ulating system given in Fig. 4 and con­ sidered in Appendix II has been tested on a 15-kva 220-volt 39.5-amp 1,500- AEr(s) K/r l r Q (sT,2 + l ) (sT Q + l ) ΦΗ (sT,2 + l ) ( sT Q + l ) ©H M/rf Ld sTfd + I ΚΦ rpm 50-cycle 3-phase machine. In Fig. 5 the block diagram of the system is given. For saturated conditions, Ld is 0.0184 henry and M is 0.182 henry. The ratio of field-leakage flux to total field flux is given by manufacturer as 10.5%. As­ suming armature leakage of same order, we admit Lfd/Lf equal to 0.21 ; introduc­ ing this value in Lfd as defined in the Nomenclature with the foregoing values of Ld and M, Lf is found equal to 3.42 henry s. The other constants are Li=Z2 = 0.91 henry n = 12.7 ohms r2 = 550 ohms fQ=3 ohms Γ12=0.073 second J Q = 0 . 0 9 second Lx =0.00574 henry Lfdx — l.S7 henrys r/==27.7 ohms 7>=0.124 second Tfdx = 0.0494 second With the rectifier used k is 1.35. K as defined in Appendix II is 1,860 and E/0 = 74 volts. The amplidyne was a 2- pole machine with 125 turns per pole for control fields 1 and 2 (Fig. 4). With the foregoing values of the con­ stants from equation 32 the incremental variation of the effective value of the armature current is in amp Ai=AËr[4.88-1.52e-J,ot- 6.9e-7'6" sin (II.8/+290)] (5) The synchronous machine operating with entirely reactive load, the reference voltage er was increased suddenly from 6.9 volts to 7.5 volts. The initial conditions were ef— 93 volts, if=3.35 amp, i=id = 2A amp, v* = 210 volts, and v = 202.5 volts. The oscillogram in Fig. 6 gives the terminal voltage and the armature cur­ rent, shown in curve a; curve b is cal­ culated with equation 5. The steady- state values after the transients were e/= 107 volts, if =3.85 amp, i=5A amp, vt = 220 volts, y = 203 volts. The difference between curves a and b is due to the time lag introduced by effects not considered in this analysis, in the variation of the terminal voltage of the synchronous machine actually increasing ■Θ—1 STf+ 1 coLd(sTfd + l) OJLN AI(S) Fig. 5. Block dia­ gram of voltage- regulating system of Fig. 4 71 fil 4 nL k t l· Ψ b -- ,££ ̂ -^ a " i = ■ = « ( 0 0.2 0A 0.6 0.8 1.0 1.2 1.4 1.6 1.8 TIME - SECONDS Fig. 6. Terminal voltage and armature current of generator as response to an increase of the reference voltage applied to the control field of amplidyne exciter a—Armature current from oscillogram b—Calculated current c—Calculated current neglecting amplidyne transients the net control ampere-turns of the ampli­ dyne. Curve c is calculated neglecting amplidyne transients, that is, taking Γ1 2=0, TQ=0. Conclusions The expressions of the transient current components have been derived from cir­ cuit equations. The ^-component of the transient cur­ rent is dependent upon the voltage applied to the field terminals and the terminal voltage component corresponding to the resultant flux component along d-axis. For operation with an entirely reactive load this voltage component is equal to the terminal voltage and is constant for a machine connected to infinite bus. The current in this case depends only upon the excitation voltage. When the synchronous machine is operating with relatively large lagging power-factor angle so that vg can be re­ garded as constant, these conclusions are still valid and the variation of the arma­ ture current is dependent practically upon the variation of its component along direct axis. In case the machine is operating with leading power-factor angle, the variation of both components of the terminal volt­ age must be taken into account. The armature current variation is almost en­ tirely dependent upon the variation of is quadrature axis component related to the power angle, whose variation however is also dependent upon the variation of the component of the resultant flux along d- 22 Hamdi-Sepen—Transfer Functions of Loaded Synchronous Machine M A R C H 1959 axis. This case is not within the scope of this paper. An example of use of the transfer func­ tions as derived has been given in the performance calculation of a voltage- regulating closed-loop system with ampli- dyne exciter, including the consideration of the saturation effects in the ampli­ dyne. Nomenclature v—voltage at the infinite bus Vq, Vd = components of v along q- and (/-axis vt = terminal voltage of the synchronous machine vtg, vw= components of v% along q- saia d- axis i=armature current id* iq — components of i along d- and ç-axis φ =power-factor angle i = power angle ω=speed, electrical radians per second Ldt Lq — self -inductances per phase M— mutual inductance between phase and field windings r=armature resistance caLx = external reactance ef—voltage applied to field terminals, also terminal voltage of amplidyne exciter if= field current Lf, Tf=self-inductance and resistance of field winding Ψά, ^î = flux linkage components along d- and reactance. In the case treated as an ex­ ample in this paper the ratio of field leakage to field flux was known. The saturated value of Lt was deduced from the value of L/d as defined in the Nomenclature. Appendix II. Calculating the Performance of Voltage- Regulating System with Amplidyne Exciter The voltage-regulating system considered is given in Fig. 4. The reference voltage er is applied to the control field circuit (1) of the amplidyne. The feedback voltage is applied to the second control field (2). This direct voltage is k,vt,vt being the effective value of the terminal voltage connected to the rectifier. The synchronous machine is represented by transfer functions as derived in Appendix I. Amplidyne performance treatments have been presented by various authors.16"18 In the following the saturation effects in the amplidyne will be taken into account. With the incremental variations of the variables, the Laplace transform equation for circuit 1 is AEr(s) = (Us+niALi s) - MsAl2(s) (24) and for circuit 2 kA Vt(s) = (L2S+r2)Al2(s) - MsAI^s) (25) From these equations, neglecting the leak­ age flux between circuits 1 and 2, with L\ equal L2t one obtains with 7 « as defined in the Nomenclature AIl(s)-AI2(s) = AEr(s) kAVt(s) ri(sT12+l) 1 (26) ΦΤ12+1) Under unsaturated conditions eQ = KE(ii-Ì2) (27) and for the current AEQG) AIQ(s) = rQ(sTQ+l) (28) The amplidyne terminal voltage incre­ mental variation which is also the variation of the voltage applied to the field terminals of the synchronous machine will be, in case of no saturation, AEf(s) = KdQAIQ(s) = AEr(s)JN(s)/n - kAVt(s)JN(s)/r2 (29) with to r- _j o > 150 I LÜ O £ 100 50J II 1Vy XI I 1 / '/f^ The terminal voltage of the amplidyne CONTROL AMPERE-TURNS PER POLE Fig. 7. Load characteristic of the amplidyne JN(s) = KßKdQ rQ(sT12+l)(sTQ+l) (30) Replacing this value of AEf(s) in equa­ tion 22B with Vq constant and taking into consideration that Δ Vtq — ωΣχΑζα (31) the effective value of Ald(s) which, in a case of an entirely reactive load as considered here, is equal to the incremental variation of the effective value of the armature current will be Al(s) = AEr(s)X KEKOQM f\tfrQ\/2 (Ld+LxXsT12+l)(sTQ+lXsTfdx+l)+ ΚΕΚ^ωΣχΜΛ/Ζ r2rjrQ\/2 (32) SATURATION EFFECTS As generally the amplidyne is operating under saturated conditions, the foregoing results need to be modified in order to take into account the saturation effects. In deriving equation 29 it has been assumed that the amplidyne load character­ istic giving the terminal voltage as a func­ tion of the resultant ampere-turns of the control circuits was a straight line through the origin. The actual load characteristic of the amplidyne used in the experimental studies reported in this paper is given in Fig. 7. The point (0) corresponds to the initial conditions, while (1) is the steady-state operating point. The linear correlation factor between ef and the resultant control ampere-turns will be taken into account by a new constant factor K instead of KEKdQ, this time along the straight line through points (0) and (1), and a constant value E/0 must be intro­ duced. ef^Efo+Kiii—Hi/rQ (33) defining the factor K which will replace KEK(IQ in equation 32, in the case of satura­ tion of the amplidyne. References 1. TWO-REACTION THEORY OP SYNCHRONOUS MACHINES, GENERALIZED METHOD OF ANALYSIS— PART I, R. H. Park. AIEE Transactions, vol. 48, July 1929, pp. 716-30. 2. Two-REACTION THEORY OP SYNCHRONOUS MACHINES—II, R. H. Park. Ibid., vol. 52, June 1933, pp. 352-55. 3. SYNCHRONOUS MACHINES (book), C. Concordia. John Wiley & Sons, Inc., New York, N. Y., 1951. 4. POWER SYSTEM STABILITY (book), S. B. Crary. John Wiley & Sons, Inc., 1947. 5. VOLTAGE VARIATION OP SUDDENLY LOADED GENERATORS, H. C. Anderson. General Electric Review, Schenectady, N. Y., vol. 48, Aug. 1945, pp. 25-33. 6. ELECTRICAL TRANSMISSION AND DISTRIBUTION RBPERENCE BOOK. Westinghouse Electric Cor­ poration, Pittsburgh, Pa., 1950. 7. T H E OPERATIONAL IMPEDANCE OP THE SYN­ CHRONOUS MACHINE, M. L. Waring, S. B. Crary. General Electric Review, vol. 35, Nov. 1932. 8. T H E EFFECTS OP GENERATOR VOLTAGE REGU­ LATORS ON STABILITY AND LINE CHARGING C A ­ PACITY, F. S. Rothe. Report no. 321, CIGRE, Paris, France, 1954. 9. EFFECT OF A MODERN AMPLIDYNE VOLTAGB REGULATOR ON UNDBREXCITBD OPERATION OP LARGE TURBINE GENERATORS, W. G. Heffron, R. A. Phillips. AIEE Transactions, vol. 71, pt. I l l , Aug. 1952, pp. 692-97. 10. FUNDAMENTAL EQUATIONS FOR ANALOGUE STUDIES OF SYNCHRONOUS MACHINES, D. B. Breedon, R. W. Ferguson. Ibid., vol. 75, pt. I l l , June 1956, pp. 297-306. 11. ANALOGUE COMPUTER REPRESENTATIONS OF SYNCHRONOUS GENERATORS IN VOLTAGE REGULA­ TION STUDIES, M. Riaz. Ibid., Dec , pp. 1178-84. 12. SOME MEASUREMENTS ON THE EXCITATION AND LOAD-ANGLE CHARACTERISTICS OF LARGE ALTERNATORS, J. W. Byrne, D. Carroll. Report no. 310, CIGRE, 1956. 13. T H E DIAGNOSIS OF STEAM TURBINE ALTER­ NATOR PERFORMANCE BY STROBOSCOPIC METHOD, E. B. Powell. Report no. 101, CIGRE, 1956. 14. SATURATION EFFECTS IN SYNCHRONOUS M A ­ CHINES, Djabir Hamdi-Sepen. AIEE Trans­ actions, vol. 73, pt. III-B, Dec. 1954, pp. 1349-53. 15. A N E W APPROACH TO THE CALCULATION OF SYNCHRONOUS MACHINE REACTANCES—PART II, M. E. Talaat. Ibid., vol. 75, pt. I l l , June 1956, pp. 317-27. 16. METADYNB STATICS (book), J. M. Pestarmi. John Wiley & Sons, Inc., 1952. 17. FUNDAMENTALS OF THE AMPLIDYNE GENERA­ TOR, J. L. Bower. AIEE Transactions, vol. 64, 1945, pp. 873-80. 18. TRANSIENT ANALYSIS OF THE METADYNE GENERATOR, M. Riaz. Ibid., vol. 72, pt. Il l* Feb. 1953, pp. 52-62. 24 Hamdi-Sepen—Transfer Functions of Loaded Synchronous Machine MARCH 1959