Construction and Operation of a Million Volt Surge Generator Citation McCann, Gilbert Donald (1935) Construction and Operation of a Million Volt Surge Generator. Master's thesis, California Institute of Technology. doi:10.7907/xc96-gk14. https://resolver.caltech.edu/CaltechTHESIS:10282024-210247502 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 June 1935 Record Number: CaltechTHESIS:10282024-210247502 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10282024-210247502 DOI: 10.7907/xc96-gk14 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16817 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 28 Oct 2024 21:22 Last Modified: 28 Oct 2024 21:23 Thesis Files PDF - Final Version See Usage Policy. 14MB Repository Staff Only: item control page

CONSTRUCTION .AND OPERATION OF A MILLION VOLT SURGE GENERA.TOR Presented to The Faculty of the Department of Electrical Engineering of The California Institute of Technology by Gilbert D. Mccann in Partial fulfillment of the requirements for the Degree of Master of Science .Tune, 1935 TABLE OF CONTENTS Generation of Surges Page l Specifications of California Institute of Technology-Surge Generator 6 Description and Plans of Structure 6 The Condenser Circuit 13 The Charging Circuit 15 Use and Definition of Test Waves 20 Attainment of Test Waves 24 Mathematical Analyses 2-5 Derivation of Equations for Simplified Circuit 28 Determination of Constants Necessary to Produce a Given Wave 30 Determination of Surge Generator Constants 38 Series Capacitance 39 Series Inductance 40 Series Resistanee 45 Distributed Capacitance to Space 46 Effects of Load Impedance 49 Determination .of Damping Resistance 50 Effect of Circuit Constants on Wave 53 Adjustment of Constants 56 LIST OF FIGURES Figure 1 Marx Surge Generator Circuit Page 2 2 Plan of Side Beams 7 3 Top View of Framework 9 4 Side View of Framework 10 5 ) 6) Views of Surge Generator and Equipment 12 7 ) 8 Surge Generator Circuit Diagram 14 9 Surge Generator Charging Circuit 16 10 Equivalent Circuit Diagrams • 26 11 Curves of Circuit Constants for ½-5 Wave 33 ~ H- " " tt If 1-10 tt M 13 tt tt tt " "l½-40 tt 35 14 15 Calculated Standard Waves for California Institute of Technology Generator 16 ) Equivalent Geometrical Circuits for 17} Inductance Calculation 37 41 18 Equivalent Circuit for Capacitance Load 51 19 Curve showing Effect of Capacitance Load 51 20 Curves showing Effects of Circuit Const ants on Wave Shape 55 LIST OF TABLES Table Page I Specifications of Kenotxons KC-1 18 II Specifiea tions of Supply Transformers 18 III Specifications of Insulating Transformer 19 IV Specifications of Auto-Transfonner 19 V Regulation Table 19 VI Circuit Constants for Standard Waves 36 FOREWORD It was the intention in preparing this thesis to present the construction and specifications of the surge generator that has just been completed in the Southern Califo.rnia Edison Company High Voltage Laboratory at the California Institute of Technology. Further, it was desired to present a determination of all the circuit constants and enough of the theory for the attainment of standard wave shapes for test purposes. However, due to the inability to obtain, as yet, ade4uate oscillograms, all of the constants of the surge generator have not been determined. 1 GENERATION OF SURGES There have been numerous circuits devised and used for the production of surges, all of which fundamentally perform the function of charging suitable condensers and then discharging them through the proper circuit constants to give the desired wave form. In some of these c;i rcuits, the condensers are charged with an A.C. potential, some with rectified A.C. and others with direct current from a D.C. generator. The type in most common use today for the production of high voltage surges employs the Marx circuit for the parallel charging of banks of condensers and the series discharging of them. The most satis- factory means of charging is by the use of high voltage rectifying tubes connected in what is knovm as the voltage doubling circuit. The principles of these two features are shown in figure 1. The condenser banks, consisting of as many condensers in series as the voltage rating of the charging circuit will permit, are charged in parallel through 1 R r;-~l I R. CIRCUIT SURGE- GFN£RATOR Piece Test l\) ~1 3 the resistances labeled (R). After they have been charged, they are switched in series through the gaps shown. The triple gap connecting the first two banks is the control gap. It is either set so that it will flash over after the banks are charged up, or it can be initiated by applying a surge to the middle sphere. The second method enables synchronization of the surge. After the first gap has flashed over, each successive gap does likewise due to the increased potential applied to it after the breakdown of the one before it. The charging resistances are of such a value that the points they connect are effectively open circuited for the transient condition. The time of discharge is so short that very little energy is lost in these resistances. By the use of the Marx circuit, very high surge voltages can be obtained with a large number of banks. The only limits to the number that can be employed are the increased time necessary to charge up the last banks and the fact that the increased number of gaps reduces the voltage, since there is an appreciable drop across 4 each of them. The voltage doubler charging circuit, as shown in figure 1, has the mid-point of the bottom condenser bank and one end of the supply transformer tied to ground during charging. The other end of the trans- former is connected to the two ends of the hank through the rectifying tubes, so that the ends are charged, one positively and one negatively, to the voltage of the supply transformer while the mid-point of the bank is at zero potential. One of the tubes is conducting during one half of t ,he cycle and the other during the second half. The bank, thus, is charged to twice the voltage of the transformer, permitting the use of one of a lower voltage rating. Also the initiating gap can be tripped by a surge of either polarity, since one sphere of the initiating gap is at a positive potential of a certain value and the other at a negative potential of the same value. In other types of charging circuits, one end of the bank is at ground potential, while the other is either positive or negative. 5 One precaution which must be taken in the design of such a charging circuit is the selection of rectifying tubes. The maximum voltage at any one time across the tubes is twice the voltage of the supply transformer. It is thus necessary to use tubes with an inverse voltage rating equal to the voltage of the condenser bank, or twice that of the supply transformer. 6 SPECIFICATIONS OF THE CALIFORNIA INSTITUTE OF TECHNOLOGY SURGE GENERATOR The surge generator just completed in the high voltage laboratory of the California Institute of Technology is of the type that has been desoribed. Description and Plans of Structure The frame v.ork was designed so that if at any time it is desirable to do so its length can be increased to permit the addition of more banks of condensers and the attainment of higher voltage. It is so built and situated in the high voltage laboratory that at least four million volts can be attained. The width of the frame work is such that six of the General Electric 50,000 volt, 5 micro-farad Pyranol condensers may be placed on each hank with the minimum required spacing. The dimensions of these condensers are given in figures 3 and 4. At the present time, the framework consists of five banks and four condensers are being used per bank, giving a rating of one million volts. It is made of Or~gon maple 1- J ~ t- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 i ?' ~ ~ ' I IQ f----- ' '-- - ~ ~ ~------0 0 0 .0 Q.; \J') ~ ~ ~ 0 ' ,.._ ;:- - ~ ~_g. ~ 0 ..,_. ______0 _ ~ 0 0 V) 0 V) "'~r.r-i l ~ "J~ 0 , I';: .... 0 ~'.'1..:.:-t::: Q; •' 01 :s ' I ~ '- - 0 0 0 0 0 0 0 0 co 0 ~ I " I() .____ ' 0 ' V') ~ § ~ - ~ ~ )) ~"')"< . 7 . ---/ /✓ I ~ \)'--, ~ 8 all of which was parafin dipped. The structure is fastened together almost entirely with bolts. The essential features of the framework are shown in figures 2, 3 and 4. As can be seen from these fig- ures, its over-all dimensions are twenty feet by seven feet three inches, and it consists of two main beams twenty feet long and cross pieces forming the cradles for the condensers constructed of two by fours. The structure is further braced by two one inch by six inch braces. The plan of the main beams is shown in figure 2. They are made of one inch by twelve inch finished maple bolted together in three layers with one-half inch bolts. The length of each board is such that all joints are evenly distributed throughout the length. are al.l tightly fitted. The joints As shown in figure 2, the bolts are arranged symetrically about each section with eight bolts per section. Figure 3 shows the top view and figure 4 a side view of the assembled framework. The supports for each bank of condensers consist of three two inch by four inch 9 TOP VlfW ..5Ul?GE ' GENER ATOR.. FRAME W ORI \ I ") _j -0 ~ 0 . 0 \ ¼ ,D / / / /0 / - -·~ ---~ · ---J--- 0 / ' I ' C) t\l 17 'I I X 6 FINISH r ,:}._ ' I fY') . z ,1 .SCA L£ 11 .3 - I XIi!, r/N/SH ---------... =/FOOT 10 F/6. ~ SID£ VJ£W OF 5URG£ G£/V£RATOR FRAM£ wORX .r ~ L/ C>fro11d.5 or i // He1np rope / .J /nsu/qTor.> ':¾ Iron rod I ii .z" hose on eoc-h side ~ ~or c/2or91n9 circuit • resis/'onces Cross piece 5 ' are ,2,''x wirh ros/e17ed An9les 1x.1x-&" Li// I; ;:"supports /'or h o s e ~ I / F 3-L/z between Ce/?ler line or each condel'Jser bank J ' IQ I !'-........ - - - - - 9 : . 7 , , Ground lead------'>--! 11 finished beams fastened to the side beams with one inch by one inch by one-eighth inch angles and one-quarter inch bolts. The two cross braces constructed of one inch by six inch finished lumber are fastened to the bottoms of the side beams with wood screws. Figure 3 shows the spacings of the condensers as they are arranged at present and the support for the gaps which runs the whole length of the framework. It consists of a runner carrying one sphere of each gap, except the triple gap, and guides upon which the other sphere of each gap is mounted. By this method, all of the gaps are adjustable simultaneously. Figure 4 shows the method of supporting the framework which is set at an angle of about sixty degrees with the floor. Its base is connected with a two inch pipe to two four inch by four inch by one-quarter inch angles which are bolted to the concrete floor with onehalf inch bolts. The two top supports are fastened to the floor of the first balcony with four inch by four inch by one-quarter inch angles, to which are fastened three-quarter inch iron rods. To each rod is fastened I 5/"aodard Rod Gap z . Keno t-rons tlg.5 ~ Fig 6 _.., L/ Suppllj Transrormers 3 . lnsula/-/on Transformer ... ~ ~-- ~ S. Discharge Resisiance /lg. 7 13 a string of 15 standard suspension insnlato:rs, which are in turn fastened to the surge generator frrunework with four strands of half inch hemp rope. The Condenser Circuit As shown in figure 8, although the condensers are arranged in five banks of four each, they are actually charged in ten sets of two each. This arrangement was necessary due to the voltage limitations of the Kenotrons which permit a maximum voltage across each set of 100 kilo-volts. There are eleven discharge gaps, all but the top being made of three inch plumbers balls. The top gap, which is located as shovm in figure~ on top of the discharge circuit framework, is made of six inch plumbers balls. All of the halls are motmted on one-quarter inch brass shanks set in maple uprights. The value of the charging resistors between each bank is 100,000 ohms, since this has been found empiric-ally to be the least resistance that will protect against a surge voltage of 100 kilo-volts. They are formed by two water columns made of one-half inch -- ::s 0 R, Rz. Rz ~here Gaf>S: 2.S"Sj>heres Rz-=- 1ogooo_,..._ RI =- ,...J'.1 ho ooo-'~ sq 000 V O.~-'>µ_ ~ R..2. 1 / Fig. 8 Rz R2. Rz. C c:7?a.:.. ro.r- Ar-ra/7ye/77en/- 20 G.£ Pyronol Capacifors ~ 6 ~ ~ -~ ~ ..._ G -~ • ...___ T A2. pl. /or Ju/ye R2. Ge_r-.7eralor 1~ I-' ~ <-> 1-.. 15 hose supported on the framework with one inch by two inch maple pieces, as shown in figure 4. The hose is cut in sections long enough to provide the proper resistance with tap water and is connected at the points where the circuit leads are fastened to it with onehalf inch o.d. copper tubing. It is, of course, necessary to adjust either the length of each section or the conductivity of the water to obtain the right resistance. In this case, ordinary tap water provides 100,000 obms resistance for the 18 inch sections. The leads in the discharge circuit are made of one-half inch o. d. copper tubing arranged so that the minimum spacing between each lead is ten inches. This is the minimum safe spacing for this type of configuration under surges with a difference of 100 kilo-Yolts between them. The Charging Circuit The charging circuit is shown in figure 9. The tubes used are General Electric Kenotrons (KCl) having 16 FIG 8 SURG£ G£N£RATOR Protecftvg, Gap To r CHARGING CIRCUIT trenelroa A, rilamenf Rheosiaf- . Trol7srormers-=- '-"'---"-"'--"-~ lnsvla fin9 Trans. - ---- - - -I 1 R, Auto I Tran.5. I L - -- IIOVa.c. _J R 1 == 50;000 fl.. R3 = 50;000A. Con fro/ Panel R'I =J~OOOJ2_ '---- - - - - - I I I I I - /i/qmen f 1 Ammeter Loa. d Afflmefer I I Vo!l-mete,:i Load '------------ 1'7 an inverse voltage rating of 100 kilo-volts. The specifications of these tubes are given in table I. As shown in figure 6, the tubes are mounted on a metal container which has in it the filament transformer immersed in transformer oil. In this manner, the primaries and secondaries of the filament transformer are insulated against the high voltage of the secondaries. There are two supply transformers used in series as shown in the circuit diagram, figure 9. These trans- formers are shown in figure 6 and their specifications are given in table II. The insulating transformer is an air core transformer and is also .shown in figure 6. The auto-transformer for voltage regulation is designed to give regulation of from 50 to 110 volts in 10 volt steps. As shown in table V, this gives a charging voltage e 0 * regulation of from 400 to 1000 kilo-volts. * e 0 is the sum of the voltages across all of the condensers at the instant of discharge. SPECIFICATIONS OF EQUIPMENT TABLE I Kenotrons Filament Voltage Current (Amp. ) Type Maximum Peak Inverse Vol_tage Maximum Peak Plate Current (11.mp.} Overall Dimensions Maximum Length Iv1inimum Length Maximum Diamete·r 9.00 32.00 Tungsten 100,000 1.00 25-1/Btt 24-?/Stt 8-1/8" Potential test-base of tube to edge of filament transformer container-flashed over at 130 KX TABLE II Supply Transfo rrae rs Core Type Mean Dimension of Window Gross Section Rating 33"xl5" 4nx 6" 50,000/110 volts Potential test-with 110 on primary-48 KV on secondary. Regulation with 40 Amps. on primary about 60%. TABLE III Insulating Transformer Core Type 34nx29" Window Oros s Sec ti on 4°x 5tt Primary 114 tarns Secondary 50 turns Taps on Primary at 16, 31 and 4?th turns Potential test-primary to secondary windings flashed over 100 KV . TABLE IV Auto-Transformer Shell Type Cross Section Windows 4'tx 4" 15tt (legs) x12n 86 Turns Primary Voltage 110 with 50, 60, 70, 80, 90, 100, and 110 volt taps for secondary TABLE V VOLTAGE CALIBRATION OF SURGE GENERATOR 110 volts applied to auto-transformer Auto-trans. voltage taps 50 60 70 80 90 100 110 Voltage on autotrans. secondary 45 59 71 84 90 95 110 Volt age across one condenser 1CV 20 28 34 39 41 45 50 eo (ICV peak) 400 560 680 '780 820 900 1000 Voltage was measured across one condenser of the bottom bank of t wo with a 12.5 cm. sphere gap. 20 USE AND DEFINITION OF TEST WAVES In the use of the surge generator, it is necessary to produce sarges that are similar to those produced by natural lightning upon transmission lines and connected apparatus. Results of tests with the use of the Cathode Ray Oscillograph of such equipment under lightning strokes show that such surges may vary between wide limits from oscillatory waves of steep wave front to non-oscillatory waves of relatively sloping front; and that the surges are modified as they progress along a transmission line by the constants of the system, so that from the same stroke parts of the line and equipment at different places will have different surges impressed upon them. In the earlier stages of surge testing, the different laboratories used a great variety of waves. It was in this st age that an attempt wa s made to define surges and many unsatisfactory definitions resulted. Waves were sometimes defined as to the portion used, whether whole or chopped; as to the steepness of the wave front, the crest value, or the shape of the tail. One very common method was to define the wave in terms 21 of an equivalent frequency by considering the wave from zero to crest value as one-fourth of a cycle. At the present time, however, it is the concensus of opinion that the majority of the surges caused by lightning and the ones which produce the most damage (cause insulation breakdown) are of short duration, have steep fronts and are non-oscillatory. Due to this and the great difficulty that has been encountered in obtaining consistant results throughout the country, the effort has been to have a few of the most representative waves standardized. Out of this effort has grown a very satisfactory method of wave definition. Considering a non-oscillatory wave, which is the standard type adopted, it is defined by three terms; the crest value in kilo-volts, the time from zero to crest value {t 1 ) in micro-seconds, and the time from zero to one-half crest value (t 2 ). See figure 15. It is obvious that specifying only two points of a curve, theoretically does not define it. But this defi- nition carries with it the ass~mption that the wave is a smooth curve wi th th e tail decreasing along an expo- 22 nential curve. Due to the similarity of surge genera- tors throughout the country, all waves produced by them and satisfying the above re quirements are essentially the same. There a.re today three waves which are somewhat st anda rd and may be adopted as such by the P..rn.erican Institute of Electrical Eng ineers. They are the ( ~ 5) micro-second wave, the (l-10) micro-second wave and the (l½-40) micro-second wave. The ( 1 5} wave gives a crest flashover value of a t least 150% of the 60 cycle flashover value where considerable time lag is involved. It is used primarily in testing insulators. The (l-10) wa ve gives flashover values of about 125% of the 60 cycle crest flashover voltage where considerable time lag is involved. The (l½-40) wave gives flashover values of about 110% of the 60 cycle values, and is more satisfactory for volt age time considerations. Flashover with all of these surges usually occur s on the tail of the wave, but as the crest value of the 23 surge is increased, it is brought nearer to tbe crest. Curves representative of the three waves as actually produced are shown in figure J.!) where it can be seen (as is generally the case) that all three waves have fronts which rise at the same rate. The difference in the time to crest value occurs in the last 10% of the voltage rise. At the present time, the (1-5) wave is less used because of the difficulty in obtaining it with the present high voltage generators and the longer discharge circuits. It has therefore been recommended* that a (1-5) wave be substituted instead. The standardization of these three surges does not mean that they are the only ones used or specified for regular testing. There are other waves used for certain types of testing. For instance, the specifi- cations for lightning arrestor testing require a wave which rises to crest in three micro-seconds. * ttRecommendations for Impulse Voltage Testing", A.I.E.E., V 52, p 46?. 24 ATTAINMENT OF TEST WAVES The problem of actually applying these standard waves to test pieces is a difficult one. Before the perfection of the Cathode Ray Oscillograph, which g ives a complete picture of the wave, the only means of determining wave shape was by means of a mathematical analysis of the circuit. Due to the :difficulty in ac- curately determining the constants of the circuit under surge conditions and of analysing such a complex circuit, accurate results were seldom obtained. Simplified ap- proximate equivalent circuits were used which did not represent true conditions. This difficulty has not yet been entirely overcome, and the Cathode Ray Oscillograph is the primary method of determining the wave shape. However, the development of the mathematics, the ability to more accurately determine circuit constants and their effect upon results have lead to much greater accuracy. Even thou gh the Cathode Ray Oscillograph has surplanted some of the former usefulness of the mathematical analysis in the determination of -wave shape and 25 magnitude of surges, it still plays an important part in surge testing. In order to use the Cathode Ray Oscillograph effectively in obtaining the desired wave, it is necessary to have some starting point. At least an ap- proximate idea must be known of the proper values of the circuit constants. Then too, the mathematical analysis affords the knowl.edge of how to correct the circuit to eliminate the deviations from the desired wave as sho wn by the Cathode Ray Oscillograph. Mathematical Analysis The complete circt1i t diag ram, if all consta nts are considered to be lumped, is shown in figure lOa. The calculation of such a circuit is obviously too difficult, and some simplifications are needed before it can be analysed. The Cathode Ray 0-scillograph cir- cuit theoretically should be constructed so as to have no effect upon the wave as applied to the test piece and should accurately record it. Thus, for the pur- poses of this analysis it can be neg lected. The values of the distributed capacitance to FIG. 10 ( A.) Control Cr Surge Gen . r---------1 I I I I I I I I I - ___ J I L ____ J I I Test- I hn ped. C1rcu/i I I I I I I L_ - - Tesr R I I Rs Ls Imped. {C.) L R I I J L ____ .J -7 · I I• {B.) _c Meas Test r - r ; - ,q-;--1 r---7 r------ · v-r--1- 1 - - - . - - - - , - - - - - . c.=:==::::.......... •o . : _l 27 ground (Cd) and the conductance to ground (G) of the surge generator proper are usually small enough to be neglected w~ thout serious error. In some of the large surge generators, however, they do become appreciable. Sometimes (Cd) is taken account of by lumping it with the capacitance of the test piece. Neglecting these quantities gives a circuit as shown in figure lOb. This circuit has been analysed for different types of loads and will be considered later. The circuit having the most practical signific ance is the one shown in figure 10c where tbe load is entirely neglected. In many cases the impedance of the load is such that it can be neglected without appreciable error, as in insulator testing. Even if tbe load is appreciable, the use of this circuit through its simplicity is important to detennine approximately the values of the circuit constants for a given wave under any loading. This, then, is the starting point in any test, and further refinements can be made to suit each particular one with the use of the Cathode Ray Oscillograph and a kno wledge of the :eff ect of the other factors upon the wave shape. 28 Derivation of Equations for the Simplified Circuit Writing Ohm's law for any instant around the circuit shown in figure 10, the following differential equation is obtained: (1) e = iR t L M = q/C where e =%=instantaneous voltage across all condensers in series q = instantaneous value of charge on condensers i - instantaneous value of current R, Land Care the three circuit constants Differentiating with respect to time (t) (2) de - Ld 2 i Rd i i dt - cft'Z + dt = C .9.9. = -i since upon discharge of dt condensers, q is decreasing Letting d = D dt de= LD 2 i + RDi = dt (3) ci (LD2 +RD+ l)i: 0 C The solu ~ion for this equation is given by e quation 4. 29 (4) i Dt D2t - A1'E 1 A2t 2 where D1 = -2L R + ~ 4L 2 - LC 1 2 R / 4R 1 D2 -- _ 2L - 4L 2 - LC Dl = -o<.+/3 D2 : -d..-J3 D1 =-{rx.-JJ) D2 =- (c<. +.,0) -(d.-J3)t -(ot.+/3)t- i -- A1E t A2E Solution for A1 and A2: (5) At instant of discharge t : 0 and i • O, since there is inductance in the circuit Equation (5) at this time reduces to O: Ai - A2 (6) A1 : - A2 Differentiating (5) and substituting in it the conditions when t - O, e quation (?) is obtained. (?) ~{ : f -(ol'. - P ) ( ci +J3 ) A 2] A1 - Substituting e quation(?) and the value of i when t into equation ( 1 ) : (8) e 0 = R( A1 t A 2 ) - L [ .-( G( - P ) A1 - =O (<X t P )A~ Solving ( 6 ) and (8) simultaneously: (9) Al : - A2 - ~ (10) i - ~ - 2ftL -(ot.-tP)t] -(«.-p)t C - 2,PL [ c. - C c Since the test piece is connected across the discha r ge 30 resistance, the voltage wave applied to the test is the voltage across the discharge resistance as given by the follo wing equati on: e = e0 -(c<.-/3)~ -(o(+p)f / 2j3L E. - E J R[ since ~ : ( 11 ) f -t«-f3>r = eo ft E ,J [ e 2 -r«-+P)t] -E The equations by the proper adjustment of the circuit constants will satisfy the conditions for a non-oscillatory wave, a critically damped wave or an oscillatory one. As has been previously mentioned, the non-oscillatory, or aperiodic case, is the one of most practical interest. However, it is sometimes desirable to produce oscillatory surges for their analysis in determining the values of the circnit constants. Determination of Circuit Constants to Produce a Given Wave It is the general case in the use of the surge generator that its capacitance is fixed. The variables are, then, R and L. The voltage has reached its crest value when~:= o. 31 Thus diffe r entiating (11) with respect tot and solving for t: (12) This is the equation for time from zero to crest value of the surge. o(_ + J3 o<. +ft Letting b = ~ and a = logE. o<.-/3 t 1 : 1 log b = 1 a 2p E 2f3 (13) (14) Solving for « and .P in terms of a, b and t 1 (15) <X. a [ b+lJ and /J • a = 2t1 2t1 b-1 The crest value e1 of the .v oltage is obtained by substituting in (11) the value of t 1 of equa tion (14). -4h a. (16) el= e 0 [~:iJ[Eb-I - E b-i I The value e2 at the time t 2 to half crest value is the follovvi ng: (17) - C( [ e2 - ~ 2 - eo_p E -(a.-ft) t;! -C -(<t+/3) fz_] Substituting in (17), the values of d. and /3 a s g iven by equation (15): (18) e2 = eo ~:i[E ,,. -t ( ~ ) -3b-1 t:, - b -t ( :!£__ ) 3..J C b-1 ~ Curves can now be plotted of e1 and 2e2, for any 32 given ratio of t 2 over t 1 against a. The intersection of the two curves gives the proper value of a to give the desired wave defined by t 2 over t 1 . From this and the equation for t 1 , the values of <X. and fJ and hence of R and L can be ob-tained. Curves showing the values of Rand Las a function of C determined in this manner for the three standard waves are shovm in figures 11, 12 and 13. From these curves the proper values of Band L can be found for a surge generator of any capacity . . In table VI are shown the proper values for the California Institute of . Technology surge generator as taken from these curves. It might be noted here that in obtaining any specified wave, the crest value of the wave cannot be adjusted by changing the circuit constants. For any given wave shape it can be varied only by varying e 0 , the voltage applied to the condensers in charging them. In figures 14 and 15 are plotted the three standard calculated waves for a capacitance of .025 micro-farads. These, then, are theoretically the waves that should be obtained with the C. I. T. surge generator. 33 /0,--,----,----;-----r-~-,-----,-----,-----,--,----,-----,---,--,---.----,----,----,.-,........... 9 t-------t--+---t----t-+---+-----+----+--l-+--l----l--+-1---+--+----+-..,.......+-~ 81-----+---1---+----+---+---1- IFC IS 10-1 MF. MULTIPLY)? 'oRL. '13y;o /I " " IO ""' " " " " " ,, I 00 +---1-------i ;T~. ,, /0-.1 ,, ,, ,, ~ ,, 'JO{JQ, ~ ?i-------t--+---t----t-+---+-----+----+--1-+--l----+-..,.......+-i---+--+----+-------+-~/.4- ~ ~ \R '? 6 r-+-----t-t\-+---+----+-+---+--+--+--+-----,1---+--+--+---+-..,.......+-1--+--+-~/Z ! <::)5 t------+---+-----++---1---+--+--l--+-I\ ~ ~ ~r<4 \ \ ~ ~ 10 ~ ' ~ \ 0.8-~ ~ ~ ~J__,-+_\_,,_+\-->.:--+--+--+--+--t--f--f--+--+--+--+---+-+--+--iQ6~ ~ ~ .? ~ I"- i\ \~--._ 01 r------_ , r'---I'--. r--.. ...____r--.._ . ---r-- 1 ---r-.____ 11-t----r-t7-11111~+::=t-11-=1t--t==t===+==do.~ I --r-_ I 0 I .e C/rcu1t J 4S CAPACITANCE •c,. 6 7 d IN MICROFARAC>,5. I Constants -/'or ;z-5 Wove. Fig. I I .9 /0 ~ 34 /4 7 /3 /FC IS /0-1 Mr. MULTIPLY 'R ''oR"t., "BY 10 ,, ,, ,, ,, ,, II ✓I 10-jl ,, /00 ,, ,, ,, ,, ,,,,,,,o-.J U "/000 " Ere. Ii!. 6 II . s 10 I 9 \ \ \ ' :: 1 \R \ \ ' \ \ I \ \. \ J \ '\ \ J "1'.. "'r--..... r---.... i\ '\ L ['-. 'I'---. .......... i r---.... r-.. t-- t----..._ -r-- 1--I -- -- - i-- t--- t---- ! I 0 I i!- J 4- CAPACITANCE 3" IN 6 T d MICROFARADS Circuit Constqnts /or 1-10 Wqve. 9 . 10 35 I I 80 ro c:, 60 ~ 50 I \ \ \ L \ \ ~ li.J 10 '\ \,) \ \ ~30 ~ \ "' ~ " "' :\. ~ I"-.. ~.zo .......... R I'--- ...... r---..... ............. ~ ............. 10 ....._ -i---r - - _ -- -r--- -I o . I i?.. ..1 + CAPACITANCE S C 6 7 8 9 IN MICROFAflAD..S Circuir Constonr.5 Tor 1-j,-.;o Wave. Fig. 15 10 36 THE CALIFORNIA INsrITUT E OF TECHNOLOGY SURGE GilliERATOR TABLE VI Circuit Constants for Standard Waves C L R Wave micro-farads micro-Henries ohms ½-5 .025 36 290 1-10 .025 130 5?0 .025 620 2300 37 1000 900 \ 700 i'... 1\ ~ 600 I'-.. ~ \\ ~ °'~ 500 :Q 400 ~ ~ r--..... ........ ' \ ~ I /0 \ .JOO ['.. "-. I\. '\ ~00 -5 / ,? ;..!... -7" 0 I"-... ,e' r-- r--,..... ~ ......... - ~ r--,.......1- 100 I 16 0 i!4- 3i?. 40 ~8 56 64- 80 T~ Micro-Seconds. Ft '9 . />/ 1000 900 ;j-f r7 80 0 700 600 0 ~ I[?5 r,v v-:-r---. ~ 1/ "' r--__ ~ =z-s ........... r----r---. ... - /-/0 r---, -- -- C I ---- I I -- -- 0 coo /00 0 ~ I J 4 M1cro-0econd.s. r, 9 15 Calculared 51-andard Waves S 38 DETEWl INATION OF THE SURGE GENERATO~ CONSTANTS The inherent constants of the circuit which must be evaluated for the control of wave shapes are the following: 1. The series capacitance which consists primarily of the capacitors. 2. The inherent inductance of the surge generator which includes the discharge circuit and ground lead. 3. The surge resistance of the connections and gaps of the surge generator proper. 4. The distributed capacitance of the surge gener- ator to space. The last item is ·usually so small that it, along with the conductance to ground, can be neglected. These constants, although distributed, must be treated as lumped and are determined by one or more of the following three methods: 1. The actual measurement with suitable equipment. 2. The c·alculation from physical considerations. 3. The calculation from analysis of oscillograms taken and.er the proper conditions. 39 None of these methods are exact. Actual measure- ments of constants are necessarily taken under steady state conditions which differ from surge conditions. The calculation from physical considerations requires simplifying assumptions which are not absolutely precise. The attainment of oscillograms under the exact conditions necessary is usually impossible, due to the values of the inherent constants themselves. Usually, however, t .his method gives the most accurate results. It is thus seen that it is very desirable to determine each constant in as many ways as possible. @eries Capacitance The series capacitance is primarily that of the condensers themselves, the values of which are given on the name plates. However, it is more accurate and some- times advisable to measure it directly with either a Schering or an Atkinson bridge. When a bridge is used, the gaps are shorted out and the charging resistors disconnected. An approximation as to the value of the capacitance 40 of the gaps can be made by the actual calculation for the capacitance of two spheres, or the gaps can be measured with a hxidge. However, it varies with different gap set-tings, making it difficult to accollnt for. This c:apaci tance is so small in most cases that it can be neglected without much error in the mathematical analysis. Calculation of the Surge Generator Inductance Calculation from the Geometrical Configuration: The first part that will be considered is that part of the discharge circuit Joining together the condensers as shown in figure loa. If it is assumed that all conduc- tors are in the same plane (which is very nearly true), little error is introduced by assuming the section (d-e}, figure 16a, to be a single straight conductor (k-1), figure 16b. If the portion represented by (k-1-m), fig- ure 16b, is further considered to be a rectangle (w-x-y-z) as in figure 16c, whose sides are~= ½k-m and 5!J_ a k-1, the configuration thus arrived at can be calculated. equivalent circuit, then, consists of four rectangular turns and two sides of a rectangle at the top. The 41 f/6./6 ( A) ( B .) ( C.) f- s J- ~~ r~~ d~~e : '\ '\ C 0 .me 0 0 \1 kc y' Ir 1-~ ~I D= 'IOJJ 0 '~~ I 0 \ C•i~I'' ~ a'= 65. 5 " ~ FIG/7 C Q., \J ~ ~ ~ V') ' Q, Ct: ~ ~ ~-~ ~ e,' /' I 0 Erv/vile/J i,._ C)' h'ec/-an9le or some II') • ii /> (} ::: b a Grovnd Lead 9~2" >I Area as t-he Tr / angle a b 42 The precise effective diameter of the conductors under surge conditions is unknovm. In this case, it was assumed equal to the physical diameter, since it is hollow tubing. All of the formulas given in the following are taken from the Scientific Bulletin of the Bureau of Standards, Volume 8 for the year 1912. Self Inductance: The self inductance of a rectangle in micro-Henries is given by the following formula: (19) LR: .00921( (ata1)log10 4 ~a 7 - alog.1o(a+g) + .oo4ff'1i (a-ta1) - a 1 log 10 (a 1 tg~ T 2(g+~) - 2(a+a1j where a is short side of rectangle a 1 tt long tt ft tt g = \fe-f+a2 d - diameter of conductor All dimensions of length and diameter are given in centimeters. The self inductance of one straight conductor of finite length is given by the following formula: (20) L = .002~1(2.303log10 4 i - .?5) micro-Henries 43 The total self inductance of the portion represented by figure 16c is 4LR + Lrs ~ Lst· Mutual Inductance: The mutual inductance of two f lat rectangular turns is given by the following equation: (21) 2 2 2 M12 = .00~321 [ alog 10 a+ / a 1-D = ..x / al+D a+ /a2+af-,n2 D + a1log10 a1+/a}+n2 ;< / a2+n2 a11-/a2+-af_... n2 ,._-- + .oos{ j a2taf➔D2 - / a 2 +n2 J D -./a.,....f_+_ n2- -,.D where n-is the distance between centers of the rectangles considered. The mutual inductance of two parallel sections of finite length is given by the following formula: 2 2 {22) M - .002 [ l,1C 2.303log1 0 1+1f -+d - / 1 2+d 2 -t- ~ where 1 is the length of conductors. The total mutual indu ctance is 0M12 t 4M13 t2M14 as calculated by equation 21, plus the mutual inductance of the length r-s with the long sides of all the rectangles. The mutual inductance of conductors with the leng·th s-t is so small that it may be neglected. 44 Discharge Circuit: There is next to be considered the inductance of the discharge circuit, including the discharge resistance and its ground lead, in conjunction with the circuit just computed. This is shown in figure 17a. The self inductance of a-band b-c can be calculated from equation 20. The mutual inductance of the set-up can be obtained by calculating the mutual inductance of an equivalent rectangle, figure 17b, whose h.ase a-b is the same as that for the triangle and whose altitude is one-half that of the triangle. Equation 22 is used for this. Determination of Inductance from Oscillograms If the resistance of the sin1ple series discharge circuit is close enough to zero, it can be calculated from the equation for the frequency of the wave produced under these conditions. 2 1 JJ may be written as When RL2 is less than LC' 4 j / ic - !~2 or p =j Equation 11 then reduces to equation 23. 45 -<X.f e = e~ £ (23) J L (E ;tt- -1°Af -£ ) -~t e = eoR£ sino't L6' (24) The period (T) of the wave given by this equation is equal to 2 f· If R is equal to zero, Tis given by the following equation: (25) T1: 2~~ If the discharge resistance is shorted out and all series resistance removed, the inductance can be found easily with the use of this fonnula. The oscillogram thus obtained will be somewhat damped due to the inherent resistance. The frequency, however, will not be appreciably affected. Land Care in the order of 10- 6 , while the inherent resistance is never over 200 ohms. Substi- tution. of these values in the equation for t will show how little R affects the frequency. Inherent Resist0nce The inherent resistance may be determined from the damping of the oscillations in the oscillogram taken for the inductance calculation. Considering equation 24: At a time t1 at which an 46 oscillation has reached a crest walue sin6't1 =land the equation becomes the following: _ e R _O(t, (26) el ~ tE At the peak of the next wave: -rx.(~ + T) R {27) ~ E L~ Where T is the period of oscillations. e1: r : the ratio of successive amplitudes (28) By obtaining the period and ratio of successive amplitudes, the inherent resistance can be found. Distributed Ga1;acitance to Space When the value of the discharge resistance is such that the wave is essentially non-oscillatory, any oscillations appearing on the crest of the wave will be due to the distributed capacitance of the suxge generator as long as there is no test load connected. 47 This capacitance can be detennined by recording the oscillation on the crest of a full wave with all inserted series resistance removed. If T2 equals the period of the secondary oscillation, Lis the inherent inductance, and CL the distributed capacitance, the equation for the determination of this is given by the following: (29) T2: 2h/i:ci The theory for this is the same as that for equation 25. An approximation of this capacitance can be made by finding the capacitance of the connecting leads of the surge generator to space. In some laboratories, this has been done by stringing up a suitable length of No. 25 g uag e wire a distance e qual to half the g enerator height from ground. The c a i:acitance of this is then measured.* * ncalculating Surge Generator Waves", McAuley and Benedict, Electric Journal, V 30, p 326 48 CALCULATION OF THE I NDUCTANCE of THE CA.LI FO HNI A I NST ITUTE OF TECHNOLO GY SURGE GEN"ER.ATOR Part shown in fi g ure 16c Part shown in fig ure l?b a: 51.7 cm.,g = 171.8cm. ·a1 :166.l cm. ,d 1.27cm. 1 a b -- 279 cm. d = 1.27 cm. = 5.96 micro-Henries Lab= 3.38 mic r o-Henries = ~ n12 = 103.5 cm. M12 :.0646 micro-Henries n13 : 207 cm. M13 : . 0135 micro-Henries n14 : 311 cm. M14 :.0061 micro-Henries lbc: 559 cm. Lbc = 7.50 micro-Henxies 1 = 279 cm. d : 279 cm. M = 1.043 micro-Henries Total::Lab+Lb 0 +M = 11.92 micro-Henries Tot al - 4LRt6M12 +4rvI13.f-2M1 4 = 24.25 micro Henries Inductance of Surge Generator = 11. 92 + 24. 25 = 36. 2microHenri es 49 EFFECTS OF THE LOAD Ilf.PEDANCE The determination of the circuit const a nts necessary to obtain the standard waves with no test apparatus in the circuit was given in the preceding section on the Attainment of Test Waves. rhere also 1 are shown the wave shapes as calculated for our surge generator. However, when the apparatus to be tested is inserted in the circuit, the wave shape may be distorted somewhat by both the test impedance and the impedance of the connecting lead. In consideration of this last point, it is always best to have the connecting lead a s short as possible. In some cases a complete picture of the effects is obtainable only through analysis of the particular circuit, which is laborious even with the use of operational Calculus. This has been treated rather thoroughly and most of the needed circnit analyses are available.* * "Impulse Generator Circuit Formulas", J. L. Thomason, A.I.E.E., V 53 p 169 . 50 In most cases, however, the only element of the test piece causing any appreciable effect is capacitance, which is so ~aall in relation to the surge generator capacitance and discharge resistance that the only important distortion of the wave is in the form of secondary oscillations appearing on the wave front and crest. This is due to the series inductance of the circuit acting with this ca:p3.citance. Figure 19 shows this effect. Indeed, in many cases these oscillations are of such small magnitude and short duration that, due to the relatively long time lag of the apparatus heing· tested, they are not considered objectionable by some engineers.* They can, however, be damped by the in- sertion of the proper series resistance. Detennination of Damping Resistance 'When the capacitance of the test is considered, the equivalent circuit is as shown in figure 18. By the use of Heaviside's Operational Calculus, the equa- "Technique of Surge Testing", F. D. Fielder, Electric Journal, V 30, n 2, p 73 51 Ls Rs R £ffecf of" Load F19. 19 Capacitance Cr 52 tion for voltage can he set up as follows: ( 30) R e = e0 RCt.P tl This can be expanded to the follo wing form: (31) e = eaA ( A -IJ(.)2-+w ':l [t-<(~ ;;>,.~{-~-« s1ni ,w f- -t -Coswi) I C. l 1 u.J Analysis of equation 31 shows that an oscillation is superimposed on the unidirectional component eoA 1 _«.t ~ (A-oc) +w' C. The oscillation can be eliminated b-y making w 2 = O. The value of R necessary to do this can be obtained by consideration of the equivalent simple series circuit with the discharge resistance neglected due to its relatively high value. (32) For such a simple circuit critical damping is attained 2 when the perarneter p =) Rs - 1 .:0 4Ls 2 LsCo R 2 1 (33) ~2 - - 4Ls L5 C0 ( 34) Rs : 2 ~ Ct Equation 34 determines the value of the damping resist- 53 ance. This is usually inserted at the terminal of the surge generator. However, it has been found in some cases better to distribute it along the surge generator circuit. When the resistance is located only at the terminal, the charging current of the condensers does not flow through it and the important damping effect is lost. The actual discrepancy is not as great as might be imagined due to the inherent resistance. This is effective in damping to a certain extent the oscillations caused by both the load capacitance and the distributed capacitance of the surge generator. When the circuit is being adjusted, there are other modifications of the wave that must be considered. Before going into this, however, it might be best to consider the effects of each constant. Effect of Circuit Constants upon Wave Shape Curves showing the effect of each constant as determined from an analysis of the circuit of figure 18 are given in figure 20. 54 Discharge Resistance: The most notable effect is shown to be upon the crest value of the voltage obtainable. Since the voltage across the test piece is the voltage across this resistance, its crest value is decreased by decreasing the resistance. As shown, the duration of the wave is almost directly proportional to the discharge resistance, while for the usual range of this resistance (0-3000) ohms, little effect is noticed upon the wave front. It can thus be said that, practically, the discharge resistance affects the tail and crest value, but not the front. Series Inductance: the inductance. Almost the reverse is true of It has little effect upon the crest value and an appreciable effect upon the wave front. The time to crest value is almost proportional to the induct ance. Its effect upon the tail of the wave, though slig ht, is not ap preciable. Load Capacitance: In the range of the capacitance of most test pieces, the effect is slight except for 14or,----.--,--.----~- L1 "6,000 4.6~x45.6 2.1 140 1140r-----,-,,--,==~~---~~-- .2 , '>O 6 46 V120 ,,,-,,:-,:-:,:-:,,-:-,0:-c,-",-- . - ~~ ~ - - - 140, cl = 0ll002'>0µf R1 ' 29-000H I.I':> v 2mrl 120 120 ~ 'a. :t. ;L9~ IOO~IOOf-4.."'--+:::..::;::::'- ':" :46 ro il.81 ao.~ soit--t-----f"=+--l-_;.-~--1-.Ll !.; I44 ~eo't""i:t--+-t--t::-c:-c-=--=-_,..--d--l---l ~1.1~ 60 8 6011--t----t--t-...::,hd--+~!:---i ~ ~ ~ i I ~ 40f--f'--l"":::t:-4'::::\--=-;:::+---!-LJ ~1.6~ 40 :::! ~ 40,f---:!=+-+:;;;::;::;;,~:;:::;::-r::==kcJ ::::15gzo ~2op--1::;;::-i::::::±:=--1f"'.'.-+-+-l---l .... 0~ 4/)00 Dampin g Jesistance 110r - - - r - - - - - ~ - ~ - - - - - - ~ ; Rz= 2,ooOH MS ~ j :s 4,? :;60•p-,Jt-4dsj=,+~-6:.j,::::::J_ LJ 2 - I 0 40 O ,120t-T,-+-+-+- -+-+-+-+---1 J8 J6 .:poo ,poo Series l nductance 0 " I C1 = 0.012',00µf O'--- - r Cz~ 0.000250J,.1 f 900µh L 1= Rr = 2,000 OHMS r '- :S 60 I f 3 [ }(, j R2:.W8f1iooOHMS Rz:10,000-' 1.S2J1.68.6 ~ 60 " Rz , 2.900 ~ j/ Rz=l,000 . I/ 20 4 I I l I.S0(26.9 0 4 0 ,u SEC 1.'> 0 .-.40.0 Az =100 2.00x20.2 \ µSEC I ~OJ~r--.-,--.--r--.-~~ ~ - -- 1 v ~ :::i. ;: ~ 61:,:( 120~120 f--f---'--L--'--l-V) is:100~100 ~ 4 i 80~ aoJ--J-!~~F T~-!-==l==:::t;::fc:::::'.I 60~ oot--+-+7"'F-+--+=--l<'.'.'.:+--1--L_J : J ~ ! 2 ~ ~2~40~40 ~ 5 ~ I 0 36 ~'--~ 00~2~00,.....,.Jo~o----,,,oc,-.,!>OO~~,~oo~ o ,ooc,-.,•~070~,~oo~,~ooo· 20<M 20 °o~-'- _J__L_6,000_j___[_8,000J__j_lO_{)OO J 72j)OOJ,,--'-~4poo R2 IN OHMS C2 INp.JJf Discharge ~esist ance Load Capacitance Curves showing effect of constants upon wave form Figure 20 bo the formation of crest osci llations. However, if the capacitance is large, it increases the front of the wave considerably. Damping Re sistance: As in the case of the discharge resistance, it has little effect upon the wave front and a proportional effect upon the duration. However, increasing this resistance cuts down the crest value of the wave considerably. Adjustment of Consta nts It is of importance to note that in the case of the simple series circuit, the effects of Land Rare practically the same as shown in these curves. It can now be seen that in correcting for crest oscillations two major difficulties arise; one in the effect upon the duration of the wave and the other upon the crest value. The introduction of darnping resistance may so increase the duration of the wave that it ~~11 be difficult to obtain some of the shorter duxation waves, such as the (½-5) or the (1-5 ). In this connection it should be noted also that 5'7 the load capacitance itself, the inherent inductance and the distributed capacitance of the surge generator are also factors which increase the wave front. The compare.ti vely large values of inherent inductance and distributed capacitance of some of the larger generators form the basis for the present proposals to have the (1-5) wave standardized to replace the (½-5). The effect of the damping resistance upon the crest value of the wave is very important in determining the voltage class of testing that can be performed. It is necessary in order to obtain the least distortion in varving Bs to vary the discharge resist., ance also, so that their sum shall be approximately the same. Thus, the increasing of Rs causes a de- creasing of R, vfuich further cuts down the crest value. BIBLIOGRAPHY Surge Generator Construction Generation of High Direct Voltage Impulses Marx, Elektrotechnische Zeitschrift, V 45 1924 Means of Producing Lightning Phenomena in Laboratory E. E. F. Creighton, A.I.E. E. Trans. V 25, p 365-39? 1906 Compact Portable 300 J{V Testing Equipment El. World, V 102, n 20 1933 Surge Generator in Sharon Laboratory O. Ackerman, El. Jl., V 29 1932 Portable Westinghouse '750 KV Surge Generator El. Jl., V 29 p 141 1932 A New Laboratory for Hi gh Voltage Lusignan and Borden, A.I. E. E., V 53 p 1255 1934 High Voltage Testing Equipment Norris and Taylor, J1. I.E. E., V 69 p 6'73 Operation and Theory M.S. Thesis, Purdue University ·J. E. Hobson, pp 65-82 1933 Calculating Surge Generator Waves Mclrn ley and Benedict, El. Jl., V 30 p 326 1933 Impulse Generator Circt1it Formulas Thomason, A.I. E. E., V 53 p 169 1934 . Characteristics of Surge Generators Bellaschi, A.I.E. E., V 51 p 936 1932 'l'echnique of St1rge Testing Fielder, El. Jl., V 30 n 2 p ?3 1933 Factors affecting Surge Potentials Torok and Ellis, El. Jl., V 30 p"381 1933 Laboratory :Measurement of Impulse Voltages Rowell and Foust, A.I. E.E., V 52 p 53? 1933 '11 he Measurement of High St1rge Voltages Bellaschi, A.I. E. E., V 52 p 544 1933 High Voltage Surge Testing Benedict, El. Jl, V 28 p 216 1951 Calculating Surge Generator Waves Foust, Kuehni, Robats, G. E. Rev., V 35 p 358 1933 Analysis of Laboratory Data McAuley, El. Jl., V 28 p 278 1 931 Laboratory Measurement of Impulses Dowell and Foust, A.I. E. E., V 52 p 53? 1933