FIFTH LECTURE V l>nte LONG DISTANCE TRANSMISSION mHREE-PHASE is used altogether for long distance transmission. Two-phase is not used any more, and direct current is being proposed, having been used abroad in a few cases : but due to the difficulty of generation and utilization, it is not probable that it will find any extended use, so that it does not need to be considered. FREQUENCY The frequency depends to a great extent on the character of the load, that is, whether the power is used for alternating current distribution — 60 cycles^-or for conversion to direct current — 25 cycles. For the transmission line, 25 cycles has the advantage that the charging current is less and the inductive drop is less, because charging current and inductance voltage are proportional to the frequency. VOLTAGE 11,000 to 13,200 volts and more recently, even 22,000 volts is most common for shorter distances, as 10 to 20 miles, since this is about the highest voltage for which generators can be built; its use therefore saves the step-up transformers, that is, the generator feeds directly into the line and to the step- down transformers for the regular load. The next step is 30,000 volts ; that is, 33,000 volts at the generator, 30,000 at the receiving end of the line. No inter- mediate voltages between this and the voltage for which generators can be wound is used, as 30,000 volts does not yet offer any insulator troubles ; but line insulators can be built at moderate cost for this voltage, and as step-up transformers 64 GENERAL LECTURES have to be used, it is not worth while to consider any lower voltage than 33,000 volts. This voltage transmits economically up to distances of 50 to 60 miles. 40,000 to 44,000 volts is the next step ; it is used for high power transmission lines of greater distance, where reliability of operation is of importance and the use of a conservative voltage therefore preferable to the attempt at economizing by the use of extra high voltages. A number of 60,000 volt systems are in more or less successful operation, and systems of 80,000 to 110,000 volts are in construction and a few in operation. Where the dis- tances are very great, power valuable, and continuity of ser- vice not of such foremost importance, such voltages are justi- fied in the present state of the art. In such very high voltage systems, the transformers are occasionally wound so that they can be connected for half voltage, for operating the line at half voltage, until the load has sufficiently increased to require full voltage; or the transformers are built for star or Y connection at full voltage, and at first operated in ring or delta connection, at — 7| = 57% of full voltage. The cost of a long distance transmission line depends on the voltage used. The cost of line conductors decreases with the square of the voltage. At twice the voltage, twice the line drop can be allowed with the same loss; at twice the voltage the current is only half for the same power, and twice the drop with half the current gives four times the resistance, that is, one-quarter the conductor section and cost. LONG DISTANCE TRANSMISSION 65 The cost of line insulators increases with increase of voltage. The cost of pole line increases with increase of voltage, since greater distance bet'.veen the conductors is necessary and so longer poles, longer cross arms, and heavier construction, and not so many circuits can be carried on the same pole line. The lower the voltage, the greater in general is the reli- ability of operation, since a larger margin of safety can be allowed. Since a part of the cost of the transmission line decreases, another part increases with the voltage, a certain voltage will be most economical. Lower voltage increases the cost of the conductor, higher voltage increases the cost of insulators and line construction, and decreases the reliability. The most economical voltage of a transmission line varies with the cost of copper. When copper is very high, higher voltages are more economical than when copper is low. The same applies to aluminum, since the price of aluminum has been varied with that of copper. Aluminum generally is used as stranded conductor. In the early days single wire gave much trouble by flaws in the wire. Aluminum expands more than copper with temperature changes, and so when installing the line in summer, a greater sag must be allowed than with copper, otherwise it stretches so tight in winter that it may tear apart. Aluminum also is more difficult to join together, since it cannot be welded. For the same conductivity an aluminum line has about twice the size, but one-half of the weight of a copper conductor, and costs 10% less; but copper has a permanent value, while the price of aluminum may sometime drop altogether, as the metal has no intrinsic value, being one of the most common 66 GENERAL LECTURES constituents of the surface of the earth, and its cost is merely that of its separation or reduction. LOSSES IN LINE DUE TO HIGH VOLTAGE The loss in the line by brush discharge or corona effect is nothing up to a certain voltage, but at a certain voltage it begins and very rapidly increases. The voltage at which a loss by corona effect begins is where the air at the surface of the conductor breaks down, becomes conducting and thus luminous. This occurs at a potential gradient of 100,000 to 120,000 volts per inch. The potential gradient is highest at the surface of the conductor. e J? o ■>* c/ Fig. 18. In Fig. i8 let R = radius of conductor. 2 d = distance between conductor centres. At a point x from the centre O the potential is c c 2 C X ^ = d' — X* d — X d + X for:x = d — R that is, at the conductor surface, it is : Ql=e LONG DISTANCE TRANSMISSION 67 Substituting this in the equation, gives : c hence: c = eR therefore the potential at point x is : 2 R X *~ d» — x' ^ and the potential gradient: _ d_f_ _ 2 R(d^ + x^) ^~ d X ~ (d* — x^)* ^ hence for : x = d — R or the conductor surface • §fo = ^ If this potential gradient becomes greater than the break- down strength of air, or ioo,cxx) volts per inch, corona effects and energy losses take place: e ^ = 100,000 gives: e = 100,000 R or E = 100,000 D, as the voltage where the corona begins, and : e E R = or D = IS the smallest radius 100,000 100,000 which can be used, at voltage E, where D is the conductor diameter = 2 R, and E is the voltage between the conductors = 2 e. For instance, wire No. 0000 D = .46" ; corona effects begin at the voltage E = 100,000 [) D^ = 46,000. ' ' For 100,000 volts the smallest diameter for which no corona effects occur is : D= ? =1" 100,000 68 GENERAL LECTURES In high potential transformers in the coils no corona effects may occur, because the diameter of the coil or the thick- ness is large enough, but the leads connecting the coils with each other and with the outside, if not chosen very large in diameter, may give corona effects and so break down. In a line or transformer, if one side is grounded, the other side has full voltage against ground, and so may give corona effects and break down ; while if not grounded, both sides have half voltage against ground and so give no corona effect. In the first case, the line or transformer so may break down, although the potential differences between the terminals are no greater than in the second case. For instance, in a 100,000 volt transformer or line, from each terminal to ground are 50,000 volts, and if the conductor diameter is 2 "> ^o corona effects occur. If now one terminal is grounded, the other terminal has 100,000 volts to ground and so at 2 " diameter gives corona effects, that is, glow and streamers which may destroy the insulating material or produce high frequency oscillations. At very high voltages it is therefore necessary to have the system statically balanced or symmetrical, that is, have the same potential differences from all the conductors to the ground. Any electric circuit, and so also the transmission line, contains inductance and capacity, and therefore stores energy as electromagnetic energy in the magnetic field due to the cur- rent, and as electrostatic energy, or electrostatic charge, due to the voltage. LONG DISTANCE TRANSMISSION 69 If: e = voltage, C = capacity. i = current, L = inductance. the electrostatic energy is : e*C 2 and the electromagnetic energy : i'L 2 In a high potential transmission line both energies are of about the same magnitude, and the energy can therefore see- saw between the two forms and thereby produce oscillations and surges resulting in the production of high voltages, which are not liable to occur in circuits in which one of the forms of stored energy is small compared with the other. In distribution systems up to 2200 volts and even some- what higher, the electrostatic energy is still negligible and only the electromagnetic energy appreciable. In static machines the electrostatic energy is appreciable, but the electromagnetic energy negligible. LINES AND TRANSFORMERS At voltages above 25,000 step-up and step-down trans- formers are always used, which are therefore a part of the high potential circuit Three-phase is always used in the transmission line. Some of the available transformer connections are given in Figs. 19 and 20. Grounding the neutral of the system has the advantage of maintaining static balance and so avoiding oscillations and disturbances in case of an accidental static unbalancing, as for 7© GENERAL LECTURES ^ i^i;;;;:;! /.) o£ir/i-o£irA ^) o£ir/<~ Y r-0£lTA a) r-r ^J 0£l77l*r s) rmsf-WMsr tf.j o^e/vasiTA r) Ttro^^AAse frM££'^/fAS0 T Fife. 19. Transformer Connections. instance, the grounding of one line. It has the disadvantage that a ground on one circuit is a short circuit and so shuts down the circuit. LONG DISTANCE TRANSMISSION 71 In connections i, 4 and 6 no neutral is available for grounding and so three separate transformers have to be installed in Y connection for getting the neutral. In connections 2 and 3 the neutral can be brought out from the transformer neutral. i? S^X /*/^AS£ OfAr7£r^fC/fL. S^^^'^ASS £>OU^^£^ £?£^£.7yf Fig. 20. Six-Phase Transformer Connections. In the T connection 5 and 7, the neutral is brought out from a point at one-third of the teaser transformer winding. Assimiing the line properly installed and insulated, break- downs may occur, either from mechanical accidents or by high voltages appearing in the line. ^^ GENERAL LECTURES HIGH VOLTAGE DISTURBANCES IN TRANSMISSION LINES These may be: A. Of fundamental frequency, that is, the same frequency as the alternating current machine circuit. B. Some higher harmonic of the generator wave, that is, some odd multiple of the generator frequency. C. Of frequencies entirely independent of the generator, or of a frequency which originates in the circuit, that is, high frequency oscillations as arcing grounds, etc. If a capacity is in series with an inductance, as the line capacity and the line inductance, the capacity reactance and the inductive reactance are opposed to each other ; if they hap- pened to be equal they would neutralize each other, the current would depend on the resistance only and therefore be very large, and with this very large current passing through the inductance and capacity, the voltage at the inductance and at the capacity would be very high. For instance, if we have 20,000 volts supplied to a circuit having a resistance of 10 ohms and a capacity reactance of 1000 ohms, then the total impedance of the circuit is V^io* + 1000' = 1000 and the current in the circuit 20,000 — = 20 amperes. 1000 If now in addition to the 10 ohms resistance and 1000 ohms capacity reactance, the circuit contains 1000 ohms inductive reactance, the total reactance of the circuit is 1000 — 1000 = o ohms, and the impedance is the same as c e the resistance, or 10 ohms. The current therefore — = ~r = LONG DISTANCE TRANSMISSION 73 2000 amperes, and the voltage at the capacity therefore is: capacity reactance times amperes = 2,000,000 volts, and the same voltage exists at the inductive reactance. These voltages are far beyond destruction. That is, if in a circuit of low resistance and high capacity reactance, a high inductive reactance is put in series with the capacity reactance, excessive voltages are produced. In a transmission line the capacity of the line consumes for instance 10% of full load current; that is, full load voltage sends only 10% of full load current through the capacity. To send full load current through the capacity so would require 10 times full load voltage. With a line reactance of 20%, 20% or ^ of full load voltage sends full load current through the inductive reactance, while 10 times full load voltage is required by the capacity reactance; the capacity reactance therefore is about 50 times and therefore cannot build up with it to excessive voltages ; but to get resonance with the fundamental frequency requires an inductive reactance about 50 times greater than the line reactance. The only reactance in the system which is large enough to build up with the capacity reactance is the open circuit reactance of the transformers. This is of about the same size as the capacity reactance, smce a transformer at open circuit and full voltage takes about 10% of full load current, and the capacity reactance also takes about 10% of full load current If therefore a high potential coil of a transformer at open secondary circuit is connected in series with a transmission line, destructive voltages may be produced, by the reactance of the transformer building up with the line capacity. In those transformer connections in which several high 74 GENERAL LECTURES potential coils of different transformers are connected between the transmission wires, this may occur if the low tension coil of one of the transformers accidentally opens and the high potential coil of this transformer then acts as inductive react- ance in series with the line capacity in the circuit of the other transformer. ~r I ^ T Fife. 21. This may occur for instance in transformer connection 2, Fig. 19, if as shown in Fig. 21, the low tension coil c opens. Then the high tension coil C is an inductive reactance in series ;c<> Fife. 22. with the line capacity from 3 to i, energized by transformer A; and C is a high inductive reactance in series with the line capacity from 3 to 2 in a circuit of voltage B. That is, from 3 to I and from 3 to 2 excessive voltages are produced. So also in T connection, Fig. 2.2, if for instance the low tension coil a opens, the corresponding high tension coil A is a high inductive reactance in series with the line capacities in a circuit LONG DISTANCE TRANSMISSION 75 of the voltages of the two halves, B and C, of the other trans- former, and excessive voltages therefore appear from i to 2 and from i to 3. This danger of excessive voltages by the accidental open- ing of a transformer low tension coil does not exist in delta connection, since in this always only one transformer connects from line to line. It is greatly reduced since the use of triple pole switches became general; and is very much less where several sets of transformers are used in multiple, since even if in one set a low tension coil opens, the other sets maintain the voltage triangle. Especially dangerous in this respect therefore is the L connection No. 6; since in this case, when using two trans- formers in open delta, for smaller systems only one set is installed and an accident to one of the transformers causes excessive voltages between its line and the two other lines. The open circuit reactance of the transformer is the only reactance high enough to give destructive voltages at gener- ator frequency, and in high potential disturbances, the trans- former connections should first be carefully investigated to see whether this has occurred.