LINES USING THE CONDUCTOR OF ONE OF THE PHASES ALSO AS PROTECTION AGAINST LIGHTNING STRIKES

V. K. Shcherbakov

I.

Annual capital investments in the construction of high-voltage power-transmission lines amount in our country to tens and even hundreds of millions of rubles. The construction of these lines is also associated with the expenditure of thousands of tons of acutely scarce nonferrous metals and high-quality steel. The need to protect high-voltage power-transmission lines against lightning strikes further increases both these capital investments and the consumption of scarce metals. Thus, equipping 110 kV lines erected on wooden supports with protective steel cables increases the cost of the lines by one and a half to two times¹ and additionally requires, for every hundred kilometers of a double-circuit line, 150–200 tons of high-quality steel cable.

Line protection may also be carried out by other means besides the suspension of a protective cable: for example, by installing along the line a large number of special lightning arresters (diverters), or by installing arresters on the line supports. However, these means of protection also usually cost no less than protection by cable, which, among a number of other types of protection, is the simplest and most reliable.

Far from all high-voltage power-transmission lines currently in operation in the USSR are equipped with the necessary means of protection against lightning strikes; the absence of protective devices is, as a rule, explained by the high cost of these devices and, to an even greater degree, by the scarcity of the materials required for installing protection—in particular, and first of all, steel cable. At the same time, it is difficult to find a region in the Union that would be entirely favorable with respect to lightning strikes. There is no need to prove in detail what often enormous material damage is caused to the national economy of the USSR by interruptions in the supply of electric power due to lightning strikes on power-transmission lines deprived of the necessary protective equipment.

In the present work, methods are proposed for constructing lightning-resistant high-voltage power-transmission lines without employing special protective means in the form of cables, diverters, arresters, etc. It is proposed that the working conductors of the line itself be used as protection against lightning strikes. One of the three conductors, in the case of a single-circuit three-phase line, or two of the six, in the case of a double-circuit line, can always be arranged on the support so that this conductor, or these conductors, would perform the role of lightning conductors, i.e., would replace the protective cables usually specially suspended for this purpose. The whole difficulty,

further consists only in ensuring the timely and rapid discharge into the ground of the energy of the lightning stroke without disrupting the insulation of the line.

This problem is solved most simply by permanently grounding the conductor of one of the phases, a conductor which, with an appropriate arrangement on the support, will provide protection for the line. The potential of this conductor relative to ground will thus be practically equal to zero, whereas the potentials of the conductors of the other two phases will reach the value $\sqrt{3}\,U_{\phi}$; operation of the line will be associated with the flow of current in the ground, sometimes of considerable magnitude. The insulation of the power transmission is placed under new operating conditions; the current in the ground and the asymmetry of the potentials of the line conductors significantly increase the harmful influence on communication wires; asymmetry of voltages and currents appears in the power transmission.

In what follows, the permissibility (insofar as possible) of the above-noted features of power transmission with a grounded phase will be clarified from the standpoint of normal operation of such a transmission. But it may already be noted preliminarily that the development of theoretical and practical electrical engineering in recent years now makes it possible to regard many phenomena accompanying the operation of an unsymmetrical transmission line as quite permissible, although not so long ago these phenomena seemed impermissible. Thus, Docent M. I. Mikhailov and Prof. P. A. Azbukin, in a book that appeared in print at the end of 1940,²) indicate comparatively simple means of protecting communication lines from the harmful interfering influence of high-voltage lines, developed recently and tested in laboratories and in the practice of operating communication lines. These means of protection make possible the parallel routing of communication lines and unsymmetrical high-voltage lines at almost any distance between them. Particularly important should be considered the achievements in the question of protection against interfering influences on single-wire communication lines, which until recently were considered defenseless in this respect.

Much should be taken into account from the experience of operating lines working according to the “two wires—ground” system, where the operating conditions of the power transmission are in many respects analogous to the operating conditions of lines with a grounded phase. In recent years the TPG system has been studied in detail by many organizations in the USSR and by individual persons, and at the same time it has been introduced comparatively rapidly into the practice of construction and operation of power transmissions. Thus, over the last decade more than a thousand kilometers of lines according to the TPG system have been built and put into operation, of which:³) 35 kV—61 km, 22 kV—220 km; almost three quarters of these lines have been built in agricultural districts.

Especially broad attention was given to the study of questions connected with the operation and design of the TPG system in the electric network of Lenenergo, where experimental sections of power transmission lines were set aside for the purposes of experimental study of the question. The results of these experimental investigations and theoretical calculations were published in 1935 in a book by Engineer P. S. Oreshkinskii.⁴)

Detailed investigations were also carried out in the Mosenergo system on an experimental 35 kV line, where the question of the influence of a power transmission operating according to the TPG system on communication wires, as well as other questions, was thoroughly examined.⁵)

²) M. I. Mikhailov and P. A. Azbukin, Overhead and Cable Communication Lines and Their Protection, Svyazizdat, 1940.

³) L. E. Ebin, “Networks Using the Ground as One of the Conductors,” Journal of Electric Power Stations, No. 8, 1939.

⁴) P. S. Oreshkinskii, Transmission of Energy by Three-Phase Current According to the “Two Wires—Ground” System, Academy of Sciences Publishing House, 1935.

⁵) Engineer A. M. Gol’dberg, “Use of the Ground as the Third Conductor in the Mosenergo System,” Journal of Electric Power Stations, No. 10, 1935.

The main difficulties that had to be overcome on the way to introducing the GPS system into practice were the following:

1) the unstudied behavior of grounding electrodes when large currents pass through them for a long time;

2) the presence of asymmetry of currents and voltages due to the asymmetry of resistances and capacitive currents of the line phases of the GPS system;

3) uncertainty regarding the possibility of using already developed and tested systems of protection against short-circuit currents;

4) increased requirements for the insulation of lines and substations, in particular for the insulation of transformers, under normal operating conditions and overvoltages;

5) a significant inductive influence on communication wires, caused by the asymmetry of the potentials of the wires and of the arrangement of the phase currents of the GPS-system line relative to the communication lines (the current of one phase passes in the earth at a great depth).

At present, on the basis of the above-mentioned experimental and theoretical studies in the systems of Lenenergo and Mosenergo, and also taking into account experience in the operation of GPS networks in agricultural districts, the following conclusions have been drawn regarding the operation of lines according to the GPS system:

1) the provision of working grounds in the GPS system presents no substantial difficulties; as the working ground, the protective grounding of substations can usually be used;

2) no serious difficulties are encountered in applying the existing types of protection against short-circuit currents in the GPS system;

3) asymmetry of currents and voltages within permissible limits can be ensured without special difficulties ^6);

4) in installations with a rated voltage up to 35 kV, transition to the GPS power-transmission system does not make it necessary to reinforce the insulation of lines and transformers;

5) the influence on communication wires, and especially on single-wire ones, is considerable; the chief part of this influence is electromagnetic influence; special studies by VEI showed that even at distances greater than 10 km there is an influence on single-wire communication lines.

Thus, taking into account the experience of operating GPS lines and the achievements in the field of protecting weak-current lines against interfering influences, it is necessary in what follows to dwell especially carefully on clarifying, chiefly, the following two questions:

1) whether the magnitude of the unavoidable asymmetry of voltages and currents in power transmissions with an earthed phase will lie within permissible limits, owing to the asymmetry of the capacitive currents of the lines and the branching of part of the line current into the earth;

2) in connection with the increase in the magnitude of the potentials of the wires of two phases relative to the earth by \(\sqrt{3}\) times when the wire of the third phase is permanently grounded, whether it is possible to preserve the existing insulation level of symmetrical three-phase power transmissions when changing over to power transmission with one phase permanently grounded at the same rated voltage; if not, how much this insulation level must be increased; in resolving the question of the insulation level, it will be necessary to take into account the possibility of new requirements for insulation arising from overvoltages and especially switching overvoltages.

It should be noted that the GPS system at a rated voltage of 110 kV and above has not been used and has not been studied; therefore, it must be assumed, the question of protecting GPS lines against lightning overvoltages has not been specially posed.

^6) Capacitive currents were not specially taken into account in the studies; the GPS system was envisaged (perhaps at first) for rated voltages up to 35 kV; possible large capacitive currents in cable networks were not taken into account.

It is important to note this because, while ensuring reliable and, perhaps, the cheapest protection of a line against direct lightning strikes by suspending a special cable, we are returning to a three-wire line, all the more since the limit of permissible current asymmetry in power transmission requires, as calculations show, the suspension, as the third conductor, not of a steel cable but of a non-ferrous-metal conductor with sufficient conductivity; admittedly, this conductor may be taken with a smaller cross-section than the cross-sections of the conductors of the other two phases, but then, among other things, its cost turns out to be no higher than the cost of a steel cable.

The permanent and solid grounding of one phase is not the only way of using the conductor of one of the phases also as protection, while ensuring the discharge of the energy of a direct strike into the earth. This discharge can be ensured while preserving the insulation of the power transmission in the form, or almost in the form, in which it is normally present in symmetrical power transmissions, with the only difference that the insulator strings of the conductor providing protection for the line are furnished with arc-diverting rings or horns; extinction of the arc, after the strike energy has been diverted to earth, is ensured by the presence at the substations of arc-extinguishing apparatus. Finally, in some cases it may prove expedient to discharge the energy of a lightning strike to earth through arresters installed on one phase on the line supports.

II

The scheme of power transmission using the conductor of one of the phases also as protection, when this conductor is permanently and solidly grounded at every support, is shown in Fig. 1. The requirements for the transient grounding resistances of the supports here are the same as in the case of suspending special cables on the supports. At the substations at the ends of the line, the grounded conductor is connected to the protective grounds of the substations and is also used at the substations for two purposes: both as the conductor and bus of one of the phases, and as protection of the substation against lightning strikes. There is every reason to suppose that during switching operations at the substations the grounded phase need not be disconnected, i.e., one may confine oneself to installing circuit breakers and disconnectors only on the two ungrounded phases.

Fig. 1.

The arrangement of the conductors on the supports may be adopted as the usual one, if one has in mind the iron supports of double-circuit lines with cables; the places of the cables on the support will be taken by the conductors of the grounded phase, and the lower cross-arm of the support will prove unnecessary; accordingly, the height and weight of the supports will be reduced at this expense.

The line capacitance currents, caused by the asymmetry of the conductor potentials (Fig. 2), will also yield an asymmetrical three-phase system. Using Maxwell’s equations, in accordance with the notation of Fig. 3, we find the charges of the conductors:

\[ \begin{aligned} q_1 &= C_{11}\cdot \overline{U}_{10} + C_{12}\cdot(\overline{U}_{10}-\overline{U}_{20}) + C_{13}\cdot(\overline{U}_{10}-\overline{U}_{30}) \\ q_2 &= C_{12}\cdot(\overline{U}_{20}-\overline{U}_{10}) + C_{22}\cdot \overline{U}_{20} + C_{23}(\overline{U}_{20}-\overline{U}_{30}) \\ q_3 &= C_{13}\cdot(\overline{U}_{30}-\overline{U}_{10}) + C_{23}\cdot(\overline{U}_{30}-\overline{U}_{20}) + C_{33}\cdot \overline{U}_{30} \end{aligned} \]

Fig. 2.

Fig. 3.

Fig. 4.

Accordingly, the phase capacitive currents are obtained as

\[ \left. \begin{aligned} \overline{I}_{c1} &= j3\omega \cdot U_1 C_{12},\\ \overline{I}_{c2} &= \sqrt{3}\cdot \omega \cdot U_1 C_{23} + j\omega\sqrt{3}\,U_1(C_{22}+C_{12})\angle -150^\circ,\\ \overline{I}_{c3} &= -\sqrt{3}\omega \cdot U_1 C_{23} + j\omega\sqrt{3}\,U_1(C_{22}+C_{12})\angle 150^\circ. \end{aligned} \right\} \]

The capacitive current of the first (grounded) phase calculated in this way will represent only the charge associated with the grounded conductor. This current will be offset by the sum of the reverse currents of the other two ungrounded phases, equal to

\[ \overline{I}_{c2}+\overline{I}_{c3} = [\sqrt{3}\cdot\omega\cdot U_1 C_{23} +j\omega\sqrt{3}\,U_1(C_{22}+C_{12})\angle -150^\circ] + [-\sqrt{3}\cdot\omega\cdot U_1 C_{23} +j\omega\sqrt{3}\,U_1(C_{22}+C_{12})\angle 150^\circ] = j\omega 3\cdot U_1(C_{22}+C_{12}). \]

The vector diagrams of the phase voltages, potentials, and capacitive currents are shown in Figs. 4 and 5.

Both the current delivered at the end of the transmission line and the capacitive current will flow along the conductor of the grounded phase only partially. Part of the current of the grounded phase will branch off into the earth. This circumstance, in addition to the asymmetry of the capacitive currents, will in itself lead to asymmetry of the phase currents of the line. The final result of the flow of a system of unbalanced currents through the line conductors will be the appearance, throughout the entire electric transmission and in the station generators, of a negative-sequence current. The permissible magnitude of the negative-sequence current in generators is regulated by the “Rules for the Technical Operation of Electric Stations and Networks,”² according to which generator operation is permitted when the inequality of currents in the phases is 10%, which is equivalent to the presence of a negative-sequence component of slightly more than 5%.

Fig. 5.

For calculating the negative-sequence component of the current in the generators, it is necessary to know the negative-sequence voltages of all elements of the electric transmission and, first of all, of the line. In turn, the symmetrical components of the phase voltages of the line are determined primarily by the symmetrical components of the phase currents, and these latter can be easily determined if the currents in the conductors of all three phases of the line are known. It may be quite permissible to assume that a symmetrical three-phase system of currents is taken off at the end of the line, if it is considered that the total asymmetry of currents and

Fig. 6.

transmission-line voltages does not exceed the permissible limits. Such an assumption will not appreciably affect the final results of the calculation. Thus, the currents in the conductors of the ungrounded phases are determined directly as currents corresponding to the power taken at the end of the line. As for the current in the conductor of the grounded phase, it will be obtained as the sum of two currents:

1) the part of the current of the grounded phase taken at the end of the line (the operating current);

2) the part of the capacitive current of the grounded phase, as the sum of the currents of the two other phases.

Note: The currents of active conductance are not taken into account here, since they are usually omitted from practical calculations because of their insignificance; if, for some reason, these currents had to be taken into account, this could be done in exactly the same way as indicated for taking account of the capacitive currents.

When dividing the currents of the grounded phase into two parts—in the conductor and in the earth—it is unfortunately impossible to make use of a simple ratio between the resistances of the conductor of the grounded phase and of the earth, since, although calculation of the resistance of the conductor–earth loop presents no difficulty, it is difficult to single out from the total resistance of this loop the part pertaining to the earth. Therefore it is necessary to consider the current of the grounded phase as the zero-sequence current of a two-phase system of currents flowing in the two ungrounded phases of the line.

Thus, the first system of line currents, due to the load, is shown in Fig. 6. Its symmetrical components will be:

\[ \overline{I}_1=\frac{1}{2}\left(\overline{I}_b-\overline{I}_c\right), \]

\[ \overline{I}_0=\frac{1}{2}\left(\overline{I}_b+\overline{I}_c\right)=\frac{1}{2}\left(-\overline{I}_a\right), \]

i.e., the current of the grounded phase (phase \(a\))

\[ \overline{I}_a=-2\overline{I}_0=-\left(\overline{I}_{bo}+\overline{I}_{co}\right). \]

Fig. 7-a.

Fig. 7-b.

The paths of the zero-sequence currents, according to the above decomposition, are shown in Figs. 7-a and 7-b.

For the separately considered phase \(b\), with reference to Fig. 7-a, one may write the equality

\[ j\overline{I}'_{bo}\omega L_{nn}+j\overline{I}''_{bo}\omega M+\overline{I}'_{bo}R_n+\left(\overline{I}'_{bo}+\overline{I}''_{bo}\right)R_n= \]

\[ =j\overline{I}'''_{bo}\omega L_{nz}+j\overline{I}'_{bo}\omega M+\overline{I}'_{bo}R_z+\left(\overline{I}'_{bo}+\overline{I}''_{bo}\right)R_n; \]

where \(\overline{I}'_{bo}\) and \(\overline{I}''_{bo}\) are the parts of the zero-sequence current in the conductor and in the earth;

\(L_{nn}\) is the self-inductance coefficient of the loop: conductor \(b\)—conductor \(a\);

\(L_{nz}\) is the self-inductance coefficient of the loop: conductor \(b\)—earth;

\(M\) — coefficient of mutual induction of the conductor–conductor loop and the conductor–ground loop;

\(R_n\) and \(R_z\) — respectively, the active resistance of one conductor of the loop and the active resistance of the ground.

The last equality makes it possible to find the ratio

\[ \frac{\overline I'_{bo}}{\overline I''_{bo}} = \frac{R_z + j(\omega L_{nz} - \omega M)} {R_n + j(\omega L_{nn} - \omega M)} . \]

The obtained ratio will not correspond to reality because, in the preceding reasoning, the mutual induction of circuits with the currents of phase \(c\) was not taken into account and, in addition, the resistance of the conductor of the grounded phase (phase \(a\)) must be doubled, since this conductor participates twice in the reasoning: both with respect to phase \(b\) and with respect to phase \(c\). Taking into account the mutual induction of all circuits and the doubled active resistance of the phase-\(a\) conductor, the ratio of the currents \(\overline I'_{bo}\) and \(\overline I''_{bo}\) is obtained as somewhat more complicated, but the order of reasoning and the character of the final result are the same \(^{8}\).

Fig. 8.

For a 110 kV transmission line with the arrangement of conductors on the support (Fig. 8) and with AC—185 conductors, and with soil resistivity \(\rho = 100\ \Omega/\text{m}^3\), the ratio is

\[ \frac{\overline I'_{bo}}{\overline I''_{bo}} = \frac{\overline I_{\text{conductor}}}{\overline I_{\text{ground}}} = \frac{0.197 + j1.20}{0.330 + j0.845} = 1.34 \angle 12^\circ, \]

i.e.

\[ \overline I_{pr} = 0.573\,\overline I_a \angle 2^\circ 30', \]

\[ \overline I_z = 0.432\,\overline I_a \angle -9^\circ 30'. \]

If the conductor of the grounded phase is made of a smaller cross-section than the conductors of the other two phases, for example, if an AC—95 conductor is taken, then the ratio

\[ \frac{\overline I'_{bo}}{\overline I''_{bo}} = \frac{\overline I_n}{\overline I_z} = 1.15 \angle 27^\circ, \]

i.e.

\[ \overline I_{pr} = 0.550\,\overline I_a \angle 12^\circ 30', \]

\[ \overline I_z = 0.477\,\overline I_a \angle -14^\circ 30'. \]

Since the capacitive current of the grounded phase is the sum of the capacitive currents of the other two phases, the two-phase unbalanced system of capacitive currents represented by phases \(b\) and \(c\), when decomposed into symmetrical components, also gives

\[ \overline I_{co} = \frac{1}{2}(\overline I_{bc} + \overline I_{cc}) = \frac{1}{2}\,\overline I_{ac}, \]

\(^{8}\) For details see V. K. Shcherbakov, Electrical calculation of three-phase transmission lines with a permanently grounded phase. Accepted for publication in Izvestiya TII.

therefore, the capacitive current of phase \(a\) may also be regarded as the sum of the zero-sequence capacitive currents of the above-mentioned two-phase unbalanced system. Taking into account that the paths of the capacitive currents and of the operating zero-sequence currents are the same, we may write that

\[ \frac{\overline{I}'_b}{\overline{I}''_b}=\frac{\overline{I}'_{bc}}{\overline{I}''_{bc}}, \]

i.e., the capacitive current in phase \(a\) is divided into two parts in the same ratio as the line current caused by the load at the end of the line.

Knowing the currents in the line conductors, as well as in other parts of the power transmission, it is no longer difficult to calculate the negative-sequence voltages and currents in the various parts of the power transmission and to determine the current unbalance in the generator.

For example, in a power transmission system—generator—step-up transformer—line—with the following data:

a) generator—58.9 MVA, 10.5 kV, \(X=14\%\), auxiliary load on the busbars 8 MW, \(\cos\varphi=0.8\);

b) transformer—60 MVA, \(X=11\%\), \(R=0.5\%\);

c) line—110 kV, double-circuit, \(l=100\) km, AS-185, conductor of the grounded phase AS-95, arrangement of conductors on the tower as in Fig. 8, \(\rho_z=100\ \Omega/\mathrm{m}^3\); power taken at the end of the line—40 MW, \(\cos\varphi_k=0.85\);—in the generator the ratio obtained is

\[ \frac{I^{(2)}}{I^1}\,100=3.93\%. \]

Consequently, on the basis of what has been set forth, it may be considered that, with respect to the occurrence of negative-sequence currents of impermissible magnitude in the generators of stations operating into a transmission line with a grounded phase, power transmission systems with a grounded phase will usually be quite satisfactory.

III.

If for some reason it is necessary to limit the current in the earth that appears when one of the phases is grounded, the conductor of the grounded phase can be rigidly connected to earth (more precisely, to the grounding device) at only one point along the length of the line, as shown in the diagram (Fig. 9).

However, the objective will be achieved only in the case of short lines, whose capacitive current is small: despite the fact that the conductor is grounded at only one point, the capacitive current, before entering the conductor of the grounded phase, flows in the earth. The possibility of the unhindered discharge of the energy of a direct strike to earth is ensured by the presence, at each tower, of spark gaps. The conductor, permanently grounded at one point, must have insulation at all other towers, shunted by an arc at the moment when the energy of a direct strike is discharged. The level of this insulation is determined by the requirement that, under the normal operating condition of the power transmission, the spark gaps should not flash over because of the voltage drop in the conductor. Consequently, this must be insulation of the order of line insulation for a nominal voltage of 6 kilovolts.

The design of the spark gaps must be such as to facilitate as much as possible the extinction of power-frequency arcs. There is reason to believe that, if the stability of the potential of the grounded conductor is ensured by rigidly connecting this conductor at one point (in Fig. 9—at point a) to “earth,” the arc-extinction conditions will be no worse than when systems are equipped with extinguishing apparatus. Oberdorfer⁹, on the basis of experiments, shows that

⁹ G. Oberdorfer, Ground faults and combating them. Energoizdat, 1932.

that earth-fault arcs with currents up to 40 A in 35, 60, and 110 kV installations went out by themselves, provided only that the arc was maintained by the residual current of undercompensation or overcompensation; that is, it must be assumed that the coil limited the oscillation of the potentials of the transmission-line conductors, and, first of all, of the conductor with damaged insulation, and that restoration of the phase potential was slowed.

Fig. 9.

In the case under consideration, arcs of greater current strength may arise, since the breakdown of some spark gap will lead to an earth fault of the conductor at one more point and thereby provide for branching off part of the current into the ground, as was explained above. Here arcs with currents of 100 amperes and more may arise, and the extinction of such arcs can apparently be ensured only by maximally reducing the potential difference at the electrodes of the spark gaps and by choosing such a design of the electrodes of these gaps in which rupture of the arc would be accelerated by its being blown out. The potential difference at the spark gaps is determined by the voltage drop in the grounded conductor and, consequently, only in short lines, several tens of kilometers long, can the necessary conditions for extinguishing the arcs of the spark gaps be obtained.

As has already been indicated, the use of the conductor of one of the phases as protection against lightning strokes can be carried out, without disturbing the usual symmetry of the insulation of the phases of the transmission line, in the following manner.

The conductor of one phase of a three-phase line, correspondingly arranged on the support (Fig. 10), is provided on each support with a spark gap guaranteeing discharge through the gap, and not along the string of insulators, under any abnormal increases in the potential of the conductor. If the given transmission line has an isolated neutral of the transformers and is provided with devices for extinguishing volt arcs of earth faults—a Petersen coil, a Bauch transformer, a Reithoffer suppressor, etc.—then, with an appropriate design of the spark gap, the lead to ground

Fig. 10.

the energy of a lightning stroke will be reliably ensured without interrupting the operation of the power transmission line. There is extensive experience in the construction and operation of spark gaps on strings; gaps with various electrode shapes (rings, half-rings, double-sided and single-sided horns, etc.) successfully cope with the task of diverting the arc away from the string. In our case it is required that the construction of the gap guarantee the impossibility of blowing the arc onto the string under any unfavorable wind direction, and that it ensure arc burning at a distance that is thermally safe for the string.

The spark gap of the phase–ground wire will, in the overwhelming majority of cases, be loaded by arcs due to an uncompensated or overcompensated current of at most 30–40 amperes. Therefore there is no particular reason to fear these short-duration arcs, and the value of the spark gaps may be reduced to a level that would ensure their not especially frequent flashovers due to switching overvoltages. This must also be done in order to be certain that, when a high potential arises on a tower, the strings of the two other phases will under no circumstances flash over.

The grounding of each tower, it goes without saying, must be performed so as to satisfy all the requirements usually imposed on the grounding of shield wires³.

The distance from the phase–ground wire conductor to the conductors of the two other phases will have to be increased to the values indicated in the following table:

This distance is only slightly greater than the distances usually adopted between the conductors of a line, and therefore the asymmetry of the conductor resistances, it may be expected, will not be significant.

Transposition will have to be abandoned, at least for all three conductors; the two lower conductors may be transposed if there is any benefit from this. The absence of transposition will have the effect of increasing the degree of influence on communication wires.

The use of the conductor of one phase as protection apparently provides reliable protection against lightning strokes for the power transmission line, but not for substations. The approaches to substations and the substations themselves must be protected by special ground wires or diverters.

The present variant of using the conductor of one phase as protection provides for mandatory equipping of the electrical system with arc-suppression devices and, most probably, with a Petersen coil. In this connection it is of some interest to note the attitude of American practice toward arc-suppression devices and, in particular, toward the Petersen coil.

Power transmission lines with a rated voltage of 110 kV and above have until now been constructed in the USSR and the USA almost exclusively with a solidly grounded neutral; in most countries of Western Europe, on the contrary, with an insulated neutral or with grounding through inductive coils. However, in recent years, as Prof. L. I. Sirotinsky⁴ noted in his time, owing to the ever-increasing electromagnetic

influence on communication wires due to enormous earth-fault currents, and the desire to reduce to a minimum the causes leading to disruption of the parallel operation of electric systems—in America they are beginning to retreat from solid grounding. Moreover, American systems are beginning to take a keen interest in the Petersen coil, which has been reflected in recent American periodical literature, filled with articles and discussions on the question of the merits and shortcomings of the Petersen coil, its tuning, and the analysis of the operation of systems equipped with Petersen coils⁵. In America, in Colorado, a 220 kV transmission line was in operation in 1938 equipped with a Petersen coil⁶; moreover, let us note that this same transmission line has two protective cables along its entire length.

In considering the question posed, it is immaterial whether the Petersen coil is precisely the apparatus required for the operation of an electric system with an isolated neutral, or whether other methods must be sought for extinguishing intermittent arcs; what is important is that practice compels abandonment of solid grounding. It is important to conclude that systems with an isolated neutral, or, what is the same thing, with neutral grounding through inductive coils with large resistances, are economically expedient, if one has in mind the practice of Western Europe and the tendencies in America in this respect.

It should finally be pointed out that, instead of arc-suppression apparatus and arc-suppression rings, the phase serving as protection may be equipped with arresters on the line supports.

Variants of using the conductor of one of the phases also as protection, without disturbing the usual symmetrical insulation of the line phases, rule out the possibility of transposing all three line conductors, unless one accepts an inevitable increase in the cost of the line. The two lower conductors can be transposed, which, as investigation of this question shows, also gives a favorable effect. Thus, for example, as applied to a transmission line with the arrangement of AS-185 conductors according to Fig. 8, in the absence of transposition an earth current of \(1.2 \cdot 10^{-2}\ \mathrm{A/km}\) appears; transposition of the two lower conductors reduces this current to \(0.74 \cdot 10^{-2}\ \mathrm{A/km}\). Some equalization of the inductive resistances of the line phases is also achieved by transposing the lower conductors. Thus, in the same example of the line the values of the self-inductance coefficient are obtained as follows:

a) without transposition

\[ \begin{aligned} L_a &= 1.44 \cdot 10^{-3}\ \mathrm{H/km},\\ L_b &= 1.28 \cdot 10^{-3}\ \mathrm{H/km},\\ L_c &= 1.48 \cdot 10^{-3}\ \mathrm{H/km},\\ L_{\mathrm{av}} &= 1.44 \cdot 10^{-3}\ \mathrm{H/km}; \end{aligned} \]

b) with transposition of the lower conductors

\[ \begin{aligned} L_a &= 1.45 \cdot 10^{-3}\ \mathrm{H/km},\\ L_b &= 1.43 \cdot 10^{-3}\ \mathrm{H/km},\\ L_c &= 1.43 \cdot 10^{-3}\ \mathrm{H/km},\\ L_{\mathrm{av}} &= 1.44 \cdot 10^{-3}\ \mathrm{H/km}. \end{aligned} \]

IV.

The insulation of power transmission lines with a grounded phase operates under new conditions in comparison with the operating conditions in symmetrical power transmission lines: the working potential of the ungrounded phases is equal to the difference of the phase—

voltages, i.e., \(\sqrt{3}\) times greater than the phase potential of a symmetrical electric transmission of the same rated voltage. Operating experience with electric transmissions under the DPZ system has shown that, in three-phase electric transmissions with rated voltage up to and including 35 kV, transition to a mode of operation with one phase permanently grounded does not require strengthening the insulation either on the line or at substations. As regards electric transmissions with rated voltage of 110 kV and above, however, there has been no experience of prolonged operation of electric transmissions with one grounded phase. It is true that in designing and calculating the insulation to ground of high-voltage installations, not only the phase voltage of the installations is taken into account, but also the line voltage of these installations; nevertheless, the insulation now existing in symmetrical high-voltage installations is designed for prolonged operation at potentials relative to ground equal to the phase voltage of these installations.

What determines the insulation level of high-voltage systems operating with a grounded neutral?—Usually the ratio of the “internal” overvoltages occurring in installations, and primarily switching overvoltages, to the phase voltage of the installations. Certain corrections are introduced here by the calculation of the required lightning-withstand capability of these installations. Analysis of switching overvoltages in electric transmissions with one phase permanently grounded shows that:

a) overvoltages when unloaded lines are disconnected give an amplitude of the incident wave on the transformer of not more than \(3U_{\phi}\), i.e., of the same magnitude as occurs in installations with a grounded neutral of transformers;

b) overvoltages when inductive loads are disconnected create a potential on the windings of the object being disconnected, relative to ground, higher than in symmetrical systems by an amount equal to one-half the phase voltage.

Other internal overvoltages:

a) resonance overvoltages, in that part of them which arises from resonance at the operating frequency and at higher harmonic components, have the same conditions for their occurrence and development in electric transmissions with a grounded phase as in symmetrical systems; as for the phenomenon of phase reversal, which in symmetrical installations under certain conditions creates overvoltages up to \(5U_{\phi}\), this phenomenon in installations with a grounded phase apparently retains the same character.

b) Arc overvoltages are absent.

Thus, only the case of disconnecting an inductive load gives, in our case, an increase of potential during overvoltages by one-half the phase voltage; but if it is taken into account that this type of overvoltage in symmetrical installations is not the most dangerous (\(\sim 4.5U_{\phi}\))\(^{14}\), it must be concluded that the insulation of symmetrical installations is suitable, from the point of view of insulation level, under the conditions of electric transmissions with a grounded phase. The requirements imposed on the insulation by atmospheric overvoltages in both cases will be the same. It remains further to check how the insulation behaves under the action of the increased operating potential.

Line insulation. The nonuniform distribution of the voltage drop along an insulator string leads to overloading of the first elements (from the conductor) of the string when a potential difference of 110 kV and above is applied to it. About 20% of the entire potential difference applied to the string falls on the first element,\(^{15}\) and this share

\(^{14}\) L. I. Sirotinskii, Overvoltages and Protection against Overvoltages in Electrical Installations, ONTI, 1937.

\(^{15}\) L. I. Sirotinskii, High-Voltage Engineering, Part II, GONTI, 1939.

almost does not change with an increase in the number of elements in the string. If the corona voltage on an element of the string is estimated at \(15 \div 20\) kV, then already in 110 kV transmission lines with a grounded phase one must expect the appearance of corona on the first element of the string. It is not entirely clear, on the basis of the information available in the literature, what the intensity of the corona must be for there already to be grounds to fear gradual destruction of the porcelain surface. In 110 kV transmission lines the corona intensity will be so insignificant that it is difficult to expect noticeable destruction during the service life of the insulation. Experiments carried out in the high-voltage laboratory of the Tomsk Industrial Institute showed the absence of visible corona on a 7-element string (P—4.5) in the dry and wet state under a voltage of 115 kV relative to earth; likewise, no increase in the active conductance of the string was detected under these conditions.

There is, however, a simple means for equalizing the voltage drops along the string: suspending metal rings at the ends of the string reduces the voltage drop on the first element by approximately a factor of two. Such rings will be absolutely necessary for 220 kV transmission lines with a grounded phase.

The insulation of transformers for transmission lines with a grounded phase must be made of equal strength both between phases and to earth; the insulation to earth of one of the phases could be somewhat weakened. It must be assumed that 110 kV transformers now being built for symmetrical three-phase systems operating with an isolated neutral will require almost no modifications when changing over to operation with a grounded phase. Transformers intended for operation in systems with a grounded neutral sometimes have somewhat weakened insulation to earth at the neutral and therefore would prove directly unsuitable for transmission lines with a grounded phase. The question of transformer design, in the sense of the rational placement of insulation inside the transformer, requires appropriate research work by special transformer laboratories in contact with transformer plants.

V.

High-voltage transmission lines exert an influence on communication wires through:

a) the magnetic field—electromagnetic influence,
b) the electrostatic field—electrostatic influence.

In turn, both kinds of influence on communication wires are subdivided into dangerous and interfering. Dangerous influences are determined primarily by short-circuit currents and therefore will depend little on the transmission system. Interfering influences, on the contrary, are determined by the normal operating condition of the transmission lines and to a very great extent by the transmission system.

The electrostatic interfering influence of a high-voltage line with a grounded phase on a single-wire communication line, according to the Electrotechnical Rules and Standards 16), is calculated by the formula:

\[ U_{в}=300 \cdot E \cdot 10^{-3}\sum \frac{b \cdot c \cdot l_n}{(n+2)(a^2+b^2+c^2)}\frac{p \cdot q}{\ } ; \]

16) “Electrotechnical Rules and Standards,” Part 1, fifth edition, 1933. The new “Standards” for calculating influence on communication lines have not yet been published, although there is information that the draft of these “Standards” is already in print.

the electrostatic effect on single-wire communication lines in the case of a three-phase symmetrical (intact) line is calculated by the formula:

\[ U_{в}=0{,}25\cdot E\cdot \sum \frac{c\cdot \delta \cdot l_n}{(n+2)(a^2+b^2+c^2)}. \]

Comparing the magnitudes of the noise voltages in these two cases, we obtain an increase in the noise voltage when one of the phases is grounded by

\[ \frac{ 300\cdot 10^{-3}\cdot E\sum \frac{b\cdot c\cdot l_n\cdot p\cdot q}{(n+2)(a^2+b^2+c^2)} }{ 0{,}25\cdot E\sum \frac{c\cdot \delta \cdot l_n}{(n+2)(a^2+b^2+c^2)} } = \frac{0{,}3\cdot b\cdot l_n\cdot p\cdot q}{0{,}25\cdot \delta\cdot l_n} \ \text{times}; \]

here \(b\) is the suspension height of the conductors of the high-current line; in approximate calculations we shall take \(b\) equal to \(12\ m\);

\(\delta\) is the distance between the conductors of the power-transmission line; in approximate calculations \(\delta\) is taken equal to \(4\ m\);

\(l_n\) is the length of the section of convergence in kilometers; in approximate calculations, as applied to symmetrical (transposed) lines, one may take \(l_n=10\ km\), bearing in mind that the length of the transposition step of high-current lines, with the conductors not arranged at the vertices of a triangle, must be no more than \(12\ km\); as applied to lines with a grounded phase, \(l_n\) is equal to the entire length of the section of convergence; if it is assumed that a \(100\ km\) power-transmission line has convergence with a communication line over its entire length, then in this case \(l_n=100\ km\);

\(p\) and \(q\) are coefficients taking into account the reduction of the effect due to cables and the neighboring forest; in approximate calculations we shall take the value of these coefficients equal to unity.

Thus, with a \(100\ km\) convergence, the noise voltage increases when one of the phases of the line is grounded by

\[ \frac{0{,}30\cdot 12\cdot 100}{0{,}25\cdot 4\cdot 10}=36\ \text{times}. \]

The electromagnetic interfering effect is determined by the strength of the currents of the phases of the power-transmission line and does not depend on the phase voltages and the potentials of the power-transmission conductors; it is determined by the system of three-phase current and by the combined action of all three phases—or, more precisely, of all the currents accompanying the operation of the power transmission; it is determined by the arrangement of the phase currents of the power transmission relative to the conductors of the communication line. The high-voltage three-phase power transmissions now in operation are practically symmetrical, carrying a symmetrical three-phase system of positive-sequence currents (practically), the sum of whose phase currents in any cross-section of the power transmission is equal to zero. Transposition of the conductors equalizes the distances of the phase conductors to the communication line. Therefore, in normal operation there will be practically no electromagnetic effect here.

A different picture is obtained in the case of power transmission with a grounded phase: in the conductors there is an unsymmetrical system of currents, only the lower conductors are transposed, and conductor transposition has no particular significance in this case. The noise voltage may be very large, and the effect of power-transmission lines on a single-wire communication line may be felt at a distance of \(10\ km\). Thus, with a ground current of \(40\ A\) and a convergence-section length of \(150\ km\), the interfering effect is felt at a distance of \(8\ km\).

However, as has already been indicated above, at the present time there is a very effective means of protecting single-wire communication lines from interfering influences. Using American experience, research workers of the Institute of Electrification of Agriculture, comrades Kuhner and Ebin, carried out a practical test of the effectiveness of using transformers with a transformation ratio equal to unity for combating interference in single-wire communication lines.^17) This method makes it possible to protect the communication line equally well from both electrostatic and electromagnetic interfering influences. It should also be added that single-wire telephone communication lines at present are not widely used.

Two-wire communication lines, with respect to electrostatic interference, are in a better position. If one takes the ratio of noise voltages in two cases: in the case of the influence of a symmetrical power-transmission line and then of a line with a grounded phase, then this ratio will be equal to

\[ \frac{ 0.125 \cdot E \cdot \sum \frac{l_s \cdot b \cdot \delta}{a^2 + b^2 + c^2} }{ 0.07 \, E \cdot \sum \frac{l_s \cdot b \cdot \delta}{a^2 + b^2 + c_2} } = \frac{0.125}{0.70} \simeq 1.8 . \]

The interfering electromagnetic influences on two-wire communication lines are also smaller than in the case of single-wire communication lines, but nevertheless, for large lengths of parallel approach, the noise voltage may reach considerable values. In this respect two-wire communication lines suffer almost exclusively on account of the asymmetry of the communication line relative to the earth. This follows quite clearly from the formula for calculating the noise voltage due to electromagnetic influence, which has the following form, according to the “Provisional instructions for protecting communication lines from the influence of three-phase-current transmission lines in which the earth is used as the third conductor,” issued by the People’s Commissariat of Communications in agreement with Glavenergo in 1934:

\[ U_v = 100 \cdot l_s \cdot I_n \cdot M_2 + 0.5 \cdot l_n \cdot I_n \cdot M_1 . \]

The first part of this formula is due to the unbalance of the communication line with respect to the power-transmission line, while the second part is due to the asymmetry of the communication line with respect to the earth. The ratio of the second part to the first gives—

\[ \frac{0.5 \cdot l_n \cdot I_n \cdot M_1}{100 \cdot l_s \cdot I_n \cdot M_2} = \frac{0.5 \cdot l_n \cdot M_1}{100 \cdot l_s \cdot M_2}. \]

For an approach of 100 meters, with \(l_n = 100\) km and \(l_s = 1\) km, this ratio is equal to

\[ \frac{0.5 \cdot 100 \cdot 180 \cdot 10^{-3}}{100 \cdot 1 \cdot 0.394 \cdot 10^{-3}} = 230; \]

the values of \(M_1\) and \(M_2\) are taken from the table in the above-mentioned “Instructions.” Consequently, the protection of two-wire communication lines in the given case comes down to the compensation of the electrical asymmetry of the communication line with respect to the earth. Appropriate means for this are available, and it appears that this task is simpler than the protection of single-wire communication lines.

^17) M. I. Mikhailov and P. A. Azbukin, Overhead and Cable Communication Lines and Their Protection. Svyazizdat, 1940.

VI.

Grounding one phase of an electric transmission line, and thereby raising the potential of the other two phases by \(\sqrt{3}\) times, changes the configuration of the electric field of the conductors of the ungrounded phases, which in turn increases the electric-field strength at the surface of these conductors and lowers the voltage at which corona begins on the conductors, if this voltage is still measured as the phase voltage of the transmission line.

According to Peek\(^{18}\), it follows that the electric-field strength at which disruptive ionization begins is approximately the same, all other conditions being equal, both in the case of two concentric cylinders and in the case of two parallel cylinders; the same also applies to the field strength at the onset of visible corona, for which Peek gives:

a) for two concentric cylinders

\[ E'_b = 31 \cdot \delta \left(1 + \frac{0.308}{\sqrt{r \cdot \delta}}\right)\ \text{kV/cm}, \]

b) for two parallel cylinders

\[ E''_b = 30 \cdot \delta \left(1 + \frac{0.301}{\sqrt{r \cdot \delta}}\right)\ \text{kV/cm}; \]

one may take \(E'_b = E''_b\).

And since near the surface of the inner cylinder of two concentric cylinders the field is uniform, one may conclude that near the surfaces of parallel cylinders the field is likewise identical around the circumference of the cylinders. The same conclusion may be reached by considering the expression for the maximum and minimum potential gradients as functions of the potential applied to a combination consisting of a cylinder and a plane arranged in parallel:\(^{19}\)

\[ E_{max} = \frac{U}{ a \sqrt{\frac{h-a}{h+a}} \cdot \ln \frac{h+\sqrt{h^2-a^2}}{a} }, \]

\[ E_{min} = \frac{U}{ a \sqrt{\frac{h+a}{h-a}} \cdot \ln \frac{h+\sqrt{h^2-a^2}}{a} }, \]

both of these expressions, as applied to a conductor above the ground, reduce to the simple relation:

\[ E \approx \frac{U}{a \cdot \ln \frac{2h}{a}}, \]

i.e., the field strength around the circumference of the conductor at its surface is the same, and, consequently, the field strength at the conductor surface may be calculated as

\[ E = \frac{q}{2 \pi r \cdot 8.84 \cdot 10^{-9}}\ \text{kV/cm}. \]

\(^{18}\) F. W. Peek, Dielectric Phenomena in High-Voltage Engineering, translated from English under the editorship of Prof. Epstein, 1934.

\(^{19}\) Prof. A. A. Smurov, High-Voltage Electrical Engineering and the Transmission of Energy, GONTI, 1931.

Bearing in mind the direct dependence between the critical corona voltage and the critical field strength, it is necessary to conclude that there is an inverse proportionality between the critical corona voltage and the charge of the conductor, if the charge of the conductor for some reason increases or decreases while the distances between conductors remain unchanged and the voltage of the transmission line remains unchanged.

The charges of the line conductors, depending on the potentials of the conductors and on the mutual arrangement of the conductors and their arrangement with respect to the ground, are determined with the aid of the well-known Maxwell equations already cited above. Thus, for example, the charge of the second conductor of a symmetrical three-phase line is determined as

\[ \bar q'_2 = C'_{12}(\alpha U_a - U_a) + C'_{22}\cdot \alpha \cdot U_a + C'_{23}(\alpha \cdot U_a - \alpha^2 U_a) = \]

\[ = U_a\left[C'_{12}(\alpha - 1) + C'_{22}\cdot \alpha + C'_{23}(\alpha - \alpha^2)\right]; \]

The charge of the same conductor when phase \(a\) is grounded (the first conductor) is determined as

\[ q_2 = C_{12}U_a(\alpha - 1) + C_{22}\cdot U_a(\alpha - 1) + C_{23}\cdot U_a(\alpha - \alpha^2) = \]

\[ = U_a\left[C_{12}(\alpha - 1) + C_{22}(\alpha - 1) + C_{23}(\alpha - \alpha^2)\right]. \]

Comparing these charges, we see that the charge of the same phase of a line with a grounded phase differs from the charge of a symmetrical line in the ratio

\[ \frac{(C_{12}+C_{22})(\alpha - 1) + C_{23}(\alpha-\alpha^2)} {C'_{12}(\alpha - 1)+C'_{22}\cdot \alpha+C'_{23}(\alpha-\alpha^2)} = \]

\[ = \frac{ \alpha + \dfrac{C'_{23}}{C_{12}+C_{22}}(\alpha-\alpha^2)-1 }{ \alpha + \dfrac{C'_{23}}{C'_{12}+C'_{22}}(\alpha-\alpha^2) - \dfrac{C'_{12}}{C'_{12}+C'_{22}} }, \]

where the capacitances with a prime refer to the symmetrical line with the corresponding arrangement of the conductors.

As applied to the line with the arrangement of AC–185 conductors according to Fig. 8, the partial capacitances take the following values:

a) in the case of two circuits—

\[ C_{12}=0.00183\cdot 10^{-6}\ F/\text{km}; \qquad C'_{12}=0.00229\cdot 10^{-6}\ F/\text{km}; \]

\[ C_{23}=0.00230\cdot 10^{-6}\ F/\text{km}; \qquad C'_{23}=0.00220\cdot 10^{-6}\ F/\text{km}; \]

\[ C_{22}=0.00312\cdot 10^{-6}\ F/\text{km}; \qquad C'_{22}=0.00300\cdot 10^{-6}\ F/\text{km}; \]

c) when one side is in operation (without taking into account the influence of the conductors of the other side)

\[ C_{12}=0.00152\cdot 10^{-6}\ F/\text{km}; \qquad C'_{12}=0.00190\cdot 10^{-6}\ F/\text{km}; \]

\[ C_{23}=0.00187\cdot 10^{-6}\ F/\text{km}; \qquad C'_{23}=0.00180\cdot 10^{-6}\ F/\text{km}; \]

\[ C_{22}=0.00435\cdot 10^{-6}\ F/\text{km}; \qquad C'_{22}=0.00425\cdot 10^{-6}\ F/\text{km}; \]

and, accordingly, the charge ratio:

a) in the case of two circuits—1.15

c) in the case of one circuit 1.24

Therefore, the critical corona voltage on the second conductor of a line with a grounded phase will be lower than in the symmetrical case by 13% and 23%, respectively, for double-circuit and single-circuit lines.

The revealed property of a transmission line with a grounded phase imposes certain restrictions with respect to the construction of single-circuit lines.

circuit lines with conductors whose cross-sections are smaller than that of AS-150 conductor.

It is interesting to note that the conductor of the grounded phase will not corona in all possible practical cases.

VII.

The economic advantages of switching to a power-transmission system using the conductor of one of the phases are most clearly represented in the variant with permanent grounding of the conductor of one of the phases. In the main they consist of the following.

1) The cross-section of the conductor of the grounded phase, as a rule, may be taken as half as large as the cross-sections of the other two phases; i.e., in effect, a double-circuit line may be made with 5 conductors instead of the usual 6 conductors of the same cross-section.

2) The need to suspend special protective cables is eliminated; i.e., two cables are saved in the case of double-circuit lines on steel towers, and four cables in the case of a double-circuit line on wooden poles.

3) The line supports, for the same spans, turn out to be lower by several meters; the wind load on the support, owing to the absence of cables, is reduced; taken together, these two circumstances, as calculations show, with suitable support designs, give a saving in the weight of the supports:

a) in the case of 110 kV steel supports, 12–15%;

b) in the case of 110 kV wooden supports, 25–30%;

c) in the case of 220 kV steel supports, up to 50%.

For a nominal voltage of 110 kV, a possible expedient design of a steel support appears to be an “American-type” support with the conductors arranged in an inverted fir-tree pattern, in which the places of the cables are occupied by the conductors of the grounded phase, and the lower crossarm is eliminated. For the same voltage, a wooden support may be made double-circuit (Fig. 11),

Fig. 11

whereby difficulties with repairing the crossarm can be avoided by installing a third leg in the middle. In this case the safety-engineering requirements concerning the possibility of repairing one circuit while the other is in operation will be fully met; the crossarm will be made composite, with the joint above the middle leg.

For a nominal voltage of 220 kV, as a first approximation one may imagine single-circuit supports of the Dnieper type.

• The above figures for savings in support weight have been calculated as applicable to the indicated types of supports.

4) A saving of 25–30% of line insulators is achieved; somewhat less than one third, because the suspension of grading rings is, in cost, equivalent to reinforcing the insulator string by approximately one element.

5) A saving of 25–30% of switching equipment and substation insulation is achieved, since there is no need to disconnect the grounded phase.

6) A saving of about one third, by weight, of the iron structures of outdoor substations is achieved; incidentally, the area occupied by outdoor substations of transmission systems with a grounded phase is approximately one and a half times smaller than the area occupied by outdoor substations of symmetrical transmission systems.

It is not entirely clear whether an increase in the cost of substation power transformers is inevitable and, if it is inevitable, to what extent. Likewise, it is not entirely clear how an increase in the operating potential by a factor of \(\sqrt{3}\) will affect the interrupting capacity of circuit breakers. Preliminary considerations suggest that any possible increase in the cost of transformers and circuit breakers will be fully offset by savings on other elements of substation equipment.

On the basis of all that has been stated above, the following general conclusions may be drawn.

The problem of using the conductor of one of the phases also as protection against lightning strikes involves a large complex of questions subject to detailed theoretical and experimental investigation; but on the basis of the considerations examined in the present work, confidence is created in the possibility of dispensing with the suspension of a special shield wire on high-voltage transmission lines and of using, for the purposes of protecting lines against lightning strikes, the conductor of one of the phases, arranging this conductor in the corresponding manner on the tower.

1. Prof. A. A. Glazunov, Electric Networks and Systems, Part 1, Appendix XVIII, 1939. ↩

2. “Rules for the Technical Operation of Electric Stations and Networks,” Gosenergoizdat, 1940. ↩

3. I. S. Stekolnikov and V. V. Yavorsky, Fundamentals of the Design of Lightning-Protection Systems, Part 1, ONTI, 1935. ↩

4. Prof. L. I. Sirotinsky, Overvoltages and Protection against Overvoltages in Electrical Installations. ONTI, 1937. ↩

5. See, for example, Transactions of the American Institute of Electrical Engineers for 1938. ↩

6. “Some Engineering Features of Petersen Coils and their Application by E. M. Hunter,” Transactions of AIEE, 1938, vol. 57, pp. 11–13. ↩