LONGITUDINAL COMPENSATION WITH SIMULTANEOUS LIMITATION OF SHORT-CIRCUIT CURRENTS

A. I. ZAITSEV

On the initiative of Comrade Stalin, the world’s largest Kuybyshev and Stalingrad hydroelectric power stations are being built. This will create the world’s largest power system, encompassing the entire central part of the USSR.

Electrical engineering has been given the task of ensuring the transmission of electric power of 1000–1500 MW over distances on the order of 1000 km. Such transmission can be carried out both by direct current and by alternating current.

High-voltage direct-current transmission has well-known advantages over three-phase energy transmission. The implementation of a normally operating installation for transmitting large power over a long distance by direct current is associated with the construction of reliable converter devices and with the creation of designs for high-voltage direct-current circuit breakers. Therefore, if the question is posed of transmitting large power over a long distance as the nearest practical task, then it can only concern three-phase current at a voltage on the order of 400 kV.

The carrying capacity of a high-voltage electric transmission line is determined to a significant degree by the conditions of stability of parallel operation of generating stations. These conditions are determined mainly by the magnitude of the inductive reactance of the electric transmission. Under the condition of full compensation of the capacitive current, neglecting the active resistance of the system and the magnetizing currents of transformers, the transmitted power is determined, as is known, by the following equation:

\[ P = \frac{E_d \cdot U}{X} \sin \delta, \tag{1} \]

where \(E_d\) is the e.m.f. of the generators; \(U\) is the voltage at the receiving end; \(X\) is the inductive reactance of the system; \(\delta\) is the angle between the vectors \(E_d\) and \(U\).

From the indicated formula one may also outline the principal ways of increasing the limit of transmitted power.

It has become evident that the use of a higher voltage (above 400 kV) for powerful electric transmission lines, with the aim of increasing the limit of transmitted power, is restricted by technical and economic possibilities. The method of increasing the power limit by reducing the inductive reactance of the electric transmission line offers considerably greater possibilities.

On the basis of an analysis of existing and proposed methods for increasing the limit of transmitted power, it may be asserted that the most expedient method of increasing the limit of transmitted power is longitudinal compensation of the parameters of the electric transmission line. This compensation may be carried out by synchronous and asynchronous machines, as well as by static capacitors.

The question of longitudinal compensation by means of rotating machines has been most fully solved by Soviet scientists—L. V. Tsukernik, I. S. Bruk, G. E. Pukhov, and others.

The asynchronous generator proposed by I. S. Bruk in 1936 makes it possible automatically to regulate the phase of the compensator e.m.f. when the phase of the current in the line changes, without the use of any regulating devices (for example, a rotating stator in Morgan’s scheme).

G. E. Pukhov’s scheme is a further development of I. S. Bruk’s scheme, in which the asynchronous motor is replaced by a synchronous one.

Calculations have shown that the required power of the rotating machines under long-distance transmission conditions is \((1.8 \div 2.5)P\), where \(P\) is the magnitude of the transmitted active power.

It should be pointed out that all schemes of longitudinal compensation by means of rotating machines have a substantial shortcoming: they require the inclusion of series transformers whose power considerably exceeds the power transmitted over the line, which undoubtedly must affect the cost of electric-power transmission.

Static capacitors appear at first glance to be the most natural and expedient means of longitudinal compensation of line inductance. Their use eliminates the need for complex regulating devices, but considerable difficulties are encountered along this path. In the event of short circuits on the line, the voltage on the capacitor plates inevitably rises. To protect them against breakdowns and to reduce short-circuit currents, all capacitor installations are provided with devices which in one way or another shunt the capacitors at the moment inadmissible voltages arise. The necessity of shunting capacitors when short-circuit currents flow through them is a negative aspect of this device, since the line is decompensated precisely at the moment when, from the standpoint of the stability of parallel operation, compensation is especially necessary. Another substantial shortcoming of the scheme using static capacitors with conventional protection is that, owing to the reduction of the line inductance, short-circuit currents increase to wholly inadmissible values. The problem of interrupting such currents becomes especially acute.

The author has developed a scheme of longitudinal compensation with static capacitors and simultaneous limitation of short-circuit currents.

Fig. 1

As is known, taking capacitors out of operation during a short circuit is necessary. It is also known that very rapid interruption of a short circuit would be a means of significantly improving the dynamic stability of electrical systems. Only this means makes it possible to raise the question of preserving dynamic stability during three-pole short circuits. Therefore, together with removing the capacitors from operation, it is desirable to make them participate in ensuring the dynamic stability of the system. This can be achieved if the capacitor is shunted not by a spark gap, as is done at present, but by a nonlinear inductive resistance.

By appropriate selection of the volt-ampere characteristics of the limiting device, i.e., of the saturation choke and of the capacitor (Fig. 1), the following operating regimes can be obtained.

1. Under normal operating conditions, the load current will flow through the capacitor and longitudinal compensation will be effected. In this case the voltage and current for the device will be the operating values—$U_{\text{oper}}$ and $I_{\text{ext.oper}}$.

2. In the event of a short circuit, the voltage across the capacitor begins to increase sharply. As the voltage rises, the magnetizing current of the reactor increases. As a result, the conductivity of the circuit decreases and an even more rapid increase is produced in the voltage at the circuit terminals, up to the resonance voltage $U_{\text{res}}$.

Fig. 2

The process by which the limiting device is drawn into resonance conditions occurs so rapidly that, in practice, it may be assumed that the additional resistance is introduced into the damaged phase instantaneously.

Fig. 3

The current in the external circuit will vary according to curve I of Fig. 1. When a short circuit occurs, this current will increase from $I_{\text{ext.oper}}$ to $I_{\text{ext.max}}$, and then will decrease to a value less than the rated current. It is impossible to completely block the current because of the active resistances of the reactor and capacitor and hysteresis, even if the resonance voltage is equal to or greater than the phase voltage. If the latter condition is satisfied, the magnitude of the current surge $\Delta I$ in the external circuit when a short circuit occurs is practically independent of the instant at which the short circuit occurs.

...and the magnitude of the current peak will not exceed \((1.5 \div 2)\) times the nominal operating current.

The nature of the transient process in the presence of the limiting device is reflected by the oscillograms shown in Figs. 2 and 3. In one case the short circuit occurred at the moment when the load current passed through a maximum (Fig. 2), and in the other, through a minimum (Fig. 3). It is evident from the oscillograms that the change in the current in the external circuit depends little on the instant at which the fault occurs and is determined mainly by the volt-ampere characteristics of the reactor and the capacitor. During the transient process the voltage across the capacitor only slightly exceeds the voltage of current resonance of the limiting device. This occurs because the conductance of the reactor, at high saturations, changes very strongly with an insignificant change in voltage.

Fig. 4

By increasing its conductance, the reactor shunts the capacitor, preventing the resonance voltage from being exceeded to any appreciable extent, as can be seen from the oscillogram presented in Fig. 4.

The magnitude of the installed capacitor power in the normal operating mode is determined by the degree of compensation. The magnitude of the latter, depending on the operating voltage of the capacitor, expressed in fractions of the phase voltage of the line, can be judged from Table 1, where the capacitive reactance is calculated in relative units. The nominal voltage of the transmission line and the nominal power transmitted along this circuit are taken as the base quantities.

Table 1

The required saturation power \(Q_{\mathrm{pr}}\) in the emergency mode must be equal to the capacitor power in this same mode.

Its magnitude as a function of the degree of compensation is given in Table 1 in fractions of the transmitted power.

The power of the reactor decreases noticeably with an increase in the operating voltage of the capacitor. The cost of the saturating reactor is still much more spe—

is reduced if one takes into account the fact that its resonant mode will not continue for long. Under normal conditions, however, only a small current should flow through the reactor winding, which in practice will not heat the windings. Therefore it is possible to allow a short-time, substantial overload of the reactor winding, permitting a current density 10–20 times greater than for an ordinary transformer. From what has been said it follows that, in determining the cost of the device, the decisive factor is the cost of the capacitors.

As has already been indicated, during short circuits the limiting device enters resonance conditions, thereby introducing additional resistances into the damaged phases virtually instantaneously. Although this resistance varies according to a nonlinear law as a function of the applied voltage, we shall regard it as constant and equal to \(Z_{\text{add}}\).

When determining the limit of the power transmitted in an emergency condition as a function of the type of short circuit, a shunting reactance \(X_k\) is introduced into the equivalent circuit of the direct sequence; it consists of combinations of the negative- and zero-sequence reactances with respect to the point of the short circuit. Unlike ordinary compensation schemes, in the present case the value of \(X_k\) must be determined with allowance for the added resistance. At present it is customary to calculate dynamic stability on the assumption that the transient emf \(E_d'\) behind the transient reactance \(X_d'\) is constant. In the case of practically instantaneous limitation of short-circuit currents, such an assumption proves unjustified and allows knowingly excessive margins. Practice shows that some systems operate stably, whereas according to calculations they should “fall apart” even with ordinary equipment present. This circumstance has already been pointed out by the technical department of the MES. In our case the calculation of dynamic stability should be carried out under the condition that the subtransient emf \(E_d''\) behind the subtransient reactance \(X_d''\) is constant. This is also confirmed by calculations of the variation of \(E_d''\) over time up to 0.03 sec, where \(E_d''\), in the presence of an automatic voltage regulator, remains practically constant.

Taking the above into account, the power transmitted during a short circuit will be equal to

\[ P = \frac{E_d'' \cdot U}{\dfrac{X_I \cdot X_{II}}{X_k} + X_{\text{system}}} \sin \delta, \tag{2} \]

where \(X_I\) is the reactance of the system up to the short-circuit point from the generating station;

\[ X_{II} \]
is the reactance of the system up to the short-circuit point from the receiving end.

The amplitude of the sinusoid (2) is smaller than for expression (1), since an additional term appears in the denominator,

\[ \frac{X_I \cdot X_{II\,2}}{X_k}. \]

The shunting reactance \(X_k\) in this case will be greatly increased and, in the limit, when the clamping of the current in the damaged phase by the circuit is complete, \(X_k\) will be equal to infinity, which is equivalent to disconnecting the short circuit.

Thus, with respect to dynamic stability, the action of the limiting device may be likened to phase-by-phase instantaneous disconnection of the fault. Under real conditions the load-angle characteristic will approach the characteristic obtained when the fault is disconnected, i.e. the dynamic-stability limit comes close to the static-stability limit.

Summing up, the following preliminary conclusions may be drawn:

1. Longitudinal compensation by static capacitors, in combination with splitting the phase conductors, significantly improves static stability.

2. Shunting the capacitor with a saturable reactor very strongly improves dynamic stability. The action of the limiting device is equivalent to phase-by-phase disconnection of a normally operating line.

3. Owing to the rapid disconnection of short-circuit currents, dynamic stability is determined by the generator’s subtransient e.m.f. \(E_d''\).

4. The problem of breaking capacity and of the thermal and dynamic stability of the equipment is simplified.

5. The cost of the limiting device is reduced due to the considerable short-time overloading of the circuit during the fault.

6. The presence of limiting devices makes it possible to move decisively toward phase-by-phase control.

7. In coupled transmission schemes, the required number of switching stations for ensuring dynamic stability is reduced, which can yield large savings in capital investment.

8. It becomes possible to concentrate all capacitors in one or two locations, since there will be no increase in short-circuit currents.

9. By introducing active resistance into the reactor circuit in the limiting loop, it becomes possible to compensate for a certain share of the active load shed during a short circuit, which will also lead to an improvement in dynamic stability.

The limiting device has successfully passed laboratory tests. The immediate task is the practical testing of this proposal under real conditions.