Semiconductor-Based Power Direction Relay Using a Parametric Frequency Divider

A. P. Pushkov

(Presented by the scientific seminar of the Department of Electric Power Stations)

As is known, directional current protections with power-direction elements have a voltage insensitivity zone—the “dead zone.” The use of so-called “memory circuits” does not eliminate the danger of incorrect operation of such protections, since the operating time of “memory circuits” is 1–1.5 periods for electromechanical-type relays [1] and 2.5–3.5 periods [2] for semiconductor power-direction relays, and any accidental delay in the action of both the starting elements and the output intermediate relays may lead to false operation of the protection.

Recently, semiconductor power-direction relays have begun to become very widely used [3, 4]. Such relays have a lower operating power with less power consumed from the measuring transformers, and they also operate more rapidly. The reduction in operating power required to shorten the “dead zone” in semiconductor power-direction relays using phase-sensitive circuits has been achieved through the use of highly sensitive null elements (a null indicator with a dc amplifier or a magnetoelectric relay). However, the use of such null elements requires increased accuracy in the manufacture and adjustment of the individual units of the relay (especially when using a circuit for comparing absolute values).

This article describes a semiconductor power-direction relay based on a two-half-period phase-sensitive circuit using transistor switches. In the relay described, in order to eliminate the “dead zone,” a device for eliminating the “dead zone” is used, containing an electromagnetic parametric frequency divider (PFD) [5]. The schematic diagram of such a relay is shown in Fig. 1.

The device for eliminating the “dead zone,” based on the principle of phase conversion during frequency multiplication and division, makes it possible to use, for energizing the relay voltage circuits, energy from the current transformers during close three-phase short circuits, when the system voltage at the installation point of the protection drops to zero and the current increases significantly; moreover, energy is supplied to the relay throughout the entire duration of the short circuit.

In general form, such a device contains a frequency doubler 1 (Fig. 1), supplied from the current transformers and connected to its

to the output of PFD 2. The output of the PFD is connected to a voltage transformer installed at the point where the protection is connected.

In such a circuit, the operating conditions of the frequency divider do not change when the current phase changes by 180°. Thus, if the instantaneous value of the current during a short circuit in the protected zone is equal to

Fig. 1. Schematic diagram of a semiconductor-based power direction relay

\[ i_1=I_m \sin(\omega t+\varphi), \tag{1} \]

and when the current vector is rotated by 180°, which may occur in the case of a short circuit “behind the back,”

\[ i_2=I_m \sin(\omega t+\varphi+\pi), \tag{2} \]

then at the output of the frequency doubler in any case

\[ i=-I_m\sin(2\omega t+2\varphi). \tag{3} \]

It is known that, in the absence of an external control signal, a frequency divider can in principle be excited in two opposite phases, 0 or \(\pi\); but since the latter is connected to the voltage transformer, the phase of the oscillations at the divider output will be determined by the phase of the network voltage. In this case, oscillations with phase 0 will arise if the phase of the signal voltage (in this case, the network voltage) lies within \(\pm \frac{\pi}{2}\). In practice, for a PFD this zone of unambiguous phase excitation is somewhat narrower and amounts to \(120\)—\(140^\circ\).

In close three-phase short circuits, when the signal voltage disappears, oscillations with the same phase as before the occurrence of the short circuit are retained for some time in the resonant winding of the PFD. Owing to the increase in current, the PFD is excited, and a voltage appears at its output whose phase is determined by the voltage phase of the preceding operating condition. In

In this case the phase of the voltage at the PFD may differ somewhat from the phase of the voltage of the preceding operating condition; however, with an appropriate choice of the circuit parameters, as is shown below, it provides a torque in the relay of the same sign as the natural electrical quantities. It is important here that the phase of the PFD voltage is uniquely determined by the phase of the voltage of the preceding operating condition when the current phase changes by 180°.

A feature of the operation of a PFD with a power relay is that its supply voltage varies over wide limits. The region in which stable parametric oscillations exist in ordinary two-core PFDs is rather small. Therefore, in the relay described here a PFD of special design is used, in which the entire magnetic core is divided into two parts that are not connected to one another. One of them—the saturating part—is a W-shaped core, on the outer limbs of which the excitation windings \(w_{\mathrm{n}}\) are placed. On the middle limb is placed the tank winding \(w_{\mathrm{k}}\), which embraces the second—П-shaped—core with an air gap.

The excitation windings are connected in series opposition; the tank winding is closed through a capacitor and forms an oscillatory circuit with it. Owing to the opposing connection of the excitation windings, energy is transferred into the circuit only as a result of variation of the parameter—the magnetic permeability of the saturating core.

The ampere-turns of the winding \(w_{\mathrm{n}}\) and the dimensions of the saturating core are chosen so that it is saturated already at the minimum current sufficient for excitation. Therefore, with a further increase in current the magnetic permeability of this magnetic core varies between its maximum and minimum values. Since the magnetic reluctance of the nonsaturating magnetic core does not change, the depth of modulation of the magnetic permeability of the equivalent magnetic core embraced by the tank winding remains practically constant. Consequently, the depth of modulation of the inductance of the oscillatory circuit also remains constant over a wide range of variation of the supply voltage. Since the existence of oscillations of half frequency in this case is due precisely to modulation of the inductance, then, with a constant modulation depth and other unchanged conditions, the amplitude of the output voltage also remains constant.

The phase current \(I_{\mathrm{p}}\) (Fig. 1), supplied to the relay, is converted by transreactor \(Tx_1\) into a voltage. The frequency doubler connected to the transreactor consists of a semiconductor bridge rectifier \(DM_1\), an \(R_1C_2\) network, and an intermediate transformer \(Tr\), which serves to separate the ac component of the voltage from the dc component. Such a frequency doubler is practically inertia-free and does not introduce phase distortions, which is of great importance when it is used in this device. A PFD is connected to the secondary winding of transformer \(Tr\). The latter, through resistors \(R_2, R_4\), is loaded by the phase-sensitive circuit and, through resistors \(R_2\)–\(R_5\), is connected to the voltage transformer.

The choice of the phase-sensitive circuit used in this relay was based on the following requirements associated with the use of the PFD:

1. In the circuit there must be no coupling between the current and voltage circuits, in order to exclude the influence of electrical quantities dependent on the current on the phase of the oscillations excited in the PFD.

2. The circuit should have as large a transmission coefficient as possible, which will make it possible to reduce the power of the PFD.

In a two-cycle phase-sensitive circuit, in addition to satisfying the listed requirements, there is high zero stability without parameter selection and with low manufacturing accuracy of the relay elements.

In Fig. 1, the value used as the voltage $\dot U_1$, which creates the current $I_{\text{н}}$ through the actuating element P, is proportional to the network voltage $\dot U_{\text{р}}$, or to the PDF voltage $\dot U_{\text{к}}$. The keys of the phase-sensitive circuit are controlled by the voltage $\dot k I_{\text{р}}$, whose phase is rigidly associated with the current of the electrical installation $\dot I_{\text{р}}$. This voltage does not create current in the circuit of the actuating element, but only commutates the transistor keys.

It is known that in such a circuit the current through the load is equal to

\[ I_{\text{н}}=\frac{\sqrt{2}}{2\pi R_{\text{р}}}\cdot U_1\cos\varphi_1, \tag{4} \]

where

$R_{\text{р}}$—the dc resistance of the winding of relay P,

$\varphi_1$—the angle between the vectors $\dot U_1$ and $\dot k I_{\text{р}}$.

As is seen from expression (4), the load current depends on the angle $\varphi_1$ in such a way that the operating zone of the relay when this phase-sensitive circuit is used will be equal to $180^\circ$.

To obtain the paraphase voltage needed for a phase-sensitive circuit of this type, the PDF contour winding is made with a center tap. In normal operation and for remote short circuits, when the PDF is not excited, the voltage $\dfrac{U_1}{2}$ is determined by the voltage supplied to the relay, $U_{\text{р}}$, by the resistance values of resistors $R_2$—$R_5$, and by the parameters of the oscillatory circuit of the PDF. For close short circuits, when $U_{\text{р}}\approx 0$, the voltage $\dfrac{U_1}{2}$ is determined by the PDF voltage and the parameters of the same elements.

The resistance values of resistors $R_2$—$R_5$ are selected so that the following two conditions are fulfilled simultaneously:

1. The vector of the signal controlling the phase of the PDF must be located in the zone of unambiguous excitation of the PDF for any values of the angle $\varphi_{\text{р}}$ between the voltage $\dot U_{\text{р}}$ and the current $\dot I_{\text{р}}$ supplied to the relay, and its magnitude must be no less than 5% of $U_{\text{к max}}$ for normal control of the phase of the PDF voltage.

2. The voltage $\dfrac{U_1}{2}$ at $U_{\text{р}}=0$ and $U_{\text{к}}=U_{\text{к max}}$ must be sufficient to operate the actuating relay.

The voltage for controlling the transistor keys is taken from the secondary winding of the transreactor Tx2. To eliminate transistor breakdown at high multiples of short-circuit current and during abrupt changes in current, semiconductor stabilitrons $D_2$—$D_5$ are connected in series-opposition in parallel with the transistor control circuits.

As was already stated above, increasing the sensitivity of the power-direction relay is necessary only to reduce the “dead zone”; therefore, the use of a device for completely eliminating the “dead zone” makes it possible to use in semiconductor relay circuits a rough zero element—a polarized relay—since the voltage applied to the relay during three-phase short circuits near the protection installation point does not

decreases relative to the specified value, determined by the voltage sensitivity of the actuating relay. The use of a coarse null element naturally makes it possible to allow larger errors in manufacture and adjustment.

The angle of maximum sensitivity of the relay depends on phase shifts both in the voltage circuit and in the current circuit, and is determined by the resistance values of resistors \(R_2—R_5\) and by the parameters of the PFD oscillatory circuit, as well as by the parameters of the elements \(R_6C_3\) and \(R_8C_4\). Resistors \(R_6\) and \(R_8\) simultaneously serve to limit the current through the Zener diodes. The angle of maximum sensitivity of the setting relay is about \(45^\circ\). When the angle of the total impedance of the line changes, there is no need to change the angle of maximum sensitivity, since for close three-phase short circuits the relay operates from the PFD voltage.

Power direction relays of all types currently in use are usually characterized by such relationships as the angular characteristic, the volt-ampere characteristic, and the dependence of the minimum operating power on the current in the current winding. All these dependences

Fig. 2. Angular characteristics of a power direction relay under different operating conditions

are characteristic of relays that have finite sensitivity and reflect the latter. For a relay using a device for eliminating the “dead zone,” such dependences cease to be necessary. What may be considered important in this case is the angular characteristic used for ideal power direction relays, for an operating power \(S_{\mathrm{op}}\approx 0\) [1,6]. For remote short circuits, such a characteristic is, in practice, the straight line of zero torque \(M_{\mathrm{vr}}\), rotated by the angle of the internal shift of the relay \(\alpha\) relative to the fixed voltage vector \(\dot U_{BC}\) for the \(90^\circ\) relay connection scheme (Fig. 2). The line of maximum torque is located perpendicular to the line of zero torque. The unshaded region shows the zone of variation of the angle \(\varphi_{\mathrm{r}}\) between the current \(\dot I_{\mathrm{r}}\) and the voltage \(\dot U_{\mathrm{r}}\), within which positive torque is ensured. In the event of a short circuit in the “dead zone,” this characteristic degenerates into the zone of unambiguous excitation of the PFD by phase (in Fig. 2 this zone is shaded); within sector I a constant positive

... torque, and in sector II it is negative. This zone must cover all possible values of the angle \(\varphi_p\).

Figure 3a shows the vector diagram of the relay when it is supplied from the network voltage. In this diagram the hatched area shows the range of variation of the angle \(\varphi_p\) for which unambiguous preselection of the PFD phase is ensured. From the size and location of the zone it is evident that unambiguous excitation of the PFD will be predetermined for \(0 \leq \varphi_p \leq 90\), i.e., for all possible angles of the total resistance of the short-circuit loop.

Figure 3b gives the vector diagram of the relay during a short circuit near the protection installation point, when \(U_p = 0\) and \(U_k = U_{k\max}\). Since the vectors \(\dot I_A\) and \(\dot U_k\) are rigidly linked to each other, for any value of \(\varphi_p\) a constant angle \(\varphi_1\) is ensured. Thus, according to (4), reliable operation of the relay will always be ensured for close-in short circuits. The angle \(\varepsilon\) between the current \(\dot I_A\) and the voltage \(\dot U_k\) after excitation of the PFD is \(70^\circ\).

Fig. 3. Vector diagrams for three-phase short circuits.

The required value of the voltage \(U_1\) when the relay is supplied from the PFD can be calculated from the following expression:

\[ U_1 = k_{\text{res}} U_{\text{op min}}, \tag{5} \]

where

\[ U_{\text{op min}} \]

is the minimum operating voltage for the relay used;

\[ k_{\text{res}} \]

is a reserve factor accounting for deterioration of relay sensitivity at high currents.

The current multiple relative to nominal current at which the PFD is excited can be adjusted by switching taps of the primary winding of the transreactor \(Tx_1\). This value is determined when calculating the short-circuit currents of the specific network and must satisfy the condition

\[ I_{\text{e}} < I_{k}^{(3)}, \tag{6} \]

where

\[ I_{\text{e}} \]

is the current at which the PFD is excited;

\[ I_{k}^{(3)} \]

is the relay current for three-phase short circuits at the boundary of the voltage dead zone in the minimum operating mode of the system.

The relay operating time when it is supplied from the network voltage does not exceed 0.04 sec at \(I_p = 2I_{\text{nom}}\); when a short circuit occurs near the protection installation point, the relay operating time does not exceed 4 periods of the fundamental frequency.

Fig. 4. Oscillogram illustrating the operation of the power relay under a three-phase metallic short circuit at the protection installation point: \(u_p\)—line voltage; \(i_p\)—phase current; \(u_1\)—voltage on the phase-sensitive circuit; \(n\)—current in the relay contact circuit

Figure 4 presents an oscillogram of a power-relay test obtained on a physical model of a line with two-sided supply. The power consumed by the relay from the current transformer depends on the pickup-current setting of the PFD, \(I_v/I_{\text{nom}}\). At \(I_v = 2I_{\text{nom}}\) it is 6 VA; when the setting is increased to \(10I_{\text{nom}}\), it is 2 VA. The power consumed by the relay from the voltage transformer in normal operation is 0.85 VA.

Conclusions

1. The proposed circuit of a power-direction relay without a “dead zone,” based on a transistor phase-sensitive circuit in which, owing to supply from the PFD during close-in short circuits, satisfactory characteristics are achieved with a crude zero element.

2. It has been shown that a power-direction relay with a device for eliminating the “dead zone” can be regarded as an ideal relay with infinite voltage sensitivity.

3. The operating time of the relay during close-in short circuits, when the voltage circuits are supplied from the PFD, does not exceed 0.08 sec.

LITERATURE

1. A. M. Fedoseev. Fundamentals of Relay Protection. GEI, 1961.
2. Yu. A. Gaeyenko. New Semiconductor Protection Relays. GITL, 1962.

1. V. I. Grinshtein. Power relays using semiconductors. Elektrichestvo, 1965, No. 11.

2. Distance protection of 35–330 kV lines. Guidelines for relay protection, issue 7 (supplement), Energiya, 1968.

3. R. A. Vainshtein, A. P. Pushkov. Inventor’s certificate No. 353311 of September 29, 1972.

4. G. I. Atabekov. Theoretical foundations of relay protection of high-voltage networks. GEI, 1957.