Measuring current transformers (CTs) serve to separate (isolate) primary and secondary circuits, as well as to bring the current magnitude to a level convenient for measurement (standard rated current of the secondary winding is 1 A or 5 A).
The device and connection diagram of a CT are shown in Fig. 4.1. The CT consists of a steel core C and two windings: primary (with the number of turns \(w_1\)) and secondary (with the number of turns \(w_2\)). Often, CTs are manufactured with two or more cores. In such designs, the primary winding is common to all cores (Fig. 4.1, b). The primary winding, made of thick wire, has several turns and is connected in series into the circuit of the element where current measurement is performed, or whose protection is carried out. Relays and instruments connected in series are connected to the secondary winding, which is made of smaller cross-section wire and has a large number of turns.
Figure 4.1. Current transformer device and diagram:
-vyivodov-obmotok-transformatorov-toka.jpg){kind=spacer}
Fig. 4.2. Terminal markings of current transformer windings\(\Phi_0 = \Phi_1 - \Phi_2\) (4.1)
The magnetic flux depends not only on the value of the current creating it, but also on the number of turns of the winding through which this current flows. The product of current and the number of turns \(F = Iw\) is called magnetomotive force and is expressed in ampere-turns (A·turns). Therefore, expression (4.1) can be replaced by the expression:
For the correct connection of CTs to each other and the correct connection of directional power relays, wattmeters, and meters to them, the terminals of the CT windings are designated (marked) by manufacturers as follows: beginning of the primary winding – \(L_1\), beginning of the secondary winding – \(u_1\), end of the primary winding – \(L_2\), end of the secondary winding – \(u_2\). During CT installation, they are usually positioned so that the beginnings of the primary windings \(L_1\) face the busbars, and the ends \(L_2\) face the protected equipment.
When marking CT windings, the beginning of the secondary winding N\((u_1)\) is considered to be the terminal from which the current exits if, at that moment, the current in the primary winding flows from the beginning N \((L_1)\) to the end K(L_2), as shown in Fig. 4.2. When connecting relay KA according to this rule, the current in the relay, as shown in Fig. 4.2, when connected through the CT, maintains the same direction as when connected directly to the primary circuit.
In normal operation, current transformers, whose secondary winding is closed to the low resistance of the current coils of instruments and relays, operate in a mode close to a short circuit.
For the safety of personnel in case of insulation breakdown between the primary and secondary windings, the secondary windings of current transformers must be mandatorily grounded.
The grounding of the secondary circuits of current transformers is performed at a single point and, as a rule, at the terminal block closest to them.
Current transformer (CT) errors. The transformation ratio of a CT, similar to that of a voltage transformer (VT), is not a strictly constant value and may deviate from its nominal value due to errors. CT errors primarily depend on the multiple of the primary current relative to the nominal primary winding current and on the load connected to the secondary winding. When the load resistance or current increases above certain values, the error increases, and the CT transitions to a different accuracy class.
For measuring instruments, the error applies to the load current range of 0.2 – 1.2 \(I_{\text{nom}}\). This error is called the accuracy class and can be equal to 0.2; 0.5; 1.0; 3.0 %.
Requirements for CTs supplying protection systems significantly differ from those for CTs supplying measuring instruments. While CTs supplying measuring instruments must operate accurately within their class at load currents close to their nominal current, CTs supplying relay protection must operate with sufficient accuracy when fault currents, significantly exceeding the nominal CT current, pass through them. For protection purposes, CTs of class P or D (for differential protection) are manufactured, in which the error at low (load) currents is not standardized. Currently, current transformers of classes 10P and 5P are produced, whose error is standardized across the entire current range.
The Rules for Electrical Installations (PUE) require that CTs intended for supplying relay protection should typically have an error of no more than 10%. A larger error is permitted in individual cases when it does not lead to incorrect actions of the relay protection. Errors arise because the actual transformation process in a CT occurs with power consumption, which is expended on creating a magnetic flux in the core, remagnetization of the core steel (hysteresis), eddy current losses, and winding heating.
Fig. 4.3 Equivalent circuit of a current transformer.
Fig. 4.4 Simplified phasor diagram of a current transformer.
The process of current transformation is well illustrated by the CT equivalent circuit shown in Fig. 4.3. In this diagram, \(Z_1\) and \(Z_2\) are the resistances of the primary and secondary windings, and \(Z_{\text{nom}}\) is the resistance of the magnetizing branch, which characterizes the power losses mentioned above.
From the equivalent circuit, it is clear that the primary current \(I_1\) entering the beginning of the primary winding N passes through its resistance \(Z_1\) and at point 'a' branches into two parallel paths. The main part of the current, which is the secondary current \(I_2\), closes through the resistance of the secondary winding \(Z_2\) and the load resistance \(Z_H\), consisting of the resistances of relays, instruments, and connecting wires. The other part of the primary current \(I_{\text{nom}}\) closes through the resistance of the magnetizing branch and, consequently, does not reach the relay connected to the CT's secondary winding. Since among all power expenditures, the largest part accounts for the creation of magnetic flux in the core, the branch between points 'a' and 'b' of the CT equivalent circuit is called the magnetizing branch, and the entire current \(I_{\text{nom}}\) flowing through this branch is called the magnetizing current.
Thus, the equivalent circuit shows that not all of the transformed primary current, equal to \(I_1 / K_I\), enters the CT's secondary winding, but only a part of it, and that, consequently, the transformation process occurs with errors.
When the secondary winding circuit of a CT is opened, it turns into a step-up transformer, the magnetizing current dramatically increases: \(I_1 = I_{\text{nom}}\) (Fig. 4.3), and at a sufficient current level, the induction in the core reaches saturation. Due to the saturation of the CT core, with a sinusoidal primary current, the magnetic flux in the core will have a trapezoidal, rather than sinusoidal, shape. Therefore, the EMF in the secondary winding, proportional to the rate of change of magnetic flux, will be very large at moments of its zero crossings, and can exceed 1000 V, which is dangerous not only for service personnel but also for the inter-turn insulation of current transformers (inter-turn short circuit is possible). In addition to the appearance of dangerous voltage on the open secondary winding, increased heating of the steel core may occur due to large losses in the steel (the so-called "steel fire"). This can not only lead to insulation damage but also to an increase in current transformer errors due to residual magnetization of the core. In the event of an inter-turn short circuit of the CT's secondary winding, the magnetizing current sharply increases, and the current at its output sharply decreases (or is completely absent). A turn-to-turn short circuit of a CT can be diagnosed by comparing its magnetizing characteristic (the dependence of the voltage across the secondary winding on the current flowing through it) with the characteristic of a healthy CT (the characteristic significantly drops).
Fig. 4.4 shows a simplified phasor diagram of a CT, from which it is clear that the secondary current vector \(I_2\) is less than the value of the primary current divided by the transformation ratio by the amount (\Delta I) and is shifted relative to it by an angle \(\delta\). Thus, the ratio of the primary and secondary current values actually has the form:
\(\dot{I}_2 = \frac{\dot{I}1 - \dot{I}{нам}}{K_I}\) (4.7)
The following types of CT errors are distinguished. Current error, or transformation ratio error, is defined as the arithmetic difference between the primary current divided by the nominal transformation ratio \(I_1 / K_I\) and the measured (actual) secondary current \(I'_2\) (segment \(\Delta I\) on the diagram in Fig. 4.4):
\(\Delta I = \frac{I_1}{K_I} - I_2\) (4.8)
Current error, %
$f = \frac{\Delta I}{I_1 K_I} \cdot 100$ (4.9)
Phase angle error is defined as the angle \(\delta\) of the shift of the secondary current vector \(I_2\) relative to the primary current vector \(I_1\) (see Fig. 4.4) and is considered positive when \(I_2\) leads \(I_1\). Total error \((\varepsilon)\) is defined as the percentage ratio of the RMS value of the difference between the instantaneous values of primary and secondary currents to the RMS value of the primary current.
For sinusoidal primary and secondary currents: \(\varepsilon = I_{\text{nom}}\). From the above, it follows that the cause of errors in current transformers is the flow of magnetizing current, i.e., the very current that creates the working magnetic flux in the CT core, ensuring the transformation of the primary current into the secondary winding. The smaller the magnetizing current, the smaller the CT errors.
As can be seen from the equivalent circuit (Fig. 4.3), the magnetizing current depends on the EMF \(E_2\) and the resistance of the magnetizing branch \(Z_{\text{nom}}\).
The electromotive force \(E_2\) can be defined as the voltage drop from the current \(I_2\) across the resistance of the secondary winding \(Z_2\) and the load resistance \(Z_н\), i.e.:
\(E_2 = I_2(Z_2 + Z_{\text{н}})\) (4.10)
The resistance of the magnetizing branch \(Z_{\text{nom}}\) depends on the design of the current transformers and the quality of the steel from which the core is made. This resistance is not constant but depends on the steel's magnetization characteristic. When the CT core steel saturates, \(Z_{\text{nom}}\) sharply decreases, which leads to an increase in \(I_{\text{nom}}\) and, as a consequence, to an increase in CT errors.
Thus, the conditions determining the errors of current transformers are: the ratio, i.e., the multiplicity, of the primary current passing through the CT to its nominal current, and the load connected to its secondary winding.
To increase the permissible secondary load, current transformers with a nominal secondary winding current of 1 A are used instead of 5 A. One-ampere current transformers can carry a load 25 times greater than five-ampere ones, provided they have the same design parameters and the same nominal primary winding current. Of course, the power consumed by the equipment remains the same, and its resistance also increases 25 times; however, a significant advantage is gained due to the possibility of using long cables with small cross-section conductors. For this reason, current transformers with secondary currents of 1 A have found application mainly in powerful extra-high voltage substations, where long cables need to be laid. In 6-35 kV networks, as a rule, 5-ampere current transformers are used, which simplify the design by requiring 5 times fewer turns to be wound. One-ampere current transformers have also found application in switchgear cells, where the transition to a 1 A secondary current in combination with the low consumption of modern relay protection systems has made it possible to produce compact current transformers that can only be placed in the small-sized cells produced by them.
Current Transformer Connection Schemes To connect relays and measuring instruments, CT secondary windings are connected in various schemes. The most common schemes are shown in Fig. 4.5.
Fig. 4.5, a shows the basic wye (star) connection scheme, which is used for protection against all types of single-phase and phase-to-phase short circuits; Fig. 4.5, b shows the incomplete wye (star) connection scheme, used primarily for protection against phase-to-phase short circuits in networks with isolated neutral points; Fig. 4.5, c shows the delta connection scheme, used to obtain the difference of phase currents (for example, for connecting transformer differential protection); Fig. 4.5, d shows the connection scheme for the difference of currents of two phases. This scheme is used for protection against phase-to-phase short circuits, similar to the scheme in Fig. 4.5, b. Fig. 4.5, e shows the connection scheme for the sum of currents of all three phases (zero-sequence current filter), used for protection against single-phase short circuits and ground faults.
Fig. 4.5, f shows the series connection scheme of two current transformers installed on the same phase. In such a connection, the load connected to them is distributed equally, i.e., it decreases by 2 times on each of them. This happens because the current in the circuit, equal to \(I_2 = I_1 / K_I\), remains unchanged, while the voltage across each CT is half of the total.
Fig. 4.5 Secondary winding connection schemes of current transformers
This considered scheme is used when low-power CTs are employed (for example, those built into circuit breaker and transformer bushings).
Fig. 4.5, g shows the parallel connection scheme of two CTs installed on the same phase. The transformation ratio of this scheme is 2 times less than the transformation ratio of a single CT.
The parallel connection scheme is used to obtain non-standard transformation ratios. For example, to obtain a transformation ratio of 37.5/5 A, two standard CTs with a transformation ratio of 75/5 A are connected in parallel.
Selection of Current Transformers Initial data. All current transformers (CTs) are selected, like other apparatus, based on the nominal current and voltage of the installation and are checked for thermal and electrodynamic withstand capability during short circuits (SCs). Additionally, CTs used in relay protection circuits are checked for error values, which, as stated above, should not exceed 10% for current and 7° for angle. To check against this condition, information materials from CT manufacturers and other reference literature provide CT characteristics and parameters:
1) Curves of the 10% multiplicity \(m\) dependence on the load resistance \(Z_K\) connected to the secondary winding of the CT. The ten percent multiplicity (m) is defined as the ratio, i.e., the multiple, of the primary current passing through the CT to its nominal current, at which the current error of the CT is 10% at a given load \(Z_H\). The phase angle error simultaneously reaches 7° (Fig. 4.4). Thus, knowing the multiplicity of the primary current passing through the CT, one can use the 10%-multiplicity curves for a given CT type to determine the permissible load \(Z_{H.\text{perm}}\), at which the CT error will not exceed 10%. Conversely, knowing the actual load value connected (or to be connected) to the CT's secondary winding \(Z_H\), one can use the 10%-multiplicity curves to determine the permissible primary current multiplicity \(m_{\text{perm}}\), at which the CT current error will also not exceed 10%.
2) Curves of the limiting multiplicity \(K_{10}\) dependence on the load resistance \(Z_H\) connected to the secondary winding (for current transformers manufactured in accordance with GOST 7746-78 *E). According to the specified GOST, the limiting multiplicity \(K_{10}\) is the maximum ratio, i.e., the maximum multiple, of the primary current passing through the CT to its nominal current, at which the total error of the CT \((\varepsilon)\) at a given secondary load does not exceed 10%. In this case, the guaranteed limiting multiplicity at the nominal secondary load \(Z_{H.\text{nom}}\) is called the nominal limiting multiplicity. Analogously to the above, using the limiting multiplicity curves, one can determine either the permissible load for a known primary current multiplicity or the permissible primary current multiplicity for a known load, at which the total error of the CT will not exceed 10%.
3) Typical magnetization curves, representing the dependence of the maximum induction values \((B)\) in the core on the RMS values of magnetic field strength \(H\) at an average magnetic path length; a defined core cross-section; (nominal value of magnetomotive force \(A)\).
\(B_{\text{max}} = \frac{E_2}{4,44 f \omega_2 S}\) (4.11)
Magnetic field strength (A/cm) is expressed by the formula:
\(H = \frac{I_{\text{нам}} \omega_2}{l}\) (4.12)
where: \(I_{\text{nom}}\) – magnetizing current, A; \(l\) – average magnetic path length, cm.
Thus, this characteristic is a characteristic of the iron from which the CT is made, and for a specific current transformer, it is recalculated into a volt-ampere characteristic taking into account the number of turns and the geometric dimensions of the core.
By determining \(B\) using the specified formula, \(H\) and the magnetizing current \(I_{\text{nom}}\) are determined from the magnetization curve, and then the secondary current of the CT:
\(I_2 = \frac{I_1}{K_I} - I_{\text{нам}}\) (4.13)
It should be noted that GOST allows for a 20% deviation of characteristics from the typical one. Therefore, the calculated characteristic should be lowered by 20% in terms of voltage. The actual magnetization characteristics (hereinafter referred to as volt-ampere characteristics), representing the dependence of the voltage across the secondary winding terminals of the CT, \(U_2\), on the magnetizing current flowing through this winding, i.e., \(U_2 = f (I_{\text{nom}})\). By using the actual magnetization characteristics, one can also determine \(I_{\text{nom}}\) and \(I_2\) and assess the permissibility of the obtained error. This characteristic is measured directly on the current transformer in use. Load of the secondary winding of current transformers. The load of the CT secondary winding consists of series-connected resistances: relays, instruments, control cable conductors, and contact connection resistance:
\(Z_{\text{н}} = Z_{\text{р}} + Z_{\text{пр}} + Z_{\text{каб}} + Z_{\text{пер}}\) (4.14)
where:
\(Z_{\text{р}}, Z_{\text{пр}}, Z_{\text{каб}}, Z_{\text{пер}}\) - resistances of relays, instruments, cable, and transition contacts, respectively.
For simplification of calculations, arithmetic rather than geometric summation of total and active resistances is performed. The load on the CT secondary winding also depends on their connection scheme and the type of short circuit. Therefore, the load should be determined for the most heavily loaded CT, taking into account the connection scheme and for the type of short circuit that yields the worst results.
Calculation formulas for the most common connection schemes of CT secondary windings and for various types of short circuits are given in Table 4.1.
Determination of Permissible Load on Current Transformers The permissible load on CTs is determined based on the following requirements: ensuring the accuracy of relay protection measuring elements during short circuits at the calculated points of the electrical network (the total CT error \(\varepsilon\) must not exceed 10%) for current protections at the setting current, for differential protection — at the end of the operating zone; to prevent protection malfunction (failure to operate) at the highest short circuit current values — normalized for electromechanical protections during short circuits in the protection installation zone.
Calculation of Load Depending on CT Connection Scheme Table 4.1
Notes:
1. The largest value (for the most loaded phase) should be substituted into the formulas in items 1–4.
2. The value of \(r_{\text{trans}}\) is in all cases taken as 0.1 Ohm.
Checking current transformers using actual magnetization characteristics is performed in the following order:
The actual load \(Z_H\) connected to the secondary winding is determined, taking into account the formulas given in Table 4.1.
The calculated primary and secondary short-circuit currents are determined, which are equal to the maximum short-circuit current at the end of the protected zone (for instantaneous overcurrent protection, the short-circuit current is equal to the pickup setting of the instantaneous element).
The calculated magnetizing current is determined, equal to \(I_{2\text{nom.calc.}} = 0.1 \cdot I_{2\text{SC.calc.}}\).
The lowest magnetization characteristic \(U_2 = f(I_{\text{nom}})\) of the tested CTs is plotted, and from this characteristic and the magnetizing current obtained above, the corresponding voltage value \(U_2\) is determined.
The permissible load resistance is determined, at which the CT error will not exceed 10% in value and 7° in angle, using the formula.
\(Z_{\text{Н.доп}} = \frac{U_2 - I_{\text{2рас}}Z_1}{0,9 I_{\text{2рас}}}\) (4.15)
For the current transformer's error not to exceed the permissible 10%, the load on its secondary winding calculated in item 1) should not exceed the value \(Z_H\) determined in item 5).
Example: Let's determine the errors of a TPL-1 3, 200/5 type CT with identical load on its secondary windings \(Z_H = 1\) Ohm. The resistance of the secondary windings is \(Z_2 = 0.3\) Ohm for a Class 1 winding and \(Z_2 = 0.4\) Ohm for a Class 3 winding. The calculated primary current is \(I_{\text{calc}} = 2000\) A.
Fig. 4.6 Magnetization characteristic of a TPL-1/3, 200/5 A type current transformer:
3. The EMFs of the secondary windings are determined using the formula: \(E_2 = I_{\text{2рас}} (Z_2 + Z_{\text{н}})\) (4.16)
for the Class 1 core - \(E_2\) = 50 (0,3 + 1) = 65 V.
for the Class 3 core - \(E_2\) = 50 (0,4 + 1) = 70 V.
4. Assuming \(E_2 = U_2\) (since their values differ insignificantly), the magnetizing current is determined from the magnetization characteristics shown in Fig. 4.6. For a Class 1 core, the magnetizing current at 65 V is \(I_{\text{nom}} = 1.1\) A. Thus, the secondary winding will carry not 50 A, but 50 - 1.1 = 48.9 A.
and the CT error will be: \( f = \frac{1.1}{50} \cdot 100 = 2.2\,\% \)
The calculated EMF of the Class 3 core is 70 V. However, from the magnetization characteristic of this core (Fig. 4.6), it is evident that starting from a magnetizing current of approximately 5.5 A, saturation occurs, as a result of which the voltage across the secondary winding remains unchanged and is approximately 51 V. Therefore, the secondary current will be equal to: \( I_2 = \frac{51}{0{,}4 + 1} = 36{,}5\,\text{A} \)
and the error of the Class 3 core will be: \( f = \frac{50 - 36{,}5}{50} \cdot 100 = 27\,\% \)
Current Distribution during Two-Phase Short Circuit Behind a Transformer with Y/∆ Connection Two-phase short circuits behind transformers with Y/∆ or ∆/Y winding connections represent a special case in terms of current distribution.
Current distribution on the wye side of a transformer with Y/∆ winding connection (Fig. 4.7, a) during a short circuit on the delta side. For simplicity, it is assumed that the transformer's transformation ratio \(k_T = 1\). In this case, the ratio of line currents of windings with a Y/∆ connection is equal to 1, and the ratio of currents in the phases $ I_Y / I_{\text{Д}} = w_{\text{Д}} / w_Y = \sqrt{3} $ (4.17)
Fig. 4.7 Current distribution and vector diagrams of currents during two-phase short circuits behind transformers with winding connections: a – Y/∆; b – ∆/Y
During a two-phase short circuit on the delta side, for example, between phases b and c (Fig. 4.7, a), the current in the undamaged phase \(I_a = 0\), and the currents in the damaged phases b and c are equal to the short-circuit current, i.e., \(I_c\) = \(-I_b\) = \(I_k\) (4.18)
As can be seen from Fig. 4.7, a, in the delta connection, the current divides into two parts: one closes through phase c winding, and the other — through the series-connected windings of phases b and a. Since the resistance of the second circuit is 2 times greater than the first, the current in phase c winding is \(I_k / 2\) or \(3 I_k / 2\), and in phases a and b windings — \(I_k / 3\).
The currents on the wye side correspond to the currents in the windings of the same-named phases of the delta and exceed them by \(\sqrt{3}\) times, considering (4.18):
$ I_A = I_{a\Delta} \sqrt{3} = I_k \cdot \sqrt{3}/3 = I_k / \sqrt{3} $ (4.19)
$ I_B = I_{b\Delta} \sqrt{3} = I_k / \sqrt{3} $ (4.20)
$ I_C = I_{c\Delta} \sqrt{3} = I_k \cdot 2 / \sqrt{3} $ (4.21)
Current Distribution during Two-Phase Short Circuit Behind a Transformer with Y/∆ Connection (continued) The picture of current distribution will be similar for short circuits between phases ab and ca. Thus, in a two-phase short circuit on the delta side of a transformer, currents appear in all three phases on the wye side. In two phases, they are equal and similarly directed. In the third phase, the current is opposite to the first two and equal to their sum, i.e., 2 times greater than each of them.
Current Distribution on the Delta Side during Two-Phase Short Circuit Behind a Transformer with ∆/Y Connection (Fig. 4.7, b). The distribution and ratio of currents on the delta side are similar to the previous case on the wye side. Analysis of the operating conditions of maximum overcurrent protection (MOCP) connected to CTs, arranged in different schemes, during a short circuit behind a Y/∆ (or ∆/Y) transformer shows:
In the full wye scheme (Fig. 3.19, b), a current appears in one phase of the scheme: $ \left(2/\sqrt{3}\right) \cdot \left(I_k / K_I\right) \text{ and in the other two } \left(1/\sqrt{3}\right) \cdot \left(I_k / K_I\right) $ the sum of currents in the neutral wire is zero. Relays I, II, III operate, but two of them have 2 times less sensitivity than the third (where \(K_I\) is the CT transformation ratio).
In the incomplete wye scheme, current flows through both phases and the return wire; in the latter, it is equal to the geometric sum of the currents of the specified phases, or the current of the phase missing from the scheme.
If the CTs happen to be in phases with smaller primary currents: \((\frac{1}{3} \cdot I_k \cdot K_I)\), then in this case, the protection sensitivity will be 2 times worse than in the full wye scheme. To eliminate this drawback, a relay should be used in the return wire, where the sum of phase currents passes, equal to the short-circuit current in the third phase:$ I_{0Л} = \frac{I_k}{\sqrt{3} K_I} + \frac{I_k}{\sqrt{3} K_I} = \frac{2I_k}{\sqrt{3} K_I} $ (4.22)
3) In the scheme with one relay connected to the current difference of two phases, the current in the relay will be absent in the case shown in Fig. 4.7, a, b.
4) In the scheme of connecting three current transformers in a delta and three relays in a wye (not shown in the figure), the current distribution is restored – in two phases BC and CA, current \(I_k\) flows, and in the third relay, the current is absent.