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CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS – OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS Stig Holst ABB Automation Products Sweden Bapuji S Palki ABB Utilities India This paper reports on some of the results of the working group WG 34.02, established by the Study Committee 34 to study and investigate co-ordination of relays and conventional current transformers (CT). The objective of the WG 34.02 work is to suggest common recommendations on how the manufacturers should specify the CT requirements and also suggest a guideline for co-ordination of relays and current transformers. certain amount of measuring errors and still maintain acceptable operation. Different relays can allow the current transformers to go into saturation after a certain time and still perform correctly. To achieve specified time to saturation the current transformer will have to be overdimensioned. The overdimensioning is influenced by the primary time constant, the secondary time constant of the current transformer and the magnitude of the DC component. The remanance also has impact on the overdimensioning. The commonly used formulae for calculation of the overdimensioning factor are often simplified considering the primary time constant and always the maximum DC component. These formulae will not give optimum dimensioning in the co-ordination of current transformers and modern numerical relays that sometimes require just very short time to saturation for correct operation. Often the overdimensioning factor is too pessimistic. In some cases it is also important to consider the case without any DC component. The paper will show and discuss a more realistic and correct method of calculating the overdimensioning factor of current transformers when co-ordinating fast numerical relays and current transformers, than what has normally been the common practice. 1. Introduction Correct operation of most protective relays is dependent on the relays being supplied with sufficient information from the high voltage system. The fault current is one of the most important quantities for the operation of the relay. The fault current has a steady state and a transient component. The DC transient part has a major role in the current transformer errors. The paper describes the basic theoretical equations for the transient dimensioning of current transformers considering the impact of different degrees of DC component. The effects of various parameters on the overdimensioning factor are discussed and recommendations on how to calculate more relevant overdimensioning factors are included. The error of a conventional current transformer is dependent on, whether the core is saturated or not. When the core is saturated the magnetizing current is large compared to the secondary current and the error is high. The degree of saturation depends on the magnitude of fault current, primary time constant, secondary time constant of the current transformer and the magnitude of the DC component. The remanence of the core will also influence the saturation. Current transformer saturation can cause both failure to operate and unwanted operation of the protection depending on the measuring principle. 2. Basic theory transformers for dimensioning of current The basic theoretical equations for the transient dimensioning of the current transformer considering the impact of switching angle as well as other factors are described in this chapter. The equations may be taken as extension to the theoretical equations given in IEC 60044-6. Theoretically the saturation and the maloperation of the protection can be avoided by considering all the negative factors when sizing the current transformer. In practice this will often result in unrealistically large and expensive current transformers. On the other hand it is not necessary that current transformers are totally free from saturation, because protective relays can tolerate a 2.1 Short circuit current The equivalent circuit of a typical fault loop can be represented by an inductance and a resistance in series (See Figure1). Assuming a sinusoidal e.m.f. 1 L where R Ts = (L0 + L2)/R2 L0/R2 is the secondary time constant of the CT q = L2/(L0 + L2) L2/L0 is the ratio of inductances. L0 is the main inductance L2 is the total inductance of the secondary circuit R2 is the total resistance of the secondary circuit G Figure 1: Equivalent circuit of a short circuit loop. v 2 Vm cost i1 i2 (1) UL L2 The short circuit current (i) may be written as i 2 I psc e t Tp cos cost U1 L0 R2 (2) UR where Figure 2: Equivalent circuit of a current transformer = Angle of switching on the voltage curve Vm = is the r.m.s. value of the generator e.m.f. Ipsc = Vm / (R2 + L2)½ is the r.m.s. value of primary symmetrical short circuit current Tp = L/R is the primary time constant = tan-1(L/R) is the phase angle difference between voltage and current By substituting the asymmetrical short circuit current in the system equation for i1, we obtain the following equation for the magnetizing current i0 for the case Tp Ts. (5) Substituting for ( - the expression (2) can be written as t i 2 I psc e Tp cos cost t t Tp qTs Tp i 0 2 I psc cos e e Ts Tp Ts (3) 1 2 I psc 2 2 Ts 1 The second term in this expression is the steady state sinusoidal variation and the first term is the transient part, which theoretically vanishes after infinite time. 1 q Ts sin q 2 Ts 2 1 cos e Ts At t = 0 it can be seen that the transient component equals the steady state component and since both have opposing polarities the current is zero at t = 0. 1 2 I psc 2 2 Ts 1 The transient component will be zero when = ± /2 and will have maximum value when = 0. Making an assumption that the network is predominantly inductive this corresponds to switching taking place on the voltage wave when it is passing through maximum and zero respectively. t 1 q Ts sin t q 2 Ts 2 1 cost In the above equation substituting, g = (q2 Ts2 + 1)/(2 Ts2 + 1) 2.2 Transmission of asymmetrical short circuit current through a CT and assuming 2 Ts2 + 1 = 2 Ts2 A CT can be represented by the equivalent circuit shown in Figure 2. From this circuit we can derive the following differential equation. di 0 di 1 1 i0 q 1 i1 dt Ts dt Ts Equation (5) can be simplified as (4) 2 K ssc I psc I pn t Tp qTs i 0 2 I psc cos e Tp Tp Ts (10) 2.4 Transient dimensioning factor t 1 q Tp qTs 2 I psc g cos sin cos e Ts Ts Tp Ts If the short circuit current is asymmetrical compared to the case of symmetrical short circuit current, and due to the DC component, saturation in the core will be reached much earlier. If saturation must not occur during the period a protective relay is carrying out the measurement, the transformer will have to be over dimensioned. This overdimensioning factor is defined by Ktf. The transient dimensioning factor Ktf is the ratio of the theoretical total secondary linked flux to the peak instantaneous value of the AC component flux. Since flux values are proportional to the corresponding magnetizing currents Ktf can be given by 1 q 2 I psc sin t g cost Ts The flux in the CT core is directly proportional to i0 and the proportionality constant is dependent upon the dimensions of the core and its permeability. K tf i 0 i 0~max From the equation above it can be seen that the magnetizing current consists of a DC component (7) Tp qTs i 0 2 I psc cos e Tp Ts (11) Substituting expressions for i0 and i0~max the transient dimensioning factor can be written as t Tp t K tf t 1 q Tp qTs 2 I psc g cos sin cos e Ts Ts Tp Ts Tp qTs cos e Tp Tp Ts 1 1 q Ts 2 g2 2 t 1 q Tp qTs sin cos e Ts g cos Ts Tp Ts 1 and an AC component i 0~ 1 q 2 I psc sint g cost Ts 1 q Ts 2 (8) 1 q sin t g cost Ts 1 The maximum value of the AC component i0~max can be given by 1 q Ts 2 1 2 1 q g 2 i 0~ max 2 I psc Ts 2 (12) g2 2 g2 2 (9) If the burden is purely resistive as in the case of static or numerical protection, L2 =0 and thus q = 0 and g can be ignored. Therefore equation (12) can be simplified and the transient dimensioning factor becomes 2.3 Symmetrical short circuit current factor The e.m.f. to be developed by the CT to pass the secondary current Isn through a CT can be given by (Rct+Rb)·Isn (13) where K tf Rct is the CT secondary winding resistance and Rb is the burden of the relay and the leads. t t TpTs Tp Ts cos e e Tp Ts t Ts sin e sint For calculating the transient factor necessary for dimensioning purpose, equation (13) can be simplified by writing sin (t +) = -1. The transient dimensioning If a short circuit current Ipsc is to pass through the CT the CT needs to be overdimensioned. Purely on the symmetrical short circuit basis, without any transient component, the overdimensioning factor of the CT depends on the magnitude of the symmetrical short circuit current and the rated primary current I pn. factor Ktf will then become K tf The symmetrical short circuit current factor Kssc is defined as the ratio of the r.m.s. value of the short circuit current Ipsc and the rated primary current Ipn. 3 t t TpTs Tp Ts cos e e Tp Ts t Ts sin e 1 (14) 2.5 Effect of remanent flux on transient dimensioning factor Thus the total overdimensioning factor Ktot can be defined as In a current transformer with a closed grain oriented iron core without any airgap, a remanant flux will remain after a current interruption. An airgap in the core will reduce the remanance. The amount of remanent flux is dependent on the CT type. Generally there are three different types of CTs: K tot K tf K rem K ssc 3. Effect of various parameters on the transient dimensioning of current transformers The transient dimensioning factor Ktf has traditionally been calculated according to the simplified equation (14) and for the case with maximum DC component, = 0. Figure 3 shows the Ktf factor as a function of the time and for some different values of the secondary time constant. The primary time constant Tp is 60 ms in this example. high remanence type CT low remanence type CT non remanence type CT The high remanence type has no limit for the remanent flux. This CT has a magnetic core without any airgap and a remanent flux might remain for almost infinite time. In this type of CT the remanent flux can be up to 70-80 % of the saturation flux. Typical examples of high remanence type CT are class P, TPS, TPX according to IEC, class P, X according to BS (British Standard) and nongapped class C, K according to ANSI/IEEE. Ktf Ts = 20 10 s 5s 15 3s 2s The low remanence type has a specified limit for the remanent flux. This CT is made with a small airgap to reduce the remanent flux to a level that does not exceed 10 % of the saturation flux. Class TPY according to IEC is a low remanence type CT. 10 1s 5 The non remanence type CT has practically negligible level of remanent flux. This type of CT has relatively big airgaps in order to reduce the remanent flux to practically zero level. Class TPZ according to IEC is a non remanence type CT. 0.5 s 0.2 0.4 0.6 0.8 1 Time in seconds Once the remanant flux is established very little of it is dissipated under service conditions and will remain in the core until it is demagnetized. According to studies carried out on CTs that had been in service, the remanance in practice can vary from 0-80 % of the saturation flux. Figure 3: Ktf as a function of the time and Ts Except for CTs with big airgaps, Ts is often a few or several seconds and the influence on Ktf is relatively small and almost negligible during the first 100 ms. In the following diagrams Ts is set to 3 s. The remanance will reduce the available margin for flux increase. This will naturally reduce the time to saturation when the remanant flux is in the same direction as the flux increase required to reproduce the primary fault current. The time to saturation is prolonged when the remanant flux is in the opposite direction. The Ktf increases when Tp increases. This is illustrated in Figure 4. Ktf 80 The remanence factor Kr is defined as the ratio of r/s where r is the remanent flux and s is the saturation flux. If the remanence factor is taken into account, the transient dimensioning factor increases by the remanence dimensioning factor Krem where K rem 1 1 K r (16) Tp = 300 ms 60 (15) 200 ms 40 2.6 The total overdimensioning factor 100 ms 20 The total overdimensioning factor depends on the value of the three factors described above, namely the symmetrical short circuit factor Kssc, the transient dimensioning factor Ktf and the remanence dimensioning factor Krem. 50 ms 30 ms 0.5 1 1.5 Time in seconds Figure 4: Ktf as a function of the time and Tp. Ts = 3 s. 4 To operate correctly each specific type of protective relay requires a certain time to saturation of the CT. In this case it is possible to draw the Ktf as a function of the primary time constant Tp. As an example Figure 5 shows the required Ktf for different values of required time to saturation. Ktf Max DC and reduced DC Modern numerical relays are often designed to be able to operate correctly even when the CT saturates after a very short time. The required minimum time to saturation for these relays is often very short. Sometimes the required time to saturation can be even less than 2 ms. To get the benefit of the short required time to saturation and be able to reduce the size of the CT we have to consider the complete expression of the Ktf factor according to equation (13). tsat 20 70 ms Ktf 16 6 50 ms =0 max DC 40 ms 12 30 ms 4 = 45 8 20 ms 4 2 50 100 150 200 Tp in ms = 90 no DC Figure 5: Ktf as a function of Tp for different values of the time to saturation. Ts = 3 s. 5 10 15 20 Time in ms Figure 7: The Ktf factor as a function of the time and different degree of DC. Ts = 3 s. So far and in all figures we have considered the Ktf factor according to the simplified equation (14) and with maximum DC component. In Figure 6 we can see the difference between the simplified equation (14), and the complete Ktf factor according to equation (13). The effect of the switching angle and different degree of DC component on the Ktf factor is also shown. It is also important to notice that the case with maximum DC component is not the most difficult case for the time shorter than 15 ms. For example, if the required time to saturation is below 2 ms, the case with almost no DC is the most difficult and has to be considered when calculating the required Ktf for the CT. For time to saturation longer than around 15 ms, the case with maximum DC must be considered. In this case it is also of interest to estimate the probability of having a fault with maximum DC. In transmission systems, where the fault current often is almost predominantly inductive, the inception of the fault has to take place on the voltage wave when the voltage is close to zero to give maximum DC component. The probability for this is normally small and it should often be possible to reduce the required K tf due to this reduced risk of maximum DC component. The theory and estimation of the probability of having fault currents with maximum DC component is outside the scope of this paper. However, it is important to notice that it is not possible to reduce the calculated Ktf in the same way if the time to saturation is shorter then 15 ms. In this case we have to consider the switching angle that gives the largest Ktf. Ktf 20 =0 max DC 15 = 45 10 5 = 90 no DC 50 100 150 200 Time in ms Figure 6: The simplified and complete Ktf as functions of the time and different degree of DC. Ts = 3 s. For each value of the required time to saturation it is possible to calculate the corresponding value of the switching angle, max, that gives the maximum value of the Ktf factor. This relation is shown in Figure 8. We can see that the primary time constant has only a small influence on the value of the switching angle. The simplification is relevant when the time is more than 15 ms in a 50 Hz system. However, for shorter time the simplified formula for Ktf is too conservative and gives too large values of Ktf. See Figure 7. 5 max the CT requirements are specified for dependability reasons. The risk of a short delay on an operation is often acceptable. If the risk of a delay is not acceptable the user has to add an extra margin to cover the remanence. However, for security reasons, it is necessary to consider the remanence when deciding the CT requirements. It is for example not acceptable to have unwanted operations from differential relays for external faults caused by remanence and CT saturation. 90 75 Tp = 30 ms 60 45 Tp = 300 ms Ktf Max DC and reduced DC 30 tsat 4 10 ms 15 3 2 4 6 8 10 12 14 16 18 20 8 ms Time to saturation in ms 2 Figure 8: The switching angle, max, which gives the maximum value of the Ktf factor as a function of time to saturation. Ts = 3 s. 6 ms 1 4. 4 ms Recommendations on how to decide the overdimensioning factor for current transformers 2 ms To be able to specify the CT requirements and the required Ktf factor we must know the maximum time to saturation required by the protective relay. If the required time to saturation is more than 15 ms in a 50 Hz system the simplified equation (14) should be used. The Ktf for different time to saturation is calculated and can be shown as functions of the primary time constant Tp. (See Figure 5.) In this case maximum DC component has been assumed. The working group WG 34.02 will give recommendations about the possibility to reduce the Ktf due to the low risk of having maximum DC component in the fault current in a high voltage transmission system. 25 50 75 100 Tp in ms Figure 9: Ktf as a function of Tp for different small values of the time to saturation. Ts = 3 s. 5. Conclusions The paper has described a more complete basic theoretical equation for the transient overdimensioning factor than normally has been published, or been used for specifying of CT requirements, and co-ordination of relays and CTs. The described equation takes into consideration the effect on the Ktf factor for different degree of DC in the fault current. Modern numerical protective relays often require only a very short time to saturation. If the required time to saturation is less than 15 ms the Ktf factor should be calculated according to the more complete equation. For this short time to saturation it is also important to consider less degree of DC in the fault current. The dimensioning of the CTs will be more correct and the overdimensioning will decrease. When the required time to saturation of the relay is less than 15 ms, the complete equation (13) shall be used. The switching angle max, which gives the maximum value of the Ktf factor, is determined for the specific required time to saturation according to Figure 8. With corresponding values of max and required time to saturation, the Ktf can be calculated as a function of the primary time constant. Figure 9 shows the results for some different values of the time to saturation. We can see that the necessary transient dimensioning factor Ktf will be very small if the required time to saturation of the relay is low. The Ktf factor is almost independent of the Tp for very low value of the time to saturation. This is because the Ktf factor has its maximum value for the case when the fault current has hardly any DC component. For higher value of the time to saturation there is a higher degree of DC in the dimensioning case, so the influence of the primary time constant on the K tf factor will increase in this case. 6. References N.E. Korponay, “The Transient Behaviour and Use of Current Transformers“, Brown Boveri Rev. vol. 62, pp. 255-261, June 1975 N.E. Korponay, “Nongapped cores, Antiremanence Cores or Linear cores for Current Transformers“, IEEE Transactions on Power Apparatus and Systems, vol. PAS-97, pp. 569-573, March / April 1978 IEC 60044-6 (1992 - 03) Instrument transformers- Part 6: Requirements for protective current transformers for transient performance. For the total overdimensioning factor we also have to consider the remanence. This is outside the scope of this paper but we will suggest some general recommendations. It should not be necessary for the manufacturer to take into account the remanence when IEEE 76 CH 1130-4 PWR Transient Response of Current Transformers, January 1976 6