ODEN:TEDX/(TEE-7217)/1-12/(26) ndustrial Electrical Engineering and Automation entral or ocal ompensation of Earth-Fault urrents in Non- Effectively Earthed Distribution Systems Dept. of ndustrial Electrical Engineering and Automation und niversity
TEE-7217 26 1 ine losses and transformer investment cost Distributed compensation is likely to be of most use in rural networks where the load density is low. The typical size of a to transformer in these networks is 1 kva. Every transformer substation will not have to be equipped with a Petersen coil. The required rating of each coil increases as the distance between the Petersen coils increase. One reason to limit the distance between the Petersen coils is the capacitive earth fault current flowing in the system. arge capacitive current causes resistive losses in the network. The resistive losses depend on the cable data. Simulations using AXKJ 95/25 and AXES 95/25 cable data have shown that as long as the distance between the Petersen coils does not exceed 2 km, losses due to capacitive current transportation will not change noticeably. The price of a Petersen coil equipped transformer is approximately two times as high as a transformer of the same rating, without the compensation coil. Assumed the price of an ordinary transformer is u, the price of an entire transformer substation is estimated at 4 pu. This means the price of the compensation coil equipped substation is 5 pu. The cost of a substation with a compensation coil equipped transformer will be 5/4 of that of an ordinary substation. f it is possible to replace only the transformers, the price difference is 2 to 1. The investment cost decrease as the distance between the compensation coils increases. 1.1 orrect fuse function f the line losses and the transformer investment cost alone where to decide the optimum spacing between the Petersen coils, the coils would not be placed closer than 2 km apart, for reasons mentioned above. n addition however, the maximum rating of the Petersen coils must allow correct function of the fuses protecting the to transformer. The constraints that determine the economical optimum are schematically described in Figure 1. ost Maximum distance due to maximum current through compensation coil Total cost nvestment cost osses Optimum Distance between compensation coils Figure 1, Schematic picture of the constraints that determine the economical optimum of the Petersen coil placing
TEE-7217 26 When the distance between the Petersen coils is as long as twenty kilometres, the current through the coil might be too large to ensure correct function of the fuses. orrect fuse function will therefore set the limit for the rating of the Petersen coils. n addition, with a distance of approximately 5 km between the units instead of 15 or 2, it might be possible to make more use of the fact that disconnection of part of the network will include disconnection of corresponding amount of compensation. 1.2 ost efficient manufacturing To keep the price of the Petersen coil equipped transformers within reasonable limits very few Petersen coil ratings will be manufactured. Distribution network owners has opted for one 12 kv rating and one 24 kv rating to keep the manufacturing cost effective.
TEE-7217 26 2 The Ndyn transformer 2.1 Protection The number of to distribution transformers in the power systems is extensive. t would be very expensive to protect them all with advanced equipment. Normally fuses are used for short circuit protection. The fuses on the and side of the transformer shall blow for two and three short circuit in the transformer. They shall also blow for one, two and three faults on the terminal. The capacitive current flowing to the transformer during a to earth fault in the network, combined with maximum load current shall not blow the fuses, i.e. must not exceed their rated current. n case of an earth fault on the side in a system with tuned Petersen coiled earthed Nyn transformers, the three s leading to the transformers will each carry one third of the inductive compensation current. Figure 2 illustrates the zero sequence current in case of a fault between a and earth. Figure 2, The earth fault current in case of a fault between one and earth Simulations using a Ndyn transformer model with each core modelled individually indicate that the load on the side does not influence the zero sequence impedance of the transformer. Hence, the side zero sequence current will not under any load condition be transformed to the side. The function of the side fuses has therefore not to be taken into consideration when selecting the compensation coil rating. Figure shows the current phasors in case of a fault between A and earth in a tuned Petersen coil earthed system. During a single to earth fault in the network the capacitive currents of the healthy s are shifted 6 degrees relative each other. The sum of the capacitive currents is of the same size as the inductive current. The
TEE-7217 26 inductive current will however divide equally between the three s. onsequently, in the individual s the inductive current will not fully compensate the capacitive current. Figure, urrent phasors in case of a fault between A and earth The current generated in each coil is denoted. Any excess inductive or capacitive current in the network will be balanced in the tuning of the central compensation coil. The distributed Petersen coils will not be tuned. The intention is however, to place the distributed Petersen coil at regulate intervals, so that the inductive current generated by each Petersen coil is equivalent to the capacitive earth fault current originated from the nearby conductors. 2.2 Winding ratio The of symmetrical voltages and currents transformed by a Nyn transformer is shifted. The ratio between the windings and the winding must be designed to accomplish the rated ratio of the transformer. The phasors in Figure 4 illustrates the shift. Figure 4, Phasors illustrating the shift between the primary and secondary side of the Ndyn transformer The transformer primary voltage is the sum of the voltages across the 1 winding and the 2 winding of the. These two voltages are shifted 6 relative each other. The of the sum of the two voltages is consequently shifted relatively the of each of the two voltages. The RMS value of the voltage across each of the can be calculated according to Equation 1. 1 2 o 2 cos Equation 1 onsider an ideal transformer. The 1 winding of A, the 2 winding of B and the y winding of a all enclose the same flux. The voltage across the winding is proportional to the number of turns of winding. The individual winding ratios can be calculated according to Equation 2.
TEE-7217 26 n N N 1 n 2 Equation 2 There is no power loss in an ideal transformer. n the case of a symmetric load the ratio between the line currents should therefore equal the inverse of the ratio between the voltages, see Equation. This is in accordance with the winding ratios calculated in Equation 2. P Equation
TEE-7217 26 Fault current calculations Assume the to transformers is of 1 kva rating. What is the maximum possible coil rating that ensures correct function of the fuses protecting the to transformer?.1 22 to.4 kv transformer.1.1 Three fault As mentioned above the fuses on the and side of the transformer shall blow for two and three short circuit in the transformer. They shall also blow for one, two and three faults on the terminal. The rated impedance of the Transfix EOBO transformer, a Ndyn transformer bought by the Swedish distribution network owners, is 4 %. A three- short circuit on the side of the transformer will result in the and currents calculated in Equation 4 and Equation 5. The three- short circuit current is symmetrical and will be transformed according to the rated ratio of the transformer. The current through the fuses in case of an internal three short circuit on the side of the transformer will depend on where in the windings the fault is located. u 1.4 pu S ps u 2 n 1 ( 22 1 ) 1 1 484Ω 19.6 Ω 2 22 1 65.6 A 19.6 Equation 4 u 1.4 pu S ps u 2 n 1 (.4 1 ) 1 1 2 1.6Ω.64 Ω.4 1.6 ka.64 Equation 5.1.2 Two fault Figure 5 illustrates the currents on the and side in case of a two- short circuit on the side.
TEE-7217 26 Figure 5, Two short circuit on side The short circuit currents are calculated in Equation 6 and Equation 7. 2 ps ps.6.1 ka 2 2 Equation 6 A2 p B2 p 2 p 2 2 ps 65A A2 p M.1 1.4 22 2.5A Equation 7 f there is a fault resistance present in the fault, or the fault occurs a certain distance away from the transformer the short circuit currents will be smaller..1. Single fault The fault current due to a single to earth fault depends on where in the network the fault occurs. Assuming the fault occurs close to the transformer the current in the faulted will depend solely on the impedance of the transformer. The current in the faulted is calculated in Equation 8. 1 1.4 pu 1.64 Ω.64 Ω Equation 8 ( 2 + ) 1.4 1.14 5.2 ka There will not be any fault current on the side of the healthy s. The
TEE-7217 26 delta winding of the Ndyn transformer balances the one fault current of the side. The stabilizing delta current is given by Equation 9. The per unit value of the current is independent of the number of turns of the delta winding. D pu D pu Equation 9 n N D Figure 6 illustrates the, and delta currents in case of a to earth fault on the side. Figure 6, Fault currents phasors while single to earth fault on the side To achieve MMF balance in the transformer the constraints in Equation 1 have to be fulfilled. Equation 11 shows the same constraints in per unit values when and are the voltages. A single to earth fault on the side will not result in any current through the earthing equipment on the side of the transformer, which is one of the main advantageous of the Ndyn transformer. According to Kirchoff s first law the sum of the currents therefore equal zero. This gives currents according to Equation 12. A B N N N B A Equation 1 2 N N N 2 A B A + B Equation 11 F F F n n n
TEE-7217 26 A A + + B B Equation 12 + + A B Figure 7 illustrates the currents in case of a single to earth fault. The currents are calculated in Equation 1. Figure 7, Single to earth fault on side A B M 5.2 1.4 22 54.6 A Equation 1 The presence of a fault resistance will highly influence all the fault currents..1.4 Simulated fault currents A transformer model d on the data in Table 1 has been used to simulate the side fault currents in case of a bolted three, two or single fault. The simulated fault is located close to the transformer. The fault current will therefore depend solely on the impedance of the transformer. The simulated fault currents are listed in Table 2. A, B and are the side currents. a, b and c are the side currents. The simulated currents differs slightly from the ideal analytical calculated currents
TEE-7217 26 TABE 1 DATA OF Ndyn TRANSFORMER Rated power Short circuit impedance Primary voltage Secondary voltage No load losses oad losses ero sequence impedance, earthing reactor and transformer 1 kva.4 pu 22 kv.4 kv.2 pu.15 pu.5 + j.175 pu TABE 2 FAT RRENTS FOR THREE, TWO AND SNGE PHASE FAT Three- short circuit Two- short circuit Single to earth A 58.7 A 29. A 1.66 A B 58.7 A 58.65 A 1.66 A 58.7 A 29. A a 228.5 A 279 A 15 A b 228.5 A 279 A c 228.5 A.1.5 Maximum load current and single fault Neither the fuses on the side or the side shall blow due to maximum load current combined with a compensation current due to a to earth fault in the network. The maximum combined current on the side is calculated in Equation 14. S 1 1 n Max oad n 22 1 Healthy Max 2.6 + A 2.6 A Equation 14 The capacitive earth fault current in a 22 kv network consisting of underground cable is approximately A per km. f the fuses are constructed to withstand currents up to 2 A the distance between the Petersen coils can be calculated as in Equation 15.
TEE-7217 26 2.6 + fault < 52 A < 2 A < 2 A 52 d 17km Equation 15.2 Vattenfall and e.on transformers The two major Swedish distribution companies Vattenfall and e.on have decided to use 1 kva transformers equipped with 15 and 1 A rated Petersen coils in their 24 and 12 kv networks. The coil rating corresponds to a distance of 5 km between the Petersen coil equipped transformers. One reason they have chosen this solution can be advantageous related to keeping the same distance between the compensation units, independent of voltage level. t is utterly important to limit the number of different transformers in discussions with manufacturers. The opted alternative might not be the ideal, but it is certain to avoid the risk of unwanted fuse operation, which is of great importance. The current in the healthy s on the side of a 24 kv system in case of a to earth fault in the network combined with the maximum load current is calculated in Equation 16. 15A Healthy fault 5A 2.6 + 5 7.6 A Equation 16 The corresponding maximum current for a 12 kv network are calculated in Equation 17. Max 1 A Healthy Max oad.a S n 1 1 11 1 n 5.2 +. 8.5 A Equation 17 5.2 A
TEE-7217 26. 12 to.4 kv transformer Table gives the analytical calculated ideal short circuit currents on the and side in case of a fault on the.4 kv terminal of a 12 to.4 kv transformer. TABE FAT RRENTS FOR THREE, TWO AND SNGE PHASE FAT Three- short circuit Two- short circuit Single to earth A 11 A 65.1 A 19 A B 11 A 1 A 19 A 11 A 65.1 A a.6 ka.1 A 5.2 A b.6 ka.1 A c.6 ka Table 1, Fault currents in case of faults in a 11 to.4 kv transformer The fault currents are much larger than the maximum load current combined with the capacitive earth fault current. Transformers equipped with 1 A rated coils can therefore be used in 12 kv network without any risk of unwanted fuse function in case of a to earth fault in the network.