transformer engineering design and practice 1_phần 8

6 Short Circuit Stresses and Strength The continuous increase in demand of electrical power has resulted in the addition of more generating capacity and interconnections in power systems. Both these factors have contributed to an increase in short circuit capacity of networks, making the short circuit duty of transformers more severe. Failure of transformers due to short circuits is a major concern of transformer users. The success rate during actual short circuit tests is far from satisfactory. The test data from high power test laboratories around the world indicates that on an average practically one transformer out of four has failed during the short circuit test, and the failure rate is above 40% for transformers above 100 MVA rating [1]. There are continuous efforts by manufacturers and users to improve the short circuit withstand performance of transformers. A number of suggestions have been made in the literature for improving technical specifications, verification methods and manufacturing processes to enhance reliability of transformers under short circuits. The short circuit strength of a transformer enables it to survive through-fault currents due to external short circuits in a power system network; an inadequate strength may lead to a mechanical collapse of windings, deformation/ damage to clamping structures, and may eventually lead to an electrical fault in the transformer itself. The internal faults initiated by the external short circuits are dangerous as they may involve blow-out of bushings, bursting of tank, fire hazard, etc. The short circuit design is one of the most important and challenging aspects of the transformer design; it has been the preferential subject in many CIGRE Conferences including the recent session (year 2000). Revision has been done in IEC 60076–5 standard, second edition 2000–07, reducing the limit of change in impedance from 2% to 1% for category III (above 100 MVA rating) transformers. This change is in line with the results of many 231 Copyright © 2004 by Marcel Dekker, Inc. 232 Chapter 6 recent short circuit tests on power transformers greater than 100 MVA, in which an increase of short circuit inductance beyond 1% has caused significant deformation in windings. This revision has far reaching implications for transformer manufacturers. A much stricter control on the variations in materials and manufacturing processes will have to be exercised to avoid looseness and winding movements. This chapter first introduces the basic theory of short circuits as applicable to transformers. The thermal capability of transformer windings under short circuit forces is also discussed. There are basically two types of forces in windings: axial and radial electromagnetic forces produced by radial and axial leakage fields respectively. Analytical and numerical methods for calculation of these forces are discussed. Various failure mechanisms due to these forces are then described. It is very important to understand the dynamic response of a winding to axial electromagnetic forces. Practical difficulties encountered in the dynamic analysis and recent thinking on the whole issue of demonstration of short circuit withstand capability are enumerated. Design parameters and manufacturing processes have pronounced effect on natural frequencies of a winding. Design aspects of winding and clamping structures are elucidated. Precautions to be taken during design and manufacturing of transformers for improving short circuit withstand capability are given. 6.1 Short Circuit Currents There are different types of faults which result into high over currents, viz. single-line-to-ground fault, line-to-line fault with or without simultaneous ground fault and three-phase fault with or without simultaneous ground fault. When the ratio of zero-sequence impedance to positive-sequence impedance is less than one, a single-line-to-ground fault results in higher fault current than a three-phase fault. It is shown in [2] that for a particular case of YNd connected transformer with a delta connected inner winding, the single-line-to-ground fault is more severe. Except for such specific cases, usually the three-phase fault (which is a symmetrical fault) is the most severe one. Hence, it is usual practice to design a transformer to withstand a three-phase short circuit at its terminals, the other windings being assumed to be connected to infinite systems/sources (of constant voltage). The symmetrical short circuit current for a three-phase two-winding transformer is given by (6.1) where V is rated line-to-line voltage in kV, ZT is short circuit impedance of the transformer, and ZS is short circuit impedance of the system given by Copyright © 2004 by Marcel Dekker, Inc. Short Circuit Stresses and Strength 233 (6.2) where SF is short circuit apparent power of the system in MVA and S is three-phase rating of the transformer in MVA. Usually, the system impedance is quite small as compared to the transformer impedance and can be neglected, giving an extra safety margin. In per-unit quantities using sequence notations we get (6.3) where Z1 is positive-sequence impedance of the transformer (which is leakage impedance to positive-sequence currents calculated as per the procedure given in Section 3.1 of Chapter 3) and VpF is pre-fault voltage. If the pre-fault voltages are assumed to be 1.0 per-unit (p.u.) then for a three-phase solid fault (with a zero value of fault impedance) we get (6.4) The sequence components of currents and voltages are [3] (6.5) For a solid single-line-to-ground fault on phase a, (6.6) Ia0=Ia1=Ia2=Ia/3 (6.7) where Z2 and Z0 are negative-sequence and zero-sequence impedances of the transformer respectively. For a transformer, which is a static device, the positive and negative-sequence impedances are equal (Z1=Z2). The procedures for calculation of the positive and zero-sequence impedances are given in Chapter 3. For a line-to-line fault (between phases b and c), (6.8) (6.9) Copyright © 2004 by Marcel Dekker, Inc. 234 Chapter 6 and for a double-line-to-ground fault, (6.10) Since a three-phase short circuit is usually the most severe fault, it is sufficient if the withstand capability against three-phase short circuit forces is ensured. However, if there is an unloaded tertiary winding in a three-winding transformer, its design must be done by taking into account the short circuit forces during a single-line-to-ground fault on either LV or HV winding. Hence, most of the discussions hereafter are for the three-phase and single-line-to-ground fault conditions. Based on the equations written earlier for the sequence voltages and currents for these two types of faults, we can interconnect the positive-sequence, negative-sequence and zero-sequence networks as shown in figure 6.1. The solution of the resulting network yields the symmetrical components of currents and voltages in windings under fault conditions [4]. Figure 6.1 Sequence networks Copyright © 2004 by Marcel Dekker, Inc. Short Circuit Stresses and Strength 235 The calculation of three-phase fault current is straight-forward, whereas the calculation of single-line-to-ground fault current requires the estimation of zero-sequence reactances and interconnection of the three sequence networks at the correct points. The calculation of fault current for two transformers under the single-line-to-ground fault condition is described now. Consider a case of delta/star (HV winding in delta and LV winding in star with grounded neutral) distribution transformer with a single-line-to-ground fault on LV side. The equivalent network under the fault condition is shown in figure 6.2 (a), where the three sequence networks are connected at the points of fault (corresponding LV terminals). The impedances denoted with subscript S are the system impedances; for example Z1HS is the positive-sequence system impedance on HV side. The impedances Z1HL, Z2HL and Z0HL are the positive-sequence, negative-sequence and zero-sequence impedances respectively between HV and LV windings. The zero-sequence network shows open circuit on HV system side because the zero-sequence impedance is infinitely large as viewed/measured from a delta side as explained in Chapter 3 (Section 3.7).When there is no in-feed from LV side (no source on LV side), system impedances are effectively infinite and the network simplifies to that given in figure 6.2 (b). Further, if the system impedances on HV side are very small as compared to the inter-winding impedances, they can be neglected giving the sequence components and fault current as (fault assumed on a phase) Figure 6.2 Single-line-to-ground fault on star side of delta/star transformer Copyright © 2004 by Marcel Dekker, Inc. ... - tailieumienphi.vn