Extending analyzed frequency range in interpretation of frequency responses measured on a distribution transformer

TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 Extending analyzed frequency range in interpretation of frequency responses measured on a distribution transformer . Dinh Anh Khoi Pham . Thi Minh Thai Pham Ho Chi Minh city University of Technology, VNU-HCM, Vietnam (Manuscript Received on July 15, 2015, Manuscript Revised August 30, 2015) ABSTRACT In the field of diagnosis of mechanical only within low frequency range. This failures in power transformer’s active part, limitation is due to the fact that, the circuit i.e., windings, leads and the core, the cannot reflect well physical phenomena at technique of Frequency Response Analysis medium and higher frequencies. (FRA) has been recently approved as the To improve the FRA performance of the main application tool. Mechanical failures in proposed method at medium frequencies for transformer windings reflect changes on transformer failure diagnosis purpose, the measured terminal frequency responses paper introduces an investigation on a normally in medium frequency range, from distributed three-phase equivalent circuit of a several to hundreds of kHz, which is in fact 200 kVA 10.4/0.46 kV Yy6 distribution not easy to interpret for diagnosis. transformer. Result of the investigation is a The authors proposed a new method simplified procedure in determination of based on simulation of a lumped three-phase electrical parameters associated with the equivalent circuit of power transformers to distributed circuit for better simulation based interpret frequency responses effectively, but FRA interpretation at medium frequencies. Keywords: Failure diagnosis, power transformer, Frequency Response Analysis, lumped equivalent circuit, distributed equivalent circuit. 1. INTRODUCTION To understand what happens in transformer’s there is no guide from current relevant CIGRE and active part after a suspected through fault or IEC standards [1, 2] to identify type and level of during transportation for diagnostic purpose, fault based on the comparison since there are so measurement of terminal frequency responses of many factors influencing measured frequency voltage ratios (end-to-end, inductive and responses such as transformer type (normal/auto), capacitive interwinding) in broad frequency winding type (disc/layer/interleaved/helical), range, e.g., from 20 Hz to 2 MHz, are often made winding number (two/three), winding connection and then compared with those performed when (vector group), winding’s terminal condition transformers were in good condition. However, (open-circuited/short-circuited/floating), Trang 39 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 measurement set-up etc. There was a national (HV and LV) winding circuits (outside parts) standard, the Chinese DL/T-2004 [3], proposing a represent electrical parameters of the whole quantative analysis but its effectiveness in winding, i.e., equivalent resistances (RH, RL) and supporting the diagnosis is limited as investigated capacitances (CsH, CsL: series; CgH, CgL: ground or in recent publications [4-6]. For illustration, shunt; Ciw: inter-winding), and winding Figure 1 shows a comparison between end-to-end connection (wye, delta) in accordance with vector frequency responses measured before and after a group. More details of the lumped circuit and clear partial axial collapse and inter-turn short- procedures in determination of its components can circuit of a tap winding of a large power be found in [4]. transformer [2]. In reality, when the deviation between compared frequency responses is small, it is difficult to diagnose fault type and level due to the above mentioned influencing factors. Figure 1. Comparison of frequency responses Figure 2. Lumped circuit of a Yy6 transformer measured on a winding before and after fault Although electrical parameters in the The authors proposed a new method for equivalent circuit for two-winding power supporting the interpretation of frequency transformers are effective for diagnosis, the responses in such a way that changes between circuit simulation based FRA interpretation is frequency responses at certain frequencies would valid within low frequency range, from 20 Hz till be transformed into changes of distinct electrical several or tens of kHz, depending on transformer parameters of power transfomers as this could and winding type. To illustrate the limitation of help to figure out fault location and somewhat the lumped circuit, Figure 3 compares a simulated level [4-6]. The proposed method was based on end-to-end frequency response with the simulation of a lumped three-phase equivalent corresponding measured one conducted at HV circuit shown in Figure 2, which has been the side of a test transformer whose details will be state-of-the-art in transformer modeling for mentioned at the end of this section. transient and frequency response analysis so far. In Figure 3, the simulation curve is valid from In the dual magnetic-electric circuit (middle 20 Hz (core region) to around 15 kHz (zero- part) in Figure 2, R1//L1, Ry//Ly are nonlinear core sequence inductance influence). At higher leg and yoke impedances, respectively; L3 are per- frequencies the lumped electrical parameters phase leakage inductances; R4//L4 are per-phase cannot reflect well the interaction between zero-sequence impedances; all of them are sectional inductances and capacitances, and frequency dependent. The high- and low-voltage Trang 40 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 therefore it is necessary to analyze the so-called respectively) and corresponding resistances / distributed circuit for interpretation of frequency conductances representing losses in core responses at these frequencies. laminations, windings’ conductors and insulations. The number of segments is selected depending on desired accuracy and circuit complexity. In order to determine electrical parameters in the distributed circuit based on analytical calculation, complete geometrical data and magnetic-electric properties of transformer components (core, windings and insulation Figure 3. Measurement and simulation of an end- system) must be available [8, 9]. For a to-end frequency response contribution to practice application, the authors Pure mechanical failures in transformer propose a new parameter identification procedure windings normally show changes on frequency where less data will be enough with aim to extend responses starting at medium frequencies [7]. For the analyzed frequency range for simulation based theoretical investigations, simulation technique frequency response interpretation. based on the distributed circuit has been exploited The test object in this paper is a 200 kVA [8, 9]. Figure 4 depicts a per-phase distributed 10.4/0.46 kV Yy6 distribution transformer whose circuit with a multi-segment HV and LV winding, measurement is shown in Figure 3. To facilitate from which the complete circuit of three-phase the investigation with the distributed circuit two-winding transformers is derived by development, after all measurements were carried combination of three of them, adding their mutual out, the transformer was disassembed to measure effect and internal terminal connection. its geometrical parameters (structure and dimensions of the core and windings). 2. DETERMINATION OF PARAMETERS IN THE DISTRIBUTED EQUIVALENT CIRCUIT 2.1 Per segment capacitances CgH0, CgL0, Ciw0 Since influence of series capacitances (CsH and CsL) is insignificant from simulation manipulation of the lumped circuit, only ground and inter-winding capacitances need to be determined and are identified from corresponding Figure 4. Per-phase distributed equivalent circuit lumped capacitances derived from the proposed In Figure 4, the HV and LV phase winding method in [4] by following relations: are divided into a number of segments each of CgH0 = CgH/n; CgL0 = CgL/n; Ciw0 = Ciw/n (1) which has equivalent electrical components: where n is the segment number to be selected self/mutual inductances (Li, Lj/Mij), ground, for investigation. series, inter-winding capacitances (Cg0, Cs0, Ciw0 Trang 41 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 Therefore, geometrical data and electric Zkm = jLkm0 + Z1(km) + Z2(km) (2) properties of windings and insulation system of where the transformer are not necessary for analytical Lkm0 mutual inductance between kth and mth calculation of the capacitances. sections without the core (air core) 2.2 Per segment inductances Li, Lj and Mij Z1(km) mutual impedance between kth While inductances in the lupmed circuit and mth sections owing to flux confined in core represent complete fluxes within core, zero- Z2(km) mutual impedance between kth sequence and leakage paths, inductances in the and mth sections owing to leakage field with core distributed circuit ‘break’ the fluxes into presence individual parts caused by current in winding The resistive component of Z represents segments and are referred as self and mutual km eddy current loss in the core whereas the inductive components. Below are analytical formulas for one is the total mutual inductance between two calculating self and mutual inductances in the sections. Self inductance is a special case of distributed circuit based on geometrical data and magnetic-electrical properties of the core. mutual inductance between a section with itself, i.e., Zkk or Zmm. Geometrical data Following are detailed formulas for Figure 5 shows geometrical data of two determination of Lkm0, Z1(km) and Z2(km). Since Lkm0 winding segments with presence of the core. For is the winding segment inductance when the core the test transformer, n = 8 segments is selected, material is non-magnetic (air core), only which is relatively a compromise between circuit geometrical data are involved. For calculating complexity and simulation accuracy for first Z1(km) and Z2(km), together with geometrical data, investigation. two input magnetic-electric properties, effective relative permeability rel and resistivity eff of the solid-considered core, must be available. Air-core inductance Lkm0 N π  r  L  μ N N ra   4 I β r K β acosβ z (3) km0 0 k m λ a  1 k 1 k k  k 1  where  0 magnetic permeability of vacuum th th  Nk, Nm turn numbers of k and m segment respectively  r, a radii of kth and mth segment from core center respectively apparent length of the Figure 5. Illustration of geometrical data of magnetic circuit winding segments and the core circuit  N constant affecting accuracy degree Analytical formulas  k  2k / summation parameter Wilcox et. al. proposed an accurate analytical  I , K modified Bessel functions solution based on Maxwell’s equations in 1 1 determination of self and mutual inductances of  z distance between two sections transformer winding segments [10]: Trang 42 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 K xb Iron-core impedance (flux in the core) Z1(km)  gx  x 0 K1xb b2 2 I mb  Z  jN N  rel 1    (4) 1(km) k m 1    c  2  j /    mbI0 mb  k  k rel eff where angular frequency  c ratio between relative permeabilities in  b core radius axial and radial direction [10].  rel effective relative permeability of the Parameter calculation solid core in axial direction To calculate impedances from (3), (4) and  skin-effect parameter m  j  rel /  eff (5), it is required that value of effective relative permeability rel and resistivity eff of the core  eff effective resistivity of the solid core should be known in advance.  I0, I1 modified Bessel functions The two parameters rel and eff can be  10 magnetic permeability of medium determined if one has measurements of outside the core self/mutual impedances of/between winding Iron-core impedance (leakage flux) Z2(km) segments as investigated in [10]. However, it is  4 not the case for this investigation and others in Z 2(km)  N k N m   h1h2w1w2 practice since all winding segments are in N transformer and cannot be broken to measure.  P1 k a2 ,  k a1 P1 k r2 ,  k r1  Therefore, a new way in identification of rel and k1 eff is proposed as follows. I1 k b  Q1 k w1,  k w2  F1 k ,bcos k z (5) K1 k b First, specific values of rel and eff are where initially assigned, e.g., the ones in [10], since the th th investigated subjects in this reference are power  h1, w1, h2, w2 dimensions of k and m segment respectively transformers (with rated power from 25 kVA to 200 MVA). Then, by comparing simulated and  a , a , r , r inner, outer radii of kth and mth 1 2 1 2 measured frequency responses at low and medium segment respectively frequencies where inductive components are 1 P  x,  y  p  x  p  y 1  k k  2   k   k  dominant, deviations between them reveal  k  whether the assigned rel and eff are correct or   p   K  L   K  L   should be adapted to compensate the deviations. 2 1 0 0 1 The procedure of identifying value of rel   2n2k1  L   and eff is based on the fact that, rel influences n  k  0.5! n  k  0.5 ! k0    much analytical inductances at low frequencies 2    k x   k y    k x   k y  whereas eff shows strong effect at medium Q1  k x,  k y   cos    cos   2 2 2   k      frequencies, as illustrated in Figures 6 and 7,    respectively. f   1 f    k  k   F    j  rel  1 k 1   g   1 f     k   k   rel  I xb  f x  x 0 I1xb Trang 43 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 3. RESULTS For first investigation with the distributed transformer circuit, due to limitation of commercial software in simulating mutual effect and frequency dependent inductance simultaneously, constant self and mutual inductances were selected for simulation whereas constant resistances/conductances were adapted Figure 6. Influence of rel on a calculated based on agreement between measured and normalized inductance (eff unchanged) simulated frequency responses within range from 10 kHz to 100 kHz. For better representation, inductances and resistances should be frequency dependent. Figure 8 shows a comparison between measurement and simulation approaches of the end-to-end frequency response. Better agreement proves that, although constant inductances/resistances were selected, the distributed circuit represents well interactions of Figure 7. Influence of eff on a calculated normalized reasonably calculated inductances and inductance (rel unchanged) capacitances between winding segments, which is 2.3 Per segment resistances and impossible with the lumped circuit at medium conductances frequencies from 10 kHz to 100 kHz. Resistance component in self and mutual impedances of winding segments representing only eddy current losses in the core is calculated using (1). In addition, another component that accounts for skin effect in the winding itself should be taken into account for a more correct equivalence. On the other hand, determination of conductances parallel with corresponding capacitances (see Figure 4) needs geometrical Figure 8. Comparison of measurement and data and electrical property of insulation system simulation of an end-to-end frequency response [9]. 4. CONCLUSION Nevertheless, influence of resistances and The paper investigated a simulation approach conductances on frequency responses is of minor in extending the analyzed frequency range for importance since they contribute only to damping frequency response interpretation based on a at resonance peaks. For simplified simulation distributed circuit of a distribution transformer. approach, they can be assigned appropriate values Results showed that the valid frequency range was so as good agreement between measurement and expanded from 20 Hz – 15 kHz to 20 Hz – simulation is achieved. Trang 44 TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K6- 2015 100 kHz, which allows interpreting influence of property of transformer insulation system for individual electrical parameters on measured capacitance calculation and help to find out frequency responses. magnetic-electric properties of the core for For determination of electrical parameters in inductance dete rmination, which are mostly the distributed circuit, the paper introduced a unavailable in reality. simplified procedure based on the proposed ACKNOWLEDGEMENT method in [4], i.e., values of lumped capacitances, This research is funded by the Ho Chi Minh and analytical calculation. This procedure would city Univerity of Technology, VNU-HCM under be beneficial for real applications since it reduces grant number T-ĐĐT-2015-18. dependence on geometrical and electrical Mở rộng giải tích vùng tần số trong phân tích đáp ứng tần số đo lường trên một máy biến áp phân phối . Phạm Đình Anh Khôi . Phạm Thị Minh Thái Trường Đại học Bách Khoa, ĐHQG-HCM, Việt Nam TÓM TẮT Kỹ thuật Phân tích đáp ứng tần số (FRA) Để phân tích các đáp ứng tần số đo lường, gần đây đã được quốc tế thống nhất sử dụng các tác giả đã đề xuất một phương pháp mới trong lĩnh vực chẩn đoán các sự cố cơ trong dựa trên mô phỏng một mạch điện thông số phần tích cực máy biến áp lực bao gồm cuộn tập trung ba pha của MBA lực, nhưng chỉ hiệu dây, đầu cực và lõi thép. Các sự cố cơ trong quả trong vùng tần số thấp, bởi vì mạch thông cuộn dây MBA làm thay đổi các đáp ứng tần số tập trung không phản ánh chính xác các số đo lường ở vùng tần số trung bình, từ vài tương tác điện từ trong MBA ở vùng tần số đến hàng trăm kHz, vốn không dễ dàng để giải trung bình và cao. thích chẩn đoán. Trang 45 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol.18, No.K6 - 2015 Để mở rộng khả năng phân tích đáp ứng cứu này là một quy trình đơn giản để xác định tần số của phương pháp đã đề xuất ở vùng tần các thông số điện trong mạch phân bố MBA số trung bình cho mục tiêu chẩn đoán sự cố, để phân tích đáp ứng tần số dựa trên mô bài báo giới thiệu một nghiên cứu về mạch phỏng tốt hơn (so với mạch tập trung) ở vùng thông số phân bố của một MBA phân phối 200 tần số trung bình. kVA 10.4/0.46 kV Yy6. Kết quả của nghiên Từ khóa: Chuẩn đoán sự cố, Máy biếp áp, Phân tích đáp ứng tần số, Frequency Response Analysis, Mạch thông số tập trung, Mạch thông số phân bố. REFERENCES [1]. CIGRE Report 342 W.G. A2.26, with series capacitance change in a power Mechanical-condition assessment of transformer winding, IEEE Int. Conf. Liquid transformer windings using FRA, (2008). Dielectr., Slovenia, (2014). [2]. IEC 60076-18, Power transformers - Part 18: [7]. Wang Z., Li J., and Sofian D. 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