Application of Frequency Response Analysis for in-service power transformers

CIGRE, IEC and IEEE have recently approved the technique of Frequency Response Analysis (FRA) as an application tool for diagnosis of mechanical failures in power transformer’s active part, i.e., windings, leads and the core. The diagnosis is based on the discrepancy between frequency responses measured on power transformers mainly at different time points. In Vietnam, utilities such as Power Transmission Companies and Power Corporations are investigating this technique for application on their power transformers. Mechanical failures in power transformers cause changes on measured frequency responses starting from a medium frequency range, from several hundreds of Hz or tens of kHz depending on transformer/winding type and power. For a reliable diagnosis, the understanding of transformer/winding structure on measured frequency responses is of importance; thus, the international standards suggested the simulation approach with physical distributed transformer circuits should be exploited. The development of physical distributed circuits of power transformers normally needs availability of internal transformer structure and material properties for an analytical approach. However, for in-service power transformers, this task is challenging since the required data are not available. For a feasible application of the simulation based FRA interpretation, this paper introduces an investigation on the development of a distributed equivalent circuit of an in-service 6.5 MVA 47/27.2 kV Yd5 power transformer. The result of this investigation is a feasible approach in determining electrical parameters in a physical distributed circuit, which supports analysis of frequency responses measured at transformer terminals for real application on in-service power transformers of utilities. Manuscript Received on January 04th, 2017, Manuscript Revised March 27th, 2016 This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number C2016-2015. Dinh Anh Khoi Pham is with the Division of High-Voltage Engineering, Department of Power Systems, Faculty of Electrical and Electronic Engineering, Ho Chi Minh City University of Technology, Vietnam National University – Ho Chi Minh City, Vietnam (e-mail: khoipham@hcmut.edu.vn).


Application of Frequency Response
Analysis for in-service power transformers Dinh Anh Khoi Pham Mechanical failures in power transformers cause changes on measured frequency responses starting from a medium frequency range, from several hundreds of Hz or tens of kHz depending on transformer/winding type and power.For a reliable diagnosis, the understanding of transformer/winding structure on measured frequency responses is of importance; thus, the international standards suggested the simulation approach with physical distributed transformer circuits should be exploited.
The development of physical distributed circuits of power transformers normally needs availability of internal transformer structure and material properties for an analytical approach.However, for in-service power transformers, this task is challenging since the required data are not available.
For a feasible application of the simulation based FRA interpretation, this paper introduces an investigation on the development of a distributed equivalent circuit of an in-service 6.5 MVA 47/27.2kV Yd5 power transformer.The result of this investigation is a feasible approach in determining electrical parameters in a physical distributed circuit, which supports analysis of frequency responses measured at transformer terminals for real application on in-service power transformers of utilities.

INTRODUCTION
or diagnosis of mechanical failures in the active part of power transformers, i.e., the leads, windings and the core, after a suspected through-fault or during transportation, measurements of frequency responses of voltage ratio at two transformer's terminals in broad frequency range from 20 Hz to 2 MHz are conducted and then compared with the corresponding ones performed when transformers were in good condition or from outer phase windings.According to the international guide and standards such as CIGRE Report [1], IEC 60076-18 [2], and IEEE PC57.(1) Of four standard frequency responses, the EEOC is often referred for the diagnosis since the influence of different components in transformers such as the core, windings and its interaction is shown in the measurement result (magnitude of the frequency response).
Currently, there are two general methods proposed from international/national standards for assessment of the measurement result to diagnose the transformer failures.The IEEE [3] and Chinese [4] standard suggested using the correlation coefficients between two frequency responses to evaluate the failure level in a quantitative analysis.
On the other hand, the IEC [2] and IEEE [3] proposed several patterns to detect failure types based on expert experience, including simulation in a qualitative analysis.It is observed that the failure can be easily or very difficult to detect since the discrepancies are very clear (Fig 5) or hard to recognize (Fig 6).This also means the expert experience is sometime ineffective since one cannot distinguish such a small deviation between the measured frequency responses at different transformer conditions in various frequency ranges.To restrict the uncertainty with expert experience that may happen in some situations like that in Fig 5, the author proposed a method for determination of electrical parameters associated with physical transformer circuits [5], from which the diagnosis is based on the change of electrical parameters, not the deviation between frequency responses.Several investigations confirmed the effectiveness of this method [6,7].
To determine electrical parameters in physical transformer circuits, another kind of frequency responses, the driving-point impedances, are used.These frequency responses are different from those proposed by the international standards (voltage ratios) and therefore called as non-standard frequency responses.There are in total four configurations of the non-standard measurement, namely, the open-circuit, short-circuit, inductive and capacitive driving-point impedances.

PHYSICAL EQUIVALENT CIRCUITS OF POWER TRANSFORMERS
This section introduces two main kinds of physical transformer circuits representing physically magnetic and electrical phenomena in three-phase two-winding power transformers for the purpose of electrical parameter based interpretation of frequency responses and failure diagnosis.

Lumped parameter circuit
The lumped (parameter) circuit of power transformers introduced in this paper is the one derived from the duality principle for the purpose of transient and frequency response analysis [8].The outer part of the circuit in Fig 7 is the winding circuit representing electrical parameters of the whole winding, i.e., equivalent resistances (RH, RL), capacitances (CsH, CsL: series; CgH, CgL: ground or shunt; Ciw: inter-winding), and winding connection (wye, delta) in accordance with vector group.Details of the circuit development and parameter determination procedures can be found in [5].
For circuit development, the electrical parameters in the lumped circuit can be determined based on analysis of measured frequency responses of driving-point impedances [5].The lumped circuit then can be used for simulation approach to interpret the influence of electrical transformer parameters on measured standard frequency responses in low frequency range, e.g., from 20 Hz to several hundreds of Hz or several tens of kHz depending on transformer/winding type and power.
For an application, the lumped circuit is helpful in the determination of the series capacitances as explained later in this paper.Analysis of the lumped circuit at different transformer conditions can provide useful indicators for diagnosis of certain mechanical failures in several test transformers [6][7].

Distributed parameter circuit
The distributed (parameter) circuit of power transformers defined in this paper is the n-section lumped-parameter ladder-network [8][9][10], which represents physically the interaction between inductances and capacitances of part of the windings starting from medium frequencies, e.g. from several hundreds of Hz or several tens of kHz.The section number n is selected depending on the compromise between desired accuracy and simulation complexity.Fig 8 shows a single-phase distributed circuit of a two-winding power transformer from which the complete three-phase circuit can be developed by adding the other twophase windings with an additional mutual effect between any couple of inductances.For circuit development, the electrical parameters in the distributed circuit could only be calculated analytically, i.e., via formulas with the availability of internal transformer structure and material properties [9-13], since the parameters represent only part of the windings.As a result, the distributed circuit has had limited application in simulation based interpretation of frequency responses measured on some specific power transformers having internal structure [9,11,12].Thus the author proposes a feasible approach (mentioned later in this paper) in the determination of electrical parameters in the distributed circuit of a 6.5 MVA 47/27.2kV Yd5 in-service power transformer for extending the application scope to black-box or in-service power transformers.For this purpose, measurements of terminal voltages according to the so-called magnetic balance test were made at 50 Hz by means of the device 'CPC100' and measurements of driving-point impedances (open-and short-circuit) were conducted in broad frequency range from 20 Hz to 2 MHz by means of the vector-network analyzer 'FRAnalyzer'.

IDENTIFICATION OF PARAMETERS IN THE LUMPED CIRCUIT OF AN IN-SERVICE POWER TRANSFORMER.
This section presents an approach for identification of only the series capacitances in the lumped circuit of the test power transformer.The remaining electrical parameters in the lumped circuit in Fig 7 such as inductances and other capacitances etc. are already calculated based on measurement analysis [4].The windings' series capacitance is the only one that cannot be identified from measurements since the series capacitance is a distinct property of the winding and it depends on only the winding structure, i.e., disc (ordinary/interleaved) or multi-layer type [14].
To identify the influence of the series capacitance on the total capacitive effect, a simple approach is proposed by comparing the measured open-circuit driving-point impedance (OC DPI) frequency response with the simulated one (without series capacitances in the lumped circuit) at a "capacitive" frequency point.In case there is a significant deviation between the measurement and simulation result, it is concluded that the windings' series capacitance has significant influence (on the total capacitive effect) and thus the capacitance could be identified.
Fig 9 and 10 compare the measured and simulated OC DPI frequency responses of a phase winding at HV and LV side, respectively, of the test transformer.It is observed from the figures that there are significant deviations between measurement and simulation at a capacitive frequency around 2 kHz, which indicates that the windings' series capacitances have a clear influence on the total capacitance effect (from CgH = 0.629 nF, CgL = 2.530 nF, Ciw = 2.171 nF [5]).The deviations become insignificant if either a value of CsH = 1.51 nF or CsL = 1.44 nF is inserted into the circuit.These values are identified separately from simulation manipulation under "trial and error" principle, which indicates that the series capacitances could not be neglected.However, there is no further information of whether which series capacitance has a dominant effect.

IDENTIFICATION OF PARAMETERS IN THE DISTRIBUTED CIRCUIT OF AN IN-SERVICE POWER TRANSFORMER.
This section introduces procedures in the determination of the main parameters in the distributed circuit, i.e., segmental inductances and capacitances, as they are key components causing resonances at medium frequencies.The conductances/resistances are of minor importance compared with inductances and capacitances since they introduce damping at resonance frequencies [9].In fact, the conductances/resistances could not be determined from measurements and their influence on resonance damping is then investigated under "trial and error" simulation principle.However, the section starts first with the introduction of the distributed circuit of two popular winding types, the ordinary disc and multi-layer winding, since one of them can be the winding type in the test transformer.The capacitance cd could be converted into another component that is in parallel with the ct according to a principle introduced later so that the total series capacitance is their combination [15].

Distributed circuit for disc and multi-layer windings in power transformers
As a result, the distributed circuit in Fig 8 can be fully applied to the disc type winding.
Fig 12 shows the configuration and equivalent circuit in the turn-level of four layers of a multilayer type winding (mutual inductances are not shown) [10].Similar to the disc winding, the multi-layer winding has two kinds of series capacitance: the turn-to-turn capacitance along a layer (e.g., ct between turns 1 and 2) and the turnto-turn capacitance between two adjacent layers (e.g., cl between turns 1 and 10).
For an acceptable solution with simulation, the number of circuit sections per layer and the layer number would be large enough.In fact, one does not know these numbers for in-service power transformers and thus an equivalent transformation is necessary to convert the multi-layer winding circuit into the disc circuit.Fig 13 illustrates the transformation of the series capacitances (ct and cl) under the assumption that there exist equipotential surfaces between layers (or discs with the disc type winding) [12,15].
In Fig 13, the cl between two layers is considered as two (2cl) connected in series.With the equipotential surfaces between layers, the (2cl) between adjacent layers can be broken and connected with that of the same layer to form the component cl in parallel with ct.As a result, the concept of total series capacitance is derived, from which the equivalent disc type winding circuit shown in Fig 8   As a result, the internal structure of the test transformer and dielectric properties of insulation systems are not required since the analytical calculation of the capacitances is not necessary.

Determination of self and mutual inductances in the distributed circuit
There are in total 30 components of self/mutual inductances of/between sections at different phases, i.e., phase A, B or C, and different sides, i.e., HV or LV side.For instance, one winding section of phase A at HV side has its own self inductance (L A ) and a mutual inductance with another section at this phase (M AA ), or other phase/side (M AB or M AC at HV side; M Aa , M Ab , or M Ac at LV side).However, due to the symmetry between windings at outer phase, there are only 12 different inductance components or matrixes (when the transformer is in good condition).
The parameter determination procedure starts with the identification of self and mutual inductances of two sections on the same phase winding, i.e., A, B or C, at low frequencies by analysis of the per-phase open-circuit driving-point impedances (OC DPIs).For transformers with starstar winding connection, there is only mutual effect between winding sections in the excited phase winding.Then voltage-current relation at the transformer terminal of the n-section excited winding of phase A (assumed at HV side) can be expressed as: UA oc = IA oc n X A + IA oc n (n 1) X AA (6) where UA oc and IA oc are r.m.s value of the applied open-circuit single phase voltage and corresponding current on the winding of phase A; X A = L A and X AA = M AA are self and mutual reactance, respectively, at low frequencies where the measured OC DPI is purely inductive.
For acceptable analysis feasibility, the self and mutual reactance/inductance are approximate: X A X AA , then equation ( 6) can be simplified into: where XA oc = UA oc /IA oc is the open-circuit driving-point reactance of the winding of phase A. By this manner, the self and mutual inductances of winding sections of phase B and C can be calculated.
The equations ( 6) and ( 7) are still applicable for star-delta winding connection of the test transformer since the mutual elimination effect in the delta winding will take place due to positive mutual inductance M Aa and negative mutual inductances M Ab and M Ac .
The next step of the parameter determination procedure is to determine the mutual inductances between sections of phase windings in different phases at low frequencies.This procedure is based on analysis of the magnetic balance test by supplying an AC voltage to a terminal (at a low frequency) when all other terminals are left floating and then measuring the voltages at these terminals.The ratios between the induced voltages at terminals of the non-tested phase windings, e.g., B or C, and the supplied voltage on the tested perphase winding, i.e., A, provide factors for calculating mutual inductances M AB and M AC from L A (for star-star winding connection).Similar to the first case, the influence of the other winding at the other side, i.e., LV, regardless of its connection (star or delta) could be neglected.
Afterward, the mutual inductances between inter-winding sections of different phases such as M Ab , M Ac could be obtained from M AB and M AC since they are proportional to the transformer ratio.
The next step of the parameter procedure is to determine mutual inductances between HV and LV winding sections at low frequencies by analysis of per-phase short-circuit driving-point impedances (SC DPIs) at low frequencies.In the short-circuit tests, for instance, the winding of phase A at one side (HV) is excited whereas the other phase winding at the other side (LV) is shortcircuited, which yields the below relationship for star-star winding connection: UA sc = IA sc n 2 X A + Ia sc n 2 X Aa (8) where UA sc , IA sc and Ia sc are r.m.s value of the applied single phase voltage, HV and LV shortcircuit currents, respectively, on the windings of phase A; X Aa = M Aa is mutual reactance at low frequencies where the measured SC DPI is purest inductive.
The short-circuit current flowing in the LV winding of phase A (Ia sc ) has the r.m.s value proportional to that of the current flowing within the HV phase winding (IA sc ) with the transformer ratio ki, which means: X Aa = (X A XA sc /n 2 )/ki (9) where XA sc = UA sc /IA sc is the short circuit driving-point reactance of the winding of phase A and ki Ia sc / IA sc .
The aforementioned steps can be applied for analysis of measurements of OC and SC DPIs of the LV delta winding to identify self and mutual of LV phase winding sections, i.e., L a , L b , L c and M Aa , M Bb , M Cc at low frequencies.
The remaining of the analysis task is to identify the calculated self and mutual inductances at medium frequencies since the inductances decrease with increasing frequency following kind of pattern introduced in [13].This could be reasonably achieved by analysis the SC DPIs since their inductive range is larger than that of the OC DPIs.Note that the inductances are determined from measurements that reflect the saturation condition of the transformer core.

RESULTS.
Simulation of the 16-section distributed circuit without windings' series capacitances in the configuration of OC DPIs also shows a significant deviation compared with the measurement at frequency of 2 kHz.However, values of the capacitances are slightly different compared with those determined using the lumped circuit (CsH = 1.81 nF or CsL = 2.02 nF) to compensate the deviations.
In addition, the distributed circuit shows its advantage in the simulation of resonances at medium frequencies against the lumped circuit.Fig 14,15 and 16 present comparisons between measurement and simulation results, which are conducted at low frequencies (LF) and medium frequencies with only CsH, CsL or an equal combination of CsH and CsL, respectively.
The agreements between measurement and simulations at low frequencies (in the range of tens and hundreds of Hz) in the figures indicate that the inductances calculated using the proposed approach in section 4.3 are acceptable.This is valuable since normally the segmental inductances in the distributed circuit should be calculated analytically using internal transformer structure and magnetic-electrical properties of the core.This suggests the selected section number of the distributed circuit should be larger for the conclusion of whether the HV or LV winding has the dominant effect of series capacitance (equal effect seems not to be a case as shown in Fig 16), which can be conducted using the so-called statespace modeling technique.
Simulation of the 16-section distributed circuit in the configuration of OC DPIs at LV side also shows the same result and therefore will not be introduced.

CONCLUSION
This paper proposes approaches in determination of electrical parameters in a physical distributed circuit of an in-service power transformer, which has not been solved completely in any publication so far.The introduced approaches should be combined with others proposed from [5][6][7][8] to analyze comprehensively electrical parameters on the distributed transformer circuit.Consequently, the practical application of this circuit on simulation based interpretation of frequency responses measured on in-service power transformers at low and medium frequencies could be feasible for the diagnosis.
Abstract-CIGRE, IEC and IEEE have recently approved the technique of Frequency Response Analysis (FRA) as an application tool for diagnosis of mechanical failures in power transformer's active part, i.e., windings, leads and the core.The diagnosis is based on the discrepancy between frequency responses measured on power transformers mainly at different time points.In Vietnam, utilities such as Power Transmission Companies and Power Corporations are investigating this technique for application on their power transformers.
149TM/D9.1 [3], there are four main types of frequency responses of voltage ratio, namely, end-to-end open-circuit, end-to-end short-circuit, capacitive and inductive interwinding, which are hereafter assigned as standard frequency responses.Fig 1 shows the measurement configuration of the end-to-end open-circuit (EEOC) configuration conducted on a Yd twowinding power transformer by means of a vectornetwork-analyzer (VNA).

Fig 1 .
Fig 1.Standard measurement configuration of the EEOC frequency response on a Yd power transformer Fig 3 introduces regions of influencing components in EEOC frequency responses of a large auto-transformer derived from simulation approach [2, 3].Note that the EEOC frequency responses change from transformer to transformer, thus the frequency response curves look different with different transformers and winding types.

Fig 3 .
Fig 3. Interpretation of EEOC frequency responses of a large autotransformer based on simulation [3]

Fig 4 .Fig 5 .
Fig 4. Photograph and frequency responses of a tap winding before and after partial axial collapse and localised inter-turn short-circuit [2]

Fig 6 .
Fig 6.Non-standard measurement configuration of the opencircuit frequency response of a driving-point impedance of a Yd power transformer

Fig
Fig 7. Lumped circuit of a Yd5 power transformer

Fig 8 .
Fig 8. Single-phase distributed circuit of a two-winding power transformer

Fig 9 .
Fig 9. Measured and simulated frequency responses of the OC DPI between terminals A-N at HV side using the lumped circuit Fig 11 shows the configuration and equivalent circuit in the turn-level of two discs of an ordinary disc type winding (ground and inter-winding capacitance, and mutual inductances are not shown) [10].If the whole equivalent circuit is straightened in the longitudinal direction, it is identical with the distributed circuit in Fig 8, except the series capacitances.In Fig 12, there are two kinds of series capacitances: the one between two consecutive turns in a disc (e.g., ct between turns 1 and 2) and the other between two turns in two adjacent discs (e.g., cd between turns 1 and 20).

Fig 13 .
Fig 13.Equivalent transformation of the multi-layer winding circuit into the disc winding circuit 4.2 Determination of segmental capacitances in the distributed circuit As the distributed circuit in Fig 8 can be applied for both disc and multi-layer type winding, there is only one variable involved with the simulation: the

Fig 14 .
Fig 14.Measured and simulated frequency responses of OC DPI between terminals A-N at HV side using the distributed circuit (CsH = 1.81 nF) is derived from the multi-layer winding circuit.