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Discriminating changes introduced in the model for the winding of a transformer based on measurements
Electric Power Systems Research 77 (2007) 851–858
Discriminating changes introduced in the model for the winding of a transformer based on measurements Subrat K. Sahoo ∗ , L. Satish Department of H.V. Engineering, Indian Institute of Science, Bangalore 560012, India Received 28 March 2006; received in revised form 14 June 2006; accepted 27 July 2006 Available online 30 August 2006
Abstract A systematic procedure is evolved that enables identification of the type-of-changes introduced in the model winding of a transformer, based on a comparison of measured neutral or line current and transfer-function with those corresponding to the reference case. Further, it was also possible to ascertain, whether the pertinent circuit element viz. series capacitance, shunt capacitance and self-inductance has increased or decreased (compared to initial value). The proposal was formulated based on analytical calculation and circuit simulation. Thereafter, the approach was experimentally verified using two model windings, and the results were found to be encouraging. Thus, it demonstrates one possible way, how interpretation of monitored data can lead to meaningful inferences. © 2006 Elsevier B.V. All rights reserved. Keywords: Diagnostic testing; Interpretation of monitored data; LVI testing; FRA/TF method
1. Introduction Power utilities perform condition monitoring on large power transformers to assess its status. Many monitoring methods have evolved over the years and each one of them is intended to ascertain some specific aspect of dielectric, thermal and mechanical integrity of the transformer. Amongst these low voltage impulse (LVI) and frequency response analysis (FRA) or transfer function (TF) method have been found to be useful in detecting winding deformations. Such deformities occur due to shortcircuit forces and sometimes may be caused due to unskilled handling during transportation [1]. Although, minor and incipient deformations/damages are generally not immediately perceivable, they are in fact potential sites from where major faults can develop subsequently. The existing detection philosophy of these methods is based on a comparison of two subsequently gathered records, and if a mismatch were to be observed, then a possible fault is implied. It is generally observed that, beyond a visual comparison, monitored data does not seem to be post-processed to draw inferences. Strictly speaking, diagnosis or interpretation of the monitored ∗
Corresponding author. Tel.: +91 80 22933179; fax: +91 80 22932373. E-mail addresses: [email protected], [email protected] (S.K. Sahoo), [email protected] (L. Satish). 0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.07.007
data has, as yet, not happened. It is desirable that every monitoring method is adequately supported by powerful diagnosis or interpretation, so that its true potential can be harnessed. In a practical scenario (e.g. when fault is implied), a diagnostic method is expected to provide assistance to the operation engineer regarding, the extent of fault, its location, and so on, such that timely action can be initiated. Instead of resorting to expensive and time-consuming disassembly of the transformer, it would be certainly advantageous to seek answers to these questions by interpretation of monitored data, as far as possible. Therefore, exploration of newer ways of interpretation is desirable. A survey of pertinent literature reveals that most publications on this topic can be classified into: • Introduce a deformation (axial, radial, etc.) on an actual winding and then examine ability of a method to detect the smallest possible change [2–8]. • Attempt to model or translate the winding deformation (i.e. physical changes) into a corresponding change in the equivalent circuit, so that, measured and computed TF are similar [4–6]. • Preliminary efforts attempting to link observed changes in TF, to the nature and location of fault, was examined via simulation studies [9].
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study evolves a logical procedure to predict the type of changes introduced, entirely based on data from terminal measurements. In this respect, it attempts to interpret monitored data and thereby show how information regarding changes (of the model winding in this case) could be extracted. The next step would be to examine possibilities of extending this method to actual windings. 3. Model employed for simulation and experiments Fig. 1. Equivalent circuit of a uniform winding of a transformer.
Thus, it emerges that monitored data has not been subjected to any rigorous interpretation or diagnosis. Generally, in practice, an expert opinion is sought. Recognising this need, the present authors recently demonstrated [10], how TF of a two-winding transformer could be interpreted and meaningful information about the origin of its natural frequencies extracted. Hence, it just goes to show how interpretation of monitored data can yield useful information. When such is the prevalent situation, it is imperative that exploratory investigations are essential. This was the main motivation. 2. Problem definition Admittedly, a full-scale solution of the above problem on an actual transformer winding is far too complicated, and to the best knowledge of the authors, has not been attempted earlier. Further, many of the complex interactions that exist between winding deformation and its influence on natural frequencies, type of change, effect on position of change, etc., are not yet fully understood. This lack of knowledge is the main bottleneck that prevents a direct solution from being addressed. Therefore, as a first step, a simplified version of the problem is initially considered to untangle some of these intricate dependencies. So, considering a single uniform winding of the transformer (as in Fig. 1) considerably reduces the complexity of the problem. With this modification, the focus of problem under investigation shifts from the transformer winding to the equivalent circuit. This step should not be construed as an oversimplification of the task, since fault discrimination and location (based on terminal measurements alone), even with respect to this circuit has not been fully understood and resolved. Therefore, starting with the representation in Fig. 1 and using data arising from terminal measurements (i.e. LVI, FRA/TF method), the following becomes the problem statement: 1. Data from LVI and FRA method is available for the reference (or initial) case. 2. A capacitance (shunt or series) and/or inductance is changed. 3. Step 1 is repeated, and the two data sets are compared. 4. Based on observed deviations, is it possible to discriminate the type of circuit change introduced? The proposed solution strategy was formulated using analytical computations and simulation studies. Then, these are experimentally verified on a model winding. Applicability of the proposed method is verified for both disc and interleaved types of windings, in simulation and experiments. Thus, this
The circuit representation in Fig. 1 comprising of series capacitance (Cs ), shunt capacitance (Cg ), self-inductance (Ls ), lumped resistance (r), and mutual inductances (Mi−j ) is known to adequately describe the lightning impulse behaviour of the transformer winding [11]. For a symmetrical circuit, all the self inductance (Ls1 , Ls2 , Ls3 , . . .) are taken as Ls , all the series capacitance (Cs1 , Cs2 , Cs3 , . . .) are taken as Cs , and all the shunt capacitance (Cg2 , Cg3 , Cg4 , . . .) are taken to be Cg (except Cg1 and Cg11 , i.e. the first and last section shunt capacitance, which are taken as Cg /2). Additionally, in such a representation, the value of any element can be varied, and hence, by changing Cs , both continuous-disc and interleaved winding configurations could be represented. Further, this representation permits analytical investigation (symbolic computation, MAPLE), computation of time and frequency-domain responses using circuit simulation software (PSPICE), as well as construction of a model winding for experimental verification. Two model windings (with 10 sections each) were used in the experiments. The self and mutual inductance values shown in Table 1 were as a result of a measurement on the model-winding done at a frequency of 1 kHz, using the 1657 L-C-R DigiBridge (GenRad, USA). These values have been used during simulation studies, so that any mismatch between measured and calculated inductances in experiments and simulation are avoided. 4. Underlying principle and solution approach For evolving the logical procedure, it was essential to initially study the nature of interrelation that exists between each circuit element, line/neutral current and natural frequencies. To achieve this, an analytical solution for the neutral current in s-domain (i.e. In (s)) was derived using nodal analysis [12]. Initially, a lossless case with solidly grounded neutral was considered for the sake of clarity. The general expression of the neutral current, for a step-input excitation, as a function of the circuit elements, for Table 1 Self and mutual inductances (Ls , Mi−j , in H/section) Model
Ls
Mi−j
I
180
II
65
m1–2 = 110.75, m1–3 = 73.97, m1–4 = 54.67, m1–5 = 42, m1–6 = 33.15, m1–7 = 26.7, m1–8 = 21.45, m1–9 = 17.6, m1–10 = 14.8 m1–2 = 36, m1–3 = 25, m1–4 = 18, m1–5 = 14, m1–6 = 10, m1–7 = 8, m1–8 = 6.3, m1–9 = 5, m1–10 = 4.25
Other Mi−j values are determined from symmetry considerations.
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Fig. 2. Percentage variation in components of line and neutral current. Capacitive component as a function of: (A) series and (B) shunt capacitance and (C) inductive component as a function of self-inductance.
an n-section network can be compactly written as: In (s) =
Csn 1 + Poly1(Cs , Cg ) Poly2(Ls , Mi−j )s2 +
Poly3(Cs , Cg , Ls , Mi−j , s) Poly4(Cs , Cg , Ls , Mi−j , s)
(1)
where Poly1 is a polynomial function of Cs and Cg alone, Poly2 is a function of Ls and Mi−j alone, while, Poly3 and Poly4 are functions of Cs , Cg , Ls , Mi−j and ‘s’. An examination of the above expression reveals that In (s) contains three terms, viz., the first term (dependent on Cs and Cg alone and independent of ‘s’) is the capacitive term, the second term (dependent on Ls and Mi−j alone and a function of 1/s2 ) is the inductive term, while the last term corresponds to the oscillatory components pertaining to the natural frequencies or poles [12]. This separable or decoupled feature between the three components is an important aspect. The fact that the first two terms are independent of each other is the most important feature, and can be explicitly shown, by substituting n = 3, and taking elements in each section to be identical. Imposing this condition, it turns out that the first two terms of In (s) are
Cs3 4Cg Cs +3Cs2 +Cg2
and s2 (3L +2M1 +4M ) , respectively. Thus, from this it is clear s 1−3 1−2 that capacitive term is dependent on only the capacitances of the circuit, while the inductive term is a function of self and mutual inductances alone. In other words, it indicates that a change in either series or shunt capacitance (made at any position) in the model will affect the capacitive term alone, keeping the inductive component unaffected. Similarly a change in self or mutual inductance anywhere in the circuit would result in a corresponding change that is confined only to the inductive term. Of course, in both these cases, the oscillatory component (i.e. natural frequencies) would change. However, if there occurs a simultaneous change in inductance and capacitance, then both these two components would undergo a change.
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Fig. 3. Variation of inductive and oscillatory components of neutral current, following a change in: (A) series capacitance and (B) self inductance.
These matters are graphically shown in Fig. 2. In subplot-A, the percentage variation of the capacitive component for In (s), when series capacitance at section-1 is varied (either increased or decreased) with respect to the reference case is shown. The subplot-B of Fig. 2 illustrates a similar variation, when shunt capacitance at section-2 is varied. From the two subplots, it is seen that changes in series and shunt capacitance influence the capacitive component of In (s) in the opposite way (i.e. an inverse relationship exists). In other words, an increase in capacitive component of In (s), results due to either an increase in series capacitance or a decrease in shunt capacitance, and vice versa for a decrease in capacitive component. So, this is another important distinguishing feature for segregating series and shunt capacitive changes. Subplot-C represents the variation of inductive component with respect to change in self-inductance in the circuit at section-1. This has a decreasing trend with increase in inductance value. The next important task was to translate these findings and inferences derived from analytical studies to those actually observable from LVI and FRA measurements. For this purpose, consider the neutral current response in time-domain, due to a standard lightning impulse. The capacitive component can be recognized by observing the initial few microseconds of the neutral current. In some cases, a zoomed version may have to be considered. So, the logic arrived at from the analytical studies can be extended here as well (examples will be discussed in next section). Unlike the capacitive component of the neutral current that exists for only the first few microseconds, the inductive component manifests as a relatively slow build-up and exists for hundreds of microseconds, over which the oscillatory components are superimposed. This aspect is not directly evident from the expressions, since it is the response for an ideal step input. Instead of this, consider Fig. 3, which shows in time-domain, variation of both inductive and oscillatory components of the neutral current, when a capacitance or inductance was changed (obtained from PSPICE for a standard lightning impulse excitation). When a capacitance change is imposed on the circuit
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Fig. 4. Flowchart-1 principle of the proposed method.
(increase or decrease), the peak value of the inductive component does not change (capacitive and inductive changes are independent of each other, as discussed earlier). However, the natural frequencies will obviously change, and this introduces a timeshift to the oscillatory components, due to which the inductive component appears to have slightly changed, which is not the case, and, if a mean-curve is drawn, then the average value of the inductive component will be found to remain unchanged. This aspect is observed in subplot-A, of Fig. 3. Next, variation of both inductive and oscillatory components of neutral current, when inductance is changed, is shown in Fig. 3, subplot-B, where it is seen that mean-value of inductive component clearly undergoes a significant change, in contrast to that seen in subplot-A. Thus, changes imposed to both inductance and capacitance elements of the circuit can be identified, based on the fact that the corresponding changes they introduce on the neutral current are well separated in time. Once the occurrence of a capacitive change is identified, the next task is to distinguish it, as either due to a change in Cs or Cg . To achieve this, information available in frequency domain, i.e. in TF, can be employed for interpretation as follows. An increase in capacitance (either series or shunt) would result in
a decrease of the natural frequencies (resulting in left-shift of poles in TF plot) with respect to reference case. And similarly, a decrease would result in their right-shift. The evolved procedure for distinguishing the various changes in the model winding are summarised below and shown as a flowchart in Fig. 4. • Separability of the components of In (s) was possible. • Capacitive and Inductive components of In (s) are independent of each other. • Cg and Cs change affect capacitive component of In (s) oppositely. The procedure developed above was found to be successful, only when one change was introduced at a time. However in practice, it is natural to expect simultaneous change in Ls and Cs or Cg . Hence, the investigation was continued further and another quantity measurable at the terminals, namely, the line current was examined for this purpose. An analytical expression, similar to that of In (s), was derived corresponding to the line current (IL (s)). These two expressions were identical, except for the first term. The capacitive component of IL (s)
Fig. 5. Flowchart-2 principle of the proposed method.
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is:
2 2 3 3 1 6Cg Cs +9Cg Cs +Cg +2Cs . 2 2 2 4Cg Cs +3Cs +Cg
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A comparison of this term with the
capacitive term of In (s) reveals that this capacitive component has a direct relation with respect to a variation in both Cg and Cs , in contrast to what was observed with In (s). That means, there is an increase in capacitive component of IL (s) when either Cs or Cg increases. This aspect is shown in subplot-A and -B of Fig. 2 respectively. From this it emerges that a simple combination of these information about the inductive and capacitive components of line and neutral current would help in discriminating changes due to both Ls and Cs or Cg . This matter is summarized in flowchart-2, Fig. 5. Thus, simultaneous changes were also distinguishable. 5. Simulation studies Applicability of proposed method was initially verified by simulation studies on a 5-section circuit (as in Fig. 1), details of which are given below. 1. Total Cg was chosen as 3.0 nF and Cs was varied. 2. Ls and Mi−j (first four Mi−j values for a 5-section), corresponding to Model I (Table 1), were used. 3. A resistance (r) of 1.2 per section was used. Three cases studies are reported, namely Case-1, Case-2 and Case-3 to discuss circuit changes (both increase and decrease) in series capacitance in section-1, shunt capacitance in section-2 and self-inductance in section-1, respectively. 5.1. Case-1: change in Cs It is generally accepted that fault detection in a transformer with interleaved winding is difficult [3,12]. So, in this case study, an interleaved winding was considered by choosing Cs = 7.5 nF/section. The reference neutral current (In (t)) and TF (up to 400 kHz, with 1 kHz resolution) were computed and stored. These two quantities were computed again, and correspond to both an increase (from 7.5 to 10 nF/section) and decrease (from 7.5 to 5.0 nF/section) in Cs , in section-1. SubplotA, in Fig. 6 represents In (t) corresponding to reference case superposed over those pertaining to increase and decrease in Cs . No perceptible change was observed in the long-term behaviour (i.e. inductive component) of In (t), between the reference case and that due to change in Cs . So, it can be inferred that there is no inductive change. Next, a zoomed view of In (t) corresponding to the initial 1–2 s is shown as an inset in subplot-A. Clearly a change was observable in the initial capacitive component with respect to the reference case, for both increase and decrease in Cs , thus indicating occurrence of a capacitive change. When Cs was increased, it resulted in a higher value of capacitive component and vice versa, as already discussed. Next, TF was computed and is shown for reference case and those corresponding to an increase and decrease in Cs . Subplot-B, in Fig. 6 shows these results. A leftshift of all the natural frequencies occurs (compared to reference TF) when Cs was increased, and a right-shift occurs when Cs
Fig. 6. Comparison of computed (A) neutral current and (B) TF, corresponding to increase and decrease in Cs , in section-1.
was decreased. Thus, occurrence of either a decrease or increase in Cs can be distinguished. 5.2. Case-2: change in Cg The series capacitance chosen for this case study was 0.15 nF per section, so that the equivalent circuit represents a continuous-disc type of winding. The reference value of Cg was 0.6 nF/section. The shunt capacitance in section-2 was changed from the original value to 0.2 nF/section and later increased to 1.0 nF/section. Fig. 7, subplot-A shows the neutral current response, depicting these changes. Similar to the previous case study, the inductive component of In (t) does not show a perceptible change, when there is a change in Cg . The initial capacitive component is shown, within subplot-A, as an inset. Unlike in the previous case study, increase in Cg results in a reduction of the capacitive component, and the reverse is true for a decrease in Cg , as illustrated in the flowchart (in Fig. 4). Fig. 7, subplot-B represents the corresponding TF. As expected, an increase in Cg results in left-shift of all the poles compared to reference TF, and a decrease in Cg results in a right-shift. Hence the knowledge
Fig. 7. Comparison of computed (A) neutral current and (B) TF, corresponding to increase and decrease in Cg , in section-2.
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6.1. Case 4: increase and decrease in Cs , at section-1
Fig. 8. Comparison of computed (A) neutral current and (B) TF, corresponding to increase and decrease in Ls , in section-1.
of the shift in TF (following the change in Cg ), along with the increase or decrease in capacitive component (from the neutral current response) together, gives the information of change in Cg , which is already elaborated in Section 4. 5.3. Case-3: change in Ls
An interleaved winding was selected (Model–I) by choosing Cg = 2.2 and Cs = 20 nF/section (corresponding to α = 3.3). In this study, series capacitance was increased from 20 to 40 nF/section and then decreased to 10 nF/section. The impulse voltage and In (t) were acquired (128 K points, sampled at 10 ns) corresponding to the reference condition, increase in Cs , and decrease in Cs respectively, and the TFs computed. Fig. 9, subplot-A, shows the initial portion of In (t) (i.e. capacitive component), zoomed up to 2.5 s for the reference case together with those corresponding to a change in Cs at section-1. A clear increase and decrease in capacitive component is seen, corresponding to an increase and decrease in Cs respectively, thus indicating that capacitance has changed. In subplot-B, the TFs are compared. A left-shift of the natural frequencies is observed compared to the reference condition when Cs is increased, and a right-shift occurs when Cs was decreased. The corresponding simulation results are included in subplot-C and subplot-D, and indicate a reasonable degree of agreement. 6.2. Case 5: increase and decrease in Cg , at section-2 The circuit configuration same as in Case 4 was adopted here. Cg , in section-2 was increased from 2.2 to 6.9 nF and
In this study, effect of a change in Ls was simulated. Although increase in Ls is rare, for sake of completeness, both an increase and decrease was considered. An interleaved winding was chosen with Cs = 7.5 nF/section. Ls in section-1 was increased from 180 to 250 H/section and decreased from 180 to 100 H/section. The inductive and oscillatory part of In (t) shows a change, as can be seen in Fig. 8, subplot-A. Whereas the capacitive component (not shown in figure), and being independent of changes in inductance, has remained unaltered, thereby indicating a change in inductance. A significant change in the inductive component in the time interval between 20 and 90 s (the observed time interval depends on the value of inductance involved) has been observed. An increase in Ls would reduce long-term magnitude of In (t) and a decrease would result in an increase in its magnitude. The corresponding TF are shown in subplot-B. Shifts in the natural frequencies were exactly as predicted. 6. Experimental results The proposed method was verified by experiments on two model windings (Fig. 1). Two models (with 10-sections each) were used, whose details are given in Table 1. For brevity, only a few sample results are presented. A low voltage recurrent surge generator (Haefely RSG 482) was used to acquire neutral current response (as a voltage across 47 ) due to a standard lightning impulse excitation (peak value of 30 V). Data was acquired using a 10-bit, 200 MSa/s digitizer (RTD 710A), and TF was computed via FFT, instead of manually sweeping the frequency. For each case study discussed, simulation results (corresponding to time and frequency ranges of interest) are also presented to enable a comparison.
Fig. 9. Comparison of measured (A) neutral current, (B) TF, corresponding to an increase and decrease in Cs , in section-1, and the corresponding simulation results (C) neutral current and (D) TF.
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Fig. 10. Comparison of measured (A) neutral current (B) TF, corresponding to an increase and decrease in Cg , in section-2, and the corresponding simulation results (C) neutral current and (D) TF.
thereafter decreased to 560 pF. Fig. 10, subplot-A shows the capacitive component for the reference case and those corresponding to the changes incorporated in Cg . An increase in capacitive component is observed for a decrease in Cg and vice versa. A comparison of the respective TFs is given in subplot-B. A left-shift of natural frequencies occurs following an increase in Cg and a right-shift of natural frequencies is observed when Cg is decreased. The simulation results pertinent to this case are shown in subplot-C and subplot-D. It may be noted here that due to quasi-static approximations employed for determining the circuit elements of such lumped parameter equivalent circuits (used to represent transformer behaviour), these models, cannot exactly replicate the frequency-dependent behaviour of its elements and hence there will occur a slight mismatch between the measured and simulated TF plots. However this mismatch gradually increases at higher frequencies, and at lower frequencies, it is of the order of a few kHz, as is observed in Figs. 9 and 10. This should not be construed as an error, but is a limitation of the representation. 6.3. Case 6: decrease in Ls , at section-1 A reduction in self-inductance, at section-1, was achieved by short-circuiting one section. Increase in self-inductance was not
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Fig. 11. Comparison of measured (A) neutral current (B) TF, corresponding to a decrease in Ls , in section-1, and the corresponding simulation results (C) neutral current and (D) TF.
considered due to operational difficulties. In this study, Model-2 was chosen with Cg = 1020, Cs = 350 pF/section (corresponding to α = 17). A clear difference (Fig. 11, subplot-A) was observable in the oscillatory part of the In (t) i.e. an increase when compared to the reference value. Subplot-B shows a comparison of TF. The reduced inductance causes an increase in the natural frequencies, as expected. These aspects are clearly seen in Section 6, and are in good agreement with the simulation results, shown in subplotC and subplot-D. 6.4. Case-7: change in Ls and Cg /Cs It is easily visualized that representation of winding deformation would naturally necessitate incorporating multiple changes into the circuit in Fig. 1. In order to consider this, simultaneous change in inductance and capacitance elements were imposed. By considering the IL (t) and In(t), it was possible to segregate the L and C changes. Model-1 was chosen for the above purpose with an α value of 2.36. 6.4.1. Decrease in Ls at section-4 and increase in Cs at section-1 The series capacitance in first section was increased from 10 to 30 nF and the series inductance was reduced from 180 to 65 H in the fourth section. An increase in capacitive component
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winding representations. Experimental results were found to be in good agreement with those predicted by simulation and analytical studies. Therefore, it is demonstrated how interpretation of monitored data (LVI and TF data) can be used to extract information about changes inside the winding. In final summary, the objective of interpreting LVI and TF data has been partially achieved. References
Fig. 12. Comparison of capacitive component of line and neutral currents when combined L and C changes are incorporated. (A) Line current and (B) neutral current. (Note: Ls in section-4, Cs is section-1 and Cg in section-2 was varied.)
is observed both for IL (t) and In (t) for an increase in Cs along with an increase in inductive and oscillatory component, as seen in the inset of Fig. 12, subplot-A and subplot-B, respectively. 6.4.2. Decrease in Ls at section-4 and decrease in Cg at section-2 In another case study, the Cg was reduced in the second section from 560 to 100 pF, while the same change (as in Case-7) in inductance was made at fourth section. A decrease in the capacitive component of IL (t), is observed (Fig. 12, subplot-A) for decrease in Cg but an increase in capacitive component is observed for In (t) (Fig. 12, subplot-B). However the inductive and oscillatory component continues to increase both in line and neutral current (seen in the inset of subplot-A and -B of Fig. 12) against the reference case. In summary an increase in capacitive component of both IL (t) and In (t) can be a result of an increase in “Cs ”, whereas an increase in capacitive component of In (t) but a decrease in capacitive component of IL (t) is a result of decrease in “Cg ”. The change in inductive component happens for both the currents in a similar way, which has an inverse relation with change in “Ls ”. The procedure follows in accordance with the Flowchart2 of Fig. 5. Thus, using the proposed approach, simultaneous changes in Ls and Cs /Cg could also be identified. For brevity more examples are not included. 7. Conclusions In a model winding, if a deviation is observed when a pair of subsequently acquired neutral/line current and TF data are compared, then it is possible to figure out, which one of the three circuit elements of the equivalent circuit, namely, series capacitance, shunt capacitance or self-inductance is responsible for the observed change. Further, it can also be inferred whether the pertinent circuit element has increased or decreased, from its initial value. The proposed approach requires data corresponding to terminal measurements, and does not impose any necessity for newer measurements. Applicability of the method was verified (to a limited extent) for both disc and interleaved type of
[1] K. Feser, J. Christian, C. Neumann, U. Sundermann, T. Liebfried, A. Kachler, M. Loppacher, The transfer function method for detection of winding displacements on power transformer after transport, short circuit or 30 years of service, CIGRE 12/33-04, Session 2000. [2] W. Lech, L. Tyminski, Detecting transformer winding damage—the low voltage impulse method, Electr. Rev. 179 (21) (1966) 768–772. [3] B.I. Gururaj, B.N. Jayaram, Use of recurrent surge generator for detecting displacement and deformations in transformer winding, IE(I) J. -EL 54 (1974) 99–102. [4] E. Rahimpour, J. Christian, K. Feser, H. Mohesini, Transfer function method to diagnose axial displacement and radial deformation of transformer windings, IEEE Trans. PWRD 18 (2) (2003) 493–505. [5] M. Florkowski, J. Furgal, Detection of transformer winding deformations based on the transfer function measurements and simulations, J 2003 Meas. Sci. Techl.-14 (2003) 1986–1992. [6] M. Wang, A.J. Vandermaar, K.D. Srivastava, Improved detection of power transformer winding movement by extending the FRA high frequency range, IEEE Trans. PWRD 20 (3) (2005) 1930–1938. [7] J.A.S.B. Jayasinghe, Z.D. Wang, P.N. Jarman, A.W. Darwin, Investigation on sensitivity of fra technique in diagnosis of transformer winding deformations, in: Proceedings of the Conference Record of IEEE International Symposium On EI, Indianapolis, USA, 2004, pp. 496– 499. [8] S.A. Ryder, Diagnosing transformer faults using frequency response analysis, IEEE EI Magn. 19 (2) (2003) 16–22. [9] T. Leibfried, EinfluB von windungsschlussen auf die ubertragungsfunktion von transformator wicklungen am beispiel homogener spulen, Electr. Eng. (1997) 99–108. [10] L. Satish, S.K. Sahoo, An effort to understand what factors affect the transfer function of a two-winding transformer, IEEE Trans. Power Deliv. 20 (2) (2005) 1430–1440. [11] P.A. Abetti, F.J. Maginniss, Natural frequency of coils and windings determined by equivalent circuit, AIEE Trans. 74 (1953) 495– 504. [12] L. Satish, A. Jain, Structure of transfer function of transformers with special reference to interleaved windings, IEEE Trans. Power Deliv. 17 (3) (2002) 754–760. Subrat K. Sahoo (S 04) was born in 1979. He received the B.E. degree (Hons.) in electrical engineering from the Indira Gandhi Institute of Technology, Sarang, India, which is affiliated with Utkal University, Orissa, India, in 2001. He completed (in August 2003) his M.Sc. (Engg.) from the Department of High Voltage Engineering, Indian Institute of Science (I.I.Sc.), Bangalore, India. He is currently registered for the Ph.D. degree in the Department of High Voltage Engineering. His research interests include diagnostics and condition monitoring of transformers. L. Satish (SM 02) was born in 1964. He received the Ph.D. degree from the Indian Institute of Science (I.I.Sc.), Bangalore, India, in 1993. Since 2001, he has been an Associate Professor with the Department of High Voltage Engineering, I.I.Sc. He was a Postdoctoral Fellow with ETH, Zurich, Switzerland, from 1993 to 1995. He was a Visiting Researcher with H.V. Institute, Helsinki University of Technology, Helsinki, Finland, during the summer of 1998. His research interests include application of signal processing to high voltage impulse testing, dynamic and static testing of ADCs, diagnostics and condition monitoring of transformers, PD measurements and pattern recognition. Dr. Satish is a member of CIGRE D1-33 in CIGRE WG D1-33.
Discriminating changes introduced in the model for the winding of a transformer based on measurements Subrat K. Sahoo ∗ , L. Satish Department of H.V. Engineering, Indian Institute of Science, Bangalore 560012, India Received 28 March 2006; received in revised form 14 June 2006; accepted 27 July 2006 Available online 30 August 2006
Abstract A systematic procedure is evolved that enables identification of the type-of-changes introduced in the model winding of a transformer, based on a comparison of measured neutral or line current and transfer-function with those corresponding to the reference case. Further, it was also possible to ascertain, whether the pertinent circuit element viz. series capacitance, shunt capacitance and self-inductance has increased or decreased (compared to initial value). The proposal was formulated based on analytical calculation and circuit simulation. Thereafter, the approach was experimentally verified using two model windings, and the results were found to be encouraging. Thus, it demonstrates one possible way, how interpretation of monitored data can lead to meaningful inferences. © 2006 Elsevier B.V. All rights reserved. Keywords: Diagnostic testing; Interpretation of monitored data; LVI testing; FRA/TF method
1. Introduction Power utilities perform condition monitoring on large power transformers to assess its status. Many monitoring methods have evolved over the years and each one of them is intended to ascertain some specific aspect of dielectric, thermal and mechanical integrity of the transformer. Amongst these low voltage impulse (LVI) and frequency response analysis (FRA) or transfer function (TF) method have been found to be useful in detecting winding deformations. Such deformities occur due to shortcircuit forces and sometimes may be caused due to unskilled handling during transportation [1]. Although, minor and incipient deformations/damages are generally not immediately perceivable, they are in fact potential sites from where major faults can develop subsequently. The existing detection philosophy of these methods is based on a comparison of two subsequently gathered records, and if a mismatch were to be observed, then a possible fault is implied. It is generally observed that, beyond a visual comparison, monitored data does not seem to be post-processed to draw inferences. Strictly speaking, diagnosis or interpretation of the monitored ∗
Corresponding author. Tel.: +91 80 22933179; fax: +91 80 22932373. E-mail addresses: [email protected], [email protected] (S.K. Sahoo), [email protected] (L. Satish). 0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.07.007
data has, as yet, not happened. It is desirable that every monitoring method is adequately supported by powerful diagnosis or interpretation, so that its true potential can be harnessed. In a practical scenario (e.g. when fault is implied), a diagnostic method is expected to provide assistance to the operation engineer regarding, the extent of fault, its location, and so on, such that timely action can be initiated. Instead of resorting to expensive and time-consuming disassembly of the transformer, it would be certainly advantageous to seek answers to these questions by interpretation of monitored data, as far as possible. Therefore, exploration of newer ways of interpretation is desirable. A survey of pertinent literature reveals that most publications on this topic can be classified into: • Introduce a deformation (axial, radial, etc.) on an actual winding and then examine ability of a method to detect the smallest possible change [2–8]. • Attempt to model or translate the winding deformation (i.e. physical changes) into a corresponding change in the equivalent circuit, so that, measured and computed TF are similar [4–6]. • Preliminary efforts attempting to link observed changes in TF, to the nature and location of fault, was examined via simulation studies [9].
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study evolves a logical procedure to predict the type of changes introduced, entirely based on data from terminal measurements. In this respect, it attempts to interpret monitored data and thereby show how information regarding changes (of the model winding in this case) could be extracted. The next step would be to examine possibilities of extending this method to actual windings. 3. Model employed for simulation and experiments Fig. 1. Equivalent circuit of a uniform winding of a transformer.
Thus, it emerges that monitored data has not been subjected to any rigorous interpretation or diagnosis. Generally, in practice, an expert opinion is sought. Recognising this need, the present authors recently demonstrated [10], how TF of a two-winding transformer could be interpreted and meaningful information about the origin of its natural frequencies extracted. Hence, it just goes to show how interpretation of monitored data can yield useful information. When such is the prevalent situation, it is imperative that exploratory investigations are essential. This was the main motivation. 2. Problem definition Admittedly, a full-scale solution of the above problem on an actual transformer winding is far too complicated, and to the best knowledge of the authors, has not been attempted earlier. Further, many of the complex interactions that exist between winding deformation and its influence on natural frequencies, type of change, effect on position of change, etc., are not yet fully understood. This lack of knowledge is the main bottleneck that prevents a direct solution from being addressed. Therefore, as a first step, a simplified version of the problem is initially considered to untangle some of these intricate dependencies. So, considering a single uniform winding of the transformer (as in Fig. 1) considerably reduces the complexity of the problem. With this modification, the focus of problem under investigation shifts from the transformer winding to the equivalent circuit. This step should not be construed as an oversimplification of the task, since fault discrimination and location (based on terminal measurements alone), even with respect to this circuit has not been fully understood and resolved. Therefore, starting with the representation in Fig. 1 and using data arising from terminal measurements (i.e. LVI, FRA/TF method), the following becomes the problem statement: 1. Data from LVI and FRA method is available for the reference (or initial) case. 2. A capacitance (shunt or series) and/or inductance is changed. 3. Step 1 is repeated, and the two data sets are compared. 4. Based on observed deviations, is it possible to discriminate the type of circuit change introduced? The proposed solution strategy was formulated using analytical computations and simulation studies. Then, these are experimentally verified on a model winding. Applicability of the proposed method is verified for both disc and interleaved types of windings, in simulation and experiments. Thus, this
The circuit representation in Fig. 1 comprising of series capacitance (Cs ), shunt capacitance (Cg ), self-inductance (Ls ), lumped resistance (r), and mutual inductances (Mi−j ) is known to adequately describe the lightning impulse behaviour of the transformer winding [11]. For a symmetrical circuit, all the self inductance (Ls1 , Ls2 , Ls3 , . . .) are taken as Ls , all the series capacitance (Cs1 , Cs2 , Cs3 , . . .) are taken as Cs , and all the shunt capacitance (Cg2 , Cg3 , Cg4 , . . .) are taken to be Cg (except Cg1 and Cg11 , i.e. the first and last section shunt capacitance, which are taken as Cg /2). Additionally, in such a representation, the value of any element can be varied, and hence, by changing Cs , both continuous-disc and interleaved winding configurations could be represented. Further, this representation permits analytical investigation (symbolic computation, MAPLE), computation of time and frequency-domain responses using circuit simulation software (PSPICE), as well as construction of a model winding for experimental verification. Two model windings (with 10 sections each) were used in the experiments. The self and mutual inductance values shown in Table 1 were as a result of a measurement on the model-winding done at a frequency of 1 kHz, using the 1657 L-C-R DigiBridge (GenRad, USA). These values have been used during simulation studies, so that any mismatch between measured and calculated inductances in experiments and simulation are avoided. 4. Underlying principle and solution approach For evolving the logical procedure, it was essential to initially study the nature of interrelation that exists between each circuit element, line/neutral current and natural frequencies. To achieve this, an analytical solution for the neutral current in s-domain (i.e. In (s)) was derived using nodal analysis [12]. Initially, a lossless case with solidly grounded neutral was considered for the sake of clarity. The general expression of the neutral current, for a step-input excitation, as a function of the circuit elements, for Table 1 Self and mutual inductances (Ls , Mi−j , in H/section) Model
Ls
Mi−j
I
180
II
65
m1–2 = 110.75, m1–3 = 73.97, m1–4 = 54.67, m1–5 = 42, m1–6 = 33.15, m1–7 = 26.7, m1–8 = 21.45, m1–9 = 17.6, m1–10 = 14.8 m1–2 = 36, m1–3 = 25, m1–4 = 18, m1–5 = 14, m1–6 = 10, m1–7 = 8, m1–8 = 6.3, m1–9 = 5, m1–10 = 4.25
Other Mi−j values are determined from symmetry considerations.
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Fig. 2. Percentage variation in components of line and neutral current. Capacitive component as a function of: (A) series and (B) shunt capacitance and (C) inductive component as a function of self-inductance.
an n-section network can be compactly written as: In (s) =
Csn 1 + Poly1(Cs , Cg ) Poly2(Ls , Mi−j )s2 +
Poly3(Cs , Cg , Ls , Mi−j , s) Poly4(Cs , Cg , Ls , Mi−j , s)
(1)
where Poly1 is a polynomial function of Cs and Cg alone, Poly2 is a function of Ls and Mi−j alone, while, Poly3 and Poly4 are functions of Cs , Cg , Ls , Mi−j and ‘s’. An examination of the above expression reveals that In (s) contains three terms, viz., the first term (dependent on Cs and Cg alone and independent of ‘s’) is the capacitive term, the second term (dependent on Ls and Mi−j alone and a function of 1/s2 ) is the inductive term, while the last term corresponds to the oscillatory components pertaining to the natural frequencies or poles [12]. This separable or decoupled feature between the three components is an important aspect. The fact that the first two terms are independent of each other is the most important feature, and can be explicitly shown, by substituting n = 3, and taking elements in each section to be identical. Imposing this condition, it turns out that the first two terms of In (s) are
Cs3 4Cg Cs +3Cs2 +Cg2
and s2 (3L +2M1 +4M ) , respectively. Thus, from this it is clear s 1−3 1−2 that capacitive term is dependent on only the capacitances of the circuit, while the inductive term is a function of self and mutual inductances alone. In other words, it indicates that a change in either series or shunt capacitance (made at any position) in the model will affect the capacitive term alone, keeping the inductive component unaffected. Similarly a change in self or mutual inductance anywhere in the circuit would result in a corresponding change that is confined only to the inductive term. Of course, in both these cases, the oscillatory component (i.e. natural frequencies) would change. However, if there occurs a simultaneous change in inductance and capacitance, then both these two components would undergo a change.
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Fig. 3. Variation of inductive and oscillatory components of neutral current, following a change in: (A) series capacitance and (B) self inductance.
These matters are graphically shown in Fig. 2. In subplot-A, the percentage variation of the capacitive component for In (s), when series capacitance at section-1 is varied (either increased or decreased) with respect to the reference case is shown. The subplot-B of Fig. 2 illustrates a similar variation, when shunt capacitance at section-2 is varied. From the two subplots, it is seen that changes in series and shunt capacitance influence the capacitive component of In (s) in the opposite way (i.e. an inverse relationship exists). In other words, an increase in capacitive component of In (s), results due to either an increase in series capacitance or a decrease in shunt capacitance, and vice versa for a decrease in capacitive component. So, this is another important distinguishing feature for segregating series and shunt capacitive changes. Subplot-C represents the variation of inductive component with respect to change in self-inductance in the circuit at section-1. This has a decreasing trend with increase in inductance value. The next important task was to translate these findings and inferences derived from analytical studies to those actually observable from LVI and FRA measurements. For this purpose, consider the neutral current response in time-domain, due to a standard lightning impulse. The capacitive component can be recognized by observing the initial few microseconds of the neutral current. In some cases, a zoomed version may have to be considered. So, the logic arrived at from the analytical studies can be extended here as well (examples will be discussed in next section). Unlike the capacitive component of the neutral current that exists for only the first few microseconds, the inductive component manifests as a relatively slow build-up and exists for hundreds of microseconds, over which the oscillatory components are superimposed. This aspect is not directly evident from the expressions, since it is the response for an ideal step input. Instead of this, consider Fig. 3, which shows in time-domain, variation of both inductive and oscillatory components of the neutral current, when a capacitance or inductance was changed (obtained from PSPICE for a standard lightning impulse excitation). When a capacitance change is imposed on the circuit
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Fig. 4. Flowchart-1 principle of the proposed method.
(increase or decrease), the peak value of the inductive component does not change (capacitive and inductive changes are independent of each other, as discussed earlier). However, the natural frequencies will obviously change, and this introduces a timeshift to the oscillatory components, due to which the inductive component appears to have slightly changed, which is not the case, and, if a mean-curve is drawn, then the average value of the inductive component will be found to remain unchanged. This aspect is observed in subplot-A, of Fig. 3. Next, variation of both inductive and oscillatory components of neutral current, when inductance is changed, is shown in Fig. 3, subplot-B, where it is seen that mean-value of inductive component clearly undergoes a significant change, in contrast to that seen in subplot-A. Thus, changes imposed to both inductance and capacitance elements of the circuit can be identified, based on the fact that the corresponding changes they introduce on the neutral current are well separated in time. Once the occurrence of a capacitive change is identified, the next task is to distinguish it, as either due to a change in Cs or Cg . To achieve this, information available in frequency domain, i.e. in TF, can be employed for interpretation as follows. An increase in capacitance (either series or shunt) would result in
a decrease of the natural frequencies (resulting in left-shift of poles in TF plot) with respect to reference case. And similarly, a decrease would result in their right-shift. The evolved procedure for distinguishing the various changes in the model winding are summarised below and shown as a flowchart in Fig. 4. • Separability of the components of In (s) was possible. • Capacitive and Inductive components of In (s) are independent of each other. • Cg and Cs change affect capacitive component of In (s) oppositely. The procedure developed above was found to be successful, only when one change was introduced at a time. However in practice, it is natural to expect simultaneous change in Ls and Cs or Cg . Hence, the investigation was continued further and another quantity measurable at the terminals, namely, the line current was examined for this purpose. An analytical expression, similar to that of In (s), was derived corresponding to the line current (IL (s)). These two expressions were identical, except for the first term. The capacitive component of IL (s)
Fig. 5. Flowchart-2 principle of the proposed method.
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is:
2 2 3 3 1 6Cg Cs +9Cg Cs +Cg +2Cs . 2 2 2 4Cg Cs +3Cs +Cg
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A comparison of this term with the
capacitive term of In (s) reveals that this capacitive component has a direct relation with respect to a variation in both Cg and Cs , in contrast to what was observed with In (s). That means, there is an increase in capacitive component of IL (s) when either Cs or Cg increases. This aspect is shown in subplot-A and -B of Fig. 2 respectively. From this it emerges that a simple combination of these information about the inductive and capacitive components of line and neutral current would help in discriminating changes due to both Ls and Cs or Cg . This matter is summarized in flowchart-2, Fig. 5. Thus, simultaneous changes were also distinguishable. 5. Simulation studies Applicability of proposed method was initially verified by simulation studies on a 5-section circuit (as in Fig. 1), details of which are given below. 1. Total Cg was chosen as 3.0 nF and Cs was varied. 2. Ls and Mi−j (first four Mi−j values for a 5-section), corresponding to Model I (Table 1), were used. 3. A resistance (r) of 1.2 per section was used. Three cases studies are reported, namely Case-1, Case-2 and Case-3 to discuss circuit changes (both increase and decrease) in series capacitance in section-1, shunt capacitance in section-2 and self-inductance in section-1, respectively. 5.1. Case-1: change in Cs It is generally accepted that fault detection in a transformer with interleaved winding is difficult [3,12]. So, in this case study, an interleaved winding was considered by choosing Cs = 7.5 nF/section. The reference neutral current (In (t)) and TF (up to 400 kHz, with 1 kHz resolution) were computed and stored. These two quantities were computed again, and correspond to both an increase (from 7.5 to 10 nF/section) and decrease (from 7.5 to 5.0 nF/section) in Cs , in section-1. SubplotA, in Fig. 6 represents In (t) corresponding to reference case superposed over those pertaining to increase and decrease in Cs . No perceptible change was observed in the long-term behaviour (i.e. inductive component) of In (t), between the reference case and that due to change in Cs . So, it can be inferred that there is no inductive change. Next, a zoomed view of In (t) corresponding to the initial 1–2 s is shown as an inset in subplot-A. Clearly a change was observable in the initial capacitive component with respect to the reference case, for both increase and decrease in Cs , thus indicating occurrence of a capacitive change. When Cs was increased, it resulted in a higher value of capacitive component and vice versa, as already discussed. Next, TF was computed and is shown for reference case and those corresponding to an increase and decrease in Cs . Subplot-B, in Fig. 6 shows these results. A leftshift of all the natural frequencies occurs (compared to reference TF) when Cs was increased, and a right-shift occurs when Cs
Fig. 6. Comparison of computed (A) neutral current and (B) TF, corresponding to increase and decrease in Cs , in section-1.
was decreased. Thus, occurrence of either a decrease or increase in Cs can be distinguished. 5.2. Case-2: change in Cg The series capacitance chosen for this case study was 0.15 nF per section, so that the equivalent circuit represents a continuous-disc type of winding. The reference value of Cg was 0.6 nF/section. The shunt capacitance in section-2 was changed from the original value to 0.2 nF/section and later increased to 1.0 nF/section. Fig. 7, subplot-A shows the neutral current response, depicting these changes. Similar to the previous case study, the inductive component of In (t) does not show a perceptible change, when there is a change in Cg . The initial capacitive component is shown, within subplot-A, as an inset. Unlike in the previous case study, increase in Cg results in a reduction of the capacitive component, and the reverse is true for a decrease in Cg , as illustrated in the flowchart (in Fig. 4). Fig. 7, subplot-B represents the corresponding TF. As expected, an increase in Cg results in left-shift of all the poles compared to reference TF, and a decrease in Cg results in a right-shift. Hence the knowledge
Fig. 7. Comparison of computed (A) neutral current and (B) TF, corresponding to increase and decrease in Cg , in section-2.
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6.1. Case 4: increase and decrease in Cs , at section-1
Fig. 8. Comparison of computed (A) neutral current and (B) TF, corresponding to increase and decrease in Ls , in section-1.
of the shift in TF (following the change in Cg ), along with the increase or decrease in capacitive component (from the neutral current response) together, gives the information of change in Cg , which is already elaborated in Section 4. 5.3. Case-3: change in Ls
An interleaved winding was selected (Model–I) by choosing Cg = 2.2 and Cs = 20 nF/section (corresponding to α = 3.3). In this study, series capacitance was increased from 20 to 40 nF/section and then decreased to 10 nF/section. The impulse voltage and In (t) were acquired (128 K points, sampled at 10 ns) corresponding to the reference condition, increase in Cs , and decrease in Cs respectively, and the TFs computed. Fig. 9, subplot-A, shows the initial portion of In (t) (i.e. capacitive component), zoomed up to 2.5 s for the reference case together with those corresponding to a change in Cs at section-1. A clear increase and decrease in capacitive component is seen, corresponding to an increase and decrease in Cs respectively, thus indicating that capacitance has changed. In subplot-B, the TFs are compared. A left-shift of the natural frequencies is observed compared to the reference condition when Cs is increased, and a right-shift occurs when Cs was decreased. The corresponding simulation results are included in subplot-C and subplot-D, and indicate a reasonable degree of agreement. 6.2. Case 5: increase and decrease in Cg , at section-2 The circuit configuration same as in Case 4 was adopted here. Cg , in section-2 was increased from 2.2 to 6.9 nF and
In this study, effect of a change in Ls was simulated. Although increase in Ls is rare, for sake of completeness, both an increase and decrease was considered. An interleaved winding was chosen with Cs = 7.5 nF/section. Ls in section-1 was increased from 180 to 250 H/section and decreased from 180 to 100 H/section. The inductive and oscillatory part of In (t) shows a change, as can be seen in Fig. 8, subplot-A. Whereas the capacitive component (not shown in figure), and being independent of changes in inductance, has remained unaltered, thereby indicating a change in inductance. A significant change in the inductive component in the time interval between 20 and 90 s (the observed time interval depends on the value of inductance involved) has been observed. An increase in Ls would reduce long-term magnitude of In (t) and a decrease would result in an increase in its magnitude. The corresponding TF are shown in subplot-B. Shifts in the natural frequencies were exactly as predicted. 6. Experimental results The proposed method was verified by experiments on two model windings (Fig. 1). Two models (with 10-sections each) were used, whose details are given in Table 1. For brevity, only a few sample results are presented. A low voltage recurrent surge generator (Haefely RSG 482) was used to acquire neutral current response (as a voltage across 47 ) due to a standard lightning impulse excitation (peak value of 30 V). Data was acquired using a 10-bit, 200 MSa/s digitizer (RTD 710A), and TF was computed via FFT, instead of manually sweeping the frequency. For each case study discussed, simulation results (corresponding to time and frequency ranges of interest) are also presented to enable a comparison.
Fig. 9. Comparison of measured (A) neutral current, (B) TF, corresponding to an increase and decrease in Cs , in section-1, and the corresponding simulation results (C) neutral current and (D) TF.
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Fig. 10. Comparison of measured (A) neutral current (B) TF, corresponding to an increase and decrease in Cg , in section-2, and the corresponding simulation results (C) neutral current and (D) TF.
thereafter decreased to 560 pF. Fig. 10, subplot-A shows the capacitive component for the reference case and those corresponding to the changes incorporated in Cg . An increase in capacitive component is observed for a decrease in Cg and vice versa. A comparison of the respective TFs is given in subplot-B. A left-shift of natural frequencies occurs following an increase in Cg and a right-shift of natural frequencies is observed when Cg is decreased. The simulation results pertinent to this case are shown in subplot-C and subplot-D. It may be noted here that due to quasi-static approximations employed for determining the circuit elements of such lumped parameter equivalent circuits (used to represent transformer behaviour), these models, cannot exactly replicate the frequency-dependent behaviour of its elements and hence there will occur a slight mismatch between the measured and simulated TF plots. However this mismatch gradually increases at higher frequencies, and at lower frequencies, it is of the order of a few kHz, as is observed in Figs. 9 and 10. This should not be construed as an error, but is a limitation of the representation. 6.3. Case 6: decrease in Ls , at section-1 A reduction in self-inductance, at section-1, was achieved by short-circuiting one section. Increase in self-inductance was not
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Fig. 11. Comparison of measured (A) neutral current (B) TF, corresponding to a decrease in Ls , in section-1, and the corresponding simulation results (C) neutral current and (D) TF.
considered due to operational difficulties. In this study, Model-2 was chosen with Cg = 1020, Cs = 350 pF/section (corresponding to α = 17). A clear difference (Fig. 11, subplot-A) was observable in the oscillatory part of the In (t) i.e. an increase when compared to the reference value. Subplot-B shows a comparison of TF. The reduced inductance causes an increase in the natural frequencies, as expected. These aspects are clearly seen in Section 6, and are in good agreement with the simulation results, shown in subplotC and subplot-D. 6.4. Case-7: change in Ls and Cg /Cs It is easily visualized that representation of winding deformation would naturally necessitate incorporating multiple changes into the circuit in Fig. 1. In order to consider this, simultaneous change in inductance and capacitance elements were imposed. By considering the IL (t) and In(t), it was possible to segregate the L and C changes. Model-1 was chosen for the above purpose with an α value of 2.36. 6.4.1. Decrease in Ls at section-4 and increase in Cs at section-1 The series capacitance in first section was increased from 10 to 30 nF and the series inductance was reduced from 180 to 65 H in the fourth section. An increase in capacitive component
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winding representations. Experimental results were found to be in good agreement with those predicted by simulation and analytical studies. Therefore, it is demonstrated how interpretation of monitored data (LVI and TF data) can be used to extract information about changes inside the winding. In final summary, the objective of interpreting LVI and TF data has been partially achieved. References
Fig. 12. Comparison of capacitive component of line and neutral currents when combined L and C changes are incorporated. (A) Line current and (B) neutral current. (Note: Ls in section-4, Cs is section-1 and Cg in section-2 was varied.)
is observed both for IL (t) and In (t) for an increase in Cs along with an increase in inductive and oscillatory component, as seen in the inset of Fig. 12, subplot-A and subplot-B, respectively. 6.4.2. Decrease in Ls at section-4 and decrease in Cg at section-2 In another case study, the Cg was reduced in the second section from 560 to 100 pF, while the same change (as in Case-7) in inductance was made at fourth section. A decrease in the capacitive component of IL (t), is observed (Fig. 12, subplot-A) for decrease in Cg but an increase in capacitive component is observed for In (t) (Fig. 12, subplot-B). However the inductive and oscillatory component continues to increase both in line and neutral current (seen in the inset of subplot-A and -B of Fig. 12) against the reference case. In summary an increase in capacitive component of both IL (t) and In (t) can be a result of an increase in “Cs ”, whereas an increase in capacitive component of In (t) but a decrease in capacitive component of IL (t) is a result of decrease in “Cg ”. The change in inductive component happens for both the currents in a similar way, which has an inverse relation with change in “Ls ”. The procedure follows in accordance with the Flowchart2 of Fig. 5. Thus, using the proposed approach, simultaneous changes in Ls and Cs /Cg could also be identified. For brevity more examples are not included. 7. Conclusions In a model winding, if a deviation is observed when a pair of subsequently acquired neutral/line current and TF data are compared, then it is possible to figure out, which one of the three circuit elements of the equivalent circuit, namely, series capacitance, shunt capacitance or self-inductance is responsible for the observed change. Further, it can also be inferred whether the pertinent circuit element has increased or decreased, from its initial value. The proposed approach requires data corresponding to terminal measurements, and does not impose any necessity for newer measurements. Applicability of the method was verified (to a limited extent) for both disc and interleaved type of
[1] K. Feser, J. Christian, C. Neumann, U. Sundermann, T. Liebfried, A. Kachler, M. Loppacher, The transfer function method for detection of winding displacements on power transformer after transport, short circuit or 30 years of service, CIGRE 12/33-04, Session 2000. [2] W. Lech, L. Tyminski, Detecting transformer winding damage—the low voltage impulse method, Electr. Rev. 179 (21) (1966) 768–772. [3] B.I. Gururaj, B.N. Jayaram, Use of recurrent surge generator for detecting displacement and deformations in transformer winding, IE(I) J. -EL 54 (1974) 99–102. [4] E. Rahimpour, J. Christian, K. Feser, H. Mohesini, Transfer function method to diagnose axial displacement and radial deformation of transformer windings, IEEE Trans. PWRD 18 (2) (2003) 493–505. [5] M. Florkowski, J. Furgal, Detection of transformer winding deformations based on the transfer function measurements and simulations, J 2003 Meas. Sci. Techl.-14 (2003) 1986–1992. [6] M. Wang, A.J. Vandermaar, K.D. Srivastava, Improved detection of power transformer winding movement by extending the FRA high frequency range, IEEE Trans. PWRD 20 (3) (2005) 1930–1938. [7] J.A.S.B. Jayasinghe, Z.D. Wang, P.N. Jarman, A.W. Darwin, Investigation on sensitivity of fra technique in diagnosis of transformer winding deformations, in: Proceedings of the Conference Record of IEEE International Symposium On EI, Indianapolis, USA, 2004, pp. 496– 499. [8] S.A. Ryder, Diagnosing transformer faults using frequency response analysis, IEEE EI Magn. 19 (2) (2003) 16–22. [9] T. Leibfried, EinfluB von windungsschlussen auf die ubertragungsfunktion von transformator wicklungen am beispiel homogener spulen, Electr. Eng. (1997) 99–108. [10] L. Satish, S.K. Sahoo, An effort to understand what factors affect the transfer function of a two-winding transformer, IEEE Trans. Power Deliv. 20 (2) (2005) 1430–1440. [11] P.A. Abetti, F.J. Maginniss, Natural frequency of coils and windings determined by equivalent circuit, AIEE Trans. 74 (1953) 495– 504. [12] L. Satish, A. Jain, Structure of transfer function of transformers with special reference to interleaved windings, IEEE Trans. Power Deliv. 17 (3) (2002) 754–760. Subrat K. Sahoo (S 04) was born in 1979. He received the B.E. degree (Hons.) in electrical engineering from the Indira Gandhi Institute of Technology, Sarang, India, which is affiliated with Utkal University, Orissa, India, in 2001. He completed (in August 2003) his M.Sc. (Engg.) from the Department of High Voltage Engineering, Indian Institute of Science (I.I.Sc.), Bangalore, India. He is currently registered for the Ph.D. degree in the Department of High Voltage Engineering. His research interests include diagnostics and condition monitoring of transformers. L. Satish (SM 02) was born in 1964. He received the Ph.D. degree from the Indian Institute of Science (I.I.Sc.), Bangalore, India, in 1993. Since 2001, he has been an Associate Professor with the Department of High Voltage Engineering, I.I.Sc. He was a Postdoctoral Fellow with ETH, Zurich, Switzerland, from 1993 to 1995. He was a Visiting Researcher with H.V. Institute, Helsinki University of Technology, Helsinki, Finland, during the summer of 1998. His research interests include application of signal processing to high voltage impulse testing, dynamic and static testing of ADCs, diagnostics and condition monitoring of transformers, PD measurements and pattern recognition. Dr. Satish is a member of CIGRE D1-33 in CIGRE WG D1-33.