FORM 2
THE PATENTS ACT, 1970 (39 of 1970)
As amended by the Patents (Amendment) Act, 2005
&
The Patents Rules, 2003
As amended by the Patents (Amendment) Rules, 2006
COMPLETE SPECIFICATION (See section 10 and rule 13)
TITLE OF THE INVENTION
A method to diagnose mechanical faults in a transformer
APPLICANTS
Crompton Greaves Limited, CG House. Dr Annie Besant Road, Worli, Mumbai 400 030, Maharashtra, India, an Indian Company
INVENTORS
Shubhangi Sachin Patil of Condition Monitoring and Diagnostic Research Centre and Kiran Kumar Munji of Analytics Centre, Crompton Greaves Ltd, Kanjur Marg, Mumbai, Maharashtra, India, both Indian Nationals
PREAMBLE TO THE DESCRIPTION
The following specification particularly describes the nature of this invention and the manner in which it is to be performed:

FIELD OF THE INVENTION
The following invention relates to the field of transformers. More specifically, the method as disclosed in the invention is relates to diagnosing mechanical faults in transformers.
BACKGROUND OF THE INVENTION
The transformers are the most important and vital component in power system. It is required for transformers to be reliable and to be in service for a long time. Failure of transformers results in substantial costs mainly caused by the outage of the power station. Therefore there is a necessity to develop methodology to diagnose and detect mechanical faults and failure tendencies in a transformer from time to time so that required maintenance can be performed such that power outages are averted.
A transformer can be considered to be a complex network of equivalent 'R' (resistance), 'L' (inductive) and 'C (capacitive) components. The contributions of this complex network of R, L, and C circuit can be from the resistance of the winding, self and mutual inductance of winding coil and capacitance between winding, between winding and core. Any form of physical damage to the transformer result in the change of R, L, C parameters and therefore the frequency response.
Typically SFRA (Sweep Frequency Response Analysis) techniques are known to identify detects and failure tendencies in transformer. However, it is difficult to predict and isolate a failure tendency or the mechanical defect using SFRA unless the transformer is mathematically modeled correctly.
There is a need to establish a methodology to diagnose the failure tendencies in

transformers such that total failures are averted. Another need for such a diagnosing arises to identify the defects that are present in faulty transformers that need repair. Usually transformers are mass manufactured based on a set of desired parameters that cater to a desired voltage range and frequency. The present invention discloses a method for diagnosing a mechanical fault in a transformer of a particular class based on the design parameters that were used to mass manufacture the particular class of transformers.
OBJECTS OF THE INVENTION
Accordingly the invention provides a diagnostic method for identifying mechanical faults and fault tendencies in a transformer.
Another object of the invention is to account for non-linearity in the inductance parameter in an equivalent electrical model for a transformer that is obtained from a magnetic model of the transformer.
DETAILED DESCRIPTION OF THE INVENTION
According to the invention a method of diagnosing the nature of mechanical faults in a faulty transformer, the method comprises the steps of:
a. obtaining a magnetic model for a transformer that is of the same make as that of
the faulty transformer and
b. converting the magnetic model in to an equivalent first electrical model and
c. performing a sweep frequency response analysis (SFRA) for the faulty transformer
and
d. performing a network synthesis for the frequency response obtained in the SFRA
to obtain an equivalent second electrical model and

e. comparing the first electrical model and second electrical model for a significant change in their R(resistive) ,L (inductive) and C (capacitive) values and determine the of mechanical fault that would have caused the significant changes in R and/or L and/or C values.
These and other aspects, features and advantages of the invention will be better understood with reference to the following detailed description, accompanying drawings and appended claims, in which,
Figure 1 illustrates a typical three phase transformer along with winding.
figure 2 illustrates a magnetic circuit mods) as obtained for the three phase transformer
according to one of steps of a diagnostic method as suggested by the invention.
Figure 3 illustrates the equivalent electrical model obtained from the magnetic circuit
model as illustrated in Figure 2.
Figure 4 illustrates a portion of the electrical model of Figure 3 that represents the outer
phase of the transformer.
Figure 5 illustrates the portion of the electrical model taking in to consideration the
electrical effect as induced by the winding of the transformer.
Figure 6 illustrating a SFRA response of a faulty DUT (device under test) and an ideal
response.
Figure 1, illustrates a typical 3 phase transformer 100, the transformer 100 is formed of limbs 1, 2 and 3 and has a yoke 10. PI and SI represent primary and secondary windings on limb 1. and similarly P2 and S2 represent primary and secondary windings on limb 2 while P3 and S3 represent primary and secondary windings on limb 3.

Figure 2 illustrates a magnetic model for the transformer. In order to derive the magnetic model for the transformer some basic calculations that are well known to a person skilled in the art need to be done. These calculations are performed to arrive at the core reluctances of limbs and yoke of the transformer. Further, to calculate for the mmf (magnetomotive force) sources, reluctances and leakage reactance values of the transformer, the physical characteristics for e.g. length, width and height of the transformer are taken in to consideration. In Figure 2, 200 represents the magnetic model for the transformer in which Msl Mpl, Ms2 Mp2 and Ms3 Mp3 represent mmf sources for primary and secondary windings in the respective limbs 1, 2 and 3. 10', 10", 10"' and 10''''' represent the reluctances that are introduced as a result of the yoke. Rsl, Rpl and 1' are the reluctances introduced due to limb 1. Similarly Rs2, Rp2 and 2' and Rs3, Rp3 and 3' are reluctances introduced due to limb 2 and limb 3.
Figure 3 illustrates an equivalent electrical model 300 derived from the magnetic model 200 of Figure 2 using duality principle as well known. Vsl Vpl, Vs2 Vp2 and Vs3 Vp3 represent the equivalent voltage sources for the mmf sources Msl Mpl, Ms2 Mp2 and Ms3 Mp3. Lsl Lpl, Ls2 Lp2 and Ls3 Lp3 represent the equivalent inductances for Rsl Rpl, Rs2 Rp2 and Rs3 Rp3 respectively. Further additional non linear inductance components LI, L-3, L3 and L4 are added to accurately model the transformer on basis of B/H curves as obtained for the material that is used for making the core of the transformer. The non linear inductance parameters are calculated using curve fitting method as commonly known and are based on LevenbeTg-Marquardtiterative process.
Further an additional non linear inductance component is added to the electrical model

300 that is represented as LI, L2, L3 and L4 to accurately model the transformer. Equations (a), (b),(c) and (d) represent the values of non linear inductance components , wherein the components are calculated by factoring a non-linear parameter k that is obtained in the following steps • calculating µr(H) using (1)

wherein µr(H)is relative permeability as a function of field
wherein µi is initial permeability wherein H is magnetic force
wherein a, b, c and d, x are coefficients which closely fit to magnetization curve obtained from using curve fitting techniques based on the well known Levenberg Marquardt's iterative process using B/H graphs that indicate the core material property.
• calculating the non-linear 'k' factor using equation (2)

wherein µ0 tsa relative constant o fthe value 8.85 * 10~13 wherein µr(H) issufostitued as calculated in equation 1 wherein N is the number windings in the transformer wherein A is the cross sectional area of the core of the transformer wherein Lj. is the magnetic length of the core of the transformer
The values for LI, L2, L3 and L4 of 300, is then calculated using the below equations

Figure 4 represents the portion of the electrical circuit 300 that represents the outer phase or inner phase as demarcated by region 20 in Figure 3. To add more accuracy in the full frequency range the inter-laminar effect is added to the circuit and these results in a more accurate circuit as represented by Figure 5. In figure 5fhe actual values for the electrical model as calculated for the transformer are illustrated.
Figure 6 illustrates the frequency response of a faulty transformer (DUT) represented by graph 62 and the frequency response of a good transformer (as modeled). The SFRA response of the faulty transformer is converted in to an electrical circuit by using known network synthesis methods and transfer function approach. The electrical circuit as obtained for the faulty transformer is shown in Figure 7. In the figure a comparative SRFA response for the ideal transformer is also shown and represented as 61. SFRA measurements for the faulty transformer and the ideal transformer clearly show a significant change at low frequency range (20Hz - 4 kHz). Equivalent circuit parameters are derived from SFRA data using transfer function approach for reference winding (U Phase). Circuit parameters for both cases are compared and calculated. The equivalent inductance for the electrical circuit as obtained faulty transformer is calculated to be 0.0028H. The actual inductance for the ideal transformer is calculated 0.029 H which is

89% change. Such a significant change can be only attributed to shorted turns. Although the invention has been described with reference to a specific embodiment, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed embodiment, as well as alternate embodiments of the invention, will become apparent to persons skilled in the art upon reference to the description of the invention. It is therefore contemplated that such modifications can be made without departing from the scope of the invention as defined in the appended claims.

We Claim,
1. A method of diagnosing the nature of mechanical faults in a faulty transformer, the
method comprising the steps of:
obtaining a magnetic model for a transformer that is of the same make as that of the faulty
transformer;
converting the magnetic model in to an equivalent first electrical model;
performing a sweep frequency response analysis (SFRA) for the faulty transformer;
performing a network synthesis for the frequency response obtained in the SFRA to obtain
an equivalent second electrical model;
compare the first electrical model and second .electrical model for a significant change in
their R(resistive) ,L (inductive) and C (capacitive) values and determine the of mechanical
fault that would have caused the significant changes in R and/or L and/or C values.
2. The method of claim 1, wherein the conversion of magnetic model in to the first electrical model is done by using a duality principle and involves accurate calculation for each of the inductances by including a non-linear inductance parameter for the core of the transformer.
3. The method of claim 1, wherein for a significant change in R (resistive) and L (inductive) values between the first electrical model and the second electrical model the
causal nature of mechanical fault are residual magnetism and/or improper core earthing
i and/or loose contacts.
4. The method of claim 1, wherein for a significant change in L (inductive) values

between the first electrical model and the second electrical model the causal nature of mechanical fault is that of shorted turns.
5. The method of claim 1, wherein for a significant change in C (capacitive) values between the first electrical model and the second electrical model the causal nature of mechanical fault is winding deformation.
6. The method of claim 1, wherein for a significant change in C (capacitive) and L (inductive) values change the causal nature of mechanical fault are winding displacement as a result of axial, radial or hoop buckling.
7. The method of claim 2, wherein the non-linear inductance for the core of the transformer is calculated by the following steps of:
• calculating µr{H) using equation 1

wherein µr(H) is relative permeability as a function of field
wherein µi is initial permeability wherein H is magnetic force
wherein a, b, c and d, x are coefficients which closely fit to magnetization curve obtained from using curve fitting techniques based on the well known Levenberg Marquardt's iterative process using B/H graphs that indicate the core material property.
• calculating a non-linear 'k' factor using equation (2)

wherein µ0 isa relative constant of the value 8.85 * 10-12
wherein µr(H) is sufostitued as calculated in equation 1
wherein N is the number windings in the transformer
wherein A is the cross sectional area of the core of the transformer
wherein Lr is the magnetic length of the core of the transformer
• calculating the non linear inductance parameter for the core of the transformer from equations (3) and equation (4) inductance as

wherein L is the inductance of the transformer without factoring the non-linear
factor wherein N is the number of windings/turns in the transformer
wherein R is the reluctance as obtained for the magnetic model of the transformer.