Transformers can be treated as a time-invariant system which can be characterized by its response to the Dirac's delta function. This impulse response is completely unique and should remain so over the system life. Therefore, it can be used as a kind of indicator to check if the internal compartments, elements or parameters have physically changed during service life. The system response is the convolution of the system impulse response with the excitation signal. This time-domain response has its equivalent response in the frequency domain. Thus, the frequency response of a time-invariant system should also remain unchanged if system parameters are unchanged. This concept can be utilized to evaluate the mechanical structure integrity as well as diagnosis of transformers and rotating machines. It is called frequency response analysis. This chapter is specifically focused on frequency response measurement and analysis of transformers.

Chapter Contents:

• Abstract
• 5.1 Introduction
• 5.2 Transformer winding deformation
• 5.2.1 Deformation types and short-circuit current
• 5.2.1.1 Radial forces
• 5.2.1.2 Axial forces
• 5.2.2 Transformer transportation causing active part displacement
• 5.3 Methods to recognize winding deformation
• 5.3.1 Short-circuit impedance
• 5.3.1.1 Short-circuit impedance concept
• 5.3.1.2 Short-circuit impedance measurement setup
• 5.3.2 Transfer function
• 5.4 Sweep frequency response analysis
• 5.5 Standard connection methods
• 5.5.1 End-to-end measurement
• 5.5.2 Inductive interwinding measurements
• 5.5.3 Capacitive interwinding measurements
• 5.5.4 End-to-end short-circuit measurements
• 5.6 FRA signature assessment
• 5.6.1 Visual assessment of FRA signature
• 5.6.2 Statistical assessment of FRA signature
• 5.7 Factors affecting frequency response signature
• 5.7.1 Winding inductance, capacitance
• 5.7.1.1 Self-and mutual-inductance in circular form
• 5.7.1.2 Self-and mutual-inductance under buckling
• 5.7.1.3 Capacitance
• 5.7.2 Series capacitance under buckling
• 5.7.3 Shunt capacitance under buckling
• 5.7.4 Tap-changer
• 5.7.5 Paper insulation deterioration
• 5.7.6 Temperature and moisture content
• 5.7.6.1 Transformer water dynamic
• 5.8 Online transformer winding deformation diagnosis
• 5.8.1 Methods for online transformer active part assessment
• 5.8.1.1 Vibration analysis
• 5.8.1.2 Communication method
• 5.8.1.3 Current deformation coefficient (CDC) method
• 5.8.1.4 Ultrasonic method
• 5.8.1.5 Short-circuit impedance (SCI) and winding stray reactance methods
• 5.8.1.6 Voltage –current locus diagram
• 5.8.1.7 Transfer function method
• 5.8.2 Online FRA setup
• 5.8.3 Online FRA (OFRA) progress and influence of bushing tap
• References

Inspec keywords: frequency-domain analysis; power transformers; transient response; frequency response; electric machines

Other keywords: rotating machines; mechanical structure integrity; service life; frequency domain; Dirac delta function; time-domain response; system impulse response; frequency response measurement; time-invariant system; excitation signal; frequency response analysis transformers; system response; system parameters; system life

Subjects: Mathematical analysis; Transformers and reactors; Reliability