Problems with ferroresonance have become increasingly common due to the advancement of power electronic in the grid, the association of sections of shielded cables with capacitive effects, and high impedance faults.

However, this is not a new problem, as transient effects in parts of the system can induce inductive potential transformers to operate in a ferroresonant condition due to frequency variations in voltage signals, insertion of harmonics, and imbalances caused by faults.

To understand the faults, whose origin involves injections of harmonics at frequencies outside that of the industrial, all components must be modeled for simulations in the time domain that are also representative in the frequency domain. In order to ensure a reliable response during simulation and consequently the final installation.

For example, representing the transformer in transient regime in the time domain with broadband frequency representation becomes extremely cumbersome and may still present very large errors for this type of modeling, discrediting all the effort employed.

Therefore, frequency domain analysis becomes not only more reliable, but also:

In simulations involving other harmonic components.

In this article, a way will be presented to map the conditions for an inductive potential transformer (IPT), especially those of 36 kV class, can operate in the ferroresonance condition and how it is possible to prevent the equipment from entering thermal and electrical collapse in case of this event.

The most agile way to map the IPT is to define:

The transfer function is the mathematical tool that allows the analysis of the frequency response, since it is from this mathematical artifact that it is possible to construct the Bode diagram, which shows where the natural resonance frequency of the IPT occurs.

An important observation is that, to better understand what the natural resonance frequency of equipment is, the reader is suggested to read the article

Knowing the Transformer Signature Through the SFRA Technique

Frequency response analysis is a set of values obtained from the insertion of a low-amplitude voltage signal with a pure frequency (in the case of a sinusoidal signal) and the measurement of the signal at the transformer output which, in the ideal case, is also sinusoidal, of the same frequency, and whose amplitude and phase may change. This mapping is called the "transformer signature".

The transformer signature allows the practical mapping of the equipment's natural resonance frequency, which can generally be done by equipment such as a Sweeper, which is based on the process of scanning a range of frequencies known as SFRA (Sweep Frequency Response Analysis).

The reader is suggested to read the master's thesis by GuilhermeFerraz,

Proposal of an Equivalent Circuit Model for Broadband Representation of Distribution Transformers

, where the reader can find this topic in greater detail and deeper explanations of this technique.

By definition, resonance occurs when the capacitive reactance and the inductive reactance of a circuit cancel each other out.

From this definition, due to the isolation of the IPTs, parasitic capacitances arise in the equipment, which, when poorly adjusted, can cause the transformer to have a very low natural resonance frequency, which can expose the equipment in grids with high levels of harmonic distortions, such as in wind farms and photovoltaic units.

From this, ways must be found in the coil geometry to distribute the voltage gradient as evenly as possible so that internal high-frequency transients are attenuated, and also so that the parasitic capacitances of the primary are as small as possible.

After studying the capacitances of the IPTs, the number of wires in the winding must be analyzed so that the natural resonance frequency can be tuned as high as possible to ensure that the harmonic component accommodating this frequency is as high as possible. However, attention must be paid to the accuracy of the equipment, since the number of turns can compromise the accuracy in the measurement of the IPTs.

Analyzing Which Harmonic Component Accommodates the Natural Resonance Frequency of the IPT

From a fully distorted sinusoidal signal, it is possible to use harmonic filters based on the Fourier series, which determine the harmonic components that make up the signal in question.

Voltage and current measuring equipment present only the final waveform of the sum of these components, however, wattmeters, for example, can present a sample spectrum of harmonic distortions and what their percentage is in the measured signal.

To exemplify this, if equipment has its natural resonance frequency at 300 Hz, when using a wattmeter to analyze the quality of energy in a given system, one must observe if there are no excesses of 5th harmonic voltages in the grids since this is the component that accommodates the natural resonance frequency of the IPT under study.

In the next article, we will discuss how unadjusted IPTs and CTs for the frequency domain influence harmonic component analyses and even the operation of protection relays. Finally, it is indispensable to mention that this article was written with significant contributions from the aforementioned Guilherme Ferraz, CEO at HVEX, and Fernando Ribeiro, Engineering Manager at

Brasformer Braspel Produtos Elétricos LTDA

, who shared some of their field experience and project development for Inductive Potential Transformers for 36 kV voltage class.

Problems with ferroresonance have become increasingly common due to the advancement of power electronics in the grid.

Frequency Response: A Signature Guiding Ferroresonance Formation

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