Ferro Resonance - Introduction,Classification and Characterstics

 

Ferro Resonance - Introduction,Classification and Characterstics

source : http://www.powerelectricalblog.com/2007/03/ferro-resonance-introductionclassificat.html

 

Introduction
The term "Ferro-resonance ", which appeared in the literature for the first time in 1920, refers to all oscillating phenomena occurring in an electric circuit which must contain at least:

• a non-linear inductance (ferromagnetic and
  saturable),
• a capacitor,
• a voltage source (generally sinusoidal),
• low losses.

Power networks are made up of a large number of saturable inductances (power transformers, voltage measurement inductive transformers (VT), shunt reactors), as well as capacitors cables, long lines, capacitor voltage transformers, series or shunt capacitor banks,voltage grading capacitors in circuit-breakers,metalclad substations). They thus present scenarios under which ferroresonance can occur.
The main feature of this phenomenon is that more than one stable steady state response is possible for the same set of the network parameters. Transients, lightning overvoltages,energizing or deenergizing transformers or loads, occurrence or removal of faults, live works, etc...may initiate ferroresonance. The response can suddenly jump from one normal steady state response (sinusoidal at the same frequency as the source) to an another ferroresonant steady state response characterised by high overvoltages and harmonic levels which can lead to serious damage to the equipment.
A practical example of such behaviour (surprising for the uninitiated) is the deenergization of a voltage transformer by the opening of a circuit-breaker. As the transformer is still fed through grading capacitors accross the circuit-breaker, this may lead either to zero voltage at the transformer terminals or to permanent highly distorted voltage of an amplitude well over normal voltage.
To prevent the consequences of ferroresonance (untimely tripping of protection devices,destruction of equipment such as power transformers or voltage transformers, production losses,...), it is necessary to:

• understand the phenomenon,
• predict it,
• identify it and
• avoid or eliminate it.

Little is known about this complex phenomenon as it is rare and cannot be analysed or predicted by the computation methods (based on linear approximation) normally used by electrical
engineers. This lack of knowledge means that it is readily considered responsible for a number of unexplained destructions or malfunctionings of equipment.
A distinction drawn between resonance and ferroresonance will highlight the specific and some times disconcerting characteristics of ferroresonance.
Practical examples of electrical power system configurations at risk from ferroresonance are used to identify and emphasise the variety of potentially dangerous configurations.Well-informed system designers avoid putting themselves in such risky situations.
Ferro Resonance
The main differences between a ferroresonant circuit and a linear resonant circuit are for a given ω :

• its resonance possibility in a wide range of
  values of C,
• the frequency of the voltage and current waves
  which may be different from that of the sinusoidal
  voltage source,
• the existence of several stable steady state
  responses for a given configuration and values

Classification of ferroresonant modes
Experience of waveforms appearing on power systems, experiments conducted on reduced system models, together with numerical simulations, enable classification of ferroresonance states into four different types.
This classification corresponds to the steady state condition, i.e. once the transient state is over, as it is difficult for a ferroresonant circuit to distinguish the normal transient state from ferroresonant transient states. However, this in no way implies that transient ferroresonance phenomena do not present a risk for electrical equipment. Dangerous transient overvoltages can occur several system periods after an event (for example following energizing of an unloaded transformer) and persist for several power system cycles.
The four different ferroresonance types are:

• fundamental mode,
• subharmonic mode,
• quasi-periodic mode,
• chaotic mode.

The type of ferroresonance can be identified:

• either by the spectrum of the current and voltage signals,
• or by a stroboscopic image obtained by measuring current i and voltage v at a given point of the system and by plotting in plane v, i the instantaneous values at instants separated
  by a system period.

The characteristics of each type of ferroresonance are defined below.
Fundamental modeVoltages and currents are periodic with a period T equal to the system period, and can contain a varying rate of harmonics. The signal spectrum is a discontinuous spectrum made up of the fundamental f0 of the power system and of its harmonics (2f0, 3f0 ...). The stroboscopic image is reduced to a point far removed from the point representing the normal state.

Subharmonic mode
The signals are periodic with a period nT which is a multiple of the source period. This state is
known as subharmonic n or harmonic 1/n.Subharmonic ferroresonant states are normally of odd order. The spectrum presents a fundamental equal to f0/n (where f0 is the source frequency and n is an integer) and its harmonics (frequency f0 is thus part of the spectrum).A stroboscopic plotted line reveals n points.

Quasi-periodic mode
This mode (also called pseudo-periodic) is not periodic. The spectrum is a discontinuous spectrum whose frequencies are expressed in the form: nf1+mf2 (where n and m are integers
and f1/f2 an irrational real number). The stroboscopic image shows a closed curve.


Chaotic mode
The corresponding spectrum is continuous, i.e. it is not cancelled for any frequency. The stroboscopic image is made up of completely separate points occupying an area in plane v, i known as the strange attractor.

Since it is not possible to discuss the different case studies here iam giving the links related to different cases of ferroresonance

Ferroresonace - Link1 Link2
Examples of ferroresonance in a high voltage power system - click here
Modeling Ferroresonance Phenomena in an Underground Distribution System - click here
Examples of Ferroresonance in Distribution sysems - click here
Summary of a recent ferroresonance study - click here