study on the non linear characteristic of power

STUDY ON THE NON LINEAR CHARACTERISTIC OF POWER TRANSFORMER AND THEIR EFFECT FERRORESONANCE

SALIZAWATI BT HJ. SHAMSUDDIN

A project report submitted in partial fulfilment of the requirement for the award of the degree of Master of Engineering (Electrical Engineering)

Faculty of Electrical Engineering Universiti Teknologi Malaysia

May 2008

To my beloved mother and father

ACKNOWLEDGEMENTS

Particularly thanks to God for the blessing that gives me a patience and

courage in finishing my project report. Firstly, I would like to take this

opportunity to thank Prof. Madya Dr. Zulkurnain Bin Abdul Malek, my thesis

supervisor for his unfailing enthusiasm and encouragement. I also would like to

thank him for all his valuable advice and assistance, suggestions and comments

in completing this project report.

I also would like to express many thanks to my parents, family and

friends for their understanding, consistent commitment and moral support in

order for me to write this project report.

ABSTRACT

Ferroresonance can occur in electrical power system and consequently

can cause damage such as due to voltage transformer overheating or power

transformer overvoltages. This study involves simulation work to simulate

various conditions under which ferroresonance can occur in typical extra high

voltage substations. The ATP-EMTP simulation program was used to model

various power system components and simulate the ferroresonance phenomena.

The effects of the non-linear characteristics of power transformers are also

studied. Methods to prevent the ferroresonance conditions from occurring and

hence avoiding equipment damages and losses were also proposed based on the

simulation work.

ABSTRAK

Feroresonan berlaku ke atas sistem kuasa elektrik yang boleh

menyebabkan kerosakan pada sistem tersebut. Contohnya kejadian pemanasan

lebihan pada pengubah voltan ataupun voltan lampau pada pengubah kuasa.

Kajian ini melibatkan kerja simulasi bagi pelbagai keadaan yang boleh

berlakunya feroresonan pada pencawang elektrik EHV. Program ATP-EMTP

merupakan satu program simulasi yang berkeupayaan untuk menghasilkan

pelbagai model komponen sistem kuasa dan seterusnya melakukan simulasi ke

atas sistem. Kajian simulasi ini melaporkan kesan sifat tak lelurus keluli

pengubah kuasa terhadap feroresanan dan kaedah untuk mengelakkan

berlakunya feroresonan. Justeru itu, kerosakan dan kerugian komponen dapat

dihindarkan.

TABLE OF CONTENS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF ABBREVIATIONS xv

LIST OF SYMBOLS xvi

1 INTRODUCTION 1

1.1 Introduction 1

1.2 Objectives 2

1.3 Scope of Work 2

1.4 Project Flow Chart 3

1.5 Organisation of Thesis 4

2 LITERATURE REVIEW 5

2.1 Introduction 5

2.2 Case Study by Zia Emin and Yu Kwong Tong: 5 Ferroresonance Experience in UK: Simulation and

Measurement

2.2.1 Objective 5 2.2.2 Voltage Transformer 6

2.2.2.1 Comparison Field Measurement and Simulation 7

Result

2.2.3 Single Phase Traction Supply Transformer 8 2.2.3.1 Comparison Field Measurement and Simulation 9

Result

2.2.4 Conclusion 9

2.3 Case Study by YK Tong: NGC Experience on Ferroresonance 10

In Power Transformer and Voltage on HV Transmission

System

2.3.1 Introduction 10

2.3.2 Power Transformers 10 2.3.3 Voltage Transformer 11

2.3.4 Measurement to Predict or Prevent Ferroresonance 11 2.4 Case Study by David A.N. Jacobson: Example of 12

Ferroresonance in High Voltage Power System 2.4.1 Objective 12

2.4.2 Wound Potential Transformer-Circuit Breaker 12 Grading Capacitor

2.4.2.1 Description of Disturbance 12

2.4.2.2 Simulation Result 13

2.4.2.3 Mitigation Options 13

2.4.3 Transformer – Circuit Breaker Grading Capacitor 14



2.4.3.3 Mitigation Options 15

2.4.4 Open Delta Potential Transformer 15



2.4.4.3 Mitigation Options 17 2.4.5 Conclusion 17

2.4 Summary 17

3 FERRORESONANCE 19

3.1 Basic of Ferroresonance 19

3.2 Main Characteristic 22

3.2.1 Sensitivity to System Parameter Value 22

3.2.2 Sensitivity to Initial Condition 24

3.3 Classification of Ferroresonance Mode 25

3.3.1 Fundamental Mode 25 3.3.2 Sub harmonic Mode 25 3.3.3 Quasi Periodic Mode 26 3.3.4 Chaotic Mode 26

3.4 Power System Ferroresonance 28 3.5 Symptoms of Ferroresonance 28

3.5.1 Audible Noise 29 3.5.2 Overheating 29

3.5.3 Arrestor and Surge Protector Failure 29

3.5.4 Flicker 30

3.5.5 Cable Switching 30

4 METHDOLOGY 32

4.1 System Modeling 32

4.2 ATP-EMTP Simulation 32

4.3 Selected model and Validation 33

4.4 Resistor and Capacitor Model 34

4.5 Overhead Transmission Lines 34

4.6 Transformer Model 34

4.6.1 Nonlinear and frequency Dependent Parameter 36 4.6.1.1 Modelling of Iron Core 36

4.6.1.2 Modelling of Eddy Currents Effects 37 5 SIMULATION: 400kV DOUBLE CIRCUIT 38

CONFIGURATION

5.1 Introduction 38

5.2 Simulation Procedures 38

5.3 Circuit Description 39

5.4 Simulation Model 40

5.4.1 Typical Overhead Line Spacing for 400kV 42

5.4.2 BCTRAN Transformer Model 44

5.4.3 Non-linear Inductance 47

5.4.4 Resistor and Capacitor Model 48

5.5 Result of Simulation for 400kV Double Circuit 48

5.6 Simulation by Changing the Magnetization Characteristic 51

5.6.1 Simulation Model 51

5.6.2 Simulation Result 56

5.6.2.1 Simulation Result for Curve 1 56




5.7 Mitigation Technique 62

5.7.1 Simulation Model 64

5.7.2 Simulation Result 64

6 CONCLUSION AND RECOMMENDATION 70

6.1 Conclusion 70

6.2 Recommendation 71

REFERENCES 72

LIST OF TABLES

TABLE NO. TITLE PAGE

5.1 Transformer Characteristic 44

5.2 Transformer Short Circuit Factory Data 45

5.3 Transformer Magnetizing Characteristic 47

5.4 Simulation Result for 400kV Double Circuit Configuration 49

5.5 Transformer Magnetizing Characteristic – Curve 1 52




5.9 The Effect of Using the Saturation -Curve 1 57




5.13 The Effect of Adding Resistor on Secondary Side 65

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Project Flow Chart 4

2.1 Single Line Diagram of Voltage Transformer 6

2.2 Reduced Equivalent Ferroresonance Circuit 6

2.3 Measurement Output Voltage 7

2.4 Digital Simulation Output Voltage 8

2.5 Single Line Diagram of Traction Supply Transformer 8

2.6 Measurement Output Volatge 9

2.7 Digital Simulation Output Voltage 9

2.8 Single Line Diagram of Wound Power Transformer Circuit 13

2.9 A Single Diagram of Main Circuit Component 14

2.10 A Single Diagram of Station Service Transformer 14

2.11 The Output Voltage Waveform of Bus Voltage 15

2.12 Typical Station 16

2.13 Example of Output Voltage 16

3.1 Resonance in RLC Circuit 20

3.2 Magnetization Curve 21

3.3 Basic Series Ferroresonance Circuit Parameter 22

3.4 Sensitivity to the System Parameter and Jump 23

Phenomenon

3.5 Sensitivity Initial Condition 24

3.6 Diagrams Illustrating the Fundamental Mode 25

of Ferroresonance

3.7 Diagrams Illustrating the Subharmonic Mode of 26

Ferroresonance

3.8 Diagrams Illustrating the Quasi Periodic Mode of 26

Ferroresonance

3.9 Diagrams Illustrating the Chaotic Mode of Ferroresonance 27

5.1 A Single Line Diagram of the Brinsworth/Thorpe Marsh 40

Circuit

5.2 Equivalent Circuit of Power Transformer 41

5.3 Line/Cable Dialog Box 43

5.4 Line Configuration 44

5.5 BCTRAN Dialog Box 46

5.6 The Saturation Curve for Nonlinear Inductor 48

5.7 The Output Voltage Waveform at TR1 Terminal–R Phase 49

5.8 The Output Voltage Waveform at TR1 Terminal–Y Phase 49

5.9 The Output Voltage Waveform at TR1 Terminal– B Phase 50

5.10 The Output Current Waveform at TR1 Terminal - R Phase 50

5.11 The Output Current Waveform at TR1 Terminal- Y Phase 50

5.12 The Output Current Waveform at TR1 Terminal- B Phase 51

5.13 Variation of Magnetization Curve 52

5.14 The Saturation Curve 1 54




5.18 The Output Voltage Waveform at TR1 Terminal–R Phase 57

5.19 The Output Current Waveform at TR1 Terminal –R Phase 57

5.20 The Output Voltage Waveform at TR1 Terminal –R Phase 58

5.21 The Output Current Waveform at TR1 Terminal–R Phase 59

5.22 The Output Voltage Waveform at TR1 Terminal –R Phase 60


5.24 The Output Voltage Waveform at TR1 Terminal – R Phase 61


5.26 Simulated Power Transformer Circuit by Adding Loading 63

Resistor at Secondary Side

5.27 The Output Voltage Waveform by Adding R=1k Ohm 65

Resistance – R Phase


Resistance – Y Phase


Resistance – B Phase

5.30 The Output Current Waveform by Adding R=1k Ohm 66






5.33 The Output Voltage Waveform by Adding R= 30k Ohm 67






5.36 The Output Current Waveform by Adding R= 30k Ohm 68






LIST OF ABBREVIATIONS

DC - Direct Current

AC - Alternating Current

ATP - Alternative Transient Program

EMTP - Electro Magnetic Transient Program

PT - Potential Transformer

GB - Grading Bank

HV - High Voltage

LV - Low Voltage

LIST OF SYMBOLS

XL - Inductance reactance

XC - Inductance capacitance

C - Capacitance

L - Inductance

C - Capacitive

R - Resistance

VL - Load Voltage

E - Voltage source

f - Frequency

w - Frequency

Z - Impedance

CHAPTER 1

INTRODUCTION

1.1 Introduction

A power quality is a term used to describe electrical power that motivates an

electrical load and the load’s ability to function properly with that electric power.

With a poor power quality, an electrical device (or load) may malfunction, fail

prematurely or not operate at all. There are many ways in which electric power can

be of poor quality and many more causes of such poor power quality.

As a general statement, any deviation from normal of a voltage source (either

DC or AC) categorized as a power quality issue. Power quality issues can be high-

speed events such as voltage impulses / transients, high frequency noise, wave shape

faults, voltage swells and sags and total power loss. Power quality issues will affect

each type of electrical equipment differently. By analyzing the electrical power and

evaluating the equipment or load, we can determine if a power quality problem

exists.

Power quality problems manifest themselves in variations in the voltage has

been obtained. This variation can be in the form of transients due to switching or

lightning strikes, sags or swells in the amplitude of the voltage, a complete

interruption in the supply, or harmonic distortion caused by non-linear loads in the

system which may likely lead to the occurrence of ferroresonance.

1.2 Objective

The main objectives of this project is to simulate the ferroresonance event on

extra high voltage substation power transformer based on parameters, features,

components and arrangements of the substation power system. An alternative

Transient Program- Electromagnetic Transient Program (ATP-EMTP) will be used

to carry out the simulation in order to study the phenomenon and therefore to

determine methods to minimize or reduce the risk of ferroresonance to power

transformers.

1.3 Scope of Work

The main scope of this project is to simulate the various conditions of

ferroresonance, which include:

i. To prove or otherwise that ferroresonance can occur at 400kV double

circuit substation;

ii. To identify the effect of magnetization characteristic of power

transformer on ferroresonance;

iii. To identify method to minimize the impacts of ferroresonance on

power transformers.

1.4 Project Flow Chart

To solve the problem, one has to first study the problem and come up with

the process flow chart, which will guide the simulator throughout the project. It is

also to give the simulator the basic overview of the system and what is required

before simulations be completed. The flow chart of this project is as shown in Figure

1.1.

Modelling the ferroresonance circuit arrangement in

ATP/EMTP

Analyze the Ferroresonance work done

Review Ferroresonance simulation done in power

system

Review previous work done on Ferroresonance

Figure 1.1: Project Flow Chart

1.5 Organisation of Thesis

Chapter 2 illustrates previous work done related on ferroresonance

phenomenon in voltage transformer and power transformer. Besides, it is also

includes some techniques for avoiding or mitigating ferroresonance. Chapter 3

describes the basics of ferroresonance, characteristics and types of ferroresonance.

Chapter 4 describes the methods that are used for the simulation. Therefore, all

information related the simulation is explained in detail with the operation. Chapter

5 presents the circuits that were used in the simulation and explains how the

simulations techniques are implemented. Lastly, chapter 6 describes the conclusion

and recommendation that is related to the project done.

Simulation and Analysis

Recommendation and Conclusion

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter reviews the previous related work done on ferroresonance.

Three case studies describe ferroresonance phenomena on voltage transformers and

power transformers in detail.

2.2 Case Study by Zia Emin and Yu Kwong Tong: Ferroresonance

Experience in UK: Simulations and Measurements [1]

2.2.1 Objective

The objective of this paper is model and analysis ferroresonance on the

system by using program ATP-EMTP. This is to compares the result with system

measurement to identify the crucial factor in ferroresonance. The case studies related

to ferroresonance in wound voltage and single-phase supply transformers.

2.2.2 Voltage Transformer

Throughout voltage transformer ferroresonance oscillation happens among

the nonlinear inductance and capacitance that remaining connected to the voltage

transformer. In this case study, energy attached to the nonlinear inductance of

voltage transformer by the open circuit grading capacitance to maintain resonance.

Figure 2.1 shows the single line diagram of voltage transformer.

Ferroresonance can happen upon opening of disconnector 3 with circuit breaker

open and either disconnector 1 or 2 closed. Alternatively it can also occur upon

closure of both disconnector 1 or 2 with circuit breaker and disconnector 3 open.

Figure 2.1: Single Line Diagram of Voltage Transformer

The system arrangement in Figure 2.1 can be reduced to equivalent circuit in Figure

2.2.

Figure 2.2: Reduced equivalent ferroresonant circuit

E is the rms supply phase voltage, Cseries is the circuit breaker grading capacitance

and Cshunt is the total phase-to-earth capacitance of the arrangement. The resistor R

represents a voltage transformer core loss that has been found to be an important

factor in the initiation of ferroresonance.

2.2.2.1 Comparison Field Measurement and Simulation Result

The measured and simulated voltage transformer at secondary voltages has

been compared. The measured was obtained after opening the disconnector 3 in

Figure 2.1. As it observed that the voltage transformer haven’t get into

ferroresonance. Although the simulation does not match the measured test waveform

exactly, its general appearance is a very close fit. It can be said that the ATP model

used in this case study is capable of predicting feasible ferroresonance modes as

long as the parameters of the system are known or can be estimated.

When the same system is tested for a second time by changing the parameter

the response is totally different from earlier and it become into sub-harmonic

ferroresonance. The shapes of measured and simulated waveforms in Figure 2.3 and

2.4 are a good match.

Figure 2.3: Measurement Output Voltage

Figure 2.4: Digital Simulation Output Voltage

2.2.3 Single Phase Traction Supply Transformer

Figure 2.3 shows the single line diagram of a traction supply transformer

arrangement. The single phase transformer is fed from two phases of the three-phase

system. Ferroresonance happens upon opening of circuit breakers 1 and 2 to de-

energize the line and the transformer. Because energy is coupled to the de-energized

network from the adjacent live parallel circuit through the inter-circuit coupling

capacitance, C series in the equivalent ferroresonant circuit. The equivalent C shunt in

the ferroresonance circuit is the phase-to-earth capacitance of the line and

transformer winding and bushing capacitance. The single line diagram in figure 2.5

can reduced to equivalent circuit in Figure 2.2.

Figure 2.5: Single Line Diagram of Traction Supply Transformer

2.2.3.1 Comparison Field Measurement and Simulation Result

Figure 2.6 and 2.7 shows the simulation result of field measurement and

digital simulation of a traction supply transformer. Obviously, the two phases

generate the transformer in prolong fundamental frequency mode ferroresonance.

Figure 2.6: Measurement Output Voltage

Figure 2.7: Digital Simulation Output Voltage

2.2.4 Conclusion

It can be concluded that the ATP model used in this case study is capable of

predicting feasible ferroresonance modes as long as the parameters of the system are

known or can be estimated.

2.3 Case Study by YK Tong: NGC Experience on Ferro resonance in Power

Transformer and Voltage Transformer on HV Transmission Systems [2]

2.3.1 Introduction

Ferroresonance or nonlinear resonance can happen when power transformer

connected to the overhead lines and voltage transformer connected to the isolated of

busbars. Hence, energy coupled through the capacitance of the parallel line or open

circuit breaker grading capacitance to maintain the resonance. In linear resonance

condition, the current and voltage dependent on frequency but ferroresonance

dependent on frequency, transformer magnetic flux and point on wave of the

initiating switching event.

2.3.2 Power Transformers

On power transformers circuit, ferroresonance can happen between the

overhead line and the transformer magnetising inductance. Subsequently the

transformer feeder de-energisation the transformer determined into saturation due to

the discharge of the capacitance -to-earth on the isolated network and a non-linear

oscillation happens between the reactive components. Ferroresonance can happen at

50Hz fundamental frequency or subharmonic frequencies at 331/2 Hz, 162/3 Hz and

10Hz.

2.3.3 Voltage Transformer

Ferroresonance happen upon de-energization of the wound voltage

transformer, an oscillation occurs between the voltage transformer inductance and

the capacitance-to-earth of any system that remaining connected to the voltage

transformer.

2.3.4 Measure to Predict or Prevent Ferroresonance

Power transformer can be avoid by the disconnection either the transformer

from feeder or parallel circuit excitation source that can provides the supply power

for sustained ferroresonance. Other practices are built-in the surge arrestors at the

power transformer that the circuit may be re–energised from the main system and

then re-energised again. A ferroresonance damping device at secondary side is

likelihood for controlling voltage transformer ferroresonance.

Voltage transformer can prevent by adding damping device such as resistor

at the secondary side. The resistance load burden will insert as soon as the

ferroresonance detected.

Presently, ferroresonance solution can acquire by using ATP simulation. The

program is very sensitive to circuit parameters and the magnetising characteristic of

the power and voltage transformer.

2.4 Case Study by David A.N. Jacobson: Example of Ferroresonance in

High Voltage Power System [3]

2.4.1 Objective

This paper represent three practical example of ferroresonance in a high

voltage power system (33kV or greater) and method of mitigating among ATP

simulation. The first example discusses a wound power transformer-circuit breaker

grading capacitor and the second discusses a transformer-circuit breaker grading

capacitor. The final case studies investigate open delta power transformer.

2.4.2 Wound Potential Transformer – Circuit Breaker Grading Capacitor

Circuit breaker used as an advanced interrupting .In high voltage

applications, multiple interrupting chamber connected in series are required to

interrupt the current and withstand the high recovery voltage. Grading capacitor

fitted in parallel with the each break to achieve an equal voltage distribution.

2.4.2.1 Description of Disturbance

Figure 2.8 demonstrates the single line diagram of wound power transformer

circuit at Dorsey s HVdc converter station 230kV. The station consists of four bus

sections on which the converter valves and transmission lines are terminated. Bus

A2 was removed for replacement breakers and to perform disconnects maintenance

and trip testing. Afterwards, potential transformer (V13F) failed. The switching

procedure de-energized bus and power transformer connected to energize B2

through grading capacitor. Normally connected to bus A2, but had been

disconnected. The ferroresonance effects failure to the power transformer.

Figure 2.8: Single line diagram of wound power transformer circuit

2.4.2.2 Simulation Result

The simulation result substantiation that ferroresonance was occurred at A2

bus. The voltage output waveform of phase A and B experienced indiscriminate

jumps between sub harmonic and normal oscillations but phase C did not practices

ferroresonance.

2.4.2.3 Mitigation Options

Resistors were connected on the power transformer secondary side of Dorsey

230kV substation. It explains that connected 200 ohm to the secondary of the system

was established to prevent ferroresonance. The damping resistor needs to dissipate

energy faster than the system can supply energy in order for the ferroresonant state

to disintegrate into ferroresonance 60 Hz operating mode.

2.4.3 Transformer – Circuit Breker Grading Capacitor


Breaker failed to latch while energize the induction motor at Dorsey

Converter Station. Ferroresonance over voltage occurred on B2 bus, where noise

level from SST1 that higher than normal. Figure 2.9 shows a single diagram of main

circuit component and Figure 2.10 shows a station service transformer.

Figure 2.9: A single diagram of main circuit component

Figure 2.10: A single diagram of station service transformer

2.4.3.2 Simulation result

Figure 2.11 exhibits simulation result of fundamental frequency mode of

ferroresonance due to high distortion and over voltage near 1.5p.u.

Figure 2.11: The output voltage waveform of bus voltage

2.4.3.4 Mitigation Option

The mitigation option of this case is being connected 200 ohm loading

resistors at secondary service transformer SST1 and SST2.

2.4.4 Open Delta Potential Transformer

Ferroresonance can happen during energization of the unloaded step down

transformer and interruption of a single line- to-ground fault on the low side of the

transformer. Three modes of ferroresonance can be observed in an open –delta

potential transformer. Low values of capacitance may cause third harmonic mode.

Medium values of capacitance may cause fundamental model of feroresonance and

higher values of capacitance could cause subharmonic modes of ferroresonance.


Figure 2.12 shows the single diagram of open –delta potential transformer.

The purpose of grounding bank is to provide zero sequence current during single

line-to-ground for ground fault protection relay to operate. Generally, the open –

delta potential transformer as a backup to ground bank to taken out for service for

maintenance.

Figure 2.12: Typical station layout

2.4.4.2 Simulation result

Figure 2.14(a) shows the unbalanced fundamental mode of ferroresonance.

Figure 2.14(b) shows the voltage output by connected loading resistor 83 ohm at

secondary side and Figure 2.14(c) explains the voltage output waveform with

connected grading bank.

Fig. 2.14: Example of output voltages, a) no mitigation, b) 83 ohm resistor

connected and c) Ground bank connected.

2.4.4.3 Mitigation Options

There are several possible solutions to prevent ferroresonance:

i. Replacing potential transformer with capacitive coupled voltage

transformer.

ii. Install potential transformer that are rated for line-to-line system

voltage.

iii. Install damping resistor in the broken – delta.

2.4.5 Conclusion

Three examples of circuit arrangements that can practice ferroresonance have

been presented. The impact of ferroresonance can vary from relay or control

disoperation to damage the equipment. Therefore mitigation strategies can be

designed before equipment is put into service to avoid ferroresonance by adding

loading resistors or replacement of the voltage transformer with capacitor voltage

transformer. Open delta voltage transformer ferroresonance can be prevented by

adding loading resistor across the open delta or close grounding transformer banks.

2.5 Summary

The first case study, it has been proven that ferroresonance in voltage

transformers and power transformers occurs due to nonlinear and dynamics in the

system. The case study analyses the performance of ferroresonance in the system by

comparing measurement data and the ATP-EMTP simulation results. The study

shows the measured and simulated voltages agree very well.

The second case study describes the ferroresonance phenomena when

connecting power transformers with overhead lines, or when connecting voltage

transformers with isolated sections of busbars. The energy in the capacitance of the

parallel lines or open circuit breaker grading capacitance is responsible for the

ferroresonance occurrence at 50Hz fundamental frequency or sub-harmonics

frequencies at 331/2Hz, 162/3Hz and 10Hz. The mitigation methods of

ferroresonance are by disconnecting the power transformer from the feeder, and for

the case voltage transformers, by adding damping devices at the secondary side of

the voltage transformer.

The third case study reports the practical examples of ferroresonance in a

high voltage system. Common elements in a ferroresonance circuit are a nonlinear

saturable inductor, capacitors, and a voltage source. The circuit also has a low-loss

characteristic. Prevention methods are by loading resistors and replacement of the

voltage transformer with a capacitor transformer.

CHAPTER 3

FERRORESONANCE

3.1 Introduction

This chapter discusses the theories, characteristics, types and symptoms

of ferroresonance.

3.2 Basics of Ferroresonance [4]

Ferroresonance does not occur regularly and it is very hard to analyze. Any

response to a sudden change in the system may jump out of a steady state into

ferroresonance condition. Therefore, the basics of ferroresonance must be

identifying. The simple RLC circuit in Figure 3.1 can be used as an aid in explaining

resonance and hence ferroresonance.

Figure 3.1: Resonance in RLC Circuit

This linear circuit is resonating when at some given source of frequency; the

inductive reactance (XL) and capacitive reactance (XC) cancel each other out. These

impedance values be forecast and they change with the frequency. Capacitance (C)

will always have a capacitive reactance as in equation (1) and inductance (L) will

always have an inductive reactance as in equation (1), where w is the frequency of

the source.

XC = 1/ jwC (1)

XL = jwL (2)

I = V / (R + XL - XC ) *V / R (3)

The current in equation (3), depends on the resistance (R). If this resistance is

small, then the current can become very large in the RLC circuit. The size of current

during resonance is equation (3).

If the inductor in Figure (2) replaced by an iron cored non-linear

inductor, the exact values of voltage and current cannot be predicted as in a

linear model. Equation (3) will not indicate the size of current produced. The

inductance becomes nonlinear due to saturation of flux in the iron core. The

understanding that ferromagnetic material saturates is very important.

Ferromagnetic material has a property of causing an increase to the magnetic

flux density, and therefore magnetic induction.

Figure 3.2: Magnetization Curve

As the current is increased, the magnetic flux density until a certain point

where the slope no longer linear and an increase in current lead to smaller and

smaller increases in magnetic flux density. This has been identified as the

saturation point. Figure 3.2 illustrates the relationship between magnetic flux

density and current. As the current increases in a ferromagnetic coil past the

saturation point, the inductance of the coil changes very quickly. This allows the

current to take on very unsafe high values. These high currents make damage on

the transformer. Most transformers have cores made from ferromagnetic

material. This is why ferroresonance is a concern for transformer operation.

When ferroresonance happens, it can be identify by certain distinct

characteristics. In ferroresonance, because the steel core is driven into saturation

so an audible noise occurs. As the core goes into a high flux density,

magnetostriction forces cause movement in the core laminations. This sound is

different from the normal hum of a transformer. Ferroresonance can cause high

over-voltages and currents. This can cause electrical damage to both the primary

and secondary circuits of a transformer. The heating cause by over-currents may

cause permanent damage to transformer insulation. Eventually, the transformer

could fail completely.

3.3 Main Characteristic [ 4 ]

Figure 3.3 is a basic series ferroresonance circuit and the curve obtained

from of the circuit shown in figure 3.5 and 3.6. These curves, illustrate the

following characteristics of ferroresonance:

i. Sensitivity to system parameter values, jump phenomenon

ii. Sensitivity to initial condition

Figure 3.3: Basic series ferroresonance circuit parameter

3.3.1 Sensitivity to system parameter values, jump phenomenon

Figure 3.4 illustrates the peak voltage VL at the terminals of the non-

linear inductance as a function peak amplitude E of the sinusoidal voltage

source.

Figure 3.4: Sensitivity to system parameters and the jump phenomenon

By gradually building up peak amplitude E from zero, the curve shows

that there are three different types of behaviour according to the value or E, as

well as the jump phenomenon:

i. For E = E1, the solution (M1n) is unique, and this corresponds to

the normal state (in the linear ),

ii. For E = E2, there are three solutions (M2n, M2i, M2f), two of which

are stable (M2n and M2f). M2n corresponds to the normal state,

whereas M2f corresponds to the ferroresonant state. The dotted

part of the curve corresponds to unstable states.

iii. For E = E’2, the voltage VL suddenly moves from the point M2 to

the point M’2 (the jump phenomenon). The point M2 is known as

a limit point,

iv. For E = E3, only the ferroresonance state (M3f) is possible.

v. When the value of E decreases from E3, the solution suddenly

moves from the point M1 (second limit point) to the point M’1.

vi. A small variation in the value of a system parameter or a transient

can cause a sudden jump between two very different stable steady

states.

3.3.2 Sensitivity to initial conditions

Whether M2n or M2f obtained depends on the initial conditions. Figure

3.5 illustrates the trajectories of the transient of pairs (Ф, VC) as a function of

time for different initial conditions (M01 and M02). Curve C describes a

boundary. If the initial conditions (residual flux, voltage at capacitor terminals)

are on one side of the boundary, the solution converges to M2n. If the initial

conditions are on the other side, the solution converges to M2f. As the point M2i

belongs to the boundary, the steady state effectively reached around this point is

extremely sensitive to the initial conditions.

Figure 3.5: Sensitivity initial condition

3.4 Classification of Ferroresonance Modes [4]

The type of ferroresonance can identify by the spectrum of the current

and voltage signals. The characteristics of each type of ferroresonance listed

below [4]:

i. Fundamental mode

ii. Subharmonic mode

iii. Quasi –periodic mode

iv. Chaotic mode

3.4.1 Fundamental mode

Figure 3.6 shows the diagrams to explain fundamental mode. The

voltages 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 reduced to a point far

removed from the point representing the normal state.

Figure 3.6: Diagrams illustrating the fundamental mode of ferroresonance

3.4.2 Subharmonic mode

Figure 3.7 shows the diagrams to explain the sub harmonic modes. The

signals are periodic with a period nT which is a multiple of the source period.

This state known as sub harmonic n or harmonic 1/n. Sub harmonic

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)

Figure 3.7: Diagrams illustrating the sub harmonic mode of ferroresonance

3.4.3 Quasi-periodic mode

Figure 3.8 shows the diagram for the quasi-periodic mode. This mode 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).

Figure 3.8: Diagrams illustrating the quasi-periodic mode of ferroresonance

3.4.4 Chaotic mode

Figure 3.9 shows the explanation for the chaotic mode. The

corresponding spectrum continuous, i.e. it not cancelled for any frequency. The

stroboscopic image made up of completely separate points occupying an area in

plane v, i known as the strange attractor.

Figure 3.9: Diagrams illustrating the chaotic mode of ferroresonance

Therefore, it can conclude that the ferroresonance is a complex

phenomenon in which there are several steady states for a given circuit, the

appearance of these states is highly sensitive to system parameter values and the

appearance of these states is highly sensitive to initial conditions.

Small variations in the value of a system parameter or a transient may

cause a sudden jump between two very different steady states and initiate one of

the four ferroresonance types. The modes most commonly encountered are the

fundamental and subharmonic ones. Abnormal rates of harmonics, over voltages/

currents, either as stable oscillation or as transients caused by ferroresonance,

often represent a risk for electrical equipment. Steady state ferroresonance

sustained by the energy supplied by the power system.

3.5 Power System Ferroresonance

Ferroresonance in a power system can result in any of the following,

alone or in combination [5]:

i. high sustained overvoltages, both phase to phase and phase to ground,

ii. high sustained overcurrents,

iii. high sustained levels of distortion to the current and voltage waveforms,

iv. transformer heating and excessively loud noise,

v. electrical equipment damage (thermal or due to insulation breakdown)

vi. apparent mis-operation of protective devices,

There are four elements for ferroresonance to occur [5]:

i. A sinusoidal voltage source -A power system generator will do quite

nicely.

ii. Ferromagnetic inductances -These can be power transformers or voltage

transformers.

iii. Capacitance -This can come from installed power system capacitors, the

capacitance to ground of transmission lines, the large capacitance of

underground cable, or the capacitance to ground of an ungrounded

system.

iv. Low resistance - This can be lightly loaded power system equipment, low

short circuit power source, or low circuit losses.

3.6 Symptoms of Ferroresonance

There are several modes of ferroresonance with varying physical and

electrical displays. Some have very high voltages and currents while others have

voltages close to normal. In this section, it will reveal the symptoms of

ferroresonance.

3.6.1 Audible Noise

Audible noise occurs when the steel core driven into saturation.

Therefore

the core goes into a high flux density, it make due to the magnetostriction of the

steel and to the actual movement of the core laminations. Ferroresonance happen

when the noise is louder than the normal hum of transformer.

3.6.2 Overheating

Another symptom of the high magnetic field is due to stray flux heating

in parts of the transformer where magnetic flux come across into the tank wall

and other metallic parts because of the core saturated repeatedly. The effect is

bubbling of the paint on the top of the tank. Ferroresonance happen, when it has

continued extended to reason overheating of some of the larger internal

connections. This may cause damage insulation structures.

3.6.3 Arrester and Surge Protector Failure

The arrester failures related to heating of the arrester block. Normally,

the people determine an open fused cut out and just replace the fuse. In the

meantime, the arrester becomes very hot on the phase and goes into thermal

runaway upon restoration of full power to that phase. The failure is often from

the arrester housing. Under-oil arresters are less vulnerable to the problem

because it can dissipate the heat due to the ferroresonance current more quickly.

Nowadays surge protectors are common in computers, office equipment and

factory machines.

3.6.4 Flicker

Utility customers often face with the problem of a wavering voltage

magnitude. For example, the light bulbs will flicker between very bright and

dim. In addition, some electronic appliances are reportedly very susceptible to

the voltages that result from some types of ferroresonance, the alleged failure

mode is unknown.

3.6.5 Cable Switching

The transformers themselves can usually withstand the over voltages

without failing. However, it not accepted for stress repeatedly because the forces

often shake things loose inside and scrape insulation structures. The cable also in

little risk unless its insulation stress reduced by aging or physical harm.

Some utilities will not execute the cable switching involving three-phase

pad mount transformers without first verifying that there is substantial load on

the transformers. It because the currents could be much higher than expected and

the peak voltages could be high enough to cause reigniting of the arc. Therefore,

it may be difficult to clear arcs when pulling cable elbows if ferroresonance in

progress.

The solution of ferroresonance during cable switching is to always drag

the elbows and energize the unit at the primary terminals. These will no external

cable capacitance to cause ferroresonance. Only a little internal capacitance and

the losses of the transformers are mostly enough to prevent resonance with the

small capacitance.

CHAPTER 4

METHODOLOGY

4.1 System Modelling

The main emphasis is to identify the models of substation components to use

in the ferroresonance studies. For each component, the importance of the model

parameters will describe and typical values shall be providing. Afterwards, the

models will be simulated using ATP-EMTP program and the output is to be

analyzed, in particular, whether ferroresonance has occurred or otherwise.

4.2 ATP-EMTP Simulation

The ATP is the PC version of the Electromagnetic Transients Program

(EMTP). The EMTP is primarily a simulation program of the electric power

industry. It a computer simulation program specially designed to study transient

phenomenon in the power system. It contains a large variety of detailed power

equipment models or builds in setups that simplify the tedious work of creating a

system representation. Generally, this simulation software can use in design of an

electrical system or in detecting or predicting an operating problem of a power

system.

ATP is a universal program system for digital simulation of transient

phenomena of electromagnetic as well as electromechanical nature. With this digital

program, complex networks and control systems of arbitrary structure can simulate.

ATP-EMTP used in this simulation process of observing the electrical response of

the transmission system. To represent the electrical response of the transmission

system, electrical model of the transmission system apparatus have to be select and

validated to gain high accuracy result.

4.3 Selected Model and Validation

Models are circuit or mathematical or electrical representation of physical

equipment so that its characteristic determined by means of an output when applied

with certain input. In ATP-EMTP simulation, the input and output that usually

observed are current, voltage, power and energy. A complete set of representation of

a transmission system are made of models for all of the power system components.

4.4 Resistor and Capacitor Model

There are various types of resistors and capacitors available in the ATP

library. This can vary from linear to non-linear and capacitor braches. However, for

this work only adopted linear branch capacitor and resistor and focusing on the non-

linear inductance.

4.5 Overhead Transmission Lines [6]

Overhead transmission lines model depends on the line length and the

highest frequency to be simulated. This simulation, the overhead transmission lines

are double circuit 400kV. The length of the overhead line circuit is approximately

37km. It represented by multi-phase models considering the distributed nature of the

line parameters due to the range of frequencies involved, phase conductors, shield

wires are explicitly modelled between towers, and only a few spans are considered.

The line parameters being clarify by line constants, using the tower structure

geometry and conductor data as input.

4.6 Transformer models [7]

Transformer model can be classified into three types. The first type is matrix

representation (BCTRAN model). The second type is saturable transformer

component model to multi-phase transformer. Both type of model can be

implemented in the ATP-EMTP. The third type is topology-based models [7].

Matrixrepresentation(BCTRANmodel)willbeusedtorepresentsingle

and three‐phase, two and three winding transformers by considering the

numberofphases,thenumberofwindings,thetypeofcore(singlephasecore,

triplexandthreephaseshelltype)andtestfrequency.Theparameterofopen

circuit and short circuit data can be obtained from factory test data. In

addition, clarify the ratings of the line‐voltage, rated power and type of

coupling.

Besides that, identify the winding connection such as an

autotransformer, wye and delta. If the connection is an auto transformer or

wye,theratedvoltageisautomaticallydividedby√3togetthewindingvoltage.

If autotransformer selected for primary and secondary winding (HV‐LV) the

impedancearerecalculateasshownbelow[8]:

Z*H‐L=ZL‐H(VH/VH–VL)2 (4)

Z*L‐T=ZL‐T (5)

Z*H‐T=ZL‐H.VH.VL+ZH‐T.VH+ZL‐T.VL(6)

(VH–VL)2(VH–VL)(VH–VL)

whereZL‐H, ZL‐T ,ZH‐T aretheimpedance(%)valuesandZ*H‐L ,Z*L‐TandZ*H‐T

arevalesthatwrittentotheBCTRANfile.

BCTRAN transformer of ATPDraw, which use an admittance matrix

representation of the form:

[v] = [R] [i] + [L] [di / dt] (7)

where [R] and j ù [L] are the real and the imaginary part of the branch impedance

matrix. In transient calculations can represent as;

[di/ dt] = [L]-1 [v] – [L] -1 [R] [i] (8)

For simulation of saturable cores, excitation may be omit from the matrix

description and attached externally at the model terminals in the form of non-linear

elements.

4.6.1 Nonlinear and Frequency-Dependant Parameters [7]

Some transformer parameters are non-linear and/or frequency dependent due

to three key effects: saturation, hysteresis and eddy currents. Saturation and

hysteresis are included in the representation of the iron core and introduce distortion

in waveforms. Excitation losses are cause by hysteresis and eddy current effects,

although in modern transformers they are mostly due to eddy current.

4.6.1.1 Modeling of Iron Cores

Iron core behaviour is represent by a relationship between the magnetic flux

density B and the magnetic field intensity H. Hysteresis loops usually have a

negligible influence on the magnitude of the magnetizing current, although

hysteresis losses and the residual flux can have a major influence on some transients,

such as inrush currents. Magnetic saturation of an iron core is representing by the

hysteretic curve, the B–H relationship that would be obtain if there were no

hysteresis effect in the material.

The saturation characteristic can be modelled by a piecewise linear

inductance with two slopes, since increasing the number of slopes does not

considerably improve the accuracy. In ferroresonance, the detailed of the saturation

characteristic is required. The specification of such inductor requires a curve relating

the flux linkage, to the current, i. The information usually available is the rms

voltage as a function of the rms current.

4.6.1.2 Modelling of Eddy Current Effects

Eddy current effects, occur at the same time in a loaded transformer that

result in a non-uniform distribution of current in the conductors, and manifest

themselves as an increase in the effective resistance and winding losses with respect

to those for direct current eddy current effects in transformer windings can be model

by Foster equivalent circuits. These circuits must be of infinite order exactly to

reproduce the impedance at all frequencies. However, a computationally efficient

circuit can be deriving by fitting only at certain pre-established frequencies. A series

model of order equal or less than 2 is adequate for low-frequency transients. A

change in the magnetic field induces also eddy currents in the iron.

Because of this, the flux density will be lower than that given by the normal

magnetization curve. As frequency changes, flux distribution in the iron core

lamination also changes. For high frequencies, the flux is confine to a thin layer

close to the lamination surface, whose thickness de-creases as the frequency

increases. This indicates that inductances representing iron path magnetization and

resistances representing eddy current losses are frequency dependent. Efficient

models intended for simulation of frequency dependent magnetizing inductances

have been derive by synthesizing Cauer equivalent circuits to match the equivalent

impedance of either a single lamination or a coil wound around a laminated iron

core limb. Inductive components of these models represent the magnetizing

reactances and have to make non-linear to account for the hysteresis and saturation

effects.

Since the high frequency components do not contribute appreciably to the

flux in the transformer core, it can be assume that only low frequency components

are responsible for driving the core into saturation. It can be justifiable to represent

as non-linear only the first section of the model, so for low frequency transients an

equivalent circuit with order equal or less than two may suffice.

CHAPTER 5

SIMULATION OF 400KV DOUBLE CIRCUIT CONFIGURATION

5.1 Introduction

In this work, a 400kV/275kV double circuit extra high Voltage substation

was chosen for the simulation study. The purpose of the simulation is to determine

conditions in which ferroresonance can occurs. If a ferroresonance does occur, then

how best can be the ferroresonance be mitigated or its effect minimised. Some of

the components’ data are not available. Hence, in this simulation work, typical data

or estimates were used for each case.

5.2 Simulation Procedures

In order for the simulation work to be successfully carried out, the following

procedures were adopted:

(i) Determinations of all parameters such as the overhead transmission line,

power transformer saturation characteristics, the power transformer and

shunt capacitance, etcetera. Estimate been made in the cases where actual

physical values cannot be obtained.

(ii) Develop an equivalent circuit to represent the actual power transformer and

its interconnections based on actual station.

(iii) Analysis of voltage and current output from an equivalent circuit.

(iv) Determine whether ferroresonance occurs or otherwise under the given

circuit parameters.

(v) Determine the mitigation techniques to prevent ferroresonance from

occurring.

The first part of the process was to gather information on the system. This

involved finding circuit diagrams, information on transformers, capacitors etcetera

and finally the nature of the load – magnetization characteristic and type of non-

linear inductance.

5.3 Circuit description

The 400kV double circuits used in this simulation were taken from

Brinsworth / Thorpe Marsh (UK transmission network) design parameter [9]. The

purpose is to exhibit of ferroresonance to occurring on the system. The length of the

parallel overhead line circuit is approximately 37 km and the feeder has a 1000MVA

400/275/13kV power transformer. Figure 5.1 shows single diagram of the

Brinsworth /Thorpe Marsh circuit arrangement.

Figure 5.1: A single line diagram of the Brinsworth/Thorpe Marsh circuit

Following is the circuit equipment condition:

i. Before switching (Transformer energized)

- All disconnector and circuit breaker were close.

ii. After switching (Transformer de-energized)

-Disconnector X303, circuit breaker X420 and T10 were open.

-Disconnector X103 was close.

5.4 Simulation Model

The system arrangement in Figure 5.1 can be reduce to equivalent circuit

in Figure 5.2. The main components of the network are;

i. Typical overhead line spacing for a 400kV double circuit;

ii. BCTRAN transformer matrix mode ;

iii. Non-linear inductance;

iv. Resistor and capacitor.

x

x

x

x

TR1

TR2

X3033

X1033

X420

T100

Thorpe Marsh 400kV

Brinsworth 275kV

Overhead line 37km

Figure 5.2: Equivalent circuit of power transformer

Transformer nonlinear characteristic

Series and Shunt Capacitances of Windings

Disconnector Circuit Breaker

Cable 170 m

Circuit Breaker

5.4.1 Typical overhead line spacing for a 400kV double circuit

In this simulation, the J.Marti model is used. The model is dependent on

frequency with constant transformation matrix. The geometrical and material data

for overhead line conductors are specify as below [6];

♦ Phase no Phase number. 0=ground wire (eliminated)

♦ RESIS: Conductor resistance at DC (with skin effect) or at Freq. Init.

(no skin effect)

♦ REACT: The frequency independent reactance for one unit spacing

(meter/foot). Only available with no skin effect.

♦ Rout: Outer radius (cm or inch) of one conductor

♦ Rin: Inner radius of one conductor. Only available with skin effect.

♦ Horiz: Horizontal distance (m or foot) from the center of bundle to a

user selectable reference line.

♦ VTower: Vertical bundle height at tower (m or foot).

♦ VMid: Vertical bundle height at mid-span (m or foot).

The height h= 2/3* VMid + 1/#*VTower is used in the

calculations.

If Auto bundling checked:

♦ Separ: Distance between conductors in a bundle (cm or inch)

♦ Alpha: Angular position of one of the conductors in a bundle,

measured counter-clockwise from the horizontal line.

♦ NB: Number of conductors in a bundle.

Figure 5.3 shows the ATP draw input window for the transmission

line/cable. A cable length of 37 km was used. Figure 5.4 shows the line

configuration.

(a) :Selectionofsystemtype(Line/Cable)

(b) Specificationofconductordata

Figure5.3:Line/Cabledialogbox. (a)Selectionof type(Line/Cable),standard

data(groundingandfrequency)andmodeldata(typeofmodelandfrequency)

(b)Specificationofconductordata.

Figure 5.4: Line configuration

5.4.2 BCTRAN transformer model

In this simulation, BCTRAN transformer matrix modelling represent three

phase and three winding transformer. The transformer characteristics available from

test report of 1000MVA transformer shown in Table 5.1.

Table 5.1: Transformer Characteristic

Rating 1000MVA

Type 400/275/13 kV (auto)

Core Construction Five Limb Core

Vector Yy0

Bolt main No

Bolt Yoke No

Vector% Ratio 4 & 5/Y/M 60/60/100

The transformer has been model in the BCTRAN component of ATP Draw

which use an admittance matrix representation of the form [9];

[ I ] = [ Y ]* [ V ] (9)

and in transient calculations can be represented as

[ di/dt ] = [ L ]-1 [ V ] – [ L ]-1 * [ R ][ I ] (10)

The elements of the matrix are deriving from open circuit and short circuit test that

made in the factory. Table 5.2 shows the data of short test factory.

Table 5.2: Transformer short circuit factory data

Impedance Power (MVA) Loss (kW)

HV-LV 15.8 1000 1764

HV-TV 117.2 1000(60) 28677 (1720.62)

LV-TV 91.5 1000(60) 29875 (1792.5)

The data used in this simulation model include impedances and losses are

rate at 1000 MVA (400/275/13kV) [9]. Figure 5.5 shows the ATPDraw input

window consist of the number of phases, the number of windings, the type of core

and test frequency. The BCTRAN data is based on the test report of a 1000 MVA

(400/275/13 kV) transformer shown in Table 5.1 and Table 5.2. It used

autotransformer-winding connection for the primary and secondary winding (HV-

LV). Therefore, the impedance calculated as shown in equation (4), (5), and (6).

(a) Open Circuit Data

(b) Short Circuit Data

Figure 5.5: BCTRAN dialog box of data according to Table 5.1 and Table 5.2 (a)

Open Circuit Data (b) Short Circuit Data.

Saturation effect has considered by attaching the non-linear inductances.

Furthermore, the average no load loss at rated voltage and frequency was 74.4kW

and average magnetizing current was 0.012% at 1000MVA base. In this simulation,

the zero sequence data was not available because the model has been set equal to the

positive data.

5.4.3 Non-linear inductance

The saturation effect has considered by attaching the non-linear inductance

(Type-98) characteristic externally in form of a non-linear inductive element branch.

Non-linear can be modelled as a two slope piecewise linear inductances with

accuracy. The slope in the saturated region above the knee reflects the air core

inductance, which is almost linear, and low compared slope in the unsaturated

region. Table 5.3 shows the transformer magnetization curve based on

manufacturer’s data. [9]

Table 5.3: Transformer magnetizing characteristic

Current (A) Flux Linkage (Wb-Turn)

7.18 48.77

7.85 52.02

8.35 55.27

19.37 58.52

35.40 61.77

78.48 65.02

222.09 65.92

5531.04 66.72

Figure 5.6 shows the magnetic core characteristics curve that been

represented by peak flux linkages versus peak currents characteristic by using an

internal SATURA – routine. Subroutine SATURATION has designed to do the

conversion with some simplifying assumptions.

Figure 5.6: The saturation curve for nonlinear inductor

5.4.4 Resistor and Capacitor Model

There are various types of resistors and capacitors available in the ATP

library. This can vary from linear to non-linear and capacitor braches. However, for

this work only adopted linear branch capacitor and resistor and focusing on the non-

linear inductance.

5.5 Result of simulation for 400kV double circuit configuration

The sinusoidal AC supply peak voltage was 326.6 kV with the 50 Hz

frequency. Upon disconnected TR1, X103 is closed and circuit breaker X303, X420

and T10 disconnected after 0.25 second. In order to get the output voltage, it has to

observed and recorded before and after the open switching operation (after 0.25

second). Table 5.4 shows the simulation results for 400kV double circuit

configuration. Figure 5.7 to 5.12 show the output voltage and current waveform for

red, yellow, and blue phase.

Table 5.4: Simulation Result for 400kV double circuit configuration

Peak Voltage at Transformer

(kV)

Peak Current at Transformer

(A)

Phase

Before After Before After

Red 181 313 4 254

Yellow 183 308 4 243

Blue 180 307 3 246

Figure 5.7: The output voltage waveform at TR1 terminal- R phase

Figure 5.8: The output voltage waveform at TR1 terminal - Y Phase

Figure 5.9: The output voltage waveform at TR1 terminal -B Phase

Figure 5.10: The output current waveform at TR1 terminal- R Phase

Figure 5.11: The output current waveform at TR1 terminal –Y Phase

Figure 5.12: The output current waveform at TR1 terminal-B Phase

It can be concluded that the fundamental mode ferroresonance waveform

have been produced by simulation at specific time. After 0.25 second, the power

transformer voltage supposes to be zero but some how the voltage or current still

maintain.

5.6 Simulation by changing the magnetization characteristic of transformer

5.6.1 Simulation model

This simulation is to investigate the effect of changing the saturation curve of

the nonlinear inductance. Figure 5.13 shows the variation of magnetization curve. It

obtains by varying the curve 1. Once the data collected, it will gather into the

simulation.

Figure 5.13: Variation of magnetization curve

Table 5.6 to 5.8 show the value of transformer magnetizing characteristics curve 1 to

curve 4.

Table 5.5: Transformer magnetizing characteristic-curve 1


7.18 48.77

7.85 52.02

8.35 55.27

19.37 58.52

35.40 61.77

78.48 65.02

222.09 65.92

5531.04 66.72

3 2 1

4

FluxlinkedWb-T

Current (A)



7.18 48.77

7.85 52.02

8.35 55.27

19.37 58.52

35.40 61.77

78.48 65.02

222.09 65.92

4200.00 68.72



7.18 48.77

7.85 52.02

8.35 55.27

19.37 58.52

35.40 61.77

78.48 65.02

222.09 65.92

3000.00 75.73



7.18 48.77

10.00 52.02

20.00 55.27

30.00 58.52

50.00 60.77

90.00 61.09

5531.04 61.89

Figure 5.14 to 5.17 shows the saturation curve plotted using peak flux linkages as a

function of peak currents for nonlinear inductor Type 98.

Figure 5.14: The saturation curve 1


5.6.2 Simulation result

The simulation was carried out using different magnetization saturation

curves. In this simulation, four saturation curves have been presented. The

sinusoidal AC supply peak voltage is 326.6 kV. Upon disconnected TR1, X103 is

closed and circuit breaker X303, X420 and T10 disconnected after 0.25 second.

5.6.2.1 Simulation result for curve 1

Table 5.9 shows the effect of using the saturation curve 1. The output voltage

and current waveform of the red phase shown in Figure 5.18 and 5.19 but the

ferroresonance still occurs.

Table 5.9: The effect of using the saturation curve 1

Peak Voltage at

Transformer

(kV)

Peak Current at

Transformer

(A)

Curve


Ferroresonance

occurrence

R 181 313 4 254 Yes

Y 183 308 4 243 Yes

B 180 307 3 246 Yes

Figure 5.18: The output voltage waveform at TR1 terminal– R phase

Figure 5.19: The output current waveform at TR1 terminal– R Phase


Table 5.10 show the effect of using the saturation curve 2. The output

voltage and current waveform of the Red Phase had shown in Figure 5.20 and 5.21

but the ferroresonance still occurs.

Table 5.10: The effect of using the magnetization curve 2

Peak Voltage at

Transformer

(kV)

Peak Current at

Transformer

(A)

Curve


Ferroresonance

occurrence

R 181 208 2.48 225 Yes

Y 182 253 3.34 204 Yes

B 178 297 2.54 203 Yes

Figure 5.20: The output voltage waveform at TR1 terminal- R Phase

Figure 5.21: The output current waveform at TR1 terminal– R Phase


Table 5.11 shows the effect of using the saturation curve 3. The output

voltage and current waveform of the Red Phase shown in Figures 5.22 and 5.23 but

the ferroresonance still occurs.

Table 5.11: The effect of using the magnetization curve3

Peak Voltage at

Transformer

(kV)

Peak Current at

Transformer

(A)

Phase


Ferroresonance

occurrence

R 181 294 4 188 Yes

Y 183 173 3.34 51.74 Yes

B 178 296 0.013 125 Yes

Figure 5.22: The output voltage waveform at TR1 terminal– R Phase

Figure 5.23: The output current waveform at TR1 terminal – R Phase


Table 5.12 show the effect of using the saturation curve 4. Figure 5.23 and

5.25 show the voltage output is reduced after 0.25 second but the current output

shows that ferroresonance still occurs.

Table 5.12: The effect of using magnetization curve 4

Peak Voltage at

Transformer

(kV)

Peak Current at

Transformer

(A)

Phase


Ferroresonance

occurrence

R 181 60 6.7 165 Yes

Y 182 10 8.1 135 Yes

B 178 62 0.11 156 Yes

Figure 5.24: The output voltage waveform at TR1 terminal – R Phase

Figure 5.24: The output current waveform at TR1 terminal–R Phase

It can conclude that the fundamental mode ferroresonance waveforms have

presented. The above results show that changes in the magnetization curves of the

transformer do not actually prevent ferroresonance from occurring. This is due to

the already highly non-linear characteristic of the iron.

5.7 Mitigation Techniques

From the previous studies, there are a number mitigation method(s) been

used in order to dampen the occurrences of ferroresonance in the power system. In

this simulation, mitigation techniques were analysed based on the previous studies

by adding resistor at secondary side of the power transformer.

Figure 5.26: Simulated power transformer circuit by adding loading resistor at secondary side (A)

A

5.7.1 Simulation model

Figure 5.26 shows the simulated power transformer circuit by adding

resistor at secondary side. Upon disconnection of TR1, X103 is closed and circuit

breakers X303, X420 and T10 disconnected after 0.25 second. In order to get the

output voltage it must be observe and recorded before and after switching operation

(after 0.25 second).

5.7.2 Simulation results

It suggested that loading resistances values from 10 Ω until 30k Ω could be

use to prevent ferroresonance. Table 5.13 shows the effect of adding the resistor on

secondary side for the case of red phase. Figure 5.27 to 5.32 show the output

waveform when a 1kΩ loading resistance was used. Figure 5.33 to 5.38 show the

output waveform when a 30k Ω loading resistance was used.

Table 5:13: The effect by adding resistor on secondary side - R Phase

Peak Voltage at

Transformer

(kV)

Peak Current at

Transformer

(A)

Resistor

Value

(Ω )


Ferroresonance

occurence

10 143 0 438 0 No

50 174 0 345 0 No

100 177 0 838 0 No

500 124 0 117 0 No

1k 125 0 59 0 No

1.2k 125 0 49 0 No

2k 125 5.1 29 0.1 No

4k 125 1 15 0.8 No

6k 125 7.7 10 0.7 No

10k 125 11 6 0 No

20k 124 160 2.9 241 Yes

30k 125 224 1.97 282 Yes

Figure 5.27: The output voltage waveform by adding R=1k ohm resistance, R Phase

Figure 5.28: The output voltage waveform by adding R=1kohm resistance ,Y Phase

Figure 5.29: The output voltage waveform by adding R=1k ohm resistance, B Phase

Figure 5.30: The output current waveform by adding R=1k ohm resistance, R Phase

Figure 5.31: The output current waveform by adding R=1k Ohm resistance, Y Phase

Figure 5.32: The output current waveform by adding R=1k Ohm resistance, B Phase

Figure 5.33: The output voltage waveform by adding R= 30k Ohm resistance, R

Phase

Figure 5.34: The output voltage waveform by adding R= 30k Ohm resistance, Y

Phase

Figure 5.35: The output voltage waveform by adding R= 30k Ohm resistance, B

Phase

Figure 5.36: The output current waveform by adding R= 30k Ohm resistance, R

Phase

Figure 5.37: The output current waveform by adding R= 30k Ohm resistance, Y

Phase

Figure 5.38: The output current waveform by adding R= 30k Ohm resistance, B

Phase

It can be concluded that the fundamental mode ferroresonance waveform

have been produced by simulation at specific time. Loading resistance acts as

damping elements that can prevent ferroresonance from occurring. The suggested

loading resistance is ranging from 10 Ω to 10k Ω. If the higher resistances are used

(more than 10k Ω), it fails to prevent ferroresonance from occurring. This method is

shown to able to absorb energy during ferroresonace conditions and therefore damp

out the phenomenon.

CHAPTER 6

CONCLUSION AND RECOMMENDATIONS

6.1 Conclusion

The simulation of ferroresonance in 400kV double circuit substation has

been presented in this work. It is established when one side of the double circuit

transmission line connected to the transformer is de-energized but remain energized

because of coupling from the parallel circuit. To avoid ferroresonance, the parallel

circuit should be switch off. Failure to detect a ferroresonance condition can lead to

overheating the transformer. Both instrument and power transformers can be subject

to ferroresonance.

The effects of changing the magnetization characteristics of the power

transformer were also presented. It seen that the variation of the magnetization curve

does not affect the ferroresonance. This is due the highly non-linear characteristic of

the iron. An actual magnetization curves may have to be obtaining from either the

manufacturer or a field test to achieve the reliable ATP simulation.

A number of mitigation methods have been proposed in order to dampen

the occurrences of ferroresonance in power system. The appropriate values of

resistance to eliminate ferroresonance have been presented in this work.

6.2 Recommendations

It is suggested to determine the values of R, L and C for the suspected

circuit that will support ferroresonance occur. Then, identify the required

resistance value to eliminate ferroresonance. The R, L and C elements in the

system will give inductive and capacitive reactances in series or parallel with the

source of the voltage need to be identified. In addition, the actual magnetization

curves have to be obtained from either the manufacturer or field test.

Carefully evaluate the location and value of resistors added to counteract

ferroresonance. It depend on the transformer connection of the suspected circuit,

the proper value for the resistive load may be connected either in the secondary

or the neutral to ground of the transformer. Nevertheless, when the resistor is

added between neutral and ground it will reduce the fault current. Therefore the

value of resistance must select to the specific ferroresonance damping

requirements, if not interfering with circuit fault protection system.

List of References

1. Zia Emin,, Yu Kwong Tong.(2001). Ferroresonance Experience in UK:

Simulations and Measurements IPST '01 - Rio de Janeiro, Brazil, June 24-

28,Paper 006.2

2. Y K Tong (1997) NGC Experience on Ferroresonace in Power Transformer

and Voltage Transformer on HV Transmission Systems. IEE

3. David A. N. Jacobson, Examples of Ferroresonance in a High Voltage Power

System Member, IEEE

4. Electrical Electrical Engineering Tutorials: Ferroresonance- Introduction,

Classification and Characteristic 20 March, 2007

5. Technical Buletin — 004a. Ferroresonance, (2002)

6. ATPDRAW version 3.5 for Windows 9x/NT/2000/XP Users' Manual (2002)

7. Juan A. Martinez-Velasco. Bruce A.Mork, Transformer Modeling for Low

Frequency Transient- The State of the Art IPST 2003, International

Conference on Power Systens Transients.

8. Hans.K. Hokaidan, Laszlo Pikler, Bruce A. Mork, New Features in

ATPDraw Version 3.5. EEUG Meeting 9-10th Hungary

9. Charalambos Charalambous, Z.D. Wang, Jie Li, Mark Osborne and Paul

Jarman.(2007)Validation of a Power Transformer Model for Ferroresonance

with System Tests on a 400 kV Circuit. IPST

10. B. Peter Daay. Ferroresonance Destroy Transformers (1191). IEE

11. M.R Iravani, Chair, A. K. S. Chaudhary, W. J. Giesbrecht, I. E. Hassan, A.

J.F.Keri, K. C. Lee,J. A. Martinez, A. S. Morched, B. A. Mork, M. Parniani,

A. Sharshar, D. Shirmohammadi, R. A. Walling, and D. A. Woodford.(2000)

Modeling and Analysis Guidelines for Slow

12. Transients—Part III: The Study of Ferroresonance. IEEE Transactions, Vol

15. No.1

13. S. Mozaffari, M.Sameti, A.C.Soudack. Effect of initial conditions on chaotic

ferroresonance in power transformers. IEE no. 19971459

14. ZhuZhu Xukai, Yang Yihan, Lian Hongbo, Tan Weipu.(2004) Study on

Ferruresonance due to Electromagnetic PT In Ungrounded Neutral System .

IEEE

15. Bernard C. Lesiutre, Jama A. Mohamed, Aleksandar M. Stankovic, (2000)

Analysis of Ferroresonance in Three-Phase Transformer.IEEE Percon

16. S. Mozaffsri, M. Samet, A.C Soudack. (1997) Effect of Initial Conditions on

Chaotic Ferroresonance in power transformer. IEE .Proceeding online no.

1971459

17. Bruce A.Mork., Parameters for Modeling Transmission Lines and

Transformers in Transient Simulations. (2001) IEEE

18. Marta Val Escudero,Ivan Duduryah, Miles Redfm.: Understanding

Ferroresonance ESB International, Ireland

19. P. Ferracci: Ferroresonance, Cahier Technirue 190 (1998). Group Schneider.

20. Dr. D.A.N. Jacobson , Dr. R. W. Menzies (2001). Investigation of Station

Service Transformer Ferroresonance in Manitoba Hydto’s 230kV Dorsey

Converter Station. IPST

study on the non linear characteristic of power

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