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TitleParameter estimation for transformer modeling
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Table of Contents
                            Michigan Technological University
Digital Commons @ Michigan Tech
	2002
Parameter estimation for transformer modeling
	Sung Don Cho
		Recommended Citation
COVER
ABSTRACT
ACKNOWLEDGMENTS
TABLE OF CONTENTS
LIST OF FIGURES
CHAPTER 1. INTRODUCTION
CHAPTER 2. INTRODUCTION TO TRANSFORMER MODELS
	2.1 Basic Transformer Structure
	2.2 STC (Saturable Transformer Component) Model
	2.3 BCTRAN Model
	2.4 Duality Transformation
	2.5 Coil/Winding Capacitance with Damping Resistance
	2.6 Parameter Estimation using Engineering Optimization
CHAPTER 3. THREE-PHASE TRANSFORMER MODEL
	3.1 STC Model
	3.2 BCTRAN Model
	3.3 Duality-Based Model
CHAPTER 4. PARAMETERS FOR TRANSFORMER MODEL
	4.1 Frequency-Dependency of Coil Resistance
	4.2 Winding Capacitance
	4.3 Magnetic Core Saturation
	4.4 Nonlinear Core Loss
	4.5 Separation of Eddy Current and Hysteresis Losses
	4.6 Hysteresis Loop Model
CHAPTER 5. DUALITY-DERIVED MODEL FOR THREE-PHASE TRANSFORMER
	5.1 Five-Legged Core Transformer
	5.2 Three-Legged Core Transformer
	5.3 Shell-form Transformer
CHAPTER 6. PARAMETER ESTIMATION FOR TRANSFOMER MODELS
	6.1 The Five-Legged Core Transformer
		6.1.1 Leakage Inductance Derivation
		6.1.2 Practical Implementation of Leakage inductance
		6.1.3 Core Saturation Model
		6.1.4 Core Loss Model
		6.1.5 ATP Implementation of Overall Transformer Model
	6.2 Three-Legged Core Transformer
		6.2.1 Leakage Inductance
		6.2.2 Core Saturation Model
		6.2.3 Core Loss Model
		6.2.4 ATP Implementation of Overall Transformer Model
	6.3 Shell-form Transformer
		6.3.1 Leakage Inductance
		6.3.2 Core Saturation
		6.3.3 Core Loss Model
		6.3.4 ATP Implementation of Overall Transformer Model
CHAPTER 7. SIMULATIONS FOR MODEL EVALUATION
	7.1 Comparison with BCTRAN Model
	7.2 Black Start Energization Cases at IVH Substation
		7.2.1 System Description
		7.2.2 Transformer Model
		7.2.3 Transmission Line Models
		7.2.4 Synchronous Generator Model
		7.2.5 Case Study Results
CHAPTER 8. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
REFERENCES
APPENDIX A: SAMPLE ATP DATA FILE
APPENDIX B: MATLAB CODE LISTING
APPENDIX C: TRANSFORMER FACTORY TEST REPORT
                        
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Michigan Technological University
Digital Commons @ Michigan

Tech
Dissertations, Master's Theses and Master's Reports
- Open

Dissertations, Master's Theses and Master's Reports

2002

Parameter estimation for transformer modeling
Sung Don Cho
Michigan Technological University

Copyright 2002 Sung Don Cho

Follow this and additional works at: http://digitalcommons.mtu.edu/etds

Part of the Electrical and Computer Engineering Commons

Recommended Citation
Cho, Sung Don, "Parameter estimation for transformer modeling", Dissertation, Michigan Technological University, 2002.
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Page 2

PARAMETER ESTIMATION
FOR TRANSFORMER MODELING




By


SUNG DON CHO




A DISSERTATION


Submitted in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY
ELECTRICAL ENGINEERING







MICHIGAN TECHNOLOGICAL UNIVERSITY

December 2002

Copyright  Sung D. Cho 2002

Page 113

- 96 -

Results of MATLAB Simulations

Using the optimization technique Fmincon, the results are a= 8.9379 and b=

0.5714 for the B-H equation. Figure 6.8 shows the B-H curve. The calculated RMS

currents for three phases are [109.2177 102.3031 102.3032]A at 100% voltage. The

calculated average rms current is 104.61 and the difference from test report is 0.412 A.

The calculated RMS phases currents are [229.3830 221.6717 221.6718]A at 110%

voltage. The calculated average RMS current is 224.24 A and the difference between test

report is 0.13 A.

0 50 100 150 200 250 300 350 400
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

H (A/m)

B
(

T
)



Figure 6.8 B-H Curve for Each Section

The magnetizing curves have the magnetic induction (B in Tesla) on the vertical

axis and magnetizing force (H in A/m) on the horizonal axis. However, in the electrical

equivalent circuit model, the magnetization inductance is represented by a piecewise

linear λ-i curve. As explained in Section 4.3, it is possible to convert magnetic induction

Page 114

- 97 -

to flux linked (λ in Wb-turn) and magnetizing force to current (i in A). The scaling

factors are given as:

λ = B × A × N (6.25)


Where, B = the magnetic induction in Tesla, A = the core cross section in m2
N = the number of winding turns of the winding the induction is referred
to.

The relation between magnetizing force and current is given as:

i=H× L (6.26)


where, H = Magnetizing force in A/m, i = current in ameperes
L = the length of the flux path through the core in meters.

Figure 6.9 shows the λ-i curve for each core section of the example transformer.

Figure 6.10 shows the current waveforms of core sections at 100% voltage simulated

using MATLAB. Figure 6.11 shows the current waveforms of lines at 100% voltage

simulated using MATLAB.

0 50 100 150 200 250 300 350 400
0

10

20

30

40

50

60

i (Ampere)

La
m

bd
a

(W
b-

t)

Leg-1
Yoke
Outer


Figure 6.9 λ-i Curve for Each Section

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APPENDIX C: TRANSFORMER FACTORY TEST REPORT

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