Summary
Read more on ELECTRAPart A – White-box models
The reliable and safe operation of the transformer requires that the dielectric stresses imposed by transient overvoltages are kept within acceptable limits. White-box models are detailed models of the transformer which permit to calculate the internal voltages in the transformer. Such models are used by the transformer manufacturers to ensure that the transformer will withstand the standard lightning impulse voltage test. CIGRE JWG A2/C4.52 has reviewed the various white-box models with consideration to parameter determination, accuracy, and possible inclusion in electromagnetic transient simulation programs for use in general transient studies. The daily-use models by manufacturers are normally lumped-parameter type models whose parameters are calculated by analytical formulae. The most common calculation procedures and model formulations are reviewed by the JWG. Comparison with measurements shows that the models can give substantial errors in the transient waveforms, although the maximum internal stresses are well represented. The accuracy is improved by introduction of empirical damping factors, while the most accurate result is achieved when calculating the model's parameters using the finite element method, with the branch impedance matrix represented by a rational model that is calculated from discrete frequency samples. The manufacturers may be reluctant to sharing their models. This TB is one of five TBs from the JWG.
Table of content
1. Introduction
1.1. Background, JWG activities, results
1.2. White-box models
1.3. References
2. Transient Voltage Calculation in Transformers
2.1. Introduction
2.2. Sources and types of transient-voltage excitation
2.3. Addressing transient-voltage performance
2.4. Accuracy vs. complexity
2.5. Winding design strategies
2.6. Model requirements: transformer design vs. network studies
2.7. References
3. Transformer Models for Electromagnetic Transient Calculations
3.1. Lumped parameter models
3.2. Distributed parameter models
3.3. Other methods
3.4. Core representation
3.5. Special modelling cases
3.6. Accessories and leads
3.7. References
4. Core Modelling
4.1. Lossless core models
4.2. Lossy core models (Including damping effects)
4.3. References
5. Parameter Determination – Analytical Capacitance Calculations
5.1. Shunt capacitance
5.2. Series capacitance
5.3. References
6. Parameter Determination – Analytical Inductance Calculations
6.1. Characteristics of winding inductances
6.2. Inductances for the calculation of fast front transients in power transformers
6.3. Some methods for the determination of the magnetic flux in the transformer for the calculation of constant inductances
6.4. Inductance calculations
6.5. State of the art of the inductance matrix calculations - The BIL test
6.6. Avoiding numerical problems
6.7. White Box Inductances behaviour at 50/60 Hz
6.8. References
7. Parameter Determination – Analytical Resistance and Conductance Calculations
7.1. Dielectric losses
7.2. Winding losses
7.3. Core losses
7.4. References
8. Coupling Between Windings of Different Legs
8.1. Coupling via core
8.2. Coupling via delta connected reactor
8.3. Coupling via tank
8.4. Capacitive coupling
8.5. Galvanic coupling
8.6. Conclusion
8.7. References
9. Incorporation of Frequency-Dependent Damping
9.1. K-Factor approach
9.2. D-Factor approach (Fergestad)
9.3. Circuit synthesis and parameter fitting methods
9.4. References
10. Bushings modelling
10.1. Simplified bushing model
10.2. Extended bushing model
10.3. Fast transient bushing models
10.4. Practical example
10.5. References
11. Finite Element Method Based Techniques
11.1. Determination of shunt and series capacitances and conductances
11.2. Determination of inductances and resistances
11.3. Lumped element circuit approach
11.4. FEM coupled to circuit solver in time/frequency domain
11.5. Other numerical methods
11.6. References
12. Solution Methods for Internal Voltage Calculations and Network Studies
12.1. Overview
12.2. White-box model differential equations
12.3. Solving the equations
12.4. Terminal equivalents
12.5. State space modelling with hiding of internal voltages
12.6. Damping factor models: including frequency dependent effects
12.7. Inclusion of model in electromagnetic simulation programs
12.8. Example: EMTP simulation using damping factor method
12.9. References
13. Shell-Type Transformers Specifics
13.1. Introduction
13.2. Modelling Shell type transformers for transient calculations
14. Shunt Reactors Specifics
15. Verification and Cross Checking
15.1. Simple checks
15.2. Example of usage of capacitive (initial) and inductive (final) distribution to verify the model
15.3. Frequency domain verifications after transformer manufacture
15.4. References
16. Experimental Validation of White-Box Models
16.1. Acknowledgements
16.2. Introduction
16.3. Brief description of transformers
16.4. Members
16.5. Time domain voltage responses: measurements and simulations
16.6. Frequency domain admittance matrix elements: measurements and calculations
16.7. Analysis of results
16.8. References
17. Experimental Model Validation: Shell-Form Transformer
17.1. Acknowledgements
17.2. Introduction
17.3. Brief description of transformer
17.4. Measurements
17.5. White-box modelling
17.6. Test cases
17.7. Results in the time domain
17.8. References
18. Conclusions
Appendix A Example of Draw-Lead type Bushing modelling
A.1. Transformer Model
A.2. Bushing Model
A.3. Bushing transient response to various voltage excitations
A.4. Effect of varying bushing geometry
A.5. Bushing failures
A.6. References
Appendix B Time domain measured and calculated values for a shell-type transformer
Appendix C Sensitivity studies with L and C matrices
C.1. Sensitivity to the number of lumped elements
C.2. Sensitivity to values of inductances L and capacitances C
C.3. Sensitivity to damping
C.4. Sensitivity to transformer terminal connections
Appendix D - Mombello’s High Frequency White-box Lossy Transformer Model
D.1. Introduction
D.2. Description of the transformer model
D.3. Transformer frequency-dependent impedance matrix fitting process
D.4. Determination of the transformer equivalent circuit parameters
D.5. Conclusions
D.6. References
Additional informations
| Publication type | Technical Brochures |
|---|---|
| Reference | 900 |
| Publication year | |
| Publisher | CIGRE |
| ISBN | 978-2-85873-605-8 |
| Study committees |
|
| Working groups | JWG A2/C4.52 |
| File size | 21 MB |
| Pages number | 204 |
| Price for non member | 203 € |
| Price for member | Free |
Authors
Bjørn Gustavsen, Convenor (NO), Angelica Rocha, Secretary (BR),
Alvaro Portillo (UY), Andrzej Holdyk (NO), Anniyappan Palani (DE), Baudilio Valecillos (CH), Behzad Kordi (CA), Bogdan Andriienko (UA), Carlos González-García (ES), Casimiro Álvarez-Mariño (ES), Daniil Matveev (RU), Davor Vujatovic (UK), Ebrahim Rahimpour (DE), Enrique Mombello (AR), Esteban Portales (CA), Federico Portillo (UY), Guillermo Andrés Díaz Flórez (CO), Gustavo H. C. Oliveira (BR), Hans De Herdt (BE), Hans Kristian Høidalen (NO), Ji-Hong Kim (KR), Jos Veens (NL), Jose Carlos Mendes (BR), José Francisco Lofrano (BR), Juliano Montanha (BR), Luiz Fernando de Oliveira (BR), Marc-Olivier Roux (CA), Maxym Ostrenko (UA), Michel Rioual (FR), Mikhail Frolov (RU), Oliver Sterz (DE), Ricardo Castro Lopes (PT), Robert Degeneff (US), Rodrigo Ronchi (MX), Rogerio Azevedo (BR), Shikin Jamil (UK), Tobias Röhrl (DE), Triomphant Ngnegueu (FR), Xosé López-Fernández (ES)
Keywords
power transformers, reactors, power systems, technical performance
Other parts
- High-Frequency Transformer and Reactor Models for Network Studies - Part D: Model interfacing and specifications
- High-Frequency Transformer and Reactor Models for Network Studies - Part B: Black-Box Models
- High-Frequency Transformer and Reactor Models for Network Studies - Part C: Grey Box Models
- High-Frequency Transformer and Reactor Models for Network Studies - Part E: Measurements and transformer design details
