# Results and publications

The project made a long step towards the overall objective of establishing a competence centre on design, analysis, verification and safe operation of subsea electric power systems for oil and gas exploitation. Vital component models and toolboxes are developed and validated, providing opportunities to analyse new phenomena with increased accuracy.

Most of the project activity was focused on developing new or improved component models (e.g. wide-band models of transformers and power umbilicals, non-linear models of transformers etc.), providing new tools and methodology (e.g. UFIELD Power Module, Matrix Fitting Toolbox and Time Domain Vector Fitting Toolbox) and perform case studies of representative subsea power supply topologies in order to demonstrate the use and capability of the simulation tools and highlight interesting phenomena, including causes and effects.

Input parameters and formats of component models have been presented, including examples of conversion routines for adaptation of standard data into model input parameters. PSCAD® has been chosen as the preferred simulation software in the project.

**Main results and achievements **

**Component modelling**

Developing new component models or improving existing ones have been the most comprehensive task in the project. This also includes development of several toolboxes in order to provide the right input parameters to the simulation program. The following overview shows a summarised status for the modelling activity in the project.

**Transformer**

- Wide band (high-frequency) model of transformer based on measurement input and Matrix Fitting Toolbox. Applicable for PSCAD
^{®}, EMPT-RV and ATP.

Simplified sketch of wide band transformer modelling work flow. The Matrix Fitting Toolbox generates a wide band model based on frequency domain measurements.

- Methodology for implementing an improved non-linear magnetic model in PSCAD
^{®}based on external calculation (ATPDraw).

**Power umbilical**

- UFIELD Power Module: Tool for calculating electrical parameters of umbilical cables based on geometry and material properties.

Illustration of UFIELD Power Module software work flow.

- Wide band model: Export of wide-band model from UFIELD to ATP, PSCAD
^{®}, EMTP-RV

**Generic toolboxes**

- Matrix fitting toolbox: Generic tool for modelling from frequency domain responses. Used in UFIELD and in transformer wide-band modelling.
- Time domain vector fitting (TD-VF): Generic tool for modelling from time domain responses. Used in extraction of frequency-dependent network equivalents of large power systems

### Phenomenon studies

Most of the phenomenon studies have been concentrated on three representative subsea power supply cases (topologies):

- Topside VSD base case – with either induction motor or permanent magnet motor

Focus: Steady state operation, transients, faults, unwanted interactions - Two topside VSD systems sharing a common power umbilical

Focus: Interaction between parallel systems caused by common umbilical - Subsea VSD base case

Focus: Coupling transient, e.g. inrush current in subsea transformer following topside breaker operation; - the importance of accurate modelling of transformer saturation.

Focus was kept on analysing system operation, fault events and transient conditions in order to identify e.g. critical operating points, possible cross coupling effects, oscillations and possible resonances.

In general the analysis tools showed very good functionality for analysing the selected phenomena and demonstrated the applicability of developed models like power umbilicals, transformers and power electronic converters.

## Publications

**Journal papers:**

A. Semlyen and B. Gustavsen, “A Half-Size Singularity Test Matrix for Fast and Reliable Passivity Assessment of Rational Models”, IEEE Trans. Power Delivery, vol. 24, no. 1, pp. 345-351, January 2009. |

B. Gustavsen and A. Semlyen, “Admittance-Based Modeling of Transmission Lines by a Folded Line Equivalent”, IEEE Trans. Power Delivery, vol. 24, no. 1, pp. 231-239, January 2009. |

B. Gustavsen and A. Semlyen, "Fast Passivity Assessment for S-parameter Rational Models via a Half-size Test Matrix", IEEE Trans. Microwave Theory and Techniques, vol. 56, no. 12, på. 2701-2708, December 2008. |

B. Gustavsen, “Fast Passivity Enforcement for Pole-Residue Models by Perturbation of Residue Matrix Eigenvalues”, IEEE Trans. Power Delivery, vol. 34, no. 4, pp. 2278-2285, October 2008. |

B. Gustavsen and C. Heitz, “Modal Vector Fitting: A Tool for Generating Rational Models of High Accuracy with Arbitrary Terminal Conditions”, IEEE Trans. Advanced Packaging, vol. 31, no. 4, pp. 664-672, November 2008. |

B. Gustavsen, “Passivity Enforcement for Transmission Line Models Based on the Method of Characteristics”, IEEE Trans. Power Delivery, vol. 34, no. 4, pp. 2286-2293, October 2008. |

B. Gustavsen and J. Nordstrom, “Pole Identification for the Universal Line Model Based on Trace Fitting”, IEEE Trans. Power Delivery, vol. 23, no. 1, pp. 472-479, January 2008. |

D. Deschrijver, B. Gustavsen and T. Dhaene, "Causality preserving passivity enforcement for traveling-wave type transmission line models", IEEE Trans. Power Delivery, vol. 24, no. 4, pp. 2461-2462, October 2009. |

B. Gustavsen and A. Semlyen, “On passivity tests for unsymmetrical models”, |

B.Gustavsen and C.Heitz, "Fast Realization of the modal Vector fitting Method for rational modeling with accurate representation of small eigenvalues", IEEE Tranm. Power Delivery, vol. 24, no. 3, pp. 1396-1405, July 2009. |

B. Gustavsen, “Study of transformer resonant overvoltages caused by cable-transformer high-frequency interaction”, |

B. Gustavsen, “A hybrid measurement approach for wide-band characterization and modeling of power transformers”, |

B. Gustavsen, “Fast passivity enforcement for S-parameter models by perturbation of residue matrix eigenvalues”, |

A. Ubolli and B. Gustavsen, ”Comparison of methods for rational approximation of simulated time domain responses: ARMA, ZD-VF, and TD-VF.”, IEEE Trans. Power Delivery, vol. 26, no. 1, pp. 279-288, Jan. 2011. |

A. Ubolli and B. Gustavsen, " Multiport frequency-dependent network equivalencing based on simulated time-domain responses", IEEE Trans. Power Delivery, vol. 27, no. 2, pp. 648-657, April 2012. |

**International conferences:**

B. Gustavsen, “Fast Passivity Enforcement of Rational Macromodels by Perturbation of Residue Matrix Eigenvalues”, Proc. 11th IEEE Workshop on Signal Propagation on Interconnects, Genova, Italy, May 2007, pp. 71-74. |

B. Gustavsen, “Robust Passivity Enforcement of Frequency Dependent Transmission Line Models”, Proc. 11th IEEE Workshop on Signal Propagation on Interconnects, Genova, Italy, May 2007, pp. 169-172. |

A.Ubolli and B.Gustavsen, "Applicability of time domain and Z-domain vector fitting to rational modeling from time domain responses with consideration to circuit solver integration method", 14th IEEE Workshop on Signal Propagation on Interconnects (SPI), Hildesheim, Germany, May 9-12, 2010, pp. 69-72. |

N.Chiesa, H.K.Høidalen, M.Lambert and M.Martinez Duro, "Calculation of inrush currents - Benchmarking of transformer models", International Conference on Power Systems Transients (IPST2011) in Delft, Netherlands, June 14-17, 2011. |

A.Ubolli and B.Gustavsen, "A digital filtrering approach for time domain vector fitting", 15th IEEE Workshop on Signal propagation on Interconnects (SPI), Naples, Italy, May 8-11, 2011, pp. 25-28. |

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