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Managing uncertainties through efficient calculation of transients and harmonic propagation in power systems
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Energy Science.ORCID iD: 0000-0002-0417-6404
2022 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Metoder för att hantera osäkerheter genom effektiv beräkning av transienter och spridning av övertoner (Swedish)
Abstract [en]

The electric power system is undergoing changes including large-scale introduction of renewable energy sources together with HVDC/FACTS, changes in the network such as increased amount of high voltage cables, industrial electrification, and changes in the load composition. These changes will impact the system in different ways and lead to challenges that must be addressed to facilitate planning, dimensioning, and operation of the system in a secure and economical way. 

The aforementioned changes introduce uncertainties in terms of operational state and modelling of both system and components. One example is the modelling of downstream networks and loads in harmonic propagation studies; the customer impedance may have a significant impact on both the resonance frequency and the damping, but its inclusion remains a challenge due to a lack of knowledge about its behaviour at harmonic frequencies. Another example is the calculation of overvoltages caused by line switching or transformer saturation in different operational states and for varying amounts of underground cable in the network. Methods for calculating overvoltages or harmonic propagation are often based on an assumed complete knowledge of the system under study; uncertainties in the system or components are typically addressed by performing Monte Carlo simulations. However, the use of Monte Carlo methods may be impractical or even unsuitable due to the number of calculations required. Deterministic methods, on the other hand, may provide overly pessimistic results leading to large design margins and high costs. 

This work investigates the application of different methods for managing uncertainties related to the calculation of overvoltages and harmonic propagation. The methods are described, and their advantages and limitations are discussed and illustrated through case studies considering typical uncertainties. Regarding harmonic propagation, two methods are considered: the first method uses copulas to aggregate the harmonic impedance of the downstream network and its loads while retaining its stochastic properties. The method is applied to several medium-voltage and low-voltage networks, and the results show that it is feasible to accurately represent the stochastic behaviour without modelling the downstream network in detail. The second method utilizes the unscented transform together with Cornish-Fisher expansion to calculate the harmonic distortion at the point of connection of a wind farm under different uncertainties. The method is able to estimate the 95% value of individual harmonics accurately when considering variations in emission and impedance, while using a limited number of calculations. 

Regarding overvoltages, three methods are considered: the first method can be used to determine representative fast front overvoltage levels for HVDC cable systems connected to HVDC overhead lines, from a limited number of calculations. The method, applicable to backflashover and shielding failure, accounts for the statistical distribution of lightning current magnitudes, as well as attenuation due to corona discharges on the line. To illustrate the proposed method, it is applied to a case study for a ±525 kV DC system. The second method considers the use of the unscented transform together with Cornish-Fisher expansion to estimate the 2%- value of switching overvoltages from a limited number of calculations. The method is evaluated by considering three-phase energization or reclosing of a line taking into account several aspects such as line length, type of feeding network, impact of trapped charge on the line, and attenuation of the overvoltage level by corona discharges. The method is shown to provide a good approximation of the 2%-value using only about one fifth to one tenth of the number of simulations typically used in traditional methods. The third method makes it possible to estimate a minimum VI-characteristic of surge arresters. This allows for accurate calculation of the absorbed energy when arresters are subjected to resonant overvoltages. 

While many uncertainties may be managed by carrying out a sufficient number of calculations, this may not always be the case. To this end, a method has been proposed to manage uncertainties during system operation, specifically considering the risk of resonant overvoltages due to transformer saturation following the clearing of a nearby line fault. The method utilizes partial disconnection of parallel cables according to a predetermined scheme to shift the system resonance frequency. The method is shown to reduce the duration of the temporary overvoltage and the stress on surge arresters and other equipment.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2022.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords [en]
Overvoltages, harmonics, uncertainties, stochastic methods
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-91960ISBN: 978-91-8048-115-1 (print)ISBN: 978-91-8048-116-8 (electronic)OAI: oai:DiVA.org:ltu-91960DiVA, id: diva2:1677841
Public defence
2022-10-21, Hörsal A, Skellefteå, 09:00 (English)
Opponent
Supervisors
Available from: 2022-06-28 Created: 2022-06-28 Last updated: 2022-10-03Bibliographically approved
List of papers
1. A Stochastic Aggregate Harmonic Load Model
Open this publication in new window or tab >>A Stochastic Aggregate Harmonic Load Model
2020 (English)In: IEEE Transactions on Power Delivery, ISSN 0885-8977, E-ISSN 1937-4208, Vol. 35, no 5, p. 2127-2135Article in journal (Refereed) Published
Abstract [en]

This article presents a stochastic aggregate harmonic load model that can be used to accurately replicate the stochastic behavior of the network impedance downstream of a point of aggregation. The method has been applied to three low voltage networks and the results show that it is able to accurately represent their stochastic behavior while significantly reducing the computational burden compared to modelling the downstream network in detail.

Place, publisher, year, edition, pages
IEEE, 2020
Keywords
Monte Carlo methods, power distribution, power system harmonics, power quality, resonance, stochastic processes
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-78459 (URN)10.1109/TPWRD.2019.2961790 (DOI)000572631700002 ()2-s2.0-85083708616 (Scopus ID)
Note

Validerad;2020;Nivå 2;2020-10-07 (alebob)

Available from: 2020-04-14 Created: 2020-04-14 Last updated: 2022-06-28Bibliographically approved
2. An Improved Statistical Method for Calculating Lightning Overvoltages in HVDC Overhead Line/Cable Systems
Open this publication in new window or tab >>An Improved Statistical Method for Calculating Lightning Overvoltages in HVDC Overhead Line/Cable Systems
Show others...
2019 (English)In: Energies, E-ISSN 1996-1073, Vol. 12, no 16, article id 3121Article in journal (Refereed) Published
Abstract [en]

HVDC cable systems connected to HVDC overhead lines are subject to fast front overvoltages emanating from the line when lightning strikes a shield wire (backflashover) or a pole conductor (shielding failure). Representative fast front overvoltage levels for HVDC cable systems are usually established without considering their statistical characteristics. A statistical method to determine overvoltages related to the acceptable mean time between failure (MTBF) for the cable system was developed previously. The method accounts for the statistical distribution of lightning current magnitudes as well as the attenuation of the overvoltage wave due to corona discharges on the line, since this effect dominates for system voltages up to about ±320 kV. To make the method suitable for higher system voltages as well, this article introduces an improved statistical method which also accounts for surge attenuation through resistive effects, soil ionization, and statistical treatment of overvoltages due to shielding failures. To illustrate the improved method, it is applied to a case study for a ±525 kV DC line. 

Place, publisher, year, edition, pages
MDPI, 2019
Keywords
HVDC, cable, overhead line, lightning, overvoltage, MTBF
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-75965 (URN)10.3390/en12163121 (DOI)000484454000084 ()2-s2.0-85071227522 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-09-11 (johcin)

Available from: 2019-09-11 Created: 2019-09-11 Last updated: 2023-08-28Bibliographically approved
3. Impact of uncertainties on resonant overvoltages following transformer energization
Open this publication in new window or tab >>Impact of uncertainties on resonant overvoltages following transformer energization
2020 (English)In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 187, article id 106503Article in journal (Refereed) Published
Abstract [sv]

A number of changes in the power system have increased the risk for more serious resonances in the harmonic frequency range. The changes also result in an increased uncertainty with regard to the frequency and damping of those resonances. Uncertainties could be related to variations with time, uncertain future developments in the grid, and the modelling of individual components. This article investigates uncertainties affecting resonant overvoltages caused by transformer energization. Several study cases investigating the impact of different uncertainties on resonances and resonant overvoltages, performed in PSCAD, are presented. The results show that some uncertainties may have a significant impact on the resulting impedance characteristics and on the resulting overvoltage levels.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
Harmonics, Power quality, Power system transmission, Transformer
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-80199 (URN)10.1016/j.epsr.2020.106503 (DOI)000556736000064 ()2-s2.0-85087381229 (Scopus ID)
Conference
13th International Conference on Power Systems Transients (IPST 2019), 16-20 June, 2019, Perpignan, France
Note

Godkänd;2020;Nivå 0;2020-08-31 (marisr);Konferensartikel i tidskrift

Available from: 2020-07-09 Created: 2020-07-09 Last updated: 2022-06-28Bibliographically approved
4. Temporary Detuning of Cablified Transmission Grids for Mitigation of Resonant Overvoltages
Open this publication in new window or tab >>Temporary Detuning of Cablified Transmission Grids for Mitigation of Resonant Overvoltages
2022 (English)In: IEEE Transactions on Power Delivery, ISSN 0885-8977, E-ISSN 1937-4208, Vol. 37, no 2, p. 1050-1057Article in journal (Refereed) Published
Abstract [en]

Changes in the power system such as an increased use of cables in transmission systems lead to lower resonance frequencies, a possible consequence being an increased risk for resonant overvoltages. This paper presents a method for protecting the power system from resonant overvoltages caused by transformer energization or fault clearing in the vicinity of large transformers. The method utilizes disconnection of cables according to a predetermined scheme that shifts the system resonance in case the harmonic voltage exceeds a threshold. Compared to other available mitigation measures, the proposed method is inexpensive, robust, and acts only when needed, thereby minimizing any impact during normal operation. The method is exemplified using a realistic network model in PSCAD, showing that by employing the method it is possible to reduce the duration of the overvoltages, and thereby the stress on surge arresters and other equipment.

Place, publisher, year, edition, pages
IEEE, 2022
Keywords
Impedance, power cables, resonance, overvoltages
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-90123 (URN)10.1109/tpwrd.2021.3076502 (DOI)000772463500040 ()2-s2.0-85105045740 (Scopus ID)
Funder
Swedish Energy Agency
Note

Validerad;2022;Nivå 2;2022-04-07 (sofila)

Available from: 2022-04-07 Created: 2022-04-07 Last updated: 2022-06-28Bibliographically approved
5. Application of Unscented Transform for Efficient Calculation of Statistics for Electromagnetic Transients
Open this publication in new window or tab >>Application of Unscented Transform for Efficient Calculation of Statistics for Electromagnetic Transients
2022 (English)In: IEEE Transactions on Power Delivery, ISSN 0885-8977, E-ISSN 1937-4208, Vol. 37, no 5, p. 3469-3476Article in journal (Refereed) Published
Abstract [en]

Uncertainties in power system studies are typically managed by Monte Carlo methods or by applying some worst case assumptions. As the number of uncertainties increases, there is a need for methods that can estimate statistical parameters from a limited number of calculations. This paper utilizes a method called the Unscented Transform together with Cornish-Fisher expansion to estimate the 2%-value of switching overvoltages using only about one tenth the number of calculations as a Monte Carlo method, with similar accuracy. The uncertainties considered are the energizing instants of the three phases. The method is illustrated through EMT simulations in PSCAD and it is shown to provide a good approximation of the 2%-value in most of the studied cases.

Place, publisher, year, edition, pages
IEEE, 2022
Keywords
Insulation coordination, Monte Carlo methods, Power system transients, Stochastic processes, Switching overvoltages
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-91954 (URN)10.1109/tpwrd.2021.3129538 (DOI)000857347300008 ()2-s2.0-85120051291 (Scopus ID)
Funder
Swedish Energy Agency, 44360-1Energy ResearchSwedish National Grid
Note

Validerad;2022;Nivå 2;2022-11-08 (hanlid)

Available from: 2022-06-28 Created: 2022-06-28 Last updated: 2022-11-08Bibliographically approved
6. Efficient Calculation of Switching Overvoltages Considering Corona Attenuation
Open this publication in new window or tab >>Efficient Calculation of Switching Overvoltages Considering Corona Attenuation
2023 (English)In: IEEE Transactions on Power Delivery, ISSN 0885-8977, E-ISSN 1937-4208, Vol. 38, no 4, p. 2735-2741Article in journal (Refereed) Published
Abstract [en]

This paper utilizes the Unscented Transform together with Cornish-Fisher expansion to estimate the 2%-value of switching overvoltages when considering the impact of trapped charge and corona attenuation. Simulations were performed using a piecewise linear corona model for twin- and triple-conductor lines. The proposed method was compared to Monte Carlo methods through simulations in PSCAD. The method is shown to be able to estimate the 2%-value with comparable accuracy to methods used in industry today, but with only one fifth of the number of calculations.

Place, publisher, year, edition, pages
IEEE, 2023
Keywords
Insulation coordination, Corona, Power system transients, Stochastic processes, Switching overvoltages
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-91959 (URN)10.1109/TPWRD.2023.3255782 (DOI)001038260400044 ()2-s2.0-85149856354 (Scopus ID)
Funder
Swedish Energy Agency, 44360-1Swedish National GridEnergy Research
Note

Validerad;2023;Nivå 2;2023-08-16 (joosat);

This article has previously appeared as a manuscript in a thesis.

Available from: 2022-06-28 Created: 2022-06-28 Last updated: 2024-03-07Bibliographically approved
7. Application of a stochastic aggregate load model to study harmonic propagation in distribution networks
Open this publication in new window or tab >>Application of a stochastic aggregate load model to study harmonic propagation in distribution networks
2021 (English)In: CIRED 2021 - The 26th International Conference and Exhibition on Electricity Distribution, 2021, p. 733-737, article id 0152Conference paper, Published paper (Refereed)
Abstract [en]

This paper has applied a method for aggregating downstream networks while retaining their stochastic properties, for use in harmonic propagation studies in distribution networks. The method has been applied to two Swedish medium-voltage networks where the connected low-voltage networks, including customer loads, are represented by stochastic aggregated harmonic load models. The results show that the studied medium-voltage networks exhibit a relatively low resonance frequency for their first resonance point. In the frequency range around the first resonance, the uncertainty in the impedance was found to be high, whereas for higher frequencies the uncertainty in the impedance characteristic was much smaller.

Keywords
Load Modelling, Monte Carlo Methods, Power System Harmonics, Resonance
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-91956 (URN)10.1049/icp.2021.1910 (DOI)
Conference
26th International Conference and Exhibition on Electricity Distribution (CIRED 2021), Online, September 20-23, 2021
Funder
Swedish Energy Agency, 44360-1Energy ResearchSwedish National Grid
Note

ISBN för värdpublikation: 978-1-83953-591-8 (elektroniskt)

Available from: 2022-06-28 Created: 2022-06-28 Last updated: 2023-01-20Bibliographically approved
8. Managing uncertainties in wind farm harmonic studies using unscented transform
Open this publication in new window or tab >>Managing uncertainties in wind farm harmonic studies using unscented transform
2022 (English)In: 2022 20th International Conference on Harmonics & Quality of Power (ICHQP) Proceedings: “Power Quality in the Energy Transition”, IEEE, 2022Conference paper, Published paper (Refereed)
Abstract [en]

Uncertainties in power system studies are often considered using Monte Carlo methods, or by the use of deterministic methods, often based on some worst-case assumptions. With an increasing number of uncertainties, there is a need for methods that can estimate statistical parameters from a limited number of calculations. This paper utilizes a method called the Unscented Transform together with Cornish-Fisher expansion to calculate harmonic distortion at the point of connection of a wind farm under different uncertainties. The method is shown to be able to estimate the 95% value of individual harmonics accurately when considering variations in emission and impedance, using only a limited number of calculations.

Place, publisher, year, edition, pages
IEEE, 2022
Series
International Conference on Harmonics and Quality of Power, ISSN 1540-6008, E-ISSN 2164-0610
Keywords
Power system harmonics, Monte Carlo methods, Stochastic processes, Wind power
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electric Power Engineering
Identifiers
urn:nbn:se:ltu:diva-91958 (URN)10.1109/ICHQP53011.2022.9808772 (DOI)000844604500100 ()2-s2.0-85133749641 (Scopus ID)978-1-6654-1639-9 (ISBN)
Conference
20th International Conference on Harmonics & Quality of Power (ICHQP 2022), Naples, Italy, May 29 - June 1, 2022
Funder
Swedish Energy Agency, 44360-1Energy ResearchSwedish National Grid
Available from: 2022-06-28 Created: 2022-06-28 Last updated: 2023-05-08Bibliographically approved

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Citation style
  • apa
  • ieee
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  • en-GB
  • en-US
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