{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T07:22:21Z","timestamp":1763018541526},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"S4","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Energy Inform"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The transition to renewable energy sources challenges the operation and stability of the electric power system. Wind and solar power generation are volatile and uncertain, and energy sources may be located far away from the centers of the load. High Voltage Direct Current (HVDC) lines enable long-distance power transmission at low losses, both within and between different synchronous power grids. HVDC interconnectors between different synchronous areas can be used to balance volatile generation by leveraging their fast control behavior, but rapid switching may also disturb the power balance. In this article, we analyze the interaction of HVDC interconnector operation and load-frequency control in different European power grids from operational data. We use explainable machine learning to disentangle the various influences affecting the two systems, identify the key influences, and quantify the interrelations in a consistent way. Our results reveal two different types of interaction: Market-based HVDC flows introduce deterministic frequency deviations and thus increase control needs. Control-based HVDC flows mitigate frequency deviations on one side as desired but generally disturb frequency on the other side. The analysis further provides quantitative estimates for the control laws and operation strategies of individual HVDC links, for which there is little public information. Furthermore, we quantify the importance of HVDC links for the frequency dynamics, which is particularly large in the British grid.<\/jats:p>","DOI":"10.1186\/s42162-022-00241-4","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:17:28Z","timestamp":1671581848000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Revealing interactions between HVDC cross-area flows and frequency stability with explainable AI"],"prefix":"10.1186","volume":"5","author":[{"given":"Sebastian","family":"P\u00fctz","sequence":"first","affiliation":[]},{"given":"Benjamin","family":"Sch\u00e4fer","sequence":"additional","affiliation":[]},{"given":"Dirk","family":"Witthaut","sequence":"additional","affiliation":[]},{"given":"Johannes","family":"Kruse","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"241_CR1","doi-asserted-by":"publisher","first-page":"52138","DOI":"10.1109\/ACCESS.2018.2870052","volume":"6","author":"A Adadi","year":"2018","unstructured":"Adadi A, Berrada M (2018) Peeking Inside the black-box: a survey on explainable artificial intelligence (XAI). IEEE Access. 6:52138\u201352160","journal-title":"IEEE Access"},{"key":"241_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2021.125834","volume":"289","author":"T Ahmad","year":"2021","unstructured":"Ahmad T, Zhang D, Huang C, Zhang H, Dai N, Song Y et al (2021) Artificial intelligence in sustainable energy industry: status quo, challenges and opportunities. J Clean Prod. 289:125834","journal-title":"J Clean Prod"},{"issue":"2","key":"241_CR3","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1038\/s41560-020-00755-9","volume":"6","author":"G Alova","year":"2021","unstructured":"Alova G, Trotter PA, Money A (2021) A machine-learning approach to predicting Africa\u2019s electricity mix based on planned power plants and their chances of success. Nat Energy. 6(2):158\u2013166","journal-title":"Nat Energy."},{"key":"241_CR4","volume-title":"Power system control and stability","author":"PM Anderson","year":"2003","unstructured":"Anderson PM, Fouad AA (2003) Power system control and stability. IEEE Press, Piscataway"},{"issue":"6","key":"241_CR5","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/18\/6\/063027","volume":"18","author":"M Anvari","year":"2016","unstructured":"Anvari M, Lohmann G, W\u00e4chter M, Milan P, Lorenz E, Heinemann D et al (2016) Short term fluctuations of wind and solar power systems. N J Phys. 18(6):063027","journal-title":"N J Phys"},{"key":"241_CR6","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.inffus.2019.12.012","volume":"58","author":"A Barredo Arrieta","year":"2020","unstructured":"Barredo Arrieta A, D\u00edaz-Rodr\u00edguez N, Del Ser J, Bennetot A, Tabik S, Barbado A et al (2020) Explainable Artificial Intelligence (XAI): concepts, taxonomies, opportunities and challenges toward responsible AI. Inf Fusion. 58:82\u2013115","journal-title":"Inf Fusion."},{"key":"241_CR7","doi-asserted-by":"crossref","unstructured":"Chen T, Guestrin C (2016) XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. KDD \u201916. New York: ACM; p. 785\u2013794","DOI":"10.1145\/2939672.2939785"},{"key":"241_CR8","doi-asserted-by":"crossref","unstructured":"Chen L, Markham P, Chen CF, Liu Y (2011) Analysis of societal event impacts on the power system frequency using FNET measurements. In: 2011 IEEE Power and Energy Society General Meeting. Detroit: IEEE; p. 1\u20138","DOI":"10.1109\/PES.2011.6039451"},{"key":"241_CR9","doi-asserted-by":"publisher","first-page":"13149","DOI":"10.1109\/ACCESS.2019.2893448","volume":"7","author":"M Chen","year":"2019","unstructured":"Chen M, Liu Q, Chen S, Liu Y, Zhang CH, Liu R (2019) XGBoost-based algorithm interpretation and application on post-fault transient stability status prediction of power system. IEEE Access. 7:13149\u201313158","journal-title":"IEEE Access."},{"issue":"10","key":"241_CR10","doi-asserted-by":"publisher","first-page":"2076","DOI":"10.1016\/j.joule.2018.06.020","volume":"2","author":"S Collins","year":"2018","unstructured":"Collins S, Deane P, Gallach\u00f3ir B\u00d3, Pfenninger S, Staffell I (2018) Impacts of inter-annual wind and solar variations on the European power system. Joule. 2(10):2076\u20132090","journal-title":"Joule."},{"key":"241_CR11","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.segan.2015.12.003","volume":"5","author":"JES de Haan","year":"2016","unstructured":"de Haan JES, Escudero Concha C, Gibescu M, van Putten J, Doorman GL, Kling WL (2016) Stabilising system frequency using HVDC between the Continental European, Nordic, and Great Britain Systems. Sustain Energy Grids Networks. 5:125\u2013134","journal-title":"Sustain Energy Grids Networks."},{"key":"241_CR12","doi-asserted-by":"crossref","unstructured":"Dijokas M, Obradovic D, Misyris G, Weckesser T, Van\u00a0Cutsem T (2021) Frequency dynamics of the Northern European AC\/DC power system: a look-ahead study. arXiv:2107.13890 [cs, eess]","DOI":"10.1109\/TPWRS.2022.3154720"},{"key":"241_CR13","unstructured":"ENTSO-E (2018) Nordic and Baltic HVDC utilisation and unavailability statistics 2017. https:\/\/eepublicdownloads.entsoe.eu\/clean-documents\/Publications\/SOC\/Nordic\/Nordic-and-Blatic-HVDC-Disturbance-Statistics-2017.pdf. Accessed 5 Sept 2022"},{"key":"241_CR14","unstructured":"ENTSO-E (2019a) HVDC links in system operations. https:\/\/eepublicdownloads.azureedge.net\/clean-documents\/SOC%20documents\/20191203_HVDC%20links%20in%20system%20operations.pdf. Accessed 5 Sept 2022"},{"key":"241_CR15","unstructured":"ENTSO-E (2019b) Report on deterministic frequency deviations. https:\/\/consultations.entsoe.eu\/system-development\/deterministic_frequency_deviations_report\/user_uploads\/report_deterministic_frequency_deviations_final-draft-for-consultation.pdf. Accessed 5 Sept 2022"},{"key":"241_CR16","unstructured":"ENTSO-E (2020) Transparency platform. https:\/\/transparency.entsoe.eu\/. Accessed 5 Sept 2022"},{"key":"241_CR17","unstructured":"ENTSO-E (2021) Ten-year network development plan: TYNDP 2020 main report. https:\/\/tyndp.entsoe.eu\/documents. Accessed 5 Sept 2022"},{"key":"241_CR18","unstructured":"ENTSO-E MARI Network Code (2017). https:\/\/www.entsoe.eu\/network_codes\/eb\/mari\/. Accessed 5 Sept 2022"},{"key":"241_CR19","unstructured":"ENTSO-E PICASSO Network Code (2017). https:\/\/www.entsoe.eu\/network_codes\/eb\/picasso\/. Accessed 5 Sept 2022"},{"key":"241_CR20","unstructured":"Elsner P, Erlach B, Fischedick M, Lunz B, Sauer U (2015) Flexibilit\u00e4tskonzepte f\u00fcr die Stromversorgung 2050: Technologien, Szenarien, Systemzusammenh\u00e4nge. M\u00fcnchen: acatech-Dt. Akad. der Technikwissenschaften"},{"key":"241_CR21","unstructured":"Fingrid, Energinet, Svenska Kraftn\u00e4t, Statnett (2014). AGREEMENT (Translation) regarding operation of the interconnected Nordic power system (System Operation Agreement). https:\/\/eepublicdownloads.entsoe.eu\/clean-documents\/Publications\/SOC\/Nordic\/System_Operation_Agreement_2014.pdf. Accessed 5 Sept 2022"},{"key":"241_CR22","unstructured":"Fingrid OYJ (2020) Frequency\u2014historical data. https:\/\/data.fingrid.fi\/en\/dataset\/frequency-historical-data. Accessed 5 Sept 2022"},{"key":"241_CR23","unstructured":"Fingrid, Energinet, Svenska Kraftn\u00e4t, Statnett, Kraftnet \u00e5land (2020) Nordic System Operation Agreement (SOA)\u2014Annex Load-Frequency Control & Reserves (LFCR); https:\/\/eepublicdownloads.azureedge.net\/clean-documents\/SOC%20documents\/LFC\/Appendix%20final.pdf. Accessed 5 Sept 2022"},{"key":"241_CR24","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.egypro.2016.10.093","volume":"99","author":"J Fleer","year":"2016","unstructured":"Fleer J, Zurm\u00fchlen S, Badeda J, Stenzel P, Hake JF, Sauer DU (2016) Model-based economic assessment of stationary battery systems providing primary control reserve. Energy Procedia. 99:11\u201324","journal-title":"Energy Procedia."},{"key":"241_CR25","unstructured":"GitHub Repository. https:\/\/github.com\/sebastianptz\/XAI-for-HVDC. Accessed 5 Sept 2022"},{"issue":"3","key":"241_CR26","doi-asserted-by":"publisher","first-page":"30001","DOI":"10.1209\/0295-5075\/121\/30001","volume":"121","author":"H Haehne","year":"2018","unstructured":"Haehne H, Schottler J, Waechter M, Peinke J, Kamps O (2018) The footprint of atmospheric turbulence in power grid frequency measurements. EPL (Europhys Lett). 121(3):30001","journal-title":"EPL (Europhys Lett)."},{"key":"241_CR27","volume-title":"The elements of statistical learning: data mining, inference, and prediction","author":"T Hastie","year":"2016","unstructured":"Hastie T, Tibshirani R, Friedman J (2016) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer, New York","edition":"2"},{"key":"241_CR28","doi-asserted-by":"crossref","unstructured":"Haugland T, Doorman G, Hystad J (2014) Structural imbalances in the nordic power system\u2014causes, future expectations and remedies. In: 11th International Conference on the European Energy Market (EEM14); p. 1\u20135","DOI":"10.1109\/EEM.2014.6861227"},{"key":"241_CR29","doi-asserted-by":"crossref","unstructured":"Jingya\u00a0Huang JH, Preece R (2017) HVDC-based fast frequency support for low inertia power systems. In: 13th IET International Conference on AC and DC Power Transmission (ACDC 2017). Manchester, UK: Institution of Engineering and Technology; p. 40(6.)","DOI":"10.1049\/cp.2017.0040"},{"key":"241_CR30","unstructured":"Ke G, Meng Q, Finley T, Wang T, Chen W, Ma W, et\u00a0al. (2017) Lightgbm: a highly efficient gradient boosting decision tree. Advances in neural information processing systems. 30"},{"issue":"11","key":"241_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.patter.2021.100365","volume":"2","author":"J Kruse","year":"2021","unstructured":"Kruse J, Sch\u00e4fer B, Witthaut D (2021a) Revealing drivers and risks for power grid frequency stability with explainable AI. Patterns. 2(11):100365","journal-title":"Patterns."},{"key":"241_CR32","doi-asserted-by":"publisher","unstructured":"Kruse J, Sch\u00e4fer B, Witthaut D (2021b) Pre-processed power grid frequency time series. Zenodo.https:\/\/doi.org\/10.5281\/zenodo.5105820. Accessed 5 Sept 2022","DOI":"10.5281\/zenodo.5105820"},{"key":"241_CR33","doi-asserted-by":"crossref","unstructured":"Kruse J, Sch\u00e4fer B, Witthaut D (2021c) Exploring deterministic frequency deviations with explainable AI. In: 2021 IEEE international conference on communications, control, and computing technologies for smart grids (SmartGridComm). IEEE; p. 133\u2013139","DOI":"10.1109\/SmartGridComm51999.2021.9632335"},{"key":"241_CR34","doi-asserted-by":"publisher","first-page":"187814","DOI":"10.1109\/ACCESS.2020.3031477","volume":"8","author":"M Kuzlu","year":"2020","unstructured":"Kuzlu M, Cali U, Sharma V, G\u00fcler O (2020) Gaining insight into solar photovoltaic power generation forecasting utilizing explainable artificial intelligence tools. IEEE Access. 8:187814\u2013187823","journal-title":"IEEE Access."},{"key":"241_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsr.2020.106552","volume":"189","author":"M Langwasser","year":"2020","unstructured":"Langwasser M, De Carne G, Liserre M, Biskoping M (2020) Enhanced grid frequency support by means of HVDC-based load control. Electr Power Syst Res.. 189:106552","journal-title":"Electr Power Syst Res."},{"key":"241_CR36","unstructured":"Lundberg SM, Lee SI (2017) A unified approach to interpreting model predictions. In: Proceedings of the 31st international conference on neural information processing systems. NIPS\u201917. New York: Curran Associates Inc.; p. 4768\u20134777"},{"key":"241_CR37","unstructured":"Lundberg SM, Lee SI (2018 ) Consistent feature attribution for tree ensembles. arXiv:1706.06060 [cs, stat]"},{"issue":"1","key":"241_CR38","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1038\/s42256-019-0138-9","volume":"2","author":"SM Lundberg","year":"2020","unstructured":"Lundberg SM, Erion G, Chen H, DeGrave A, Prutkin JM, Nair B et al (2020) From local explanations to global understanding with explainable AI for trees. Nat Mach Intell. 2(1):56\u201367","journal-title":"Nat Mach Intell."},{"key":"241_CR39","unstructured":"Machowski J, Lubosny Z, Bialek JW, Bumby JR (2020) Power system dynamics: stability and control.  Wiley, New Jersey"},{"key":"241_CR40","doi-asserted-by":"crossref","unstructured":"Milano F, D\u00f6rfler F, Hug G, Hill DJ, Verbi\u010d G (2018) Foundations and challenges of low-inertia systems (invited paper). In: 2018 Power Systems Computation Conference (PSCC). Dublin: IEEE; p. 1\u201325","DOI":"10.23919\/PSCC.2018.8450880"},{"key":"241_CR41","unstructured":"National Grid ESO (2020) Historic frequency data. https:\/\/www.nationalgrideso.com\/balancing-services\/frequency-response-services\/historic-frequency-data. Accessed 5 Sept 2022"},{"issue":"12","key":"241_CR42","doi-asserted-by":"publisher","first-page":"2561","DOI":"10.1140\/epjst\/e2014-02214-y","volume":"223","author":"T Pesch","year":"2014","unstructured":"Pesch T, Allelein HJ, Hake JF (2014) Impacts of the transformation of the German energy system on the transmission grid. Eur Phys J Spec Top.. 223(12):2561\u20132575","journal-title":"Eur Phys J Spec Top."},{"issue":"12","key":"241_CR43","doi-asserted-by":"publisher","first-page":"6209","DOI":"10.1109\/TAC.2017.2703302","volume":"62","author":"BK Poolla","year":"2017","unstructured":"Poolla BK, Bolognani S, D\u00f6rfler F (2017) Optimal placement of virtual inertia in power grids. IEEE Trans Autom Control. 62(12):6209\u20136220","journal-title":"IEEE Trans Autom Control."},{"key":"241_CR44","doi-asserted-by":"publisher","unstructured":"P\u00fctz S, Sch\u00e4fer B, Witthaut D, Kruse J (2022) Supplementary data: revealing interactions between HVDC cross-area flows and frequency stability with explainable AI. Zenodo; https:\/\/doi.org\/10.5281\/zenodo.6761727Accessed 5 Sept 2022","DOI":"10.5281\/zenodo.6761727"},{"key":"241_CR45","doi-asserted-by":"publisher","first-page":"42200","DOI":"10.1109\/ACCESS.2020.2976199","volume":"8","author":"R Roscher","year":"2020","unstructured":"Roscher R, Bohn B, Duarte MF, Garcke J (2020) Explainable machine learning for scientific insights and discoveries. IEEE Access. 8:42200\u201342216","journal-title":"IEEE Access."},{"issue":"1","key":"241_CR46","doi-asserted-by":"publisher","first-page":"6362","DOI":"10.1038\/s41467-020-19732-7","volume":"11","author":"L Rydin Gorj\u00e3o","year":"2020","unstructured":"Rydin Gorj\u00e3o L, Jumar R, Maass H, Hagenmeyer V, Yalcin GC, Kruse J et al (2020) Open database analysis of scaling and spatio-temporal properties of power grid frequencies. Nat Commun. 11(1):6362","journal-title":"Nat Commun."},{"issue":"28","key":"241_CR47","first-page":"307","volume":"2","author":"LS Shapley","year":"1953","unstructured":"Shapley LS (1953) A value for n-person games. Contrib Theory Games. 2(28):307\u2013317","journal-title":"Contrib Theory Games."},{"issue":"5","key":"241_CR48","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1109\/MPE.2020.3001417","volume":"18","author":"T Tellefsen","year":"2020","unstructured":"Tellefsen T, van Putten J, Gjerde O (2020) Norwegian hydropower: connecting to continental Europe. IEEE Power Energy Mag. 18(5):27\u201335","journal-title":"IEEE Power Energy Mag."},{"key":"241_CR49","unstructured":"TransnetBW GmbH (2020) Regelenergie Bedarf + Abruf. https:\/\/www.transnetbw.de\/de\/strommarkt\/systemdienstleistungen\/regelenergie-bedarf-und-abruf. Accessed 5 Sept 2022"},{"issue":"3","key":"241_CR50","doi-asserted-by":"publisher","first-page":"7290","DOI":"10.3182\/20140824-6-ZA-1003.02615","volume":"47","author":"A Ulbig","year":"2014","unstructured":"Ulbig A, Borsche TS, Andersson G (2014) Impact of low rotational inertia on power system stability and operation. IFAC Proc Vol. 47(3):7290\u20137297","journal-title":"IFAC Proc Vol."},{"key":"241_CR51","doi-asserted-by":"crossref","unstructured":"Van\u00a0Hertem D, Gomis-Bellmunt O, Liang J (2016) HVDC grids: for offshore and supergrid of the future. Wiley, New Jersey","DOI":"10.1002\/9781119115243"},{"key":"241_CR52","doi-asserted-by":"crossref","unstructured":"Weissbach T, Welfonder E (2009) High frequency deviations within the european power system: origins and proposals for improvement. In: 2009 IEEE\/PES power systems conference and exposition. Seattle: IEEE; p. 1\u20136","DOI":"10.1109\/PSCE.2009.4840180"},{"key":"241_CR53","doi-asserted-by":"crossref","unstructured":"Witthaut D, Hellmann F, Kurths J, Kettemann S, Meyer-Ortmanns H, Timme M (2021) Collective nonlinear dynamics and self-organization in decentralized power grids. Rev Mod Phys","DOI":"10.1103\/RevModPhys.94.015005"},{"key":"241_CR54","unstructured":"50Hertz Transmission GmbH and Amprion and TenneT TSO and TransnetBW (2012) Netzentwicklungplan Strom. http:\/\/www.netzentwicklungsplan.de. Accessed 5 Sept 2022"}],"container-title":["Energy Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42162-022-00241-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s42162-022-00241-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42162-022-00241-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:30:11Z","timestamp":1671582611000},"score":1,"resource":{"primary":{"URL":"https:\/\/energyinformatics.springeropen.com\/articles\/10.1186\/s42162-022-00241-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":54,"journal-issue":{"issue":"S4","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["241"],"URL":"https:\/\/doi.org\/10.1186\/s42162-022-00241-4","relation":{},"ISSN":["2520-8942"],"issn-type":[{"value":"2520-8942","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,21]]},"assertion":[{"value":"21 December 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"46"}}