Bi-level coordinated restoration for the distribution system and multi-microgrids Article Swipe
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1016/j.ijepes.2024.110371
Microgrids (MGs) play an important role in enhancing the resilience of distribution systems (DSs). However, each MG has its own operation scheme and the ownership obstructs the coordination of restoration resources from different MGs. To address this problem, this paper proposes a bi-level coordinated restoration framework for the distribution system operators (DSOs) and the microgrid operators (MGOs). In the framework, MGOs report their surplus capacity to DSO once an extreme event occurs, and then DSO dispatches its own resources and orders MGOs’ supporting capacity. After receiving the order, MGOs dispatch distributed generators and energy storage systems to provide the surplus power. The proposed framework is capable of finding the optimal restoration scheme provided that the autonomy of MGs is retained. The stochastic programming is leveraged to model the uncertainty of renewable energy, and the coordinated restoration framework is formulated as a bi-level mixed integer linear programming (BMILP). The relaxation-based bi-level reformulation and decomposition (RBRD) algorithm is adopted to effectively achieve the global optimal solution. The effectiveness of the proposed method is validated on a test system comprised of the IEEE 33-bus system and three IEEE 13 node test feeders.
Related Topics
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.ijepes.2024.110371
- OA Status
- gold
- Cited By
- 2
- References
- 44
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404468510
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4404468510Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1016/j.ijepes.2024.110371Digital Object Identifier
- Title
-
Bi-level coordinated restoration for the distribution system and multi-microgridsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-11-18Full publication date if available
- Authors
-
Hao Zhu, Xiaotian Sun, Haipeng Xie, Lingfeng Tang, Zhaohong BieList of authors in order
- Landing page
-
https://doi.org/10.1016/j.ijepes.2024.110371Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1016/j.ijepes.2024.110371Direct OA link when available
- Concepts
-
Distribution (mathematics), Computer science, Engineering, Mathematics, Mathematical analysisTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2Per-year citation counts (last 5 years)
- References (count)
-
44Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4404468510 |
|---|---|
| doi | https://doi.org/10.1016/j.ijepes.2024.110371 |
| ids.doi | https://doi.org/10.1016/j.ijepes.2024.110371 |
| ids.openalex | https://openalex.org/W4404468510 |
| fwci | 0.73833695 |
| type | article |
| title | Bi-level coordinated restoration for the distribution system and multi-microgrids |
| awards[0].id | https://openalex.org/G5975505939 |
| awards[0].funder_id | https://openalex.org/F4320327040 |
| awards[0].display_name | |
| awards[0].funder_award_id | EIPE21312 |
| awards[0].funder_display_name | State Key Laboratory of Electrical Insulation and Power Equipment |
| biblio.issue | |
| biblio.volume | 164 |
| biblio.last_page | 110371 |
| biblio.first_page | 110371 |
| topics[0].id | https://openalex.org/T10454 |
| topics[0].field.id | https://openalex.org/fields/22 |
| topics[0].field.display_name | Engineering |
| topics[0].score | 0.998199999332428 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2208 |
| topics[0].subfield.display_name | Electrical and Electronic Engineering |
| topics[0].display_name | Optimal Power Flow Distribution |
| topics[1].id | https://openalex.org/T10223 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9957000017166138 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2207 |
| topics[1].subfield.display_name | Control and Systems Engineering |
| topics[1].display_name | Microgrid Control and Optimization |
| topics[2].id | https://openalex.org/T10917 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9955999851226807 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2207 |
| topics[2].subfield.display_name | Control and Systems Engineering |
| topics[2].display_name | Smart Grid Security and Resilience |
| funders[0].id | https://openalex.org/F4320327040 |
| funders[0].ror | |
| funders[0].display_name | State Key Laboratory of Electrical Insulation and Power Equipment |
| is_xpac | False |
| apc_list.value | 2800 |
| apc_list.currency | USD |
| apc_list.value_usd | 2800 |
| apc_paid.value | 2800 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 2800 |
| concepts[0].id | https://openalex.org/C110121322 |
| concepts[0].level | 2 |
| concepts[0].score | 0.4884432852268219 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q865811 |
| concepts[0].display_name | Distribution (mathematics) |
| concepts[1].id | https://openalex.org/C41008148 |
| concepts[1].level | 0 |
| concepts[1].score | 0.3759429454803467 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[1].display_name | Computer science |
| concepts[2].id | https://openalex.org/C127413603 |
| concepts[2].level | 0 |
| concepts[2].score | 0.3425436019897461 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[2].display_name | Engineering |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.14318805932998657 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C134306372 |
| concepts[4].level | 1 |
| concepts[4].score | 0.0 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[4].display_name | Mathematical analysis |
| keywords[0].id | https://openalex.org/keywords/distribution |
| keywords[0].score | 0.4884432852268219 |
| keywords[0].display_name | Distribution (mathematics) |
| keywords[1].id | https://openalex.org/keywords/computer-science |
| keywords[1].score | 0.3759429454803467 |
| keywords[1].display_name | Computer science |
| keywords[2].id | https://openalex.org/keywords/engineering |
| keywords[2].score | 0.3425436019897461 |
| keywords[2].display_name | Engineering |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.14318805932998657 |
| keywords[3].display_name | Mathematics |
| language | en |
| locations[0].id | doi:10.1016/j.ijepes.2024.110371 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S168377509 |
| locations[0].source.issn | 0142-0615, 1879-3517 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 0142-0615 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | International Journal of Electrical Power & Energy Systems |
| locations[0].source.host_organization | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_name | Elsevier BV |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320990 |
| locations[0].source.host_organization_lineage_names | Elsevier BV |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | International Journal of Electrical Power & Energy Systems |
| locations[0].landing_page_url | https://doi.org/10.1016/j.ijepes.2024.110371 |
| locations[1].id | pmh:oai:doaj.org/article:118121ff7c604195b7cebd671facaaf4 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | International Journal of Electrical Power & Energy Systems, Vol 164, Iss , Pp 110371- (2025) |
| locations[1].landing_page_url | https://doaj.org/article/118121ff7c604195b7cebd671facaaf4 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5101796931 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-3911-2240 |
| authorships[0].author.display_name | Hao Zhu |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Hao Zhu |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5042142745 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-2538-8841 |
| authorships[1].author.display_name | Xiaotian Sun |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Xiaotian Sun |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5053299650 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-9845-0058 |
| authorships[2].author.display_name | Haipeng Xie |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Haipeng Xie |
| authorships[2].is_corresponding | False |
| authorships[3].author.id | https://openalex.org/A5013657565 |
| authorships[3].author.orcid | |
| authorships[3].author.display_name | Lingfeng Tang |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Lingfeng Tang |
| authorships[3].is_corresponding | False |
| authorships[4].author.id | https://openalex.org/A5020110830 |
| authorships[4].author.orcid | https://orcid.org/0000-0002-8458-0887 |
| authorships[4].author.display_name | Zhaohong Bie |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | Zhaohong Bie |
| authorships[4].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1016/j.ijepes.2024.110371 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Bi-level coordinated restoration for the distribution system and multi-microgrids |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10454 |
| primary_topic.field.id | https://openalex.org/fields/22 |
| primary_topic.field.display_name | Engineering |
| primary_topic.score | 0.998199999332428 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2208 |
| primary_topic.subfield.display_name | Electrical and Electronic Engineering |
| primary_topic.display_name | Optimal Power Flow Distribution |
| related_works | https://openalex.org/W4391375266, https://openalex.org/W2899084033, https://openalex.org/W2748952813, https://openalex.org/W2390279801, https://openalex.org/W4391913857, https://openalex.org/W2358668433, https://openalex.org/W4396701345, https://openalex.org/W2376932109, https://openalex.org/W2001405890, https://openalex.org/W4396696052 |
| cited_by_count | 2 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 2 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1016/j.ijepes.2024.110371 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S168377509 |
| best_oa_location.source.issn | 0142-0615, 1879-3517 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 0142-0615 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | International Journal of Electrical Power & Energy Systems |
| best_oa_location.source.host_organization | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_name | Elsevier BV |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| best_oa_location.source.host_organization_lineage_names | Elsevier BV |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | International Journal of Electrical Power & Energy Systems |
| best_oa_location.landing_page_url | https://doi.org/10.1016/j.ijepes.2024.110371 |
| primary_location.id | doi:10.1016/j.ijepes.2024.110371 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S168377509 |
| primary_location.source.issn | 0142-0615, 1879-3517 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 0142-0615 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | International Journal of Electrical Power & Energy Systems |
| primary_location.source.host_organization | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_name | Elsevier BV |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320990 |
| primary_location.source.host_organization_lineage_names | Elsevier BV |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | International Journal of Electrical Power & Energy Systems |
| primary_location.landing_page_url | https://doi.org/10.1016/j.ijepes.2024.110371 |
| publication_date | 2024-11-18 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W2277817011, https://openalex.org/W2604739525, https://openalex.org/W4210512752, https://openalex.org/W6701129319, https://openalex.org/W4210741998, https://openalex.org/W3115906425, https://openalex.org/W2883019382, https://openalex.org/W3047728991, https://openalex.org/W2912652734, https://openalex.org/W2906041468, https://openalex.org/W2799787357, https://openalex.org/W2912447180, https://openalex.org/W3070953475, https://openalex.org/W2613326656, https://openalex.org/W4224234346, https://openalex.org/W2560738052, https://openalex.org/W3034020703, https://openalex.org/W2290410061, https://openalex.org/W2988319714, https://openalex.org/W2888193559, https://openalex.org/W3180948253, https://openalex.org/W2462278955, https://openalex.org/W4213356201, https://openalex.org/W2894506939, https://openalex.org/W2797119662, https://openalex.org/W2945690175, https://openalex.org/W4381415965, https://openalex.org/W4285121179, https://openalex.org/W4200443967, https://openalex.org/W3118498762, https://openalex.org/W3111982844, https://openalex.org/W3004864110, https://openalex.org/W4320719819, https://openalex.org/W2318920527, https://openalex.org/W2343206695, https://openalex.org/W4320015781, https://openalex.org/W2791638530, https://openalex.org/W2737460467, https://openalex.org/W2571088323, https://openalex.org/W2913490916, https://openalex.org/W3121888262, https://openalex.org/W3100416601, https://openalex.org/W2553137950, https://openalex.org/W3162651815 |
| referenced_works_count | 44 |
| abstract_inverted_index.a | 41, 140, 173 |
| abstract_inverted_index.13 | 185 |
| abstract_inverted_index.In | 57 |
| abstract_inverted_index.MG | 16 |
| abstract_inverted_index.To | 34 |
| abstract_inverted_index.an | 3, 68 |
| abstract_inverted_index.as | 139 |
| abstract_inverted_index.in | 6 |
| abstract_inverted_index.is | 104, 118, 123, 137, 155, 170 |
| abstract_inverted_index.of | 10, 28, 106, 116, 129, 166, 177 |
| abstract_inverted_index.on | 172 |
| abstract_inverted_index.to | 65, 96, 125, 157 |
| abstract_inverted_index.DSO | 66, 74 |
| abstract_inverted_index.MGs | 117 |
| abstract_inverted_index.The | 101, 120, 147, 164 |
| abstract_inverted_index.and | 22, 52, 72, 79, 92, 132, 151, 182 |
| abstract_inverted_index.for | 46 |
| abstract_inverted_index.has | 17 |
| abstract_inverted_index.its | 18, 76 |
| abstract_inverted_index.own | 19, 77 |
| abstract_inverted_index.the | 8, 23, 26, 47, 53, 58, 86, 98, 108, 114, 127, 133, 160, 167, 178 |
| abstract_inverted_index.IEEE | 179, 184 |
| abstract_inverted_index.MGOs | 60, 88 |
| abstract_inverted_index.MGs. | 33 |
| abstract_inverted_index.each | 15 |
| abstract_inverted_index.from | 31 |
| abstract_inverted_index.node | 186 |
| abstract_inverted_index.once | 67 |
| abstract_inverted_index.play | 2 |
| abstract_inverted_index.role | 5 |
| abstract_inverted_index.test | 174, 187 |
| abstract_inverted_index.that | 113 |
| abstract_inverted_index.then | 73 |
| abstract_inverted_index.this | 36, 38 |
| abstract_inverted_index.(MGs) | 1 |
| abstract_inverted_index.After | 84 |
| abstract_inverted_index.event | 70 |
| abstract_inverted_index.mixed | 142 |
| abstract_inverted_index.model | 126 |
| abstract_inverted_index.paper | 39 |
| abstract_inverted_index.their | 62 |
| abstract_inverted_index.three | 183 |
| abstract_inverted_index.(DSOs) | 51 |
| abstract_inverted_index.(DSs). | 13 |
| abstract_inverted_index.(RBRD) | 153 |
| abstract_inverted_index.33-bus | 180 |
| abstract_inverted_index.energy | 93 |
| abstract_inverted_index.global | 161 |
| abstract_inverted_index.linear | 144 |
| abstract_inverted_index.method | 169 |
| abstract_inverted_index.order, | 87 |
| abstract_inverted_index.orders | 80 |
| abstract_inverted_index.power. | 100 |
| abstract_inverted_index.report | 61 |
| abstract_inverted_index.scheme | 21, 111 |
| abstract_inverted_index.system | 49, 175, 181 |
| abstract_inverted_index.(MGOs). | 56 |
| abstract_inverted_index.MGOs’ | 81 |
| abstract_inverted_index.achieve | 159 |
| abstract_inverted_index.address | 35 |
| abstract_inverted_index.adopted | 156 |
| abstract_inverted_index.capable | 105 |
| abstract_inverted_index.energy, | 131 |
| abstract_inverted_index.extreme | 69 |
| abstract_inverted_index.finding | 107 |
| abstract_inverted_index.integer | 143 |
| abstract_inverted_index.occurs, | 71 |
| abstract_inverted_index.optimal | 109, 162 |
| abstract_inverted_index.provide | 97 |
| abstract_inverted_index.storage | 94 |
| abstract_inverted_index.surplus | 63, 99 |
| abstract_inverted_index.systems | 12, 95 |
| abstract_inverted_index.(BMILP). | 146 |
| abstract_inverted_index.However, | 14 |
| abstract_inverted_index.autonomy | 115 |
| abstract_inverted_index.bi-level | 42, 141, 149 |
| abstract_inverted_index.capacity | 64 |
| abstract_inverted_index.dispatch | 89 |
| abstract_inverted_index.feeders. | 188 |
| abstract_inverted_index.problem, | 37 |
| abstract_inverted_index.proposed | 102, 168 |
| abstract_inverted_index.proposes | 40 |
| abstract_inverted_index.provided | 112 |
| abstract_inverted_index.algorithm | 154 |
| abstract_inverted_index.capacity. | 83 |
| abstract_inverted_index.comprised | 176 |
| abstract_inverted_index.different | 32 |
| abstract_inverted_index.enhancing | 7 |
| abstract_inverted_index.framework | 45, 103, 136 |
| abstract_inverted_index.important | 4 |
| abstract_inverted_index.leveraged | 124 |
| abstract_inverted_index.microgrid | 54 |
| abstract_inverted_index.obstructs | 25 |
| abstract_inverted_index.operation | 20 |
| abstract_inverted_index.operators | 50, 55 |
| abstract_inverted_index.ownership | 24 |
| abstract_inverted_index.receiving | 85 |
| abstract_inverted_index.renewable | 130 |
| abstract_inverted_index.resources | 30, 78 |
| abstract_inverted_index.retained. | 119 |
| abstract_inverted_index.solution. | 163 |
| abstract_inverted_index.validated | 171 |
| abstract_inverted_index.Microgrids | 0 |
| abstract_inverted_index.dispatches | 75 |
| abstract_inverted_index.formulated | 138 |
| abstract_inverted_index.framework, | 59 |
| abstract_inverted_index.generators | 91 |
| abstract_inverted_index.resilience | 9 |
| abstract_inverted_index.stochastic | 121 |
| abstract_inverted_index.supporting | 82 |
| abstract_inverted_index.coordinated | 43, 134 |
| abstract_inverted_index.distributed | 90 |
| abstract_inverted_index.effectively | 158 |
| abstract_inverted_index.programming | 122, 145 |
| abstract_inverted_index.restoration | 29, 44, 110, 135 |
| abstract_inverted_index.uncertainty | 128 |
| abstract_inverted_index.coordination | 27 |
| abstract_inverted_index.distribution | 11, 48 |
| abstract_inverted_index.decomposition | 152 |
| abstract_inverted_index.effectiveness | 165 |
| abstract_inverted_index.reformulation | 150 |
| abstract_inverted_index.relaxation-based | 148 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 95 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile.value | 0.70182656 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |