The Power Domination Toolbox
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918524134359040 |
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| author | Koch, Johnathan Bjorkman, Beth |
| author_facet | Koch, Johnathan Bjorkman, Beth |
| contents | Phasor Measurement Units (PMUs) are placed at strategic vertices in an electrical power network to monitor the flow of power. Determining the minimum number and optimal placement of PMUs is modeled by the graph theoretic process called Power Domination. This paper describes the Power Domination Toolbox (PDT), which efficiently identifies a minimum number of PMU locations that monitor the entire network. The PDT leverages graph theoretic literature to reduce the complexity of determining optimal PMU placements by: reducing the order of the graph (contraction), leveraging zero forcing forts, sorting the remaining solution space, and parallel computing. The PDT is a drop-in replacement of the current state-of-the-art exhaustive search algorithm in Python and maintains compatibility with SageMath. The PDT can identify minimum PMU placements for graphs with hundreds of vertices on personal computers and can analyze larger graphs on high performance computers. The PDT affords users the ability to investigate power domination on graphs previously considered infeasible due to the number of vertices resulting in a prohibitively long run-time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_13446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Power Domination Toolbox Koch, Johnathan Bjorkman, Beth Combinatorics 05C69, 68R10, 05C57 Phasor Measurement Units (PMUs) are placed at strategic vertices in an electrical power network to monitor the flow of power. Determining the minimum number and optimal placement of PMUs is modeled by the graph theoretic process called Power Domination. This paper describes the Power Domination Toolbox (PDT), which efficiently identifies a minimum number of PMU locations that monitor the entire network. The PDT leverages graph theoretic literature to reduce the complexity of determining optimal PMU placements by: reducing the order of the graph (contraction), leveraging zero forcing forts, sorting the remaining solution space, and parallel computing. The PDT is a drop-in replacement of the current state-of-the-art exhaustive search algorithm in Python and maintains compatibility with SageMath. The PDT can identify minimum PMU placements for graphs with hundreds of vertices on personal computers and can analyze larger graphs on high performance computers. The PDT affords users the ability to investigate power domination on graphs previously considered infeasible due to the number of vertices resulting in a prohibitively long run-time. |
| title | The Power Domination Toolbox |
| topic | Combinatorics 05C69, 68R10, 05C57 |
| url | https://arxiv.org/abs/2305.13446 |