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Emerging distribution systems with a proliferation of distributed energy resources are facing with new challenges, such as voltage collapse and power flow congestion in unsymmetrical network configurations. As a fundamental tool that could help quantify these new challenges and further mitigate their impacts on the secure and economic operation of distribution systems, effective AC optimal power flow (ACOPF) models and solution approaches are in urgent need. This study focuses on ACOPF of three‐phase four‐conductor configured distribution systems, in which neutral conductors and ground resistances are modelled explicitly to reflect practical situation. In addition, by leveraging the Kirchhoff's current law (KCL) theorem and the effect of zero injections, voltage variables of neutrals and zero‐injection phases can be effectively eliminated. The ACOPF problem is formulated as a convex semidefinite programming (SDP) relaxation model in complex domain. In recognising possible solution inexactness of SDP relaxation model, a Karush–Kuhn–Tucker condition based process is further proposed to effectively recover feasible solutions to the original ACOPF problem by calculating a set of computational‐inexpensive non‐linear equations. Numerical studies on a modified IEEE 123‐bus system show the effectiveness of the proposed SDP relaxation model with variable reductions and the feasible solution recovery process for three‐phase four‐conductor configured distribution systems.
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Categorical Databases for Mathematical Formalization of AC Optimal Power Flow
It has been decades since category theory was applied to databases. In spite of their mathematical elegance, categorical models have traditionally had difficulty representing factual data, such as integers or strings. This paper proposes a categorical dataset for power system computational models, which is used for AC Optimal Power Flows (ACOPF). In addition, categorical databases incorporate factual data using multi-sorted algebraic theories (also known as Lawvere theories) based on the set-valued functor model. In the advanced metering infrastructure of power systems, this approach is capable of handling missing information efficiently. This methodology enables constraints and queries to employ operations on data, such as multiplicative and comparative processes, thereby facilitating the integration between conventional databases and programming languages like Julia and Python’s Pypower. The demonstration illustrates how all elements of the model, including schemas, instances, and functors, can modify the schema in ACOPF instances.
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- Award ID(s):
- 1851602
- PAR ID:
- 10515344
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-6654-9071-9
- Page Range / eLocation ID:
- 1 to 5
- Subject(s) / Keyword(s):
- Optimal Flow, Optimal Power Flow, AC Optimal Power Flow, Power System, Classification Datasets, Categorical Model, Functor, Optimization Problem, Information Exchange, Algebra, Loss Of Resistance, Topological Changes, Semidefinite Programming, Time Overhead, Optimization Solver, Second-order Cone Programming, Galaxy Server, Power Flow Equations, Composition Rules, Database Schema, Power Flow Problem, Duality Gap, Colimits
- Format(s):
- Medium: X
- Location:
- College Station, TX, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/TPEC56611.2023.10078526
