References

Page status: bibliography and source register.

The bibliography below is generated from references.bib. Inclusion means that a source is relevant to the knowledge base; it does not imply endorsement of every claim or modeling assumption in that source.

[1]
[2]
C.-W. Ho, A. E. Ruehli and P. A. Brennan. The Modified Nodal Approach to Network Analysis. IEEE Transactions on Circuits and Systems 22, 504–509 (1975). 1 2 3
[3]
G. D. Hachtel, R. K. Brayton and F. G. Gustavson. The Sparse Tableau Approach to Network Analysis and Design. IEEE Transactions on Circuit Theory 18, 101–113 (1971). 1 2
[4]
B. Park, J. T. Holzer and C. DeMarco. A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow. IEEE Transactions on Power Systems 34, 637–647 (2019). 1 2 3
[5]
Electric Power Research Institute. OpenDSS Solution Techniques (n.d.). Current-injection fixed-point solution and direct initialization; accessed 2026-08-17. 1 2 3 4
[6]
Electric Power Research Institute. Power Conversion Elements (n.d.). Norton primitive-admittance and compensation-current formulation; accessed 2026-08-17. 1
[7]
Electric Power Research Institute. Fault Study Mode Equations (n.d.). Mode-specific nodal and short-circuit equations; accessed 2026-08-17. 1 2 3
[8]
A. M. Kettner and M. Paolone. On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems. IEEE Transactions on Power Systems 34, 444–453 (2019), arXiv:1712.08764. 1 2 3 4 5
[9]
Electric Power Research Institute. Load (n.d.). Load-model and admittance-mode documentation; accessed 2026-08-17. 1
[10]
G. V. Iswaran, S. Thakar, S. Nekkalapu, V. Vittal and M. Khorsand. Development of an Application-Directed Distribution Network Equivalent for Transmission Planning Studies. IEEE Transactions on Power Systems (2026). Accepted author version; application-directed feeder equivalent with PV/load aggregation and power-flow/EMT validation; accessed 2026-08-17. 1
[11]
F. Geth, R. Heidari and A. Koirala. Computational Analysis of Impedance Transformations for Four-Wire Power Networks with Sparse Neutral Grounding. In: Proceedings of the ACM International Conference on Future Energy Systems (e-Energy '22) (2022); pp. 105–113. Phase-to-neutral impedance transformation and neutral-voltage recovery algorithm. 1 2
[12]
C. L. Fortescue. Method of Symmetrical Co-Ordinates Applied to the Solution of Polyphase Networks. Transactions of the American Institute of Electrical Engineers 37, 1027–1140 (1918). 1 2
[13]
T. Kavitha, K. Mehlhorn, D. Michail and K. E. Paluch. An $\widetilde{O}(m^2n)$ Algorithm for Minimum Cycle Basis of Graphs. Algorithmica 52, 333–349 (2008). 1
[14]
M. Coppo, F. Bignucolo and R. Turri. Generalised Transformer Modelling for Power Flow Calculation in Multi-Phase Unbalanced Networks. IET Generation, Transmission & Distribution 11, 3843–3852 (2017). 1 2
[15]
[16]
L. Gan and S. H. Low. Chordal Relaxation of OPF for Multiphase Radial Networks. In: 2014 IEEE International Symposium on Circuits and Systems (ISCAS) (2014); pp. 1812–1815. 1 2 3
[17]
L. Gan and S. H. Low. Convex Relaxations and Linear Approximation for Optimal Power Flow in Multiphase Radial Networks. In: 2014 Power Systems Computation Conference (2014); pp. 1–9, arXiv:1406.3054. 1 2 3
[18]
F. Dörfler and F. Bullo. Kron Reduction of Graphs with Applications to Electrical Networks. IEEE Transactions on Circuits and Systems I: Regular Papers 60, 150–163 (2013), arXiv:1102.2950. 1 2 3 4 5 6 7
[19]
J. C. Baez and B. Fong. A Compositional Framework for Passive Linear Networks. Theory and Applications of Categories 33, 1158–1222 (2018), arXiv:1504.05625. 1 2 3
[20]
S. Y. Caliskan and P. Tabuada. Towards Kron Reduction of Generalized Electrical Networks. Automatica 50, 2586–2590 (2014), arXiv:1207.0563. 1 2 3
[21]
J. B. Ward. Equivalent Circuits for Power-Flow Studies. Transactions of the American Institute of Electrical Engineers 68, 373–382 (1949). 1 2 3
[22]
A. Monticelli, S. Deckmann, A. Garcia and B. Stott. Real-Time External Equivalents for Static Security Analysis. IEEE Transactions on Power Apparatus and Systems PAS-98, 498–508 (1979). 1 2
[23]
J. Machowski, A. Cichy, F. Gubina and P. Omahen. External Subsystem Equivalent Model for Steady-State and Dynamic Security Assessment. IEEE Transactions on Power Systems 3, 1456–1463 (1988). 1 2
[24]
[25]
[26]
F. Geth and B. Liu. Notes on BIM and BFM Optimal Power Flow With Parallel Lines and Total Current Limits. In: 2022 IEEE Power & Energy Society General Meeting (PESGM) (2022). Parallel-line consistency, total-terminal-current limits, and BIM/BFM SOC formulations. 1
[27]
R. D. Zimmerman, C. E. Murillo-Sánchez and R. J. Thomas. MATPOWER Case File Format (n.d.). MATPOWER 8.1 documentation of version-2 case fields, including zero rating and tap conventions; accessed 2026-09-06. 1 2
[28]
S. Boyd and L. Vandenberghe. Convex Optimization (Cambridge University Press, 2004). Chapter 5: duality and sensitivity analysis. 1
[29]
M. A. Hammer, J. Dunfield, K. Headley, N. Labich, J. S. Foster, M. Hicks and D. Van Horn. Incremental Computation with Names. In: Proceedings of the 2015 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications (2015). Author manuscript revised 2021; from-scratch consistency is a property of its specified calculus. 1
[30]
J.-B. Tristan and X. Leroy. Formal Verification of Translation Validators: A Case Study on Instruction Scheduling Optimizations. In: Proceedings of the 35th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (2008). 1
[31]
F. Geth, S. Claeys and R. Heidari. On the Implementation of the Fixed Point Iteration Current Injection Method to Solve Four-Wire Unbalanced Power Flow in PowerModelsDistribution.jl (2023), arXiv:2305.04405. Technology description of matrix-valued four-wire component models and nodal current-injection iteration. 1 2
[32]
W. Jang, S. Mohapatra, T. J. Overbye and H. Zhu. Line-Limit-Preserving Power System Equivalent. In: 2013 IEEE Power and Energy Conference at Illinois (PECI) (2013); pp. 206–212. Open-access author copy. 1 2
[33]
M. A. Wortman, D. L. Allen and L. L. Grigsby. Techniques for the Steady State Representation of Unbalanced Power Systems: Part I. A Systematic Building Block Approach to Network Modeling. IEEE Transactions on Power Apparatus and Systems PAS-104, 2805–2814 (1985). 1 2
[34]
J. J. Grainger and W. D. Stevenson. Power System Analysis (McGraw-Hill, 1994). Sections 7.2–7.3 give the primitive-admittance building blocks and equivalent lattice for mutually coupled branches. 1 2
[35]
A. Dziendziel, H. Kocot and P. Kubek. Construction and Modeling of Multi-Circuit Multi-Voltage HVAC Transmission Lines. Energies 14, 421 (2021). 1 2
[36]
D. A. Tziouvaras, H. J. Altuve and F. Calero. Protecting Mutually Coupled Transmission Lines: Challenges and Solutions. In: 2014 67th Annual Conference for Protective Relay Engineers (2014); pp. 30–49. 1 2
[37]
International Electrotechnical Commission. IEC Common Information Model: MutualCoupling (2022). Generated documentation for the IEC 61970-301 MutualCoupling class; accessed 2026-08-25. 1 2 3
[38]
PowSyBl contributors. Grid Model Extensions: Line Couplings (2026). Version 7.3.0-RC1 documentation; accessed 2026-08-25. 1 2
[39]
PowerWorld Corporation. Mutual Impedance Records (n.d.). Zero-sequence mutual impedance records with branch identities, dot convention, and coupled-section fractions; accessed 2026-08-25. 1 2 3
[40]
R. Yan and T. K. Saha. Analysis of Unbalanced Distribution Lines with Mutual Coupling across Different Voltage Levels and the Corresponding Impact on Network Voltage. IET Generation, Transmission & Distribution 9, 1727–1737 (2015). 1 2
[41]
W. H. Kersting. The Modeling and Analysis of Parallel Distribution Lines. IEEE Transactions on Industry Applications 42, 1126–1132 (2006). 1 2
[42]
R. Diestel. Graph Theory. 6 Edition, Vol. 173 of Graduate Texts in Mathematics (Springer, 2025). 1
[43]
J. L. Gross, J. Yellen and M. Anderson. Graph Theory and Its Applications. 3 Edition (CRC Press, 2019).
[44]
R. B. Bapat. Graphs and Matrices. 2 Edition, Universitext (Springer, 2014). 1 2
[45]
B. Bollobás. Modern Graph Theory. Vol. 184 of Graduate Texts in Mathematics (Springer, 1998). 1
[46]
S. Seshu and M. B. Reed. Linear Graphs and Electrical Networks (Addison-Wesley, 1961). 1 2 3
[47]
Y. Song, D. J. Hill and T. Liu. Local Stability of DC Microgrids: A Perspective of Graph Laplacians with Self-Loops. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC) (IEEE, 2017); pp. 2629–2634. 1
[48]
Electric Power Research Institute. Line (n.d.). Multiphase two-port nominal-pi line model; accessed 2026-08-17. 1
[49]
J. Oxley. Matroid Theory. 2 Edition (Oxford University Press, 2011). 1
[50]
J. H. van Lint and R. M. Wilson. A Course in Combinatorics. 2 Edition (Cambridge University Press, 2001). 1
[51]
Zepben. TopologicalNode, CIM100 Datamodel (n.d.). Generated CIM100 documentation; accessed 2026-08-13. 1 2 3 4 5 6 7
[52]
ENTSO-E. Common Grid Model Exchange Standard (CGMES) Library (n.d.). Official CGMES and CIM exchange-profile library; accessed 2026-08-13. 1 2 3 4
[53]
PowSyBl contributors. How to Manage Topological Views? (n.d.). Accessed 2026-08-13. 1 2 3 4 5
[54]
H. Ehrig, K. Ehrig, U. Prange and G. Taentzer. Fundamentals of Algebraic Graph Transformation (Springer, 2006). 1 2 3 4 5
[55]
International Electrotechnical Commission. IEC 60617 Database: Graphical Symbols for Diagrams (2026). International graphical-symbol database; accessed 2026-08-17. 1
[56]
International Electrotechnical Commission. IEC 61082-1: Preparation of Documents Used in Electrotechnology – Part 1: Rules (2014). Rules for presentation of electrotechnical documents and diagrams; accessed 2026-08-17. 1
[57]
International Electrotechnical Commission. IEC 61970-453: Energy Management System Application Program Interface – Part 453: Diagram Layout Profile (2014). CIM-linked diagram layout exchange; accessed 2026-08-17. 1
[58]
International Electrotechnical Commission. IEC 61850-6: Configuration Description Language for Communication in Electrical Substations Related to IEDs (2024). Substation configuration and switchyard structure exchange; accessed 2026-08-17. 1
[59]
IEEE Power and Energy Society. IEEE C57.12.70-2020: Standard for Standard Terminal Markings and Connections for Distribution and Power Transformers (2020). Transformer terminal, polarity, neutral, grounding, and connection conventions; accessed 2026-08-17. 1
[60]
D. Sarkar, O. Waddell and R. K. Dybvig. A Nanopass Framework for Compiler Education. Journal of Functional Programming 15, 653–667 (2005). 1
[61]
PowerModelsDistribution contributors. Engineering Data Model (n.d.). Accessed 2026-08-13. 1 2 3 4
[62]
PowerModelsDistribution contributors. Conversion to Mathematical Model (2020). Documentation generated 2020-06-30; accessed 2026-08-13. 1 2 3 4
[63]
Electric Power Research Institute. Circuit Reduction for OpenDSS Version 8.5 (n.d.). Accessed 2026-08-13. 1 2 3
[64]
MATPOWER contributors. Data Model Object (n.d.). Developer data-model documentation; accessed 2026-08-13. 1
[65]
Z. K. Pecenak, V. R. Disfani, M. J. Reno and J. Kleissl. Multiphase Distribution Feeder Reduction. IEEE Transactions on Power Systems 33, 1320–1328 (2018). 1 2 3
[66]
A. J. van der Schaft and B. M. Maschke. Port-Hamiltonian Systems on Graphs. SIAM Journal on Control and Optimization 51, 906–937 (2013). 1 2
[67]
C. S. Cheng and D. Shirmohammadi. A Three-Phase Power Flow Method for Real-Time Distribution System Analysis. IEEE Transactions on Power Systems 10, 671–679 (1995). 1 2
[68]
R. D. Zimmerman and H.-D. Chiang. Fast Decoupled Power Flow for Unbalanced Radial Distribution Systems. IEEE Transactions on Power Systems 10, 2045–2052 (1995). 1 2
[69]
J. R. Carson. Wave Propagation in Overhead Wires with Ground Return. Bell System Technical Journal 5, 539–554 (1926). 1 2
[70]
C. Grudzien, D. Deka, M. Chertkov and S. N. Backhaus. Structure- and Physics-Preserving Reductions of Power Grid Models. Multiscale Modeling & Simulation 16, 1916–1947 (2018), arXiv:1707.03672. 1
[71]
J. Sistermanns, M. Hotz, W. Utschick, D. Hewes and R. Witzmann. Feature- and Structure-Preserving Network Reduction for Large-Scale Transmission Grids. In: 2019 IEEE Milan PowerTech (2019); pp. 1–6, arXiv:1903.11590. 1
[72]
M. Farrokhabadi and L. Vanfretti. An Efficient Automated Topology Processor for State Estimation of Power Transmission Networks. Electric Power Systems Research 106, 188–202 (2014). 1 2
[73]
L. Moreau and P. Missier. PROV-DM: The PROV Data Model. W3C Recommendation (2013). Provenance entities, activities, agents, derivations, and constraints; accessed 2026-08-17. 1 2