References and further reading

This specification stands on a large body of work in distribution-system modelling and optimal power flow. The lists below point to the textbooks that develop the underlying physics and the papers this model builds on directly. This is a reference page — it introduces no model content.

Textbooks

Distribution-system modelling (component models, Carson/Kron impedance, unbalanced analysis):

• W. H. Kersting, Distribution System Modeling and Analysis, CRC Press (4th ed., 2017). The standard reference for line/cable impedance (Carson's equations, Kron reduction), transformer connections, and unbalanced power flow — the physics behind the line, impedance-derivation, and transformer pages.
• T. A. Short, Electric Power Distribution Handbook, CRC Press (2nd ed., 2014). A practical, equipment-oriented companion covering feeders, grounding, and protection.
• R. C. Dugan, M. F. McGranaghan, S. Santoso, H. W. Beaty, Electrical Power Systems Quality, McGraw-Hill (3rd ed., 2012). Background on unbalance, harmonics, and the power-quality phenomena that motivate conductor-level modelling. See also OpenDSS (Dugan/EPRI), the reference implementation this spec is validated against.

Optimal power flow and its mathematics:

• S. H. Low, Power System Analysis: Analytical Tools and Structural Properties (forthcoming graduate textbook). A rigorous, notation-first treatment of network models and OPF; freely available on registration at netlab.caltech.edu/book_reg. Its complex stacked-vector style is close to the notation used here.
• S. H. Low, "Convex Relaxation of Optimal Power Flow, Parts I & II," IEEE Trans. Control of Network Systems, 2014. Foundational for the relaxations that lift the current–voltage formulation used here to power/lifted-voltage spaces.

Accessible introductions and lecture notes

Approachable complements to the textbooks above for readers getting into distribution networks — and especially for building intuition about transformer loss models — where Steven Low's book covers the mathematics underneath:

• Z. Wang, distribution-systems course notes, Iowa State University: Introduction to Distribution Systems (EE455), Distribution System Transformers (EE555 — connections and loss models), and Real Distribution System Modeling and Analysis (EE653). Clear, worked treatments of feeder components and how transformer losses map onto the equivalent circuit.
• S. Claeys, G. Deconinck, F. Geth, "Decomposition of n-winding transformers for unbalanced optimal power flow," IET Generation, Transmission & Distribution 14(24):5961–5969, 2020, doi:10.1049/iet-gtd.2020.0776 — a useful reference for conceptualising the transformer loss model.

Foundational papers for this model

The four-wire current–voltage (IVR-EN) formulation, its benchmarking, and the device models:

• S. Claeys et al., "Optimal power flow in four-wire distribution networks: Formulation and benchmarking," Electric Power Systems Research, 2022. The four-wire OPF formulation this specification extends.
• D. M. Fobes, S. Claeys, F. Geth, C. Coffrin, "PowerModelsDistribution.jl: An open-source framework for exploring distribution power flow formulations," Electric Power Systems Research, 2020. The IVRENPowerModel lineage of the OPF engine.
• F. Geth, H. Ergun, "Real-Value Power-Voltage formulations of, and bounds for, three-wire unbalanced optimal power flow," 2023. The real-valued bound machinery behind the engineering bounds.
• F. Geth et al., "Considerations and design goals for unbalanced optimal power flow benchmarks," Electric Power Systems Research, 2024. The benchmarking philosophy behind this Task Force effort.
• R. Heidari, F. Geth, "Improved algebraic inverter modeling for four-wire power flow optimization," Electric Power Systems Research, 2024. The inverter modelling behind the IBR page (including the shared-DC-link STATCOM coupling).
• R. C. Dugan, "A perspective on transformer modeling for distribution system analysis," IEEE PES General Meeting, 2003. Background for the transformer winding models and grounding conventions.
• R. Yan, Y. Li, T. K. Saha, L. Wang, M. I. Hossain, "Modeling and Analysis of Open-Delta Step Voltage Regulators for Unbalanced Distribution Network With Photovoltaic Power Generation," IEEE Transactions on Smart Grid 9(3):2224–2234, 2018, doi:10.1109/TSG.2016.2609440. The common-neutral open-delta step-voltage-regulator model behind the regulator page (open_delta_regulator).

Benchmark libraries and test systems

• S. Babaeinejadsarookolaee et al., "The Power Grid Library for benchmarking AC optimal power flow algorithms" (PGLib-OPF), 2019. The transmission-side, positive- sequence analogue of what this Task Force provides for unbalanced distribution.
• K. P. Schneider et al., "Analytic Considerations and Design Basis for the IEEE Distribution Test Feeders," IEEE Trans. Power Systems, 2018. The IEEE Distribution Test Feeder Working Group's library (including the 8500-node feeder).

Tools

• OpenDSS (EPRI) — the distribution power-flow reference this specification's implementation is validated against.
• PowerModelsDistribution.jl — the Julia framework whose IVRENPowerModel inspired this formulation.
• BMOPFTools.jl — the implementation this specification is sourced from.