Three-phase power flow calculations using the current injection method
Abstract
This paper presents a new sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method. The three-phase current injection equations are written in rectangular coordinates resulting in an order 6n system of equations. The Jacobian matrix is composed of 6/spl times/6 block matrices and retains the same structure as the nodal admittance matrix. Practical distribution systems were used to test the method and to compare its robustness with that of the backward/forward sweep method.
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A three-phase power-flow method based on the current-injection mismatch variant of the Newton-Raphson algorithm can be applied to both radial and weakly meshed networks.
“This approach can be applied to both radial and weakly meshed networks, and the current-injection formulation provides a convenient way to model the combined effect of loads, rooftop PV systems and other devices connected at different nodes of the distribution network.”
From Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study (2026) · cites this paper as [97]
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Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study
Rahman, O., Elphick, S., & Robinson, D. A. (2026) · Electronics · doi:10.3390/electronics15051074 · Cited by 3 · see citing works
Assymmetry in distribution systems: causes, harmful effects and remedies
Plummer, I. (2022) · doi:10.31390/gradschool_theses.1490 · Cited by 1
Chung, S., Zhang, Y., Wang, Z., & Ding, F. (2024) · arXiv · doi:10.48550/arxiv.2407.19253 · Cited by 3 · see citing works
“Particular characteristics of distribution systems, such as high R / X ratios, unbalanced operation, and radial network structures, necessitate the development of dedicated solutions for the PF problem [1], [2].”
Background
- Authors
- Garcia, P. A. N., Pereira, J. L. R., Carneiro, S., da Costa, V. M., & Martins, N.
- Affiliations
- Universidade Federal do Rio de Janeiro (BR)
- Universidade Federal de Juiz de Fora (BR)
- Venue
- IEEE Transactions on Power Systems
- Published
- 2000-05
- Volume
- 15
- Issue
- 2
- Pages
- 508-514
- ISSN
- 0885-8950 (ISSN-L)
- OpenAlex
- W2154951274
- Cited by
- 438
- References
- 0
- Citations by year
- 2026: 8 · 2025: 14 · 2024: 14 · 2023: 22 · 2022: 30 · 2021: 29 · 2020: 31 · 2019: 33 · 2018: 24 · 2017: 24 · 2016: 25 · 2015: 25 · 2014: 24 · 2013: 27 · 2012: 19
- FWCI
- 4.32
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Power Systems (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Optimal Power Flow Distribution
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Power System Optimization and Stability
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Power Quality and Harmonics
- Keywords
- three-phase power flow, current injection method, unbalanced power systems, Newton's method, Cartesian coordinates, distribution systems
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