Power flow in four-wire distribution networks—General approach
Open accessAbstract
The neutral wire in most power flow software is usually merged into phase wires using Kron's reduction. Since the neutral wire and the ground are not explicitly represented, neutral wire and ground currents and voltages remain unknown. In some applications, like power quality and safety analyses, loss analysis, etc., knowing the neutral wire and ground currents and voltages could be of special interest. In this paper, a general power flow algorithm for three-phase four-wire radial distribution networks, considering neutral grounding, based on backward-forward technique, is proposed. In this novel use of the technique, both the neutral wire and ground are explicitly represented. A problem of three-phase distribution system with earth return, as a special case of a four-wire network, is also elucidated. Results obtained from several case studies using medium- and low-voltage test feeders with unbalanced load, are presented and discussed.
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These impacts are exacerbated in four-wire LV networks with MEN configuration, where neutral currents and neutral-to-ground potentials are strongly influenced by unbalanced load and PV allocation across phases.
“These impacts are exacerbated in four-wire LV networks with multiple earthed neutral (MEN) configuration, where neutral currents and neutral-to-ground potentials are strongly influenced by unbalanced load and PV allocation across phases [8][9][10][11].”
From Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study (2026) · cites this paper as [9]
The indexed Abstract describes four-wire distribution networks with neutral grounding and case studies using unbalanced loads; it also says neutral and ground currents and voltages are represented. It does not address PV allocation across phases, identify a multiple-earthed-neutral (MEN) configuration, or establish that the stated impacts are exacerbated in such networks. (LLM, conf=0.84)
Experimental — accuracy not yet measuredSubsequent studies extended PV impact analysis to more realistic unbalanced three-phase models, but explicit representation of neutral conductors was often neglected.
“Subsequent studies extended this to more realistic unbalanced three-phase models; however, explicit representation of neutral conductors was often neglected [9].”
From Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study (2026) · cites this paper as [9]
The available passages identify a paper on four-wire distribution networks but do not discuss PV impact studies or whether unbalanced three-phase models often neglected neutral conductors. Searches for neutral conductors and unbalanced three-phase power flow returned only metadata, so our copy does not establish the attributed claim. (LLM, conf=0.70)
Experimental — accuracy not yet measuredIn unbalanced LV networks, neutral currents can exceed the current in one or more phase conductors.
“In unbalanced LV networks, neutral currents can exceed the current in one or more phase conductors, as reported in reference [9] (using a Backward-Forward substitutionbased modelling approach).”
From Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study (2026) · cites this paper as [9]
The available indexed passages contain the paper’s title and bibliographic information, but no substantive results or methods. Searches for neutral currents exceeding phase currents and for the backward-forward modelling approach returned no relevant passage, so the attributed finding cannot be checked against our copy. (LLM, conf=0.72)
Experimental — accuracy not yet measuredMore recent contributions have highlighted the need to model neutral and ground explicitly in multi-grounded four-wire systems to correctly capture neutral currents, neutral-to-ground voltages and associated safety margins.
“More recent contributions have highlighted the need to model neutral and ground explicitly, particularly in multi-grounded four-wire systems, to correctly capture neutral currents, neutral-to-ground voltages and associated safety margins [8][9][10][11].”
From Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study (2026) · cites this paper as [9]
The available copy shows the paper’s title and bibliographic metadata, but no substantive passage addressing explicit neutral-and-ground modeling, multi-grounding, neutral currents, neutral-to-ground voltages, or safety margins. Searches for those terms returned only the title and metadata, so the attributed claim cannot be verified from our copy. (LLM, conf=0.70)
Experimental — accuracy not yet measuredThe backward-forward sweep algorithm performs very well in radial distribution feeders with relatively high R/X ratios, but it is not generally suitable for meshed network topologies.
“The backward-forward sweep algorithm [9] is known to perform very well in radial distribution feeders with relatively high R/X ratios, but it is not generally suitable for meshed network topologies.”
From Voltage Regulation in Rooftop PV-Rich Distribution Networks: A Review and Detailed Case Study (2026) · cites this paper as [9]
The available passages contain bibliographic material (labeled Abstract, no page number), not a discussion of the algorithm’s performance or topology limits. Searches for backward-forward sweep, high R/X ratios, and radial versus meshed networks found no passage that addresses the claim. (LLM, conf=0.68)
Experimental — accuracy not yet measured
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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
- Authors
- Ciric, R. M., Feltrin, A. P., & Ochoa, L. F.
- Affiliations
- Universidade Estadual Paulista (Unesp) (BR)
- ORCID
- Ochoa, L.F.
- Venue
- IEEE Transactions on Power Systems
- Published
- 2003-11
- Volume
- 18
- Issue
- 4
- Pages
- 1283-1290
- ISSN
- 0885-8950 (ISSN-L)
- OpenAlex
- W2764348045
- Cited by
- 265
- References
- 0
- Citations by year
- 2026: 5 · 2025: 3 · 2024: 9 · 2023: 7 · 2022: 10 · 2021: 32 · 2020: 14 · 2019: 20 · 2018: 15 · 2017: 22 · 2016: 9 · 2015: 7 · 2014: 17 · 2013: 15 · 2012: 15
- FWCI
- 6.02
- Type
- journal article
- Language
- en
- Open access
- Locations
- IEEE Transactions on Power Systems (publishedVersion)
- Research Explorer (The University of Manchester) (publishedVersion, other-oa)
- Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) (submittedVersion)
- UNESP Institutional Repository (São Paulo State University) (submittedVersion)
- Funders
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Universidade Estadual Paulista
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Optimal Power Flow Distribution
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Power Quality and Harmonics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Power System Optimization and Stability
- Keywords
- power flow, neutral wire, ground current, neutral grounding, earth return, unbalanced loads, radial distribution systems, low-voltage feeders, medium-voltage feeders
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