Voltage Unbalance in DER-Rich Networks — When Solar PV Helps and When It Doesn’t
| Network | IEEE European LV Test Feeder — 55 load buses, 0.416 kV nominal |
| DER integrated | 40 single-phase PV panels, 2.5 kW each — 100 kW total, grid-following inverters |
| Three load scenarios | Low, medium, and high phase imbalance — same total load, different phase distribution |
| Key paradox | PV integration reduced unbalance in the medium-imbalance scenario but worsened it in the low-imbalance scenario |
| Measurement problem | IEEE PVUR1 and PVUR2 indices can overestimate VUF by a factor of 10× — making them unreliable for DER-rich networks |
| Most accurate index | CIGRE unbalance factor = exact reformulation of the true IEC VUF — using only line voltage magnitudes |
| Tool used | OpenDSS power flow analysis on IEEE European LV Test Feeder |
| स्रोत | Zabihi, Badesa & Hernandez, arXiv:2505.23435, Universidad Politécnica de Madrid, मई 2025 |
01 Context — Two Problems in One
As distributed energy resources proliferate on low-voltage distribution networks, power quality engineers face two related but distinct challenges. The first is the physical problem: single-phase PV panels, EV chargers, and battery storage systems connect unevenly across the three phases of a distribution feeder, creating or modifying voltage unbalance in ways that conventional network analysis did not need to anticipate. The second is the measurement problem: the existing portfolio of voltage unbalance indices — defined by IEEE, आईईसी, कोई, and CIGRE over decades of standards development — do not all respond the same way to the phase angle deviations that DER introduces, and some can give misleadingly large or small readings depending on network conditions.
This case study presents the findings of a 2025 study by Zabihi, Badesa, and Hernandez at the Universidad Politécnica de Madrid (UPM), which investigated both problems simultaneously on the IEEE European LV Test Feeder — a 55-bus, 0.416 kV network representing a realistic European low-voltage distribution configuration. The study’s two key findings are: first, that PV integration can either worsen or improve voltage unbalance depending on the baseline load distribution; and second, that the commonly used IEEE PVUR1 and PVUR2 indices can overestimate the true VUF by a factor of 10× or more, making them unreliable as planning tools for DER-rich networks.[1]
Utilities planning DER integration on LV feeders routinely use simplified voltage unbalance indices to assess compliance with the 2% VUF limit. If the index being used can overestimate the true VUF by 10×, a feeder that is actually compliant may appear non-compliant — triggering expensive mitigation that is not needed. उल्टे, if the index underestimates VUF (as LVUR does in certain scenarios), a non-compliant feeder may appear to pass. The choice of measurement index is not a technical detail — it directly affects investment decisions that can run to millions of dollars per feeder.
02 The Measurement Index Problem
Five voltage unbalance indices are in current use by different standards organisations. They differ fundamentally in what they measure, how they measure it, and how accurately they approximate the true voltage unbalance factor under real network conditions:[1]
| Index | मानक | Input required | Accuracy vs. VUF (1–2% range) | Phase angle included? |
|---|---|---|---|---|
| VUF (सत्य) | आईईसी / आईईईई 1159 | Phase voltage magnitudes + angles | संदर्भ (1.000) | Yes |
| CIGRE | CIGRE | Line voltage magnitudes only | Exact (1.000) | Yes (implicitly) |
| LVUR | कोई | Line voltage magnitudes only | 0.866 - 1.005 | Partially |
| PVUR1 | आईईईई एसटीडी 141 | Phase voltage magnitudes only | 0 – 10.7× | नहीं |
| PVUR2 | आईईईई एसटीडी 112 / 936 | Phase voltage magnitudes only | 0 – 16.1× | नहीं |
Both PVUR1 and PVUR2 use only phase voltage magnitudes — they completely ignore phase angle deviations. In a conventional balanced network with symmetrical loads, phase angle deviations are small and this simplification introduces only minor error. But single-phase PV panels, single-phase EV chargers, and unequally distributed single-phase loads all create phase angle deviations that are comparable in magnitude to the voltage magnitude deviations. In this regime, PVUR1 and PVUR2 can return values an order of magnitude different from the true VUF — in either direction. Using these indices to assess DER integration compliance is engineering malpractice.
03 Three Unbalance Scenarios — Same Load, Different Phase Distribution
The study used three load scenarios on the IEEE European LV Test Feeder — each with approximately the same total load (~160–170 kW) but with different distributions across the three phases, creating low, medium, and high initial voltage unbalance:[1]
| Scenario | Phase A load share | Phase B load share | Phase C load share | VUF max (before PV) | VUF mean (before PV) |
|---|---|---|---|---|---|
| I — Low unbalance | 31.7% | 39.5% | 28.8% | 0.982% | 0.787% |
| II — Medium unbalance | 22.2% | 31.5% | 45.3% | 1.625% | 1.255% |
| III — High unbalance | 22.1% | 59.3% | 18.6% | 2.081% | 1.558% |
Scenario III with a VUF maximum of 2.081% already exceeds the EN 50160 planning limit of 2% before any DER is added. Scenarios I and II are within limits. The question the study addresses is: what happens to these unbalance levels when 40 single-phase PV panels are added to the network?
04 PV Integration — A Counterintuitive Result
40 single-phase PV panels at 2.5 kW each — 100 kW total, grid-following type — were added to the IEEE European LV Test Feeder and the voltage unbalance was recalculated for all three scenarios. The results were counterintuitive:[1]
| Scenario | VUF mean before PV | VUF mean after PV | Change | Effect |
|---|---|---|---|---|
| I — Low unbalance | 0.787% | 0.963% | +22% | Worsened |
| II — Medium unbalance | 1.255% | 0.702% | −44% | Improved |
| III — High unbalance | 1.558% | 1.484% | −5% | Marginal |
The counterintuitive result in Scenario I occurs because the 40 single-phase PV panels are distributed across the three phases independently of the load distribution. In Scenario I, the load is already reasonably balanced (31.7/39.5/28.8%). Adding 100 kW of generation that is itself unevenly distributed across phases introduces a new source of asymmetry — the generation phase distribution — which adds to rather than cancels the existing load unbalance. In Scenario II, the load is significantly skewed (22.2/31.5/45.3%), and the PV phase distribution happens to inject more generation into the over-loaded phase, partially compensating the existing unbalance. The net effect depends entirely on how well the PV phase distribution matches the inverse of the load phase distribution — a parameter that utilities rarely control in residential connection approval processes.
05 Power Quality Perspective
This study delivers two findings that should directly change how utilities approach DER integration planning. The first — that PV can worsen voltage unbalance in already-balanced feeders — overturns the common assumption that distributed generation is neutral or beneficial to unbalance. The second — that IEEE PVUR1 and PVUR2 indices are unreliable in DER-rich networks — has immediate implications for any utility still using these indices for LV feeder compliance assessment.
The measurement index finding is the more immediately actionable one. PVUR1 and PVUR2 are widely used in North American utility practice because they require only voltage magnitude measurements — readily available from existing metering. The CIGRE index and the true IEC VUF require either phasor measurement (for VUF) or line-to-line voltage calculations (for CIGRE), both of which are available from modern power quality instruments but not from standard energy meters. The practical consequence is that utilities using PVUR indices to assess DER integration compliance may be making the wrong decisions — either blocking compliant connections or approving non-compliant ones — based on a measurement artefact rather than a real physical condition.
This study formalises what experienced PQ engineers have known informally for years: the choice of voltage unbalance index matters, and it matters more in DER-rich environments than in conventional networks. From a utility PQ engineering perspective, the right approach for LV feeder unbalance assessment in high-DER scenarios is to use the CIGRE index — it is computationally accessible (requires only line voltage magnitudes, available from any Class A PQ instrument), mathematically exact (identical result to the true VUF), and avoids the phase angle measurement requirement that makes the IEC definition difficult to implement in standard monitoring deployments. The fact that CIGRE has not been adopted in North American standards is a historical accident, not a reflection of its technical merit.
सन्दर्भ
- Zabihi A, Badesa L, Hernandez A. “Evaluation of Voltage Unbalance Metrics in Distribution Networks with High DER Penetration.” arXiv:2505.23435, Universidad Politécnica de Madrid (UPM), मई 2025. Available: arxiv.org/abs/2505.23435
- इन 50160:2010+A3:2019. Voltage characteristics of electricity supplied by public electricity networks. CENELEC, Brussels.
- आईईईई एसटीडी 1159-2019. IEEE Recommended Practice for Monitoring Electric Power Quality. आईईईई, न्यू यार्क, NY, 2019.
- आईईसी 61000-4-30:2015+एएमडी1:2021. Electromagnetic compatibility — Part 4-30: बिजली की गुणवत्ता माप तरीकों. आईईसी, Geneva.
- NEMA MG-1-2021. Motors and Generators. National Electrical Manufacturers Association, Rosslyn, VA.
Zabihi A, Badesa L, Hernandez A. “Evaluation of Voltage Unbalance Metrics in Distribution Networks with High DER Penetration.” arXiv:2505.23435, Universidad Politécnica de Madrid, मई 2025.
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This case study is presented in summary and commentary form for educational purposes. The PQ Perspective section (अनुभाग 5) and SVG diagrams are original IPQDF editorial content by Denis Ruest, M.Sc. (Applied), P.Eng. (ret.). IPQDF does not claim authorship of the original research.