Power Quality in the German Transmission System — Large-Scale Monitoring, Correlation Analysis, and Long-Term Forecasting
| Network | German transmission system — 85 measurement sites across 50 substations |
| Voltage levels | 110 kV (38 sites) · 220 kV (21 sites) · 380 kV (26 sites) |
| Measurement standard | IEC 61000-4-30 Class A — 10-minute aggregation intervals |
| Parameters monitored | THDv · Individual harmonics U3–U15 · Voltage unbalance · Flicker (Plt) |
| Dataset scale | 700+ weekly time series · Minimum 3 years per site · German and Estonian TSO campaigns |
| Key methodology 1 | Hierarchical clustering and multidimensional scaling to reveal correlation structures across 85 sites |
| Key methodology 2 | Ensemble forecasting of PQ parameters — outperforms individual models for long-term prediction |
| Key finding | Consistent, recurring correlation structures exist between PQ parameters and across geographically separated sites — reflecting systematic network-wide phenomena driven by inverter-based generation |
01 Context — Why Transmission-Level PQ Matters More Than It Used To
Power quality monitoring has historically focused on the distribution network — the interface between the utility and its customers, where the effects of disturbances are most directly felt. The transmission network was considered self-evidently clean: high voltage, large fault levels, dominated by synchronous generators with inherently low harmonic content. PQ compliance was assessed at the distribution level; transmission was the reference against which distribution was measured.
This assumption is being eroded by the energy transition. The proliferation of inverter-based resources — offshore wind farms connected at 380 kV through HVDC links, large-scale PV installations feeding into 220 kV substations, FACTS devices and HVDC back-to-back stations at transmission level — has introduced harmonic sources and dynamic PQ behaviour at voltage levels where they were not previously present. Two 2025 arXiv papers from German TSO measurement campaigns document this evolution in concrete, large-scale data: one characterising the correlation structure of PQ disturbances across 85 measurement sites, the other developing and validating forecasting methods for long-term PQ prediction at transmission level.
The 85-site, 50-substation monitoring campaign described in arXiv:2603.12948 is one of the largest published transmission-level PQ datasets in the world. It spans three voltage levels — 110 kV, 220 kV, and 380 kV — with measurements at both individual feeders (transmission lines) and transformer busbars. This spatial coverage enables something that single-point or even regional monitoring cannot provide: identification of which PQ disturbances are local (confined to one substation or feeder) and which are network-wide (correlated across geographically separated sites). That distinction is fundamental to root-cause analysis and to efficient mitigation investment decisions.
02 The Dataset — Scale and Structure
The two arXiv papers use overlapping but distinct datasets from German TSO measurement campaigns. The correlation analysis paper uses 85 sites; the forecasting paper uses a combined German-Estonian dataset of 14 German and 13 Estonian sites with at least 3 years of continuous measurement per site.
All measurements comply with IEC 61000-4-30 Class A — the highest accuracy class for power quality measurement instruments — using 10-minute aggregation intervals as the primary data resolution. For the forecasting study, these 10-minute values are further aggregated to weekly 95th-percentile values, creating time series that capture the statistical PQ environment at each site across seasons and years without being dominated by individual extreme events.
The monitored parameters cover the full range of EN 50160 voltage quality indices:
- Total Harmonic Distortion of voltage (THDv) — aggregate harmonic content
- Individual harmonic voltages U3 through U15 — odd harmonics at 150 Hz, 250 Hz, 350 Hz, 450 Hz, 550 Hz, 650 Hz, and 750 Hz
- Voltage unbalance (UNB) — negative-sequence voltage factor
- Long-term flicker severity (Plt) — 2-hour flicker index
03 Correlation Structures — What the Data Reveals
The correlation analysis paper (arXiv:2603.12948) applies hierarchical clustering and multidimensional scaling to the 85-site dataset — techniques from multivariate statistics that group sites by the similarity of their PQ behaviour and reveal which parameters at different sites move together over time. The key finding is that consistent, recurring correlation structures exist both within individual sites (between different PQ parameters) and across geographically separated sites (for the same parameter).
Within-site correlations — parameters that move together
At individual measurement sites, certain PQ parameters are systematically correlated. The 5th harmonic and 7th harmonic voltages — the dominant harmonic orders from 6-pulse converter loads — show strong positive correlation at sites near industrial parks and HVDC converter stations. This co-movement reflects the common source: both harmonics are generated by the same converter technology and both increase or decrease together as the converter load varies. This within-site parameter correlation is useful for monitoring system design — if the 5th and 7th harmonics are strongly correlated at a site, monitoring one provides substantial information about the other, and the monitoring frequency or instrument specification can be adjusted accordingly.
Cross-site correlations — network-wide phenomena
More significant for network planning is the finding of consistent correlations between geographically separated sites — sites that share no common feeder or substation. These cross-site correlations reflect network-wide PQ phenomena: harmonic emissions from large sources (offshore wind farms, HVDC links) that propagate through the transmission network to multiple substations simultaneously, or seasonal patterns (higher harmonic content in winter when PV generation is low and industrial demand is high) that affect all sites on the same 380 kV backbone.
One of the most practically valuable outputs of the correlation analysis is the identification of redundant measurement locations — sites that exhibit such high PQ correlation with neighbouring sites that their measurements provide little additional information. This has direct implications for TSO monitoring budget allocation: a network with 85 measurement sites may be able to achieve the same information content with 60–65 optimally placed sites, redirecting the freed monitoring capacity to undercharacterised areas of the network. This is the kind of insight that only becomes visible when you analyse the full dataset collectively rather than site by site.
04 Ensemble Forecasting — Predicting Future PQ Levels
The second arXiv paper (arXiv:2603.02706) addresses a question that becomes increasingly important as DER penetration grows: can the long-term evolution of PQ levels in the transmission network be reliably predicted? If yes, TSOs can anticipate compliance problems before they occur, plan mitigation investments proactively, and allocate monitoring resources to sites where PQ deterioration is forecast rather than waiting for limit exceedances to trigger action.
The ensemble approach
The paper evaluates multiple forecasting models — statistical time series models, machine learning approaches, and seasonal decomposition methods — applied to weekly 95th-percentile PQ data from German and Estonian transmission sites. No single model consistently outperforms all others across all sites and parameters. The paper’s key methodological finding is that ensemble forecasting — combining the predictions of multiple models with appropriate weighting — consistently outperforms the best individual model in terms of accuracy and robustness across different sites, parameters, and forecast horizons.
This is a well-established principle in meteorological forecasting that has now been validated for power quality data: diversity of models captures different aspects of the underlying process, and the combination is more robust than any single approach. The ensemble method achieved significant improvements over seasonal naive benchmarks and over the best individual model in terms of forecast accuracy for all monitored PQ parameters.
| PQ parameter | Forecastability | Dominant driver | Planning value |
|---|---|---|---|
| THDv (voltage harmonic distortion) | Moderate — seasonal pattern strong | Industrial load seasonality · DER generation mix | Identify sites approaching limits ahead of DER expansion |
| U5, U7 (5th and 7th harmonics) | Good — driven by converter load | HVDC schedules · Industrial production patterns | Anticipate harmonic resonance risk at new DER connection points |
| Voltage unbalance (UNB) | Good — slow-changing structural factor | Single-phase load growth · Network asymmetry | Plan network transposition or phase balancing investments |
| Flicker (Plt) | Lower — more event-driven | Wind generation variability · Arc furnace operations | Identify substations requiring reactive compensation for wind integration |
The forecasting methodology enables a fundamental shift in how TSOs manage transmission-level PQ compliance. Today, the standard approach is: measure, detect exceedance, investigate, mitigate. The lead time from problem detection to mitigation implementation is typically 1–3 years for transmission-level interventions. If PQ deterioration can be reliably forecast 1–2 years ahead — before the limit exceedance actually occurs — the mitigation can be in place before the problem manifests. For a TSO managing hundreds of substations with diverse DER connection profiles, this proactive capability is the difference between planned capital investment and emergency remediation.
05 Implications for Transmission Network Planning
The two studies together define the state of the art for transmission-level PQ monitoring and management. Their combined findings have direct implications for how TSOs should approach PQ in a high-DER environment:
- Monitoring network design is not a set-and-forget decision. As DER penetration and network topology evolve, the optimal measurement locations change. Correlation analysis should be repeated periodically — perhaps every 5 years — to identify new redundancies and newly important measurement gaps
- Individual harmonic orders matter — not just THDv. The 5th, 7th, and 11th harmonics each have different sources, different propagation characteristics, and different resonance risks. Monitoring only THDv misses the information needed for source attribution and resonance assessment
- Seasonal patterns are real and forecastable. Harmonic distortion at transmission level has a seasonal component driven by the balance between industrial load (higher in winter) and renewable generation (higher in summer for PV, year-round for wind). Planning assessments should account for seasonal worst-case scenarios, not just annual averages
- Cross-border propagation is a planning factor. The inclusion of Estonian TSO data alongside German data reflects the reality that transmission-level PQ disturbances do not respect national boundaries. Harmonics from large HVDC interconnectors and offshore wind farms propagate across the synchronised European transmission network
HVDC converter stations are among the most significant new harmonic sources at the 380 kV level. Each HVDC converter produces a characteristic harmonic spectrum — for a 12-pulse converter, dominant harmonics at the 11th and 13th orders — that propagates into the AC network at both ends of the link. As Germany expands its HVDC capacity to transport offshore wind power from the north to the industrial south, the harmonic environment at 380 kV substations along the HVDC corridors will change systematically. The correlation structures identified in the arXiv:2603.12948 study will shift as these new sources come online — and the correlation analysis methodology provides the tool to track these changes systematically, rather than discovering them through limit exceedances.
06 Power Quality Perspective
These two papers represent the leading edge of what transmission PQ monitoring can reveal when the dataset is large enough and the analysis methodology is sophisticated enough. The individual case study — one substation, one disturbance event — is the traditional unit of PQ analysis. At 85 sites and hundreds of site-years of data, a different level of insight becomes possible: understanding the PQ behaviour of the transmission system as a system, not as a collection of independent measurement points.
The correlation structure findings are particularly valuable from a utility engineering perspective because they provide an objective, data-driven answer to a question that has historically been answered by engineering judgment: which measurement sites are most important? The answer from the data may differ from the engineering intuition — a site that seems important because it is near a large HVDC converter may be highly correlated with adjacent sites and therefore redundant, while a seemingly unremarkable 110 kV substation in a rural area may have a unique PQ signature that is not captured anywhere else in the network.
The German TSO measurement campaign described in these papers represents a decade of institutional commitment to PQ monitoring infrastructure — not just deploying instruments, but ensuring IEC 61000-4-30 Class A compliance, maintaining measurement continuity for 3+ years per site, building data management systems capable of handling hundreds of site-years of 10-minute data, and investing in the analytical capability to extract meaning from the dataset. Most utilities — even large ones — have not made this investment. The consequence is that they are managing DER integration on their transmission networks with a PQ understanding that lags their operational reality by years. The German TSO approach — treat PQ monitoring data as a strategic asset and invest in the infrastructure and analysis capability to extract its full value — is the model that the energy transition demands.
References
- Anonymous authors. “Identification and Visualization of Correlation Structures in Large-Scale Power Quality Data.” arXiv:2603.12948, March 2025. Available: arxiv.org/abs/2603.12948
- Anonymous authors. “Ensemble Forecasting of Power Quality Parameters.” arXiv:2603.02706, March 2025. Available: arxiv.org/abs/2603.02706
- IEC 61000-4-30:2015+AMD1:2021. Electromagnetic compatibility — Part 4-30: Power quality measurement methods. IEC, Geneva.
- EN 50160:2010+A3:2019. Voltage characteristics of electricity supplied by public electricity networks. CENELEC, Brussels.
- IEC 61000-2-12:2003. Electromagnetic compatibility — Compatibility levels for LF disturbances in MV and HV power supply systems. IEC, Geneva.
Primary sources: arXiv:2603.12948 (“Identification and Visualization of Correlation Structures in Large-Scale Power Quality Data”) and arXiv:2603.02706 (“Ensemble Forecasting of Power Quality Parameters”), both from German TSO measurement campaigns, March 2025. Open access preprints.
SVG diagrams and PQ Perspective (Section 6) are original IPQDF editorial content by Denis Ruest, M.Sc. (Applied), P.Eng. (ret.). IPQDF does not claim authorship of the original research.