ドイツの送電システムの電力品質 — 大規模モニタリング, 相関分析, と長期予測
| ネットワーク | German transmission system — 85 measurement sites across 50 substations |
| Voltage levels | 110 kVの (38 sites) ・・ 220 kVの (21 sites) ・・ 380 kVの (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 |
| 重要な発見 | 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の, 220 kVの, と 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 ヘルツ, 250 ヘルツ, 350 ヘルツ, 450 ヘルツ, 550 ヘルツ, 650 ヘルツ, と 750 ヘルツ
- 電圧不平衡 (UNB) — negative-sequence voltage factor
- Long-term flicker severity (PLT) — 2-hour flicker index
03 Correlation Structures — What the Data Reveals
相関分析論文 (arXiv:2603.12948) 階層的クラスタリングと多次元スケーリングを 85 サイトのデータセットに適用します。これは、PQ 動作の類似性によってサイトをグループ化し、異なるサイトのどのパラメータが時間の経過とともに一緒に移動するかを明らかにする多変量統計からの手法です。. 重要な発見は、一貫性があることです, 反復相関構造は個々のサイトの両方に存在します (異なる PQ パラメータ間) 地理的に離れたサイト間でも (同じパラメータに対して).
サイト内の相関 - 一緒に移動するパラメータ
個別の測定現場で, 特定の PQ パラメータは体系的に相関しています. 5 次高調波と 7 次高調波電圧 (6 パルス コンバータ負荷からの主要な次数) は、工業団地や HVDC コンバータ ステーションに近い場所で強い正の相関を示します。. この共同運動は共通のソースを反映しています: 両方の高調波は同じコンバータ技術によって生成され、コンバータの負荷が変化すると両方とも増加または減少します。. このサイト内パラメータの相関関係は、サイトで 5 次高調波と 7 次高調波に強い相関がある場合、システム設計のモニタリングに役立ちます。, 一方を監視すると、もう一方に関する重要な情報が得られます, それに応じてモニタリング頻度や機器の仕様を調整できます。.
サイト間の相関 - ネットワーク全体の現象
ネットワーク計画にとってより重要なのは、地理的に離れたサイト、つまり共通の給電線や変電所を共有しないサイト間の一貫した相関関係を発見することです。. これらのクロスサイト相関は、ネットワーク全体の PQ 現象を反映しています。: 大規模な発生源からの高調波放射 (洋上風力発電所, HVDC リンク) 送電網を介して複数の変電所に同時に伝播する, または季節柄 (太陽光発電量が少なく産業需要が高い冬季の高調波含有量) 同じ上のすべてのサイトに影響を与える 380 kVバックボーン.
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 アンサンブル予測 — 将来の PQ レベルの予測
2 番目の arXiv 論文 (arXiv:2603.02706) DER の普及が進むにつれてますます重要になる問題に対処します: 伝送ネットワーク内の PQ レベルの長期的な変化を確実に予測できるか? はいの場合, TSO はコンプライアンス上の問題を発生前に予測できます, 緩和投資を積極的に計画する, 制限超過を待ってアクションを起こすのではなく、PQ の劣化が予測されるサイトに監視リソースを割り当てます。.
アンサンブルアプローチ
この論文では、複数の予測モデル、つまり統計的時系列モデルを評価しています。, 機械学習のアプローチ, 季節分解法 - ドイツとエストニアの送信サイトからの毎週の 95 パーセンタイル PQ データに適用. すべてのサイトおよびパラメーターにわたって、一貫して他のモデルを上回る単一モデルはありません。. 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 |
| 電圧不平衡 (UNB) | Good — slow-changing structural factor | Single-phase load growth · Network asymmetry | Plan network transposition or phase balancing investments |
| ちらつき (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. 今日は, 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:
- ネットワーク設計の監視は、一度設定すれば終わりというものではありません. DER の普及とネットワーク トポロジの進化に伴い, 最適な測定場所が変わる. 相関分析は定期的に、おそらく毎回繰り返す必要があります。 5 年 — 新たな冗長性と新たに重要な測定ギャップを特定するため
- THDv だけでなく、個々の高調波次数も重要です. 5番目, 7番目の, と 11 次高調波はそれぞれ異なるソースを持っています, 異なる伝播特性, およびさまざまな共振リスク. THDvのみをモニタリングすると、発生源の帰属と共鳴の評価に必要な情報が欠落します
- 季節パターンは現実的であり、予測可能です. 送信レベルの高調波歪みには、産業用負荷間のバランスによって引き起こされる季節成分があります。 (冬にはもっと高くなります) そして再生可能発電 (夏はPVが高くなる, 一年中風が吹く). 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のレベル. 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 電力品質の観点
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. に 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. ドイツの TSO アプローチ — PQ モニタリング データを戦略的資産として扱い、その価値を最大限に引き出すためのインフラストラクチャと分析機能に投資 — は、エネルギー転換に求められるモデルです.
参照
- 匿名の著者. “大規模な電力品質データにおける相関構造の特定と視覚化。” arXiv:2603.12948, 3月 2025. 利用可能: arxiv.org/abs/2603.12948
- 匿名の著者. “電力品質パラメータのアンサンブル予測。” arXiv:2603.02706, 3月 2025. 利用可能: arxiv.org/abs/2603.02706
- IEC 61000-4-30:2015+AMD1:2021. 電磁両立性 - パート 4-30: 電力品質測定方法. IEC, ジュネーブ.
- IN 50160:2010+A3:2019. 公共電力網から供給される電力の電圧特性. CENELEC, ブリュッセル.
- IEC 61000-2-12:2003. 電磁適合性 — MV および HV 電源システムにおける LF 障害に対する適合性レベル. IEC, ジュネーブ.
一次情報源: arXiv:2603.12948 (“大規模な電力品質データにおける相関構造の特定と可視化”) そしてarXiv:2603.02706 (“電力品質パラメータのアンサンブル予測”), どちらもドイツの TSO 測定キャンペーンによるものです, 3月 2025. オープンアクセスのプレプリント.
SVG 図と PQ パースペクティブ (セクション 6) Denis Ruest によるオリジナルの IPQDF 編集コンテンツです, 修士号. (適用済み), P.Eng. (レット。). IPQDF は元の研究の著者であることを主張していません.