電力特性 Harmonics · Measurement Inflow · Outflow Phase Angle Analysis 技術リファレンス

Harmonic Inflow and Outflow: Determining the Direction of Harmonic Current Using Phase Angle Analysis

デニスRuest, 修士号. (適用済み), P.Eng. (レット。) ・・ IPQDF・テクニカルリファレンスシリーズ・・ソース: HIOKI E.E. Corporation — Guidebook for Power Quality Measurement

01 Why Harmonic Direction Matters

Measuring the magnitude of harmonic voltage and current distortion at a point on the network tells you how bad the harmonic situation is. It does not tell you where the harmonics are coming from. In a real distribution network, multiple loads and multiple harmonic sources coexist on the same bus. When a harmonic compliance problem is identified, the first engineering question is: この設備はネットワークに流出する高調波を生成していますか?, それともネットワークから流入する高調波を受信しているのでしょうか？? 答えによって緩和の責任者が決まります.

この違い — 高調波流入と. 流出 — 日本の配電網ガイドラインにおける高調波責任配分の基礎となっており、高調波制限が強化され、複数の非線形負荷が共通のバスを共有するにつれて、他の規制枠組みでも関連性が高まっています。. 方向の決定にはTHD測定以上のものが必要です。測定点での高調波電圧と高調波電流の間の位相関係の分析が必要です。.[1]

ユーティリティの観点 – PCC で方向性が重要な理由

実用性の観点から, a customer generating harmonic current that flows out into the network is a source of harmonic pollution affecting other customers on the same feeder. A customer receiving harmonic current that flows in from the network is a victim of that pollution. These are very different situations with different remedies and different responsibility assignments. IEEE 519 limits apply to the harmonic current a customer injects into the network — outflow — not to what the customer receives. A utility engineer investigating a harmonic complaint needs to know direction before assigning responsibility.

02 Two Methods for Judging Inflow and Outflow

方法 1 — Harmonic power polarity

The first method uses the sign of the harmonic active power (P_H) at each harmonic order. Harmonic power is the product of harmonic voltage, 高調波電流, and the cosine of the phase angle between them. A positive harmonic power indicates the installation is consuming that harmonic — inflow. A negative harmonic power indicates it is generating that harmonic — outflow.[1]

This method is theoretically clean but has a practical limitation: harmonic power levels decrease rapidly with increasing harmonic order. The 11th harmonic power is typically a small fraction of the 5th harmonic power. At higher orders, the harmonic power signal approaches the noise floor of the measurement instrument, making polarity determination unreliable. This method works well for the dominant low-order harmonics (3RD, 5番目の, 7番目の) but becomes unreliable for the 11th, 13番目の, 以上.[1]

方法 2 — Harmonic voltage-current phase difference (θ)

The second method uses the phase angle difference between the harmonic voltage and the harmonic current at each harmonic order — denoted θ. This is a more robust approach because it is based on phase angle measurement rather than power magnitude, and phase angle can be determined accurately even when harmonic magnitudes are small.[1]

For 3-phase 3-wire installations using the 2-meter measurement method (3P3W2M), the recommended metric is the sum phase angle θ_和 — the harmonic voltage-current phase difference computed from the sum of the measured quantities across both measurement channels. This sum approach provides a more stable and representative value than individual phase measurements for 3-phase systems.

Inflow / Outflow Decision Rule — θ_和

Inflow (consuming harmonics)

−90° ≤ θ_和 ≤ +90°

Outflow (generating harmonics)

−180° to −90° or +90° to +180°

Recommended procedure — HIOKI guidance

HIOKI recommends a two-step judgment process. 最初の, confirm that the harmonic current amplitude is significant — if the harmonic current is small relative to the fundamental, direction judgment is less meaningful regardless of method. 2番目の, apply the θ_和 criterion to determine inflow or outflow. The θ_平均 graph in the HIOKI Model 9624-50 PQA HiVIEW Pro application software provides the appropriate averaged phase angle display for this judgment.[1]

03 Measurement Setup

パラメータ	価値 / Configuration
Circuit type	3-相3線 (3P3W2M — 2-meter method)
電圧レベル	6.6 kV distribution circuit
Measurement instrument	HIOKI Power Quality Analyzer with PQA HiVIEW Pro software (Model 9624-50)
Key display	Harmonic voltage-current phase difference time plot — θ_平均グラフ
Harmonics monitored	基本的な (1セント), 3RD, 5番目の, 7番目の

The 3P3W2M configuration uses two current sensors and two voltage measurements to fully characterize the 3-phase 3-wire system. ザ “和” phase angle approach is specific to this configuration — it combines the measurements from both channels to produce a single θ_和 value per harmonic order that is representative of the overall 3-phase harmonic flow direction.[1]

04 Analysis Examples: Four Harmonic Orders, Four Different Behaviours

The following examples are drawn from measurements on a 6.6 kVの回路. The time plots show the harmonic voltage-current phase difference (θ_和) over time for each harmonic order. The inflow/outflow boundary is at ±90°.[1]

基本的な (1st harmonic) and 5th harmonic — Inflow

Time plot of harmonic voltage-current phase difference for fundamental and 5th harmonic showing inflow

イチジク. 1. Time plot of θ_和 for the fundamental (ブラウン) and 5th harmonic (緑). Both remain within the −90° to +90° inflow zone throughout the measurement period, confirming that the installation is consuming both the fundamental power and the 5th harmonic. ソース: HIOKI E.E. 法人.[1]

The fundamental wave is in inflow — this is expected, as the installation is consuming real power from the network. The 5th harmonic is also predominantly inflow, indicating that the dominant 5th harmonic source is elsewhere on the network and this installation is receiving it. This installation is a victim of 5th harmonic pollution, not a source of it.

3rd harmonic — Outflow

Time plot of harmonic voltage-current phase difference for 3rd harmonic showing outflow

イチジク. 2. Time plot of θ_和 for the 3rd harmonic (赤). The phase angle consistently falls outside the ±90° inflow zone, in the −180° to −90° or +90° to +180° range — confirming 3rd harmonic outflow. This installation is generating 3rd harmonic current that flows into the network. ソース: HIOKI E.E. 法人.[1]

The 3rd harmonic is outflow — this installation is a 3rd harmonic source. Note that the 3rd harmonic is characteristic of single-phase non-linear loads (スイッチモード電源, fluorescent lighting) rather than 3-phase 6-pulse drives. Its presence as an outflow harmonic on a 6.6 kV circuit suggests single-phase loading on the secondary side of distribution transformers fed from this circuit.

Note on the 180° wrap-around in time plots

The vertical lines visible in the time plots where the phase difference appears to jump between +180° and −180° (またはその逆) are not discontinuities in the harmonic behaviour — they are an artifact of the ±180° representation of a cyclic angle. When θ_和 crosses the +180°/−180° boundary, the display wraps around. The underlying phase angle is continuous; only the display representation jumps. This is important to recognize when interpreting time plots — a phase angle that crosses 180° is still consistently in the outflow zone, not switching between inflow and outflow.[1]

7th harmonic — Outflow

Time plot of harmonic voltage-current phase difference for 7th harmonic showing outflow

イチジク. 3. Time plot of θ_和 for the 7th harmonic (ブルー). Outflow confirmed — the phase angle remains outside the ±90° inflow zone. The 180° wrap-around is visible as vertical transitions in the trace. ソース: HIOKI E.E. 法人.[1]

The 7th harmonic is also outflow. Together with the 3rd harmonic outflow, this suggests the installation contains significant non-linear load generating harmonic current into the 6.6 kVネットワーク. The 5th harmonic inflow observed earlier indicates the 5th harmonic on this bus is coming from elsewhere — the local installation’s own 5th harmonic generation is being masked or dominated by an external 5th harmonic source.

Judgment Examples 1 と 2 — Applying the θ_平均 display

Judgment Example 1 — HIOKI PQA HiVIEW Pro θavg harmonic time plot display

イチジク. 4. Judgment Example 1 — θ_平均 harmonic time plot in HIOKI PQA HiVIEW Pro. The averaged phase angle display provides a cleaner basis for inflow/outflow determination than raw θ_和 point-by-point values. ソース: HIOKI E.E. 法人.[1]

Judgment Example 2 — HIOKI PQA HiVIEW Pro θavg harmonic time plot display

イチジク. 5. Judgment Example 2 — θ_平均 harmonic time plot. A second scenario demonstrating application of the inflow/outflow judgment methodology using the averaged phase angle display. ソース: HIOKI E.E. 法人.[1]

HIOKI PQA HiVIEW Pro harmonic analysis display showing phase difference results

イチジク. 6. HIOKI PQA HiVIEW Pro harmonic analysis display — tabular view of harmonic voltage-current phase difference results by harmonic order. ソース: HIOKI E.E. 法人.[1]

HIOKI PQA HiVIEW Pro harmonic inflow/outflow summary display

イチジク. 7. HIOKI PQA HiVIEW Pro summary display of harmonic inflow/outflow judgment results across all monitored harmonic orders. ソース: HIOKI E.E. 法人.[1]

HIOKI PQA HiVIEW Pro harmonic time plot with inflow/outflow zone indicators

イチジク. 8. HIOKI PQA HiVIEW Pro 高調波時間プロット (流入/流出ゾーンインジケーター付き) — ±90° 境界がマークされています, θから高調波の方向を視覚的に直接判断できるようになります。_平均トレース. ソース: HIOKI E.E. 法人.[1]

05 日本の規制枠組み: 高調波流出電流制限

日本は、配電レベルでの高調波責任の配分に関する最も発達した国の枠組みの一つを持っています。. 経済産業省は9月に「高調波抑止対策ガイドライン」を公表した。 1994 — 高電圧または超高圧電源を受けている需要側の顧客からの高調波流出電流に特に適用される制限を確立する.[2]

電圧歪みの制限

6.6 kVシステム: 全高調波電圧歪み ≤ 5%
特別高圧システム: 全高調波電圧歪み ≤ 3%

高調波流出電流制限

The Japanese guideline expresses harmonic current limits in milliamperes per kilowatt of contracted power — a normalization that makes limits independent of customer size and directly proportional to the customer’s power contract. Upper limit values are specified per harmonic order, with lower limits for higher-order harmonics. The per-kW normalization means a larger customer has proportionally more harmonic current allowance — but must also comply at every harmonic order independently.[2]

Utility perspective — the per-kW normalization

The Japanese per-kW contracted power normalization is an elegant approach to harmonic responsibility allocation. It recognizes that larger customers draw more current and therefore have a larger absolute harmonic current budget — but that budget scales with their contracted power, not with their actual harmonic performance. A customer who installs effective harmonic mitigation can operate well within their per-kW allowance even at large contracted power levels. A customer with no mitigation will exceed the limit regardless of size as non-linear load fraction increases. The normalization provides a level playing field across customer sizes.

This direction-based regulatory framework — limiting outflow rather than total harmonic current — is the key distinction from IEEE 519’s point-of-common-coupling approach. IEEE 519 limits the harmonic current a customer injects at the PCC, which is effectively an outflow limit. The Japanese guideline makes the outflow concept explicit and applies it at the individual harmonic order level with per-kW normalization. The measurement methodology described in this article — θ_和 phase angle analysis — is the tool that makes this outflow-based regulation auditable.

06 PQ の視点: Direction as a Diagnostic Tool

6.1 When direction analysis changes the diagnosis

The most important implication of harmonic direction analysis is that a high THD measurement at a customer’s service entrance does not automatically mean the customer is responsible for it. If the harmonic current is inflow — arriving from the network — the customer is a victim and the source is elsewhere on the feeder. Requiring the customer to install harmonic filters in this situation wastes money and may not improve the network harmonic situation at all.

逆に, a customer with modest THD levels at their service entrance may still be a significant harmonic outflow source if their contracted power is large — the per-kW Japanese limit could be exceeded even when absolute THD appears acceptable. Direction analysis at each harmonic order is the only way to correctly characterize responsibility.

6.2 Practical application in a harmonic investigation

A practical harmonic investigation sequence using this methodology:

Measure harmonic voltage and current at the point of interest — confirm that harmonic amplitudes are significant enough to justify direction analysis
Apply the θ_和対象となる各高調波次数に対する基準
どの高調波次数が流入しているかを特定する (ネットワークソース) そしてどれが流出するのか (ローカルソース)
流出高調波用: 原因となる局所的な非線形負荷を特定し、緩和オプションを評価する
流入高調波用: ネットワークを調査して、責任のあるソース (同じフィーダ上の他の顧客) を見つけます。, ネットワークの共振条件, ユーティリティ機器

6.3 IPQDF 記事シリーズへの接続

このシリーズの技術記事 (第1条～第3条) 6パルスドライブの高調波特性とネットワークコンポーネントとの相互作用を確立しました。. ケーススタディでは、高調波が軽減されないまま放置されると何が起こるかを実証しました。. この技術リファレンスは、別の次元の画像を完成させます: the measurement methodology needed to determine whether a given installation is a harmonic source or a harmonic receiver — the prerequisite for assigning responsibility and selecting the correct mitigation strategy.

The θ_和 phase angle method described here is instrument-specific in its implementation (HIOKI PQA HiVIEW Pro in this example) but the underlying principle — that harmonic current direction is determined by the phase relationship between harmonic voltage and harmonic current — is universal. Any power quality analyzer that reports harmonic phase angles can support this analysis, with appropriate interpretation of the measurement conventions used by that instrument.

Key takeaway

Harmonic magnitude tells you how bad the distortion is. Harmonic direction tells you who is responsible. Both measurements are needed before any remediation decision can be made with confidence. A THD measurement without direction analysis is an incomplete harmonic investigation.

参照

[1] HIOKI E.E. 法人, “高調波の流入と流出,” で 電力品質測定のためのガイドブック, HIOKI E.E. 法人, Nagano, 日本. 利用可能: hioki.com
[2] Ministry of Economy, Trade and Industry (METI), 日本, “Guideline for Harmonics Deterrence Countermeasures on Demand-Side that receives High Voltage or Extra High-Voltage,” Official Report, 9月 30, 1994.