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

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: is this installation generating harmonics that flow out into the network, or is it receiving harmonics that flow in from the network? The answer determines who is responsible for mitigation.

This distinction — harmonic inflow vs. outflow — is the basis of harmonic responsibility allocation in Japan’s distribution network guidelines and is increasingly relevant in other regulatory frameworks as harmonic limits tighten and multiple non-linear loads share common buses. Determining direction requires more than a THD measurement — it requires analysis of the phase relationship between harmonic voltage and harmonic current at the measurement point.[1]

02 Two Methods for Judging Inflow and Outflow

Método 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, corriente armónica, 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, 5ª, 7ª) but becomes unreliable for the 11th, 13ª, and above.[1]

Método 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_sum — 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.

03 Measurement Setup

The 3P3W2M configuration uses two current sensors and two voltage measurements to fully characterize the 3-phase 3-wire system. La “sum” phase angle approach is specific to this configuration — it combines the measurements from both channels to produce a single θ_sum 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 circuito kV. The time plots show the harmonic voltage-current phase difference (θ_sum) over time for each harmonic order. The inflow/outflow boundary is at ±90°.[1]

Fundamental (1st harmonic) and 5th harmonic — Inflow

Higo. 1. Time plot of θ_sum for the fundamental (marrón) and 5th harmonic (verde). 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. Fuente: HIOKI E.E. Corporación.[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

Higo. 2. Time plot of θ_sum for the 3rd harmonic (rojo). 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. Fuente: HIOKI E.E. Corporación.[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 (switch-mode power supplies, 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.

7th harmonic — Outflow

Higo. 3. Time plot of θ_sum for the 7th harmonic (azul). Outflow confirmed — the phase angle remains outside the ±90° inflow zone. The 180° wrap-around is visible as vertical transitions in the trace. Fuente: HIOKI E.E. Corporación.[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 network. 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 y 2 — Applying the θ_avg display

Higo. 4. Judgment Example 1 — θ_avg harmonic time plot in HIOKI PQA HiVIEW Pro. The averaged phase angle display provides a cleaner basis for inflow/outflow determination than raw θ_sum point-by-point values. Fuente: HIOKI E.E. Corporación.[1]

Higo. 5. Judgment Example 2 — θ_avg harmonic time plot. A second scenario demonstrating application of the inflow/outflow judgment methodology using the averaged phase angle display. Fuente: HIOKI E.E. Corporación.[1]

Higo. 6. HIOKI PQA HiVIEW Pro harmonic analysis display — tabular view of harmonic voltage-current phase difference results by harmonic order. Fuente: HIOKI E.E. Corporación.[1]

Higo. 7. HIOKI PQA HiVIEW Pro summary display of harmonic inflow/outflow judgment results across all monitored harmonic orders. Fuente: HIOKI E.E. Corporación.[1]

Higo. 8. HIOKI PQA HiVIEW Pro harmonic time plot with inflow/outflow zone indicators — the ±90° boundaries are marked, enabling direct visual determination of harmonic direction from the θ_avg trace. Fuente: HIOKI E.E. Corporación.[1]

05 Japanese Regulatory Framework: Harmonic Outflow Current Limits

Japan has one of the most developed national frameworks for harmonic responsibility allocation at the distribution level. The Ministry of Economy and Industries issued its Guideline for Harmonics Deterrence Countermeasures in September 1994 — establishing limits that apply specifically to harmonic outflow current from demand-side customers receiving high-voltage or extra-high-voltage supply.[2]

Voltage distortion limits

• 6.6 kV system: Total Harmonic Voltage Distortion ≤ 5%
• Extra high-voltage system: Total Harmonic Voltage Distortion ≤ 3%

Harmonic outflow current limits

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]

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_sum phase angle analysis — is the tool that makes this outflow-based regulation auditable.

06 PQ Perspective: 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.

A la inversa, 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:

1. Measure harmonic voltage and current at the point of interest — confirm that harmonic amplitudes are significant enough to justify direction analysis
2. Apply the θ_sum criterion to each harmonic order of interest
3. Identify which harmonic orders are inflow (network source) and which are outflow (local source)
4. For outflow harmonics: identify the local non-linear loads responsible and assess mitigation options
5. For inflow harmonics: investigate the network for the responsible source — other customers on the same feeder, network resonance conditions, utility equipment

6.3 Connection to the IPQDF article series

The technical articles in this series (Articles 1–3) established the harmonic signatures of 6-pulse drives and their interaction with network components. The case studies demonstrated what happens when harmonics are left unmitigated. This technical reference completes a different dimension of the picture: 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_sum 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.

Referencias

1. [1] HIOKI E.E. Corporación, “Entrada y salida de armónicos,” en Guía para la Medición de Calidad de Energía, HIOKI E.E. Corporación, Nagano, Japón. Available: hioki.com
2. [2] Ministry of Economy, Trade and Industry (METI), Japón, “Guideline for Harmonics Deterrence Countermeasures on Demand-Side that receives High Voltage or Extra High-Voltage,” Official Report, Septiembre 30, 1994.