VSD Harmonic Analysis

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System voltage *

System frequency (Hz) *

Short circuit level *

MVA

Source resistance per phase

Source reactance per phase

[[ vsd.vsd_id || 'VSD-' + String(index + 1).padStart(2, '0') ]]

VSD identifier

Power *

Load

Power factor

Efficiency

Rectifier type

Input line reactor

Reactor inductance

DC link choke

Active front end (AFE)

Maximum harmonic order

Summation method

Method for combining harmonics from multiple VSDs

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Calc number

Tag number

Title

Description

Revision

Company name

Project number

Prepared by

Project name

Client company

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Calculation No.: Calc-001
Revision: A
Description:
Created By: Engineer Name

Project: Project Name
Project No.: P001
Client: Client Name

This calculation analyzes harmonic distortion from 1 Variable Speed Drive(s) connected to a 415V switchboard. The analysis includes harmonic current generation, total harmonic distortion (THD), voltage distortion, and compliance with IEEE 519-2022 and IEC 61000-2-2 standards. <br><br>Variable Speed Drives (VSDs) are non-linear loads that draw harmonic currents from the power system. These harmonics can cause transformer heating, neutral conductor overloading, capacitor bank failures, and equipment malfunction. Proper analysis ensures compliance with power quality standards and prevents equipment damage.

Parameter	Symbol	Value	Notes
System Voltage	V_LL	415 V	Line-to-line voltage
System Frequency	f	50 Hz	Electrical frequency
Short Circuit Level	S_sc	10 MVA	Available fault level at switchboard
Short Circuit Current	I_sc	13.9 kA	Calculated from S<sub>sc</sub>
Source Resistance	R_s	10 mΩ	Resistive component of source impedance
Source Reactance	X_s	50 mΩ	Reactive component of source impedance
Number of VSDs	N	1	Total Variable Speed Drives analyzed
Total VSD Power	P_total	75 kW	Sum of all VSD operating power

Short Circuit Current

Calculate available short circuit current from fault level

Formula: $ I_{sc} = \frac{S_{sc} \times 10^6}{\sqrt{3} \times V_{LL}} $

The short circuit current at the 415V switchboard is 13912A

Formula: $ I_{sc} = \frac{10.0 \times 10^6}{\sqrt{3} \times 415} = 13912 \; \text{A} $

Parameter	Symbol	Value	Notes
VSD-01 - Rated Power	P₁	100 kW	VSD 1 rated power
VSD-01 - Load	Load₁	75 %	Operating load percentage
VSD-01 - Fundamental Current	I_1,1	116 A	Fundamental (50Hz) current
VSD-01 - THD	THD₁	26.5 %	Individual THD
VSD-01 - Rectifier Type		6-pulse	Rectifier configuration

Fundamental Current

The fundamental current for each VSD is calculated from the operating power, efficiency, and power factor. For multiple VSDs, the fundamental currents are summed arithmetically as they are all at the same frequency (50Hz or 60Hz).

Formula: $ I_1 = \frac{P}{\sqrt{3} \times V_{LL} \times \eta \times PF} $

Sum of fundamental currents from all 1 VSD(s)

Formula: $ I_{1,total} = \sum_{i=1}^{N} I_{1,i} = 115.61 \; \text{A} $

Harmonic Current Generation

Harmonic currents are generated at characteristic frequencies: h = kq ± 1, where q is the pulse number and k is a positive integer. For a 6-pulse VSD, characteristic harmonics are 5th, 7th, 11th, 13th, 17th, 19th, etc. The magnitude depends on: • Ih,base: Baseline harmonic as % of fundamental (from manufacturer data) • Kload: Load correction factor (harmonics reduce at light load) • Kreactor: Input reactor reduction factor (3-5% reactance reduces harmonics by 30-50%) • Kdc: DC link choke reduction factor (further reduces harmonics) • Kpulse: Pulse number factor (12-pulse eliminates 5th/7th, 18-pulse eliminates up to 17th)

Formula: $ I_h = I_1 \times \frac{I_{h,base}}{100} \times K_{load} \times K_{reactor} \times K_{dc} \times K_{pulse} $

Harmonic Summation

Phasor random summation (realistic scenario, assumes random phase displacement between VSDs). This is the recommended method per IEEE 519 for multiple non-linear loads with uncorrelated operation.

Formula: $ I_{h,total} = \sqrt{\sum_{i=1}^{N} I_{h,i}^2} $

Current THD Calculation

Total Harmonic Distortion of current (THDI) represents the ratio of harmonic content to fundamental

Formula: $ THD_I = \frac{\sqrt{\sum_{h=2}^{h_{max}} I_h^2}}{I_1} \times 100\% $

Assessment: SEVERE - Very high distortion, mitigation required

Formula: $ THD_I = \frac{\sqrt{936.78}}{115.61} \times 100\% = 26.47\% $

Voltage Distortion

Harmonic currents flowing through the source impedance create harmonic voltage distortion. Rs and Xs are per-phase (star-equivalent) values, so Vh is a line-to-neutral voltage. The impedance increases with harmonic order (h) due to the inductive reactance component. This means higher-order harmonics create proportionally larger voltage distortion.

Formula: $ V_h = I_h \times Z_{s,h} = I_h \times \sqrt{R_s^2 + (h \times X_s)^2} $

Total Harmonic Distortion of voltage (THDV)

Formula: $ THD_V = \frac{\sqrt{\sum_{h=2}^{h_{max}} V_h^2}}{V_1} \times 100\%, \quad V_1 = \frac{V_{LL}}{\sqrt{3}} $

Assessment: MODERATE - Mitigation may be beneficial

Formula: $ THD_V = \frac{\sqrt{\sum V_h^2}}{239.6} \times 100\% = 7.99\% $

Transformer K-Factor

The K-factor quantifies additional transformer heating due to harmonic currents. Standard transformers are rated K-4. Harmonic loads require higher K-rated transformers to prevent overheating and premature failure. Recommended Transformer Rating: K-13 (moderate harmonic environment)

Formula: $ K = \sum_{h=1}^{h_{max}} \left(\frac{I_h}{I_{rms}}\right)^2 \times h^2 $

Select transformer rated for K-13 (moderate harmonic environment)

Formula: $ K = 11.17 $

Neutral Conductor Current

Triplen harmonics (3rd, 9th, 15th, 21st, etc.) do not cancel in the neutral conductor of a three-phase four-wire system. Instead, they add arithmetically, potentially causing neutral current to exceed phase current. VSD loads are single-phase equivalent and triplen harmonics typically have lower magnitude than in traditional three-phase non-linear loads. Neutral Current Ratio: 0.0% Assessment: NORMAL - Standard neutral conductor adequate

Formula: $ I_n = \sqrt{I_3^2 + I_9^2 + I_{15}^2 + I_{21}^2 + \ldots} $

Ratio to fundamental: 0.0%

Formula: $ I_n = 0.00 \; \text{A} $

IEEE 519-2022 Compliance

<b>IEEE 519-2022: IEEE Standard for Harmonic Control in Electric Power Systems</b><br><br>This standard provides limits for harmonic distortion to ensure power quality. Compliance is evaluated at the Point of Common Coupling (PCC).<br><br><b>Current Distortion Limits (TDD - Total Demand Distortion):</b><br>• TDD Limit: 15.0%<br>• Calculated TDD: 26.47%<br>• Current Compliance: <b>FAIL</b><br><br><b>Voltage Distortion Limits (THD<sub>V</sub>):</b><br>• THD<sub>V</sub> Limit: 8.0%<br>• Calculated THD<sub>V</sub>: 7.99%<br>• Voltage Compliance: <b>PASS</b><br><br><b>Overall IEEE 519 Compliance: ✗ FAIL</b>

IEC 61000-2-2 Compliance

<b>IEC 61000-2-2: Electromagnetic Compatibility - Environment - Compatibility Levels for Low-Frequency Conducted Disturbances</b><br><br>This standard specifies electromagnetic compatibility levels for individual harmonic voltages in low-voltage power supply systems.<br><br>No significant harmonics to evaluate<br><br><b>Overall IEC 61000 Compliance: ✗ FAIL</b>

Mitigation Recommendations

<b>Harmonic Mitigation Recommendations</b><br><br>Based on the harmonic analysis, the following mitigation measures are recommended:<br><br><b>1.</b> Install DC link chokes on 6-pulse drives for additional harmonic reduction.<br><br>

Parameter	Symbol	Value	Notes
Total Fundamental Current	I₁	116 A	Sum of fundamental currents from all VSDs
Total RMS Current	I_rms	120 A	Root mean square of total current
Current THD	THD_I	26.5 %	Total harmonic distortion of current
Voltage THD	THD_V	7.99 %	Total harmonic distortion of voltage
K-Factor	K	11.2	Transformer K-factor rating required
Neutral Current	I_n	0 A	Triplen harmonic current in neutral
Crest Factor	CF	1.43	Peak to RMS current ratio
IEEE 519 Current TDD	TDD	26.5 %	Total demand distortion
IEEE 519 Compliance		FAIL	Overall IEEE 519-2022 compliance status
IEC 61000 Compliance		FAIL	Overall IEC 61000-2-2 compliance status

Created By
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Checked
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Approved
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Client Approved
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