VSD Harmonic Analysis — help

Overview

Analyses harmonic distortion from Variable Speed Drives (VSDs) on an electrical switchboard per IEEE 519-2022 and IEC 61000-2-2. Calculates individual and combined harmonic current spectra for up to 20 VSDs, voltage distortion at the point of common coupling, Total Harmonic Distortion (THD), Total Demand Distortion (TDD), transformer K-factor, neutral conductor current from triplen harmonics, and crest factor. Supports 6-, 12-, 18- and 24-pulse rectifier configurations, input line reactors, DC link chokes, and Active Front End (AFE) drives. Provides compliance checking against IEEE 519 and IEC 61000 limits with automatic mitigation recommendations.

Input Parameters

Switchboard Parameters

Parameter	Type	Default	Range	Description
`system_voltage`	Number	415 V	100 – 1,000,000 V	Line-to-line voltage
`system_frequency`	Enum: 50 / 60	50 Hz	—	Electrical system frequency
`short_circuit_level_mva`	Number	10 MVA	0.1 – 10,000 MVA	Available fault level at switchboard
`source_resistance`	Number	0.01 Ω	0.0001 – 100 Ω	Resistive component of the source impedance, per phase (star equivalent)
`source_reactance`	Number	0.05 Ω	0.0001 – 100 Ω	Reactive component of the source impedance at the fundamental, per phase (star equivalent)

Analysis Settings

Parameter	Type	Default	Range	Description
`max_harmonic_order`	Integer	50	10 – 100	Highest harmonic order to calculate
`summation_method`	Enum: arithmetic / phasor_random	phasor_random	—	Method for combining harmonics from multiple VSDs. arithmetic = direct sum (worst case); phasor_random = root-sum-square (realistic)

VSD Array Entries (1 – 20 drives)

Parameter	Type	Default	Range	Description
`vsd_id`	String	VSD-01	—	Identifier / tag name for the drive
`rated_power_kw`	Number	100 kW	0.1 – 100,000 kW	Drive rated power
`load_percent`	Number	75%	0 – 120%	Operating load as percentage of rated
`power_factor`	Number	0.95	0.5 – 1.0	Displacement power factor
`efficiency_percent`	Number	95%	50 – 99%	Drive efficiency
`rectifier_type`	Enum: 6 / 12 / 18 / 24	6	—	Rectifier pulse number
`has_input_reactor`	Boolean	false	—	Whether an input line reactor is fitted
`reactor_inductance_mh`	Number	0 mH	0 – 1,000 mH	Input reactor inductance (ignored if reactor not fitted)
`has_dc_choke`	Boolean	false	—	Whether a DC link choke is fitted
`is_afe`	Boolean	false	—	Whether this is an Active Front End drive (< 5% THD)

Output Results

Output	Unit	Description
`short_circuit_current`	A	Available short circuit current at switchboard
`total_fundamental_current`	A	Sum of fundamental currents from all VSDs
`total_rms_current`	A	RMS of total current including all harmonics
`total_thd_current`	%	Current total harmonic distortion (THD_I)
`total_thd_voltage`	%	Voltage total harmonic distortion (THD_V)
`total_harmonics`	A (dict)	Combined harmonic current spectrum {order: amps}
`voltage_harmonics`	V (dict)	Harmonic voltage spectrum, per phase (line-to-neutral) {order: volts}
`k_factor`	—	Transformer K-factor for derating assessment
`neutral_current`	A	Neutral conductor current from triplen harmonics
`crest_factor`	—	Peak-to-RMS current ratio (CF = I_peak / I_rms)
`ieee_519_compliance`	dict	IEEE 519-2022 compliance status, SCR, TDD, and individual harmonic checks
`iec_61000_compliance`	dict	IEC 61000-2-2 voltage compatibility level compliance
`recommendations`	list	Automatic mitigation recommendations when limits are exceeded

Formulas

Fundamental Current per VSD

\[ I_1 = \frac{P_{rated} \times \frac{Load\%}{100}}{\eta \times PF \times \sqrt{3} \times V_{LL}} \times 1000 \]

Where \(P_{rated}\) is rated power (kW), \(Load\%\) is operating load percentage, \(\eta\) is efficiency (decimal), \(PF\) is displacement power factor, and \(V_{LL}\) is line-to-line voltage (V). The factor of 1000 converts kW to W.

Characteristic Harmonics

\[ h = k \cdot q \pm 1 \]

Where \(q\) is the rectifier pulse number (6, 12, 18, or 24) and \(k\) is a positive integer. For a 6-pulse VSD the characteristic harmonics are 5, 7, 11, 13, 17, 19, 23, 25, …

6-Pulse Baseline Harmonic Magnitudes

Harmonic Order	Magnitude (% of I₁)
5	20.0
7	14.0
11	9.0
13	7.0
17	6.0
19	5.0
23	4.0
25	4.0
29	3.5
31	3.0
35	2.5
37	2.5
41	2.0
43	2.0
47	1.5
49	1.5

For harmonics not listed in the table, the 1/h rule is used: \(I_{h,base} = 100 / h\) (%).

Harmonic Current with Correction Factors

\[ I_h = I_1 \times \frac{I_{h,base}}{100} \times K_{load} \times K_{reactor} \times K_{dc} \times K_{pulse} \]

Each correction factor modifies the baseline harmonic magnitude.

Load Correction Factor

\[ K_{load} = 0.6 + 0.4 \times \frac{Load\%}{100} \]

Harmonics reduce at light load. At 100% load \(K_{load} = 1.0\); at 0% load \(K_{load} = 0.6\).

Input Reactor Correction Factor

\[ K_{reactor} = \min\!\left(1.0, \;\left(0.5 + 0.5 \times \frac{X_s}{X_s + X_{reactor}}\right) \times \left(1.0 - \frac{0.3}{h}\right)\right) \]

Where \(X_s\) is source reactance (Ω) and \(X_{reactor} = 2\pi f \times L_{mH}/1000\). Input reactors are most effective on lower-order harmonics. If no reactor is fitted, \(K_{reactor} = 1.0\).

DC Link Choke Correction Factor

\[ K_{dc} = \begin{cases} 0.7 & \text{if DC choke fitted} \\ 1.0 & \text{otherwise} \end{cases} \]

Pulse Number Correction Factor

\[ K_{pulse} = \begin{cases} 1.0 & \text{6-pulse (baseline)} \\ 0.0 & \text{harmonic eliminated by higher pulse config} \\ 0.25 & \text{12-pulse (characteristic harmonics)} \\ 0.15 & \text{18-pulse (characteristic harmonics)} \\ 0.10 & \text{24-pulse (characteristic harmonics)} \end{cases} \]

A 12-pulse rectifier eliminates the 5th and 7th harmonics (and other \(h = 6k \pm 1\) not in \(h = 12k \pm 1\)). Characteristic harmonics that survive are reduced.

Harmonic Summation — Multiple VSDs

Arithmetic (worst case):

\[ I_{h,total} = \sum_{i=1}^{N} I_{h,i} \]

Phasor random / RSS (realistic):

\[ I_{h,total} = \sqrt{\sum_{i=1}^{N} I_{h,i}^{\,2}} \]

Phasor random summation (RSS) is the default and recommended method per IEEE 519 for multiple non-linear loads with uncorrelated operation.

Current THD

\[ THD_I = \frac{\sqrt{\displaystyle\sum_{h=2}^{h_{max}} I_h^{\,2}}}{I_1} \times 100\% \]

Total Demand Distortion (TDD)

\[ TDD = \frac{\sqrt{\displaystyle\sum_{h=2}^{h_{max}} I_h^{\,2}}}{I_L} \times 100\% \]

TDD uses the maximum demand load current \(I_L\) as the denominator rather than the fundamental. For this calculator, \(I_L\) is approximated by the total fundamental current. IEEE 519 limits are specified in terms of TDD, not THD.

Short Circuit Ratio (SCR)

\[ SCR = \frac{I_{sc}}{I_{load}} \]

Where \(I_{sc} = \frac{S_{sc} \times 10^6}{\sqrt{3} \times V_{LL}}\). The SCR determines which row of IEEE 519 current limits applies.

IEEE 519 TDD Limits by SCR

SCR	h < 11	11 ≤ h < 17	17 ≤ h < 23	23 ≤ h < 35	h ≥ 35	TDD
< 20	4.0%	2.0%	1.5%	0.6%	0.3%	5.0%
20 – 50	7.0%	3.5%	2.5%	1.0%	0.5%	8.0%
50 – 100	10.0%	4.5%	4.0%	1.5%	0.7%	12.0%
100 – 1000	12.0%	5.5%	5.0%	2.0%	1.0%	15.0%
> 1000	15.0%	7.0%	6.0%	2.5%	1.4%	20.0%

K-Factor (Transformer Derating)

\[ K = \sum_{h=1}^{h_{max}} \left(\frac{I_h}{I_{rms}}\right)^{\!2} \times h^2 = \frac{I_1^{\,2} + \displaystyle\sum_{h=2}^{h_{max}} I_h^{\,2} \, h^2}{I_{rms}^{\,2}} \]

Per IEEE C57.110, each harmonic is referred to the total rms current \(I_{rms} = \sqrt{I_1^{\,2} + \sum I_h^{\,2}}\) and the \(h = 1\) term is included, so a pure sinusoid gives \(K = 1\). The K-factor quantifies additional eddy-current heating in a transformer due to harmonic load currents. Standard transformers are rated K-4. Higher K-factors require specially rated (K-9, K-13, K-20) or derated transformers.

Voltage Distortion

\[ V_h = I_h \times Z_{s,h} = I_h \times \sqrt{R_s^{\,2} + (h \times X_s)^2} \]

Harmonic currents create voltage distortion across the source impedance. The impedance increases with harmonic order \(h\) because \(X_{s,h} = h \times X_s\). \(R_s\) and \(X_s\) are per-phase (star-equivalent) values, e.g. \(Z_s = V_{LL}^2 / S_{sc}\), so \(V_h\) is a line-to-neutral voltage.

\[ THD_V = \frac{\sqrt{\displaystyle\sum_{h=2}^{h_{max}} V_h^{\,2}}}{V_1} \times 100\%, \qquad V_1 = \frac{V_{LL}}{\sqrt{3}} \]

Both \(V_h\) and \(V_1\) are phase (line-to-neutral) quantities. For a purely reactive source this reduces to \(V_h / V_1 = h \times I_h / I_{sc}\). The IEC 61000-2-2 individual levels use the same base, \(V_h / V_1\).

Neutral Current from Triplen Harmonics

\[ I_N = \sqrt{\sum_{n=1}^{\infty} \left(3 \times I_{3n}\right)^2} \]

Triplen harmonics (3rd, 9th, 15th, 21st, …) are zero-sequence and add arithmetically in the neutral of a three-phase four-wire system. The factor of 3 accounts for the three phases.

Crest Factor

\[ CF = \frac{I_{peak}}{I_{rms}} \]

For a pure sinusoid \(CF = \sqrt{2} \approx 1.414\). Harmonic distortion alters the crest factor. The calculator reconstructs the waveform from 100 samples per cycle to determine the true peak.

Worked Examples

The 21 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_harmonics; worked examples for every calculation).

#	Case	I₁ (A)	SCR	THD-I %	TDD %	THD-V %	Result
1	250 kW 12-pulse drive	385.4	72.2	3.34	3.34	0.853	PASS
2	400 kW 18-pulse drive at 690 V	333.8	75.2	1.23	1.23	0.354	PASS
3	200 kW 24-pulse drive at 480 V, 60 Hz	226.6	79.6	0.57	0.57	0.197	PASS
4	Single 75 kW drive at 80 % load (former help example 1)	92.5	150.4	27.06	27.06	2.206	FAIL
5	160 kW active front end drive	246.6	56.4	4.00	4.00	0.663	PASS
6	55 kW drive with DC-link choke	84.8	164.1	20.59	20.59	1.538	FAIL
7	High X/R source (X/R = 20)	115.6	120.3	26.47	26.47	2.747	FAIL
8	100 kW drive at 25 % load, pf 0.90, η 90 %	42.9	324.0	20.59	20.59	0.779	FAIL
9	Spectrum truncated at the 13th harmonic	115.6	120.3	24.25	24.25	1.424	FAIL
10	Mixed fleet at 690 V: 6-pulse overloaded, 12-pulse, reactor and AFE	1,404.6	23.8	15.07	15.07	7.951	FAIL
11	100 kW drive with 3 mH line reactor	115.6	120.3	12.89	12.89	1.347	FAIL
12	Resistive source (X/R = 1) at 480 V, 60 Hz	84.0	114.6	25.89	25.89	2.003	FAIL
13	300 kW drive at 100 % load (SCR 20–50 row)	462.5	30.1	29.42	29.42	11.988	FAIL
14	Small drive with DC choke on a stiff 50 MVA bus (SCR > 1000)	20.8	3,342.6	16.06	16.06	0.059	PASS
15	150 kW 12-pulse drive on a 2 MVA bus (SCR < 20)	231.2	12.0	3.34	3.34	5.119	FAIL
16	Single 100 kW 6-pulse drive on a 10 MVA bus	115.6	120.3	26.47	26.47	2.697	FAIL
17	Three identical 75 kW drives, RSS summation	260.1	53.5	15.28	15.28	3.504	FAIL
18	450 kW of 6-pulse drives on a 1000 kVA transformer: THDv fails	693.7	40.1	29.42	29.42	9.044	FAIL
19	Two identical drives, arithmetic summation	231.2	60.2	26.47	26.47	5.395	FAIL
20	Two drives with 1.5 mH line reactors, RSS summation (former help example 2)	232.1	149.9	10.61	10.61	0.891	PASS
21	Weak 0.5 MVA source: voltage distortion fails	115.6	6.0	26.47	26.47	52.204	FAIL

Example 1 — 250 kW 12-pulse drive

A 12-pulse rectifier cancels the 5th/7th and keeps 11, 13, 23, 25 … at 25 % of the 6-pulse baseline.

Given: 415 V, 50 Hz bus with a 20 MVA three-phase fault level, source X/R 5. Drives — P-101: 250 kW at 100 % load, pf 0.95, η 95 %, 12-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 20 × 10⁶ / (√3 × 415) = 27.824 kA; Z = V² / S_sc = 415² / 20 MVA = 0.008611 Ω per phase (star equivalent) split by X/R 5 → R = 0.001689 Ω, X = 0.008444 Ω

Fundamental I₁(P-101) = 250 × 1 / (0.95 × 0.95) × 1000 / (√3 × 415) = 385.38 A

Correction factors P-101: K_load = 0.6 + 0.4 × 1 = 1.00, K_dc = 1, 12-pulse → only h = 12k ± 1 at K_pulse = 0.25

Spectrum

I₁₁ = I₁ × I_11,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 8.67 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 8:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
11	8.67	2.25	4.5	0.806	0.336
13	6.74	1.75	4.5	0.740	0.309
23	3.85	1.00	1.5	0.748	0.312
25	3.85	1.00	1.5	0.814	0.340
35	2.41	0.62	0.7	0.712	0.297
37	2.41	0.62	0.7	0.753	0.314

THD-I / TDD THD_I = √ΣI_h² / I₁ = 12.89 / 385.38 = 3.34 %; TDD = THD_I with I_L taken as I₁; I_rms = √(385.38² + 12.89²) = 385.59 A. SCR = I_sc/I₁ = 27,824 / 385.38 = 72.2 → IEEE 519 row SCR 50–100 (TDD 12 %) → 3.34 vs limit 12.00 % PASS

Voltage distortion V₁₁ = 8.67 × √(0.001689² + (11 × 0.008444)²) = 0.806 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 2.044 / 239.60 = 0.853 % vs the 8 % limit for V ≤ 1 kV → 0.853 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 50–100 row (h<11 10 %, 11–16 4.5 %, 17–22 4 %, 23–34 1.5 %, ≥35 0.7 %): none of the orders exceeds its row limit → 0 order(s) over limit PASS

IEC 61000-2-2 worst V₂₅/V₁ = 0.814 / 239.60 = 0.340 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (385.38² + 58,599) / 385.59² = 1.39 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.406 (√2 = 1.414 for a sine)

Result 4/4 checks pass → PASS; THD_I 3.3 %, THD_V 0.85 %; governing: current tdd

Reference Hand calculation: I1(P-101) = 250 kW × 1 / (0.95 × 0.95) / (√3 × 415 V) = 385.38 A. Isc = 20 MVA / (√3 × 415 V) = 27.824 kA; SCR = 72.2 → IEEE 519 row 50–100 (TDD limit 12 %). K_load = 0.6 + 0.4 × 1 = 1.00; 12-pulse keeps h = 12k ± 1 at K_pulse = 0.25; I11 = 8.671 A. THDi = √ΣIh² / I1 = 12.890 / 385.38 = 3.34 % (= TDD, IL taken as I1) vs 12 % → PASS. Z = 415² / 20 MVA = 0.008611 Ω, X/R 5 → R = 0.001689, X = 0.008444 Ω; V11 = I11 × √(R² + (11X)²) = 0.806 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 0.853 % vs 8 % → PASS. No individual order exceeds its row limit. IEC 61000-2-2: worst V25/V1 = 0.340 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 1.39; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.406 (validation case c0017-12-pulse-250kw)

Example 2 — 400 kW 18-pulse drive at 690 V

18-pulse: only h = 18k ± 1 survive at 15 % of baseline; the mine-site 690 V bus passes every check.

Given: 690 V, 50 Hz bus with a 30 MVA three-phase fault level, source X/R 5. Drives — CV-01: 400 kW at 90 % load, pf 0.95, η 95 %, 18-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 30 × 10⁶ / (√3 × 690) = 25.102 kA; Z = V² / S_sc = 690² / 30 MVA = 0.01587 Ω per phase (star equivalent) split by X/R 5 → R = 0.003112 Ω, X = 0.01556 Ω

Fundamental I₁(CV-01) = 400 × 0.9 / (0.95 × 0.95) × 1000 / (√3 × 690) = 333.77 A

Correction factors CV-01: K_load = 0.6 + 0.4 × 0.9 = 0.96, K_dc = 1, 18-pulse → only h = 18k ± 1 at K_pulse = 0.15

Spectrum

I₁₇ = I₁ × I_17,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 2.88 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 4:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
17	2.88	0.86	4	0.763	0.192
19	2.40	0.72	4	0.711	0.178
35	1.20	0.36	0.7	0.654	0.164
37	1.20	0.36	0.7	0.692	0.174

THD-I / TDD THD_I = √ΣI_h² / I₁ = 4.12 / 333.77 = 1.23 %; TDD = THD_I with I_L taken as I₁; I_rms = √(333.77² + 4.12²) = 333.79 A. SCR = I_sc/I₁ = 25,102 / 333.77 = 75.2 → IEEE 519 row SCR 50–100 (TDD 12 %) → 1.23 vs limit 12.00 % PASS

Voltage distortion V₁₇ = 2.88 × √(0.003112² + (17 × 0.01556)²) = 0.763 V; V₁ = V_LL/√3 = 690/√3 = 398.37 V; THD_V = √ΣV_h² / V₁ = 1.412 / 398.37 = 0.354 % vs the 8 % limit for V ≤ 1 kV → 0.354 vs limit 8.000 % PASS

IEC 61000-2-2 worst V₁₇/V₁ = 0.763 / 398.37 = 0.192 % vs the 2 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (333.77² + 8,233) / 333.79² = 1.07 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.416 (√2 = 1.414 for a sine)

Result 4/4 checks pass → PASS; THD_I 1.2 %, THD_V 0.35 %; governing: current tdd

Reference Hand calculation: I1(CV-01) = 400 kW × 0.9 / (0.95 × 0.95) / (√3 × 690 V) = 333.77 A. Isc = 30 MVA / (√3 × 690 V) = 25.102 kA; SCR = 75.2 → IEEE 519 row 50–100 (TDD limit 12 %). K_load = 0.6 + 0.4 × 0.9 = 0.96; 18-pulse keeps h = 18k ± 1 at K_pulse = 0.15; I17 = 2.884 A. THDi = √ΣIh² / I1 = 4.121 / 333.77 = 1.23 % (= TDD, IL taken as I1) vs 12 % → PASS. Z = 690² / 30 MVA = 0.015870 Ω, X/R 5 → R = 0.003112, X = 0.015562 Ω; V17 = I17 × √(R² + (17X)²) = 0.763 V; THDv = √ΣVh² / V1, V1 = 690 / √3 = 398.37 V (per-phase Vh over the phase voltage): 0.354 % vs 8 % → PASS. No individual order exceeds its row limit. IEC 61000-2-2: worst V17/V1 = 0.192 % vs 2 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 1.07; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.416 (validation case c0017-18-pulse-690v)

Example 3 — 200 kW 24-pulse drive at 480 V, 60 Hz

24-pulse on a 60 Hz North-American bus: harmonics 23, 25, 47, 49 only at 10 % of baseline.

Given: 480 V, 60 Hz bus with a 15 MVA three-phase fault level, source X/R 5. Drives — CH-1: 200 kW at 85 % load, pf 0.95, η 95 %, 24-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 15 × 10⁶ / (√3 × 480) = 18.042 kA; Z = V² / S_sc = 480² / 15 MVA = 0.01536 Ω per phase (star equivalent) split by X/R 5 → R = 0.003012 Ω, X = 0.01506 Ω

Fundamental I₁(CH-1) = 200 × 0.85 / (0.95 × 0.95) × 1000 / (√3 × 480) = 226.57 A

Correction factors CH-1: K_load = 0.6 + 0.4 × 0.85 = 0.94, K_dc = 1, 24-pulse → only h = 24k ± 1 at K_pulse = 0.1

Spectrum

I₂₃ = I₁ × I_23,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 0.85 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 4:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
23	0.85	0.38	1.5	0.295	0.106
25	0.85	0.38	1.5	0.321	0.116
47	0.32	0.14	0.7	0.226	0.082
49	0.32	0.14	0.7	0.236	0.085

THD-I / TDD THD_I = √ΣI_h² / I₁ = 1.29 / 226.57 = 0.57 %; TDD = THD_I with I_L taken as I₁; I_rms = √(226.57² + 1.29²) = 226.57 A. SCR = I_sc/I₁ = 18,042 / 226.57 = 79.6 → IEEE 519 row SCR 50–100 (TDD 12 %) → 0.57 vs limit 12.00 % PASS

Voltage distortion V₂₃ = 0.85 × √(0.003012² + (23 × 0.01506)²) = 0.295 V; V₁ = V_LL/√3 = 480/√3 = 277.13 V; THD_V = √ΣV_h² / V₁ = 0.545 / 277.13 = 0.197 % vs the 8 % limit for V ≤ 1 kV → 0.197 vs limit 8.000 % PASS

IEC 61000-2-2 worst V₂₅/V₁ = 0.321 / 277.13 = 0.116 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (226.57² + 1,308) / 226.57² = 1.03 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.414 (√2 = 1.414 for a sine)

Result 4/4 checks pass → PASS; THD_I 0.6 %, THD_V 0.20 %; governing: current tdd

Reference Hand calculation: I1(CH-1) = 200 kW × 0.85 / (0.95 × 0.95) / (√3 × 480 V) = 226.57 A. Isc = 15 MVA / (√3 × 480 V) = 18.042 kA; SCR = 79.6 → IEEE 519 row 50–100 (TDD limit 12 %). K_load = 0.6 + 0.4 × 0.85 = 0.94; 24-pulse keeps h = 24k ± 1 at K_pulse = 0.1; I23 = 0.852 A. THDi = √ΣIh² / I1 = 1.287 / 226.57 = 0.57 % (= TDD, IL taken as I1) vs 12 % → PASS. Z = 480² / 15 MVA = 0.015360 Ω, X/R 5 → R = 0.003012, X = 0.015062 Ω; V23 = I23 × √(R² + (23X)²) = 0.295 V; THDv = √ΣVh² / V1, V1 = 480 / √3 = 277.13 V (per-phase Vh over the phase voltage): 0.197 % vs 8 % → PASS. No individual order exceeds its row limit. IEC 61000-2-2: worst V25/V1 = 0.116 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 1.03; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.414 (validation case c0017-24-pulse-480v-60hz)

Example 4 — Single 75 kW drive at 80 % load (former help example 1)

A bare 6-pulse drive at 80 % load: K_load = 0.92 and the full 49-order spectrum give THDi 27 %, failing the 15 % TDD limit.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — VSD-01: 75 kW at 80 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(VSD-01) = 75 × 0.8 / (0.95 × 0.95) × 1000 / (√3 × 415) = 92.49 A

Correction factors VSD-01: K_load = 0.6 + 0.4 × 0.8 = 0.92, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 17.02 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	17.02	18.40	12	1.438	0.600
7	11.91	12.88	12	1.409	0.588
11	7.66	8.28	5.5	1.423	0.594
13	5.96	6.44	5.5	1.308	0.546
17	5.11	5.52	5	1.466	0.612
19	4.25	4.60	5	1.365	0.570

THD-I / TDD THD_I = √ΣI_h² / I₁ = 25.03 / 92.49 = 27.06 %; TDD = THD_I with I_L taken as I₁; I_rms = √(92.49² + 25.03²) = 95.82 A. SCR = I_sc/I₁ = 13,912 / 92.49 = 150.4 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 27.06 vs limit 15.00 % FAIL

Voltage distortion V₅ = 17.02 × √(0.003378² + (5 × 0.01689)²) = 1.438 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 5.285 / 239.60 = 2.206 % vs the 8 % limit for V ≤ 1 kV → 2.206 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 100–1000 row (h<11 12 %, 11–16 5.5 %, 17–22 5 %, 23–34 2 %, ≥35 1 %): Harmonic 5: 18.40% exceeds limit 12.00%; Harmonic 7: 12.88% exceeds limit 12.00%; Harmonic 11: 8.28% exceeds limit 5.50%; +12 more → 15 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 1.437 / 239.60 = 0.600 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (92.49² + 97,917) / 95.82² = 11.60 (specify a K-rated transformer); crest factor I_peak/I_rms from the reconstructed waveform = 1.434 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 27.1 %, THD_V 2.21 %; governing: current tdd

Reference Hand calculation: I1(VSD-01) = 75 kW × 0.8 / (0.95 × 0.95) / (√3 × 415 V) = 92.49 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 150.4 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.8 = 0.92; I5 = 17.018 A. THDi = √ΣIh² / I1 = 25.030 / 92.49 = 27.06 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 1.438 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 2.206 % vs 8 % → PASS. Individual orders over the row limit: h5 18.40 % > 12 %, h7 12.88 % > 12 %, h11 8.28 % > 5.5 %, h13 6.44 % > 5.5 % (+11 more). IEC 61000-2-2: worst V25/V1 = 0.600 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 11.60; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.434 (validation case c0017-75kw-80pct-load)

Example 5 — 160 kW active front end drive

An AFE rectifier injects 2 % at 5/7/11/13 only (THDi 4 %), passing IEEE 519 and IEC 61000-2-2 with margin.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — AFE-1: 160 kW at 100 % load, pf 0.95, η 95 %, active front end. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(AFE-1) = 160 × 1 / (0.95 × 0.95) × 1000 / (√3 × 415) = 246.64 A

Correction factors AFE-1: AFE → I₅ = I₇ = I₁₁ = I₁₃ = 2 % × I₁

Spectrum

I₅ = 0.02 × 246.64 → 4.93 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 4:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	4.93	2.00	10	0.417	0.174
7	4.93	2.00	10	0.583	0.243
11	4.93	2.00	4.5	0.917	0.383
13	4.93	2.00	4.5	1.083	0.452

THD-I / TDD THD_I = √ΣI_h² / I₁ = 9.87 / 246.64 = 4.00 %; TDD = THD_I with I_L taken as I₁; I_rms = √(246.64² + 9.87²) = 246.84 A. SCR = I_sc/I₁ = 13,912 / 246.64 = 56.4 → IEEE 519 row SCR 50–100 (TDD 12 %) → 4.00 vs limit 12.00 % PASS

Voltage distortion V₅ = 4.93 × √(0.003378² + (5 × 0.01689)²) = 0.417 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 1.590 / 239.60 = 0.663 % vs the 8 % limit for V ≤ 1 kV → 0.663 vs limit 8.000 % PASS

IEC 61000-2-2 worst V₁₃/V₁ = 1.083 / 239.60 = 0.452 % vs the 3 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (246.64² + 8,857) / 246.84² = 1.14 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.413 (√2 = 1.414 for a sine)

Result 4/4 checks pass → PASS; THD_I 4.0 %, THD_V 0.66 %; governing: current tdd

Reference Hand calculation: I1(AFE-1) = 160 kW × 1 / (0.95 × 0.95) / (√3 × 415 V) = 246.64 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 56.4 → IEEE 519 row 50–100 (TDD limit 12 %). AFE: I5 = I7 = I11 = I13 = 2 % × I1; I5 = 4.933 A. THDi = √ΣIh² / I1 = 9.866 / 246.64 = 4.00 % (= TDD, IL taken as I1) vs 12 % → PASS. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 0.417 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 0.663 % vs 8 % → PASS. No individual order exceeds its row limit. IEC 61000-2-2: worst V13/V1 = 0.452 % vs 3 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 1.14; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.413 (validation case c0017-afe-160kw)

Example 6 — 55 kW drive with DC-link choke

A DC choke scales the whole 6-pulse spectrum by 0.7; THDi drops from 29.4 % to 20.6 % but still fails the 15 % TDD limit.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — FAN-2: 55 kW at 100 % load, pf 0.95, η 95 %, 6-pulse, DC choke. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(FAN-2) = 55 × 1 / (0.95 × 0.95) × 1000 / (√3 × 415) = 84.78 A

Correction factors FAN-2: K_load = 0.6 + 0.4 × 1 = 1.00, K_dc = 0.7, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 11.87 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	11.87	14.00	12	1.003	0.419
7	8.31	9.80	12	0.983	0.410
11	5.34	6.30	5.5	0.992	0.414
13	4.15	4.90	5.5	0.912	0.381
17	3.56	4.20	5	1.022	0.427
19	2.97	3.50	5	0.952	0.397

THD-I / TDD THD_I = √ΣI_h² / I₁ = 17.46 / 84.78 = 20.59 %; TDD = THD_I with I_L taken as I₁; I_rms = √(84.78² + 17.46²) = 86.56 A. SCR = I_sc/I₁ = 13,912 / 84.78 = 164.1 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 20.59 vs limit 15.00 % FAIL

Voltage distortion V₅ = 11.87 × √(0.003378² + (5 × 0.01689)²) = 1.003 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 3.686 / 239.60 = 1.538 % vs the 8 % limit for V ≤ 1 kV → 1.538 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 100–1000 row (h<11 12 %, 11–16 5.5 %, 17–22 5 %, 23–34 2 %, ≥35 1 %): Harmonic 5: 14.00% exceeds limit 12.00%; Harmonic 11: 6.30% exceeds limit 5.50%; Harmonic 23: 2.80% exceeds limit 2.00%; +9 more → 12 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 1.002 / 239.60 = 0.418 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (84.78² + 47,632) / 86.56² = 7.32; crest factor I_peak/I_rms from the reconstructed waveform = 1.438 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 20.6 %, THD_V 1.54 %; governing: current tdd

Reference Hand calculation: I1(FAN-2) = 55 kW × 1 / (0.95 × 0.95) / (√3 × 415 V) = 84.78 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 164.1 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 1 = 1.00; K_dc = 0.7; I5 = 11.870 A. THDi = √ΣIh² / I1 = 17.457 / 84.78 = 20.59 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 1.003 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 1.538 % vs 8 % → PASS. Individual orders over the row limit: h5 14.00 % > 12 %, h11 6.30 % > 5.5 %, h23 2.80 % > 2 %, h25 2.80 % > 2 % (+8 more). IEC 61000-2-2: worst V25/V1 = 0.418 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 7.32; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.438 (validation case c0017-dc-choke-55kw)

Example 7 — High X/R source (X/R = 20)

Same bus and drive as the baseline but X/R 20 puts almost all of Z into X, so every V_h = I_h·√(R² + (hX)²) is higher.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 20. Drives — VSD: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 20 → R = 0.0008600 Ω, X = 0.01720 Ω

Fundamental I₁(VSD) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A

Correction factors VSD: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 20.81 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	20.81	18.00	12	1.790	0.747
7	14.57	12.60	12	1.754	0.732
11	9.36	8.10	5.5	1.772	0.740
13	7.28	6.30	5.5	1.629	0.680
17	6.24	5.40	5	1.826	0.762
19	5.20	4.50	5	1.700	0.710

THD-I / TDD THD_I = √ΣI_h² / I₁ = 30.61 / 115.61 = 26.47 %; TDD = THD_I with I_L taken as I₁; I_rms = √(115.61² + 30.61²) = 119.60 A. SCR = I_sc/I₁ = 13,912 / 115.61 = 120.3 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 26.47 vs limit 15.00 % FAIL

Voltage distortion V₅ = 20.81 × √(0.0008600² + (5 × 0.01720)²) = 1.790 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 6.582 / 239.60 = 2.747 % vs the 8 % limit for V ≤ 1 kV → 2.747 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 100–1000 row (h<11 12 %, 11–16 5.5 %, 17–22 5 %, 23–34 2 %, ≥35 1 %): Harmonic 5: 18.00% exceeds limit 12.00%; Harmonic 7: 12.60% exceeds limit 12.00%; Harmonic 11: 8.10% exceeds limit 5.50%; +12 more → 15 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 1.790 / 239.60 = 0.747 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (115.61² + 146,415) / 119.60² = 11.17 (specify a K-rated transformer); crest factor I_peak/I_rms from the reconstructed waveform = 1.435 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 26.5 %, THD_V 2.75 %; governing: current tdd

Reference Hand calculation: I1(VSD) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 120.3 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; I5 = 20.810 A. THDi = √ΣIh² / I1 = 30.607 / 115.61 = 26.47 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 20 → R = 0.000860, X = 0.017201 Ω; V5 = I5 × √(R² + (5X)²) = 1.790 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 2.747 % vs 8 % → PASS. Individual orders over the row limit: h5 18.00 % > 12 %, h7 12.60 % > 12 %, h11 8.10 % > 5.5 %, h13 6.30 % > 5.5 % (+11 more). IEC 61000-2-2: worst V25/V1 = 0.747 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 11.17; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.435 (validation case c0017-high-x-r-20)

Example 8 — 100 kW drive at 25 % load, pf 0.90, η 90 %

Light load lowers K_load to 0.70 while poor pf and efficiency raise the fundamental current for the same shaft kW.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — VSD: 100 kW at 25 % load, pf 0.9, η 90 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(VSD) = 100 × 0.25 / (0.9 × 0.9) × 1000 / (√3 × 415) = 42.94 A

Correction factors VSD: K_load = 0.6 + 0.4 × 0.25 = 0.70, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 6.01 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	6.01	14.00	12	0.508	0.212
7	4.21	9.80	12	0.498	0.208
11	2.71	6.30	5.5	0.503	0.210
13	2.10	4.90	5.5	0.462	0.193
17	1.80	4.20	5	0.518	0.216
19	1.50	3.50	5	0.482	0.201

THD-I / TDD THD_I = √ΣI_h² / I₁ = 8.84 / 42.94 = 20.59 %; TDD = THD_I with I_L taken as I₁; I_rms = √(42.94² + 8.84²) = 43.84 A. SCR = I_sc/I₁ = 13,912 / 42.94 = 324.0 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 20.59 vs limit 15.00 % FAIL

Voltage distortion V₅ = 6.01 × √(0.003378² + (5 × 0.01689)²) = 0.508 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 1.867 / 239.60 = 0.779 % vs the 8 % limit for V ≤ 1 kV → 0.779 vs limit 8.000 % PASS

IEC 61000-2-2 worst V₂₅/V₁ = 0.508 / 239.60 = 0.212 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (42.94² + 12,217) / 43.84² = 7.32; crest factor I_peak/I_rms from the reconstructed waveform = 1.438 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 20.6 %, THD_V 0.78 %; governing: current tdd

Reference Hand calculation: I1(VSD) = 100 kW × 0.25 / (0.9 × 0.9) / (√3 × 415 V) = 42.94 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 324.0 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.25 = 0.70; I5 = 6.011 A. THDi = √ΣIh² / I1 = 8.841 / 42.94 = 20.59 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 0.508 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 0.779 % vs 8 % → PASS. Individual orders over the row limit: h5 14.00 % > 12 %, h11 6.30 % > 5.5 %, h23 2.80 % > 2 %, h25 2.80 % > 2 % (+8 more). IEC 61000-2-2: worst V25/V1 = 0.212 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 7.32; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.438 (validation case c0017-light-load-low-efficiency)

Example 9 — Spectrum truncated at the 13th harmonic

max_harmonic_order = 13 keeps only 5, 7, 11, 13: THDi falls from 26.5 % to 24.3 % and the K-factor drops accordingly.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — VSD: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 13.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(VSD) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A

Correction factors VSD: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 20.81 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 4:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	20.81	18.00	12	1.759	0.734
7	14.57	12.60	12	1.723	0.719
11	9.36	8.10	5.5	1.740	0.726
13	7.28	6.30	5.5	1.599	0.667

THD-I / TDD THD_I = √ΣI_h² / I₁ = 28.04 / 115.61 = 24.25 %; TDD = THD_I with I_L taken as I₁; I_rms = √(115.61² + 28.04²) = 118.96 A. SCR = I_sc/I₁ = 13,912 / 115.61 = 120.3 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 24.25 vs limit 15.00 % FAIL

Voltage distortion V₅ = 20.81 × √(0.003378² + (5 × 0.01689)²) = 1.759 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 3.413 / 239.60 = 1.424 % vs the 8 % limit for V ≤ 1 kV → 1.424 vs limit 8.000 % PASS

IEC 61000-2-2 worst V₁₃/V₁ = 1.599 / 239.60 = 0.667 % vs the 3 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (115.61² + 40,801) / 118.96² = 3.83 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.464 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 24.2 %, THD_V 1.42 %; governing: current tdd

Reference Hand calculation: I1(VSD) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 120.3 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; I5 = 20.810 A. THDi = √ΣIh² / I1 = 28.036 / 115.61 = 24.25 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 1.759 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 1.424 % vs 8 % → PASS. Individual orders over the row limit: h5 18.00 % > 12 %, h7 12.60 % > 12 %, h11 8.10 % > 5.5 %, h13 6.30 % > 5.5 %. IEC 61000-2-2: worst V13/V1 = 0.667 % vs 3 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 3.83; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.464 (validation case c0017-max-order-13)

Example 10 — Mixed fleet at 690 V: 6-pulse overloaded, 12-pulse, reactor and AFE

Four different drives summed arithmetically, one at 120 % load (K_load 1.08); shows how each topology contributes per order.

Given: 690 V, 50 Hz bus with a 40 MVA three-phase fault level, source X/R 8. Drives — SAG-1: 500 kW at 120 % load, pf 0.95, η 95 %, 6-pulse; BALL-1: 500 kW at 90 % load, pf 0.95, η 95 %, 12-pulse; CYC-1: 200 kW at 75 % load, pf 0.95, η 95 %, 6-pulse, 0.8 mH line reactor; AFE-2: 315 kW at 100 % load, pf 0.95, η 95 %, active front end. Arithmetic (in-phase) summation of the 4 drives, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 40 × 10⁶ / (√3 × 690) = 33.470 kA; Z = V² / S_sc = 690² / 40 MVA = 0.01190 Ω per phase (star equivalent) split by X/R 8 → R = 0.001476 Ω, X = 0.01181 Ω

Fundamental I₁(SAG-1) = 500 × 1.2 / (0.95 × 0.95) × 1000 / (√3 × 690) = 556.28 A; I₁(BALL-1) = 500 × 0.9 / (0.95 × 0.95) × 1000 / (√3 × 690) = 417.21 A; I₁(CYC-1) = 200 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 690) = 139.07 A; I₁(AFE-2) = 315 × 1 / (0.95 × 0.95) × 1000 / (√3 × 690) = 292.05 A; ΣI₁ = 1,404.61 A

Correction factors SAG-1: K_load = 0.6 + 0.4 × 1.2 = 1.08, K_dc = 1, 6-pulse K_pulse = 1; BALL-1: K_load = 0.6 + 0.4 × 0.9 = 0.96, K_dc = 1, 12-pulse → only h = 12k ± 1 at K_pulse = 0.25; CYC-1: K_load = 0.6 + 0.4 × 0.75 = 0.90, X_reactor = 2π × 50 × 0.8/1000 = 0.2513 Ω → K_reactor(5) = min(1, (0.5 + 0.5 × 0.01181/(0.01181 + 0.2513)) × (1 − 0.3/5)) = 0.491, K_dc = 1, 6-pulse K_pulse = 1; AFE-2: AFE → I₅ = I₇ = I₁₁ = I₁₃ = 2 % × I₁

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 138.29 A; 4 drives summed per order (arithmetic); V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	138.29	9.85	7	8.169	2.051
7	98.71	7.03	7	8.162	2.049
11	74.65	5.31	3.5	9.699	2.435
13	59.38	4.23	3.5	9.117	2.289
17	39.90	2.84	2.5	8.012	2.011
19	33.26	2.37	2.5	7.463	1.873

THD-I / TDD THD_I = √ΣI_h² / I₁ = 211.74 / 1,404.61 = 15.07 %; TDD = THD_I with I_L taken as I₁; I_rms = √(1,404.61² + 211.74²) = 1,420.48 A. SCR = I_sc/I₁ = 33,470 / 1,404.61 = 23.8 → IEEE 519 row SCR 20–50 (TDD 8 %) → 15.07 vs limit 8.00 % FAIL

Voltage distortion V₅ = 138.29 × √(0.001476² + (5 × 0.01181)²) = 8.169 V; V₁ = V_LL/√3 = 690/√3 = 398.37 V; THD_V = √ΣV_h² / V₁ = 31.673 / 398.37 = 7.951 % vs the 8 % limit for V ≤ 1 kV → 7.951 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 20–50 row (h<11 7 %, 11–16 3.5 %, 17–22 2.5 %, 23–34 1 %, ≥35 0.5 %): Harmonic 5: 9.85% exceeds limit 7.00%; Harmonic 7: 7.03% exceeds limit 7.00%; Harmonic 11: 5.31% exceeds limit 3.50%; +12 more → 15 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 9.041 / 398.37 = 2.270 % vs the 1.5 % compatibility level FAIL

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (1,404.61² + 7,191,248) / 1,420.48² = 4.54; crest factor I_peak/I_rms from the reconstructed waveform = 1.433 (√2 = 1.414 for a sine)

Result 1/4 checks pass → FAIL; THD_I 15.1 %, THD_V 7.95 %; governing: current tdd

Reference Hand calculation: I1(SAG-1) = 500 kW × 1.2 / (0.95 × 0.95) / (√3 × 690 V) = 556.28 A; I1(BALL-1) = 500 kW × 0.9 / (0.95 × 0.95) / (√3 × 690 V) = 417.21 A; I1(CYC-1) = 200 kW × 0.75 / (0.95 × 0.95) / (√3 × 690 V) = 139.07 A; I1(AFE-2) = 315 kW × 1 / (0.95 × 0.95) / (√3 × 690 V) = 292.05 A; total I1 = 1404.61 A (arithmetic summation of the per-order currents). Isc = 40 MVA / (√3 × 690 V) = 33.470 kA; SCR = 23.8 → IEEE 519 row 20–50 (TDD limit 8 %). K_load = 0.6 + 0.4 × 1.2 = 1.08; I5 = 138.291 A. THDi = √ΣIh² / I1 = 211.737 / 1404.61 = 15.07 % (= TDD, IL taken as I1) vs 8 % → FAIL. Z = 690² / 40 MVA = 0.011902 Ω, X/R 8 → R = 0.001476, X = 0.011811 Ω; V5 = I5 × √(R² + (5X)²) = 8.169 V; THDv = √ΣVh² / V1, V1 = 690 / √3 = 398.37 V (per-phase Vh over the phase voltage): 7.951 % vs 8 % → PASS. Individual orders over the row limit: h5 9.85 % > 7 %, h7 7.03 % > 7 %, h11 5.31 % > 3.5 %, h13 4.23 % > 3.5 % (+11 more). IEC 61000-2-2: worst V25/V1 = 2.270 % vs 1.5 % → NOT compliant. K = (I1² + ΣIh²h²)/Irms² = 4.54; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.433 (validation case c0017-mixed-fleet-690v)

Example 11 — 100 kW drive with 3 mH line reactor

Input-reactor attenuation: K_reactor = (0.5 + 0.5·Xs/(Xs+Xr))·(1 − 0.3/h) is order-dependent, so the 5th drops more than the 49th.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — PMP-3: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse, 3 mH line reactor. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(PMP-3) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A

Correction factors PMP-3: K_load = 0.6 + 0.4 × 0.75 = 0.90, X_reactor = 2π × 50 × 3/1000 = 0.9425 Ω → K_reactor(5) = min(1, (0.5 + 0.5 × 0.01689/(0.01689 + 0.9425)) × (1 − 0.3/5)) = 0.478, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 9.95 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	9.95	8.61	12	0.841	0.351
7	7.09	6.14	12	0.839	0.350
11	4.63	4.01	5.5	0.861	0.359
13	3.62	3.13	5.5	0.795	0.332
17	3.12	2.70	5	0.896	0.374
19	2.61	2.25	5	0.836	0.349

THD-I / TDD THD_I = √ΣI_h² / I₁ = 14.90 / 115.61 = 12.89 %; TDD = THD_I with I_L taken as I₁; I_rms = √(115.61² + 14.90²) = 116.57 A. SCR = I_sc/I₁ = 13,912 / 115.61 = 120.3 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 12.89 vs limit 15.00 % PASS

Voltage distortion V₅ = 9.95 × √(0.003378² + (5 × 0.01689)²) = 0.841 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 3.227 / 239.60 = 1.347 % vs the 8 % limit for V ≤ 1 kV → 1.347 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 100–1000 row (h<11 12 %, 11–16 5.5 %, 17–22 5 %, 23–34 2 %, ≥35 1 %): Harmonic 35: 1.13% exceeds limit 1.00%; Harmonic 37: 1.14% exceeds limit 1.00% → 2 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 0.883 / 239.60 = 0.369 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (115.61² + 36,514) / 116.57² = 3.67 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.434 (√2 = 1.414 for a sine)

Result 3/4 checks pass → FAIL; THD_I 12.9 %, THD_V 1.35 %; governing: individual current harmonics

Reference Hand calculation: I1(PMP-3) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 120.3 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; X_reactor = 2π × 50 × 3 mH = 0.9425 Ω, X_s = 0.01689 Ω → K_reactor(5) = min(1, (0.5 + 0.5 × 0.01689/(0.01689 + 0.9425)) × (1 − 0.3/5)) = 0.4783; I5 = 9.953 A. THDi = √ΣIh² / I1 = 14.899 / 115.61 = 12.89 % (= TDD, IL taken as I1) vs 15 % → PASS. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 0.841 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 1.347 % vs 8 % → PASS. Individual orders over the row limit: h35 1.13 % > 1 %, h37 1.14 % > 1 %. IEC 61000-2-2: worst V25/V1 = 0.369 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 3.67; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.434 (validation case c0017-reactor-3mh-attenuation)

Example 12 — Resistive source (X/R = 1) at 480 V, 60 Hz

X/R 1 splits Z equally into R and X; harmonic voltages are lower and the current checks still fail.

Given: 480 V, 60 Hz bus with a 8 MVA three-phase fault level, source X/R 1. Drives — HVAC-1: 90 kW at 70 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 8 × 10⁶ / (√3 × 480) = 9.623 kA; Z = V² / S_sc = 480² / 8 MVA = 0.02880 Ω per phase (star equivalent) split by X/R 1 → R = 0.02037 Ω, X = 0.02037 Ω

Fundamental I₁(HVAC-1) = 90 × 0.7 / (0.95 × 0.95) × 1000 / (√3 × 480) = 83.96 A

Correction factors HVAC-1: K_load = 0.6 + 0.4 × 0.7 = 0.88, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 14.78 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	14.78	17.60	12	1.535	0.554
7	10.34	12.32	12	1.490	0.538
11	6.65	7.92	5.5	1.496	0.540
13	5.17	6.16	5.5	1.373	0.496
17	4.43	5.28	5	1.537	0.555
19	3.69	4.40	5	1.431	0.517

THD-I / TDD THD_I = √ΣI_h² / I₁ = 21.73 / 83.96 = 25.89 %; TDD = THD_I with I_L taken as I₁; I_rms = √(83.96² + 21.73²) = 86.73 A. SCR = I_sc/I₁ = 9,623 / 83.96 = 114.6 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 25.89 vs limit 15.00 % FAIL

Voltage distortion V₅ = 14.78 × √(0.02037² + (5 × 0.02037)²) = 1.535 V; V₁ = V_LL/√3 = 480/√3 = 277.13 V; THD_V = √ΣV_h² / V₁ = 5.551 / 277.13 = 2.003 % vs the 8 % limit for V ≤ 1 kV → 2.003 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 100–1000 row (h<11 12 %, 11–16 5.5 %, 17–22 5 %, 23–34 2 %, ≥35 1 %): Harmonic 5: 17.60% exceeds limit 12.00%; Harmonic 7: 12.32% exceeds limit 12.00%; Harmonic 11: 7.92% exceeds limit 5.50%; +12 more → 15 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 1.506 / 277.13 = 0.543 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (83.96² + 73,831) / 86.73² = 10.75 (specify a K-rated transformer); crest factor I_peak/I_rms from the reconstructed waveform = 1.435 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 25.9 %, THD_V 2.00 %; governing: current tdd

Reference Hand calculation: I1(HVAC-1) = 90 kW × 0.7 / (0.95 × 0.95) / (√3 × 480 V) = 83.96 A. Isc = 8 MVA / (√3 × 480 V) = 9.623 kA; SCR = 114.6 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.7 = 0.88; I5 = 14.778 A. THDi = √ΣIh² / I1 = 21.734 / 83.96 = 25.89 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 480² / 8 MVA = 0.028800 Ω, X/R 1 → R = 0.020365, X = 0.020365 Ω; V5 = I5 × √(R² + (5X)²) = 1.535 V; THDv = √ΣVh² / V1, V1 = 480 / √3 = 277.13 V (per-phase Vh over the phase voltage): 2.003 % vs 8 % → PASS. Individual orders over the row limit: h5 17.60 % > 12 %, h7 12.32 % > 12 %, h11 7.92 % > 5.5 %, h13 6.16 % > 5.5 % (+11 more). IEC 61000-2-2: worst V25/V1 = 0.543 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 10.75; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.435 (validation case c0017-resistive-source-x-r-1)

Example 13 — 300 kW drive at 100 % load (SCR 20–50 row)

SCR 30 selects the 8 % TDD row; the bare 6-pulse spectrum exceeds it by a wide margin, THDv 12.0 % fails the 8 % limit and V17–V25 breach the IEC 61000-2-2 levels.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — CRUSH-1: 300 kW at 100 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(CRUSH-1) = 300 × 1 / (0.95 × 0.95) × 1000 / (√3 × 415) = 462.45 A

Correction factors CRUSH-1: K_load = 0.6 + 0.4 × 1 = 1.00, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 92.49 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	92.49	20.00	7	7.816	3.262
7	64.74	14.00	7	7.657	3.196
11	41.62	9.00	3.5	7.733	3.227
13	32.37	7.00	3.5	7.108	2.967
17	27.75	6.00	2.5	7.967	3.325
19	23.12	5.00	2.5	7.420	3.097

THD-I / TDD THD_I = √ΣI_h² / I₁ = 136.03 / 462.45 = 29.42 %; TDD = THD_I with I_L taken as I₁; I_rms = √(462.45² + 136.03²) = 482.04 A. SCR = I_sc/I₁ = 13,912 / 462.45 = 30.1 → IEEE 519 row SCR 20–50 (TDD 8 %) → 29.42 vs limit 8.00 % FAIL

Voltage distortion V₅ = 92.49 × √(0.003378² + (5 × 0.01689)²) = 7.816 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 28.724 / 239.60 = 11.988 % vs the 8 % limit for V ≤ 1 kV → 11.988 vs limit 8.000 % FAIL

Individual orders Each I_h/I₁ against the SCR 20–50 row (h<11 7 %, 11–16 3.5 %, 17–22 2.5 %, 23–34 1 %, ≥35 0.5 %): Harmonic 5: 20.00% exceeds limit 7.00%; Harmonic 7: 14.00% exceeds limit 7.00%; Harmonic 11: 9.00% exceeds limit 3.50%; +13 more → 16 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 7.810 / 239.60 = 3.260 % vs the 1.5 % compatibility level FAIL

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (462.45² + 2,892,148) / 482.04² = 13.37 (specify a K-rated transformer); crest factor I_peak/I_rms from the reconstructed waveform = 1.436 (√2 = 1.414 for a sine)

Result 0/4 checks pass → FAIL; THD_I 29.4 %, THD_V 11.99 %; governing: voltage thd

Reference Hand calculation: I1(CRUSH-1) = 300 kW × 1 / (0.95 × 0.95) / (√3 × 415 V) = 462.45 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 30.1 → IEEE 519 row 20–50 (TDD limit 8 %). K_load = 0.6 + 0.4 × 1 = 1.00; I5 = 92.490 A. THDi = √ΣIh² / I1 = 136.030 / 462.45 = 29.42 % (= TDD, IL taken as I1) vs 8 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 7.816 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 11.988 % vs 8 % → FAIL. Individual orders over the row limit: h5 20.00 % > 7 %, h7 14.00 % > 7 %, h11 9.00 % > 3.5 %, h13 7.00 % > 3.5 % (+12 more). IEC 61000-2-2: worst V25/V1 = 3.260 % vs 1.5 % → NOT compliant. K = (I1² + ΣIh²h²)/Irms² = 13.37; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.436 (validation case c0017-scr-20-50-band)

Example 14 — Small drive with DC choke on a stiff 50 MVA bus (SCR > 1000)

SCR above 1000 allows TDD 20 %; a 30 kW drive at 45 % load with a DC choke (THDi 16.1 %) passes all four checks.

Given: 415 V, 50 Hz bus with a 50 MVA three-phase fault level, source X/R 5. Drives — AUX-1: 30 kW at 45 % load, pf 0.95, η 95 %, 6-pulse, DC choke. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 50 × 10⁶ / (√3 × 415) = 69.560 kA; Z = V² / S_sc = 415² / 50 MVA = 0.003445 Ω per phase (star equivalent) split by X/R 5 → R = 0.0006760 Ω, X = 0.003378 Ω

Fundamental I₁(AUX-1) = 30 × 0.45 / (0.95 × 0.95) × 1000 / (√3 × 415) = 20.81 A

Correction factors AUX-1: K_load = 0.6 + 0.4 × 0.45 = 0.78, K_dc = 0.7, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 2.27 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	2.27	10.92	15	0.038	0.016
7	1.59	7.64	15	0.038	0.016
11	1.02	4.91	7	0.038	0.016
13	0.80	3.82	7	0.035	0.015
17	0.68	3.28	6	0.039	0.016
19	0.57	2.73	6	0.036	0.015

THD-I / TDD THD_I = √ΣI_h² / I₁ = 3.34 / 20.81 = 16.06 %; TDD = THD_I with I_L taken as I₁; I_rms = √(20.81² + 3.34²) = 21.08 A. SCR = I_sc/I₁ = 69,560 / 20.81 = 3,342.6 → IEEE 519 row SCR > 1000 (TDD 20 %) → 16.06 vs limit 20.00 % PASS

Voltage distortion V₅ = 2.27 × √(0.0006760² + (5 × 0.003378)²) = 0.038 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 0.141 / 239.60 = 0.059 % vs the 8 % limit for V ≤ 1 kV → 0.059 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR > 1000 row (h<11 15 %, 11–16 7 %, 17–22 6 %, 23–34 2.5 %, ≥35 1.4 %): none of the orders exceeds its row limit → 0 order(s) over limit PASS

IEC 61000-2-2 worst V₂₅/V₁ = 0.038 / 239.60 = 0.016 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (20.81² + 1,746) / 21.08² = 4.91; crest factor I_peak/I_rms from the reconstructed waveform = 1.438 (√2 = 1.414 for a sine)

Result 4/4 checks pass → PASS; THD_I 16.1 %, THD_V 0.06 %; governing: current tdd

Reference Hand calculation: I1(AUX-1) = 30 kW × 0.45 / (0.95 × 0.95) / (√3 × 415 V) = 20.81 A. Isc = 50 MVA / (√3 × 415 V) = 69.560 kA; SCR = 3342.6 → IEEE 519 row 1000–inf (TDD limit 20 %). K_load = 0.6 + 0.4 × 0.45 = 0.78; K_dc = 0.7; I5 = 2.272 A. THDi = √ΣIh² / I1 = 3.342 / 20.81 = 16.06 % (= TDD, IL taken as I1) vs 20 % → PASS. Z = 415² / 50 MVA = 0.003445 Ω, X/R 5 → R = 0.000676, X = 0.003378 Ω; V5 = I5 × √(R² + (5X)²) = 0.038 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 0.059 % vs 8 % → PASS. No individual order exceeds its row limit. IEC 61000-2-2: worst V25/V1 = 0.016 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 4.91; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.438 (validation case c0017-scr-above-1000-dc-choke-pass)

Example 15 — 150 kW 12-pulse drive on a 2 MVA bus (SCR < 20)

SCR 12 selects the strictest IEEE 519 row (TDD 5 %, 11–16 at 2 %): TDD 3.4 % passes but the 11th (2.25 %) and the 23rd–49th exceed their individual limits, and V23/V25 exceed the IEC 61000-2-2 level.

Given: 415 V, 50 Hz bus with a 2 MVA three-phase fault level, source X/R 5. Drives — M-150: 150 kW at 100 % load, pf 0.95, η 95 %, 12-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 2 × 10⁶ / (√3 × 415) = 2.782 kA; Z = V² / S_sc = 415² / 2 MVA = 0.08611 Ω per phase (star equivalent) split by X/R 5 → R = 0.01689 Ω, X = 0.08444 Ω

Fundamental I₁(M-150) = 150 × 1 / (0.95 × 0.95) × 1000 / (√3 × 415) = 231.23 A

Correction factors M-150: K_load = 0.6 + 0.4 × 1 = 1.00, K_dc = 1, 12-pulse → only h = 12k ± 1 at K_pulse = 0.25

Spectrum

I₁₁ = I₁ × I_11,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 5.20 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 8:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
11	5.20	2.25	2	4.833	2.017
13	4.05	1.75	2	4.442	1.854
23	2.31	1.00	0.6	4.491	1.874
25	2.31	1.00	0.6	4.881	2.037
35	1.45	0.62	0.3	4.271	1.783
37	1.45	0.62	0.3	4.515	1.884

THD-I / TDD THD_I = √ΣI_h² / I₁ = 7.73 / 231.23 = 3.34 %; TDD = THD_I with I_L taken as I₁; I_rms = √(231.23² + 7.73²) = 231.35 A. SCR = I_sc/I₁ = 2,782 / 231.23 = 12.0 → IEEE 519 row SCR < 20 (TDD 5 %) → 3.34 vs limit 5.00 % PASS

Voltage distortion V₁₁ = 5.20 × √(0.01689² + (11 × 0.08444)²) = 4.833 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 12.265 / 239.60 = 5.119 % vs the 8 % limit for V ≤ 1 kV → 5.119 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR < 20 row (h<11 4 %, 11–16 2 %, 17–22 1.5 %, 23–34 0.6 %, ≥35 0.3 %): Harmonic 11: 2.25% exceeds limit 2.00%; Harmonic 23: 1.00% exceeds limit 0.60%; Harmonic 25: 1.00% exceeds limit 0.60%; +4 more → 7 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 4.881 / 239.60 = 2.037 % vs the 1.5 % compatibility level FAIL

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (231.23² + 21,096) / 231.35² = 1.39 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.406 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 3.3 %, THD_V 5.12 %; governing: individual current harmonics

Reference Hand calculation: I1(M-150) = 150 kW × 1 / (0.95 × 0.95) / (√3 × 415 V) = 231.23 A. Isc = 2 MVA / (√3 × 415 V) = 2.782 kA; SCR = 12.0 → IEEE 519 row 0–20 (TDD limit 5 %). K_load = 0.6 + 0.4 × 1 = 1.00; 12-pulse keeps h = 12k ± 1 at K_pulse = 0.25; I11 = 5.203 A. THDi = √ΣIh² / I1 = 7.734 / 231.23 = 3.34 % (= TDD, IL taken as I1) vs 5 % → PASS. Z = 415² / 2 MVA = 0.086112 Ω, X/R 5 → R = 0.016888, X = 0.084440 Ω; V11 = I11 × √(R² + (11X)²) = 4.833 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 5.119 % vs 8 % → PASS. Individual orders over the row limit: h11 2.25 % > 2 %, h23 1.00 % > 0.6 %, h25 1.00 % > 0.6 %, h35 0.62 % > 0.3 % (+3 more). IEC 61000-2-2: worst V25/V1 = 2.037 % vs 1.5 % → NOT compliant. K = (I1² + ΣIh²h²)/Irms² = 1.39; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.406 (validation case c0017-scr-below-20-12-pulse)

Example 16 — Single 100 kW 6-pulse drive on a 10 MVA bus

Baseline bare 6-pulse spectrum: fundamental from kW/load/pf/efficiency, THDi 26.5 % against the 100–1000 SCR row.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — VSD: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(VSD) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A

Correction factors VSD: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 20.81 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	20.81	18.00	12	1.759	0.734
7	14.57	12.60	12	1.723	0.719
11	9.36	8.10	5.5	1.740	0.726
13	7.28	6.30	5.5	1.599	0.667
17	6.24	5.40	5	1.792	0.748
19	5.20	4.50	5	1.669	0.697

Voltage distortion V₅ = 20.81 × √(0.003378² + (5 × 0.01689)²) = 1.759 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 6.463 / 239.60 = 2.697 % vs the 8 % limit for V ≤ 1 kV → 2.697 vs limit 8.000 % PASS

IEC 61000-2-2 worst V₂₅/V₁ = 1.757 / 239.60 = 0.733 % vs the 1.5 % compatibility level PASS

Result 2/4 checks pass → FAIL; THD_I 26.5 %, THD_V 2.70 %; governing: current tdd

Reference Hand calculation: I1(VSD) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A. Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 120.3 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; I5 = 20.810 A. THDi = √ΣIh² / I1 = 30.607 / 115.61 = 26.47 % (= TDD, IL taken as I1) vs 15 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 1.759 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 2.697 % vs 8 % → PASS. Individual orders over the row limit: h5 18.00 % > 12 %, h7 12.60 % > 12 %, h11 8.10 % > 5.5 %, h13 6.30 % > 5.5 % (+11 more). IEC 61000-2-2: worst V25/V1 = 0.733 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 11.17; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.435 (validation case c0017-single-6pulse-415v)

Example 17 — Three identical 75 kW drives, RSS summation

RSS summation of three equal drives gives √3 × one drive per order, so THDi falls to 1/√3 of a single drive.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — P1: 75 kW at 75 % load, pf 0.95, η 95 %, 6-pulse; P2: 75 kW at 75 % load, pf 0.95, η 95 %, 6-pulse; P3: 75 kW at 75 % load, pf 0.95, η 95 %, 6-pulse. RSS (random-phase) summation of the 3 drives, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(P1) = 75 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 86.71 A; I₁(P2) = 75 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 86.71 A; I₁(P3) = 75 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 86.71 A; ΣI₁ = 260.13 A

Correction factors P1: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1; P2: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1; P3: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 27.03 A; 3 drives summed per order (rss); V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	27.03	10.39	10	2.285	0.953
7	18.92	7.27	10	2.238	0.934
11	12.17	4.68	4.5	2.260	0.943
13	9.46	3.64	4.5	2.078	0.867
17	8.11	3.12	4	2.329	0.972
19	6.76	2.60	4	2.169	0.905

THD-I / TDD THD_I = √ΣI_h² / I₁ = 39.76 / 260.13 = 15.28 %; TDD = THD_I with I_L taken as I₁; I_rms = √(260.13² + 39.76²) = 263.15 A. SCR = I_sc/I₁ = 13,912 / 260.13 = 53.5 → IEEE 519 row SCR 50–100 (TDD 12 %) → 15.28 vs limit 12.00 % FAIL

Voltage distortion V₅ = 27.03 × √(0.003378² + (5 × 0.01689)²) = 2.285 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 8.396 / 239.60 = 3.504 % vs the 8 % limit for V ≤ 1 kV → 3.504 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 50–100 row (h<11 10 %, 11–16 4.5 %, 17–22 4 %, 23–34 1.5 %, ≥35 0.7 %): Harmonic 5: 10.39% exceeds limit 10.00%; Harmonic 11: 4.68% exceeds limit 4.50%; Harmonic 23: 2.08% exceeds limit 1.50%; +9 more → 12 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 2.283 / 239.60 = 0.953 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (260.13² + 247,075) / 263.15² = 4.55; crest factor I_peak/I_rms from the reconstructed waveform = 1.438 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 15.3 %, THD_V 3.50 %; governing: current tdd

Reference Hand calculation: I1(P1) = 75 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 86.71 A; I1(P2) = 75 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 86.71 A; I1(P3) = 75 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 86.71 A; total I1 = 260.13 A (rss summation of the per-order currents). Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 53.5 → IEEE 519 row 50–100 (TDD limit 12 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; I5 = 27.033 A. THDi = √ΣIh² / I1 = 39.759 / 260.13 = 15.28 % (= TDD, IL taken as I1) vs 12 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 2.285 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 3.504 % vs 8 % → PASS. Individual orders over the row limit: h5 10.39 % > 10 %, h11 4.68 % > 4.5 %, h23 2.08 % > 1.5 %, h25 2.08 % > 1.5 % (+8 more). IEC 61000-2-2: worst V25/V1 = 0.953 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 4.55; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.438 (validation case c0017-three-drives-rss)

Example 18 — 450 kW of 6-pulse drives on a 1000 kVA transformer: THDv fails

A 1000 kVA, 5 % transformer (20 MVA at 415 V) feeding a 450 kW bare 6-pulse drive: THDv 9.0 % on the phase voltage fails the 8 % IEEE 519 limit (referred to the line-to-line voltage it would read 5.2 % and wrongly pass).

Given: 415 V, 50 Hz bus with a 20 MVA three-phase fault level, source X/R 6. Drives — MCC-VSD: 450 kW at 100 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 20 × 10⁶ / (√3 × 415) = 27.824 kA; Z = V² / S_sc = 415² / 20 MVA = 0.008611 Ω per phase (star equivalent) split by X/R 6 → R = 0.001416 Ω, X = 0.008494 Ω

Fundamental I₁(MCC-VSD) = 450 × 1 / (0.95 × 0.95) × 1000 / (√3 × 415) = 693.68 A

Correction factors MCC-VSD: K_load = 0.6 + 0.4 × 1 = 1.00, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 138.74 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	138.74	20.00	7	5.895	2.461
7	97.11	14.00	7	5.776	2.411
11	62.43	9.00	3.5	5.834	2.435
13	48.56	7.00	3.5	5.362	2.238
17	41.62	6.00	2.5	6.010	2.508
19	34.68	5.00	2.5	5.598	2.336

THD-I / TDD THD_I = √ΣI_h² / I₁ = 204.05 / 693.68 = 29.42 %; TDD = THD_I with I_L taken as I₁; I_rms = √(693.68² + 204.05²) = 723.06 A. SCR = I_sc/I₁ = 27,824 / 693.68 = 40.1 → IEEE 519 row SCR 20–50 (TDD 8 %) → 29.42 vs limit 8.00 % FAIL

Voltage distortion V₅ = 138.74 × √(0.001416² + (5 × 0.008494)²) = 5.895 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 21.670 / 239.60 = 9.044 % vs the 8 % limit for V ≤ 1 kV → 9.044 vs limit 8.000 % FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 5.892 / 239.60 = 2.459 % vs the 1.5 % compatibility level FAIL

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (693.68² + 6,507,334) / 723.06² = 13.37 (specify a K-rated transformer); crest factor I_peak/I_rms from the reconstructed waveform = 1.436 (√2 = 1.414 for a sine)

Result 0/4 checks pass → FAIL; THD_I 29.4 %, THD_V 9.04 %; governing: voltage thd

Reference Hand calculation: I1(MCC-VSD) = 450 kW × 1 / (0.95 × 0.95) / (√3 × 415 V) = 693.68 A. Isc = 20 MVA / (√3 × 415 V) = 27.824 kA (1000 kVA, 5 % impedance transformer on an infinite bus: S_sc = 1 MVA / 0.05); SCR = 40.1 → IEEE 519 row 20–50 (TDD limit 8 %). K_load = 0.6 + 0.4 × 1 = 1.00; I5 = 138.735 A. THDi = √ΣIh² / I1 = 204.046 / 693.68 = 29.42 % (= TDD, IL taken as I1) vs 8 % → FAIL. Z = 415² / 20 MVA = 0.008611 Ω per phase (star equivalent), X/R 6 → R = 0.001416, X = 0.008494 Ω; V5 = I5 × √(R² + (5X)²) = 5.895 V per phase; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 9.044 % vs 8 % → FAIL (cross-check, reactive part only: V5/V1 ≈ 5 × I5 / Isc = 5 × 138.74 / 27824 = 2.49 %). Individual orders over the row limit: h5 20.00 % > 7 %, h7 14.00 % > 7 %, h11 9.00 % > 3.5 %, h13 7.00 % > 3.5 % (+12 more). IEC 61000-2-2: worst V25/V1 = 2.459 % vs 1.5 % → NOT compliant. K = (I1² + ΣIh²h²)/Irms² = 13.37; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.436 (validation case c0017-transformer-1mva-thdv-fail)

Example 19 — Two identical drives, arithmetic summation

Arithmetic (in-phase) summation doubles every harmonic order; the detailed spectrum lists I5 and V5.

Given: 415 V, 50 Hz bus with a 10 MVA three-phase fault level, source X/R 5. Drives — A: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse; B: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation of the 2 drives, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 10 × 10⁶ / (√3 × 415) = 13.912 kA; Z = V² / S_sc = 415² / 10 MVA = 0.01722 Ω per phase (star equivalent) split by X/R 5 → R = 0.003378 Ω, X = 0.01689 Ω

Fundamental I₁(A) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A; I₁(B) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A; ΣI₁ = 231.23 A

Correction factors A: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1; B: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 41.62 A; 2 drives summed per order (arithmetic); V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	41.62	18.00	10	3.517	1.468
7	29.13	12.60	10	3.446	1.438
11	18.73	8.10	4.5	3.480	1.452
13	14.57	6.30	4.5	3.199	1.335
17	12.49	5.40	4	3.585	1.496
19	10.41	4.50	4	3.339	1.394

THD-I / TDD THD_I = √ΣI_h² / I₁ = 61.21 / 231.23 = 26.47 %; TDD = THD_I with I_L taken as I₁; I_rms = √(231.23² + 61.21²) = 239.19 A. SCR = I_sc/I₁ = 13,912 / 231.23 = 60.2 → IEEE 519 row SCR 50–100 (TDD 12 %) → 26.47 vs limit 12.00 % FAIL

Voltage distortion V₅ = 41.62 × √(0.003378² + (5 × 0.01689)²) = 3.517 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 12.926 / 239.60 = 5.395 % vs the 8 % limit for V ≤ 1 kV → 5.395 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 50–100 row (h<11 10 %, 11–16 4.5 %, 17–22 4 %, 23–34 1.5 %, ≥35 0.7 %): Harmonic 5: 18.00% exceeds limit 10.00%; Harmonic 7: 12.60% exceeds limit 10.00%; Harmonic 11: 8.10% exceeds limit 4.50%; +13 more → 16 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 3.515 / 239.60 = 1.467 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (231.23² + 585,660) / 239.19² = 11.17 (specify a K-rated transformer); crest factor I_peak/I_rms from the reconstructed waveform = 1.435 (√2 = 1.414 for a sine)

Result 2/4 checks pass → FAIL; THD_I 26.5 %, THD_V 5.39 %; governing: current tdd

Reference Hand calculation: I1(A) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A; I1(B) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A; total I1 = 231.23 A (arithmetic summation of the per-order currents). Isc = 10 MVA / (√3 × 415 V) = 13.912 kA; SCR = 60.2 → IEEE 519 row 50–100 (TDD limit 12 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; I5 = 41.621 A. THDi = √ΣIh² / I1 = 61.214 / 231.23 = 26.47 % (= TDD, IL taken as I1) vs 12 % → FAIL. Z = 415² / 10 MVA = 0.017223 Ω, X/R 5 → R = 0.003378, X = 0.016888 Ω; V5 = I5 × √(R² + (5X)²) = 3.517 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 5.395 % vs 8 % → PASS. Individual orders over the row limit: h5 18.00 % > 10 %, h7 12.60 % > 10 %, h11 8.10 % > 4.5 %, h13 6.30 % > 4.5 % (+12 more). IEC 61000-2-2: worst V25/V1 = 1.467 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 11.17; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.435 (validation case c0017-two-drives-arithmetic)

Example 20 — Two drives with 1.5 mH line reactors, RSS summation (former help example 2)

Line reactors halve the low-order harmonics and a DC choke takes a further 30 % off the second drive; RSS summation.

Given: 415 V, 50 Hz bus with a 25 MVA three-phase fault level, source X/R 5. Drives — VSD-01: 110 kW at 100 % load, pf 0.95, η 96 %, 6-pulse, 1.5 mH line reactor; VSD-02: 55 kW at 75 % load, pf 0.95, η 94 %, 6-pulse, 1.5 mH line reactor, DC choke. RSS (random-phase) summation of the 2 drives, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 25 × 10⁶ / (√3 × 415) = 34.780 kA; Z = V² / S_sc = 415² / 25 MVA = 0.006889 Ω per phase (star equivalent) split by X/R 5 → R = 0.001351 Ω, X = 0.006755 Ω

Fundamental I₁(VSD-01) = 110 × 1 / (0.96 × 0.95) × 1000 / (√3 × 415) = 167.80 A; I₁(VSD-02) = 55 × 0.75 / (0.94 × 0.95) × 1000 / (√3 × 415) = 64.26 A; ΣI₁ = 232.06 A

Correction factors VSD-01: K_load = 0.6 + 0.4 × 1 = 1.00, X_reactor = 2π × 50 × 1.5/1000 = 0.4712 Ω → K_reactor(5) = min(1, (0.5 + 0.5 × 0.006755/(0.006755 + 0.4712)) × (1 − 0.3/5)) = 0.477, K_dc = 1, 6-pulse K_pulse = 1; VSD-02: K_load = 0.6 + 0.4 × 0.75 = 0.90, X_reactor = 2π × 50 × 1.5/1000 = 0.4712 Ω → K_reactor(5) = min(1, (0.5 + 0.5 × 0.006755/(0.006755 + 0.4712)) × (1 − 0.3/5)) = 0.477, K_dc = 0.7, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 16.46 A; 2 drives summed per order (rss); V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	16.46	7.09	12	0.556	0.232
7	11.73	5.05	12	0.555	0.232
11	7.66	3.30	5.5	0.569	0.238
13	5.99	2.58	5.5	0.526	0.219
17	5.16	2.22	5	0.592	0.247
19	4.31	1.86	5	0.553	0.231

THD-I / TDD THD_I = √ΣI_h² / I₁ = 24.63 / 232.06 = 10.61 %; TDD = THD_I with I_L taken as I₁; I_rms = √(232.06² + 24.63²) = 233.37 A. SCR = I_sc/I₁ = 34,780 / 232.06 = 149.9 → IEEE 519 row SCR 100–1000 (TDD 15 %) → 10.61 vs limit 15.00 % PASS

Voltage distortion V₅ = 16.46 × √(0.001351² + (5 × 0.006755)²) = 0.556 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 2.134 / 239.60 = 0.891 % vs the 8 % limit for V ≤ 1 kV → 0.891 vs limit 8.000 % PASS

Individual orders Each I_h/I₁ against the SCR 100–1000 row (h<11 12 %, 11–16 5.5 %, 17–22 5 %, 23–34 2 %, ≥35 1 %): none of the orders exceeds its row limit → 0 order(s) over limit PASS

IEC 61000-2-2 worst V₂₅/V₁ = 0.584 / 239.60 = 0.244 % vs the 1.5 % compatibility level PASS

K-factor, crest K = (I₁² + ΣI_h²h²) / I_rms² = (232.06² + 99,805) / 233.37² = 2.82 (K-4 transformer adequate); crest factor I_peak/I_rms from the reconstructed waveform = 1.433 (√2 = 1.414 for a sine)

Result 4/4 checks pass → PASS; THD_I 10.6 %, THD_V 0.89 %; governing: current tdd

Reference Hand calculation: I1(VSD-01) = 110 kW × 1 / (0.96 × 0.95) / (√3 × 415 V) = 167.80 A; I1(VSD-02) = 55 kW × 0.75 / (0.94 × 0.95) / (√3 × 415 V) = 64.26 A; total I1 = 232.06 A (rss summation of the per-order currents). Isc = 25 MVA / (√3 × 415 V) = 34.780 kA; SCR = 149.9 → IEEE 519 row 100–1000 (TDD limit 15 %). K_load = 0.6 + 0.4 × 1 = 1.00; X_reactor = 2π × 50 × 1.5 mH = 0.4712 Ω, X_s = 0.00676 Ω → K_reactor(5) = min(1, (0.5 + 0.5 × 0.00676/(0.00676 + 0.4712)) × (1 − 0.3/5)) = 0.4766; I5 = 16.455 A. THDi = √ΣIh² / I1 = 24.632 / 232.06 = 10.61 % (= TDD, IL taken as I1) vs 15 % → PASS. Z = 415² / 25 MVA = 0.006889 Ω, X/R 5 → R = 0.001351, X = 0.006755 Ω; V5 = I5 × √(R² + (5X)²) = 0.556 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 0.891 % vs 8 % → PASS. No individual order exceeds its row limit. IEC 61000-2-2: worst V25/V1 = 0.244 % vs 1.5 % → compliant. K = (I1² + ΣIh²h²)/Irms² = 2.82; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.433 (validation case c0017-two-drives-reactors-rss)

Example 21 — Weak 0.5 MVA source: voltage distortion fails

A 100 kW drive on a 0.5 MVA generator bus (SCR 6, X/R 3): THDv 52 % is far over the 8 % limit, every IEC 61000-2-2 order from V5 to V25 is breached and every check fails.

Given: 415 V, 50 Hz bus with a 0.5 MVA three-phase fault level, source X/R 3. Drives — GEN-VSD: 100 kW at 75 % load, pf 0.95, η 95 %, 6-pulse. Arithmetic (in-phase) summation, orders up to h = 50.

Source I_sc = S_sc / (√3 × V) = 0.5 × 10⁶ / (√3 × 415) = 0.696 kA; Z = V² / S_sc = 415² / 0.5 MVA = 0.3444 Ω per phase (star equivalent) split by X/R 3 → R = 0.1089 Ω, X = 0.3268 Ω

Fundamental I₁(GEN-VSD) = 100 × 0.75 / (0.95 × 0.95) × 1000 / (√3 × 415) = 115.61 A

Correction factors GEN-VSD: K_load = 0.6 + 0.4 × 0.75 = 0.90, K_dc = 1, 6-pulse K_pulse = 1

Spectrum

I₅ = I₁ × I_5,base/100 × K_load × K_reactor × K_dc × K_pulse (first drive) → 20.81 A; V_h = I_h × √(R² + (hX)²) per phase. Dominant orders of 16:

h	I_h (A)	% of I₁	IEEE 519 limit %	V_h (V)	% of V₁
5	20.81	18.00	4	34.077	14.222
7	14.57	12.60	4	33.359	13.923
11	9.36	8.10	2	33.677	14.055
13	7.28	6.30	2	30.951	12.918
17	6.24	5.40	1.5	34.688	14.477
19	5.20	4.50	1.5	32.306	13.483

THD-I / TDD THD_I = √ΣI_h² / I₁ = 30.61 / 115.61 = 26.47 %; TDD = THD_I with I_L taken as I₁; I_rms = √(115.61² + 30.61²) = 119.60 A. SCR = I_sc/I₁ = 696 / 115.61 = 6.0 → IEEE 519 row SCR < 20 (TDD 5 %) → 26.47 vs limit 5.00 % FAIL

Voltage distortion V₅ = 20.81 × √(0.1089² + (5 × 0.3268)²) = 34.077 V; V₁ = V_LL/√3 = 415/√3 = 239.60 V; THD_V = √ΣV_h² / V₁ = 125.082 / 239.60 = 52.204 % vs the 8 % limit for V ≤ 1 kV → 52.204 vs limit 8.000 % FAIL

Individual orders Each I_h/I₁ against the SCR < 20 row (h<11 4 %, 11–16 2 %, 17–22 1.5 %, 23–34 0.6 %, ≥35 0.3 %): Harmonic 5: 18.00% exceeds limit 4.00%; Harmonic 7: 12.60% exceeds limit 4.00%; Harmonic 11: 8.10% exceeds limit 2.00%; +13 more → 16 order(s) over limit FAIL

IEC 61000-2-2 worst V₂₅/V₁ = 34.004 / 239.60 = 14.192 % vs the 1.5 % compatibility level FAIL

Result 0/4 checks pass → FAIL; THD_I 26.5 %, THD_V 52.20 %; governing: voltage thd

Reference Hand calculation: I1(GEN-VSD) = 100 kW × 0.75 / (0.95 × 0.95) / (√3 × 415 V) = 115.61 A. Isc = 0.5 MVA / (√3 × 415 V) = 0.696 kA; SCR = 6.0 → IEEE 519 row 0–20 (TDD limit 5 %). K_load = 0.6 + 0.4 × 0.75 = 0.90; I5 = 20.810 A. THDi = √ΣIh² / I1 = 30.607 / 115.61 = 26.47 % (= TDD, IL taken as I1) vs 5 % → FAIL. Z = 415² / 0.5 MVA = 0.344450 Ω, X/R 3 → R = 0.108925, X = 0.326774 Ω; V5 = I5 × √(R² + (5X)²) = 34.077 V; THDv = √ΣVh² / V1, V1 = 415 / √3 = 239.60 V (per-phase Vh over the phase voltage): 52.204 % vs 8 % → FAIL. Individual orders over the row limit: h5 18.00 % > 4 %, h7 12.60 % > 4 %, h11 8.10 % > 2 %, h13 6.30 % > 2 % (+12 more). IEC 61000-2-2: worst V25/V1 = 14.192 % vs 1.5 % → NOT compliant. K = (I1² + ΣIh²h²)/Irms² = 11.17; crest factor from the reconstructed waveform (100 samples/cycle, zero phase) = 1.435 (validation case c0017-weak-source-thdv-fail)

Standards & References

IEEE 519-2022 — IEEE Standard for Harmonic Control in Electric Power Systems. Defines TDD and voltage THD limits at the Point of Common Coupling (PCC).
IEC 61000-2-2 — Electromagnetic Compatibility — Environment — Compatibility Levels for Low-Frequency Conducted Disturbances and Signalling in Public Low-Voltage Power Supply Systems.
IEC 61000-3-12 — Limits for harmonic currents produced by equipment connected to public low-voltage systems with input current > 16 A and ≤ 75 A per phase.
IEEE C57.110 — IEEE Recommended Practice for Establishing Liquid-Immersed and Dry-Type Power and Distribution Transformer Capability When Supplying Nonsinusoidal Load Currents (K-factor basis).
AS/NZS 61000.3.6 — Assessment of emission limits for the connection of distorting installations to MV, HV and EHV power systems.

Tips & Limitations

Tips

Use phasor random (RSS) summation for realistic results when VSDs operate independently. Use arithmetic only for worst-case assessment or when drives are synchronised.
A 3–5% input line reactor is the most cost-effective mitigation, typically reducing 5th harmonic current by 40–50%.
12-pulse drives eliminate the 5th and 7th harmonics entirely and are recommended for drives > 200 kW.
Active Front End (AFE) drives produce < 5% THD and can regenerate energy, but cost 30–50% more than standard 6-pulse drives.
K-factor ≤ 4 means a standard transformer is adequate. K-factor > 13 warrants a K-rated or derated transformer.
Triplen harmonics (3rd, 9th, 15th) are not characteristic of 6-pulse VSDs, so neutral overloading is rarely a concern for pure VSD loads.
Higher fault levels (larger S_sc) produce higher SCR values, which grant more lenient IEEE 519 TDD limits.

Limitations

Steady-state only — transient harmonic behaviour during motor acceleration/deceleration is not modelled.
Balanced three-phase system — unbalanced phase loading and background voltage distortion are not considered.
Baseline data — the 6-pulse harmonic magnitudes use typical values. Actual magnitudes depend on drive manufacturer, DC bus capacitance, and load type. Replace baseline values with manufacturer data where available.
Phase angles ignored — phasor random summation assumes random phase displacement. For precise cancellation analysis (e.g., phase-shifted multi-pulse transformers), a full phasor simulation is needed.
IEEE 519 TDD denominator — the calculator uses the sum of fundamental currents as the demand current \(I_L\). For installations where maximum demand differs from the sum of VSD loads, manually adjust the interpretation.
No passive filter modelling — tuned passive harmonic filters are not directly modelled. Their effect can be approximated by reducing individual harmonic magnitudes in the baseline table.

Developer Guide

Architecture

File layout:

components/c0017_vsd_harmonic_analysis/component.py — Component registration, parameter schema (PARAMETER_SCHEMA), calculator class, summary cards builder, QR code generator
components/c0017_vsd_harmonic_analysis/calculations.py — Pure math functions, baseline harmonic tables, IEEE 519 / IEC 61000 limit tables, correction factors, compliance checks, mitigation logic (no Django dependencies)
components/c0017_vsd_harmonic_analysis/equations.py — Equation builder producing ARTICLES.md-compliant article list for the PDF/HTML report
components/c0017_vsd_harmonic_analysis/excel_generator.py — Excel export of harmonic spectrum and results

The calculator class is VSDHarmonicAnalysisCalculator(ElectricalCalculator). It delegates all computation to the standalone function calculate_vsd_harmonic_analysis(data).

Key data structures:

BASELINE_6PULSE_HARMONICS — dict mapping harmonic order to baseline magnitude (% of fundamental)
IEEE_519_CURRENT_LIMITS — list of tuples defining (SCR_min, SCR_max, individual limits by harmonic band, TDD limit)
IEEE_519_VOLTAGE_LIMITS — dict keyed by voltage class with individual and THD limits
IEC_61000_VOLTAGE_LIMITS — dict mapping harmonic order to compatibility level (%)

Code Paths

Key functions in calculations.py:

Function	Purpose
`calculate_vsd_harmonic_analysis(data)`	Main entry point — orchestrates the full analysis and returns the results dict
`calculate_vsd_harmonics(…)`	Compute harmonic spectrum for a single VSD (fundamental current, correction factors, per-harmonic currents)
`get_characteristic_harmonics(pulse, max_order)`	Return characteristic harmonic orders for a given pulse number using \(h = kq \pm 1\)
`calculate_load_correction_factor(load%)`	Load correction: \(K_{load} = 0.6 + 0.4 \times load\%/100\)
`calculate_reactor_correction_factor(x_s, x_r, h)`	Input reactor attenuation factor per harmonic order
`calculate_dc_choke_correction_factor(has_choke)`	Returns 0.7 if choke fitted, else 1.0
`calculate_pulse_correction_factor(pulse, h)`	Elimination/reduction factor for multi-pulse configs
`calculate_afe_harmonics(I1)`	Simplified spectrum for Active Front End drives (2% per low-order harmonic)
`sum_harmonic_currents(vsd_results, method)`	Combine per-VSD spectra using arithmetic or RSS summation
`calculate_total_thd(harmonics, I1)`	Current THD calculation
`calculate_voltage_distortion(I_h, Z_s)`	Voltage distortion from harmonic currents through source impedance
`calculate_voltage_thd(V_h, V_phase)`	Voltage THD calculation
`check_ieee_519_compliance(…)`	Full IEEE 519-2022 compliance check (voltage + current + individual harmonics)
`check_iec_61000_compliance(V_h, V_phase)`	IEC 61000-2-2 voltage compatibility level check
`calculate_k_factor(harmonics, I1)`	Transformer K-factor: \(\sum (I_h/I_1)^2 \times h^2\)
`calculate_neutral_current(harmonics)`	Neutral current from triplen harmonics (3× arithmetic sum in neutral)
`calculate_crest_factor(I1, harmonics, f)`	Waveform reconstruction to find peak-to-RMS ratio
`recommend_mitigation(thd, compliance, vsds)`	Automatic mitigation recommendations based on THD levels and SCR

Testing

Running tests:

pytest calcs/components/c0017_vsd_harmonic_analysis/ -v
pytest calcs/test_c0017* -v

Worked examples: the examples above are generated from the MCP validation corpus (mcp_public/validation/cases/fe_calc_harmonics/) by python manage.py generate_help_examples --tool fe_calc_harmonics, which writes _vsd_harmonic_analysis_examples.html; every case must pass its expectations before the fragment is written, and calcs/test_help_examples.py checks the committed fragment is current.

How to extend:

To add new harmonic baseline data (e.g., manufacturer-specific spectra), extend or replace BASELINE_6PULSE_HARMONICS in calculations.py.
To support additional rectifier topologies, add entries to the reduction_factors dict in calculate_pulse_correction_factor() and update the rectifier_type enum in PARAMETER_SCHEMA.
To add new compliance standards, follow the pattern of check_ieee_519_compliance() — define limit tables as module-level constants and implement a dedicated check function.
To model passive or active filters, add a new correction factor function (following the pattern of calculate_reactor_correction_factor()) and multiply it into the harmonic current formula in calculate_vsd_harmonics().
Write tests covering the new functionality including edge cases (zero power, 0% load, maximum harmonic order).