# Neutral Currents in Three Phase Wye Systems

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1 POWER SYSTEMS ENGINEERING DATA PUBLISHED BY SQUARE D, OSHKOSH, WISCONSIN Subject: Neutral Currents in Three Phase Wye Systems by Robert Arthur Square D Company Oshkosh, Wisconsin (414) and R. A. Shanahan, P.E. Square D Company Lexington, Kentucky (606) ABSTRACT: This paper: Discusses current signatures of single phase non-linear loads and examines the relationship of these signatures to neutral current in wye-connected three phase electrical systems. Establishes formulas for estimating maximum neutral current under various total harmonic current distortion levels for both balanced and unbalanced load conditions. Shows that neutral conductor oversizing is not necessary in 480Y/77V systems, but may be necessary in 08Y/10V systems under unusual circumstances. These discussions apply to 480Y/77V electrical systems in the United States and 600Y/346V lighting distribution systems in Canada.

4 Line Current = 1 Computer Per Phase Neutral Current = 173% of Line Line Current = 7 Computers Per Phase Neutral Current = 171% of Line Line Current = 10 Computers Per Phase Neutral Current = 153% of Line Figure 4: Both load population and the effects of source impedance on voltage tend to reduce neutral current. NEUTRAL CURRENT AND TOTAL HARMONIC DISTORTION Total Harmonic Distortion (THD) is a percentage representing the deviation of a waveform from the ideal sinusoid. The formula for current THD is: Table 1: Third harmonic in single phase non-linear load current is the major contributor to neutral current. Other harmonics, including triplens such as 9th, 15th, etc., provide insignificant contribution. Harmonic I h Harmonic I h %THD = 100 I + I 3 + I 4 + I 5 + I h I 1 Where: h = harmonic number I h = current at harmonic h in per-unit of total rms current Every waveshape has harmonic components. In the case of a sinusoid, the harmonic component consists of the 1st harmonic, or fundamental, with no other harmonics present %THD = %THD = 38.0 %Neutral = %Neutral = Square D All Rights Reserved 5

5 The THD of a sinusoid is 0%. Typical unfiltered single phase electronic loads produce current distortions that contain large amounts of 3rd harmonic, with decreasing percentages of 5th, 7th, 9th, 11th, 13th, 15th, and so on. Of those harmonics, only the 3rd, 9th, 15th, etc., contribute to the neutral problem. Harmonics in this sequence are identifiable as triplen harmonic numbers that are evenly divisible by 3. Because of their lower current levels and higher frequencies, the 9th, 15th and higher triplen harmonics distort the neutral current only slightly and do not have a significant effect on actual rms neutral current. Therefore, to accurately estimate the percent neutral current that would result from three identical non-linear phase currents, simply multiply the 3rd harmonic (as a percentage of total rms current), times 3 (see Table 1, page 5). Thus, a minimum of 33.33% of 3rd harmonic is required to produce a 100% neutral current. This strong relationship between the 3rd harmonic and neutral current leads to an equally strong relationship between neutral current and line current THD. Table 1, page 5 shows that by considering the 1st and 3rd harmonics only in the THD formula, and setting the 3rd harmonic value to 33.33% to produce 100% neutral current, the minimum THD to produce this current is 35.36%. Note that if other harmonics are present, they merely raise the THD number, but do not significantly increase neutral current. For that reason, a THD of 35.36% is the minimum limit of line current distortion required to produce 100% neutral current in a balanced wye system. For a more general rule, the following guideline relationships can be calculated: Given: I 1 = Fundamental current as a per-unit of total rms current I 3 = Third harmonic current as a per-unit of total rms current The %THD increases when harmonics other than fundamental and third are considered. 1. %THD > 100 I 3 I 1 = 100. Since I 1 and I 3 are defined as per-unit of total rms current, and since I 1 > I 3, then: I 1 + I 3 < 1 or 3. Combining equations 1 and : %THD > 100 or I 3 < I 3 1 I 3 % THD 10,000 + (%THD) I 3 I 1 I 1 < 1 I 3 4. Since all harmonics other than 3rd have an insignificant effect on neutral current: %Neutral 300 I 3 5. Note that since the maximum neutral current is 173%, the maximum 3rd harmonic is times the total rms line current. Combining equations 3 and 4: %Neutral < % THD 300 up to 173% neutral 10,000 + (%THD) This relationship in equation 5 is a good guideline for estimating the maximum, balanced neutral current for THD values up to about 150%. Because third harmonic reaches its maximum at 57.7% of total rms current, equation 5 becomes increasingly inaccurate as the neutral value approaches 173%. As a result, although equation 5 estimates that a minimum of 70.7% line current THD is required to reach the 173% maximum, in practice it typically takes 80 90% THD to achieve maximum neutral levels. For example, a lighting ballast is rated at 10% THD. What will be the maximum, balanced load neutral current on the lighting panel? % Neutral < = 3000 = 9.9% of 10,000 + (10) 10,100 line current LIGHTING BALLASTS Table : Current harmonic limits for lighting ballasts. Harmonic Maximum Value Fundamental (by definition) 100% nd Harmonic 5% 3rd Harmonic 30% Individual Harmonics > 11th 7% Odd Triples 30% Harmonic Factor (Distortion Factor) 3% The lighting industry has established limits on harmonic currents for lighting ballasts which are outlined in ANSI Standard C Table is a portion of Table 3 from ANSI Standard C The table is quite comprehensive in that it puts limits on specific low-order harmonics (nd and 3rd), high-order harmonics (>11th), and odd triples. To further encourage the use of the low THD ballast designs, some utility companies offer energy saving rebates only for electronic ballasts that have THD values less than 0%. Each ballast manufacturer has a large selection in the <0% range. In reality, most of the products fall in this range, see Table 3. Table 3 : THD ranges for various types of ballasts compared with office equipment. Device Type THD Older Rapid Start Magnetic Ballast 10 9% Electronic I.C. Based Ballast 4 10% Electronic Discrete Based Ballast 18-30% Newer Rapid Start Electronic Ballast <10% Newer Instant Start Electronic Ballast 15 7% High Intensity Discharge (HID) Ballast 15 7% Office Equipment % Square D All Rights Reserved

10 Square D Company 3300 Medalist Drive Oshkosh, WI USA Square D and are Registered Trademarks of Square D Company. Order No. 0104ED9501R8/96 Replaces No. 0104ED9501 Printed in USA 5K FP 8/ Square D All Rights Reserved

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