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3w Auto Estimator Equations

The document outlines equations for estimating impedance in 3W Auto transformers based on empirical data and ANSI standards. It provides formulas for calculating positive and zero sequence impedances, as well as tertiary impedance estimates. Additionally, it includes methods for estimating resistance and reactance ratios for different winding configurations.

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Karim Ullah PW ELE BATCH 22
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© © All Rights Reserved
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15 views4 pages

3w Auto Estimator Equations

The document outlines equations for estimating impedance in 3W Auto transformers based on empirical data and ANSI standards. It provides formulas for calculating positive and zero sequence impedances, as well as tertiary impedance estimates. Additionally, it includes methods for estimating resistance and reactance ratios for different winding configurations.

Uploaded by

Karim Ullah PW ELE BATCH 22
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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3W Auto Impedance Estimator Equations

Given: Max MVA %Zps is Linearized from Empirical Data X/R Ratio is Estimated from ANSI C37.010
(OFAF) %𝑍𝑝𝑠 ≈ 0.0071 𝑂𝑁𝐴𝑁 + 5.225
3
𝑂𝐹𝐴𝑁 = 𝑂𝐹𝐴𝐹
4
3
𝑂𝑁𝐴𝑁 = 𝑂𝐹𝐴𝐹
5

Given: Rated MVA


(ONAN)

5
𝑂𝐹𝐴𝑁 = 𝑂𝑁𝐴𝑁
4
5
𝑂𝐹𝐴𝐹 = 𝑂𝑁𝐴𝑁
3 Positive Sequence
%𝑍
𝑍𝑝𝑠𝑝𝑢 =
100
𝑍𝑝𝑠𝑝𝑢
𝑅𝑝𝑠𝑝𝑢 =
1 + 𝑋𝑅𝑟𝑎𝑡𝑖𝑜 2
2 2
𝑋𝑝𝑠𝑝𝑢 = 𝑍𝑝𝑠𝑝𝑢 − 𝑅𝑝𝑠𝑝𝑢
3W Auto Δ Tertiary
Zpt and Zst
Positive Sequence
ONANTertiary is Estimated as 1/3 ONANPS
1
𝑂𝑁𝐴𝑁𝑇𝑒𝑟𝑖𝑎𝑟𝑦 ≈ 𝑂𝑁𝐴𝑁𝑃𝑆
3

Zpt/Zps is Linearized from Empirical Data Zst/Zps is Linearized from Empirical Data
𝑍𝑝𝑡 ≈ 𝑍𝑝𝑠 0.0022 𝑂𝑁𝐴𝑁𝑇𝑒𝑟𝑖𝑎𝑟𝑦 + 0.9931 𝑍𝑠𝑡 ≈ 𝑍𝑝𝑠 0.0025 𝑂𝑁𝐴𝑁𝑇𝑒𝑟𝑖𝑎𝑟𝑦 + 0.8179

Zero Sequence
Zps0 Zpt0 and Zst0 are Estimated Relative to Positive Sequence
𝑅𝑝𝑠0 = 𝑅𝑝𝑠+ 𝑍𝑝𝑡0 𝑍𝑝𝑠0 𝑅𝑝𝑡+ 𝑋𝑝𝑡+
= 𝑅𝑝𝑡0 = 𝑅𝑝𝑠0 𝑋𝑝𝑡0 = 𝑋𝑝𝑠0
𝑋𝑝𝑠0 ≈ 0.9𝑋𝑝𝑠+ 𝑍𝑝𝑡+ 𝑍𝑝𝑠+ 𝑅𝑝𝑠+ 𝑋𝑝𝑠+
𝑍𝑠𝑡0 𝑍𝑝𝑠0 𝑅𝑠𝑡+ 𝑋𝑠𝑡+
= 𝑅𝑠𝑡0 = 𝑅𝑝𝑠0 𝑋𝑠𝑡0 = 𝑋𝑝𝑠0
𝑍𝑠𝑡+ 𝑍𝑝𝑠+ 𝑅𝑝𝑠+ 𝑋𝑝𝑠+
3W Auto Δ Tertiary (Buried)
this method uses all windings with same MVABase = ONANPS

Zpt and Zst


Positive Sequence

Xpt is Estimated using Xps Xst is Estimated using Xps


3 1
𝑋𝑝𝑡 ≈ 𝑋𝑝𝑠 𝑋𝑠𝑡 ≈ 𝑋𝑝𝑠
2 2
Rpt is Estimated from X/R Ratio Rst is Estimated from X/R Ratio
𝑋𝑝𝑡 𝑋𝑠𝑡
𝑅𝑝𝑡 = 𝑅𝑠𝑡 =
𝑋𝑅𝑟𝑎𝑡𝑖𝑜 𝑋𝑅𝑟𝑎𝑡𝑖𝑜

Zero Sequence
Zps0 Zpt0 and Zst0 are Estimated Relative to Positive Sequence
𝑅𝑝𝑠0 = 𝑅𝑝𝑠+ 𝑍𝑝𝑡0 𝑍𝑝𝑠0 𝑅𝑝𝑡+ 𝑋𝑝𝑡+
= 𝑅𝑝𝑡0 = 𝑅𝑝𝑠0 𝑋𝑝𝑡0 = 𝑋𝑝𝑠0
𝑋𝑝𝑠0 ≈ 0.9𝑋𝑝𝑠+ 𝑍𝑝𝑡+ 𝑍𝑝𝑠+ 𝑅𝑝𝑠+ 𝑋𝑝𝑠+
𝑍𝑠𝑡0 𝑍𝑝𝑠0 𝑅𝑠𝑡+ 𝑋𝑠𝑡+
= 𝑅𝑠𝑡0 = 𝑅𝑝𝑠0 𝑋𝑠𝑡0 = 𝑋𝑝𝑠0
𝑍𝑠𝑡+ 𝑍𝑝𝑠+ 𝑅𝑝𝑠+ 𝑋𝑝𝑠+
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