tgδ X cosφ

Modified on Wed, 20 Jul, 2022 at 10:11 AM

  • Angle φangle between the real component and the magnitude module under study;
  • Angle δ: angle between the magnitude module under study and its imaginary component.
    Figure 1 - Graphical representation between φ and δ 

  • cosφ: created index to define how much of a electrical magnitude is active in relation with its apparent magnitude. To determinate, for an example, how much a electric current is really active related to its apparent current, we have the formula bellow:

  • tgδ: created to compare real and imaginary component of a value. In electrical currents case:

    It is easy to notice that, even if the conceptual approach of each index is different, both of them seek to quantify how much a determined electrical magnitude is lagged related with its reference.

    In case of a system which is relevant to know this lag value in a current formed by mostly capacitive load, which is the case of measure the tap bushing leakage current, the angle δ is too small while the angle φ is close to 90°. Furthermore , is important to notice that: δ = 90 - φ.

    When the angle δ is too small, its tangent value will be almost the same of the φ cosine. For an example:


    Angletgδcosφ Diference
    0%0,0000000%
    0,01°0,01745%0,0001751,52.10^-6%
    0,02°0,03491%0,0003496,09.10^-6%
    0,03°0,05236%0,0005241,37.10^-5%
    0,04°0,06981%0,0006982,43.10^-5%
    0,05°0,08727%0,0008733,80.10^-5%
    0,06°0,10472%0,0010475,48.10^-5%
    0,07°0,12217%0,0012227,46.10^-5%
    0,08°0,13963%0,0013969,74.10^-5%
    0,09°0,15708%0,0015710,00012%
    0,1°0,17453%0,0017450,00015%
    0,2°0,34907%0,0034910,00061%
    0,3°0,5236%0,0052360,00137%
    0,4°0,69814%0,0069810,00243%
    0,5°0,87269%0,0087270,00380%
    0,6°1,04724%0,0104720,00548%
    0,7°1,22179%0,0122170,00746%
    0,8°1,39635%0,0139620,00974%
    0,9°1,57093%0,0157070,01233%
    1,74551%0,0174520,01523%
    3,49208%0,0348990,06095%
    8,74886%0,0871550,38198%


    From the listed data above it is possible to see that, the even when the tgδ is too high (3,5% when δ δ ≈ 2°), the difference between it and the cosφ barely achieves 0,06%. Even when δ is equal to 5° the difference will be less than 0,5%, this way, agreed in electrical engineering that tgδ and cosφ are the same while δ is a very small angle.  

    Figure 2 - Circuit

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