tgδ X cosφ

Created by Deleted Agent, Modified on Wed, 20 Jul, 2022 at 10:11 AM by Deleted Agent

Angle φ: angle 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:

Angle	tgδ	cosφ	Diference
0°	0%	0,000000	0%
0,01°	0,01745%	0,000175	1,52.10^-6%
0,02°	0,03491%	0,000349	6,09.10^-6%
0,03°	0,05236%	0,000524	1,37.10^-5%
0,04°	0,06981%	0,000698	2,43.10^-5%
0,05°	0,08727%	0,000873	3,80.10^-5%
0,06°	0,10472%	0,001047	5,48.10^-5%
0,07°	0,12217%	0,001222	7,46.10^-5%
0,08°	0,13963%	0,001396	9,74.10^-5%
0,09°	0,15708%	0,001571	0,00012%
0,1°	0,17453%	0,001745	0,00015%
0,2°	0,34907%	0,003491	0,00061%
0,3°	0,5236%	0,005236	0,00137%
0,4°	0,69814%	0,006981	0,00243%
0,5°	0,87269%	0,008727	0,00380%
0,6°	1,04724%	0,010472	0,00548%
0,7°	1,22179%	0,012217	0,00746%
0,8°	1,39635%	0,013962	0,00974%
0,9°	1,57093%	0,015707	0,01233%
1°	1,74551%	0,017452	0,01523%
2°	3,49208%	0,034899	0,06095%
5°	8,74886%	0,087155	0,38198%

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