74b11bd7-3739-42b1-bb21-ff5fc73d359c 6 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Given a three phase set of voltages :

I.U I.V I.W 31 mat 25.68 30.08 19.07 31 mat : 25.68 30.08 19.07 31 mat

Separate into positive and negative sequence line-to-line components a=exp \[REGION[c08d9fdd24f54456a3178ae935ea72fe]]\ :i2π3/*(*

a exp i 2 * π 3 / *^:

a i 2 * π 3 / * exp : 0.5 - 0.866 i * +

I.U a 0^I.U * : 25.68

I.V a 1^I.V * : 47355271367880052 - 615348059642739 i * + (* 1110223024625160 /

I.W a 2^I.W * : 47675355271367880052 - 615348059642739 i * + (2^* 1262177448353620000000000000000000 /

I.1 13 / (a 0^I.U * a 1^I.V * + a 2^I.W * + (* : 0.3683 3.1783 i * -

I.1 abs 3.1996

6.25

I.2 13 / (a 0^I.U * a 2^I.V * + a 1^I.W * + (* : 24.9433 1.6537 1013 -^* i * +

I.2 abs 24.9433

24.59

I.0 13 / (a 0^I.U * a 0^I.V * + a 0^I.W * + (* : 0.3683 3.1783 i * +

Once the above is fixed the bottom will be corrected;

aa 0 :

I.2 I.1 / abs 7.7958

V.a 0 :

V.b i aa π + 2 / (* exp :

I.1 I.2 / abs 0.1283

V.c i - (aa π + 2 / (* exp :

I.1 I.2 /

.232

is a three-phase voltage, then its corresponding sequence components are calculated using the following transformation.

V.abc V.a V.b V.c 13 mat transpose :

I.2 1 .232 / (I.1 * :

a1 2 i * π 3 / * exp :

V.a V.b + V.c + 21015 -^* -

a2 a1 2^:

V.a 0

is the symmetric transformation matrix

V.b 11015 -^* - i +

T 1111 a1 a2 1 a2 a1 33 mat :

V.012 T V.abc * :

I.abc T 1 -^I.012 * ≡

is the zero, positive, and negative sequence voltage components respectively

V.012 V.0 V.1 V.2 13 mat transpose ≡

V.012 21015 -^* - 1.7321 - 3.1774 1015 -^* i * - 1.7321 3.2682 1015 -^* i * + 31 mat

T 1111 0.5 - 0.866 i * + 0.5 - 0.866 i * - 1 0.5 - 0.866 i * - 0.5 - 0.866 i * + 33 mat

V.abc 011015 -^* - i + 11015 -^* - i - 31 mat

sanity check V.012 T V.abc * : 21015 -^* - 1.7321 - 2.9683 1015 -^* i * - 1.7321 2.9683 1015 -^* i * + 31 mat