PowerWiki: Symmetrization

At line 25 changed 3 lines.

Mezi uzly 2 a 3 nechť je zapojena reálná zátěž o vodivosti ''G'' (S). Požadujeme, aby po připojení admitancí

''Y''[{Sub par='12'}] (S) a ''Y''[{Sub par='13'}] (S) byla zátěž reálná a symetrická; dalším požadavkem je, aby

činný výkon odebíraný zátěží zůstal nezměněn, matematizujme tyto požadavky:\\ \\

Let real load is connected between nodes 2 and 3 with conductivity of ''G'' (S). We require load to be real and symmetrical after connection of admittances

''Y''%%sub 12%% (S) and ''Y''%%sub 13%% (S) real power (picked by the load) has to stay without any changes is the next demand. We translate these requirements to the mathematical language:\\ \\

At line 29 changed 3 lines.

~# zachování činného výkonu: ''Y''[{Sub par='12'}] a ''Y''[{Sub par='13'}] jsou ryze imaginární,\\

~# výsledné zapojení neodebírá jalový výkon: ''Y''[{Sub par='12'}] = -''Y''[{Sub par='13'}]; položme ''Y''[{Sub par='12'}] = ''j.Y'', ''Y''[{Sub par='13'}] = ''-j.Y'',\\

~# symetrie odebíraných proudů: ''I''[{Sub par='1'}] = ''k.U''[{Sub par='1'}], ''I''[{Sub par='2'}] = ''k.U''[{Sub par='2'}], ''I''[{Sub par='3'}] = ''k.U''[{Sub par='3'}].

~# conservation of the real power: ''Y''%%sub 12%% and ''Y''%%sub 13%% are purely imaginary,\\

~# výsledné zapojení neodebírá jalový výkon: ''Y''%%sub 12%% = -''Y''%%sub 13%%; položme ''Y''%%sub 12%% = ''j.Y'', ''Y''%%sub 13%% = ''-j.Y'',\\

~# symetrie odebíraných proudů: ''I''%%sub 1%% = ''k.U''%%sub 1%%, ''I''%%sub 2%% = ''k.U''%%sub 2%%, ''I''%%sub 3%% = ''k.U''%%sub 3%%.

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''U''[{Sub par='1'}] = ''U'', ''U''[{Sub par='2'}] = ''U.a''[{Sup par='2'}], ''U''[{Sub par='3'}] =

''U''%%sub 1%% = ''U'', ''U''%%sub 2%% = ''U.a''%%super 2%%, ''U''%%sub 3%% =

At line 40 changed 3 lines.

''I''[{Sub par='1'}] = ''I''[{Sub par='12'}] + ''I''[{Sub par='13'}] = ''j.Y.''(''U''[{Sub par='1'}] -

''U''[{Sub par='2'}]) - ''j.Y.''(''U''[{Sub par='1'}] - ''U''[{Sub par='3'}]) = ''j.Y.U.''(1 -

''a''[{Sup par='2'}]) - ''j.Y.U.''(1 - ''a'') = ''k.U''[{Sub par='1'}] = ''k.U''\\

''I''%%sub 1%% = ''I''%%sub 12%% + ''I''%%sub 13%% = ''j.Y.''(''U''%%sub 1%% -

''U''%%sub 2%%) - ''j.Y.''(''U''%%sub 1%% - ''U''%%sub 3%%) = ''j.Y.U.''(1 -

''a''%%super 2%%) - ''j.Y.U.''(1 - ''a'') = ''k.U''%%sub 1%% = ''k.U''\\

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''I''[{Sub par='2'}] = ''I''[{Sub par='23'}] - ''I''[{Sub par='12'}] = ''G.''(''U''[{Sub par='2'}] -

''U''[{Sub par='3'}]) - ''j.Y.''(''U''[{Sub par='1'}] - ''U''[{Sub par='2'}]) = ''G.U.''(''a''[{Sup par='2'}]

- ''a'') - ''j.Y.U.''(1 - ''a'') = ''k.U''[{Sub par='2'}] = ''k.U.a''[{Sup par='2'}]\\

''I''%%sub 2%% = ''I''%%sub 23%% - ''I''%%sub 12%% = ''G.''(''U''%%sub 2%% -

''U''%%sub 3%%) - ''j.Y.''(''U''%%sub 1%% - ''U''%%sub 2%%) = ''G.U.''(''a''%%super 2%%

- ''a'') - ''j.Y.U.''(1 - ''a'') = ''k.U''%%sub 2%% = ''k.U.a''%%super 2%%\\

At line 48 changed 3 lines.

''I''[{Sub par='3'}] = -''I''[{Sub par='23'}] - ''I''[{Sub par='13'}] = -''G.''(''U''[{Sub par='2'}] -

''U''[{Sub par='3'}]) - (-''j.Y'')''.''(''U''[{Sub par='1'}] - ''U''[{Sub par='3'}]) =

-''G.U.''(''a''[{Sup par='2'}] - ''a'') + ''j.Y.U.''(1 - ''a'') = ''k.U''[{Sub par='3'}] =

''I''%%sub 3%% = -''I''%%sub 23%% - ''I''%%sub 13%% = -''G.''(''U''%%sub 2%% -

''U''%%sub 3%%) - (-''j.Y'')''.''(''U''%%sub 1%% - ''U''%%sub 3%%) =

-''G.U.''(''a''%%super 2%% - ''a'') + ''j.Y.U.''(1 - ''a'') = ''k.U''%%sub 3%% =

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''k.U.''(1 + ''a''[{Sup par='2'}] + ''a'') = 0, neboť platí 1 + ''a''[{Sup par='2'}] + ''a'' = 0.

''k.U.''(1 + ''a''%%super 2%% + ''a'') = 0, neboť platí 1 + ''a''%%super 2%% + ''a'' = 0.

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''P'' = Re{''U.G.U''} + Re{''a''[{Sup par='2'}]''.U.'' (''a''[{Sup par='2'}]''.U.G'')[{Sup par='*'}] } = ''U''[{Sup par='2'}]

''P'' = Re{''U.G.U''} + Re{''a''%%super 2%%''.U.'' (''a''%%super 2%%''.U.G'')%%super *%% } = ''U''%%super 2%%

At line 67 changed 4 lines.

''.G.''(1 + ''a''[{Sup par='2'}]''.''(''a''[{Sup par='2'}])[{Sup par='*'}] +

''a.a''[{Sup par='*'}]) = ''U''[{Sup par='2'}]''.G.''(1 + ~|''a''[{Sup par='2'}]~|[{Sup par='2'}] +

~|''a''~|[{Sup par='2'}]) = ''U''[{Sup par='2'}]''.G.''(1 + ~|''a''|[{Sup par='4'}] +

~|''a''~|[{Sup par='2'}]) = ''U''[{Sup par='2'}]''.G.''(1 + 1 + 1) = 3.''U''[{Sup par='2'}].G

''.G.''(1 + ''a''%%super 2%%''.''(''a''%%super 2%%)%%super *%% +

''a.a''%%super *%%) = ''U''%%super 2%%''.G.''(1 + ~|''a''%%super 2%%~|%%super 2%% +

~|''a''~|%%super 2%%) = ''U''%%super 2%%''.G.''(1 + ~|''a''|%%super 4%% +

~|''a''~|%%super 2%%) = ''U''%%super 2%%''.G.''(1 + 1 + 1) = 3.''U''%%super 2%%.G

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Činný výkon původního zapojení před připojením symetrizačních členů byl: ''P'' = ''G.''([Symetrizace/sqrt(3).png]''.U'')[{Sup par='2'}] = 3''.U''[{Sup par='2'}]''.G''.

Činný výkon původního zapojení před připojením symetrizačních členů byl: ''P'' = ''G.''([Symetrizace/sqrt(3).png]''.U'')%%super 2%% = 3''.U''%%super 2%%''.G''.