LKC sistema a N fili
∑ k = 1 N I k ¯ = 0 {\displaystyle \sum _{k=1}^{N}{\overline {I_{k}}}=0}
P = ∑ k = 1 N E k ¯ ⋅ I k ¯ {\displaystyle P=\sum _{k=1}^{N}{\overline {E_{k}}}\cdot {\overline {I_{k}}}}
P ′ = ∑ k = 1 N ( E k ¯ − V O ′ O ¯ ) ⋅ I k ¯ = ∑ k = 1 N E k ¯ ⋅ I k ¯ − V O ′ O ¯ ⋅ ∑ k = 1 N I k ¯ 0 = P {\displaystyle {\begin{aligned}P\,'&=\sum _{k=1}^{N}({\overline {E_{k}}}-{\overline {V_{O'O}}})\cdot {\overline {I_{k}}}\\&=\sum _{k=1}^{N}{\overline {E_{k}}}\cdot {\overline {I_{k}}}-{\overline {V_{O'O}}}\cdot {\cancelto {0}{\sum _{k=1}^{N}{\overline {I_{k}}}}}\\&=P\end{aligned}}}
∑ k = 1 N i k ( t ) = 0 ∀ t {\displaystyle \sum _{k=1}^{N}i_{k}(t)=0\quad \forall t}
p ( t ) = ∑ k = 0 N e k ( t ) i k ( t ) {\displaystyle p(t)=\sum _{k=0}^{N}e_{k}(t)\,i_{k}(t)}
p ′ ( t ) = ∑ k = 0 N ( e k ( t ) − v O ′ O ( t ) ) i k ( t ) {\displaystyle p'(t)=\sum _{k=0}^{N}(e_{k}(t)-v_{O'O}(t))\,i_{k}(t)}
p ′ ( t ) = ∑ k = 0 N e k ( t ) i k ( t ) − v O ′ O ( t ) ∑ k = 1 N i k ( t ) 0 = p ( t ) ∀ t {\displaystyle p'(t)=\sum _{k=0}^{N}e_{k}(t)\,i_{k}(t)-v_{O'O}(t)\,{\cancelto {0}{\sum _{k=1}^{N}i_{k}(t)}}=p(t)\quad \forall t}
