The inertia constants of two groups of machines which do

The inertia constants of two groups of machines which do not swing together are M₁ and M₂. The equivalent inertia constant of the system is

The swing equations for the two machines are,

d²δ₁	=	P_a1	=	P_s1 - P_e2
dt²	=	M	=	M₁

and	d²δ₂	=	P_a²	=	P_s2 - P_e2
	dt²		M		M₂

If δ = δ₁ – δ₂, then relative angle between the two rotor axis,

d²δ	=	d²δ₁	-	d²δ₂	=	P_s1 - P_e2	-	P_s2 - P_e2
dt²	=	dt²	-	dt²	=	M₁	-	M₂

or	M₁M₂	.	d²δ	=	M₂P_s1 - M₁P_s2	=	Md²δ	= P_s - P_e
	M₁ + M₂		dt²		M₁ + M₂		dt²

where M =	M₁M₂
	M₁ + M₂

P_s =	M₂P_s2
	M₁ + M₂

and P_e =	M₂P_e1 - M₁P_e2
	M₁ + M₂