Patent Document ID: 8977524
Application ID: 13413086
Patent Flag: 1

Claim One:
1. A method for approximating an optimal power flow of a smart electric power grid, comprising the steps of: providing a cost function that models a smart electric power grid having N buses iε[1,N] connected by branches i,jε[1,N]×[1, N] with connection matrix R ij = { 1 , ∃ ⁢ branch ⁢ ⁢ i , j , 0 , otherwise , in terms of bus control vector u i that include voltage magnitudes V i , phase angles θ i , and shunt switch positions Q 1• , bus dependent variables vector x i that include net active x i P and reactive x i Q power injection, wherein superscripts P and Q respectively refer to the net active power injection and the reactive power injection, branch control vector u ij , that includes transformer tap selections t ij and phase shifts φ ij , and dependent branch variable vector x ij , that includes net active x ij P and reactive x ij Q power injections, constraining the bus and branch control vectors, and the bus and branch dependent variables vectors based on physical and operational requirements and actual measurements; deriving a set of linear equations that minimize said cost function subject to the constraints, from an expression of an extremum of said cost function with respect to all arguments; reducing a dimension of the linear equations by solving for a subset of the linear equations; re-organizing the reduced dimension linear equations into primal and dual parts; and decomposing the re-organized reduced dimensional linear equations into two systems of block matrix equations, wherein a solution of said two systems of block matrix equations yields conditions for a lowest cost per kilowatthour delivered through said smart electric power grid, wherein the steps of reducing a dimension of the linear equations, re-organizing the reduced dimension linear equations, and decomposing the re-organized reduced dimensional linear equations into two systems of block matrix equations are performed by a computer processor.