Interior point method for reformulated optimal power flow model

Patent metadata

Field	Value
Publication number	US-8977524-B2
Application number	US-201213413086-A
Country	US
Kind code	B2
Filing date	Mar 6, 2012
Priority date	Mar 6, 2012
Publication date	Mar 10, 2015
Grant date	Mar 10, 2015

Abstract

A method for approximating an optimal power flow of a smart electric power grid includes providing a cost function that models a smart electric power grid having buses connected by branches, deriving a set of linear equations that minimize the cost function subject to constraints from an expression of an extremum of the 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 which can be solved by a series of back substitutions. A solution of the two systems of block matrix equations yields conditions for a lowest cost per kilowatthour delivered through the smart electric power grid.

First claim

What is claimed is:

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.

2. The method of claim 1 , wherein said cost function is

f
⁡

(

x
,
u

)

=

∑

i
=
1

N

⁢

⁢

[

1
2

⁢

x
i
T

⁢

V
i
X

⁢

x
i

+

1
2

⁢

u
i
T

⁢

V
i
U

⁢

u
i

+

S
i
X

⁢

x
i

+

S
i
U

⁢

u
i

]

+

∑

i
,

j
=
1

N

⁢

R
ij

·

⁢

[

1
2

⁢

x
ij
T

⁢

W
ij
X

⁢

x

Assignees

• Legbedji Motto Alexis
• Duzgun Ruken
• Akrotirianakis Ioannis
• Chakraborty Amit
• Siemens Ag

Inventors

• Legbedji Motto Alexis
• Duzgun Ruken
• Akrotirianakis Ioannis
• Chakraborty Amit

Classifications

• H02J2105/55

  according to an economic condition, e.g. tariff-based load management · CPC title

• H02J2103/30

  Simulating, planning, modelling, reliability check or computer assisted design [CAD] of electric power networks · CPC title

• Y02B70/3225

  Demand response systems, e.g. load shedding, peak shaving · CPC title

• Y04S20/222

  Demand response systems, e.g. load shedding, peak shaving · CPC title

• H02J2003/146

  Electricity · mapped topic