Integrated Voltage and Var optimization process for a distribution system

1. A method for determining optimal settings for controllable taps u t of voltage regulating transformers and capacitor bank witches u c in a distribution network, comprising:

receiving a network model and determining a set of state variables x and control variables u;

using an objective function, calculating an overall objective value of the network under initial control variables u;

performing a var optimization calculation with the controllable tap settings u t of the controllable taps fixed at an initial value, or the best value found so far, to output an optimized set of control settings u c of the capacitor bank switches;

performing a voltage optimization calculation with the control settings u c fixed at the best solution found so far, to output an optimal set of control settings u t ;

using said objective function, evaluating the system performance using said optimal set of control settings u t and u c and repeating said steps of performing var optimization and performing voltage optimization until either the control values u t and u c do not change from one iteration to the next, the objective function value does not change or if the new objective function value is greater than the last; and

outputting said control values u t and u c to a distribution control system.

2. The method of claim 1 wherein said step of performing voltage optimization further comprises:

constructing a sequence of quadratic programs (QP) based on first order approximation to generate trial solutions and performing full non-linear unbalanced load flow on the trial solution to determine the actual improvement in said objective function before accepting the trial solution;

discretizing the non-integer QP solution and performing systematic adjustment to identify the trial solution that produces performance improvement in non-linear unbalanced load flow simulation; and

initially generating a best control setting and associated objective value, and iteratively updating the best solution and objective value.

3. The method according to claim 2 wherein the method further includes calculating jacobian matrix J 1 -J 9 according to the equations,

J

1

=

∂

g

∂

x

;

⁢

J

2

=

∂

g

∂

u

;

⁢

J

3

=

-

(

∂

g

∂

x

)

-

1

⁢

∂

g

∂

u

;

⁢

J

4

=

∂

v

∂

u

+

∂

v

∂

x

·

J

3

;

J

5

=

∂

i

∂

u

+

∂

i

∂

x

·

J

3

;

⁢

J

6

=

∂

v

K

d

∂

u

+

∂

v

K

d

∂

x

·

J

3

;

⁢

J

7

=

∂

v

K

q

∂

u

+

∂

v

K

q

∂

x

·

J

3

;

J

8

=

∂

i

K

d

∂

u

+

∂

i

K

d

∂

x

·

J

3

;

⁢

J

9

=

∂

i

K

q

∂

u

+

∂

i

K

q

∂

x

·

J

3

.

4. The method according to claim 2 wherein the method further includes building said quadratic problem using said J 1 -J 9 .

5. The method according to claim 2 wherein the method further includes checking for convergence, wherein if convergence is determined, the best control set is output and if not converged, the program returns to said step of calculating jacobian matrix J 1 -J 9 and constructing a new QP and proposing trail correction to the control variables by solving the QP.

6. A method according to claim 1 wherein said step of performing var optimization comprises:

receiving a network model and building a set of controls S c and a set of conductors S b in the network model;

solving a base case unbalanced load flow for a base network;

determining initial current values I i d (0),I i q (0) for each conductor S b in the base case;

initializing the load flow model to an initial case and, for each control in S c ;

perturbing the capacitor status for each control in S c and determining a new load flow for the model with the perturbed capacitor status;

calculating new currents I i d ,I i q for each conductor in S b using the new load flow and determine current sensitivity vectors S d ,S q according to ΔI i d =I i d −I i d (0), ΔI i q =I i q −I i q (0);

constructing, using the initial load flow solution and the current sensitivity vectors S d , S q , a MIQCQP;

solving said MIQCQP to output optimal control settings for S c ; and

outputting said optimal control settings.

7. The method according to claim 6 wherein said MIQCQP is calculated according to:

min

⁢

∑

i

∈

S

b

⁢

r

i

⁡

(

(

I

i

d

)

2

+

(

I

i

q

)

2

)

s

.

t

.

⁢

(

I

i

d

)

2

+

(

I

i

q

)

2

≤

(

I

i

max

)

2

,

⁢

∀

i

⁢

∈

S

b

I

d

-

S

i

d

⁡

(

u

-

u

⁡

(

0

)

)

=

I

d

⁡

(

0

)

,

⁢

∀

i

⁢

∈

S

b

I

q

-

S

i

q

⁡

(

u

-

u

⁡

(

0

)

)

=

I

q

⁡

(

0

)

,

⁢

∀

i

⁢

∈

S

b

u

lb

≤

u

≤

u

ub

u

⁢

∈

n

.