Optimal Reactive Power Planning Based on Quadratic Programming Function of MATLAB Optimization Toolbox - Intelligent Computing for Sustainable Energy and Environment - page 317

1-1-10 0
01000
00 1 1 1
00 0 1 0
00001

 

 

 

A =   

(5)



 

 

 

where, for example, A = , it means that the direction of branch power l is a input 1

nl ,

power for the node n ,

n A = , it means that the branch power l is a output power
for the node n , the number 0 means the node and branch don't have the direct
relationship, the meanings of other elements are same as above.
When the matrix A is obtained, then, can get the power of each branch according
the following equation:

-1

,

P P

 
 
 
 

01 1

P P

12 2

A ⋅ =

 
 
 
 

P P

(6)

13 3

P P

34 4

P P

35 5

The active power loss in the situation of peak load before compensating the reactive
power also can calculated by the branch power, is shown as following[5]:

2 2

NL

PQ +



l l

Δ= P R (7)

0 l

V

2

l = 1

N

where,

V

is the rated voltage,

R is the resistance of branch.

3.2 A Method of Solving Δ P Σ

The specific expression of Δ P Σ is shown as following:

( )

2

PQQ

2

+ -

NL



l l l c ,

(8)

Δ P = R

Σ l

V

2

l = 1

N

NC



Q = α Q (9)

lc , lci , ci

i =1

where, Q is the sum of the branch l downstream nodes' compensation capacities,

lc

is an NL N × adjacency matrix, its meaning can be explained by the Fig.1, if the
nodes 2, 4 and 5 are the planned reactive compensation nodes, then, the adjacency
matrix α of the Fig.1 is shown as following:

α