Optimal Reactive Power Planning Based on Quadratic Programming Function of MATLAB Optimization Toolbox - Intelligent Computing for Sustainable Energy and Environment - page 318

111
100
= 011
010
001

 

 

 

α  

(10)

 

 

 

 

where, the value of the variable =0, it means that the set of

downstream nodes of the branch l don't contain the capacitor node ci ;

α is only 0 or 1, α

lci lci

=1, it
means that the set of downstream nodes of the branch l contain the capacitor node
ci .

α

lci

3.3 A Method of Solving

V

The specific expression of

V is shown as following:
( )

PR +- Q Q X

NL NL

 

l l l l c , l

(11)

VV =- β Δ VV =- β

k s kl , l s kl ,

V

l =1 l =1

N

where, is the voltage drop of the branch

after the reactive power compensation, β is a KV N × adjacency matrix [4], it
means that the channel from the power supply point s to the node k go past which
branches.
In the Fig.1, if the nodes 2, 4 and 5 are the nodes of voltage constraints, then, the
adjacency matrix β of the Fig.1 is shown as following:

V is the power supply point voltage,

Δ

11000
=10110
101 01

 

 

β

(12)

 

 

 

The value of the variable β =1, it means that the channel from the

power supply point s to the node k go past the branch l ,

β is 0 or 1,

kl kl

β =0, it means that the
channel from the power supply point s to the node k don't go past the branch l .

kl

3.4 Quadratic Expressions of Mathematical Model

Because of Δ don't contain the decision variable, so don't consider it in the

optimization calculation, and quadratic programming function returns the minimum
value of the objective function, this paper uses the annual economic benefits as the
objective function, the optimization purpose is to get the maximum annual economic
benefits, so the objective function should convert into the form of equation (13).