Optimal Reactive Power Planning Based on Quadratic Programming Function of MATLAB Optimization Toolbox - Intelligent Computing for Sustainable Energy and Environment - page 316

3 Quadratic Programming

Because of the paper's optimization process is achieved with the help of quadratic
programming function in MATLAB Optimization Toolbox, so should convert the
objective function and constraints of the above section into the standard form of
quadratic programming.
The standard form of quadratic programming:

1



T T

min fx ( ) = xHx f x +


 

2

Ax b
Axb
lb

⋅≤

(4)




⋅=

eq eq



  ≤≤ x ub

where,

H

is a mm × matrix, A is a nm × matrix, A is a nm × matrix,

eq

n
eq bR

xf lbub ,, , ∈ R

m

, b , ∈ .

3.1 A Method of Solving Δ

For the optimal reactive power planning, this paper uses a simplified method to obtain
the branch power according to the load forecast data and the relationship of node-
branch. Now, through a simple example to illustrate this method:

P

P

12

P P P

01 13 35

P P

P

P

34

P

Fig. 1. Simplified illustration of a power distribution network

In the Fig.1, 0-5 are the node numbers (0 is the power supply point), 0 P - 3 P is the
branch power of each branch which are unknown parameters(the subscript numerical
sequence means the direction of power flow), P - P is the load power of each node
(if the node is not load node, then the corresponding power is zero), the node-branch
association matrix A of Fig.1 is shown as following: