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Particle swarm optimization applied Chapter | 10 253
the sensitivity of state variables to a desired system parameter, here a method
is proposed to determine the generators responsible to perform the reactive
dispatch, based on the reactive power variation with the voltage. The modi-
fied tangent vector is computed according to the following equation:
2 3
0
^
6 7
6 7
½
TV mod 5 J mod 21 6 0:1 7 ð10:11Þ
^
6 7
4 5
0
where J mod is the calculated Jacobian matrix from the converged power flow
with the insertion of reactive power equations of generators that were
selected for the dispatch. For the sake of this, the PV bus in the analysis is
considered to be of PQ type.
The vector on the right side of (10.11) contains all elements equal to zero
except for the equivalent of the reactive power equation of generator under
analysis. The value 0.1 is arbitrary and can be any one, since the participa-
tion factor of each generator will not change once the system analysis
method is linearized.
10.6 Particle swarm optimization for reactive power dispatch
The PSO is an optimization method based on particle swarm and inspired
by the sociobiological behavior of birds group [16,17]. For the problem
formulation an initial population with size s is determined, where each
particle i represents a candidate solution. It initializes randomly for each
particle at a current position, x i , and assigns a current velocity, v i . Besides, x i
is also the best individual position achieved by particle y i . From this initial
data, the iterative process is performed as follows:
Step 1: For each particle i in s:
1. Calculate the objective function, f, which in this case corresponds to the
electrical losses minimization, which is formulated in (10.6).
2. Determine y i (10.12):
ð
y i tðÞ if fy i tðÞð Þ # fx i t 1 1ÞÞ
ð
y i t 1 1ð Þ 5 ð10:12Þ
ð
x i t 1 1ð Þ if fy i tðÞÞ . fx i t 1 1ÞÞ
ð
ð
Step 2: Evaluation indicators:
There are two different types of evaluation indicators for improving the
position in relation to the desired objective, called gbest (best overall)
