Page 163 - AJWEP-v22i2

Enhanced renewable integration for power system stability

the ACO algorithm. To effectively mitigate oscillatory Third stage – pheromone updating: Once all ants have
behavior and ensure stable grid operation, the ACO found a solution, each ant deposits a pheromone (τ ) on
ab
algorithm has the ability to dynamically adjust and the trail. The pheromone is now updated according to
optimize control settings in real-time. Equation III:
Table 1 displays the ACO parameters and their
corresponding values, which are used to modify the π (t)=(1−ρ)τ (t)+∆τ (t) (III)
ab
ab
ab
settings of the FACTS controllers. The fundamental Pheromone evaporation is applied to prevent faulty
process of ACO has been represented into four essential convergence and improper judgments, where ρ is the
phases: pheromone evaporation rate (0 < ρ ≤ 1), and ∆τ (t) is
(i) Initialization given by Equation IV: ab
(ii) Probabilistic ant movement
NA
(iii) Update of pheromones () (IV)
k
t
t
(iv) Stopping condition. ab k1 ab
First stage – initialization: The goal is to identify the where NA represents the total count of ants and
t
shortest route between two points at the nodes of the is the quantity of pheromone left by k ants at
ab
solution space, with the ant colony initially established the nodes i and j, calculated as follows:
randomly. Initialization considers the pheromone L , if the k-th ant uses nodes a and b in its
Q
t
ab
k
concentration at the boundaries, the suggested value, tour; otherwise, the entire tour length represented by the
and the ant’s choice. k-th ant is L , and Q is a constant.
k
Second stage – probabilistic ant movement: At each Fourth stage – stopping condition: Ants examine
step of the process, ants make decisions to discover a each path, considering the viability and cost of each
satisfactory solution based on a probabilistic strategy tour. If the minimal stopping condition is satisfied, the
that depends on the statistical data and pheromone program terminates. Otherwise, it returns to Stage 2 and
values. The probability of an ant moving from point A continues searching for the best solution, disregarding
to point B is given by: the number of repetitions.

t ()

P k ab t () ab ab (II) 4.1. FACTS controllers with ACO algorithm
ak t () The ACO algorithm continuously tracks system

ak

kallowed k dynamics, evaluates controller behavior, and modifies
where, control parameters. This adaptability ensures that the
P represents the probability of moving from area dampening capabilities of the power system remain
k
ab
A to B, effective across a range of conditions. The ACO’s job
τ is the pheromone, is to find the path between the starting point and the
η is a heuristic value. endpoint that minimizes time while being the most
The constant parameters α and β control the influence optimal solution.
of pheromones versus the heuristic value. After visiting
each node, the next visit or iteration is chosen based on 4.1.1. ACO algorithm
probability. A population of m ants (solutions) is generated at random
to start the process. Each ant k (k = 1, 2., m) denotes a
Table 1. Parameters of ACO and their values solution string, in which a chosen value is assigned to
ACO parameters Value each variable. Following the performance index, the ant
Iteration nn 100 is then graded. To provide the best potential solution,
Number of ants 50 the pheromone concentration on every path (variable
α 0.8 value) is modified as follows:
Every arc is given a specific amount of pheromone at
β 0.2 the beginning of the search. When an ant k reaches node
Evaporation rate 0.9 i, it follows a pheromone trail to calculate the likelihood
Number of parameters 4 that node j will be selected as the next node.
Number of nodes 200 The probability of an ant moving from node i to node
Abbreviation: ACO: Ant colony optimization. j is given by:

Volume 22 Issue 2 (2025) 157 doi: 10.36922/ajwep.8393