### Related Literature
proposed [31] the gradient descent algorithm in the OPF design to solve two problems from a power system: minimize the fuel cost and improve the dynamic performance. The efficiency of the approach has been verified in the 68-bus test system integrating a solar farm. [PERSON] used [32] a variant of the gradient algorithm that works online with the OPF problem from the radial electric networks. The algorithm has been tested in various networks having a computational time between 0.27 and 2.35 s. An approach based on the reduced gradient method combined with the augmented Lagrangian method with barriers has been applied by [PERSON] in [33]. The results obtained in the case of the IEEE 30-bus system highlighted a reduced number of iterations (six iterations). Table 1 presents a synthesis of some representative approaches proposed in the literature after 2015, highlighting the treated topic, the contributions, and the proposed optimization method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference Year** & **The Treated Topic** & **Contribution** & **Optimization Method** \\ \hline
[20] & 2021 & Impact of the grid regulation & Investigation of the optimal utilization of grid capacity in the presence of high wind energy penetration in a hydropower dominated system & Linear programming—classic optimization \\ \hline
[21] & 2020 & Contingency Constrained Optimal Power Flow & Optimal power flow model that forces the network to meet all constraints under contingency & Quadratic Programming—classic optimization \\ \hline
[22] & 2019 & Optimal power flow problems for hybrid power systems containing renewable energy sources (wind and solar power) & Developing and solving different constrained optimal power flow problems using a hybrid approach & Sequential quadratic programming improved with an imperialist competitive algorithm—hybrid optimization \\ \hline
[23] & 2017 & Optimal power flow problem & A new solution to the alternating current optimal power flow problem based on successive linear approximation of power flow equations & Successive linear approximation—classic optimization \\ \hline
[24] & 2017 & Optimal operation of power system incorporating wind energy with demand-side management & Dynamic economic dispatch considering discrete penetration levels of wind energy and utilizing the demand-side management & Genetic algorithm—meta-heuristic optimization \\ \hline
[25] & 2021 & Optimal power flow based on the wind sources integrated into the power system & A stochastic optimal power flow to obtain the best solution for the scheduled power from wind farms with the low operational costs & Aquila optimizer—meta-heuristic optimization \\ \hline
[26] & 2018 & Multi-objective optimal dispatch considering wind power and interactive load & The characteristics of interactive load are analyzed based on the traditional day-ahead dispatch model to reduce the influence of wind power variability & Quantum particle swarm optimization—meta-heuristic optimization \\ \hline
[27] & 2016 & Optimal operation of a power system including the solar and wind energy sources. & The optimal operation of a hybrid power system including the solar and energy sources based on an improved PSO algorithm & Particle swarm optimization—meta-heuristic optimization \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Synthesis of the approaches proposed in the literature. The comparison based on the number of iterations and computational time highlighted better performances of classical algorithms from the mathematical programming. Thus, if the IEEE-30 bus system is taken as the reference, meta-heuristic algorithms led to a high number of iterations (in the order of hundreds) and a computational time (in the order of minutes): (Cuckoo search--5.75 min [29], particle swarm optimization--5.71 min [29], and Aquila optimizer--11.6 min [25]) compared with the classical mathematical programming (quadratic programming--0.5 s [21] and reduced gradient algorithm--0.27 s [32]).