*2.2. Generator Sensitivity Factor*

The generator sensitivity factor (GSF) is expressed as the ratio of incremental change in real power flowing in bus '*i*' connected between buses '*j*' and '*k*' to the incremental change in the active power supply of the generator as shown below. Generators are rescheduled based on highest negative indexes.

$$\Delta GSF\_{\mathcal{S}^n} = \frac{\Delta P\_{j\mathcal{k}}}{\Delta P\_{\mathcal{S}^n}} \tag{23}$$

Congestion managemen<sup>t</sup> is formulated using the Newton–Raphson power flow method. Congestion results in the power flow violation in certain transmission lines and the congestion cost have been computed. Then the novel FPA is schemed as an efficient optimizing tool for rescheduling cost minimization as well as reducing the system losses. Further the rescheduling congestion cost is compared with and without the application of FPA is computed. The effectiveness of the proposed Algorithm is proven in terms of minimized congestion cost and its validation is presented in Figure 1. The efficacy of FPA algorithm incorporating with PHSU is then investigated in terms of congestion cost minimization, as shown in Figure 2. The impetus to carry out this work relies on a novel methodology for figuring out complexity that arises in managing the congestion. Despite the fact the problem of managing congestion has been endorsed in the literature for decades, at most gets committed on meta-heuristic and artificial intelligence approaches. Iteration number and population size are the typical monitoring criterion shared among these different methodologies. Distinct from these general monitoring criterions, some techniques incorporates algorithmic based specific tuning criterion like mutation rate and cross-over rate in the Genetic Algorithm (GA). Lack of proper tuning of algorithmic parameters can lead to local minima and increases time of computation for convergence. Particle Swarm Optimization (PSO) handles inertial weight adjustments. Although Simulated Annealing (SA) can solve optimization problems of complicated nature, the drawback is the inability to obtain the best solution without integrating another technique in it. Further, Harmony Search Algorithm (HSA) embodies the heed on memory rate and adjustments in pitch weight. Thus the fulfillment of the final solution is attained by the legitimate control of this algorithmic based specific tuning criterion. Commemorating these concepts, the proposed paper employs the implementation of FPA Algorithm. This relies on the mechanism of levy flight using a common probability switching parameter thus eliminating the need of algorithmic based specific tuning criterion and makes it effective for optimization problems.

**Figure 1.** Congestion cost minimization using Flower Pollination Algorithm (FPA) and its validation with other optimization techniques (Part I).

**Figure 2.** Congestion cost minimization using FPA incorporating Pumped Hydro Storage Unit (PHSU) and its validation (Part II).
