**5. Results and Discussions**

The proposed method is schemed considering IEEE modified 30-bus system, which consists of six generator buses and 24 load buses. The slack node has been assigned as bus number 1. The numbering of buses has been done in a way that the generator buses are numbered first followed by load bus. Figure 4 depicts the single line diagram of the modified IEEE 30-bus system considered here.

**Figure 4.** Single line diagram of modified IEEE 30-bus system.

Contingency analysis was conducted under the base load condition to identify the harmful contingencies. Here the outage of line 1–2 with normal loading is considered and has been illustrated out in Figure 5. It is ascertained from Figure 5. The actual power flow violation rises to 1.14%, 2.13%, and 1% in the lines connected between 1 and 3, 2 and 6, and 4 and 6, respectively. The system has been simulated with a line outage so as to create the contingency and results of line flow and its violations are reported in Table 1. Here, from Table 1 we can observe that there are three lines those are violating their limit that is line number 1, 5, and 6 which have 130 MW, 65 MW, and 90 MW of line flow limit, respectively. The power flows on the three violated lines are nearly 148 MW, 138 MW, and 90 MW. Even though the line 6 is violating by a small amount that is nearly equal to 0.59 MW, it has also been taken into consideration in the calculation. Congestion due to outage of line 1–2 and its effect on network framework parameters has been tabulated in Table 2. Here, due to congestion the percentage of overload on the congested line is reflected. The most overloaded line among the three lines that has to ge<sup>t</sup> congestion due to the line outage of lines 1–2 is the line connecting between buses 2 and 6.

The amount of power violated by each of the congested line is also shown in Figure 6. The line 2–6 has violated the limits the most that is nearly 73 MVA of power. The total amount of power violated due to the outage is 92.292 MVA. This power violation has to be now rescheduled through other lines so as to ge<sup>t</sup> rid of the congestion that has appeared. It is highlighted from Figure 7 the increase in overload amounts to 13.89%, 113.29%, and 0.65% in the lines connected between 1–3, 2–6, and 4–6, respectively. This violation is one of the issues critically faced by ISO. To achieve this task, the novel FPA is schemed as an efficient optimizing tool for congestion cost minimization as well as reduces the system losses. The stimulus of the present effort is to benefit the ISO in reliving the congestion. The rescheduling line flow is compared with and without the application of FPA is computed. The Flower Pollination Algorithm is used here as an optimization tool and it can be seen that the result obtained in Table 3 reflects its validity. The line which were violating the their line flow limits are now under the limits of their flow after the rescheduling of the generators is done by utilizing the FPA as shown in Figure 8.

**Figure 5.** Effect of MVA violations due to an outage.


**Table 1.** Line flows in test case.

**Table 2.** Impact on network framework parameters due to outage of lines 1–2.


**Figure 6.** Power violation between lines due to line outage between lines 1–2.

**Figure 7.** Effect of overload due to an outage.



Table 4 indicates the economic cost analysis of cost before rescheduling is 941.208 \$/hr, while after rescheduling it reduces to 460.616 \$/hr. Here the expedition between the global and local search using levy flight mechanism ensures the optimal output. This validates the effectiveness of the algorithm. Further the changes in active power rescheduling have been graphically depicted in Figure 9.



**Figure 8.** Mitigation of congestion employing Flower Pollination Algorithm.

**Figure 9.** Comparison of power rescheduling in the modified IEEE 30-bus system employing FPA.

The results gained from the implementation of FPA for alleviation of congestion are tabulated in Table 5. With the results obtained in [16], the effectiveness of the proposed algorithm is illustrated with the reduction in congestion cost of 1.60%, 1.55%, 1.17%, and 1.07% as compared with other optimization algorithms like Simulated Annealing (SA), Random Search Method (RSM), Particle Swarm Optimization (PSO), and Teaching Learning-Based Optimization (TLBO). The best effective final solution is attained due to the legitimate control of the algorithmic based specific tuning criterion. Figure 10 infers that Flower Pollination Algorithm (FPA) yields the minimum congestion of 460.616 \$/hr as compared with the results obtained with other optimization techniques. Figure 11 validates the effectiveness of the algorithm in terms of its convergence in seven iterations as compared with 25 iterations in SA and RM, while 50 iterations are required in PSO to obtain solution consistency. Table 6 provides the parametric settings of the proposed FPA with other optimization techniques.

**Table 5.** Validation of proposed FPA with other optimization techniques.

**Figure 10.** Effectiveness of proposed FPA with other optimization techniques.

**Figure 11.** Convergence curve for managing congestion using FPA'.



### **6. Congestion Management with PHSU**

In this proposed work, to replenish the varying load demand nature, a PHSU unit has been incorporated with the test system. PHSU is operated in generator mode when there is power inadequacy while operated in pumping mode where there is power sufficiency. Thus PHSU helps in minimize the cost of congestion while maintaining the voltage figuration, The test case considering the modified IEEE 30 bus system has been simulated with a line outage 1–2 so as to create the contingency and results in violations of power flow between lines 1–3, 2–6, and 4–6, respectively. Considering this

outage, BSF are then computed for different load buses. The bus with the highest negative index is chosen to be the optimal location for PHSU placement. Here, it is evident from Table 7 that the ideal location for PHSU placement is obtained at bus 4. This is pictorially depicted in Figure 12 The feasible location of PSHU placement is attained assuming sufficient availability of water resource and reservoir area. GSF is then calculated for rescheduling active power of generators. Thus the placement of PHSU at bus 4 yields the minimized congestion cost of 361.450 \$/hr as compared to bus 16 with 756.03 \$/hr higher cost of congestion. This infers the efficiency of FPA in terms of congestion cost reduction. Active powers of the generators are then rescheduled through the computed GSF as inferred from Table 8 Generators with the highest negative sensitivities are opted for participation in rescheduling Table 9.

**Table 7.** Sensitivity factor without PHSU.

**Figure 12.** FPA-based suitable choice of PHSU for managing congestion.

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**Table 8.** Sensitivity factor without PHSU.


### **Table 9.** Rescheduling with PHSU.


Figure 12 interprets the incremental changes in value of rescheduling of real powers of the generators with the incorporation of PSHU. This facilitates meeting the objective of yielding minimum cost of congestion. The results gained from the implementation of FPA for alleviation of congestion influencing other network criterion is tabulated in Table 10. This investigates the e ffective minimization of power losses and security enhancement after employing EPA. The total loss in the system was 8.177 MW, which was also reduced to 5.217 MW after conducting congestion management, and further reduced to 4.208 MW after the incorporation of PHSU. Further the considerable improvement in voltage portrait is also tabulated.


**Table 10.** Influence of FPA on other network criterion in the test case.

The PHSU is placed at load bus number 4 which is selected based on the most sensitive bus sensitivity factor. The PHSU is connected to the bus 16 and the results are tabulated. The generation cost is 736.426 \$/hr and the congestion cost incurred to the consumer is 361.450 \$/hr after the implementation of the pumped storage hydro unit at bus 4, as pictorially depicted in Figure 13. Table 11 infers the alleviation of congestion after the incorporation of PHSU employing FPA.

**Figure 13.** FPA-based cost comparison in placement of PHSU for managing congestion.



From Table 12, it is inferred that the rescheduling cost using FPA is considerable reduced by 1.27% with the PHSU placement. Furthermore, the superiority of the FPA is shown in terms of congestion cost reduction of 2.04% after the application of FPA algorithm employing PHSU placement as depicted pictorially in Figure 14. Thus the effectiveness of the FPA algorithm is proven in terms of minimized congestion cost and other parameters that influence the network framework criterion.

**Table 12.** Cost comparison with and without PHSU employing with and without FPA.


**Figure 14.** FPA-based cost comparison with and without placement of PHSU for managing congestion.
