In order to determine the efficiency of the hybridization of the two metaheuristic methods with population to control the reactive power, the transformation ratio of the transformers and the voltage of the nodes corresponding to the values of the minimum losses, a program under the MATLAB environment was developed.
For the update of N affected individuals.
Until the stopping criterion is reached.
To evaluate the performance of the hybrid method, we have it applied on a small network, the electrical network IEEE 14 nodes (International Explorer Electrical Engineering) [15
], then on the West Algerian network with 102 nodes [1
]. A comparative study of the results will be presented later for each network.
4.1. The Electrical Network IEEE14 Nodes
The electrical network IEEE 14 nodes is a part of the American power grid (specifically in the US Midwest) dating from February 1962. It was introduced in the IEEE Common Data Format by Rich Christie at the University of Washington in August 1993 [15
It contains 10 load nodes, 4 generation nodes, 3 transformers, and 20 lines [15
]. The limit of the voltages in the nodes is between 0.99 p.u
and 1.1 p.u
The results of the control variables are shown in Figure 2
for the node voltage, Table 1
for the generated power and transformation ratios, as well as the minimum loss values and execution time in Table 2
The curve in Figure 2
shows the voltage profile in the different nodes of the 14-node network for the different cases studied; we noticed after the application of optimization methods that the voltages in the nodes improved compared to the first case, which is the power flow, the voltages are approaching the upper limit.
shows the reactive powers generated by the generators as well as the steps of the transformation ratios of the controllers into transformer loads. It can be seen that the values are within the given limits, for the balance generator in the PSO and hybrid methods, the reactive power consumed is low compared to the other two methods.
shows the loss values and execution time of the different methods. It can be seen that the losses are reduced by the PSO method but the time is much more significant, while the hybrid method gives a considerable reduction of active losses in the network lines and an acceptable execution time.
The results show that the hybrid method minimized the active losses with a percentage of 6.49%, the AG 6.34%, and the PSO 6.12% (Table 2
), while keeping the control variables within the limits (Table 1
and Figure 2
). Thus, the hybrid method is more effective than the other two methods, AG and PSO.
At this stage, one applied the methods to the Algerian Western Network with 102 nodes.
4.2. The Algerian Western Wetwork with 102 Nodes
The Algerian network is characterized by long transmission lines, an uneven distribution of reactive power reserves among available generators, as well as an insufficient number of shunt capacitors.
As a consequence, operators are routinely facing severe voltage problems (violation), and the reactive power dispatch has become one of the most relevant concerns in the control center for the western Algerian transmission system.
This network is constituted of three subnetworks that are the 400 kV electrical network, the 220 kV electrical network and the 60 kV electrical network (see Figure 3
The essential data for the Algerian Western Network are reported in Table 3
The limits of the variables of control are given in Table 4
and Table 5
4.3. Results Analysis
As a first step, a study was performed by the fast decoupled load flow method (FDLF) to visualize the profile of nodes voltage and active losses.
Then, the optimization of the network by the GA and PSO methods was made, separately. In the end, the sequential hybridization of these two methods was applied. This optimization consists of controlling the voltages of the nodes.
In Figure 4
, the variation of the voltage on the nodes in different cases before and after the optimization for GA, PSO, and GA-PSO hybridization are drawn in the case of the 400 kV electrical network. It appears that these variations obey practically the range of acceptance within the imposed limits.
The case of the 220 kV electrical network is presented in Figure 5
. Before optimizations, the voltage at the 26th node is exceeding the maximal limit according to the (FDLF) graph. This anomaly disappeared after applying the optimization methods, i.e.; GA, PSO, and GA–PSO hybridization.
For the 60 kV electrical network, Figure 6
b shows the presence of several violations of the voltage limits that concern the nodes (85, 86, 87) and (92 to 98). The use of the three methods of optimization has corrected these anomalies.
The generated reactive powers obtained from the methods lay in their authorized ranges (see Table 6
The transformation ratios obtained from these methods are in agreement with their range of variation as shown in Table 7
In Table 8
, we reported the results concerning the minimal losses in the network and the duration of the execution of programs.
The results presented in Table 6
show that the hybrid GA–PSO method gives the minimum value of active losses (29.19 MW), while the GA method (36.60 MW) and the PSO method (45.07 MW), so the hybrid method, gives a remarkable reduction of 21.87 MW compared to the initial value of the active losses (51.06 MW by the FDLF method).
For the execution time, we noticed that the hybrid method is faster than the PSO method but slower than the GA.
So in terms of loss reduction, the hybrid method is more efficient, but in terms of speed, the AG method is faster.
The results presented in this section show that:
At the level of voltages (at the tension’s level) in the nodes, the FDLF method shows several exceedances of the lower limit in nodes 85 and 92 also for the upper limit in nodes 94, 95, 96, 97, 98. The application of GA, PSO, and hybrid optimization methods eliminates these exceedances, but the hybrid method is the one that gives the most appropriate voltage profile.
For the control variables, it can be seen that the reactive powers of generators have remained within the limits imposed. Also, the transformer transformation ratios are pushed towards the upper limits for both the PSO and hybrid methods.
For losses, we noticed (it was noted) that the application of the hybrid method gives a good reduction of active losses and also a minimum execution time.