Optimal Allocation of Fixed and Switched Capacitors for Unbalanced Radial Distribution Feeders Using Artificial Intelligence-Based Approach*
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I. Implementation, Testing and Results The proposed methodology of optimal allocation of fixed and switched capacitors for unbalanced radial distribution feeders was implemented using the trial edition of Borland C++ Builder 6.0. A matrix header file matrix.h was downloaded from the internet [5] to assist the matrix operation in the project. This matrix header file, also known as Matrix TCL Lite which is a free version of Matrix TCL Pro, provides easy to use functions and can handles large matrices operations.The proposed method was tested and applied to two distribution test feeders for five test cases. The program was run using 650 MHz Pentium III microprocessor. The first test system is the 24 kV, 34 bus test distribution feeder with systems peak load at 1100H, and the second is the 13.2 kV Tarlac Electric Cooperative II or TARELCO II with 166 buses and a systems peak load at 2000H-modified by [6] for demonstration purposes. Both are characterized by unbalanced three phase, two-phase and single-phase loads with single phase, two-phase and three-phase lateral feeders. Both of the two test systems were used by [6] for the same problem using Sequential Quadratic Programming method. Test case 1 Representation
Table 4-1.
Representation for any possible solution for fixed capacitor compensation
For the purpose of comparison, the standard values used in [6] was used in this test case. Using binary gray code representation, the capacitor sizes was encoded in table 4-2.
Table 4-2. 3 bit gray code representation of compensation capacitors for test case 1 Using sensitivity analysis, 22 candidate location was selected. Thus, if capacitor sizes are represented in 3 bits, any possible solution or individual has a string length of 66 bits. Note that for 22 candidate locations, 1 load level, and 6 capacitor sizes, there are 622 possible solutions. And that would take a longer time to search for the best combination of compensation if no defined method for the search process was used!
Parameters
Results
Table 4-3. System losses and minimum voltage of IEEE 34 bus test feeder before compensation For illustration purposes, the program was terminated only after 200 generations. The program was run for five trials. Each run takes around one and a half hours to finish 200 generations. The graph and the summary of the results of the five trials are shown in table 4-4 and table 4-5 and
Table 4-4. Summary of the results of load flow after compensation in test case 1.
Figure 4-1. Convergence curve of the 5 trials for 100 generations in test case 1. For illustration purposes, 101st - 200th generation was not plotted. Moreover, savings did not significantly increases after 100 generations.
Table 4-5. Output optimal fixed capacitor compensation of the five trials Based on the above figures, although GAs are base on stochastic processes, the savings after several generations for five trials are almost the same. The best solution of the five trials ,3rd trial, was selected and compared to the results obtained by [6] using SQP. The comparison of the solution of the two methods is given as follows;
Table 4-6. Comparison of the output between SQP and AI based approach of capacitor allocation Notice from table 4-6 that the
capacitor allocation using GA gives a higher savings than using SQP. This
shows that for this particular test case, AI performs much better than the
method used by [6].
Introduction
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