|
*J.C. Miras, Undergraduate Student
Project, Department of Electrical and Electronics Engineering,
University of the Philippines, Diliman,(2004)
Implementation,
Testing and Results (continued)
Test case 4
In the previous test cases, we only consider a particular node or bus as a candidate location if all of the three-phase wires are present at that node. In this test case, we study the effect on the amount of savings of considering the single-phase and two-phase lateral feeders as a candidate location for optimization. That is, depending on the magnitude of sensitivity factor, if all of the three phases are present at any node, then that node is a candidate location for balanced three-phase capacitor bank. However, if only a single-phase or double-phase wires are present, then it is a candidate location for single-phase or two-phase capacitors. This was tested on both IEEE 34-bus test feeder and TARELCO II feeder.
Representation was extended by adding a representation for non-three-phase lateral feeders at any node for each load level. 15 candidate locations for balance capacitors and 5 candidate locations for each phase of non-three-phase lateral feeders were selected for capacitor allocation. The length of the string therefore doubles to 360. A population of 360 was used.
The program was run for five trials with 200 generations for IEEE 34 bus and 100 generations for TARELCO II feeder. It was observed that the annual savings significantly increase if single-phase and two-phase lateral feeders are considered in the optimization procedure. Summaries of the results are given in tables 4-12 and 4-13.
| Trials |
Peak power loss (KW) |
Annual energy loss (KWh) |
Compensation Cost ($) |
Annual Saving ($) |
| 1 |
225.489 |
1,080,952.284 |
8,200 |
19,037.37 |
| 2 |
225.442 |
1,081,177.015 |
8,200 |
19,034.04 |
| 3 |
225.437 |
1,080,415.142 |
8,200 |
19,037.06 |
| 4 |
224.371 |
1,078,111.694 |
8,600 |
18,967.308 |
| 5 |
226.782 |
1,084,871.061 |
7,800 |
19,024.25 |
| Mean |
225.504 |
1,081,105.439 |
8,200 |
19,027.206 |
Table 4-12. Summary of the result of load flow for IEEE 34 bus test feeder after compensation considering single-phase and two-phase lateral feeders.
| Trials |
Peak power loss (KW) |
Annual energy loss (KWh) |
Compensation Cost (Pesos) |
Annual Saving (Pesos) |
| 1 |
56.863 |
185,400.930 |
33,750 |
69,767.62 |
| 2 |
57.026 |
185,261.059 |
33,750 |
69,804.27 |
| 3 |
59.378 |
188,397.218 |
26,250 |
69,557.82 |
| 4 |
58.190 |
186,829.708 |
30,000 |
69,693.87 |
| 5 |
58.162 |
186,425.071 |
30,000 |
70,375.04 |
| Mean |
57.924 |
186,462.8 |
30,750 |
69839.724 |
Table 4-13. Summary of the result of load flow for TARELCO II feeder after compensation considering single and two-phase lateral feeders.
Test case 5
In this test case, the effect of varying GA parameters on test case 2 was studied. Such parameters that were varied are mutation probability, and population size. We also study the effect on the quality of solution if the complexity of the problem is increased. Complexity of the problem can be increased if the number of possible solutions is also increased. That is, we increased the complexity of the problem by increasing the number of candidate locations or/and increasing the number of possible capacitor sizes.
Summary of the results for this test case with varying mutation probability is given in table 4-14
| Mutation probability |
Savings ($) |
| 10/L |
13,972.68 |
| 5/L |
15,620.73 |
| 1/L |
17,360.09 |
| 0.1/L |
17,370.99 |
Table 4-14: Output Savings after 100 generations with varying mutation rate.
As the mutation probability increases, the generated savings from the solved capacitor placement decreases. This is due to the fact that if the mutation probability is too high, the search is almost random and does not converge to near optimal solution.
The effect of varying population size is summarized in table 4-15. Since a larger population size introduces a larger search space and lessens the possibility of premature convergence, the savings from allocated capacitor compensation increases if the population size is increased.
| Population size |
Savings ($) |
Run time |
| 4L |
17371.55 |
4 hrs 26min 22.97s |
| 3L |
17356.28 |
3 hrs 40min 19.9 s |
| 2L |
17360.09 |
2 hrs 29 min 23.88s |
| 1L |
17191.99 |
1 hr 14 min 8.9 s |
Table 4-15. Output Savings after 100 generations with varying population size.
For the analysis of the effect of the degree of complexity to the output solution, the program was run for 4 cases;
| Cases |
Condition |
Savings ($) |
| Case 1 |
Same as in test case 2 |
17360.085 |
| Case 2 |
21 candidate locations w/ 5 capacitor sizes |
17351.8 |
| Case 3 |
15 candidate locations w/ 8 capacitor sizes |
17264.88 |
| Case 4 |
20 candidate locations w/ 8 capacitor sizes |
16749.16 |
Table 4-16. Conditions for different cases and the output
savings after 100 generations with varying problem complexity.
For problems with higher degree of complexity, the quality
of the generated solution decreases. Moreover, the initial solution
generated by random initialization is very far from the optimal solution.
However, the output solution is still acceptable at the expense of
increasing complexity.
Introduction
Problem
Formulation and Solution
Implementation,
Testing and Results
Testing
and Results (continued1)
Testing
and Results (continued2)
Conclusion
and References
|