By Weerakorn Ongsakul, Dieu Ngoc Vo
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Extra info for Artificial Intelligence in Power System Optimization
The diagram of the network is depicted in Fig. 17. 3. 3 ~ ~ 2 1 18 15 19 14 4 8 6 ~ ~ 7 12 5 13 ~ 9 17 16 10 11 26 20 ~ 25 24 22 28 27 21 29 30 Fig. 17 IEEE 30 bus test system. 2 Generator cost function of the IEEE 30 bus system. 3 Emissions of the IEEE 30 bus system. ESO2 ( PGi ) = d SO2i . PGi3 + cSO2i . PGi2 + bSO2i . PGi + aSO2i ENOx ( PGi ) = d NOxi . PGi3 + cNOxi . PGi2 + bNOxi . PGi + aNOxi ECO2 ( PGi ) = dCO2i . PGi3 + cCO2i . PGi2 + bCO2i . 0 For the implementation of the linear fuzzy programming method, these functions are linearized into 5 piece-wise linear functions.
PGi is the column matrix representing the set of real power generation of the generator connected to bus i; d is the vector representing a fuzzy objective function. 99) is represented by a fuzzy set with the membership functions of i(x). i(x) that can be interpreted as the degree to which PGi satisﬁes the fuzzy objective function. Here, 1(x) is the degree of satisfaction of PGi for the objective function, whereas 2(x) to 4(x) are the degrees of satisfaction of PGi for the total system’s NOx, SOx and CO2 emissions, respectively.
At different points in the slope, total cost obtained and emission level will vary inversely. The point where the best compromise between the objectives is reached is the best trade-off between cost and emission. To observe the trade-off between two objectives, the slope of the sigmoid function is changed from 10–5 to 105 while the penalty factors are ﬁxed at 10–5 and other parameters change corresponding to the slope. The obtained generation cost and emission level curves with different slopes are shown in Fig.
Artificial Intelligence in Power System Optimization by Weerakorn Ongsakul, Dieu Ngoc Vo