Transmission Expansion Planning in Deregulated Power ... - tuprints

6 Fuzzy Risk Assessment 87
appropriateness indices must be ranked. Many methods were presented for ranking fuzzy
numbers. Here, we use convex combination of left and right integral values [27], [75]-[76],
centroid indices [77], and extended centroid index [77] for ranking fuzzy numbers.
6.5 Case Study: IEEE 30 Bus Test System
The proposed approach is applied to IEEE 30 bus test system [62], [64]. Figure 5.1 shows the
single line diagram of IEEE 30 bus test system. Data of generators, loads, and transmission
lines are given in tables 5.2-5.4. To demonstrate that the fuzzy risk assessment overcomes the
shortcomings of conventional risk assessment method, four different cases are considered.
Case 1: Consider the IEEE 30 bus test system with eight different scenarios which were
identified in section 5.3.2. It is assumed that all scenarios have the same degree of occurrence.
In section 5.3.2, PDFs of LMPs were computed for the peak load of planning horizon of the
existing network at different scenario. If between each two buses that have average LMP
difference greater than $5/MWhr a new transmission line is suggested, we have 113 decision
alternatives (candidates) including alternative “do nothing”. Standard deviation of mean of
LMP weighted with mean of sum of generation power and load (WGD) is used for measuring
the goodness of expansion plans. The following approaches are used for selecting the final plan:
• Conventional risk assessment with minimax regret criterion (MMR),
• Conventional risk assessment with minimum expected cost criterion (MEC),
• Fuzzy risk assessment with the following methods for ranking fuzzy numbers:
• x of centroid point (XC),
• distance of centroid point from zero (DC),
• distance of extended centroid point from zero (DEC),
• convex combination of right and left integral values with α=0 (I0), α=0.5 (I5), and
α=1 (I1).
Tables 6.7 and 6.8 show WGD and regrets for plans 1-28, 5-29, 14-29, 16-29 in $/MWhr. In
this case all above approaches select plan 5-29 as the final plan. As it is shown in table 6.8,
this plan is robust in five scenarios. It also has the minimax regret and minimum expected
cost.