3.2 Complete Models of FPF
Now we will perform the exercise of comparing AC
SFPF with classical AC FPF models. Considering
the model based on FPF, the boundary load flow
(BLF) (Dimitrovski and Tomsovic, 2004) we will
use the IEEE 14 and 118 test systems. Data of these
networks can be seen at (http://www.ee.washington
.edu/research/pstca/. The BLF uses an interactive
procedure in order to enhance the results accuracy in
cases of considerable non linearity due to large
uncertainty in input data. The characteristic points
for IEEE 14 bus test system at α=0 are assumed to
be 0.0 and 2.0 of the central values (rectangular
fuzzy numbers). Performing the comparison with the
exact values calculated with the SFPF shows that
some “artificially uncertainty” is still present in the
BLF results. Table 3 shows results for voltage
magnitudes. The same kinds of results (not shown)
were also obtained for active power flows. Using the
118 bus test system also Gouveia and Matos (2008)
found differences between the FPF, BLF (that falls
under same philosophy of FPF) and SFPF. Those
differences are exposed for some of the variables of
this network (Table 4). Now the characteristic points
for α=0 are assumed to be 0.6 and 1.4 of the central
values.
Table 3: Voltage values (pu) IEEE 14 bus test system.
α=0, [0.0-2.0]
Bus BLF SFPF AC
4 0.978 1.045 0.992 1.045
5 0.981 1.042 0.996 1.042
7 1.024 1.089 1.051 1.088
9 1.001 1.101 1.028 1.101
10 0.997 1.096 1.020 1.096
11 1.025 1.084 1.038 1.083
12 1.036 1.072 1.039 1.072
13 1.023 1.074 1.028 1.074
14 0.972 1.089 0.992 1.088
Table 4: Voltage and Power Flow Values (p.u.) for some
variables of IEEE 118 test system.
Var. FPF BLF Sym. FPF
V44 0.94 1.03 0.87 1.01 0.96 1.01
P68-69 -17.44 14.92 -21.10 13.27 -3.74 1.39
Q68-69 0.39 1.86 0.84 9.25 1.07 1.33
4 CONCLUSIONS
The use of SFPF doesn’t consider a slack bus or
linearization procedures as happens at the traditional
formulation of FPF. At FPF the use of these
simplifications have as a consequence a distortion of
the results mainly due the influence of the slack bus.
While in the deterministic power flow formulations
the slack bus only compensate the uncertainty in loss
estimation, at classical FPF compensates the
uncertainty that comes from all other buses. Adding
to this the linearization procedures used, results
shown “excessive” uncertainty as shown in this
paper at the several IEEE networks tested. Finally,
the SFPF models have the drawback of requiring
solving a great number of optimization problems but
are completely symmetric regarding the buses. This
is not a real problem since SFPF are addicted to
long-term planning studies. However justify future
work in order to improve simulation times.
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