Page 116 - Decision Making Applications in Modern Power Systems

82 Decision Making Applications in Modern Power Systems

FIGURE 3.16 The electrical network of the North-Eastern Power Grid of India.

Fig. 3.16 [29]. The geographical information pertaining to these buses is
given in Table 3.6.
The connectivity matrix B is constructed, and the optimal locations are
determined for achieving complete observability of the power system. A
minimum of five PMUs, placed at bus 1 (Bongaigaon), bus 3 (Balipara),
bus 5 (Biswanath Chariali), bus 8 (Kathalguri), and bus 11 (Silchar),
are required. For determining the optimum PDC location, the risk with
uncertainty incorporated is calculated for all possible PDC locations.
The number of intermediate repeaters depends on the topological distance
between the PMU and the PDC. If the latitude and longitude of the PMU
and the PDC are (ϕ 1 , ψ 1 ) and (ϕ 2 , ψ 2 ), the geographical distance d between
them can be calculated using the Haversine formula as given in Eqs. (3.17)
(3.19) [30]. The geographical distances between the PMUs and the PDC are
shown in Table 3.7 along with the number of optical repeaters.
d 5 Rad 3 Z ð3:17Þ

p ffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Z 5 2 3 atan2 a; ð 1 2 aÞ ð3:18Þ
ϕ 2 ϕ ψ 2 ψ

a 5 sin 2 1 2 1 cos ϕ cos ϕ sin 2 1 2 ð3:19Þ
2
1
2 2
where Rad is the radius of the Earth 5 6371 km and atan2 (x, y) is the princi-
pal value of arc tangent of y/x expressed in radians.
When the PMU at bus 1 or its communication network fails, bus 2
becomes unobservable. When the PMU at bus 3 or its communication