SECTION 6.4 THE POWER-FLOW PROBLEM
327
shown in Figure 3.9 for a two-winding transformer, Figure 3.20 for a threewinding transformer, or Figure 3.25 for a tap-changing transformer.
Input data for each transmission line include the per-unit equivalent p
circuit series impedance Z 0 and shunt admittance Y 0 , the two buses to which
the line is connected, and maximum MVA rating. Similarly, input data for
each transformer include per-unit winding impedances Z, the per-unit exciting branch admittance Y, the buses to which the windings are connected, and
maximum MVA ratings. Input data for tap-changing transformers also include maximum tap settings.
The bus admittance matrix Ybus can be constructed from the line and
transformer input data. From (2.4.3) and (2.4.4), the elements of Ybus are:
Diagonal elements:
O¤-diagonal elements:
EXAMPLE 6.9
Ykk ¼ sum of admittances connected to bus k
Ykn ¼ "ðsum of admittances connected
between buses k and nÞ
k0n
ð6:4:2Þ
Power-flow input data and Ybus
Figure 6.2 shows a single-line diagram of a five-bus power system. Input data
are given in Tables 6.1, 6.2, and 6.3. As shown in Table 6.1, bus 1, to which a
generator is connected, is the swing bus. Bus 3, to which a generator and a
load are connected, is a voltage-controlled bus. Buses 2, 4, and 5 are load
buses. Note that the loads at buses 2 and 3 are inductive since Q 2 ¼ "QL2 ¼
"2:8 and "QL3 ¼ "0:4 are negative.
For each bus k, determine which of the variables Vk , dk , Pk , and Q k are
input data and which are unknowns. Also, compute the elements of the second row of Ybus .
SOLUTION The input data and unknowns are listed in Table 6.4. For bus 1,
the swing bus, P1 and Q1 are unknowns. For bus 3, a voltage-controlled bus,
FIGURE 6.2
Single-line diagram for
Example 6.9
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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pp. 294–378
25795_06_ch06_p294-378
(p. 327)
328
CHAPTER 6 POWER FLOWS
TABLE 6.1
Bus input data for
Example 6.9*
Bus
1
2
3
4
5
Type
Swing
Load
Constant
voltage
Load
Load
V
per
unit
d
degrees
PG
per
unit
QG
per
unit
PL
per
unit
QL
per
unit
QGmax
per
unit
QGmin
per
unit
1.0
—
1.05
0
—
—
—
0
5.2
—
0
—
0
8.0
0.8
0
2.8
0.4
—
—
4.0
—
—
"2.8
—
—
—
—
0
0
0
0
0
0
0
0
—
—
—
—
* Sbase ¼ 100 MVA, Vbase ¼ 15 kV at buses 1, 3, and 345 kV at buses 2, 4, 5
Bus-to-Bus
R0
per unit
X0
per unit
G0
per unit
B0
per unit
Maximum
MVA
per unit
2–4
2–5
4–5
0.0090
0.0045
0.00225
0.100
0.050
0.025
0
0
0
1.72
0.88
0.44
12.0
12.0
12.0
TABLE 6.2
Line input data for
Example 6.9
R
per
unit
X
per
unit
Gc
per
unit
Bm
per
unit
Maximum
MVA
per unit
Maximum
TAP
Setting
per unit
0.00150
0.00075
0.02
0.01
0
0
0
0
6.0
10.0
—
—
TABLE 6.3
Transformer input data
for Example 6.9
Bus-to-Bus
1–5
3–4
TABLE 6.4
Input data and
unknowns for
Example 6.9
Bus
1
2
3
4
5
Input Data
Unknowns
V1 ¼ 1:0, d1 ¼ 0
P2 ¼ PG2 " PL2 ¼ "8
Q 2 ¼ QG2 " QL2 ¼ "2:8
V3 ¼ 1:05
P3 ¼ PG3 " PL3 ¼ 4:4
P4 ¼ 0, Q4 ¼ 0
P5 ¼ 0, Q5 ¼ 0
P1 , Q1
V2 , d2
Q3 , d3
V4 , d4
V5 , d5
Q3 and d3 are unknowns. For buses 2, 4, and 5, load buses, V2 , V4 , V5 and
d 2 , d4 , d5 are unknowns.
The elements of Ybus are computed from (6.4.2). Since buses 1 and 3 are
not directly connected to bus 2,
Y21 ¼ Y23 ¼ 0
Using (6.4.2),
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
(AutoPDF V7 8/12 14:39)
Thomson-U (7.375x9.25") Tmath&GillSans
J-1711 Glover
Rev1:(CKN)27/4/2007
pp. 294–378
25795_06_ch06_p294-378
(p. 328)