Transient Stability Calculations by Computer

It is obvious that a digital computer program can be readily written to carry out the simple studies of Section 8.5. If a load-flow program is readily available, then improved accuracy will be obtained if, for each value of dn, the actual power output of the generators is calculated. At the same time, the effect of the excitation system and the governor movement can be included. Such calculations make use of numerical integration packages based on mathematical concepts. Techniques such as trapezoidal integration provide fast and sufficiently accurate results for many stability studies; more accurate techniques, such as Runge-Kutta (fourth order), predictor-corrector routines, and so on, can be employed if the improved accuracy and longer run times can be economically justified. Most commercial stability programs offer various options for inclusion of generator controls, system switching and reclosing, compensator modelling, and transformer tap-change operation, according to some input criteria. Packages dealing with 1000 generators, 2000 lines, and 1500 nodes are available.

Example 8.4

Consider the network of Figure 8.10. Data for generators, transformers, lines and loads are given in Tables 8.2-8.5

Network for Example 8.4

Figure 8.10 Network for Example 8.4

Table 8.2 Generator data

G1

G2

G3

Rating (MVA)

750

750

250

Xs (p.u)

1.7

1.7

1.6

Rs (p.u)

Xd'(p.u)

0.05

0.05

0.06

0.35

0.35

0.3

Xd" (p.u)

0.25

0.25

0.25

Td' (s)

8.0

8.0

8.0

Td" (s)

0.03

0.03

0.03

H(s)

6.5

6.5

6.0

Table 8.3 Transformer data

T1

T2

T3

Rating (MVA)

750

750

250

Xi (p.u)

0.15

0.15

0.12

R (p.u)

0

0

0

Table 8.4 Line data

LN1

LN2

LN3

LN4

X(V)

115

115

115

9

R(V)

11

11

11

0.9

Y(mS)

1450

1450

1450

115

Table 8.5 Load data

L1

L2

P (MW)

600

1000

Q (MVAr)

50

100

The network shown in Figure 8.10 was implemented in the IPSA computer simulation package. First a fault applied to Bus 3 at 2 sec and cleared after 80 ms (less than the critical clearance angle). The angle of G1 with respect to that of G2 and power through line LN1 is shown in Figure 8.11(upper trace). Similar results for a clearance time of 600 ms (greater than the critical clearance angle) is shown in Figure 8.11(lower trace).

Angle of generator G1 and power through line LN1 before and after a fault at BUS 3. For 80 ms clearance time (upper trace). For 400 ms clearance time (lower trace)

Figure 8.11 Angle of generator G1 and power through line LN1 before and after a fault at BUS 3. For 80 ms clearance time (upper trace). For 400 ms clearance time (lower trace)

As can be seen from Figure 8.11(upper trace) the angle between the two generators swings but comes back to a stable point after about 25 ms. When the fault clearance time is longer than the critical clearance time, the machines lose synchronism and pole slipping occurs, as shown in Figure 8.11(lower trace).

 
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