Page 153 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 141

Fig. 4.20 TCSC upgraded test networkand power flow results.

Table 4.6 Nodal complex voltages of TCSC upgraded network

Voltage System nodes
information
North South Lake Main Elm
jVj (p.u.) 1.06 1 0.987 0.984 0.972
y (degrees) 0 2.04 4.73 4.81 5.7

For equations corresponding to node m the subscripts l and m are exchanged in
equations (4.81)±(4.82).
For the case when the SPS is controlling active power flowing from nodes l to m at
a value P reg the set of linearized power flow equations are
lm
2 3
@P l @P l @P l @P l @P l
2 3 @f 2 3
@y l @y m @jV l j @jV m j
P l y l
6 7
@P m @P m @P m @P m
6 @P m 7
6 P m 7 6 @y l @y m @jV l j @jV m j @f 7 6 y m 7
6 7 6 7
6 @Q l @Q l @Q l @Q l @Q l 7
Q l ˆ 6 @f
6 7 7 jV l j 7 (4:83)
6
@y l @y m @jV l j @jV m j
6 7 6 7
6 7
Q m 6
4 5 @Q m @Q m @Q m @Q m @Q m 7 jV m j 5
4
@y l @y m @jV l j @jV m j
4 @f 5 f
P lm
@P lm @P lm @P lm @P lm @P lm
@y l @y m @jV l j @jV m j @f
The active power flow mismatch equation in the SPS is,
P lm ˆ P reg P calc (4:84)
lm lm
where equation (4.5) in Section 4.2.3 may be used for the purpose of calculating P calc
lm
and to derive the relevant Jacobian terms in equation (4.83).