Page 152 - Power Electronic Control in Electrical Systems

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140 Power flows in compensation and control studies

For the case when the TCSC 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 2 3
@y l @y m @jV l j @jV m j @X TCSC
P l y l
@P m @P m @P m @P m
6 7
6 @P m 7
6 P m 7 @y l @y m @jV l j @jV m j 6 y m 7
6 @X TCSC 7
6 7 6 7
@Q l @Q l @Q l @Q l
6 @Q l 7
6 Q l 7 6 jV l j 7 (4:78)
@y l @y m @jV l j @jV m j 7
ˆ 6
6 7 @X TCSC 6 7
6 7
4 Q m 5 @Q m @Q m @Q m @Q m 4 jV m j 5
6 @Q m 7
@y l @y m @jV l j @jV m j
4 @X TCSC 5
P lm X TCSC
@P lm @P lm @P lm @P lm @P lm
@y l @y m @jV l j @jV m j @X TCSC
The active power flow mismatch equation in the TCSC is,
P lm ˆ P reg P calc (4:79)
lm lm
and the state variable X TCSC of the series controller is updated at the end of iteration
(r) using the following equation
(r)
(r)
X (r ‡ 1) ˆ X TCSC ‡ X TCSC (4:80)
TCSC
4.6.3 Numerical example 6
The original network has been modified to include one TCSC to compensate the
transmission line connecting nodes Lake and Main. The TCSC is used to maintain
active power flow towards Main at 21 MW. The initial condition of the TCSC is set
at 50% of the transmission line inductive reactance given in Table 4.2, i.e. X ˆ 1:5%.
Convergence was obtained in five iterations to a power mismatch tolerance of
e 10 12 . The power flow results are shown on Figure 4.20 and the nodal voltage
magnitudes and phase angles are given in Table 4.6.
Since the TCSC cannot generate active power, there is an increase in active power
flowing towards Lake node, through the transmission lines connecting North to
Lake and South to Lake, in order to meet the increase in active power specified at
the sending end of the TCSC. In the transmission line South±Lake, the active power
flow increases from 24.47 MW in the original network to 25.5 MW at the sending end
of the line whereas in the transmission line North±Lake, the increase is from
41.79 MW to 42.43 MW.
It should be remarked that transmission line Lake±Main was series compensated to
increase the active power flow from 19.38 MW to 21MW, which is just under 8% active
power increase. The nodal voltage magnitudes do not change compared to the base case
but the voltage phase angles do change; particularly at Lake node where there is a
negative increase of almost one degree to enable increases in active power flows.
4.6.4 SPS power flow modelling

TheactiveandreactivepowersinjectedatnodeslandmbytheSPSshowninFigure4.3are

2
P l ˆjV l j G ll ‡jV l jjV m j(G lm cos (y l y m ) ‡ B lm sin (y l y m )) (4:81)
2
Q l ˆ jV l j B ll jV l jjV m j(B lm cos (y l y m ) G lm sin (y l y m )) (4:82)