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132 Power flows in compensation and control studies
The Jacobian elements for node two are:
@P 2 @P 2 @Q 2 @Q 2
9:45254 0:998334 0:948417 8:574958
j
@y 2 @ V 2 j @y 2 @ V 2 j
j
The solution of the linearized system of equations is
(2) (2)
P 2 9:45254 0:998334 y 2
j
Q 2 0:948417 8:574958 V 2 j
(2)
y 2 0:107042 0:012462 0:051583 0:006425
(4:62)
j
V 2 j 0:011839 0:117996 0:07246 0:009161
The voltage magnitude and phase angle at node two at the end of the second iteration
are
(2) (1) (2)
y 2 0:1 0:006425 0:106425
(4:63)
j V 2 j 0:95 0:009161 0:940839
At this stage, the complex voltages at nodes one and two are
(2)
V 1 10
p:u: (4:64)
V 2 0:940839 0:106425
These voltages are quite close to the actual solution. If the procedure is repeated for
6
two more iterations then P 2 and Q 2 become smaller than 10 .
4.4.6 Numerical example 4
The test system shown in Figure 4.17 is used in this example (Stagg and El-Abiad,
1968). The original figure has been redrawn to accommodate the power flow results.
In subsequent examples in this chapter, the system is used in modified form, to
illustrate how the various FACTS controllers perform in network-wide applications.
The original test system is solved using a power flow computer program written in
C using object-oriented programming (OOP) techniques (Fuerte-Esquivel, 1997).
The power flow results are shown on Figure 4.17 and the nodal voltage magnitudes
and phase angles are given in Table 4.1. The network parameters required for the
power flow study are given in Tables 4.2±4.4. This power flow solution will be used as
the base case against which all other solutions will be compared.
In conventional power flow calculations, generators are set to generate a pre-
specified amount of active power, except the Slack generator which is left free, since
it has to generate sufficient active power to meet any shortfall in system generation. It
will also generate or absorb any reactive power excess in the system. In this example,
the generator connected at the North node is selected to be the Slack generator,
generating 131.12 MW and 90.81 MVAr. The voltage magnitude was kept at 1.06 p.u
and the voltage phase angle at 0 . The generator connected at the South node was set
to generate 40 MW and the power flow solution indicates that it absorbs 61.59 MVAr
to keep the nodal voltage magnitude at the specified value of 1 p.u. The remaining
three nodes contain no equipment to provide local reactive support and their nodal
