Page 123 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 111

A phase shifting controller with the complex phase angle relationships:
T V ˆ cos f ‡ j sin f and T I ˆ cos f j sin f has the following transfer admittance
matrix
1
I l 1 (cos f ‡ j sin f) V l
ˆ (4:4)
I m X t (cos f j sin f) 1 V m
where X t is the leakage reactance of the series transformer and T V and T I are
complex tap changing variables related to each other by the conjugate operation.
Their magnitude is 1 and their phase angle is f.
The active power transfer across the phase shifter P lm is calculated using the
following expression

P reg ˆ jV l kV m j sin(y l y m f) (4:5)
lm
X t
Suitable adjustment of the phase angle f enables regulation of active power P reg
lm
across the phase shifter. It should be remarked that the phase shifter achieves
phase angle regulation at the expense of consuming reactive power from the
network.

4.2.4 The STATCOM

The STATCOM is the static counterpart of the rotating synchronous condenser
but it generates/absorbs reactive power at a faster rate because no moving parts are
involved. In principle, it performs the same voltage regulation function as the SVC
but in a more robust manner because unlike the SVC, its operation is not impaired
by the presence of low voltages (IEEE/CIGRE, 1995). It goes on well with
advanced energy storage facilities, which opens the door for a number of new
applications, such as energy markets and network security (Dewinkel and Lamoree,
1993).
The schematic representation of the STATCOM and its equivalent circuit are shown
in Figure 4.4. A fuller representation of the STATCOM is shown in Figure 1.10.
The STATCOM has the ability to either generate or absorb reactive power by
suitable control of the inverted voltage jV vR j€ y vR with respect to the AC voltage on
the high-voltage side of the STATCOM transformer, say node l, jV l j€ y l .
In an ideal STATCOM, with no active power loss involved, the following reactive
power equation yields useful insight into how the reactive power exchange with the
AC system is achieved
2 2
jV l j jV l kV vR j jV l j jV l kV vR j
Q vR ˆ cos (y l y vR ) ˆ (4:6)
X vR X vR X vR
where y vR ˆ y l for the case of a lossless STATCOM.
If jV l j > jV vR j then Q vR becomes positive and the STATCOM absorbs reactive
power. On the other hand, Q vR becomes negative if jV l j < jV vR j and the STATCOM
generates reactive power.
In power flow studies the STATCOM may be represented in the same way as
a synchronous condenser (IEEE/CIGRE, 1995), which in most cases is the model