Environmental Engineering Reference
In-Depth Information
PV Buses
For large synchronous generators, the
Q
is often not specifi ed, and instead it is the voltage
V
that is known. This is because such generators are fi tted with AVRs that hold the
V
constant.
To accommodate this, in load fl ow analysis nodes where such generators are connected are
referred to as
PV buses
and are dealt with a little differently in the maths. Unfortunately,
PV
buses are sometimes described as
generator buses
, which makes sense so long as all the
generators are large synchronous generators with AVRs.
As renewable energy generators increase in size, utilities have been developing regulations
requiring that such generators behave in a traditional manner. Multimegawatt wind turbines
connected to the network through PWM inverters may therefore be required to regulate the
local bus voltage. In such cases the node has to be treated as a
PV
bus.
Slack, Swing or Reference Bus
The two types of buses described earlier require that the
P
s are specifi ed at all the network
nodes before the load fl ow calculations are initiated. This does not make sense in terms of
the conservation of power principle because the transmission losses in the system are not
known before the solution is arrived at! This conundrum is resolved by allowing one bus that
has a generator connected to it to be specifi ed in terms of the magnitude
V
and angle
of its
voltage. Such a bus is known as a
slack, swing or reference bus
. The voltage at this bus acts
as the reference with respect to which all other bus voltages are expressed. At the end of the
load fl ow the calculated
P
and
Q
at this bus take up all the slack associated with the losses
in the transmission.
δ
5.6.5 The Load Flow Calculations
In small networks, it is often possible to obtain valid and useful results by direct application
of the mathematical analysis presented earlier. Also, larger networks can often be reduced to
equivalent circuits that can be solved in the same way. However, load fl ow analysis of any
system beyond a few nodes is carried out by a computer.
Each bus of a power network is characterized by a number of variables. For a network
with predominantly reactive transmission line impedances all these variables are linked by
the complex Equation (4.7a), replicated below:
VV
X
V
X
⎡
⎢
⎤
⎥
=+
AB
B
(
)
S
=−
sin
δ
+
j
VV
−
cos
δ
PQ
j
(4.7a)
B
B
A
B
B
t
t
This equation describes the performance of a synchronous generator but it is equally appli-
cable to a transmission line linking two buses. Note that there are four variables associated
with each bus: the active and reactive power injected or extracted at the bus and the magnitude
and angle of the bus voltage. The complex Equation (4.7a) can be split into two separate
equations, one for the real part and another for the imaginary part. For a network with
n
nodes, there are 2
n
simultaneous equations to be solved; hence at each node two of the four
variables have to be specifi ed. All this fi ts neatly with the earlier arrangement of specifying
buses in terms of
P
and
Q, P
and
V
or
V
and
.
The solution of the 2
n
equations describing the network is not a trivial task! The basic
Equation (4.7a) linking the node variables is nonlinear because it contains products of the
δ
