Page 162 - Power Electronic Control in Electrical Systems

//SYS21/F:/PEC/REVISES_10-11-01/075065126-CH004.3D ± 150 ± [106±152/47] 17.11.2001 9:54AM

150 Power flows in compensation and control studies

Based on equations (4.100)±(4.104), the linearized equation for the HVDC light is
given below for the case when nodal voltage magnitude is controlled at node m by the
inverter and active power flow is controlled by the rectifier at node l (Acha, 2002)
2 3
@P l @P l 0 0 @P l
2 3 2 3
@y l @jV l j @y vR1
P l y l
6 7
@Q l @Q l
6 0 0 @Q l 7
6 Q l 7 @y l @jV l j 6 jV l j 7
6 @y vR1 7
6 7 6 7
6 0 0 @P m @P m 7
6 P m 7 6 y m 7 (4:105)
@y m @jV vR2 j 0 7
ˆ 6
6 7 6 7
6 7
4 Q m 5 @Q m @Q m 7 jV vR2 j 5
4
6 0 0 0
@y m @jV vR2 j
4 5
P bb y vR1
@P bb @P bb @P bb @P bb @P bb
@y l @jV l j @y m @jV vR2 j @y vR1
The variable voltage magnitude jV vR2 j and the voltage phase angle y vR1 are selected to
be the state variables. Also, P bb is the power mismatch given by equation (4.104),
which corresponds to the case when the converters are connected back-to-back.
If this is not the case and the converters are connected in series via a DC cable then
the voltage drop across the cable would be included in the constraint equation.
Additional equations become necessary to cater for the increased number of state
variables, with the DC equations being used to this end. At the end of iteration (r),
the voltage magnitude jV vR2 j and phase angle y vR1 are updated
(r ‡ 1) (r) (r)
jV vR2 j ˆjV vR2 j ‡ jV vR2 j (4:106)
y (r ‡ 1) ˆ y (r) ‡ y (r) (4:107)
vR1
vR1
vR1
If the converters are connected back-to-back, a simple model based on the concept of
PV and PQ nodes may be used instead. For the control case considered in equation
(4.105), the rectifier is modelled as a PQ node and the inverter as a PV node.
However, it should be noticed that this model may lack control flexibility.
The UPFC in the modified five-node network used in Example 8 was replaced with
an HVDC light system to enable 40 MW and 2 MVAr to be transmitted towards
Main via the transmission line Lake±Main. Moreover, the rectifier is set to control
nodal voltage magnitude at Lake node at 1 p.u. As expected, the power flow solution
agrees with the solution given in Example 8.
4.7.6 Numerical example 9
A further power flow solution is carried out for the case when the HVDC light
replaces the UPFC in the five-node network. In this example, the active power
generated by the generator in South node is specified to increase from 40 to
88.47 MW and the nodal voltage magnitudes at North and South are fixed at
1.036 p.u. and 1.029 p.u., respectively. The active power leaving the HVDC Light
towards Main is set at 25 MW. The inverter is set to absorb 6 MVAr and the rectifier
to regulate nodal voltage magnitude at Lake at 1 p.u. The nodal voltage magnitudes
and phase angles are given in Table 4.11 and the power flow results are shown in
Figure 4.24.
The objective to control active and reactive powers and voltage magnitude at the
target values is achieved with the following voltage magnitudes and phase angles of