Optimal Firing-Angle Control of Cascaded HVDC Converters
For Minimum Reactive Power Demand
D. A. Deib and H. W.Hill
Ohio University
Department of Electrical & Computer Engineering
Athens, Ohio 45701
Abstract
-
An asymmetrical firing strategy for the
cascaded converters of a HVDC link i s proposed,
resulting in minimum reactive power compensation at
both ends of the dc link. Both 6- and 12-pulse converters,
in unipolar and bipolar operation, are considered. In
addition to reactive power reduction, ac and de
harmonics are greatly reduced.
In this paper, the asymmetrical firing of more than
two series converters is proposed to minimize the
reactive power demand at both ends of a HVDC link.
The concept can be applied for 6- or 12-pulse
converters, in both unipolar and bipolar operation. In
addition to reactive power minimization, there is a
reduction in both ac and dc harmonics at the dc link
ends, compared with the conventional symmetrical
phase control.
Introduction
Line-commutated phase-controlled converters have
several shortcomings for both rectification and
inversion. At reduced dc voltage level the phasecontrolled converter requires a large amount of reactive
power compensation. With constant dc current and no
commutation reactance, the converter ac current
displacement power factor angle is equal to the firing
angle. Practically, the transformer leakage reactance
and the ac system input impedance cause commutation
overlap, further decreasing the converter power-factor
@8[I, 21.
There are several methods of converter pf
improvement, featuring either asymmetrical or
symmetrical firing within the 6-pulse converter. In the
first case, the 6-pulse converter consists of a pair of
asymmetrically fired 3-pulse groups. This method can
only be used when one 6-pulse converter is used. It
suffers from additional harmonics at both ac and dc
sides, as well as the possibility of commutation failure
[3]. Therefore, this method is limited to low power
converters. Symmetrical firing within the 6-pulse
converter is more promising. For two series-connected
converters the individual 6-pulse converters can be
controlled symmetrically, but the two converters can be
controlled as asymmetrical groups. One of the
asymmetrical groups is fully advanced (or retarded) to
minimize its reactive power, while the other one is
phase-controlled to give the desired dc voltage. [3,4].
Proposed Techniques
It was shown in [3] that for two converters the
minimum reactive power demand can be achieved if
they are controlled asymmetrically. One of the
converters is fully advanced (for rectifier operation), or
fully retarded (for inverter operation), and the other one
is phase-controlled to get the desired dc voltage level.
The asymmetrical firing is generalized in this paper
for N cascaded converters for both unipolar and bipolar
operation of HVDC links; specific examples show N
equal to 4 and 8. In order to minimize the reactive
power demand of N cascaded converters, one converter
only should be phase-controlled, and the rest (N-1) can
Converter Number
Table 1. Firing strategy for a 4 converter dc link
lhis work waa N ~ ~ O I W
in~part by the Ohio Academic chpuenge Program
in Power Elcaranica/Tnduatridcontrds.
662
0-7803-0982-0193 $3.00 1993 IEEE
This reactive power is maximum (1 pu) when the dc
voltage is zero. The rest of the converters, which are
fully advanced or fully retarded, have a dpf of
be either fully advanced or fully retarded, consuming
minimum reactive power. The fully advanced
converter would act as a rectifier with 1 pu output dc
voltage, and the fully retarded converter would act as
an inverter with -1 pl dc voltage.
The numbers of fully advanced and fully retarded
converters depend on the desired dc voltage level. For
example, suppose the desired dc voltage for a fourconverter dc link is from 1 pu to 0.5 pu. In this case,
three converters can be fully advanced to a total output
voltage of 0.75 pu, and the fourth converter can be
phase-controlled with an output voltage from 0.25 pu
(at a firing angle a = 0) to -0.25 pu (at a = 1c - U&.
Table (1) shows the control strategy for the 4 converters
for both modes of operation. Note that, at any instant
only one converter is controlled and three converters
are uncontrolled.
The output dc voltage for the ith 6-pulse phasecontrolled converter, with commutation overlap less
than 600,is given by :
dPG=
1+cos
U,
(4)
and each one of them consumes minimum per-unit
reactive power Qo
QO
=
2u,-sin2u,
4(1- COS U,)
(5)
In the examples of this paper a maximum overlap
angle (U,) of 25’ is assumed at zero firing angle, but
any other value could be used. For any firing angle
higher than zero, the overlap can be obtained from:
Harmonic Analysis
VQ =-3 m ,
IC
V,,, is the peak phase voltage at the converter side, and
q is the firing angle of the ith phase-controlled converter. The total dc voltage of N cascaded converters is:
The p-pulse, current-source, phase-controlled
converter generates characteristic harmonics of orders
pq & 1 at the ac side, and pq at the dc side, where q is
any positive integer.
These harmonics are complex functions of both the
firing angle a and the commutation overlap angle U.
The complex values of the characteristic dc voltage
harmonics for the symmetrical 6-pulse converter are
computed from (7a) as [l]:
For a base value of the per-unit dc voltage, we will
take the maximum total dc voltage of N cascaded 6[ 1 + COS U, 1.
pulse phase-controlled converters:
2
I-
n-1
J
The total dc harmonics of N cascaded converters are:
The corresponding displacement power factor (dpf)
of the ac current is
N
Vnt=
E
i=l
vni
The dc Voltage Distortion Factor, VDF, is given by
and the per-unit reactive power consumed is
Q = 2ui+sin 2ai - sin 2(ai + ui)
COS ai - COS (ai + ui)]
(3)
663
k being the highest harmonic to be considered, the
sixtieth in this case.
Results
For a Y/A-connected transformer, the complex rms
values of the ac input current characteristic harmonics
are given by (9a) [ 11, where the phase voltage is taken
as a refemce, and the dc side current h is constant.
The asymmetrical firing is applied here for two
cases: four 12-pulse converters and eight 6-pulse
converters. Unipolar and bipolar operation is studied in
each case.
Case I, Fig. 1 shows the firing strategy for four
I -
I
n- 1
I
and the fundamental current is:
For the YE-connected transformer the input current
harmonics are:
-( +Id
InY-
-b
forn=l,11,13,23,25
forn=5,7, 17, 19,...
The input current harmonics for a 12-pulse phasecontrolled converter are given by:
For symmetrical cascaded converters, the harmonics
are calculated for one of the converters, and the
harmonics of the same order are added algebraically for
all the conv.erters. For asymmetrical firing, the
harmonic contribution of each converter can be
calculated separately and then added to the others as a
complex quantity. The total ac current harmonics of
the N cascaded 6-, or 12-pulse phase-controlled
converters will be:
The maximum value of the fundamental ac current
will be used as the base value for the per-unit ac
currents.
cascaded 12-pulse converters. The corresponding
displacement power factor and reactive power demand
are shown in Figs. 2 and 3, respectively. The results
are compared with the conventional symmetrical 12pulse operation. It is clear that the asymmetrical firing
results in power factor improvement and reactive power
saving, especially at low voltage level. Figs. 4 and 5
also show a comparison between the ac harmonics, of
both the proposed firing technique and the symmetrical
12-pulse operation. In these Figs. there is a notable
reduction of both the fundamental and harmonic
currents at both ends of a dc link. This will reduce the
transmission and filtering losses. Figs. 6 and 7 show a
comparison between the dc harmonics, of both the
proposed firing technique and the symmetrical 12-pulse
operation, where the proposed scheme has reduced the
dc harmonics drastically.
For bipolar operation with 2-series 12-pulse
converters at each pole, the above firing strategy can be
used with some adjustment. A 12-pulse converter is
actually a pair of 6-pulse converters, one with a Y E and the other with a Y/A-connected transformer.
Therefore, at each pole there are four 6-pulse
converters. The firing strategy of each pole can be
similar to that of Fig. 1. In this case, a converter with a
Y/Y connection at one pole and a converter with a Y/A
connection at the other pole should be controlled at any
instant to maintain the 12-pulse operation between the
pairs of 6-pulse converters.
2 Fig. 8 shows the firing strategy for eight
cascaded 6-pulse converters, in unipolar operation. The
corresponding dpf, reactive power, fundamental ac
current, ac harmonics, dc voltage distortion, and dc
harmonics are shown in Figs. 9 to 14, respectively. In
this case, both the reactive power and the harmonics are
reduced, as compared with symmetrical 6-pulse
operation.
664
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0.5
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per-unit dc voltage
Fig. 4. Fundamental ac current. (a) for the poposed scheme of Fig.
1. (b) for conventional 12-pulse phase control.
-OS pa-unit voltage
Fig. 1. Optimal firing-angle strategy for 4 12-pulse converters. for
minimum r e d v e power compmpcltion.
0.1
c
1
------*-
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a
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a
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k3 0.2-
b
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/
0
Bc
-1
0.5
1
-05 per-unit voltage
0
0.5
1
p - u n i t dc voltage
Fig. 5. Input currat harmonics. (a & b) 11th & 23rd. respectively.
Fig. 2. Displacementpower factor. (a) for the proposed scheme of
for the proposed scheme of Fig. 1. (c & d) 11th & 23rd.
Fig. 1. (b) for conventional 12-pulse phase control.
respectively. for conventional 12-pulse phase control
-1
-Oe5
0.5
I
T
0
t
I
B
9 0.6-
I
0.4
I
I
I
,
9
-s&
0.2
E 0.1
-0
0
0
0.5
1
P-unit dc voltage
Fig. 3. Reactive power demand (a) for the pqosed scheme of Fig.
1. (b) for umventidl2-pulse phase control.
-1
-0.5
\
\
I
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/
I
0.3
'b
.B
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:A
1
0
0.5
1
per-unit dc voltage
Fig. 6. DC voltage distortion factor. (a) for the proposed scheme of
Fig. 1. (b) for conventional 12-pulse phase control
665
-1
-0.5
n I<,-
".l
0
0.5
1
per-unit dc voltage
Fig. 10. Reactive power demand (a) for the proposed scheme of
-1
per-unit dc voltage
Fig. 7. Per-unit dc voltage harmonics. (a & b) 12th & 24th
respectively, for the proposed scheme of Fig. 1. (c & d) for
conventional 12-pulsephase control.
-0.5
Fig. 8. (b) for conventional 6-puke phase control.
1.2 I
0.2
Fig. 8. Optimal firing-angle strategy for 8 6-pulse converters. for
minimum reactive power compensation.
'
-1
I
J
-0.5
per-unit fc voltage
0.5
1
Fig. 11. Fundamental ac current. (a) for the proposed scheme of
Fig. 8. (b) for conventional 6-pulse phase control.
02.1-,
c
\I
0.05
0
0.5
1
per-unit dc voltage
Fig. 12. Input current h o n k s . (a & b) 5th & 7th. respectively,
for the proposed scheme of Fig. 8. (c & d) 5th & 7th
respectively. for conventional 6-pulse phase control
-1
Fig. 9. Displacement power factor. (a) for the proposed scheme of
Fig. 1. (b) for conventional 6-pulse phase control.
666
-0.5
Also,this firing scheme can be used for the above
12-pulse example to reduce the reactive power demand
more than that of Fig. 3, with a penalty in the ac and dc
harmonics.
For bipolar operation with 4-series 6-pulse
converters at each pole, the firing strategy of case 1 can
be used for each pole, if bipolar symmetry is required.
The reactive power demand is the same as that of Fig.
3, but the harmonic distortion will be higher than that of
case 1.
I
-05
O'l
0
per-unit dc voltage
0.5
1
Fig. 13. Voltage distortion factor. (a) for the proposed scheme of
Fig. 8. (b) for c o m e n t i d 6-pllse phase control.
0.35
1
I
Conclusions
A new firing strategy for N cascaded, 6- or 12-pulse,
phase-controlled converters has been proposed to
minimize the reactive power demand. In addition to
reactive power minimization a great reduction in both
ac and dc harmonics appears to result, reducing filtering
requirements for both ac and dc sides of a HVDC link.
This would reduce the capital and operating costs of a
dc link.
References
[l]. E.W. Kimbark, "Direct Current Transmission volume I,"
Wiley Interscience. 1971.
[2]. J Arrillaga, "High Voltage Direct CurrentTransmission,"
per-unit dc voltage
Fig. 14. Per-unitdc harmonics. (a & b) 6th & 12th for the proposed
scheme of Fig. 8. (c & d) for conventional 6-pulse phase
COnh.01.
667
Peter Peregrinus Ltd.
[3]. W. McMurray, "A Study of Asymmetrical Gating for
Phase-Controlled Converters," IEEE Trans. on Ind.
Awl., Vol. IA-8, NO.3, p ~289-295,
.
M a y / J u t ~1972.
[4]. S. Arabi and M. 2.Tarnawecky, "Differential Firing in
Series Tapping of HVDC Transmission," IEE Fourth
International Conf. on AC & DC Power Transmission,
London, pp. 260-264,Sept. 1985.