COBEP_2007

CRITICAL ANALYSIS OF CAPACITOR-COMMUTATED CONVERTERS (CCC)
José Alberto Fernandes Ferreira Jr. Ricardo Paulino Marques Walter Kaiser
Escola Politécnica da Universidade de São Paulo – Depto. PEA ,
Av. Prof. Luciano Gualberto Trav.3 no
158 CEP:05508-900 São Paulo, SP - Brasil
jaffjunior@yahoo.com rpm@lac.usp.br kaiser@lac.usp.br
Abstract – Capacitors in series with the AC branches in
line-commutated converters improve DC voltage
regulation and extend operation beyond the normally
attainable control angles. This paper presents the
operating characteristic of capacitor–commutated
converters, including valve voltage stress and attainable
control range for particular capacitor values, for a wide
DC load current range. Also mathematical formulations
of DC voltage versus current characteristic and
commutation angles versus current are presented for
thyristor rectifiers.
Keywords – Capacitor-commutated converter, HVDC,
Rectifier
I. INTRODUCTION
The capacitor-commutated converter (CCC) is a
conventional line commutated three-phase bridge converter
with capacitors in series with the AC phase connections. The
capacitors reduce the reactive power requirements and
provide an additional voltage contribution to the valves
allowing commutation in firing angle regions normally
unattainable in conventional converters. Potential
applications in HVDC transmission have been reported
[1,4,5,6] and functional products using this technology are
already available [5,6]. This converter has also potential
application in other special high power applications such as
in electrolysis rectifiers.
The basic equations describing steady-state operation of
the CCC were first proposed in [1]. The aim of this paper is
to establish a thorough understanding of the capacitive
commutation technique and also provide a critical analysis of
the converter parameters at load current variations.
II. VOLTAGE REGULATION IN BRIDGE RECTIFIER
CONVERTERS
The general principles employed in the analysis of the
bridge rectifier converter under steady state conditions, fully
covered in the literature [2,3], have been directed at
situations where AC branches are purely inductive and
assume continuous and perfectly smoothed DC current as
indicated in Fig. 1.
The odd (1,3,5) and even (2,4,6) valves are associated
with the positive G+ and negative G- half-bridges
respectively. Transition of the current from one valve to the
other cannot take place instantaneously because of reactances
in the AC branches and the transition period is known as
commutation period or overlapping angle µ.
1 3 5
4 6 2
ea
eb
ec
i
L
L
L
G+
G-
Fig. 1. Three-phase bridge rectifier with inductive commutation
The rectifier’s DC voltage versus current curve
encompasses three operation modes (see Fig. 2). Within the
normal load range, the rectifier operates in MODE 1, with
independent commutation in both half bridges. Also only one
valve of each half bridge carries current between successive
overlap periods. When DC current increases, the rectifier
operates in MODE 2, with independent commutation in both
half bridges. However, in this mode the converter operates
continuously in the commutation process. At higher DC
currents, the rectifier operates in MODE 3 with three or four
valves conducting simultaneously and commutations in both
half-bridge circuits interfering with each other.
Instead of assuming an approximate relation between
alternating and direct currents, a common scaling factor is
used in order to obtain consistent equations irrespective of
the side of the converter taken as reference. For convenience,
DC open circuit voltage Uo and peak value of phase-to-phase
short circuit current Isc are proposed [2] as voltage and
current base values in the following analysis.
π
⋅⋅
== m
OBASE
E
UV
33
, (1)
L
E
II m
SCBASE
⋅ω⋅
⋅
==
2
3
, (2)
where Em is the phase-to-neutral voltage peak value and L is
the commutation inductance.
Figure 2 shows the normalized DC voltage versus current
curve and Fig. 3 presents the behavior of overlap angle µ as a
function of the normalized DC current of the three phase
bridge from no-load to short-circuit for various firing angle
values [3].

α=30o
α=45o
α=60o
α=0o
α=0o
α=0o
e p/ α≤30°
MODE 1 MODE 2 MODE 3
2
3
2
1
3
32
pupu IU
2
1
1−=
2
1
2
3
pupu IU −=
4
3
puU
1
2
3
pupu IcosU
2
1
−α=
4
3
1
pupu I)(cosU
2
3
6
3 −
π
−α=
p/ α≥30°
puI
pupu IU
2
3
3−=
0
π
⋅⋅
= m
BASE
E
V
33
L
E
II m
SCBASE
⋅ω⋅
⋅
==
2
3
Fig. 2. Three-phase bridge rectifier - DC voltage versus current.
45°
60°
30°
15°
α=0°
45°
α≤30
30°
10°
20°
40°
50°
60°
70°
80°
90°
100°
110°
120°
µ
0
1 puI
2
1
2
3
3
32
α=0°
)](sin[Ipu
o
301
3
1
−µ+=
)]cos()(sin[Ipu
oo
3060
3
1
−α+−µ+α=
)cos(cosIpu µ+α−α=
L
E
II m
SCBASE
⋅ω⋅
⋅
==
2
3
Fig. 3. Three-phase bridge rectifier – Overlap angle µ versus
current.
III. CCC ELEMENTARY MODE OF OPERATION
Figure 4 shows the three-phase full-wave bridge converter
configuration with added series capacitors. Neglecting line
inductances, the capacitor voltages are trapezoidal and in
steady state their mean voltages are null.
1 3 5
4 6 2
ea
eb
ec
i
G+
G-
C
C
C
L
L
L
Fig. 4. Three-phase rectifier with capacitive commutation
The peak value of the capacitor voltages is independent of
the commutation overlap and given by:
C
I
V maxC
⋅ω
⋅
π
=
3
, (3)
where, C is the commutation capacitance, I is the DC load
current, VCmax is the maximum capacitor voltage and ω is the
line frequency.
Figure 5 shows the composition of the phase voltages and
capacitor voltages that produces the shifted commutation
voltages URECT at the rectifier output. The capacitor allows
the rectifier to operate with negative firing angles α. The
extent to which the firing angle can be advanced beyond the
normal region (inductive commutation) depends on the phase
shift with respect to original AC supply waveform.
eab eba
ia
eac ebc eca ecb
URECT
ib ic
iaib ib
α
µ
eac+ebc
2
0° 60°-60° 120° 180° 240°-120°
θ
θ
vCbvCc vCa
θ
∆VC=VCa-VCc θ
Fig. 5. DC rectifier voltage, capacitor voltages and currents.
A more realistic system description should take in to
account the inductive line impedances and therefore
additional capacitor voltage changes ∆V1 and ∆V2 appear
during commutation for outgoing and incoming phases, as
shown in the detail of Fig.6.
incoming phaseoutgoing phase
θ
µ
ia ib
θ
+VCmax
−VCmax
∆V1
∆V2
VC1
VC2
Fig. 6. Detail of additional capacitor voltage changes 1V∆ and
2V∆ due to the inductor during commutation.

IV. ANALYTICAL FORMULATION OF THE CCC
COMMUTATION PROCESS
The following assumptions for modeling apply: i) AC
voltage is stiff and may be represented by an ideal sinusoidal
source in series with a lossless inductance, ii) DC current is
ripple-free and constant, iii) valves are ideal with zero on-
resistance and infinite off-resistance; changes between these
two states are instantaneous and iv) valves are fired at
intervals of one sixth of a cycle (60°). The converter will be
analyzed only within the normal load range where the
commutations in both half-bridge circuits proceed
independently. For convenience, DC open circuit voltage Uo
and peak value of phase-to-phase short circuit current Isc as
in (2) are proposed as voltage and current base values in the
following analysis.
A. Computation of commutation current and ovelap angle.
Figure 7 presents the frequency domain equivalent circuit
of the commutation from valve 1 to valve 3. The voltage
source LI denotes the initial condition of full direct current in
the outgoing phase.
Ea(s)
I/s
I1(s)
I2(s)
VC10/s
VC20/s
Eb(s)
sL
sL
1/sC
1/sC
LI
Fig. 7. Equivalent circuit of the CCC during commutation from
valve 1 to valve 3.
At the beginning of the commutation, the capacitors in the
incoming and outgoing phases are charged to:
C
I
VC
⋅ω
⋅
π
−=
302
, (4)
1
01 3
V
C
I
VC ∆−
⋅ω
⋅
π
= , (5)
where ∆V1 is the change of the capacitor voltage during
commutation in the outgoing phase. Correspondingly, the
change of the capacitor voltage in the incoming phase will be
denoted ∆V2. The sum of these terms is given by;
C
I
VV
⋅ω
⋅µ
=∆+∆ 21 , (6)
where µ is the commutation angle (see Fig. 4).
The instantaneous line-to-neutral e(θ) and corresponding
line-to-line v(θ) voltages of the ac sources are given by:
)cos(Ev
)cos(Ev
)cos(Ev
)cos(Ee
)cos(Ee
)cos(Ee
mcb
mba
mac
mc
mb
ma
6
5
3
2
3
6
3
3
3
π
+θ⋅⋅=
π
−θ⋅⋅=
π
+θ⋅⋅=
π−θ⋅=
π
−θ⋅=
π
+θ⋅=
. (7)
With reference to Fig. 7, substituting the initial conditions
given in (4) and (5) and adopting the base values defined in
(1) and (2) the normalized Laplace transform of the outgoing
phase current is:
,
s
]sin
1k
k
V
k
3
I
3
k
[s
2
I
1k
cos
s
1k
sin
s
1k
cos
s
2/I
)s(I
2
o
2
o21pu
pu
2
22
22
PU
pu1
pu
ω+
ω⋅α⋅
−
+∆⋅
⋅π
−⋅
π
+⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
−
α
−
−
+
ω+
ω⋅
−
α
−⋅
−
α
−=
(8)
where:
Ipu DC current p.u. value;
α firing angle;
pu
V1∆ outgoing capacitor voltage change in p.u.;
ωo
CL ⋅
1 ;
k ω
ωo .
Equation (8) in the time domain is given by
( )
).k(sinV
k
))k(sinsinkkcoscos)cos((
k
))kcos()k(sink(I)(i
pu
pupu
θ⋅∆⋅
⋅π
+
θ⋅α⋅−θ⋅α+α+θ−
−
+
+θ⋅+θ⋅⋅
π
−⋅=θ
1
3
1
1
2
1
32
1
2
1
.(9)
At end of commutation the outgoing current vanishes, i.e.,
01 =µ)(i and therefore
3
k
]I
4
k
)cos(
1k
sinktgcos
[V pu22
22
k
2
pu1
π⋅
⋅⋅
µ⋅
++α⋅
−
⋅−⋅
=∆ µ
µµµ
.(10)
Another expression relating Ipu with ∆V1pu results from the
fact that ∫
µ
θθ
ω
=∆
0
11
1
d)(i
C
V and is given by
( )
( )
.I
3
k
1kcos
]kcos
3
k
ksin
2
1
)
32
1
(k[
3
k
)1k(cos)1k(
kcossinkksincos)(sink
V
pu
2pu1
⋅
π⋅
⋅
+µ
µ
π⋅
+µ+
π
−µ
+
+
π⋅
⋅
+µ⋅−
µ⋅α⋅+µ⋅α+µ+α⋅−
=∆
(11)
From (10) and (11) Ipu is given by
11
2
2
2
23
2
2
222
−
+α
⋅
+⋅−
−⋅⋅
⋅=
µ
µπµ
µµµ
k
)(sin
tg)(k
)sincostgk(
I
k
k
pu . (12)
B. Commutation conditions.
In a three-phase bridge rectifier commutation can only
take place when the valves involved are directly polarized.
Therefore the following voltage conditions in outgoing and
incoming phases have to be met:
outcapoutincapin vvvv −>− . (13)
The admissible firing angle condition is given by:
pupu VI
k
sin 1
2
3
3
∆⋅
π
+⋅
π
−≥α . (14)

An expression for the admissible firing angles is obtained
from (10) and (12) in (14).
µ⋅µ⋅−µ+µ⋅−−+µ⋅−µ−µ⋅
µ+⋅µ⋅−µ+⋅µ⋅+µ−µ−µ⋅
≤α
π
π
ksinsink)kcos)(coskk()sinkksin)((k
)cos(ksink)kcos(sink)cosk)(cos(k
tg
12
11
22
3
4
2
3
42
.(15)
C. Mean DC bridge output voltage.
The normalized mean direct voltage over a complete cycle
as a function of control angle α and commutation angle µ is
given by
∫∫
α+
π
α+µ
α+µ
α
θ+θ
⋅π
==
33
]dvdv[
UU
U
U
pucomwithoutrectpucomrect
oo
pu
(16)
∫
∫
α+
π
α+µ
α+µ
α
θ∆+
π
−α−θ⋅
⋅π
⋅−
π
−θ
π
+
+θ∆+α−θ⋅
⋅π
−θ⋅
π⋅
π
=
3
1
2
1
2
2
3
2
663
2
3
46
33
]d)V))((
k
I)cos((
d)V)(
k
I)cos(([U
pupu
pupupu
or
pupupu V)(I
k
)(
)cos(cos
U 1
22
2
3
2
64
3
2
∆⋅µ
π
−+⋅
π
⋅µ−
π
µ
+
µ+α+α
= .(17)
In order to facilitate physical interpretations, it is
convenient to rewrite (17) using (6) expressed in p.u. values,
resulting in
)VV()(
)cos(cos
U pupupu 121
4
3
2
∆−∆⋅−
π
µ
+
µ+α+α
= . (18)
The first term in the equation above is identical to the
expression for the DC-voltage in a conventional inductive
commutated rectifier. Two contributions from the series
capacitance have impact on the DC-voltage. The most
significant is presented in the first term, meaning that
capacitance lowers the overlap angle µ and thereby increases
the DC-voltage. The contribution in the second term is
negligibly small and is caused by a difference between the
charging voltages of the incoming capacitor ∆V2pu, and the
outgoing capacitor ∆V1pu during the overlap interval.
D. Valve voltage stress.
The peak voltages for capacitive commutation can
substantially exceed those of inductive commutation,
particularly for high k values (low capacitances). The valve
voltage waveform in one cycle is separated into eight
intervals; one is a straight line (valve conducts) and other
seven are arc lines (see Figs 11 and 15). The peak voltage in
each interval usually occurs at their boundaries and the valve
peak voltage is the maximum among the intervals peak
value.
V. CCC OPERATION ANALYSIS
Depending on k values, the AC branch impedance can be
inductive (k<1) or capacitive (k>1). This paper considers
only converter steady-state operation as rectifier with
balanced capacitor voltages and within the normal load range
where the commutations in both half-bridges circuits proceed
independently.
A. Capacitive operation (k>1).
Figure 8 shows the behavior of the commutation angle µ
as a function of DC current Ipu and firing angle α for
different k values. The higher k (the smaller the capacitance)
the more commutation-aiding voltage is produced for a
particular DC current and the smaller is the overlap period.
As a consequence, the maximum commutation angle never
reaches 60°.
0
10
20
30
40
50
60 0
1
2
3
0
10
20
30
40
50
60
α
µ
Ipu
k=4
k=1.001
k=1.5
k=2
k=2.5
Fig. 8. Capacitive operation (k>1) - Curve relating overlap (µ) and
firing (α) angles to DC current (Ipu) for different k values.
Figure 9 shows the DC voltage Upu versus DC current Ipu
characteristics for different firing angles α and k values.
Comparing the DC characteristic for this case and for
inductive commutation, it can be noticed that the capacitance
diminishes the overlap angle µ improving DC voltage
regulation characteristic for the same current conditions.
0
20
40
60
0
1
2
3
0
0.2
0.4
0.6
0.8
1
k=4
k=1.001
k=1.5
k=2
k=2.5
α
Upu
Ipu
Fig. 9. Capacitive operation (k>1) - DC voltage (Upu) versus DC
current (Ipu) for different firing angles (α) and k values.
Figure 10 obtained from (15), with overlap angle limited
to 0°≤µ≤60°, shows the extent to which the firing angle can

be advanced beyond the normal region (inductive
commutation) as a function of DC current for different k
values. Notice that in Figs. 10 and 13 the admissible
operation region lies above the curves. Commutation cannot
occur in the region below the curves. If the load current
exceeds a minimum value, commutations can take place at
any firing angle (0<α<360°) whereby reactive power can be
consumed or supplied by the converter.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Ipu
α
k=4
k=1.001
k=1.5
k=2
k=2.5
Fig. 10. Capacitive operation (k>1) – Admissible negative firing
angle (α) versus DC current (Ipu) for different and k values.
Figure 11 shows the valve voltage waveform obtained by
computational simulation for a given firing angle and dc
current value and different k values and k=0 (inductive
commutation).
-3.0
-2.0
-1.0
0
1.0
2.0
3.0
Valvevoltage(p.u.)
k = 0
k = 1.5
k = 2.0
k = 2.5
Fig. 11. Capacitive operation (k>1) – Valve voltage waveform for
α=0°, Ipu =0.5 and different and k values.
Notice that peak voltages of the valves can substantially
exceed those for inductive commutation, particularly if
capacitor values are small in order to achieve higher
maximum firing angles. For a given capacitor value, the peak
voltages are not necessarily exceeded, provided operation is
restricted to certain range of firing angles and DC current. In
a typical specification for HVDC systems, the valve stress is
limited to approximately 110% of that of the conventional
converter [8].
B. Inductive operation (k<1).
For k<1, an increase in capacitance tends to an effective
short-circuit and operation tends to conventional inductive
commutation for k=0.
Figure 12 shows the behavior of the commutation angle µ
as a function of DC current Ipu and firing angle α for
different k values. It can be noticed that for a particular
current, the overlap angle is inversely proportional to k. Also,
the current range where commutations in both half bridges
occur independently (operation MODE 1 in Fig. 2) becomes
larger.
0
10 20
30
40 50 60 0
1
2
3
0
10
20
30
40
50
60
µ
α
Ipu
k=0.999
k=0.8
k=0.6
k=0.4
k=0.2
k=0
Fig. 12. Inductive operation (k<1) - Curve relating overlap (µ) and
firing (α) angles to DC current (Ipu) for different k values.
Figure 13 shows the DC voltage Upu versus DC current Ipu
characteristics for different firing angles α and k values.
Notice again that the presence of the capacitance C
diminishes the overlap angle µ, improving DC voltage
regulation for the same current conditions.
0
20
40
60
0
1
2
3
0
0.2
0.4
0.6
0.8
1
Upu
Ipu
α
k=0.999k=0.8
k=0.6
k=0.4k=0.2
k=0
Fig. 13. Inductive operation (k<1) - DC voltage (Upu) versus DC
current (Ipu) for different firing angles (α) and k values.
Figure 14 was obtained from (15), with overlap angle
limited to 0°≤µ≤60°. The region above the curve for a given
k defines the range of negative firing angles as a function of
DC current for which steady state operation is attainable. The
smaller the capacitance (higher k), the more commutation-
aiding voltage is produced for any given direct current.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-30
-25
-20
-15
-10
-5
0
Ipu
α
k=0.999
k=0.8
k=0.6
k=0.4
k=0.2
k=0
Fig. 14. Inductive operation (k<1) – Admissible negative firing
angle (α) versus DC current (Ipu) for different and k values.
Figure 15 shows the valve voltage waveform obtained by
computational simulation for a given firing angle and DC
current value and different k values, including k=0 (inductive
commutation).
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Valvevoltage(p.u.)
k = 0
k = 0.4
k = 0.8
Fig. 15. Inductive operation (k<1) – Valve voltage waveform for
α=0°, Ipu =0.5 and different and k values.
For k<1 the voltage stress on the valve is considerably
lower than at capacitive operation, but the capacitance values
are much higher.
VI. FINAL REMARKS
This paper presents a detailed mathematical analysis of
the fundamental behavior in steady state operation of the
bridge rectifier with series capacitances in the AC branches.
This converter operates with smaller overlap angles than
the standard inductive commutated rectifiers, improving DC
voltage regulation.
The capacitor values and DC current determine the
admissible firing angle range. The operating range can be
extended in the first and fourth quadrants by reducing
capacitor value at the expense of higher valve voltage stress.
The desired operation range must be weighted against the
necessary capacitor rating and any increased voltage stress
imposed on the valves. During transient operation conditions,
sudden changes in the firing angle can cause an appreciable
increase in the valve conduction interval. Therefore,
additional voltage limiting arresters are a required feature in
the capacitors to protect them against overcharging.
The CCC is an attractive option for HVDC systems,
where besides energy transmission, the converter has to
deliver reactive power.
REFERENCES
[1] J. Reeve, J. A. Baron, G. A. Hanley, “Technical
Assessment of Artificial Commutation of HVDC
Converters with Series Capacitors”, IEEE Transactions
on Power Apparatus and Systems, v. 87, n. 10, pp 1830-
1840, 1968.
[2] G. Möltgen, “Line Commutated Thyristor Converters”,
Siemens AG, 1972.
[3] W. Hartel, Stromrichterchaltungen, Berlin, Springer
Verlag, 1977.
[4] S. Gomes Jr., T. Jonsson, D. Menzies, R. Ljungqvist,
“Modeling Capacitor Commutated Converters in Power
System Stability Studies”, IEEE Trans. on Power
Systems, Vol. 17, No. 2, pp. 371-377, May 2002.
[5] M. Meisingset, “Application of capacitor commutated
converters in multi-infeed HVDC-schemes”, Siemens
Winnipeg, Manitoba, Canada, 2000.
[6] V. K. Sood, “HVDC and FACTS controllers”, Kluwer
Academic Publishers, Massachusetts, USA 1st
Edition,
2004.
[7] Y. Kazachkov, “Fundamentals of a Series Capacitor
Commutated HVDC Terminal”, IEEE Transactions on
Power Delivery, v. 13, n. 4, pp. 1157-1161, October 1998.
[8] W. Hammer, “Dynamic Modeling of Line and Capacitor
Commutated Converters for HVDC Power
Transmission”, Diss. Swiss. Fed. Inst. of Tech. Zurich.

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