1926
IEEE
Transactions on Power Delivery,
Vol.
8,
No.
4,
October
1993
EXPANDABLE MULTITERMINAL
DC
SYSTEMS
BASED
ON
VOLTAGE
DROOP
B.K.
Johnson
R.H.
Lasseter F.L. Alvarado
R.
Adapa
Member Fellow Senior Member Senior Member
University
of
Idaho University
of
Wisconsin-Madison
EPRI
Abstract
This paper introduces a decentralized control scheme
for the parallel connection of multiple rectifiers feeding
a dc network with numerous inverters. The coordina-
tion of multiple HVdc systems without explicit commu-
nication is accomplished by the use of dc-side voltages
as
a
“droop” mechanism. The dc side voltage serves
the role of frequency in an ordinary ac system. The
approach is most suitable to superconducting dc sys-
tems and to dc systems that span small distances and
where voltage is relatively uniform throughout the dc
system. This paper presents the concept in the context
of a high capacity superconducting
10
KV
urban infeed.
Keywords: Superconducting power transmission, Power
distribution, High power converters.
INTRODUCTION
Multiterminal HVdc (MTdc) systems use extensions
of the techniques from two terminal systems. These
techniques assume several control modes (loops) at each
converter, with logic which decides between modes.
Typical operating modes found in two terminal systems
include control of dc voltage, dc current, extinction an-
gle, firing angle and
a
voltage dependent current limit.
The transition and set point of each control mode is
tightly coordinated with the other converter and its
control action.
As
these concepts are extended to multi-
terminal systems, the complexity becomes excessive. A
five terminal system with two control modes per termi-
nal has thirty two possible states of control.
For
three
control modes per terminal, there are over
200
oper-
ating states possible. If we add contingencies for loss
of
one terminal, additional complexity is added to the
design of the controls.
It is difficult to build multiterminal systems with
93
WM
070-3 PWRD
A
paper recommended and approved
by the IEEE Transmission and Distribution Committee
of the IEEE Power Engineering Society for presenta-
tion at the IEEE/PES 1993 Winter Meeting, Columbus,
OH,
January 31
-
February
5,
1993. Manuscript sub-
mitted September
1,
1992; made available for printing
December
14,
1992.
more than five terminals. ‘The most complex systems
in operation today use only three terminals.
This is
in conflict with the desire to have small “off-the-shelf”
converters which could be added to a system
as
load
growth requires. This could involve hundreds of small
converters at greatly reduced cost per
KW.
To design
such systems the tight coordination between controls on
different converters must be broken without reliance on
fast communications. Instead of using methods devel-
oped for point-to-point HVdc control, the paradigms of
the ac system are more useful. Traditional ac systems
have used to advantage the natural variability of de-
mand with frequency and voltage. The supply system
is designed, by means of the notion of droop, to per-
mit the balancing of demand with supply at all times.
Surely, control center regulation and economic. dispatch
are important to the efficient operation of the system,
but the system is inherently stable without reliance on
communications
[l,
2,
31.
This paper introduces
a
sim-
ilar notion for certain multi-terminal dc systems: those
that are tightly coupled electrically. The ideal situa-
tion is a lossless dc system, whether meshed
or
not.
The primary emphasis of this paper is on the use of a
superconducting low voltage dc system. The concept
is simple: all of the terminals in a superconducting dc
transmission system reach equal steady-state voltages
since there is no resistive voltage drop in
a
supercon-
ductor. Changes in dc voltage propagate throughout
the dc system, and can be used for control in a fashion
similar to the we of change in frequency on ac systems.
One advantage of this approach
is
its expandabil-
ity: inverters can be added at arbitrary locations. The
concept appears most suitable initially for use in high
capacity urban infeeds where modularity is important.
LVDC TRANSMISSION SYSTEMS
The elimination of resistive losses in superconducting
cables allows the use of low voltage/high current trans-
mission. A transmission system can operate at a single
voltage level from generator to distribution. This elim-
inates
or
reduces the need for transformers. Low volt-
age levels reduce dielectric losses and insulation costs
[4].
All superconductors, particularly high tempera-
ture superconductors, experience ac losses. This sug-
gests that dc transmission may be advantageous. Ad-
0885-8977193/$03.00
Q
1993
IEEE
1927
vantages of dc must be balanced against an additional
cost for power conversion and the potential complexity
of multi-converter systems. Superconducting dc trans-
mission require smaller cables and less refrigeration
as
a result of lower losses. A dc system experiences losses
within converters and harmonic losses within cables.
The evolution of dc systems has been hampered by
the difficulties associated with multi-converter config-
urations. Initial application of superconducting low
voltage dc (LVdc) systems will probably begin with
point to point dc systems. Using the ideas in this pa-
per, these systems can be expanded by adding paral-
lel taps
for
additional rectifier and inverter terminals.
The low voltage level allows for simple modular con-
verters. The voltage level can be on the order
of
10
kV, eliminating the need for series connection of devices
within converters. Simple six-pulse modules could be
connected in parallel to achieve a desired current rat-
ing. This suggests
a
system with a large number of
“off
the shelf’’ mass produced converter modules. A
typical LVdc transmission system could consist of nu-
merous rectifiers feeding hundreds of inverter terminals.
The LVdc system could continue to grow through the
addition of terminals and lines, forming
a
dc mesh for
increased transmission reliability.
For
more details on
the concept of superconducting meshed systems, refer
to
[SI.
MTDC SYSTEMS
Traditional control schemes for multiterminal HVdc
(MTdc) systems are extensions
of
the point to point
HVdc system control concepts, which are based on the
notion of control modes
[7].
The basic control scheme
regulates the mesh voltage level at one converter termi-
nal, and operates the remaining terminals in a current
regulation mode. The terminal regulating voltage is
unable to control its local current. Its current is deter-
mined by the current demands of other converter termi-
nals. This is undesirable for an inverter that is sched-
uled to supply
a
mostly passive load system. There-
fore, voltage control during normal operation is limited
to rectifiers. The current limits of the voltage regu-
lating converter can create problems during transients.
Many implementations of this basic scheme depend on
the presence of
a
central controller to balance current
orders between converters. This requires fast commu-
nication to coordinate currents during a disturbance
[8,
9,
10, 111.
A
scheme with the ability to coordi-
nate control without fast communication was proposed
by Lasseter, Krueger, and Povh
[12].
Schemes for con-
trolling a mesh connected multiterminal HVdc systems
run into difficulty when one of the converters reaches a
current limit. The voltage regulating converter changes
to current regulation mode. One of the other converters
must then regulate dc voltage. The scheme described in
[12]
is able to change modes through an intricate design
of the control characteristics
This approach to control results in a complicated and
carefully customized overall control scheme for a large
system. It becomes increasingly difficult to determine
which converter should assume voltage regulation fol-
lowing mode changes
as
system size increases.
A
desirable multi-converter dc system could have
multiple dispersed rectifiers feeding an arbitrary num-
ber of inverters. The control scheme
for
such a system
must be able to handle converter limits without fast
communication or intricate mode switching. The con-
trol scheme must be general rather than tailored to a
specific system layout. This will make the system sim-
pler to expand.
Regulating the mesh voltage at a single terminal is
undesirable. A more effective scheme is to operate all
of the rectifier terminals in a joint voltage regulation
mode. The overall control system must be designed to
respond properly to faults and disturbances. The key is
for the system to be able to maintain stable operation
in the face of disturbances without reliance on commu-
nications among converters, even it this operating point
is suboptimal. The system can then be moved to
a
bet-
ter operating point with communications. The control
system must be designed to provide damping to the dc
system, since there is little inherent damping provided
by the cables.
Superconducting cables change several key system
characteristics, and have a major impact on control
op
tions. There is no longer a current dependent dc voltage
drop. Voltage regulation sets
a
single voltage level for
all the terminals. Also, cables have
a
self-protective
nature: large overcurrents cause the superconductive
cables to quench,
so
they no longer operate in
a
zero
resistance, superconducting state.
DC
VOLTAGE
DROOP CONTROL
A
distributed voltage regulation scheme must main-
tain consistent sharing of current between the rectifiers.
A
useful analogy is the use of frequency droop to pro-
vide natural regulation characteristics for all generators
in the system.
A
sloping power versus frequency natu-
ral regulation characteristic is used for each generator
to regulate the initial distribution of real power among
generators. This scheme uses a change
in
frequency
as
a
signal for the control system to meet changes in power
demand. Natural regulation requires no communica-
tions, and it is followed by load-frequency control which
refers to automatic means of regulation responsive to
frequency, tie flows and other system variables
[2].
A voltage droop scheme can be implemented for or-
dinary dc systems, but it is easier to implement for
a superconducting system. Each of the nodes on the
dc system reaches the same steady-state voltage level.
Thus, it is possible to use the voltage on the dc system
as
a signal. This is the key concept in this paper.
1928
The analogy to generators is not perfect. The control
of ac voltage provided by generators has no counterpart
in the regulation of the dc mesh, since reactive power
is not
a
valid concept for the dc network. Voltage re-
places frequency
as
a system-wide signal, and there is
no second quantity that needs regulation.
Built-in rectifier droop
Each line commutated rectifier bridge has a current
dependent voltage drop due to commutation overlap.
This can be modeled
as
a
resistance in steady-state
converter models
[5].
Rectifier operation in a constant
firing angle mode can be modeled
as
a
voltage source
connected to the mesh through
a
resistance. Thus, line
commutated rectifiers have a “built-in” droop. Changes
in the current drawn off of the rectifiers alter the volt-
age drop across the resistance. The change in current
divides between several rectifier terminals according to
their equivalent resistances via current division. The
system will settle into
a
new steady-state at a different
voltage level following
a
change in total current.
The system response to changes in current demand
is similar to that with frequency droop on ac systems.
This can be demonstrated for a system with three par-
allel connected rectifier bridges. Figure
1
shows a sim-
plified model for three rectifiers feeding
a
dc system rep-
resented
as
a
variable current load. Each of the three
rectifiers features identical droop resistances. The dis-
tribution
of
a
change in current between the rectifiers
is based on
a
simple resistive current divider. This is
demonstrated in equations
1
and
2.
This representa-
tion is sufficient for observing steady
state
operating
points. All of the nodes reach equal steady state op-
erating voltages. This is not adequate for representing
the dynamics of the changes because the dc system isn’t
included. The RL time constant between the slope of
the droop characteristic, and the inductance in the path
between a given rectifier and the inverter that changed
its current demand affects the response.
Alto,
=
AZ,
+
AZ2
+
AZ3
The system begins in an initial state with each rec-
tifier supplying
7000A
to the mesh at
7500V,
shown
as
operating point A of Figure
2.
The total current drawn
by the dc system is then decreased by
3kA.
The system
operating voltage increases
as
the current is decreases,
Fig.
1:
Simplified Equivalent
of dc
System Fed
by
Three Rectifiers
shown
as
point
B
on the figure, where each of the rec-
tifiers supplies
6kA.
Operating point C on Figure
2
shows
a
case where
rectifier
3
shuts down. The other two rectifiers pick up
the load supplied by that rectifier, increasing their cur-
rents to
9kA.
A
well designed system will have sufficient
excess capacity in the rectifier terminals to operate with
any one of the terminals out of service.
Dynamics
of
droop control
The built-in droop for
a
large rectifier is quite small.
It takes a large change in current to change the mesh
voltage level significantly. This is desirable for normal
operation since it will result in a relatively constant dc
voltage level. This makes it simpler to regulate power
at the inverters.
changes in current bring the generators to their
MVA
limits without a significant change in the mesh voltage.
Large changes in the dc voltage can be used to trigger
load shedding at the inverters. In such
a
case a steeper
slope on the droop characteristic would be desirable.
This would allow more ability for the inverters to help
the system reach
a
stable point.
The built in droop on each rectifier terminal has some
disadvantages. The relative slopes of individual droop
characteristics are fixed by the physical parameters of
the generator
or
transformer connected to each rectifier.
This may result in a case where a small rectifier will
have flatter characteristics than a large rectifier, and
will pick up a greater share of the current swings. This
is desirable only if large rectifier terminals are treated
as
the “base loaded rectifiers.”
The slope of the droop of each of the rectifier ter-
minals can be adjusted dynamically. The firing angle
of the rectifier can be varied to give the effect of an
additional resistance,
K,,
appearing
as:
However, it also means that large
,
This provides the ability compute the trajectory of
(Y
to give
a
desired droop. The new firing angle is cal-
culated through the series of steps shown in equations
4
and
5,
where
Vdes
is the desired dc voltage for a given
1929
5
a
7
6
5
Fig.
2:
Example
of
the
dc
Droop
Scheme
for
the
Sys-
tem
of
Figure
1
current level, and
Vest
is an fictitious voltage source
used to get the controlled characteristic to intersect the
characteristic of the built- in droop
at
a
selected point.
Thus,
(Y
can be computed to make the rectifier appear
to have
a
different, or even variable commutation drop.
Vdes
4-
Rc
*
Idc
vdo
cos((Y)
=
(5)
Inverter
droop
and load shedding
The inverters can feed either passive loads
or
an
ac system that must maintain synchronism with other
parts of the system (there may be
a
parallel ac path).
In either case, it is possible to adjust inverters to control
both ac voltage and ac frequency (which in the case of a
synchronously connected system should actually trans-
late into a phase angle control, not frequency control).
The frequency
or.
phase signal of the inverters may be
derived from a power or current setpoint established for
the inverters. It is well known that most loads are sen-
sitive to both voltage and frequency.
It is possible to
carry out the concept of droop one step further, and
use the voltage at the dc side of the inverters
as
a sig-
nal to the inverter to adjust its ac-side load to some ex-
tent by adjusting either its voltage or its frequency (or
phase angle), or
a
combination of the two. In this way,
a certain measure of demand control is exercised auto-
matically, precisely
as
is the case in an ordinary ac-only
power system, but this time using the dc side voltage
as
a surrogate for the ac frequency signal. This slight
demand control based on dc voltage helps stabilize the
system:
as
the voltage increases due to a reduction in
power demand somewhere in the system, not only do
the rectifiers reduce their power output, but also the
inverters increase theirs, and vice-versa.
In more extreme contingency and outage cases, sim-
ple inverter droop may not be sufficient to stabilize the
system. In these cases it is possible to design specific in-
verter characteristics intended to produce selective load
shedding. If the inverters adjust their phase based on
a preset power order,
a
fall in dc mesh voltage level
requires the inverters to increase their dc current in or-
der to continue to supply constant power to their loads.
This increase in current may cause the dc voltage to fall
further, and can lead to system collapse.
This problem can be avoided by adding a voltage de-
pendent current limit
for
the inverters. Figure
3
shows
a typical inverter characteristic with the inverter regu-
lating power for
V&
>
VDC,;,,
and then entering
a
VD-
COL
mode below this voltage. This limit is designed
such that the current drawn by the inverter will reach
zero at a set level.
This control results in the system reaching a new
steady state where none of the inverters is able to reach
its current
or
power setpoint, but it does keep the sys
tem in operation. This type of forced load shedding
on the part of the inverters would allow the system to
recover from the loss of
a
one
or
more generators or
rectifiers without the need for total shut down. This
feature of inverter operation provides an additional, al-
beit somewhat more drastic, droop characteristic to the
system similar to underfrequency load shedding in ac
systems. The set points
of
the inverters can be ad-
justed in an automated manner by a central control
US-
ing communications,
as
is now the case with automatic
generation control. A high priority load will have lit-
tle loss in current
as
the dc voltage falls, while a low
priority load could shut down after
a
small voltage sag.
Rectifier limits
The rectifier operates in an
am;,,
mode for much of
its normal operating range. Large increases in cur-
rent cause the rectifier to hit limits
[13].
The rectifiers
must be operated to have sufficient reserve capability,
so
that the loss of a single rectifier permits the uninter-
rupted operation of the system after the droop controls
make the system settle into a new steady-state operat-
ing
point.
In the examples below, the rectifier remains
at
a,;,,
until the rectifier current reaches
1.3
per unit. At this
point it enters a mode where the slope of the droop
characteristic changes. The slope is adjusted
so
that the
1930
Rectifier
2
Rectifier
3
Inverter
1
Inverter
2
Inverter
3
VDC
105 MW
7
kA
a
=
5O
105 MW
7
kA
cy
=
5O
75 MW 5
kA 7
=
25"
105
MW
7
kA
7
=
25'
135 MW 9
kA
Y
=
25'
Control
IDC
Redifier Inverter
Fig.
3:
Complete Rectifier Control Characteristic
VDCOL
Fig.
4:
Superconducting Point to Point System with
Parallel Taps
dc voltage level falls to
0.85
per unit when the current
reaches
1.6
per unit. The rectifier then enters a current
control mode to maintain the current level at
1.6
per
unit. The rectifier enters a voltage dependent current
order limit (VDCOL) mode if the dc voltage level con-
tinues to fall. This allows the rectifier to starve the fault
by increasing its firing angle to
90".
Figure
3
shows the
complete control characteristic of the rectifier.
The boundaries where the rectifiers switch modes are
consistent among all rectifiers. This scheme has no dif-
ficulties if there are slight errors between the transi-
tions of different rectifiers, since there is always
at
least
one rectifier in voltage control mode. If one converter
changes modes, it changes the current sharing ratio be-
tween the other rectifiers, but the system remains
sta-
ble. The inverters enters a voltage control mode when
the rectifiers enter the controlled droop mode.
STUDY SYSTEM RESULTS
Assume a superconducting urban infeed based on a
high current, low voltage dc line with parallel connected
rectifier and inverter terminals. Figure
4
shows the con-
figuration of such
a
system. The system is build around
a
152
km dc line, with parallel rectifier taps at
20
km
and
50
km. There are also two parallel inverter taps at
110
km and
135
km. Table
1
provides details.
This system can be further expanded through the
addition of parallel taps on the dc line. The converter
IConverter
I
Power ICurrentI Firing
I
I
Rating
I
Rating
I
Angle
Rectifier
1 I105 MW
I
7
kA I
Q
=
5"
Table
1:
Converter Terminal Ratings for
6
Terminal dc
System
settings need not be changed, although adding inverter
terminals may tax the rectifier current limits.
System model
Each of the inverter terminals is assumed to be con-
nected to an ac system represented by an infinite bus.
The inverters are connected to an ideal three phase volt-
age source through
a
Y-Y
transformer.
The line commutated CSI's are all represented by de-
tailed models. The inverters operate in current control
mode until the voltage falls below
0.95
per unit. They
then enter a VDCOL mode, and shut down when the
voltage reaches
0.85
per unit. The mesh is represented
using lumped inductor models to represent the cables.
There are no circuit breakers or other protective devices
used on the dc system.
Loss
of
a Rectifier Terminal
The first case simulates rectifier
1
shutdown and
restart. Upon initial startup all three rectifiers ap-
proach
7000A.
The rectifier currents are shown in Fig-
ure
5(a). The inverter currents are shown in Figure
5(b).
The voltage falls far enough to cause the invert-
ers to enter their VDCOL modes, and fail to meet their
current setpoints while rectifier
1
is
off.
Figure
5(c)
shows the dc voltage levels. The plot shows both the
actual dc voltage and the average voltage level. The
voltage falls
as
the remaining recitifiers increase their
currents to replace the inverter that shuts down.
Inverter Startup Followed
by
dc
Fault
The next case looks at the startup of inverter
3,
fol-
lowed by a resistive fault (with
Rf
=
0.lQ)
near in-
verter
2.
This resistance shows
a
worst case operating
point for the rectifiers. The fault voltage moves the
rectifiers into their current limit control modes, but is
high enough to keep them from entering their VDCOL
modes. Figure 6(a) shows the rectifier currents. The
first increase is due to the startup of the inverter. They
later increase further, and settle into
a
new operating
point. This is because the rectifiers are in the max-
imum current mode rather than the VDCOL. Figure
6(b) shows the inverter currents. The current for in-
verter
3
increases, and then all of the currents go to