March 20, 1981
LIDS-P-1080
SMALL-SIGNAL CONTROL OF MULTITERMINAL DC/AC
LARGE-SCALE POWER SYSTEMS*
by
Sherman M. Chan
Norman A. Lehtomaki
Michael Athans
Room 35-308
Laboratory for Information and Decision Systems
Massachusetts Institute of Technology
Cambridge, MA 02139
*This research was supported by the U.S. Department of Energy,
Division of Electric Energy Systems, under contract DE-AC0178RA03395.
Submitted for presentation as a short paper at the 20th IEEE
Conference on Decision and Control, San Diego, CA, December
1981.
__-----_---__----_---_---____________________________________
Note: Address all correspondence to Prof. M. Athans at the
above address.
SU M MARY
The full paper will contain a progress report on the
development of a decentralized methodology for dynamic control
of
large-scale ac power networks using
networks.
multiterminal dc
The paper will update the preliminary
results
presented by the authors at the 18th CDC [1].
The paper will discuss the following key issues:
(1)
A general methodology for identifying different classes
of distributed and decentralized control
strategies for
multiterminal dc (MTDC) power networks embedded in a
large-scale ac system,
using the tools of modern multi-
variable control theory.
(2) Tradeoffs between control coordination strategies as a
function of the control objective,
sensor measurements,
and real-time communication requirements.
(3)
Issues that arise due to dynamic aggregation procedures
to obtain a simple model for control system design.
(4) The robustness properties of alternate designs evaluated
by singular value frequency-domain criteria.
The methodology and design procedures will be illustrated by
considering a 42-machine model of the Western U.S. power
system with a seven-terminal dc network configuration.
2
EXTENDED
ABSTRACT
I. BACKGROUND
Two-terminal dc systems have been used worldwide for bulk
power
transmission
and
for
stability
enhancement
[2-4].
Successful applications of two-terminal dc systems suggest
that even greater flexibility in power dispatch and enhancement in ac-system stability can be realized by a multiterminal
dc (MTDC) system where three or more dc converters are interconnected by a common dc network [5].
An MTDC network embedded in an ac system is an effective
control element for damping electromechanical oscillations
which occur between areas connected by long,
ties.
relatively weak
The controller design techniques developed for two-
terminal systems are in general not applicable to the multiterminal case; because controllers for two-terminal system are
single-input and single-output,
whereas controllers for MTDC
systems are multi-input and multi-output.
a systematic
methodology for the
synthesis of MTDC controllers.
This paper proposes
modeling,
analysis
and
The term "methodology" here
refers to a procedure that is not system specific.
Such a
general procedure is made possible by motivating the research
and interpreting the results
in terms
attributes of MTDC/ac power systems.
3
of
the physical
II.
MODELING ISSUES
The modeling requirement for MTDC/ac systems is unique in
that a global approximation of the entire interconnected power
system is required.
The proposed procedure advocates the use
of the recently developed singular perturbation techniques for
reducing a large system model to a multi-area, classicalmachine model that is small enough for contol design purposes
The general philosophy in modeling requirements and
[9].
tradeoffs will be discussed in detail
in the paper.
The
effects of model aggregation and robustness properties of the
design will also be discussed.
III. CONTROLLABILITY AND OBSERVABILITY
A physical understanding of the ac/dc power system is
facilitated by techniques of modal decomposition.
Special
methods for computing quantitative measures of controllability
and observability are developed.
A key considerations in
these computations turns out to be the scaling of the left and
right
eigenvectors.
This problem
is
solved by a "unit-
momentum" criterion which permits physical interpretation of
controllability and observability measures.
IV.
CONTROL SYSTEM SYNTHESIS
The physical insights are exploited in the controller
synthesis procedure,
resulting in an easy-to-use methodology
4
that is capable of producing a viable design within a few
iterations.
Specifically, the linear-quadratic (LQ) technique
is used for finding a first-cut design, and the LQ gain is
then used for computing output-feedback gains via a leastsquares optimization algorithm.
design
The cost functional of the LQ
is found using the modal interpretation of system
dynamics.
A method due
to
extremely useful for moving
poles) at a time.
Solheim
[10]
is
found
to be
one pole (or one pair of complex
The output approximation to the state-
feedback is done with information-structure constraints of
varying degrees of decentralization,
which require different
tactical communication requirements.
V.
NUMERICAL STUDIES
The design procedure is demonstrated on a 42-machine
representation of the Western U.S. power system.
Results show
that only certain modes of oscillation can be controlled by
the MTDC network.
scheme
In addition,
the completely decentralized
is not satisfactory in terms of performance.
The
minimum communication requirement is found to be the information on the coherent areas in the immediate vicinity of the
voltage-setting
terminal.
A
detailed
discussion
communication/performance tradeoffs will be given.
tion,
on
In addi-
the robustness characteristics quantified by singular-
value diagrams
[6-8]
in
the frequency
5
domain will be
presented.
REFERENCES
[1]
N.A. Lehtomaki, S.M. Chan, N.R. Sandell,Jr., M. Athans,
et al. "Robust
Control of Multiterminl DC/AC
Systems," Proceedins of the 18th IEEE Conference on
Decision and Control, pp. 886-896, December 1979.
[2]
F.J. Ellert and N.G. Hingarani, "HVDC for the Long Run,"
IEEE Spectrum, pp. 36-42, August 1976.
[3]
E. Rumpf, "The Operating Performance of HVDC Systems
Throughout the World during 1975-1978," Proceedings of
symposium on "Incorporating HVDC Power
the DOE
System Planning," pp. 1-23,
Transmission into
Phoenix, AZ, March 1980.
[4]
IEEE Committee Report, "Dynamnic Performance Characteristics of North America HVDC Systems for Transient and
Dynamic Stability Evaluations," paper 81 WM 083-5, presented at the IEEE PES Winter Meeting, February 1981.
[5]
J. Reeve, "Multiterminal HVDC Power Systems," IEEE Trans.
on Power Apparatus and Systems, pp. 729-737, March 1980.
[6]
J.C. Doyle, "Robustness of Multiloop Linear Feedback
Systems," Proceedings of the IEEE Conf. on pgcision and
Control, San Diego, CA, January 1979.
[7]
M.F. Barrett, "Conservatism with Sector Based Robustness
Tests," Report 79SRC90, Honeywell Systems and Research
Center, also topical report No.3 for DOE contract ET-78C-01-3391.
[8]
N.A. Lehtomaki, "Practical Robustness Measures in
Multivariable Control System Analysis," Ph.D. Thesis,
Dept. of Electrical Engineering and Computer Science,
M.I.T., 1981.
[9]
J.R. Winkleman, J.H. Chow, B.C. Bowler, B. Avramovic and
P.V. Kokotovic, "An Analysis of Interarea Damping of
Multi-Machine Systems," IEEE Trans. on Power Apparatus
and Systems, pp. 754-763, February 1981.
[10] O.A. Solheim, "Design of Optimal Control System with
Prescribed Eigenvalues," InternLational
Control, pp. 143-160, 1972.
6
Journal of