28-06-2013, 03:21 PM
EIGEN VALUE TECHNIQUES FOR SMALL SIGNAL STABILITY ANALYSIS IN POWER SYSTEM STABILITY
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ABSTRACT
Many advanced techniques are being developed for Power Systems Stability Assessment. We can use
Eigen value techniques for the purpose of increasing the calculation performance of eigen-algorithms for
Power System Small Signal Stability Analysis.
Firstly, we introduce a bulge chasing algorithm called the BR algorithm which is a novel and
efficient method to find all Eigen values of upper Hessenberg matrices and has never been applied to eigenanalysis
for power system small signal stability analysis. This paper analyzes differences between the BR
and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and
storage requirement on the basis of Eigen –value calculation.
Secondly, we propose a method of small-signal stability analysis of power systems with
microgrids which is based on the development of an integrated model in quadratic form and subsequent
development of the transition matrix of the overall system. The Eigen values of the transition matrix
provide the small-signal stability properties of the system.
INTRODUCTION
Small signal stability analysis in power
systems is aimed at determining the properties of
operation parameter variations that are
independent from disturbance intensity. Eigen
value analysis is used to reveal the quantitative
information of different stability modes for
power system small signal stability problems. To
find efficient algorithms with excellent
convergence properties and appropriate
calculation precision, while using less storage
space and less computational time, has been one
of major objectives of Eigen value analysis
research for small signal stability analysis.
Methods for Eigen value analysis in power
system small signal stability include complete
Eigen analysis and partial Eigen analysis.
Matrix Storage Space Requirements
The overall Matrix storage space
requirement of the QR algorithm is determined
by the summation of the space to save full
Hessenberg matrices (n×n) and the space to save
real and imaginary parts of calculated eigen
values (2×n) during two subroutines. Storage
space required in the subroutine of forming
upper Hessenberg matrices is (n×n+n×n).
Storage space required for eigenvalue calculation
is (n×n+2×n).
DER Model
The interaction of the utility system and
DERs is rather complex because DERs are
interfaced to the grid via various types of power
electronic converters. Furthermore, each
manufacturer uses proprietary converter designs.
For the purposes of this paper we used a generic
converter model, which is illustrated in Figure 4.
The converter consists of three PWM voltage
sourced converters, one for each phase. It is
connected to the utility system via a three-phase
transformer. The secondary of the transformer
can be wye-connected or delta-connected [25]-
[27].
CONCLUSION
The performance of the BR algorithm is
compared with that of the QR algorithm for
power system small signal stability Eigen value
analysis. An improvement of 30%–60% in CPU
time and up a factor of over 100 in matrix
storage space in terms of required storage space
is achieved by the BR algorithm compared with
the QR algorithm. The calculation results from
numerical experiments demonstrate that the BR
algorithm is an efficient algorithm and a more
powerful tool than the QR algorithm in eigenvalue
analysis of large-scale power systems.