Robust Nonlinear Excitation Control Based on A Novel Adaptive
Back-stepping Design for Power Systems



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INTRODUCTION

Excitation control of power systems is a very important,
effective and economic method in improving stability.
Recently, advanced nonlinear control techniques have been
used in the excitation control of power system [1-11], such
as nonlinear geometric theory [1,2], direct feedback linearization
[3-6], sliding-mode control [7], intelligent control
[8], back-stepping [9-11], in order to overcome the disadvantages
of controllers by using linear control theory and
linearized model around an operating point in the case of
large uncertainties. A most successful nonlinear excitation
scheme is based on the direct feedback linearization [3-6]. It
was shown in the literatures that the dynamics of the power
system can be exactly linearized by employing nonlinear
pre-compensation so that linear control theory can be used
while preserving the nonlinearities, however, this method
requires the exact model of system and cancels useful
nonlinearities, so it will be not effective in the setting where
there are some unknown parameters in the mathematical
models of systems.


THE EXTENDED ALGORITHM

This section extends the adaptive back-stepping method
[12] which is for systems in so-called parametric feedback
to a general form whose “virtual” control parameters are
functions of system feedback states.


EXCITATION CONTROL OF POWER SYSTEMS

In this section, we apply the proposed method to the
stabilization of excitation systems where the damping coefficient
can not be measured accurately [10]. Note that the
mechanical input power Pm is treated as a constant in our
design of excitation control, i. e. , it is assumed that the
governor action is slow enough not to have any significant
impact on the machine dynamics.


SIMULATION RESULTS

The system under study is shown in Fig. 1 (there is an
equivalence relationship between E
q and Pe), and the data
of the system are given in Appendix A. Suppose the related
variables in feedback law are available by estimation and
measurement [14]. In order to investigate the effectiveness
of the proposed controller, we will make comparisons with
the classical adaptive back-stepping controller and fullinformation
controller, which is obtained by assuming the
parameters are known and applying standard back-stepping
from [16]. The classical adaptive back-stepping controller
derived by the adaptive back-stepping method from [17] or
[18] is given in Appendix B.


CONCLUSION
The main contributions of this paper are extension of a
novel adaptive back-stepping algorithm to a general case
and its application to excitation control of single machine
infinite bus systems to improve performances of system responses
and parameter estimation. Simulation results compared
with the classical back-stepping and full-information
schemes show that the validation of the extension and
superiority of the proposed controller for excitation systems.
This method can be easily applied to multi-machine systems
to realize the decentralized control. Further researches will
be devoted to extend this algorithm to systems with more
general unknown parameters and disturbance.