Kl. Praprost et Ka. Loparo, A STABILITY THEORY FOR CONSTRAINED DYNAMIC-SYSTEMS WITH APPLICATIONS TO ELECTRIC-POWER SYSTEMS, IEEE transactions on automatic control, 41(11), 1996, pp. 1605-1617
Citations number
20
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control","Engineering, Eletrical & Electronic
This paper develops a stability theory for constrained dynamic systems
which are defined as dynamic systems whose state trajectories are res
tricted to a particular set within the state space called the feasible
operating region, Many physical systems may be modeled as constrained
dynamic systems because certain variables or functions of variables a
re often required to remain within acceptable ranges, A restricted sta
bility region for constrained systems is defined as the set of points
whose trajectories start and remain within the feasible operating regi
on for all t greater than or equal to 0. The stability analysis is res
tricted to this region as trajectories hitting the boundary are infeas
ible and considered to be unstable, We also define the restricted asym
ptotic stability region ol restricted domain of attraction as the set
of points whose trajectories start and remain within the feasible oper
ating region for all t greater than or equal to 0 and converge to the
stable equilibrium point as t --> infinity. In [4]-[6], Venkatasubrama
nian et nl, characterized the stability boundary for differential-alge
braic-equation (DAE) systems which are dynamic systems with algebraic
equality constraints, In [8], we used their results and some results f
rom bifurcation theory to show that for DAE systems, parts of the stab
ility boundary are formed by trajectories that are tangent to the boun
dary of the solution sheet on which the algebraic equations have a uni
que solution, In this paper, using similar techniques as contained in
[4], we develop stability results for systems that are constrained to
remain within a subset of the state space (i.e., the feasible operatin
g region), This modeling framework is particularly useful for represen
ting systems with inequality constraints, Also, for systems with equal
ity constraints, we can develop an approximate model that is arbitrari
ly close to the original system, The main theoretical result of this p
aper is a characterization of the boundary of the restricted asymptoti
c stability region (i.e., quasistability boundary), Specifically, me s
how that the quasistability boundary includes trajectories that are ta
ngent to the boundary of the feasible operating region, Our primary ap
plication of these results is analyzing electric power system stabilit
y following the occurrence of a network fault, We assume that the elec
tric power protection system operates to clear the fault condition but
that the post-fault trajectories should remain within the feasible op
erating region of the new system configuration, A computational proced
ure was developed in [8] to estimate the critical clearing time for a
network fault based on the tangent trajectory results, This method is
also extended in this paper to include the more general constrained dy
namic system representation, An example is then included to illustrate
the use of this computational method in estimating the critical clear
ing time for a network fault.