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Large Scale Systems Stability under Structural and Singular Perturbations pp 263ā€“359Cite as

Large-scale power systems stability

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Abbreviations

N:

number of system's generators (or machines)

n, n=Nāˆ’1:

contrary to the previous chapters n does not denote here the dimension of system's state

Aij=EjEjYij Di :

mechanical damping coefficient of i-th generator

Dij :

electromagnetic damping coefficient between i-th and j-th generators

Ei :

modulus of i-th generator's internal electromotive force (voltage)

ki=M āˆ’1i Mi :

inertia coefficient of i-th generator

Pmi :

mechanical power delivered to the i-th generator from its turbine

Pei :

electrical power delivered by the i-th generator to the network

pmi :

variation of the mechanical power of i-th generator

P omi :

steady state value of Pmi

P omi :

steady state value of Pmi

Pi=Pmiāˆ’P omi PiN=Piāˆ’PN Y:

admittance matrix of the network reduced at the internal generator nodes

Yij Ī±iĪ¼ āˆ’1i :

modulus of the ij-th element of Y; Yij =Yji gain of the first order proportional regulator of i-th generator

\(\Gamma _i = \lambda _i + \lambda _{Ni} + \sum\limits_{\begin{array}{*{20}c}{j = 1} \\{j \ne 1} \\\end{array} }^n {\lambda _{ij} }\) :

rotor angle of i-th generator relative to a reference

Ī“ij=Ī“iāˆ’Ī“j Ī“ oi :

the equilibrium under consideration of i-th generator

Ī“ oiN Īøji Ī»i=DiM āˆ’1i :

value of Ī“iN at the equilibrium state argument of the ij-th element of Y; Īøij=Īøji if Ī»i=Ī», constant for i=1,2,...N, one speaks of

Ī»:

ā€œuniformā€ (mechanical) damping

Ī»ij=DijM āˆ’1i Ī›ij=Ī»ijāˆ’Ī»Nj āˆ‡i=1,2,...,n Ī›Ni=Ī»Nāˆ’Ī»i+Ī»iN Ī¼ āˆ’1i :

time constant of the first order proportional speed regulator of i-th generator

ĻƒiN=Ī“iNāˆ’Ī“ oiN Ļƒij=ĻƒiNāˆ’ĻƒjN Ī©i :

rotor speed of i-th generator above the synchronous speed: \(\Omega _i = \dot \delta _i\)

Ī© oi :

the value of Ī©i at the steady state operation called ā€œequilibrium stateā€

Ī©ij=Ī©iāˆ’Ī©j Ļ‰i=Ī©iāˆ’Ī© oi Ļ‰ij=Ļ‰iāˆ’Ļ‰j Ī“, Ļƒ, Ī© (Ī“, Ī©):

without subscript these letters denote vectors state vector with variables Ī“i, Ī©i, i=1,2,...,n

(Ī“ S, 0):

value of the state vector at the SEP

(Ī“ ui, 0):

value of the state vector at the i-th UEP

CCT or tc :

Critical Clearing Time

COA:

Center Of Angles

SEP:

Stable Equilibrium Point of the system in its post-fault configuration

UEP:

Unstable Equilibrium Point surrounding SEP

SDE:

Stability Domain Estimate

PSDE:

Practical SDE

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(1987). Large-scale power systems stability. In: Grujić, L.T., Martynyuk, A.A., Ribbens-Pavella, M. (eds) Large Scale Systems Stability under Structural and Singular Perturbations. Lecture Notes in Control and Information Sciences, vol 92. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006855

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