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The Q-mismatches a r e c a l c u l a t e d e x a c t l y f o r t h e b u s e s s i t u a t e d i n t h e v i c i n i t y o f t h e o u t a g e d element and a p p r o x i m a t i v e l y f o r t h e b u s e s t h a t are e l e c t r i c a l l y away from t h e p e r t u r b a t i o n . I n t h i s s t e p , t h e c o n v e r g e n c e r a t e o f i n d i v i d u a l nodes o u t s i d e t h e p e r t u r b a t i o n a r e a i s e x p l o i t e d a n d t h e small Q-mismatches a r e z e r o e d . 2 ) It u s e s t h e e l e c t r i c a l d i s t a n c e c o n c e p t [ l ] t o p r e d i c t t h e b u s e s on which m a j o r v o l t a g e s h i f t s c a n o c c u r a f t e r t h e c o n t i n g e n c y . C o m p u t a t i o n a l e f f o r t s a r e s a v e d u s i n g t h e a p p r o x i m a t e Q-mismatch c a l c u l a t i o n s a n d by u s i n g t h e s p a r s e v e c t o r t e c h n i q u e s f o r t h e n o n -z e r o m i s m a t c h e s ( F a s t Forward/Back s o l u t i o n s ) . The number of b u s v o l t a g e s t o b e s o l v e d i s d r a s t i c a l l y reduced and t h e a c c u r a c y o f t h e s o l u t i o n remains good .R e s u l t s of t e s t s w i t h a 2 0 6 buses-299 b r a n c h e s o f 400 kV r e d u c e d French network a r e g i v e n t o i l l u s t r a t e t h e performance o f t h e method. Kev

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LEG-ENSIEG (C.N.R.S. UA-355) Domainc Univcrsitairc, J3p 46, 38102 Saint Martin d'Ilbcs Ccdcx -FRANCE AIWI'RACT -This paper presents two methods to dctcriiiine a niimimum load to be shcd using lincar programming to avoid risks of voltage instability. The aini of calculations is to minimizc the load to be shed in ordcr to assure that cithcr voltage profile is maintaincd within ncccssary boundaries. or indicators of voltage instability are lower than or equal to a threshold value. Variables of thcse methods aria real and reactive powcrs to be shcd. Thc first method uscs sensitivities with constraints of voltagcs (Vmill 5 V < Vmax). In this inethod. hcse constraints are formcd locally. Thc sccond method uses indicators of voltage instability with coristraints of indicators (0 5 I3 5 nthr=ho)d). In ordcr to dcvclop such a sccond method in a timcly fashion, indicators arc developed to assess tlic risk of voltage collapse at a particular bus, and a scnsitivity matrix coup1ir.g the amount of load to be slicd and the indicator is computed. The advantages of thc proposed methods arc viable network security, short computing times and low memory requirements due to the use of sparse vector tcchniqucs. The methods dcvelopcd have been tcstcd with tlic 30 bus New-England test systcm and with a 206 bus 400 kV simplificd Frcnch nictwork with satisfactory results.