Voltage and Reactive Power Control at Distribution Substations

Transcription

1 oag a Rav Pow Coo a Dsbuo Subsaos P.Ya. EKE.F.D. JUGES Pos Gaua Poga Ea Egg Pofa Caho Uvsy of as Gas Av. Do Jos Gaspa, Bo ozo - G BRAZI F.J.A. OIEIRA A. EEK R. KOWATSCUK COPE Tassso Paaa Sa Egy Copay Rua P. Agosho, Cuba - PR BRAZI Absa: - Ths pap pss sus of sah a a povg h pfoa of voag a av pow oo a sbuo subsaos qupp wh wo- o h-wg u-oa ap hagg asfos o h bass of vopg ospog hos, agohs, a a a- oo sys. Th ps sus ov a auoa oo of asfo aps a shu apao baks sa a ow a/o voag asfo wg buss. Th objv of oog asfo aps s h obsva of sab voag vs a h ow a voag wg buss. To az ffv oo aos h opo of opos oo oos s ou o ooa qus of h ow a voag wg buss. Coog apao baks s assoa wh fuos of asssa obsvg voag qus a av pow opsao. To s paas fo oo sys ug (a bas a ays) a appoah, bas o appyg xpa sg a h o Cao suao, a a ospog opug sys a us. Th ps sus p o o pov h pfoa of voag a av pow oo povg a sab fquy of asfo ap ouaos a apao bak swhgs. Ky-Wos: - U-oa Tap Chagg Tasfos, oag Coo, Copos Coo Coos, Rav Pow Copsao, Coo Sys, Coo Sys Tug. Iouo Th sab voag vs a h ow voag wg buss of sbuo subsao asfos a by voag qus of gy osus (h sab voag vs ay aso b f by osaos of oa aag). Wh subsaos a qupp wh h-wg asfos, h sab voag vs a h voag wg buss a by h ssy of ag apab voags fo woks f by hs buss (h osaos of oa aag ay ak pa as w). Taoay, h voag vs a a f a h pag sag a ay b gv o of h foowg fos []: voag sps = f (T ) a = f (T ) p o, voag sps = f ( P ) a = f ( P ) p o av pow, a a oo s = a b P a = a b P (ahough h a woks jusfyg h uy of usg oa oo s (fo xap, []), hs s hav o fou paa appaos). Bss, h sab voag vs a ay b f as a- vaus [3]. Th sus of h pap a a a povg h sab voag vs a ( h foowg, w aayz h as of uzg hwg asfos baus h us of wowg asfos s a paua as) u ay of h o abov fos of h ao. Th ps sus a a o h ga voag a av pow oo fo subsaos qupp wh u-oa ap hagg asfos a shu apao baks sa a h ow a/o voag wg buss. Th fuo of oog asfo aps s h obsva of h sab voag vs a. Th oo of apao baks ovs fuos of asssa obsvg voag qus of h ow a voag wg buss as w as of h hgh voag wg buss a wh av pow opsao. Cosg hs, h pap sbs

2 pg hs fuos. To fuf h fuo of oog asfo aps h opo of opos (bw h ow a voag wg buss) oo oos s ou. Th ps sus hav b az wh h fawok of a a- oo sys ha s bfy sb. S voag a av pow oo s bas o usg a bas a ays, h qusos of h so a os o pov sab vs of ap ouaos a apao bak swhgs. Ahough h pap s y assoa wh voag a av pow oo a subsaos qupp wh u-oa ap hagg asfos wh shu apaos baks, s sus a asy x fo h us of oh yps of voag oo a av pow opsao qup. Coo of Tasfo Taps Cosg a paa h-wg asfo quva u [4], s possb o ps h voag a h ow voag wg bus as foows: = () wh s h voag a h hgh voag wg bus, s h voag op aog h hgh voag wg, a s h voag op aog h voag wg bus: Th voag v a h voag wg bus ay b ps as foows: = () wh s h voag op aog h voag wg. Th subsuo of () () ps o o oba h foowg oaos: a = (3) =. (4) Th oao (3) aks possb o asf ay qu of h voag wg bus o h ow voag wg bus. I s o ffu o show ha h appao of (3) povs ug o h ow voag wg bus h foowg way: ( ) ( P R Q X ( P R Q X. ) = ). (5) Appyg (4), s possb o u voag wg bus as foows: = ( P R Q X ) ( ) ( P R. Q X ) o h. (6) I (5) a (6), P a Q a asu av pow a av pow of h ow voag wg bus, P a Q a asu av pow a av pow of h voag wg bus, R a X a ssa a aa of h ow voag wg fo h ap, R a X a ssa a aa of h voag wg fo h ap, a a asu voags of h ow a voag wg buss; a a oa voags of h ow a voag wgs; s h voag of h hgh voag wg ospog o h ap. O h bass of (5), s possb o az h a of opos oo oos as foows: = α α ( ). (7) Th us of (6) as o = α α ( ). (8) I (7) a (8), α a α a h wgh faos fo h ow a voag wg buss, spvy, suh ha α α =. Th us of (7) o (8) aows fo ooag oo oos f by h qus of h ow a voag wg buss. Ths ooao ps o o a possb oaos h qus o as ujusf osaos ap hags a, hfo, o as a fquy of hs hags. Bss, h us of (7) o (8) povs h suffy o hav oy o f bus (h ow voag bus wh appyg (7) o h voag bus wh appyg (8)) wh voag asus a h possby o az voag oo wh h us of a bas a ays [5,6] h foowg way, fo xap, f h ow voag wg bus s h f o. I s possb o f a o a ba = ± (9) ±

3 a a xo a ba ± = ± () suh ha. s ous h xo a ba ±, h h ap hag us b az ay (qup suy osaos). s ous h o a ba ±, h h ssy of h ap hag s f by a y fo voag vaao. Ths y ay b f ug a sg ay T = wh s h bw wo asus of a s h ub of asus fg h uao of T. Assu ha ug T (af h asu ha xs ), h auua aa fo > s S, a h auua aa fo s S. A so fo h ap hag s a f S > S. S S, h h ap s o hag a h aayss of h y s az fo h x asu xg. A sa sagy s us f s ss ha. Th suao sus show ha hs appoah povs ovg fao of h y fo voag vaao. O of h os poa qusos opag u-oa ap hagg asfos s ug a fquy of ap hags o obsvg h aoa h v fo a gv po of o pov a opos bw voag quay a aby of asfo opao [5,6]. Thus, h pob ass o s apab obaos of,, a T, whh a paas fo ug. A appoah o sovg hs pob s os bow. Coo of Shu Capao Baks Th oo of apao baks s assoa wh fuos ha ay b ps as foows: ) asssa obsvg spf voag s a h hgh voag wg buss of asfos; ) asssa oog asfo aps o pov h sab voag vs a h as of h f ag fo h asfo ap hag; 3) av pow opsao o pov sab av pow osupo/gao vs Q a h hgh voag wg buss of asfos (hs vs ay b gv ay of h fos ha hav b os fo spfyg a ). Th oos ha a o b obsv fo ay opao of apao baks a h foowg: h, ay apao bak swhg o o swhg off us o a o voag vs, whh a hgh ha,, a a ow ha,, a p apab voag vs a h hgh,, a ow voag wg buss. Ths vs ay b gv ay of h fos ha hav b os fo spfyg a. Bow w os h agoh (Agoh ) of swhg o apao baks fo pg h fs fuo a h agoh (Agoh ) of swhg o apao baks fo pg h h fuo. Ths ho s assoa wh h fa ha h so fuo, fo h subsaa a agoh pos of vw, s os o h fs o. Agoh. A ay oo poss sp, a asu voag v of h hgh voag wg bus s opa wh., h go o opao 4; ohws go o h x opao.. I s fo a s of apao baks sa a h voag wg bus ha ay b swh o. (Th a osao of apao baks sa a h voag wg bus s assoa wh X, ha os o a o a sgfa hag of hs bus voag a, hfo, has a sa fu o h ssy of asg h ub of ap hags.) Fo ay avaab apao bak, h voag vs,, a a aua fo h ap =. <, <, a <, h hs apao bak bogs o. 3. =, h go o opao 5; ohws go o h x opao. 4. Aog apao baks bogg o, h sah s az o s h u apao bak sz ha ay opsa h vau. h s h apao bak ha ay opsa, h go o opao ; ohws go o h x opao.

4 5. I s fo a s of apao baks sa a h ow voag wg bus ha ay b swh o. Fo ay avaab apao bak, h voag vs,, a a aua fo h ap =. <, <, a <, h hs apao bak bogs o. 6. =, h go o opao 8; ohws go o h x opao. 7. Aog apao baks bogg o, h sah s az o s h u apao bak sz ha ay opsa h vau. h s h apao bak ha ay opsa, h go o opao ; ohws go o h x opao. 8. I s fo a s Υ. 9. Υ =, h go o opao 4; ohws go o h x opao.. Aog apao baks bogg o Υ, h sah s az o s h apao bak ha has h hghs fu o h voag v.. Th xuo of h fuo of auoa oo of asfo aps s susp.. Th s apao bak s swh o. 3. Th xuo of h fuo of auoa oo of asfo aps s so. 4. Th azao of h fuo s op. Th agoh of swhg off apao baks fo pg h fs fuo ay ps a aaog a. Agoh. A ay oo poss sp, h asu (o sa) av pow Q of h hgh voag wg bus s opa wh Q. h osu av pow Q < Q o h ga av pow Q > Q, h go o opao ; ohws go o h x opao.. Th agu of Q Q s aayz. Q Q s ss ha haf sz of h u apao bak sa a h voag wg bus ha ay b swh o a ss ha haf sz of h u apao bak sa a h ow voag wg bus ha ay b swh o, h go o opao ; ohws go o h x opao. j Q j 3. Capao baks Q, a, sa a h voag wg bus ha ay b swh o a o as j Q, j Q Q Q, j Q j, a apao baks Q, a, sa a h ow voag wg bus ha ay b swh o a o as Q, j Q Q Q, j. 4. I s fo a s of apao baks sa a h voag wg bus ha ay b swh o. Fo ay avaab apao bak, h voag vs,, a a aua fo h ap =. <, <, a <, h hs apao bak bogs o. 5. I s fo a s of apao baks sa a h ow voag wg bus ha ay b swh o. Fo ay avaab apao bak, h voag vs,, a a aua fo h ap =. <, <, a apao bak bogs o. 6. I s fo a s Υ. <, h hs 7. Υ =, h go o opao ; ohws go o h x opao. 8. Aog apao baks bogg o Υ, h sah s az o s h apao bak ha af swhg o as h v of av pow Q of h hgh voag wg bus, whh s oss o Q. 9. Th xuo of h fuo of auoa oo of asfo aps s susp.. Th s apao bak s swh o.. Th xuo of h fuo of auoa oo of asfo aps s so.. Th azao of h fuo s op. Th agoh of swhg off apao baks fo pg h h fuo ay ps a aaog a. Th xuo of h fuos a o oog apao baks s assoa wh h ospog o hs fuos ays T, T, a T 3. Takg o aou h ss of hs fuos, s aua o hav T < T < T. 3

5 3 Coo Sys a Tug Is Paas Th ps sus hav b az wh h fawok of h a- oo sys RPC (h bas aguag s C) a fo ao wh hawa avaab a sbuo subsaos. Th sys aows fo ay of h fos a abov fo spfyg h sab voag vs a a h ow a voag wg buss, h pssb upp,, a a ow,, a voag vs fo h hgh,, a ow voag wg buss, a h sab av pow vs Q a h hgh voag wg buss. Th sys aso ps vs spfaos fo h o a xo a bas. Fo xap, hy ay b f as aowg o as a guao pso fo h pak oa sa. Th oo sys has b s o h bass of a- aa. A ps s ou opao pa of h Paaa Sa Egy Copay. As was a abov, h obsva of h aoa fquy of ap hags s assoa wh sg apab obaos of h paas,, a T. Ths so ay b az o h bass of os ( = f,, T ) () fg h aoshp bw h ub of ap hags a h paas fo ug. Th osuo s bas o xpa sg [7]. Th objv of faoa xpa sg s o ogaz xps (wh a a sys o s o) so as o axz h aou of foao oba fo a a ub of xps wh suaousy aowg a sasa vauao of h su aby. Th xpa sg hqu s bas o vayg faos o a ub of vs. A fu faoa xp s assoa wh oug xps fo a obaos of fao vs. I s oo o us h fu faoa xp wh vayg faos o wo vs. I as h pfoa of xps a aows fo osug os of h yp: y = b b x b = < = x x b p x x x p.... () < < p I s assu ha faos a ak h u x a axu x vaus ( x x x, =,..., ) a a gv h oaz fo: x x x =, =,..., (3) x wh x =. 5( x x ) a x =. 5( x x ). I s aua ha x a x ospo o a, spvy, fo x. Usg h oaz faos, s possb o bu os y = b b x b < x x b p x x x p... (4) < < p u o () as a su of subsug (3). A ax fo h fu faoa xp wh wo faos s show Tab. Th ou wh x s ou o a osa of (4). 3 Tab. ax fo h sg Faos Fao Pou x x x x. x y - - y - - y y 3 4 y 4 Th u fo fog h fu xp as s sp: o osu h ax fo faos s ssay o us ouby h ax fo faos. I h fs as, hs ax s op by h h fao o h u v a, h so as, by h h fao o h axu v. Th xpa sg s assoa wh h op of ohogoa aays [7]. Baus h ovaa s zo aog h ffs sa, aows a p sao of ffs, a h offs of (4) ay b aua as foows: b = = x b = x x y,, =,..., ( < = y, =,...,, (5) ), (6) b = p x x xp y, =,, p =,..., ( < < p). (7)

6 Cosg ha >, aa oba h fu xp hav foao xssvss, ha aows o o bu os o h bass of so-a faoa xp. Is as a oba as a su of ug a ub of xps of h fu xp wo, fou,. s a pag ao ffs of a sgfa (fo xap, x x Tab ) by w paas. Th g ub of h pas (g) fs h xpa sg. A hqu [7] fo vauag xp sus us sg: h hoogy of spsos, h sgfa of o offs, a h o aquay. Ths sags a oo fo xps a o a syss (wh s possb o pfo paa xps h pos of a faoa spa f by ah of h xp ax). w spak abou opuaoa xps wh a o, hs usa has a sgfa pa. Fs of a, h possby o pfo paa xps as o sas of spsos of y ha a qua o zo a pos a o ssssss o s h spso hoogy. Bss, sg h sgfa of o offs a h o aquay uzs h op of pouby spso [7] assoa wh spsos of y a faoa spa pos. O way aou hs pob s os [8] a aows o o sa h pouby spso as p =. b D( y). (8) Th us of (8) aks possb o s h sgfa of offs of h o a s aquay o h bass of h Su s o a h Fsh s o, spvy [7]. Wh bug os of h yp (), ah xp s assoa wh h o Cao suao (bas o ypa o wgh ay oa uvs) of oo sys bhavo fo h obao of h u paa vs f by h ospog of h xp ax. To az pous of h o Cao suao h opug sys CSS has b vop (h bas aguag s C). Exp h us of h sys osas s ffvss fo bug os of h yp () a fo sg h paas fo ug h oo sys. 5 Couso Th pob of voag a av pow oo a subsaos qupp wh wo- o h wg u-oa ap hagg asfos has b os wh h fawok of s w sa. Th souo of h pob s bas o oug h opo of opos oo oos. Th agohs fo opag apao baks hav b aboa o p h vs fuos. Th ps sus hav b az wh h fawok of h a- oo sys. Th sys aows fo povg h pfoa voag a av pow oo, ha has b of by s sg o h bass of a- aa. To pov h sab fquy of asfo ap ouaos a apao bak swhgs h appoah (bas o xpa sg a h o Cao suao) a h ospog opug sys hav b vop o s h paas fo ug h oo sys. Rfs: [] P. Ek, F. Fa,. Popov a.w. Saga, Ipovg ffy of voag oo sbuo syss, Po. Baza Sa o E Egy Quay, 996, pp [] Yu.S. Zhzko a A.X. Xaza, Rqus o guao s a f s u hogous osu oas, Pobs of Tha Eoyas, o.64, o., 977, p.5-54 ( Russa). [3] A.. Pakhovk, P.Ya. Ek, a A.F. Boako, os a hos of Opzg a Coog os of Opao of E Pow Suppy Syss, ISDO, 994 ( Ukaa). [4] C.A. Goss, Pow Sys Aayss, Wy, 986. [5].S. Caov, og a aayss of uoa ap-hagg asfo oo syss, IEEE Tasaos o Pow Appaaus a Syss, o.3, o.7, 984, pp [6].A. kov,.i. Ihk, a.s. sv, oag Rguao Ea Pow Syss, Egoaoza, 985 ( Russa). [7] G.E.P. Box, W.G. u, a J.S. u, Sass fo Exps. A Iouo o Dsg, Daa Aayss a o Bug, Wy, 978. [8] P.Ya. Ek,.F.D. Jugs,.A.R. Gaa, a F.P.G. Paa, Fuzzy og bas appoah o voag a av pow oo pow syss, Iaoa Joua of Copu Rsah, o appa.