Identification of Inactive Constraints for SCED Model Considering Uncertain Power Injection

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1 34 34 Vo.34 o.34 Dec.5, Proceens of the CSEE 2014 Chn.Soc.for Eec.En. DOI / pcsee (2014) TM (1() ) Ientfcaton of Inactve Constrants for SCED Moe Consern Uncertan Power Inecton DIG Tao 1, BO Ru 2, GUO Qna 1, SU Honbn 1, HUAG Can 3, LI Fanxn 3 (1. State Key Lab of Contro an Smuaton of Power Systems an Generaton Equpments (Dept. of Eectrca Enneern, Tsnhua Unversty), Haan Dstrct, Ben , Chna; 2. Mwest ISO, St. Pau, M 55108, USA; 3. Department of Eectrca Enneern an Computer Scence, The Unversty of Tennessee, Knoxve, T 37996, USA) ABSTRACT: Wth the constant expanson of power r, a are number of securty constrants have put tremenous chaenes to the onne economc spatch. An effcent too to emnate the nactve constrants becomes necessary for securty constrants economc spatch (SCED) n are power systems. In ths paper, consern the uncertanty of renewabe enery nteraton, a fast an effectve metho to entfy the nactve securty constrants was propose. Frsty, the efnton of uncertan nactve securty constrants an a necessary an suffcent conton to entfy those were presente respectvey. Consern the tme-consumn entfcaton, we reaxe the feasbe reon of orna SCED moe an utze reey aorthm to qucky emnate part of nactve constrants. Then another necessary an suffcent conton was propose an verfe, where the remann nactve constrants cou be entfe. Throuh the smuaton of 24-tme peros 9-bus system an 96-tme peros IEEE 118-bus system, the spee an effectveness of propose metho were verfe. Moreover, the resuts can hep spatch operators to ocate the transmsson nes wth the hhest coneston rsk. (973 )(2013CB )( ) ( ) The atona Basc Research Proram of Chna (973 Proram) (2013CB228203); atona atura Scence Founaton of Chna ( ); atona Scence Fun for Dstnushe Youn Schoars ( ). KEY WORDS: securty constrants economc spatch (SCED); nactve constrants; poyheron; reey aorthm; uncertanty IEEE [1-5] (securty constrane economc spatchsced) [1-2] [3] [4-6]

2 () () SCED L T T LT [7-8] SCED [9] [10-11] Larane [12] [13] 85% [13] [13] SCED 1 SCED SCED SCED mn T 2 { [ ap, () t bp, () t c]} (1) t1 1 a b c T P, (t) t 1 P, ( t) P, ( t), t 1,2... T (2) 1 1 P, (t) t 2 P () t P () t P (), t t 1,2... T (3), () mn,,, P mn t P t t, () 3 R ( t) P ( t) P ( t1) R ( t), t 1,2... T (4) own up,, R own () t R up () t t 4 P () t P () t P (), t 1,2... (5) L, L, L, L P L, () t ( ) L [14](5) L,, k, k, k, k L, k 1 k 1 (6) P () t G P () t H P () t P () t G,k H,k

3 P () t [ P (), t P ()], t 1,2... (7),,, [ P ( t), P ( t)] t,, / (2)(3)(4)(6)(7) (Poyheron) (7) SCED (8)(8) 1 (2) 2 (4) (3) 3 (6) 4 (7) SP MP 0 F EP F, P P P PL GP HP PL P [ P, P ] mn mn (8) 2 SCED 1 {xr n Axb} Ax b {xr n A - xb - } Ax b 1 F. 1 Defnton of certan an uncertan nactve constrant * ={xr n A - xb - A x=b } * Farkas Fourer-Monzkn [15] B- [16] [17] * * {xr n AxbA x b } 1() Z Ax Zb x y {xr n yr m Ax+BybCxy[y mn y ]} 1 Z Ax+By Zb yx, (9) - Ax+By Ax+By (9) mn yx, y yy x (9)- n x nm z(x T, y T ) T R nm (9) Z D z Π{zR nm Dzf } z A B C 0 D 0 I 0 I f b y y mn T [ ] (10) I m Zf

4 SCED (8) 3 2 (11) + (11) 2 GP HP P GP HP P (11) L, L, 2 [13] T Larane (11) P, P P, P Z G, P, H, P, 1 1 Z G, P, H, P, 1 1 s.t. (12) (13) P, P, (14) 1 1 P P P P P P mn,,, mn,,, (15) (12)(14)(15) Z (13)(15) Z 1 Z Z Z Z Z Z Z P L, Z P L, Z Z P L, Z P L, P L, Z P L, (12)(15) (12)(15) P P P P P P (12)(15) + ( P T, P T ) T ( P T, P T ) T (12)(16) (17)(13)(18) mn G, P, H, P, G, P, P, H, ( P, P, ) (16) 1 ( ) mn Z G, P, H, P, G, P, H, P, (17) 1 mn Z H, P, G, P, G, P, H, P, (18) 1 (19)(20) mn ( P, P, ) ( P, P, ) (19) 1 1 mn P, P, P, P, (20) (21) (22) P P P P P P P P mn mn,,,, mn,,,, 0 P P P 0 P P P mn,,, mn,,, + (21) (22) (23)(25)(26) Z Z (24)(26),,,, mn Q G P H P () Z Q P Z Q PL, L,

5 s.t. P, P Z G P + H P P, P,,,, 1 1 Z G P H P,,,, 1 1 (23) (24) mn P, P, P, P, (25) P P P 0 P P P mn,,, mn,,, 3.2 (26) (23)(26) [18] (23) (27) (28) P [ P, P,..., P, P,,1,2,, 1 T P, 2,..., P, ] T,1,2,, 1, 2, (27) c [ G, G,..., G, H, H,..., H ] (28) ΔP c mn P, P, c S 1, S 2,, S 2 V0 W01 mn 3 P P P S S S S,, 4V P P P W c P S S mn W 1 1 V V P S +1 3 S,, 1 1 mn Z W mn V P P P 5 ( P P V),, 1 1 W W c S 5 ( )o( ) Z Z SCED x1 [6,14] x1 2 2[6,14] 55 2 x1 [6,14] 22 x1, x1 2 [6,14] 4 x1, [0,10] x1 y 0 x1 2 2y55 2x1 y22 x1,, y x1 2 y 4 0 x1, 10, 6 y Z ( x 2 x 2 y) x1 y 14 s.t. 0 x1, 10,0 y 8 212x 2 10 x 1 4x 3 0 Z 1 24 Q Z Z Q =52<55 Z 2 38>22 Z 3 30>

6 (a) (a) 2 2 x 1 (a) 2 x (c) 2 x 1 (b) x 1 () 3 2 F. 2 Reatonshp of securty constrants an reaxe feasbe reons IEEE 9 matpower [19] ( 3) % SCED 1 20 s F. 3 Loa curve for 24 tme peros 1 (1 ) Tab. 1 Resuts wth orna transmsson capacty /s s SCED s s (t, ) t ( 3) Tab. 2 Resuts wth 0.9 transmsson capacty /s

7 Tab. 3 Tme peros an ne number n Tabe 2 (t,) (11,5); (13,5); (15,5); (16,5); 1 (17,5); (18,5); (21,5); (22,5); (23,5) (1,5); (1,3); (2,5); (2,3); (3,5); (3,3); (4,5); (4,3); (5,5); (5,3); (6,5); (6,3); (7,5); (7,3); (8,5); (8,3); (9,5); (9,3); (10,5); (10,3); 2 (11,5); (11,3); (13,5); (14,5); (14,3); (15,5); (15,3); (16,5); (16,3); (17,5); (18,5); (21,5); (22,5); (22,3); (23,5); (23,3); (24,5); (24,3) IEEE ( 4) % F. 4 Loa curve for 96 tme peros s h mn 5 20% 1 3 h ( 4 (10%) Tab. 4 Resuts wth orna transmsson capacty (10% uncertanty) (20%) Tab. 5 Resuts wth 1.1 transmsson capacty (20% uncertanty) %) mn 5 90% SCED [1] [J] E (7) Yu YxnWan JnranLü XaoyanSecurty vaue base expanson pannn of power system wth nteraton of are-scae wn power[j]scence Chna Technooca Scences (7) (n Chnese) [2] [J] (4)41-47 Sun YuanzhanWu JunL Guoeet adynamc economc spatch consern wn power penetraton base on wn spee forecastn an stochastc prorammn[j]proceens of the CSEE200929(4) 41-47(n Chnese) [3] [J]201135(2) Yan ZhennTan GuoqnA eneraton scheun

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