14 7 2010 7 ELECTRI C MACHINES AND CONTROL Vol. 14 No. 7 July 2010 1 1 1 2 2 1. 200240 2. 200122 IEEE - 30 TM 731 A 1007-449X 2010 07-0041- 07 Active / reactive power coordinated optimization in power systems comprehensive energy saving SUN Wei-qing 1 WANG Cheng-min 1 ZHANG Yan 1 YU Guo-qin 2 ZHU Da-kang 2 1. School of Electronic Information and Electrical Engineering Shanghai Jiaotong University Shanghai 200240 China 2. Shanghai Municipal Electric Power Company Shanghai 200122 China Abstract Considering limitation of optimizing active and reactive power flow separately it established an active /reactive power coordinated optimization model of comprehensive energy saving in power systems and distributed the network active power losses to generators optimally to minimize the total generation cost. Made converged control variables to optimal solution domain rapidly using gradient method and treated node voltage and branch flow violations using node type conversion and branch type conversion respectively. Once the active inequality constraint set was basically defined in optimal solution domain used Newton method to gain the exact optimal solution. Thus avoided calculation efficiency problem caused by frequent adjustment of active inequality constraint set in Newton method. The research results can provide referential evidences for the coordinated optimal control between automatic generation control AGC and automatic voltage control AVC systems. Results of case study on IEEE 30-bus system validate the proposed model and algorithm. Key words smart grids comprehensive energy saving coordinated optimization node type conversion branch type conversion 2009-11 - 20 2006AA05Z214 1985 1970 1958 1962 1973
42 14 0 1 10-12 10 11 12 Pareto 2-3 4 5 1 6 2 1-1. 1 7 3 1 2 f 1 x = a i P 2 Gi + b i P Gi + c i 1 N 4 g f 2 x = P Gi - P D 2 P Gi i a i b i c i i P D x 1 2 9 8
7 43 P Li P Gi P L / P Li = P L / P Gi 8 P' Li 4 P * Gi 1 1 L 1 = a i P 2 Gi + b i P Gi + c i - λ( P Gi - PD ) P' Gi P * Gi + P' Li = P' Gi 3 K - T P * Gi λ * L 1 / P Gi = 2a i P * Gi + b i - λ * = 0 L 1 / λ = P * Gi - P D = 0 4 f 3 x = a i P * Gi + P Li 2 + b i P * Gi + P Li + c i P Li L P L = a i P 2 Li + 2a i P * Gi + b i P Li - γ( - PL ) 7 K - T P' Li γ' L P L / P Li = 2a i P' Li + P * Gi + b i - γ' 1 - P L / P Li = 0 8 L P L / γ = P' Li - P L = 0 1 4 1 13 1. 2 4 P Li + P i x = P Gi 9 Q Li + Q i x = Q Gi + Q Ci P Gi Q Gi P Li Q Li P i x Q i x i Q Ci i 5 P Li i P N Gimin g P Gi P Gimax P Li = P L 5 f 1 P * Gi Q Gimin Q Gi Q Gimax S Gimin S Gi S Gimax 10 Q Cimin Q Ci Q Cimax f P L = f 3 - f 1 P * Gi = a i P 2 L i + 2a i P * Gi + b i P L i i =1 V imin V i V imax 6 I ik I ikmax 6 i k = 1 2 N 1 9 10 2 2. 1
44 14 R i ik+jx ik S 觶 i I 觶 ik jb ik jb ik S 觶 k f x 9 g x = O10 h x O Fig. 1 π circuit figure Ⅰ S i = p i + jq i S k = p k + jq k L = f x + α T v i = V g g x 11 i θ i v k = V k θ k I ik = I ik ik R K - T ik + jx ik i k L / x = f / x + g / x T α g = O L / α g = g x = O 12 ik R I ik + jx ik = v i - v k 13 * α g vi = p i - jq i / ( I ik - jv i Bik ) 14 12 I ik cos ik R ik - I ik sin ik X ik = V i cosθ i - V k cosθ k I ik cos ik X ik + I ik sin ik R ik = V i sinθ i - V k sinθ k 2. 1. 1 4 PV V i cosθ i - V k cosθ k V i sinθ i - V k sinθ k 2 2 1 2 Ⅰ PQ PQV P 14 i - k PQV P P I 15 15 16 PQV ΔE [ ΔS ] = H N ΔI [ J L ] [ ΔV ] 17 2. 1. 2 ΔE ΔS ΔI ΔV H N J L 17 16 ΔE = O ΔI = - H - NL - 1 J - 1 NL - 1 ΔS 18 ΔI ΔS ΔI = ΔI ij Δ ij T ΔS = ΔP 1 π ΔQ T 1 V i I ik cos ik π Ⅰ - θ i = p i k B ik = - q i 15 PV PQ V i I ik sin ik - θ i - V 2 i 16 PV 15
7 J S = - H - NL - 1 J - 1 NL - 1 = J11 S J 12 S [ J 21 S J ] 22 S 19 25 ΔI [ l Δ ] = J11 S J 12 H J S ΔP [ l J 21 S J ] [ 22 S ΔQ ] T Δx [ 20 J O ] [ Δα ] [ = - L' / x L' / α] 25 H H = 2 L' / x i x j J J = g / x h ΔI l = J 11 S ΔP + J 12 I / x T S ΔQ 21 α α = α g α I T 25 J 12 S J 11 S 25 J 12 S = O J 11 S 3 J I ΔI l = J I ΔP G IEEE-30 18 2 V B = 100 kv S B = 100 MVA 10-5 min - J T u ΔP G s. t. ΔP Gi = 0 I + J I ΔP G I max 22 J u 1 C C C ΔP G ΔP Gi ΔP G 2. 2 C h I x = O 10 12 16 17 9 L' = f x + α T g g x + α T I h I x 23 K - T 45 24 1. 1 pu 0. 95 pu 2-6 1051. 51 1 228. 88 14. 43% 2 5 7 L' / x = f / x + g / x T α g + h I / x T α I = 0 15 23 24 25 26 29 L' / α g = g x = 0 L' / α I = h I x = 0 2 IEEE - 30 Fig. 2 Diagram of IEEE 30 - bus system 24 α I 1 999. 95 18. 63% 3 13 14 18 4 6 19 20 22 21 C 11 C 8 27 28 30
46 14 2-6 5 0. 415 72 pu - 0. 051 39 pu 0. 418 88 pu 5 1 5 1 Table 1 Calculated results of coordinated optimization model branch flow violation not considered 2 2-5 2-6 - 7-5 2-6 5 2-6 V i / pu θ i / P Gi / pu Q Gi / pu 1 1. 050 0 1. 854 1-0. 346 3 2 1. 046-4. 09 0. 378 1 0. 6 5 1. 006-10. 59 0. 212 6 0. 170 9 8 1. 002-8. 32 0. 268 1 0. 299 9 11 1. 050-9. 32 0. 1-0. 054 8 13 1. 080-10. 19 0. 12 0. 042 2 10 1. 077-12. 08 / 0. 579 9 24 1. 055-13. 01 / 0. 111 3 2-6 0. 4 pu I 2 2-6 0. 396 46 pu - 0. 052 80 pu branch flow violation considered V i / pu θ i / P Gi / pu Q Gi / pu 1 1. 05 0 1. 593 8-0. 388 0 2 1. 051-3. 50 0. 434 6 0. 6 5 1. 016-8. 78 0. 402 0 0. 159 4 8 1. 023-7. 59 0. 203 6 0. 241 9 11 1. 10-7. 82 0. 143 6 0. 133 9 13 1. 072-9. 05 0. 134 9-0. 000 4 10 1. 079-11. 04 / 0. 371 7 24 1. 058-12. 04 / 0. 111 9 1 2 3 Table 3 3 Deviation of generator active power outputs 1 2 5 8 11 13 ΔP Gi / pu - 0. 260 0. 057 0. 189-0. 065 0. 044-0. 015 3 1 5 2-6 2 5 1 2 1 1-2 2 2 2 2 4 1 2 0. 399 96 pu 1 079. 31 3 2 Table 2 Calculated results of coordinated optimization model 1. J. 2009 33 9 1-4. XIAO Shijie. Consideration of technology for constructing Chinese smart grid J. Automation of Electric Power Systems 2009 33 9 1-4. 2. J. 1991 11 6 41-49. HU Zhuguang FU Shuti. Real time online optimal power flow J. Proceedings of the CSEE 1991 11 6 41-49. 3. J. 1994 7 14 19-25. YANG Yigang PENG Jianchun ZHOU Yicheng et al. The research of real and reactive power economic dispatch in hydro-thermal power systems J. Proceedings of the CSEE 1994 7 14 19-25. 4. J. 1986 2 1 111-120. LI Linchuan WEN Ju. Optimal load flow by decoupling into real and reaction power optimization J. Journal of Xi an Jiaotong University 1986 2 1 111-120. 5. J. 2005 29 22 61-65. YU Xiaoyan YU Jilai. A dynamic power flow algorithm with joint
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