Active / reactive power coordinated optimization in power systems comprehensive energy saving

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Ἀριστόδημε Παπαφιλίππου
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1 ELECTRI C MACHINES AND CONTROL Vol. 14 No. 7 July IEEE - 30 TM 731 A X 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 China 2. Shanghai Municipal Electric Power Company Shanghai 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 AA05Z

2 Pareto 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

3 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 = 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

4 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 ) 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 PV V i cosθ i - V k cosθ k V i sinθ i - V k sinθ k Ⅰ PQ PQV P 14 i - k PQV P P I PQV ΔE [ ΔS ] = H N ΔI [ J L ] [ ΔV ] ΔE ΔS ΔI ΔV H N J L 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

5 7 J S = - H - NL - 1 J - 1 NL - 1 = J11 S J 12 S [ J 21 S J ] 22 S 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 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 L' = f x + α T g g x + α T I h I x 23 K - T pu pu % L' / x = f / x + g / x T α g + h I / x T α I = 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 % C 11 C

6 pu pu pu Table 1 Calculated results of coordinated optimization model branch flow violation not considered V i / pu θ i / P Gi / pu Q Gi / pu / / pu I pu pu branch flow violation considered V i / pu θ i / P Gi / pu Q Gi / pu / / Table 3 3 Deviation of generator active power outputs ΔP Gi / pu pu Table 2 Calculated results of coordinated optimization model 1. J XIAO Shijie. Consideration of technology for constructing Chinese smart grid J. Automation of Electric Power Systems J HU Zhuguang FU Shuti. Real time online optimal power flow J. Proceedings of the CSEE J 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 J LI Linchuan WEN Ju. Optimal load flow by decoupling into real and reaction power optimization J. Journal of Xi an Jiaotong University J YU Xiaoyan YU Jilai. A dynamic power flow algorithm with joint

7 7 47 regulation of active and reactive power J. Power System Technology MOYANO C F SALGADO R S BARBOZA L V. On the determination of adjusted OPF solutions C / / IEEE International Symposium on Circuits and Systems May Island of Kos Greece M. PAN Kaiyan ZHANG Pei. Different handling methods for remote RONCERO J R. Integration is key to smart grid management C / /CIRED Seminar Smart Grids for Distribution 2008 IET- CIRED June Frankfurt Germany J J BINKOU Alhabib YU Yixin SUN Gang. Security region based WANG Chengmin JIANG Chuanwen HUANG Rui. Loop type real and reactive power optimization of power systems J. Proceedings of the CSEE nalysis J. Advanced Technology of Electrical Engineering conversion and regulation of line flow violation based on loop a- and 10 RAMESH V C LI Xuan. A fuzzy multi-objective approach to contingency constrained OPF J. IEEE Transactions on Power Systems DAS D B PATVARDHAN C. New multi-objective stochastic search technique for economic load dispatch J. IEE Proceedings-Generation Transmission and Distribution ABIDO M A. Multi-objective particle swarm optimization for optimal power flow problem C / / The 12th International Meddle- East Power System Conference South Valley University March Aswan Egypt J ZHANG Lizi XIE Guohui ZHU Ze et al. Quasi marketization model of energy-saving generation dispatching J. Automation of Electric Power Systems J generator control in power flow calculation J. Automation of E- lectric Power Systems PRABHA Kundur. Power System Stability and Control M. USA The McGraw-Hill Companies Inc Energy J WANG Chengmin JIANG Chuanwen. Research on sensitivity a- nalysis method based on line current variable J. Transactions of China Electrotechnical Society M 檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪檪 J J ZHANG Yuejin JIANG Jianzhong TU Guanzhen. Application of numerical-analytical method to magnetic fieldg computation in rotating electric machines J Transactions of China Electrotechni- 8. J. cal Society YANG Jiaqiang HUANG Jin KANG Min et al. Electronic pole changing technique of multi-phase induction motor J. Electric Machines and Control M M J WEN Jiabin ZHANG Jinbao WANG Jitao. Magnetic field parameter calculation of permanent magnet oscillating generator. Electric Machines and Control

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