Robust Real-Time Dispatch Considering the Injection Shift Factor Estimation Errors
Zhai Hefeng1, Yang Ming1, Wang Dong2, Cheng Fenglu3, Liu Daowei4
1. Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education Shandong University Jinan 250061 China; 2. State Grid Qingdao Power Supply Company Qingdao 266002 China; 3. State Grid Shandong Electric Power Maintenance Company Jinan 250000 China; 4. China Electric Power Research Institute Beijing 100192 China
Abstract Injection shift factors (ISFs) are important linear sensitivity factors in power grid operation analysis. They are commonly used in the security verification of branch power flow with a certain power generation dispatch plan. The estimation errors of ISFs easily result in the deviation of branch power flow calculation, and further threaten the power grid operation security. Accordingly, a robust real-time dispatching method considering the estimation errors of ISFs is proposed in this paper. The probabilistic ISF estimation model based on Bayesian linear regression is firstly presented using real-time measurement data. Then the ISF error intervals are acquired by solving the estimation model. Aiming to minimize the system operating cost, a real-time dispatching model is built, taken into account the nodal power injection disturbance as well as the ISF estimation errors. The solving algorithm of the model is provided based on the Soyster robust optimization method. Calculation tests on simple 6-bus system, the IEEE 118-bus system and the IEEE 300-bus system validate the proposed approach.
[1] Zhang M, Guan Y. Two-stage robust unit com- mitment problem[J/OL].[2016-11-10]. http://www. optimization-online.org/DB_FILE/2009/10/2427.pdf. [2] 杨明, 韩学山, 王士柏, 等. 不确定运行条件下电力系统鲁棒调度的基础研究[J]. 中国电机工程学报, 2011, 31(增刊1): 100-107. Yang Ming, Han Xueshan, Wang Shibo, et al. Fundamental research for power system robust dispatch under uncertain operating condition[J]. Proceedings of the CSEE, 2011, 31(S1): 100-107. [3] 梅生伟, 郭文涛, 王莹莹, 等. 一类电力系统鲁棒优化问题的博弈模型及应用实例[J]. 中国电机工程学报, 2013, 33(19): 47-56. Mei Shengwei, Guo Wentao, Wang Yingying, et al. A game model for robust optimization of power systems and its application[J]. Proceedings of the CSEE, 2013, 33(19): 47-56. [4] 魏韡, 刘锋, 梅生伟. 电力系统鲁棒经济调度(一):理论基础[J]. 电力系统自动化, 2013, 37(17): 37-43. Wei Wei, Liu Feng, Mei Shengwei. Robust and economical scheduling methodology for power systems: part one theoretical foundations[J]. Auto- mation of Electric Power Systems, 2013, 37(17): 37-43. [5] 魏韡, 刘锋, 梅生伟. 电力系统鲁棒经济调度(二):应用实例[J]. 电力系统自动化, 2013, 37(18): 60-67. Wei Wei, Liu Feng, Mei Shengwei. Robust and economical scheduling methodology for power systems, part two: application examples[J]. Automation of Electric Power Systems, 2013, 37(18): 60-67. [6] 陈建华, 吴文传, 张伯明, 等. 安全性与经济性协调的鲁棒区间风电调度方法[J]. 中国电机工程学报, 2014, 34(7): 1033-1040. Chen Jianhua, Wu Wenchuan, Zhang Boming, et al. A robust interval wind power dispatch method considering the tradeoff between security and economy[J]. Proceedings of the CSEE, 2014, 34(7): 1033-1040. [7] 李志刚, 吴文传, 张伯明. 消纳大规模风电的鲁棒区间经济调度(一): 调度模式与数学模型[J]. 电力系统自动化, 2014, 38(20): 33-39. Li Zhigang, Wu Wenchuan, Zhang Boming. A robust interval economic dispatch method accommodating large-scale wind power generation, part one: dispatch scheme and mathematical model[J]. Automation of Electric Power Systems, 2014, 38(20): 33-39. [8] 李志刚, 吴文传, 张伯明. 消纳大规模风电的鲁棒区间经济调度(二): 不确定集合构建与保守度调节[J]. 电力系统自动化, 2014, 38(21): 32-38. Li Zhigang, Wu Wenchuan, Zhang Boming. A robust interval economic dispatch method accommodating large-scale wind power generation, part two: uncer- tainty set modeling and conservativeness adjustment[J]. Automation of Electric Power Systems, 2014, 38(21): 32-38. [9] 杨明, 程凤璐, 韩学山. 电力系统实时调度的有效静态安全域法[J]. 中国电机工程学报, 2015, 35(6): 1353-1362. Yang Ming, Cheng Fenglu, Han Xueshan. Real-time dispatch based on effective steady-state security regions of power system[J]. Proceedings of the CSEE, 2015, 35(6): 1353-1362. [10] 童小娇, 文强, 周任军, 等. 基于鲁棒优化的自发电计划[J]. 长沙理工大学学报: 自然科学版, 2010, 7(2): 58-65. Tong Xiaojiao, Wen Qiang, Zhou Renjun, et al. Self-scheduling based on robust optimization[J]. Journal of Changsha University of Science and Technology: Natural Science, 2010, 7(2): 58-65. [11] 刘鸿, 刘建华, 唐民. 计及机组不确定损耗成本的鲁棒安全经济调度[J]. 电力系统及其自动化学报, 2014, 26(4): 61-66. Liu Hong, Liu Jianhua, Tang Min. Optimal placement of distributed uncertain loss cost robust security economical dispatch[J]. Proceedings of the CSU- EPSA, 2014, 26(4): 61-66. [12] 李伟, 陈驾宇, 潘志, 等. 基于鲁棒优化的含径流式小水电的电力系统安全经济调度[J]. 电力学报, 2012, 27(6): 574-577. Li Wei, Chen Jiayu, Pan Zhi, et al. Robust optimization for power system security economic dispatch with run-of small hydropower[J]. Journal of Electric Power, 2012, 27(6): 574-577. [13] Wang Q, Watson J P, Guan Y. Two-stage robust optimization for N-k contingency-constrained unit commitment[J]. IEEE Transactions on Power Systems, 2013, 28(3): 2366-2375. [14] 艾小猛, 韩杏宁, 文劲宇, 等. 考虑风电爬坡事件的鲁棒机组组合[J]. 电工技术学报, 2015, 30(24): 188-196. Ai Xiaomeng, Han Xingning, Wen Jinyu, et al. Robust unit commitment considering wind power ramp events[J]. Transactions of China Electro- technical Society, 2015, 30(24): 188-196. [15] 于丹文, 杨明, 翟鹤峰, 等. 鲁棒优化在电力系统调度决策中的应用研究综述[J]. 电力系统自动化, 2016, 40(7): 134-143. Yu Danwen, Yang Ming, Zhai Hefeng, et al. An overview of robust optimization used for power system dispatch and decision-making[J]. Automation of Electric Power Systems, 2016, 40(7): 134-143. [16] Chen Y C, Dominguez-Garcia A D, Sauer P W. Online computation of power system linear sensiti- vity distribution factors[C]//2013 IREP Symposium- Bulk Power System Dynamics and Control-IX Optimization, Security and Control of the Emerging Power Grid Supplement, Rethymno, 2013: 1-4. [17] 唐民, 童小娇, 文强. 计及网络参数不确定的含风电场安全经济调度[J]. 电力系统及其自动化学报, 2012, 24(2): 27-34. Tang Min, Tong Xiaojiao, Wen Qiang. Security economic dispatch of power system integrated with wind farms considering uncertainty of network parameters[J]. Proceedings of the CSU-EPSA, 2012, 24(2): 27-34. [18] 徐岩, 应璐曼, 王增平. 基于最大树理论的分阶段相量测量单元配置方案[J]. 电工技术学报, 2016, 31(4): 155-162. Xu Yan, Ying Luman, Wang Zengping. Staged phasor measurement unit placement algorithm based on theory of maximum tree[J]. Transactions of China Electrotechnical Society, 2016, 31(4): 155-162. [19] Eissa M M, Elmesalawy M M, Hadhoud M M A. Wide area monitoring system based on the third generation universal mobile telecommunication system (UMTS) for event identification[J]. Inter- national Journal of Electrical Power & Energy Systems, 2015, 69: 34-47. [20] 李虹, 李卫国, 熊浩清. WAMS中计及量测函数非线性项的电力系统自适应动态状态估计[J]. 电工技术学报, 2010, 25(5): 155-161. Li Hong, Li Weiguo, Xiong Haoqing. Adaptive dynamic state estimation including nonlinearities of measurement function in WAMS[J]. Transactions of China Electrotechnical Society, 2010, 25(5): 155-161. [21] 薛安成, 张兆阳, 毕天姝. 基于自适应抗差最小二乘的线路正序参数在线辨识方法[J]. 电工技术学报, 2015, 30(8): 202-209. Xue Ancheng, Zhang Zhaoyang, Bi Tianshu. Online identification of transmission line positive-sequence parameters based on adaptive robust least squares[J]. Transactions of China Electrotechnical Society, 2015, 30(8): 202-209. [22] Chen Y C, Dominguez-Garcia A D, Sauer P W. Measurement-based estimation of linear sensitivity distribution factors and applications[J]. IEEE Transa- ctions on Power Systems, 2014, 29(3): 1372-1382. [23] Zhang B, Wang D, Yang M, et al. A measurement- based estimation method of injection shift factors[C]// International Conference on Power System Techno- logy, Chengdu, 2014: 401-407. [24] 王栋, 杨明, 韩学山, 等. 电力系统注入转移分布因子的概率估计[J]. 电力系统自动化, 2015, 39(22): 46-52. Wang Dong, Yang Ming, Han Xueshan, et al. Probabilistic estimation of power system injection shift factor[J]. Automation of Electric Power Systems, 2015, 39(22): 46-52. [25] Yang M, Wang D, Wang M Q, et al. A probabilistic approach for power system injection shift factor estimation[J]. International Journal of Electrical Power & Energy Systems, 2016, 81: 317-323. [26] Soyster A L. Convex programming with set-inclusive constraints and applications to inexact linear pro- gramming[J]. Operations Research, 1973, 21(5): 1154- 1157. [27] Koop G, Poirier D J, Tobias J L. Bayesian econo- metric methods[M]. New York: Cambridge University Press, 2007. [28] Casella G, George E I. Explaining the Gibbs sampler[J]. American Statistician, 1992, 46(3): 167- 174. [29] Gibbs sampling[EB/OL]. [2016-11-10]. https://en. wikipedia.org/wiki/Gibbs_sampling. [30] Blake A, Mumtaz H. Applied bayesian econometrics for central bankers[R]. Bank of England, Technical Handbook No. 4, 2012. [31] 颜伟, 赵瑞锋, 赵霞, 等. 自动发电控制中控制策略的研究发展综述[J]. 电力系统保护与控制, 2013, 41(8): 149-155. Yan Wei, Zhao Ruifeng, Zhao Xia, et al. Review on control strategies in automatic generation control[J]. Power System Protection and Control, 2013, 41(8): 149-155. [32] Bertsimas D, Sim M. The price of robustness[J]. Operations Research, 2004, 52(1): 35-53. [33] 程凤璐. 在线经济调度的鲁棒优化方法研究[D]. 济南: 山东大学, 2015. [34] 谢俊, 李振坤, 章美丹, 等. 机组调峰的价值量化与费用补偿[J]. 电工技术学报, 2013, 28(1): 271-276. Xie Jun, Li Zhenkun, Zhang Meidan, et al. Peaking value quantification and cost compensation for generators[J]. Transactions of China Electrotechnical Society, 2013, 28(1): 271-276. [35] 黎嘉明, 郑雪阳, 艾小猛, 等. 独立海岛微网分布式电源容量优化设计[J]. 电工技术学报, 2016, 31(10): 176-184. Li Jiaming, Zheng Xueyang, Ai Xiaomeng, et al. Optimal design of capacity of distributed generation in island standalone microgrid[J]. Transactions of China Electrotechnical Society, 2016, 31(10): 176-184. [36] Wang M Q, Gooi H B, Chen S X. Optimising probabilistic spinning reserve using an analytical expected-energy-not-supplied formulation[J]. IET Generation Transmission & Distribution, 2011, 5(7): 772-780. [37] 杨明, 韩学山, 李智, 等. 扰动转移分布因子及风电对超前调度直流潮流约束的关键扰动分析[J]. 电力系统保护与控制, 2011, 39(13): 32-35. Yang Ming, Han Xueshan, Li Zhi, et al. Key disturbance analysis of the influence of disturbance shift distribution factor and wind power on the DC flow constraints of advance dispatch[J]. Power System Protection and Control, 2011, 39(13): 32-35. [38] MathWorks. MATLAB parallel computing tool- box[Z/OL]. https://cn.mathworks.com/products/parallel- computing. [39] Christie R. Power system test case archive[Z/OL]. http://motor.ece.iit.edu/data/. [40] Zimmerman R D, Murillo-Sanchez C E, Thomas R J. MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education[J]. IEEE Transactions on Power Systems, 2011, 26(1): 12-19.
2017, Vol. 32 
