考虑光伏不确定性的低压配电网分散无功补偿鲁棒优化配置
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摘要
为提高电压质量,降低线路损耗,在考虑光伏出力随机波动和负荷预测误差的基础上,提出了低压配电网无功补偿分散配置的鲁棒优化模型。模型以配电台区总网损最小为目标,采用不确定集描述负荷功率以及影响光伏出力的光照强度和温度等不确定变量,约束条件包括了节点电压的上下限和无功补偿容量的上下限,以及补偿装置安装点总数的限制。利用变形的S型函数近似逼近符号函数以实现对模型中不可导函数的光滑化,并通过双层优化方法将含不确定变量的鲁棒优化模型转化为双层确定性优化模型进行交替求解,最后采用内点法优化求解确定性优化模型以得到分散无功补偿鲁棒优化配置方案。通过对某个实际低压配电网台区进行分析计算,结果表明所提出的分散无功补偿配置鲁棒优化方法得到的补偿方案能够满足光伏出力和负荷在其波动区间内任意变化时所有节点的电压均在合格范围内,具有良好的工程实用性。
In order to improve voltage quality and reduce line loss, a robust optimization model of distributed reactive power compensation for low voltage(LV) distribution network is proposed, considering random fluctuation of photovoltaic(PV) output and forecasting error of load power. In this model, objective is to minimize total power loss of distribution network, with uncertain variables of load power, light intensity and temperature affecting PV output discribed as uncertain set. Its constraints include upper and lower limits of node voltage and reactive power compensation capacity, and limit of total number of installed compensation devices. A deformed S-function is used to approximate symbolic function to smooth non-differentiable function in the model. Bi-level optimization method is used to transform robust optimization model with uncertain variables to bi-level deterministic optimization model, which is solved alternately. Finally, interior point method is adopted to solve the deterministic model to obtain robust optimal allocation scheme of reactive power compensation. Analysis of a real LV distribution network demonstrates that the obtained robust optimal allocation scheme of reactive power compensation can ensure all node voltage qualified no matter how LV output and load power changes in their own fluctuation interval, so the scheme is more applicable in engineering.
In order to improve voltage quality and reduce line loss, a robust optimization model of distributed reactive power compensation for low voltage(LV) distribution network is proposed, considering random fluctuation of photovoltaic(PV) output and forecasting error of load power. In this model, objective is to minimize total power loss of distribution network, with uncertain variables of load power, light intensity and temperature affecting PV output discribed as uncertain set. Its constraints include upper and lower limits of node voltage and reactive power compensation capacity, and limit of total number of installed compensation devices. A deformed S-function is used to approximate symbolic function to smooth non-differentiable function in the model. Bi-level optimization method is used to transform robust optimization model with uncertain variables to bi-level deterministic optimization model, which is solved alternately. Finally, interior point method is adopted to solve the deterministic model to obtain robust optimal allocation scheme of reactive power compensation. Analysis of a real LV distribution network demonstrates that the obtained robust optimal allocation scheme of reactive power compensation can ensure all node voltage qualified no matter how LV output and load power changes in their own fluctuation interval, so the scheme is more applicable in engineering.
引文
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[14]王淳,高元海.基于概率统计的含间歇性分布式发电的配电网无功优化[J].电网技术,2014,38(4):1032-1037.Wang Chun,Gao Yuanhai.Probability statistics based reactive power optimization of distribution network containing intermittent distributed generations[J].Power System Technology,2014,38(4):1032-1037(in Chinese).
[15]苏建徽,余世杰,赵为,等.硅太阳电池工程用数学模型[J].太阳能学报,2001,22(4):409-412.Su Jianhui,Yu Shijie,Zhao Wei,et al.Investigation on engineering analytical model of silicon solar cells[J].Acta Energiae Solaris Sinica,2001,22(4):409-412(in Chinese).
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[17]王一波,伍春生,廖华,等.大型并网光伏发电系统稳态模型与潮流分析[J].清华大学学报:自然科学版,2009,49(8):1093-1097.Wang Yibo,Wu Chunsheng,Liaohua,et al.Steady-state power flow analyses of large-scale grid-connected photovoltaic generation system[J].Journal of Tsinghua University:Science and Technology,2009,49(8):1093-1097(in Chinese).
[18]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):134-148.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):134-148(in Chinese).
[19]李斯,周任军,童小娇,等.基于盒式集合鲁棒优化的风电并网最大装机容量[J].电网技术,2011,35(12):208-213.Li Si,Zhou Renjun,Tong Xiaojiao,et al.Robust optimization with box set for maximum installed capacity of wind farm connected to grid[J].Power System Technology,2011,35(12):208-213(in Chinese).
[20]向月,刘俊勇,魏震波,等.考虑可再生能源出力不确定性的微电网能量优化鲁棒模型[J].中国电机工程学报,2014,34(19):3063-3072.Xiang Yue,Liu Junyong,Wei Zhenbo,et al.Robust model of microgrid energy optimization with uncertain renewable energy sources[J].Proceedings of the CSEE,2014,34(19):3063-3072(in Chinese).
[21]Ben-Tal A,Nemirovski A.Robust optimization methodology and applications[J].Mathematical Programming,2002,92(3):453-480.
[22]彭春华,谢鹏,陈臣.大规模光伏电站接入电网可调节鲁棒优化调度[J].中国电机工程学报,2014,34(25):4324-4332.Peng Chunhua,Xie Peng,Chen Chen.Adjustable robust optimal dispatch of power system with large-scale photovoltaic power stations[J].Proceedings of the CSEE,2014,34(25):4324-4332(in Chinese).
[23]王函韵,胡骅,朱卫东,等.信息不确定性对电网无功优化的影响[J].中国电机工程学报,2005,25(13):24-28.Wang Hanyun,Hu Hua,Zhu Weidong,et al.The impact of parameter uncertainty on reactive source optimization[J].Proceedings of the CSEE,2005,25(13):24-28(in Chinese).
[24]姚伟锋,赵俊华,文福拴,等.基于双层优化的电动汽车充放电调度策略[J].电力系统自动化,2012,36(11):30-37.Yao Weifeng,Zhao Junhua,Wen Fushuan,et al.A charging and discharging dispatching strategy for electric vehicles based on bi-level optimization[J].Automation of Electric Power Systems,2012,36(11):30-37(in Chinese).
[25]程莹,刘明波.含离散控制变量的大规模电力系统无功优化[J].中国电机工程学报,2002,22(5):55-60.Cheng Ying,Liu Mingbo.Reactive-power optimization of large-scale power systems with discrete control variables[J].Proceedings of the CSEE,2002,22(5):55-60(in Chinese).
[2]郑欣,陈文炜,林舜江,等.考虑泵类负荷特性的低压配电网潮流计算[J].电力系统保护与控制,2014,42(20):25-31.Zheng Xin,Chen Wenwei,Lin Shunjiang,et al.Power flow calculation of low voltage distribution network including pump loads[J].Power System Protection and Control,2014,42(20):25-31(in Chinese).
[3]陈昕玥,唐巍,陈禹,等.基于机会约束规划含光伏发电的配电网故障恢复[J].电网技术,2014,38(1):99-106.Chen Xinyue,Tang Wei,Chen Yu,et al.Chance Constrained Programming Based Fault Recovery of Distribution Network Containing Photovoltaic Generations[J].Power System Technology,2014,38(1):99-106.
[4]吴小刚,刘宗歧,田立亭,等.独立光伏系统光储容量优化配置方法[J].电网技术,2014,38(5):1271-1276.Wu Xiaogang,et al.Optimized Capacity Configuration of Photovoltaic Generation and Energy Storage Device for Stand-Alone Photovoltaic Generation System[J].Power System Technology,2014,38(5):1271-1276.
[5]Bialasiewicz J T.Renewable energy systems with photovoltaic power generators:operation and modeling[J].IEEE Transactions on Industrial Electronics,2008,55(7):2752-2758.
[6]Alam M J E,Muttaqi K M,Sutanto D.A three-phase power flow approach for integrated 3-wire MV and 4-wire multi-grounded LV networks with rooftop solar PV[J].IEEE Transactions on Power Systems,2013,28(2):1728-1737.
[7]丁明,王伟胜,王秀丽,等.大规模光伏发电对电力系统影响综述[J].中国电机工程学报,2014,34(1):1-14.Ding Ming,Wang Weisheng,Wang Xiuli,et al.A review on the effect of large-scale PV generation on power systems[J].Proceedings of the CSEE,2014,34(1):1-14(in Chinese).
[8]陈炜,艾欣,吴涛,等.光伏并网发电系统对电网的影响研究综述[J].电力自动化设备,2013,33(2):26-32.Chen Wei,Ai Xin,Wu Tao,et al.Influence of grid connected photovoltaic system on power network[J].Electric Power Automation Equipment,2013,33(2):26-32(in Chinese).
[9]刘东冉,陈树勇,马敏,等.光伏发电系统模型综述[J].电网技术,2011,35(8):47-52.Liu Dongran,Chen Shuyong,Ma Min,et al.A review on models for photovoltaic generation system[J].Power System Technology,2011,35(8):47-52(in Chinese).
[10]张丽,徐玉琴,王增平,等.包含分布式电源的配电网无功优化[J].电工技术学报,2011,26(3):168-174.Zhang Li,Xu Yuqin,Wang Zengping,et al.Reactive power optimization for distribution system with distributed generators[J].Transactions of China Electrotechnical Society,2011,26(3):168-174(in Chinese).
[11]邢海军,程浩忠,张逸.基于多种主动管理策略的配电网综合无功优化[J].电网技术,2015,39(6):1504-1510.Xing Haijun,Cheng Haozhong,Zhang Yi.Reactive power comprehensive optimization in distribution network based on multiple active management schemes[J].Power System Technology,2015,39(6):1504-1510(in Chinese).
[12]陈海焱,陈金富,段献忠.含风电机组的配网无功优化[J].中国电机工程学报,2008,28(7):40-45.Chen Haiyan,Chen Jinfu,Duan Xianzhong.Reactive power optimization in distribution system with wind power generators[J].Proceedings of the CSEE,2008,28(7):40-45(in Chinese).
[13]张璐,唐巍,丛鹏伟,等.含光伏发电的配电网有功无功资源综合优化配置[J].中国电机工程学报,2014,34(31):5525-5533.Zhang Lu,Tang Wei,Cong Pengwei,et al.Optimal configuration of active-reactive power sources in distribution network with photovoltaic generation[J].Proceedings of the CSEE,2014,34(31):5525-5533(in Chinese).
[14]王淳,高元海.基于概率统计的含间歇性分布式发电的配电网无功优化[J].电网技术,2014,38(4):1032-1037.Wang Chun,Gao Yuanhai.Probability statistics based reactive power optimization of distribution network containing intermittent distributed generations[J].Power System Technology,2014,38(4):1032-1037(in Chinese).
[15]苏建徽,余世杰,赵为,等.硅太阳电池工程用数学模型[J].太阳能学报,2001,22(4):409-412.Su Jianhui,Yu Shijie,Zhao Wei,et al.Investigation on engineering analytical model of silicon solar cells[J].Acta Energiae Solaris Sinica,2001,22(4):409-412(in Chinese).
[16]Coelho R F,Cancer F,Martins D C.A proposed photovoltaic module and array mathematical modeling destined to simulation[C]//IEEE International Symposium on Industrial Electronics(ISIE 2009).Seoul,Korea:IEEE,2009:1624-1629.
[17]王一波,伍春生,廖华,等.大型并网光伏发电系统稳态模型与潮流分析[J].清华大学学报:自然科学版,2009,49(8):1093-1097.Wang Yibo,Wu Chunsheng,Liaohua,et al.Steady-state power flow analyses of large-scale grid-connected photovoltaic generation system[J].Journal of Tsinghua University:Science and Technology,2009,49(8):1093-1097(in Chinese).
[18]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):134-148.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):134-148(in Chinese).
[19]李斯,周任军,童小娇,等.基于盒式集合鲁棒优化的风电并网最大装机容量[J].电网技术,2011,35(12):208-213.Li Si,Zhou Renjun,Tong Xiaojiao,et al.Robust optimization with box set for maximum installed capacity of wind farm connected to grid[J].Power System Technology,2011,35(12):208-213(in Chinese).
[20]向月,刘俊勇,魏震波,等.考虑可再生能源出力不确定性的微电网能量优化鲁棒模型[J].中国电机工程学报,2014,34(19):3063-3072.Xiang Yue,Liu Junyong,Wei Zhenbo,et al.Robust model of microgrid energy optimization with uncertain renewable energy sources[J].Proceedings of the CSEE,2014,34(19):3063-3072(in Chinese).
[21]Ben-Tal A,Nemirovski A.Robust optimization methodology and applications[J].Mathematical Programming,2002,92(3):453-480.
[22]彭春华,谢鹏,陈臣.大规模光伏电站接入电网可调节鲁棒优化调度[J].中国电机工程学报,2014,34(25):4324-4332.Peng Chunhua,Xie Peng,Chen Chen.Adjustable robust optimal dispatch of power system with large-scale photovoltaic power stations[J].Proceedings of the CSEE,2014,34(25):4324-4332(in Chinese).
[23]王函韵,胡骅,朱卫东,等.信息不确定性对电网无功优化的影响[J].中国电机工程学报,2005,25(13):24-28.Wang Hanyun,Hu Hua,Zhu Weidong,et al.The impact of parameter uncertainty on reactive source optimization[J].Proceedings of the CSEE,2005,25(13):24-28(in Chinese).
[24]姚伟锋,赵俊华,文福拴,等.基于双层优化的电动汽车充放电调度策略[J].电力系统自动化,2012,36(11):30-37.Yao Weifeng,Zhao Junhua,Wen Fushuan,et al.A charging and discharging dispatching strategy for electric vehicles based on bi-level optimization[J].Automation of Electric Power Systems,2012,36(11):30-37(in Chinese).
[25]程莹,刘明波.含离散控制变量的大规模电力系统无功优化[J].中国电机工程学报,2002,22(5):55-60.Cheng Ying,Liu Mingbo.Reactive-power optimization of large-scale power systems with discrete control variables[J].Proceedings of the CSEE,2002,22(5):55-60(in Chinese).