Internal Reactive Power Optimization of Offshore Wind Farms Using Second-Order Cone Convex Relaxation

ZHANG Lei, JIANG Zhenqiang, NI Jiahua, ZHOU Hu, LU Yanyan, XIANG Ji

Electric Power Construction ›› 2024, Vol. 45 ›› Issue (1) : 92-101.

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Electric Power Construction ›› 2024, Vol. 45 ›› Issue (1) : 92-101. DOI: 10.12204/j.issn.1000-7229.2024.01.009
Renewable Energy and Energy Storage

Internal Reactive Power Optimization of Offshore Wind Farms Using Second-Order Cone Convex Relaxation

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Abstract

This paper proposes a reactive power optimization model for offshore wind farms based on second-order cone convex relaxation for reducing active network loss. The model considers the grid stability requirements and safety margin involved in the optimal power flow process and optimizes the reactive power output of each turbine to maximize the active power output, reduce the network loss, and improve the overall power output of a wind farm. Through mathematical optimization of the second-order cone convex relaxation, the power flow is improved, the line active power loss is reduced, and the power-flow optimization problem under various constraints is solved. Finally, with the Zhoushan Putuo wind farm as an example, the reactive power output of each wind turbine is optimized and compared with the results of heuristic particle swarm optimization and the classical interior-point optimization algorithm. The comparison shows that the proposed method can significantly reduce active power loss and improve the overall active power output of the wind farm.

Key words

offshore wind farm / reactive power optimization / optimal power flow / convex optimization

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Lei ZHANG , Zhenqiang JIANG , Jiahua NI , et al . Internal Reactive Power Optimization of Offshore Wind Farms Using Second-Order Cone Convex Relaxation[J]. Electric Power Construction. 2024, 45(1): 92-101 https://doi.org/10.12204/j.issn.1000-7229.2024.01.009

References

[1]
潘小海, 伍勇旭, 李东. 双碳发展对我国的影响及应对策略[J]. 技术经济, 2021, 40(9): 172-180.
PAN Xiaohai, WU Yongxu, LI Dong. The impact and coping strategies of peak carbon dioxide emissions and carbon neutrality development on China[J]. Journal of Technology Economics, 2021, 40(9): 172-180.
[2]
王深, 吕连宏, 张保留, 等. 基于多目标模型的中国低成本碳达峰、碳中和路径[J]. 环境科学研究, 2021, 34(9): 2044-2055.
WANG Shen, Lianhong, ZHANG Baoliu, et al. Multi objective programming model of low-cost path for China’s peaking carbon dioxide emissions and carbon neutrality[J]. Research of Environmental Sciences, 2021, 34(9): 2044-2055.
[3]
庄贵阳, 魏鸣昕. 城市引领碳达峰、碳中和的理论和路径[J]. 中国人口·资源与环境, 2021, 31(9): 114-121.
ZHUANG Guiyang, WEI Mingxin. Theory and pathway of city leadership in emission peak and carbon neutrality[J]. China Population, Resources and Environment, 2021, 31(9): 114-121.
[4]
王彩霞, 时智勇, 梁志峰, 等. 新能源为主体电力系统的需求侧资源利用关键技术及展望[J]. 电力系统自动化, 2021, 45(16): 37-48.
WANG Caixia, SHI Zhiyong, LIANG Zhifeng, et al. Key technologies and prospects of demand-side resource utilization for power systems dominated by renewable energy[J]. Automation of Electric Power Systems, 2021, 45(16): 37-48.
[5]
王振浩, 李金伦, 王欣铎, 等. 风电接入真双极MMC-MTDC系统直流故障穿越协调控制策略[J]. 电力建设, 2022, 43(10): 26-36.
Abstract
由于柔性直流输电系统通常采用架空线进行直流输电,其故障发生率较高。当系统发生单极短路接地故障后,通过真双极接线方式可将故障极不平衡功率转带给非故障极。根据换流站的功率裕度将不平衡功率分为自消纳和协同消纳情况,针对自消纳情况,通过送端双极换流站间的功率转带即可实现故障穿越;针对协同消纳情况,设计换流站及耗能电阻间的协调控制策略,考虑到耗能电阻投入时长有限,采用后续风机切机的方式减少直流系统内不平衡功率。最后,通过PSCAD验证了所提控制策略的有效性。仿真结果表明,该策略能有效避免故障范围的扩大,确保系统的安全运行。
WANG Zhenhao, LI Jinlun, WANG Xinduo, et al. DC fault ride-through coordinated control strategies for bipolar MMC-MTDC system with wind power connected[J]. Electric Power Construction, 2022, 43(10): 26-36.

Because DC system usually adopts overhead line for DC transmission, its failure rate is high. When a single-pole short-circuit grounding fault occurs in the system, the unbalanced power of the fault pole can be transferred to the non-fault pole through the real-bipolar wiring mode. The unbalanced power can be divided into self-absorption and collaborative absorption according to the power margin of the converter station. For the self-absorption situation, fault ride-through can be realized by power transfer between sending end bipolar converter stations. For the situation of collaborative absorption, the coordinated control strategies between converter station and energy dissipation resistance are designed. Considering the limited input time of energy dissipation resistance, unbalanced power in DC System is reduced by sub-sequent generator cutting. Finally, the effectiveness of the proposed control strategy is verified in PSCAD. The simulation results show that the strategy can effectively avoid the expansion of fault range and ensure the safe operation of the system.

[6]
屈博, 刘畅, 李德智, 等. “碳中和”目标下的电能替代发展战略研究[J]. 电力需求侧管理, 2021, 23(2): 1-3, 9.
QU Bo, LIU Chang, LI Dezhi, et al. Research on the development strategy of electric energy substitution under the target of “carbon neutralization”[J]. Power Demand Side Management, 2021, 23(2): 1-3, 9.
[7]
国家能源局. 风电发展“十三五”规划[R]. 北京: 国家能源局, 2016.
[8]
陈鸿琳, 刘新苗, 余浩, 等. 基于近似动态规划的海上风电制氢微网实时能量管理策略[J]. 电力建设, 2022, 43(12): 94-102.
Abstract
电解水制氢(power-to-hydrogen,PtH)装置耦合海上风电运行,在促进风电消纳的同时可以制备绿色氢能,推进工业领域的无碳化进程,因而备受关注。文章开展海上风电制氢微网的实时能量管理策略研究。首先,构建海上风电制氢微网的实时能量管理模型,包含海上风电、电制氢装置以及储氢罐等元件。然后,提出基于近似动态规划(approximate dynamic programming,ADP)的微网实时能量管理策略,采用分段线性函数近似状态值函数以应对不确定性因素。最后,通过算例验证所提策略的有效性和优越性。在所提策略下,海上风电通过电制氢装置就地消纳,实现氢气的提前制备和存储。以具备精准预测技术的理想算例为基准,所提策略在满足正态分布的实时测试场景下,优化准确率平均值大于99%。
CHEN Honglin, LIU Xinmiao, YU Hao, et al. Real-time energy management strategy based on approximate dynamic programming for offshore wind power-to-hydrogen microgrid[J]. Electric Power Construction, 2022, 43(12): 94-102.

Introducing power-to-hydrogen (PtH) into offshore wind farms can assist the integration of wind power and produce green hydrogen, which accelerates decarbonization in industrial sectors and has attracted attention worldwide. In these circumstances, this paper studies the real-time energy management strategy of the offshore wind PtH microgrid. First, the real-time energy management model of the offshore wind PtH microgrid is proposed, including offshore wind farms, PtH devices and hydrogen storage tanks. Then, real-time energy management strategy based on approximate dynamic programming (ADP) is proposed. The value function is approximated by piece-wise linear functions (PLFs) to cope with uncertainties in the microgrid. Finally, the effectiveness and superiority of the proposed strategy is verified by case studies. Under the proposed strategy, offshore wind power can be consumed by PtH, achieving production and storage of hydrogen in advance. On the basis of the ideal case with perfect forecasting, the proposed strategy has an average optimization accuracy of more than 99% in real-time test scenarios with normal distribution.

[9]
王诗超, 孙仕达, 郝为瀚, 等. 基于VSC与DRU的混合级联型海上风电直流外送系统控制与阻抗建模[J]. 电力建设, 2022, 43(4): 38-48.
Abstract
混合级联型海上风电直流外送系统具有高压、大容量、投资成本低等优势,但其并网稳定性问题一直备受关注,而系统阻抗建模是分析稳定性的基础。基于电压源型换流器(voltage-source converter,VSC)与二极管整流器(diode rectifier units,DRU)的混合级联型海上风电直流外送系统,建立了VSC-DRU混合级联换流站的详细数学模型;为实现直流外送系统中有功功率主动分配和交流集电系统电压稳定,研究了含滤波电容电流反馈的VSC功率-电压调节控制策略;采用小信号扰动方法,考虑锁相环输出相角调节、有源阻尼控制及功率控制影响,推导并分析了闭环控制下VSC-DRU混合级联换流站的详细阻抗模型,为研究系统稳定性提供了依据。最后,在PSCAD/EMTDC中进行仿真验证,结果表明所提控制策略具有良好的功率-电压调节性能,并通过频率扫描法验证了所建详细阻抗模型的正确性。
WANG Shichao, SUN Shida, HAO Weihan, et al. Control and impedance modeling of offshore wind power hybrid cascaded DC transmission system based on of VSC and DRU[J]. Electric Power Construction, 2022, 43(4): 38-48.

Offshore wind power integration system applying hybrid cascaded DC transmission has the advantages of high voltage, large capacity and low investment cost, but its stability has gained many concerns. And the system impedance modeling is the basis for analyzing stability. In this paper, a detailed mathematical model of VSC-DRU hybrid cascaded valve station is established. In order to realize active power distribution and AC voltage control of the DC transmission system, the power-voltage control strategy of VSC with filter capacitor current feedback is studied. Considering the influence of output phase-angle adjustment of phase-locked loop, active damping control and power control, the detailed impedance model of VSC-DRU hybrid cascaded valve station is derived and analyzed by using small-signal disturbance method, which provides a basis for studying stability. Finally, the simulation results in PSCAD/EMTDC show that the proposed control has good performance of power-voltage regulation. And the correctness of the established detailed impedance model is verified by the frequency-scanning method.

[10]
蒋智化, 刘连光, 刘自发, 等. 直流配电网功率控制策略与电压波动研究[J]. 中国电机工程学报, 2016, 36(4): 919-926.
JIANG Zhihua, LIU Lianguang, LIU Zifa, et al. Research on power flow control and the voltage fluctuation characteristics of DC distribution networks based on different control strategies[J]. Proceedings of the CSEE, 2016, 36(4): 919-926.
[11]
CHEN P C, SALCEDO R, ZHU Q C, et al. Analysis of voltage profile problems due to the penetration of distributed generation in low-voltage secondary distribution networks[J]. IEEE Transactions on Power Delivery, 2012, 27(4): 2020-2028.
[12]
FARHADI M, MOHAMMED O A. Real-time operation and harmonic analysis of isolated and non-isolated hybrid DC microgrid[J]. IEEE Transactions on Industry Applications, 2014, 50(4): 2900-2909.
[13]
MA J C, YUAN L Q, ZHAO Z M, et al. Transmission loss optimization-based optimal power flow strategy by hierarchical control for DC microgrids[J]. IEEE Transactions on Power Electronics, 2017, 32(3): 1952-1963.
[14]
HAYES B P, ILIE I S, PORPODAS A, et al. Equivalent power curve model of a wind farm based on field measurement data[C]// 2011 IEEE Trondheim PowerTech. IEEE, 2011: 1-7.
[15]
LIU X. An improved interpolation method for wind power curves[J]. IEEE Transactions on Sustainable Energy, 2012, 3(3): 528-534.
[16]
江岳文, 张金辉. 考虑风电接纳水平及负荷增长的海上风电场多阶段规划[J]. 电力自动化设备, 2022, 42(2): 85-91, 111.
JIANG Yuewen, ZHANG Jinhui. Multi-stage planning of offshore wind farm considering wind power accommodation level and load increase[J]. Electric Power Automation Equipment, 2022, 42(2): 85-91, 111.
[17]
唐程辉, 张凡, 张宁, 等. 基于风电场总功率条件分布的电力系统经济调度二次规划方法[J]. 电工技术学报, 2019, 34(10): 2069-2078.
TANG Chenghui, ZHANG Fan, ZHANG Ning, et al. Quadratic programming for power system economic dispatch based on the conditional probability distribution of wind farms sum power[J]. Transactions of China Electrotechnical Society, 2019, 34(10): 2069-2078.
[18]
刘宁, 米志伟, 刘栋, 等. 基于均匀分布阵列的海上多能联合发电规划及优化[J]. 可再生能源, 2020, 38(12): 1662-1669.
LIU Ning, MI Zhiwei, LIU Dong, et al. Planning and optimization method of offshore multi-energy hybrid generation system based on uniform distributed array[J]. Renewable Energy Resources, 2020, 38(12): 1662-1669.
[19]
LEHMANN K, GRASTIEN A, VAN HENTENRYCK P. AC-feasibility on tree networks is NP-hard[J]. IEEE Transactions on Power Systems, 2016, 31(1): 798-801.
[20]
BIENSTOCK D, VERMA A. Strong NP-hardness of AC power flows feasibility[J]. Operations Research Letters, 2019, 47(6): 494-501.
We prove that testing feasibility for an AC power flow system is a strongly NP-hard problem. (C) 2019 Elsevier B.V.
[21]
邰世文, 商剑平. 煤炭码头卸车调度问题多目标优化模型及算法[J]. 运筹与管理, 2018, 27(6): 91-99.
Abstract
本文针对煤炭码头卸车调度问题,提出了相应的多约束多目标优化模型,并设计了采用仿真推演策略解码的遗传算法求解。首先,本文考虑列车、煤种、场存、设备、翻堆线和卸车作业过程等约束条件,以卸车效率最大和列车在港时间最短为目标,构建了煤炭码头卸车调度问题多目标数学模型。然后,综合运筹学、遗传算法以及仿真技术,给出了煤炭码头卸车调度问题遗传算法详细设计,包括组合式编码和仿真推演解码方法,染色体生成算法,适应度函数设计,以及采用多种策略的遗传操作及修正等,并列出了算法步骤。实例测试表明,本算法的执行效率高而且优化效果好,结果适用。
TAI Shiwen, SHANG Jianping. Multi-objective optimization model on unloading scheduling problem of coal terminal and its genetic algorith[J]. Operations Research and Management Science, 2018, 27(6): 91-99.
This paper puts forward a multi-objective constrained optimization model on unloading scheduling problem of coal terminal and the design of the genetic algorithm in which a simulation strategy is used to decode. First, the optimization model on unloading job scheduling problem is established with the multi-objective concerning maximizing the rate of unloading and minimizing the total time of train in port and some constraints including trains, coals, stocks, equipment, dumping lines and unloading processes. On the basis of summing up operations research, genetic algorithm and simulation, the genetic algorithm is designed including the improved coding and decoding with the simulation and deduction method, the way of chromosome generation, the design of fitness, genetic operation and correction using multiple strategies. Besides, the paper lists the steps of the genetic algorithm. Finally, the actual numerical experiment and the successful application have shown that the solution has a high execution efficiency and satisfactory effect.
[22]
王海军, 杜丽敬, 马士华. 震后应急物流系统中双目标开放式选址: 路径问题模型与算法研究[J]. 管理工程学报, 2016, 30(2): 108-115.
WANG Haijun, DU Lijing, MA Shihua. Model and algorithms for integrated open location and routing problem in emergency logistics under earthquake[J]. Journal of Industrial Engineering and Engineering Management, 2016, 30(2): 108-115.
[23]
李桂丹, 王佳琦, 靳新悦, 等. 风电场内部无功分配优化策略[J]. 电力系统及其自动化学报, 2019, 31(7): 123-128.
LI Guidan, WANG Jiaqi, JIN Xinyue, et al. Optimization strategy for reactive power allocation in wind farm[J]. Proceedings of the CSU-EPSA, 2019, 31(7): 123-128.
[24]
牛东晓, 赵东来, 杨尚东, 等. 基于改进粒子群算法的海上风电汇集方式与并网优化研究[J]. 中南大学学报(自然科学版), 2019, 50(12): 3146-3155.
NIU Dongxiao, ZHAO Donglai, YANG Shangdong, et al. Research on convergence mode and grid-connected optimization of offshore wind power based on improved particle swarm optimization algorithm[J]. Journal of Central South University (Science and Technology), 2019, 50(12): 3146-3155.
[25]
林哲, 胡泽春, 宋永华. 最优潮流问题的凸松弛技术综述[J]. 中国电机工程学报, 2019, 39(13): 3717-3728.
LIN Zhe, HU Zechun, SONG Yonghua. Convex relaxation for optimal power flow problem: a recent review[J]. Proceedings of the CSEE, 2019, 39(13): 3717-3728.
[26]
马骞, 邓卓明, 吴云亮, 等. 受端电网STATCOM布点及容量规划的凸松弛方法[J]. 南方电网技术, 2021, 15(6): 64-70.
MA Qian, DENG Zhuoming, WU Yunliang, et al. Convex relaxation method of STATCOM location and capacity planning in receiving-end power grid[J]. Southern Power System Technology, 2021, 15(6): 64-70.
[27]
肖遥, 别朝红, 黄格超, 等. 基于二阶锥最优潮流的机会约束分布鲁棒优化研究[J]. 电网技术, 2021, 45(4): 1505-1517.
XIAO Yao, BIE Zhaohong, HUANG Gechao, et al. Chance-constrained distributional robust optimization based on second-order cone optimal power flow[J]. Power System Technology, 2021, 45(4): 1505-1517.
[28]
巨云涛, 黄炎, 张若思. 基于二阶锥规划凸松弛的三相交直流混合主动配电网最优潮流[J]. 电工技术学报, 2021, 36(9): 1866-1875.
JU Yuntao, HUANG Yan, ZHANG Ruosi. Optimal power flow of three-phase hybrid AC-DC in active distribution network based on second order cone programming[J]. Transactions of China Electrotechnical Society, 2021, 36(9): 1866-1875.
[29]
GAN L W, LI N, TOPCU U, et al. Exact convex relaxation of optimal power flow in radial networks[J]. IEEE Transactions on Automatic Control, 2015, 60(1): 72-87.
[30]
顾承红, 艾芊. 基于改进内点法的含风电场的系统最优潮流计算[J]. 中国电力, 2007, 40(1): 89-93.
GU Chenghong, AI Qian. Optimal power flow calculation based on the improved interior method for a system integrated with wind farms[J]. Electric Power, 2007, 40(1): 89-93.
[31]
李桂丹, 王佳琦, 靳新悦, 等. 风电场内部无功分配优化策略[J]. 电力系统及其自动化学报, 2019, 31(7): 123-128.
LI Guidan, WANG Jiaqi, JIN Xinyue, et al. Optimization strategy for reactive power allocation in wind farm[J]. Proceedings of the CSU-EPSA, 2019, 31(7): 123-128.

Funding

National Natural Science Foundation of China(62173295)
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