在理想化的线性时不变集总参数正弦稳态电路中探讨无功功率，梳理出了无功功率定义的两种等价方法；从阻抗的瞬时功率入手，将瞬时功率分解为有功分量和无功分量，给出阻抗串联模型、并联模型时有功分量和无功分量的准确表达式。通过计算分析典型电路的无功分量表明：理想线性电容电感元件的串联或并联、电阻电感电容串联（RLC）或三者并联以及阻抗串联的单口网络中感性负载与容性负载的无功能量吞吐反相，而感性阻抗和容性阻抗并联，三相电路的无功能量吞吐不可能反相；无功能量既可能在电源与负载之间流动，也可能在各负载之间流动；负载侧网络的总吞吐幅度不一定等于网络中各负载无功功率的代数和。
Reactive power is one of important physical quantities in physics and engineering. In this paper, the concept of reactive power is classified in linear, time invariant, or lumped parameter circuits with ideal sinusoidal steady-state excitation. Two equivalent methods for the definition of reactive power are presented first. The instantaneous power of impedance is decomposed into active power and reactive power. Accurate expressions of active and reactive components of the instantaneous power are given for both series models and parallel models of impedance. Results based on our calculations and analysis of the reactive component of typical circuits give the conclusions. The reactive energy of inductive and capacitive load throughput can be reversed in one-port circuits of ideal linear capacitors and inductors in series or parallel, RLC in series or parallel, and impedance series. In contrast, reactive energy cannot be reversed in circuits of inductive impedance and capacitive impedance in parallel, or in circuits with three-phase loads. In addition, reactive energy can flow between the power supply and each load, and also flow between each load. Finally, the throughput amplitude of the whole load-side network is not necessarily equal to the algebraic sum of the reactive power of each of the loads in the network.
[1] 秦文萍, 王鹏, 韩肖清, 等. 电力系统有功和无功功率充裕度评估[J]. 电力系统自动化, 2014, 38(1):28-33. Qin W P, Wang P, Han X Q, et al. Adequacy evaluation of active and reactive power in power system[J]. Automation of Electric Power Systems, 2014, 38(1):28-33. (in Chinese)
[2] 董大伟. 浅谈无功功率的产生和补偿技术[J].中国电力教育,2011(27):104-105. Dong D W. Discussion on reactive power generation and compensation technology[J]. China Electric Power Education, 2011(27):104-105. (in Chinese)
[3] 秦曾煌. 电工学(上册)[M]. 7版. 北京:高等教育出版社, 2009:108-181. Qin Z H. Electro technician (the first volume)[M]. 7th ed. Beijing:Higher Education Press, 2009:108-181. (in Chinese)
[4] 李翰荪. 简明电路分析基础[M]. 北京:高等教育出版社, 2014:457-462. Li H S. Fundamentals of concise circuit analysis[M]. Beijing:Higher Education Press, 2014:457-462. (in Chinese)
[5] 燕庆明. 电路分析基础[M]. 3版.北京:高等教育出版社,2012:173-220. Yan Q M. Electric circuit analysis[M]. 3rd ed. Beijing:Higher Education Press, 2012:173-220. (in Chinese)
[6] Alexander C K, Sadiku M N O. Fundamentals of electric circuits[M]. Beijing:China Machine Press, 2013:457-488.
[7] 包国荣. 论正确理解无功功率概念[J]. 咸宁师专学报,1993(2):43-47. Bao G R. On correctly understanding the concept of reactive power[J]. Journal of Xianning Teachers College,1993(2):43-47. (in Chinese)
[8] 田社平,陈洪亮. 关于无功功率的讨论[J]. 电气电子教学学报,2012,34(1):23-35. Tian S P, Chen H L. Discussion on reactive power[J]. Journal of Electrical & Electronic Engineering Education, 2012, 34(1):23-35. (in Chinese)
[9] 汪小娜, 单潮龙, 何坊, 等. 对无功功率物理意义的讨论[J]. 物理与工程, 2014, 24(2):34-36. Wang X N, Shan C L, He F, et al. Disscussion on physical significance of reactive power[J]. Physics and Engineering, 2014, 24(2):34-36. (in Chinese)
[10] 王茂海, 孙元章. 三相电路中功率现象的解释及无功功率的分类[J]. 中国电机工程学报, 2003, 23(10):63-66. Wang M H, Sun Y Z. Analysis of power phenomenon and classification of reactive power in three-phase circuit[J]. Proceedings of the CSEE, 2003, 23(10):63-66. (in Chinese)
[11] Alok Kumar. Reactivepower control in electrical power transmission system[J]. International Journal of Engineering Trends and Technology, 2013, 4(5):1707-1709.
