三相非正弦多重矢量功率理论

Three-phase Power Multivector Theory under Non-sinusoidal Conditions

功率理论是以电路中的能量流动和物理现象为基础,通过数学表达式对功率特性进行准确描述,在电能计量、谐波和无功补偿等方面具有重要意义。随着电力电子技术的广泛应用,现代电力系统中非正弦和不对称问题日益严重,但传统无功功率定义仅在正弦条件下有意义,在非正弦下无功功率的补偿方案缺乏理论支撑。文中基于几何代数法建立了多重矢量功率理论,其功率分量包括有功功率、分散功率、Budeanu无功功率、畸变无功功率以及相间不平衡功率。该方法适用于非正弦单相和三相电路,能够很好地描述功率分量,并遵循电路中的基本定理。最后在不同的工况下对功率进行仿真计算,结果表明划分后的各部分功率能够被准确测量,且物理意义明确,验证了该方法的有效性。

Based on the energy flow and physical phenomena in the circuit, power theory accurately describes the power characteristics through mathematical expressions and is of great significance in terms of electric energy measurement, harmonics and reactive power compensation. With the widespread application of power electronic technology, non-sinusoidal and asymmetry problems in modern power systems are more serious. But the definition of traditional reactive power is only meaningful for sinusoidal circuits, and lacks theoretical support for reactive power compensation strategy under non-sinusoidal conditions. Based on the geometric algebra approach, we proposed the power multivector theory to solve such problems, which includes active power, scattered power, Budeanu’s reactive power, distortion reactive power and unbalanced power between phases. This approach is suitable for both non-sinusoidal single-phase circuits and three-phase circuits. It can describe the power components well and follows the basic theorem in the circuit. Finally, the power under different working conditions was calculated and simulated to verify this theory. The results show that the power components after division can be accurately measured, and the physical meaning is clear.