非整周期采样下电功率测量的误差分析

Error analysis for electrical power measurements with non-integer-period sampling

利用基于相关原理的智能仪器测量周期信号的各种电参数时,由于硬件条件的限制,非整周期采样所致误差无法被完全消除。为了减小该误差,提出一种定量修正方法,以实现电功率的精密测量。该方法以含谐波的电气信号功率测量为例,从时域平均功率定义出发,采用正弦函数的一阶T ay lor展开,推导出因非整周期采样造成的测量误差的解析表达式和相应的修正公式。实验结果表明:恰当地选择采样频率和采样周期数以减小信号周期偏差,且控制初始采样时刻,使电压和电流初始采样值的乘积接近于所测电功率的大小,这些均可在很大程度上降低测量误差。

When measuring the electrical characteristics of periodic signals using intelligent instruments based on the correlation principle, errors caused by non-integer-period sampling cannot be eliminated completely due to hardware restrictions. Such errors can be reduced with a quantitative correction method designed for precise measurements of the electrical power. For the signals with various harmonic components, the definition of the average power in the time domain and the first-order Taylor formula on sinusoidal function are used to develop an analytical expression for the measurement error and a correction formula. The results indicate that the error can be reduced substantially by properly selecting the sampling frequency and number of periods to reduce the period bias and controlling the initial sampling time so that the product of the initial voltage and current are close to the measured electrical power.