A Measuring Method of the Single-Phase AC Frequency, Phase, and Reactive Power Based on the Hilbert Filtering

This paper presents a novel measuring method based on the Hilbert filtering for the digital monitoring of the single-phase ac frequency, phase, and reactive power. According to this method, the sampled voltage signal passes a pair of the Hilbert filters. Then, the ac frequency and phase can be obtained by the phase detection and the phase-locked loop algorithm. Additionally, the sampled current signal also makes its phase shift by the other Hilbert filter. The current output is multiplied by the one of the phase-shifted voltage signals, and the reactive power is acquired from the dc component of the product. Because a type of infinite impulse response (IIR) Hilbert filters with low-order and small phase-shift error is adopted, this measuring method cannot only obtain fast and accurate digital monitoring results but also be easily realized with the DSP or other microprocessor programming codes. This method has been successfully applied in the design of a digital multifunctional power instrument

I. Introduction

In power systems, the present digital measurement and control instruments require that acquiring electrical parameters should be based on the sampled output data from the analog-to-digital converter (ADC). Thus, some conventional measuring methods of the frequency, phase, and reactive power cannot satisfy the update design requirements. For example, the counting method [1] and the phase-locked loop logic circuit method [2], [3], which are popular in frequency and phase measurement, are difficult to directly realize with the sampled data and microprocessor software. Another method (the discrete Fourier transform [4]) can also be used to analyze the ac frequency and phase. However, the accuracy of this method is dependent on the sampled point number and the calculation precision, and the calculated phase angle is not the phase value at the current sampling time. The measurement of the reactive power has similar problems. Currently, there are two different definitions of reactive power. One definition is expressed as$$Q = \sqrt{(U \cdot I)^{2} - P^{2}}\eqno{\hbox{(1)}}$$where and are the rms values of the voltage and current, is the apparent power, and is the active power. According to this definition, three parameters of , , and should be measured beforehand, and the accuracy of each parameter will affect the reactive power result. Another definition can acquire the total reactive power of the fundament and harmonics, which is expressed as$$Q = \sum_{k = 1}^{N}Q_{k} = \sum_{k = 1}^{N}U_{k}I_{k}\sin\varphi_{k}\eqno{\hbox{(2)}}$$where and are the rms values of each voltage and current component, is the phase difference between each voltage and current component, is the reactive power of each component, and is the maximum order of the measured harmonics. , , and in (2) can be obtained through the Fourier transform, but such an algorithm is complex and nonreal-time. Engineers with Siemens Corporation in Germany have utilized finite impulse response (FIR) Hilbert filters to complete the reactive power measurement of (2) [5]. Because the FIR Hilbert filters must have very high order to satisfy phase-shift accuracy, the Siemens' method requires a lot of calculation.