α α = 1-4 T /N i U i = 槡 2 U rms sin i - 1 α N U 5 U 2 = 1 U 2 N N i = U2 rms i = 1 N [ N - sinnαcos N - 1 α sin ] 2 α pulse width modulation

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1 Electri c Machines and Control Vol. 18 No. 1 Jan DSP FLUKE Norma % TP 216 A X Synchronous sampling measuring method of the single-cycle true RMS of motor non-sinusoidal power supply voltage LIU Gang CHEN Shu-xin LUO Wei-dong School of Mechanical Engineering University of Science and Technology Beijing China Abstract Aiming at the problem of measuring the true root-mean-square RMS of pulsing AC voltage on the motor stator windings this paper proposes a real-time measuring method of the single-cycle true RMS of non-sinusoidal periodic signal. According to the definition of true RMS AC voltage it adopted digital discrete synchronous sampling measuring method used DSP to sample the instantaneous value of non sinusoidal pulse width modulation voltage and combined the hardware synchronization method with the software synchronous method in order to accomplish the real-time accurate measurement of the true RMS of non-sinusoidal periodic AC voltage signal. In this paper it compared the results of this method by measuring the true RMS of pulsing AC voltage on the motor stator windings with the results of FLUKE Norma 5000 power analyzer. The relative error is less 1%. This method can measure not only the true RMS of non-sinusoidal periodic signal but also the true RMS of the sinusoidal AC voltage. Key words motor non-sinusoidal power supply single-cycle true RMS digital discrete synchronous sampling hardware synchronization method software synchronization method AA BAB02B07 Z

1 113 0 α α = 1-4 T /N i U i = 槡 2 U rms sin i - 1 α N U 5 U 2 = 1 U 2 N N i = U2 rms i = 1 N [ N - sinnαcos N - 1 α sin ] 2 α pulse width modulation PWM α = T /N N > 2 sinnα = 0 sinα 0 6 7-9 RMS /DC

2 α α = 1-4 T /N i U i = 槡 2 U rms sin i - 1 α N U 5 U 2 = 1 U 2 N N i = U2 rms i = 1 N [ N - sinnαcos N - 1 α sin ] 2 α pulse width modulation PWM α = T /N N > 2 sinnα = 0 sinα RMS /DC Fig. 1 Phase current and line voltage of the stator windings After a Hall sensor TMS320F28335 U = U rms 2 1 U rms = U 2 N N i 3 1 δ = U - U rms U 2 - U 2 rms = U rms U rms U + U rms U2 - U 2 rms 2U 2 rms 2 sinnαcos N - 1 α δ = 4 2Nsinα 1 4 α T /N U rms = 槡 1 T T u 2 t d t 0 1 u 1 u 2 u 3 u N N 槡 i = 1 α T /N T u t 2 DSP u t 2

114 18 DSP AD 15 非正弦脉宽调制电压信号全波精密整流电路硬件同步信号 AD TMS320F28335 过零比较 GPIO 电路 N 2 T /N Fig. 2 Hardware model of the method 3 2 DSP 3.

3 Line voltage of the stator windings and its synchronous signal 系统启动 DSP AD 0 ~ 3 V U 1 U ON 4 周期内对被测信号 3 T N T /N T 4 DSP AD 3 DSP GPIOA DSP AD AD N AD

3 DSP AD 15 非正弦脉宽调制电压信号全波精密整流电路硬件同步信号 AD TMS320F28335 过零比较 GPIO 电路 N 2 T /N Fig. 2 Hardware model of the method 3 2 DSP 3. 3 V DSP AD AD DSP AD N V(2V/div) TMS320F28335 AD 12. 5M 80ns 3 5 Fig. 3 Line voltage of the stator windings and its synchronous signal 系统启动 DSP AD 0 ~ 3 V U 1 U ON 4 周期内对被测信号 3 T N T /N T 4 DSP AD 3 DSP GPIOA DSP AD AD N AD 在同步信号的一个进行 N 次等间隔采样, 将结果存在数组中并记录下采样次数 N 初始化 SYSCLK AD GPIO 检测 GPIO 输入同步信号升沿和下降沿将 AD 采得的结果通过牛顿迭代公式计算, 得到一个硬件同步信号周期内的交流信号有效值结束 4 Fig. 4 Line voltage and phase current of the stator After full-wave precision rectifier circuit f x = x 2 - M = 0 Fig. 5 5 The flow chart of system software N 3 3

1 115 f x x 0 1 f x = f x 0 + x - x 0 f' x 0 + x - x 0 2 f x 0 + 2 y f y = f x 0 + y - x 0 f' x 0 + y - x 0 2 f x 0 + 2 y FLUKE Norma 5000 f x 0 + y - x 0 f' x 0 = 0 2 y = x 0 - f x 0 /f' x 0 Table 2

4 1 115 f x x 0 1 f x = f x 0 + x - x 0 f' x 0 + x - x 0 2 f x y f y = f x 0 + y - x 0 f' x 0 + y - x 0 2 f x y FLUKE Norma 5000 f x 0 + y - x 0 f' x 0 = 0 2 y = x 0 - f x 0 /f' x 0 Table 2 The measurements and error of unregular sinusoidal signal x N = x N f x N - 1 /f' x N - 1 f x = x 2 - M ( ) x N = 0. 5 x N M x N - 1 f' x = 2x 5 x 1 = u 1 DSP N 2 M 5 x N N N % FLUKE Norma 5000 AD 80ns Hz FLUKE Norma 5000 FLUKE Norma ~ 1000 Hz 3 MHz 340 khz 0. 05% V 1 Norma 5000 V 2 e e = V 2 - V 1 δ δ = e /V Table 1 The measurements and error of regular sinusoidal signal Fig. 6 The signal with changing period and voltage and its synchronous sampling signal /V V 1 /V V 2 /V e /V δ /% % 1 2 /Hz V 1 /V V 2 /V e /V δ /% V(2V/div) DSP 1 3

5 EGALON J CAUX S MAUSSION P et al. Multiphase system for metal disc induction heating modeling and RMS current con TMS320F28335 AD trol J J % AD detection circuit based on LT1088 J tific Instrument MOHNS E IHLENFELD W G K. transfer with thermal converters J RMS /DC 1 BOLLEN M H J GOOSSENS P ROBERT A. Assessment of voltage dips in HV-networks deduction of complex voltage from the measured RMS voltage J. IEEE Transactions on Power Delivery ZHANG Weiqiang YING Jianping LIANG Rongqing et al. Predictable characteristics of the fluorescent lamp electrodes with the constant RMS voltage heating method during the preheating phase J. IEEE Transactions on Power Electronics HE Zhongyi XING Yan. Distributed control for UPS modules in parallel operation with RMS voltage regulation J. IEEE Transactions on Industrial Electronics YANG X X KRATZ M. Power system flicker analysis by RMS voltage values and numeric flicker meter emulation J. IEEE Transactions on Power Delivery WANG Zhenhua. Novel pseudo RMS current converter for sinusoidal signals using a CMOS precision current rectifier J. IEEE Transactions on Instrumentation and Measurement J XIA Hongyong HUANG Shaogang. Influence of field current pulsation on no-load voltage waveform of armature windings J. Electric Machines and Control / 20 MIN M PARVE T RONK A et al. Synchronous sampling and J demodulationin an instrument for multifrequency bioimpedance LI Li HUANG Songbai WANG Hongliang. Combined three- measurement J. IEEE Transactions on Instrumentation and phase inverter operating in voltage or current control mode J. E- lectric Machines and Control J WANG Dong WU Xinzhen GUO Yunjun et al. Determination of harmonic voltages for fifteen-phase induction motors with non-sinusoidal supply J. Proceedings of the CSEE IEEE Transactions on industry applications LT1088 DONG Aihua SHI Zhina. High accuracy voltage effective value. Chinese Journal of Scien- Fast synchronous AC-DC-. IEEE Transactions on Instrumentation and Measurement WALTRIP B C OLDHAM N M. Wideband wattmeter based on RMS voltage measurements J. IEEE Transactions on Instrumentation and Measurement J CHEN Zhihui JIANG Changsheng YAN Yangguang. Digital voltage measurement algorithms in a digital voltage regulator J. Transactions of China Electrotechnical Society KOLANKO J K. Accurate measurement of power energy and true RMS voltage using synchronous counting J. IEEE Transactions on Instrumentation and Measurement M IUZZOLINO R GUILHERME W. High-accuracy methods and measurement procedures for power quality parameters using the digital synchronous sampling technique J. IEEE Transactions on Instrumentation and Measurement FLEYER M LINDEN A HOROWITZ M et al. Multirate synchronous sampling of sparse multiband signals J. IEEE Transactions on Signal Processing COURTEAU R BOSE T K. A high-precision RF vector analyzer 6. based on synchronous sampling J. IEEE Transactions on Instrumentation and Measurement OVERNEY F JEANNERET B. RLC bridge based on an automated synchronous sampling system J. IEEE Transactions on Instrumentation and Measurement Measurement

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1 22 2 2018 2 Electri c Machines and Control Vol. 22 No. 2 Feb. 2018 1 2 3 3 1. 214082 2. 214082 3. 150001 DOI 10. 15938 /j. emc. 2018. 02. 005 TM 301. 4 A 1007-449X 2018 02-0033- 08 Research of permanent