[논문해석] Automatic Power Frequency Rejection Instrumentation for Nonintrusive Frequency Signature Tracking

0. 원문

https://ieeexplore.ieee.org/document/9152122

Automatic Power Frequency Rejection Instrumentation for Nonintrusive Frequency Signature Tracking

 

1. 내용

(0) Abstract

This article presents a design for data acquisition hardware that can automatically track and reject utility frequency components of a measured current or voltage waveform. Measurements of subtle harmonic content in the waveform can therefore be made with the full dynamic range of the on-board analog-to-digital converter. This permits the detection of small, higher frequency signals for applications to condition-based maintenance and energy scorekeeping. Experimental demonstrations in this article show the hardware prototype isolating the rotor slot harmonics in a motor’s input current. The highresolution measurements of slot harmonics permit the estimation of motor speed from the detected slot harmonic frequency and the rejected fundamental frequency. The performance and accuracy of the speed estimator are demonstrated with both steady-state and transient experiments.

이 논문은 측정된 전류 또는 전압 파형의 유틸리티 주파수 성분을 자동으로 추적하고 제거할 수 있는 데이터 수집 하드웨어 설계를 제시합니다. 따라서 파형의 미세한 고조파 내용을 온보드 아날로그-디지털 변환기의 전체 동적 범위로 측정할 수 있습니다. 이를 통해 상태 기반 유지보수와 에너지 점수 계산을 위한 소형 고주파 신호를 감지할 수 있습니다. 본 논문의 실험적 시연에서는 모터의 입력 전류에서 로터 슬롯 고조파를 분리하는 하드웨어 프로토타입을 보여줍니다. 슬롯 고조파의 고해상도 측정을 통해 감지된 슬롯 고조파 주파수와 제거된 기본 주파수로부터 모터 속도를 추정할 수 있습니다. 속도 추정기의 성능과 정확도는 정상 상태 및 과도 상태 실험을 통해 입증되었습니다.

 

(1) Introduction

VALUABLE information for diagnostics, control, and energy-scorekeeping may be found over a range of frequencies and amplitudes in utility waveforms. The ac utility effectively creates a substantial “carrier frequency” component at the utility frequency that indicates real and reactive power demand. Other frequency content, for example, in the current waveforms demanded by a load, can serve as important tell-tale signatures for identifying loads and recognizing operating state and fault conditions. This additional frequency content may be at harmonic multiples of the utility frequency, or distributed in other ways, for example, as a multiple or function of both utility frequency and slip frequency in a motor. The relative amplitude of signals like current at the utility frequency versus motor slot harmonic frequencies may vary over several orders of magnitude [1]. This creates a significant practical problem in achieving an adequate dynamic range to observe all signals of interest. The problem is compounded by normal variations in the utility frequency, which complicates the design of data acquisition instrumentation for making complete measurements of interest.

진단, 제어, 에너지 점수 계산을 위한 유용한 정보는 유틸리티 파형의 다양한 주파수와 진폭 범위에서 찾을 수 있습니다. 교류 유틸리티는 실제 및 무효 전력 수요를 나타내는 유틸리티 주파수에서 상당한 "캐리어 주파수" 성분을 효과적으로 생성합니다. 예를 들어 부하가 요구하는 전류 파형의 다른 주파수 성분은 부하 식별, 운영 상태 인식 및 고장 조건 식별을 위한 중요한 신호로 작용할 수 있습니다. 이러한 추가 주파수 성분은 유틸리티 주파수의 고조파 배수일 수 있으며, 또는 모터의 유틸리티 주파수와 슬립 주파수의 배수나 함수로 분포될 수 있습니다. 유틸리티 주파수에서의 전류와 모터 슬롯 고조파 주파수와 같은 신호의 상대 진폭은 여러 자릿수에 걸쳐 변할 수 있습니다【1】. 이는 관심 신호를 모두 관찰하기 위해 충분한 동적 범위를 확보하는 데 있어 중요한 실질적 문제를 야기합니다. 유틸리티 주파수의 정상적인 변동으로 인해 관심 신호의 완전한 측정을 위한 데이터 수집 장비 설계가 더욱 복잡해지는 문제가 발생합니다.

 

This article presents a custom design for data acquisition hardware that can automatically track and reject “carrier (utility) frequency” content in a nonintrusive current measurement, permitting the resolution of subtle higher harmonic content with the full dynamic range of an available analogto- digital converter (ADC). This new instrumentation design automatically tracks variations in utility frequency and adapts to ensure reliable measurements of relatively small signals which are present in the waveform of interest.

이 논문은 비침습적 전류 측정에서 "캐리어(유틸리티) 주파수" 성분을 자동으로 추적하고 제거할 수 있는 맞춤형 데이터 수집 하드웨어 설계를 제시합니다. 이를 통해 사용 가능한 아날로그-디지털 변환기(ADC)의 전체 동적 범위로 미세한 고조파 성분을 분해할 수 있습니다. 이 새로운 계측기 설계는 유틸리티 주파수의 변동을 자동으로 추적하고 적응하여 관심 파형에 존재하는 상대적으로 작은 신호를 신뢰성 있게 측정할 수 있도록 합니다.

 

Knowledge of shaft speed, for example, assists with many control and monitoring applications for electric machines [2]–[7]. Using invasive approaches for speed estimation adds sensors to machines, adding complexity and cost [2]–[4]. Installation of the sensors, cables for power and communication, and interface circuits requires additional work and space. These approaches are also vulnerable to faults in each component [6]. Noninvasive, speed sensorless monitoring can reliably estimate speed [6]–[15] with varying approaches and effort. Commonly used estimation methods require detailed motor models [8]–[10] with accurate parameter estimates [10], [11]. Machine saliencies [12], [13] and magnetic variations [14], [15] allow for speed estimation without dedicated speed sensors or a detailed machine model. These signals create tell-tale signs at frequencies higher than the utility, which can be examined.

예를 들어, 샤프트 속도에 대한 지식은 전기 기계의 많은 제어 및 모니터링 응용 프로그램에 도움이 됩니다【2】–【7】. 속도 추정을 위한 침습적 접근 방식은 기계에 센서를 추가하여 복잡성과 비용을 증가시킵니다【2】–【4】. 센서 설치, 전력 및 통신을 위한 케이블, 인터페이스 회로는 추가 작업과 공간을 필요로 합니다. 이러한 접근 방식은 각 구성 요소의 고장에도 취약합니다【6】. 비침습적, 속도 센서 없는 모니터링은 다양한 접근 방식과 노력으로 속도를 신뢰성 있게 추정할 수 있습니다【6】–【15】. 일반적으로 사용되는 추정 방법은 정확한 매개변수 추정치를 가진 상세한 모터 모델을 필요로 합니다【8】–【10】,【10】,【11】. 기계의 돌출성【12】,【13】과 자기적 변동성【14】,【15】을 통해 전용 속도 센서나 상세한 기계 모델 없이도 속도 추정이 가능합니다. 이러한 신호는 유틸리티보다 높은 주파수에서 특징적인 징후를 만들어 내며, 이를 분석할 수 있습니다. 

 

However, three problems challenge efforts to implement practical nonintrusive speed sensors for electric machines.

First, slot harmonic signals are much smaller in size and located in higher frequency bands when compared with the fundamental component of current. Notch filters have been applied to attenuate the line frequency component and amplify high-frequency harmonics [1], [16]. Subtle variations in the utility frequency can defeat the efficacy of this approach as utility waveforms slide out of the stopband of a tightly tuned filter. Second, as shaft speed changes with mechanical load, the slot harmonic frequencies change with changing machine slip. Complex circuit solutions can phase-lock to these changes [17]–[19], but digital signal processing methods permit more flexible implementations assuming a reliable measurement of slot harmonics can be made [20]–[22]. Third, because an electric machine typically generates a family of harmonics, tracking applications can become confused by coincident changes in utility frequency and higher harmonic, for example, slip-related frequency [1], [15], [22], [23].

그러나 전기 기계에 대한 실용적인 비침습 속도 센서를 구현하는 데에는 세 가지 문제가 있습니다. 첫째, 슬롯 고조파 신호는 기본 전류 성분에 비해 훨씬 작고 높은 주파수 대역에 위치해 있습니다. 노치 필터는 라인 주파수 성분을 약화시키고 고주파 고조파를 증폭하는 데 사용되었습니다【1】,【16】. 유틸리티 주파수의 미세한 변동은 유틸리티 파형이 정밀하게 조정된 필터의 정지 대역을 벗어나면서 이 접근 방식의 효율성을 떨어뜨릴 수 있습니다. 둘째, 샤프트 속도가 기계적 부하와 함께 변화하면 슬롯 고조파 주파수도 기계 슬립의 변화와 함께 변합니다. 복잡한 회로 솔루션은 이러한 변화를 위상 고정할 수 있지만【17】–【19】, 디지털 신호 처리 방법은 슬롯 고조파의 신뢰할 수 있는 측정이 가능하다는 가정하에 더 유연한 구현을 허용합니다【20】–【22】. 셋째, 전기 기계는 일반적으로 고조파 군을 생성하므로, 추적 응용 프로그램은 유틸리티 주파수와 슬립 관련 주파수 등 높은 고조파의 동시 변동으로 인해 혼란을 겪을 수 있습니다【1】,【15】,【22】,【23】.

 

This article also presents a nonintrusive speed estimation method using the proposed tracking hardware and demonstrates the speed estimation performance with induction motors as a working example. The data acquisition board with an automatically tunable notch filter tracks utility frequency and provides high resolution measurements of higher harmonics as the utility frequency experiences inevitable variations. To detect key slot harmonics from the filtered data, a slot harmonic tracking algorithm is proposed. It includes an optimization process to increase the accuracy of frequency detection and improve dynamic performance. Reliable harmonic tracking is achieved as the motor load varies by taking advantage of the inherent slip range typically observed for efficient operation in most induction machines. The accuracy and dynamic performance of the proposed speed estimation techniques are verified through experiments at various operating conditions and are used to demonstrate the utility of the proposed instrumentation and harmonic tracking algorithm for enhanced nonintrusive load monitoring.

이 논문은 제안된 추적 하드웨어를 사용한 비침습적 속도 추정 방법을 제시하고, 유도 전동기를 예시로 하여 속도 추정 성능을 입증합니다. 자동으로 조정 가능한 노치 필터가 있는 데이터 수집 보드는 유틸리티 주파수를 추적하고, 유틸리티 주파수가 불가피하게 변동하는 동안 고조파를 고해상도로 측정합니다. 필터링된 데이터에서 주요 슬롯 고조파를 감지하기 위해 슬롯 고조파 추적 알고리즘이 제안되었습니다. 이 알고리즘은 주파수 감지 정확도를 높이고 동적 성능을 향상시키기 위한 최적화 과정을 포함합니다. 모터 부하가 변화함에 따라 대부분의 유도 전동기에서 효율적인 작동을 위해 관찰되는 고유한 슬립 범위를 활용하여 신뢰할 수 있는 고조파 추적이 달성됩니다. 제안된 속도 추정 기술의 정확성과 동적 성능은 다양한 작동 조건에서 실험을 통해 검증되었으며, 개선된 비침습적 부하 모니터링을 위한 제안된 계측 장비와 고조파 추적 알고리즘의 유용성을 입증하는 데 사용되었습니다.

 

(2) Frequency Signature

Most impedance loads draw current signatures with frequency content beyond the utility frequency. Induction motors, an industry workhorse, for example, have rotor slots that create harmonics in phase currents, voltages, and machine fluxes [1], [16]. These harmonics can be measured in the air-gap flux, stator current, and stator voltage at frequencies

대부분의 임피던스 부하는 유틸리티 주파수를 초과하는 주파수 성분을 가진 전류 신호를 끌어옵니다. 예를 들어 산업의 주력인 유도 전동기는 로터 슬롯이 있어 위상 전류, 전압 및 기계 플럭스에 고조파를 생성합니다【1】,【16】. 이러한 고조파는 공극 플럭스, 고정자 전류 및 고정자 전압에서 측정될 수 있습니다.

where fs is the supply frequency, k = 0, 1, 2, . . . is the order of rotor slot harmonics, R is number of rotor slots, p is the number of pole pairs, nd = 0, ±1, . . . is the order of rotor eccentricity or decentering as it rotates with respect to the stator, s is the rotor slip, and v = ±1, ±3, . . . is the order of stator MMF harmonics [12]. If the motor is mechanically healthy (n_d = 0) and fed with a pure sinusoidal supply (v = 1), the harmonic content in the line current demanded by the machine can be expected to distribute around a simplified set of slot harmonic frequencies that may be well represented or tracked by following the “principal slot harmonic” (PSH) at k = 1, expressed as follows:

여기서 \( f_s \)는 공급 주파수, \( k = 0, 1, 2, \ldots \)는 로터 슬롯 고조파의 차수, \( R \)는 로터 슬롯의 수, \( p \)는 극쌍의 수, \( nd = 0, \pm1, \ldots \)는 로터의 편심 또는 고정자에 대한 회전 중심 이탈의 차수, \( s \)는 로터 슬립, \( v = \pm1, \pm3, \ldots \)는 고정자 자기모터힘(MMF) 고조파의 차수를 나타냅니다【12】. 
모터가 기계적으로 건전하고(\( n_d = 0 \)) 순수한 사인파 공급을 받는다면(\( v = 1 \)), 기계가 요구하는 라인 전류의 고조파 성분은 다음과 같이 \( k = 1 \)에서의 "주요 슬롯 고조파"(\( PSH \))를 따라 잘 표현되거나 추적될 수 있는 단순화된 슬롯 고조파 주파수 집합 주위에 분포할 것으로 예상할 수 있습니다:

 

Fig. 1 shows a measured example of the current spectrum of a three-phase induction motor at 60-Hz supply. The frequency spectrum was obtained by the discrete Fourier transform (DFT) of the motor current data sampled for 10 s. The test motor with 18 rotor slots and 2 pole pairs was running at 1657.7 r/min. There are several peaks at different frequencies, each point indicating where a current harmonic is present. As shown in (1), three factors are involved in the creation of harmonics: rotor slots, rotor eccentricity, and stator MMF harmonics. Harmonics at different frequencies are generated by different combinations of k, nd, and v. Often, as seen for the test motor, the PSH has the largest amplitude. With R and p fixed by the motor structure, the frequency of the PSH depends only on the rotor slip and the supply frequency. Thus, tracking PSH is an effective way to estimate the rotor slip

which typically ranges for practical induction machines between 0% and 5%. The PSH is therefore an example of a valuable harmonic that can be measured, in principle, by a nonintrusive power monitor to track machine operation and to differentiate the activity and operation of several machines on the same power service. Unfortunately, the PSH may be several orders of magnitude smaller in amplitude than the utility frequency fundamental current. It is therefore difficult to locate. This problem is exacerbated by any variations in the utility frequency, which happen frequently, and which complicates the design of a filter to reject fundamental frequency current.

그림 1은 60Hz 공급 시 삼상 유도 전동기의 전류 스펙트럼의 측정 예를 보여줍니다. 이 주파수 스펙트럼은 모터 전류 데이터를 10초 동안 샘플링하여 이산 푸리에 변환(DFT)을 통해 얻었습니다. 18개의 로터 슬롯과 2개의 극쌍을 가진 테스트 모터는 1657.7 r/min으로 작동했습니다. 각 주파수에서 여러 피크가 나타나며, 각 피크는 고조파 전류가 존재하는 지점을 나타냅니다. 식 (1)에서 알 수 있듯이, 로터 슬롯, 로터 편심, 고정자 MMF 고조파라는 세 가지 요소가 고조파 생성에 관여합니다. 서로 다른 주파수에서의 고조파는 k, nd, v의 다양한 조합에 의해 생성됩니다. 종종 테스트 모터에서 볼 수 있듯이 PSH는 가장 큰 진폭을 가집니다. 모터 구조에 의해 R과 p가 고정되면 PSH의 주파수는 로터 슬립과 공급 주파수에만 의존하게 됩니다. 따라서 PSH를 추적하는 것은 로터 슬립을 추정하는 효과적인 방법입니다.
실용적인 유도 전동기에서 로터 슬립은 일반적으로 0%에서 5% 사이입니다. 따라서 PSH는 원칙적으로 비침습적 전력 모니터를 통해 측정하여 기계 작동을 추적하고 동일한 전력 서비스에서 여러 기계의 활동과 작동을 구별하는 데 사용할 수 있는 유용한 고조파의 예입니다. 그러나 PSH는 유틸리티 주파수의 기본 전류에 비해 진폭이 여러 자릿수 작을 수 있습니다. 따라서 이를 찾기가 어렵습니다. 이 문제는 유틸리티 주파수의 변동이 자주 발생하여 기본 주파수 전류를 차단하기 위한 필터 설계를 복잡하게 함으로써 더욱 악화됩니다.

 

(3) Data Acquisition, Processing, and Filtering

To improve the detectability of rotor slot harmonics, this section introduces the architecture of a data acquisition, processing, and filtering board that can selectively and adaptively reject larger signal components in favor of much smaller harmonics. Fig. 2 shows a block diagram of the design, which provides eight-channels of simultaneously sampled data at sampling rates as high as 24 kHz. Two key features offered by the design include a zero-crossing detector for line frequency estimation and a switched capacitor (SC) notch filter with tunable center frequency. A microcontroller coordinates the operation of the SC filter and data sampling. One of the eight input channel signals is selected for the slot harmonic detection by the microcontroller using an 8:1 multiplexer.

로터 슬롯 고조파의 탐지 가능성을 향상시키기 위해, 이 섹션에서는 더 큰 신호 성분을 선택적으로 그리고 적응적으로 제거하여 훨씬 작은 고조파를 선호할 수 있는 데이터 수집, 처리 및 필터링 보드의 아키텍처를 소개합니다. 그림 2는 설계의 블록 다이어그램을 보여주며, 최대 24kHz의 샘플링 속도로 동시에 샘플링된 8채널 데이터를 제공합니다. 이 설계가 제공하는 두 가지 주요 기능은 라인 주파수 추정을 위한 영점 교차 검출기와 조정 가능한 중심 주파수를 가진 스위치드 커패시터(SC) 노치 필터입니다. 마이크로컨트롤러는 SC 필터와 데이터 샘플링의 작동을 조정합니다. 마이크로컨트롤러는 8:1 멀티플렉서를 사용하여 8개의 입력 채널 신호 중 하나를 선택하여 슬롯 고조파를 감지합니다.

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The zero-crossing detector allows the microcontroller to detect the frequency of the dominant (for example, utility frequency) fundamental component in the chosen signal. It consists of op-amp circuits for scaling and biasing, and a hysteresis comparator depicted in Fig. 3. The front-end lowpass filter eliminates input noise that can cause undesirable transitions in the comparator output and also attenuates harmonics other than the fundamental. Then, the comparator generates a pulse signal from which the microcontroller estimates the fundamental frequency of the signal. As shown in Fig. 3, a hysteresis comparator with adjustable hysteresis band helps ensure accurate zero-crossing detection with a potential phase delay that does not affect fundamental frequency estimation.

제로 크로싱 감지기는 마이크로컨트롤러가 선택한 신호에서 주요 (예: 유틸리티 주파수) 기본 성분의 주파수를 감지할 수 있게 합니다. 이는 스케일링 및 바이어스 조정을 위한 오프셋 앰프 회로와 그림 3에 나타낸 히스테리시스 비교기로 구성됩니다. 전단 필터는 비교기 출력에서 원하지 않는 전환을 일으킬 수 있는 입력 잡음을 제거하고, 기본 주파수 이외의 고조파를 약화시킵니다. 그런 다음, 비교기는 펄스 신호를 생성하여 마이크로컨트롤러가 신호의 기본 주파수를 추정할 수 있습니다. 그림 3에서 볼 수 있듯이, 조절 가능한 히스테리시스 밴드를 가진 히스테리시스 비교기는 기본 주파수 추정에 영향을 미치지 않는 잠재적인 위상 지연을 보장하며 정확한 제로 크로싱 감지를 돕습니다.

 

Considering that the SC notch filter is a discrete-time filter, a second-order low-pass filter is applied before the SC filter as an antialiasing filter to restrict the bandwidth of the input signal [24]. The cutoff frequency of the antialiasing filter is set to 3.1 kHz, much higher than the input frequency band of interest, allowing for a tradeoff between aliasing and bandwidth. Then, the SC notch filter is implemented with a cascade of two second-order notch filters constructed using the LTC 1060 from Linear Technology, Milpitas, CA, USA. The center frequencies are adjustable with an external clock provided by the microcontroller. The microcontroller adapts the clock frequency to follow the fundamental signal, and therefore allows the notch filter to effectively attenuate the line frequency component even if the line frequency changes. 

SC 노치 필터는 이산 시간 필터이므로, 입력 신호의 대역폭을 제한하기 위해 SC 필터 이전에 2차 저역 통과 필터가 앤티앨리어싱 필터로 적용됩니다 [24]. 앤티앨리어싱 필터의 절단 주파수는 입력 주파수 대역보다 훨씬 높은 3.1 kHz로 설정되어, 에일리어싱과 대역폭 사이의 균형을 가능하게 합니다. 그런 다음, SC 노치 필터는 LTC 1060을 사용하여 구성된 두 개의 2차 노치 필터를 연속적으로 사용하여 구현됩니다. 이 필터의 중심 주파수는 마이크로컨트롤러가 제공하는 외부 클럭에 의해 조정될 수 있습니다. 마이크로컨트롤러는 기본 신호를 따라 클럭 주파수를 적응적으로 조절하므로, 라인 주파수가 변동하더라도 노치 필터가 효과적으로 라인 주파수 구성 요소를 감쇠시킬 수 있습니다. 

 

The structure of the proposed fourth-order SC notch filter, which consists of the LTC 1060, an external clock and gain-tuning resistors, is illustrated in Fig. 4(a). The overall structure is based on a state-variable filter design with twostage integration. Each filter block can produce various filter functions, such as lowpass, bandpass, highpass, notch, and all-pass. Here, each SC block is configured to work like a second-order filter circuit as shown in Fig. 4(b) and provide the following transfer function:

제안된 4차 SC 노치 필터의 구조는 LTC 1060, 외부 클럭 및 이득 조정 저항으로 구성되며, 그림 4(a)에 나와 있습니다. 전체 구조는 두 단계 적분을 통한 상태 변수 필터 설계에 기반을 두고 있습니다. 각 필터 블록은 저역 통과, 대역 통과, 고역 통과, 노치, 올패스 등 다양한 필터 기능을 생성할 수 있습니다. 여기서 각 SC 블록은 그림 4(b)에 나와 있는 것처럼 2차 필터 회로처럼 구성되어 다음 전달 함수를 제공합니다:

 

where H0 is the filter gain when the frequency approaches zero or half the clock frequency, Q is the quality factor, and ωn is the notch frequency. The first block is designed using R1 to R5, as 

where fCLK is the frequency of the external clock signal from the microcontroller. The ratio of the clock frequency to the notch frequency is fixed by resistance values. The second filter block is also designed with the same principle, using R6 to R10. Two filter blocks are designed to have the same frequency ratio, allowing the microcontroller to tune their cutoff frequencies to the supply frequency simultaneously. The microcontroller detects the supply frequency by capturing the timer value on every rising edge of the input pulse signal from the zero-crossing detector. Then, the clock frequency for notch filter tuning is calculated considering the frequency ratio, and finally the clock signal is generated by a pulsewidth modulator (PWM) module in the microcontroller.

여기서 \( H_0 \)는 주파수가 제로에 접근하거나 클럭 주파수의 절반일 때의 필터 이득을 나타내며, \( Q \)는 품질 계수이고, \( \omega_n \)은 노치 주파수입니다. 첫 번째 블록은 \( R_1 \)에서 \( R_5 \)를 사용하여 설계되며, 다음과 같은 전달 함수를 가집니다:
여기서 \( f_{CLK} \)는 마이크로컨트롤러에서 외부 클럭 신호의 주파수를 나타냅니다. 클럭 주파수와 노치 주파수의 비율은 저항 값에 의해 고정됩니다. 두 번째 필터 블록도 동일한 원리로 설계되며, \( R_6 \)에서 \( R_{10} \)을 사용합니다. 두 필터 블록은 같은 주파수 비율을 가지도록 설계되어, 마이크로컨트롤러가 공급 주파수에 맞춰 동시에 그들의 절단 주파수를 조정할 수 있습니다. 마이크로컨트롤러는 제로 크로싱 감지기에서 입력 펄스 신호의 매 라이징 엣지에서 타이머 값을 캡처함으로써 공급 주파수를 감지합니다. 그런 다음, 노치 필터 조정을 위한 클럭 주파수는 주파수 비율을 고려하여 계산되고, 최종적으로 마이크로컨트롤러의 펄스폭 변조기(PWM) 모듈에 의해 클럭 신호가 생성됩니다.

 

The overall transfer function of the SC notch filter cascade is

where the subscript “1” and “2” stand for the first and second filter blocks, respectively. The quality factors determine the ratio of the center frequency to stopband width. In Fig. 5, the green dash-dot curve, blue-dashed curve, and red solid curve represent Bode plots of the transfer function when Q2 is 0.5, 2, and 10, respectively, while Q1 is fixed to 3.625. As shown in Fig. 5, for larger Q2, the stopband is narrower. A large Q-factor is preferred for the proposed board, in which the notch filter is used to eliminate a single frequency component.

위에서 첫 번째 필터 블록을 나타내는 "1" 및 두 번째 필터 블록을 나타내는 "2" 하위 첨자입니다. 품질 계수는 중심 주파수와 정지대역 폭의 비율을 결정합니다. 그림 5에서 녹색 점선, 파란 점선, 빨간 실선 곡선은 각각 Q2가 0.5, 2, 10 일 때의 전달 함수의 보데 플롯을 나타냅니다. 이 때 Q1은 고정된 값 3.625입니다. 그림 5에서 볼 수 있듯이, Q2가 클수록 정지대역이 좁아집니다. 제안된 보드에서는 단일 주파수 구성 요소를 제거하기 위해 노치 필터가 사용되므로 큰 Q-팩터가 선호됩니다. 

In addition to the bandwidth, the Q-factors determine the filter damping ratio. If the supply frequency varies from ωi to ωf at time τ , the fundamental component of a measured signal can be generally expressed with a step change

대역폭 외에도 Q-팩터는 필터 감쇠 비율을 결정합니다. 공급 주파수가 시간 τ에 걸쳐 ωi에서 ωf로 변할 때, 측정 신호의 기본 성분은 일반적으로 스텝의 변화를 가지고 표현된

where Ai and Af are the amplitudes, and φi and φ f are the phases before and after time τ , respectively. As the fundamental frequency, that is the supply frequency, changes the period of the pulse train output by the zero-crossing detector changes accordingly. The microcontroller, which updates the period information on the rising edge of the input pulse, adjusts the filter clock period proportionally.

Ai와 Af는 각각 시간 τ 이전과 이후의 진폭을 나타내며, φi와 φf는 각각 시간 τ 이전과 이후의 위상을 나타냅니다. 기본 주파수인 공급 주파수가 변화하면 제로 크로싱 감지기에 의해 출력된 펄스 트레인의 주기도 그에 따라 변화합니다. 마이크로컨트롤러는 입력 펄스의 상승 에지에서 주기 정보를 업데이트하며, 필터 클럭 주기를 비례적으로 조정합니다.

Fig. 6 illustrates the transition of the pulse wave, vp, and notch frequency, ωn, when the supply frequency changes from 60 to 50 Hz. In Fig. 6, the flag changes from 0 to 1 to show the point at which the input frequency changes. At the time τ , the supply frequency drops to 50 Hz, and the period of the pulse wave increases. The microcontroller detects the change in period on the first rising edge after time τ , occurring at time t1. The transient period Tt between edges before and after τ is determined as

그림 6은 공급 주파수가 60 Hz에서 50 Hz로 변할 때 펄스 파형 vp와 노치 주파수 ωn의 변화를 보여줍니다. 그림 6에서 깃발은 입력 주파수가 변경되는 지점을 나타내기 위해 0에서 1로 변경됩니다. 시간 τ에서 공급 주파수가 50 Hz로 감소하면서 펄스 파형의 주기가 증가합니다. 마이크로컨트롤러는 시간 τ 이후 첫 번째 상승 에지에서 주기 변화를 감지하며, 이는 t1 시간에 발생합니다. τ 이전과 이후의 엣지 사이의 일시적 주기 Tt는 다음과 같이 결정됩니다:

where ωt is the transient angular frequency between ωi and ωf . On the next rising edge at time t2, the microcontroller obtains period information regarding the final frequency and outputs the corresponding clock signal. Thus, the center frequency of the SC notch filter changes over two steps in time as follows:

여기서 ωt는 ωi와 ωf 사이의 일시적 각 주파수입니다. t2 시간에 다음 상승 에지에서 마이크로컨트롤러는 최종 주파수에 대한 주기 정보를 얻고 해당하는 클럭 신호를 출력합니다. 따라서 SC 노치 필터의 중심 주파수는 다음과 같이 두 단계로 시간에 걸쳐 변경됩니다:

As an exception, if the supply frequency changes exactly on the rising edge, the center frequency is adjusted directly from ωi to ω f without a transient period. 

예외적으로 공급 주파수가 상승 에지에서 정확히 변경되면, 일시적 주기 없이 바로 ωi에서 ωf로 중심 주파수가 조정됩니다.

 

With this model, we can predict the performance of the filter. The time-domain signal in (7) can be converted to an s-domain function by Laplace transform as

이 모델을 사용하여 필터의 성능을 예측할 수 있습니다. 식 (7)의 시간 영역 신호는 Laplace 변환을 통해 s-도메인 함수로 변환될 수 있으며, 이는 다음과 같이 표현됩니다:

where L{} is the Laplace transform of the function. With (10) as a model of the input signal, the output voltage of the SC notch filter is determined as (11), as shown at the bottom of the next page in the frequency domain.

In (11), C represents the amplitude of each voltage component, determined by the amplitude and frequency of the input signal and the characteristics of the SC notch filter. The subscript “c” and “s” stand for the cosine and sine components, and the subscript “τ ” means that the voltage appears after time τ . This expression is applied before and after transients with discrete changes in the notch frequency, ωn, resulting from supply frequency variations as in (9).

여기서 L{}은 함수의 Laplace 변환을 나타냅니다. 입력 신호의 모델로서 식 (10)을 사용할 때, SC 노치 필터의 출력 전압은 다음과 같이 결정됩니다 (11), 이 식은 다음 페이지 아래에서 주파수 영역에서 보여집니다.

여기서 C는 각 전압 성분의 진폭을 나타내며, 입력 신호의 진폭 및 주파수, 그리고 SC 노치 필터의 특성에 의해 결정됩니다. 하위 첨자 "c"와 "s"는 코사인 및 사인 성분을 나타내며, 하위 첨자 "τ"는 시간 τ 이후에 나타나는 전압을 의미합니다. 이 식은 (9)와 같이 공급 주파수 변화로 인해 노치 주파수 ωn이 이산적으로 변화할 때의 일시적 전환 전후에 적용됩니다.

The transfer function, GSC, is used on the assumption that the line frequency disturbance is small. The initial value of the output voltage is redefined as the value at that point when ωn changes. The output voltage has four components oscillating at different frequencies as separated by square brackets. The voltages in the first two brackets are steady sinusoidal signals with constant amplitudes. Their amplitudes are zero if the center frequency of the notch filter matches the signal frequency. When the supply frequency changes, the center frequency of the SC notch filter is tuned to the changed supply frequency at the first rising edge or the second one that follows. These sine waves exist for the time required for the notch frequency to be adjusted and not after that.

전달 함수 GSC는 선 주파수 간섭이 작다는 가정 하에 사용됩니다. 출력 전압의 초기값은 노치 주파수 ωn이 변경되는 지점에서의 값으로 재정의됩니다. 출력 전압에는 대괄호로 구분된 서로 다른 주파수에서 진동하는 네 개의 성분이 있습니다. 첫 두 개의 대괄호의 전압은 진폭이 일정한 정현파 신호입니다. 그들의 진폭은 노치 필터의 중심 주파수가 신호 주파수와 일치할 경우에는 제로입니다. 공급 주파수가 변경될 때, SC 노치 필터의 중심 주파수는 첫 번째 상승 에지 또는 그 후의 두 번째 상승 에지에서 변경된 공급 주파수에 맞추어 조정됩니다. 이러한 사인 파형은 노치 주파수가 조정되는 시간 동안 존재하며, 그 이후에는 존재하지 않습니다.

Unlike them, the voltages in the last two brackets are transient sine waves with amplitudes that decay over time. As shown in Fig. 6, they appear in transients if the amplitude or frequency of the input signal changes and then diminish. The damping ratios that indicate how rapidly transient oscillations decay depend on the quality factors of two notch filter blocks

그와 달리, 마지막 두 개의 대괄호의 전압은 시간이 지남에 따라 감소하는 일시적 사인 파형입니다. 그림 6에서 보여지듯이, 입력 신호의 진폭이나 주파수가 변할 때 일시적 진동이 발생하고 그 이후 점차 감소합니다. 일시적 진동이 얼마나 빨리 감쇠되는지를 나타내는 감쇠 비율은 두 노치 필터 블록의 Q-팩터에 따라 결정됩니다:

The smaller the Q-factor, the greater the damping ratio and the faster the transient oscillations are attenuated. The bottom two waveforms in Fig. 6 show the output voltages for different Q2 values. Q1 was fixed to 3.625 as in Fig. 5. As expected, the transient oscillation damped quickly within about 150 ms when Q2 was small, while the oscillation damped relatively slowly over about 400 ms when Q2 was large. Thus, the Q-factor of the proposed notch filter is designed to be large enough to sharply drop the gain of the center frequency, but not too large to dampen transient oscillations in a short time.

Q-팩터가 작을수록 감쇠 비율이 커지며 일시적 진동이 빨리 감쇠됩니다. 그림 6의 하단 두 파형은 다른 Q2 값에 대한 출력 전압을 보여줍니다. Q1은 그림 5와 같이 3.625로 고정되었습니다. Q-팩터는 제안된 노치 필터가 중심 주파수의 이득을 급격히 줄이는 데 충분히 크지만, 일시적 진동을 짧은 시간 내에 감쇠시키지 않도록 설계되었습니다.

 

The resistance values that determine the gains and Q-factors of the two notch filter blocks in Fig. 4 are designed as in Table I. The orange curve in Fig. 7 shows the designed gains of the SC notch filter. It is designed to have a sharp drop in gain near the center frequency to accurately remove only the line frequency component. It is also intended to amplify the gain in the high frequency range by about 18 dB, that is about eight times, to detect relatively small slot harmonics. The purple dots in Fig. 7 represent the experimentally measured gains of the practically implemented notch filter. The designed and measured gains are compared in the wide frequency range on the logarithmic scale in Fig. 7(a) and in the frequency range of interest around 60 Hz in Fig. 7(b). The implemented notch filter provides a gain very close to that designed. 

표 I에 나와 있는 바와 같이 Fig. 4의 두 노치 필터 블록의 이득과 Q-팩터를 결정하는 저항 값들이 설계되었습니다. Fig. 7의 주황색 곡선은 SC 노치 필터의 설계된 이득을 보여줍니다. 이 필터는 중심 주파수 근처에서 이득이 급격히 감소하여 선 주파수 구성 요소만 정확히 제거할 수 있도록 설계되었습니다. 또한 상대적으로 작은 슬롯 고조파를 감지하기 위해 고주파 영역에서 약 18 dB (약 8배) 정도의 이득을 증폭하는 것을 목표로 합니다. Fig. 7의 보라색 점들은 실제 구현된 노치 필터의 실험적으로 측정된 이득을 나타냅니다. 설계된 이득과 측정된 이득은 로그 스케일에서 넓은 주파수 범위에서 Fig. 7(a) 및 주변의 주파수 범위에서 60 Hz 주변에서 Fig. 7(b)에서 비교됩니다. 구현된 노치 필터는 설계된 이득과 매우 유사한 이득을 제공합니다.

 

Fig. 8 shows the experimental results to verify the transient notch filtering performance, which automatically detects then removes the fundamental component. In the experiment, the supply frequency dropped from 60 to 50 Hz and then increased back to 60 Hz. The A-phase motor current signal is used for the fundamental frequency detection. The output voltage of the A-phase current sensor was input to the zero-crossing detector and notch filter. As shown in the second waveform of Fig. 8(a), both the frequency and amplitude of the motor currents changed in a transient state of frequency change and then converged to the new values. Fig. 8(b) shows magnified waveforms around time τ when the frequency drops. As shown in the third waveform, the fundamental frequency of the A-phase current was detected on its rising edge, and the center frequency of the notch filter was automatically tuned. As a result, the fundamental component was successfully attenuated within 0.2 s when the frequency suddenly either dropped or increased.

 

A total of eight signals are selected for analog-to-digital conversion, based on user configuration. They are scaled and biased to fit the input range of the ADC, an ADS131A04 from Texas Instruments, Dallas, TX, USA, which allows simultaneous sampling of four channels at high data rates. Two ADCs are daisy chained to perform simultaneous sampling of all eight channels of data. Serial digital data are passed to the microcontroller using the Serial Peripheral Interface (SPI) connection at 16-bit resolution and 8-kHz sampling rate for our experiments. The prototype board allows the user to receive data via Ethernet, USB, UART, or I2C. In our experiments, we recover six channels of raw utility three-phase voltages and currents, one channel for the estimated utility or fundamental frequency, and one channel for a filtered current waveform with the fundamental removed. This filtered waveform can be inspected for subtle harmonics, as described in the speed sensing demonstration in Section IV.

총 8개의 신호가 사용자 설정에 따라 아날로그-디지털 변환(ADC)을 위해 선택됩니다. 이들은 ADC로의 입력 범위에 맞게 스케일링 및 바이어스가 조정됩니다. ADC는 Texas Instruments의 ADS131A04로, 이는 미국 텍사스에 위치한 회사입니다. 이 ADC는 4개 채널을 고속 데이터 속도로 동시에 샘플링할 수 있습니다. 두 개의 ADC가 데이지 체인 구성을 통해 모든 8개 채널의 데이터를 동시에 샘플링합니다. 직렬 디지털 데이터는 16비트 해상도와 8 kHz 샘플링 속도로 SPI(Serial Peripheral Interface) 연결을 통해 마이크로컨트롤러로 전달됩니다. 프로토타입 보드는 이더넷, USB, UART 또는 I2C를 통해 사용자가 데이터를 수신할 수 있게 합니다. 우리의 실험에서는 유틸리티 세상 또는 기본 주파수 추정을 위한 하나의 채널과 기본 주파수가 제거된 필터링된 전류 파형을 위한 하나의 채널을 포함하여 6개의 유틸리티 3상 전압 및 전류의 원시 채널을 복구합니다. 이 필터링된 파형은 IV절의 속도 감지 데모에서 설명된 것처럼 섬세한 고조파를 검사하는 데 사용될 수 있습니다.

 

Fig. 9(a) and (b) shows the prototype acquisition system, with different functional regions of the board identified in the images. Fig. 10 shows example data transferred to a desktop computer via Ethernet by simultaneously sampling eight-channel data at 8 kHz with the prototype. Sine waves were input to the first four channels, and pulse waves were input to the 5th to 8th channels. The base frequencies were increased from 60 to 800 Hz, then 4000 Hz in Fig. 10(a)–(c), respectively.

Fig. 9(a)와 (b)는 보드의 다른 기능 영역을 식별한 프로토타입 취득 시스템을 보여줍니다. Fig. 10은 프로토타입을 사용하여 8 kHz에서 8채널 데이터를 동시에 샘플링하여 이더넷을 통해 데스크탑 컴퓨터로 전송된 예제 데이터를 보여줍니다. 첫 번째 네 채널에는 사인 파형이 입력되었고, 다섯 번째에서 여덟 번째 채널에는 펄스 파형이 입력되었습니다. 기본 주파수는 Fig. 10(a)에서 (c)까지 각각 60에서 800 Hz로 증가하고, 마지막으로 4000 Hz로 증가했습니다.

 

(4) Principle Slot Harmonic Tracking

 

(5) Speed Estimation Performance

 

(6) Conclusion

This article has demonstrated a custom data acquisition system tailored to the needs of nonintrusive power monitoring on the ac utility. The board can be applied in any application where a wide range of interesting harmonics are “buried” in a large fundamental frequency waveform. The transient performance and settling time of the board’s tracking capability can be predicted with analytical tools described in this article. The performance of the system has been demonstrated for rotor slot harmonic tracking and speed estimation. The combination of the prototype design and the tracking algorithm has been proved experimentally to estimate the speed quickly and accurately in transient as well as steady state.

본 논문은 교류 유틸리티에서의 비침투 전력 모니터링 필요에 맞춘 맞춤형 데이터 획득 시스템을 소개하였습니다. 이 보드는 큰 기본 주파수 파형에 "숨겨진" 다양한 흥미로운 고조파가 포함된 모든 응용 프로그램에 적용될 수 있습니다. 보드의 추적 능력의 일시적 성능과 안정 시간은 본 논문에서 설명된 분석 도구로 예측할 수 있습니다. 시스템의 성능은 로터 슬롯 고조파 추적 및 속도 추정을 위해 검증되었습니다. 프로토타입 설계와 추적 알고리즘의 결합은 실험적으로 전이 및 정상 상태에서 속도를 빠르고 정확하게 추정하는 데 효과적임이 입증되었습니다.