A quick response peak detector for variable frequency three-phase ...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 41, NO. 4, AUGUST 1994

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A Quick Response Peak Detector for Variable Frequency Three-phase Sinusoidal Signals Ching-Tsai Pan, Member, IEEE, and Maoh-Chin Jiang

Abstract- An instantaneous peak detector for three-phase variable frequency sinusoidal signals is proposed. The three-phase characteristic is fully used in the proposed detector to achieve instantaneous response and frequency independence characteristics. A very simple hardware implementation circuit is also presented for minimizing the number of analog computational components. Moreover, the proposed detector possesses excellent linearity and low sensitivity to small voltage unbalance and harmonic distortion. Because of its promising accuracy and transient response, it can be used in many systems such as the voltage regulator of an uninterruptible power supply (UPS), an automatic line voltage regulator, or electric generators, etc., to improve the system transient performance. Theoretical analysis, hardware implementation,and some experimental results are also detailed in this paper.

I. INTRODUCTION

A

In this paper, a novel peak detector for three-phase variable frequency sinusoidal signal is proposed. Due to application of the characteristic of balanced three-phase system, the proposed detector can achieve instantaneous response and frequency independence characteristics. In addition, the proposed detector also has the following merits: This detector has very nice linearity characteristic up to full scale. It does not require any reactive component. It is less sensitive to small amplitude and phase unbalance. The proposed detector is less sensitive to small harmonic distortion (i.e., acceptable in practical applications). It can also be used to detect abnormal voltage conditions and serve as a monitor. The contents of this paper may be briefly outlined as follows. The detector circuit as well as its operation principle is first described in Section 11. Effects of nonideal input waveforms are then analyzed in Section 111. A hardware circuit is then constructed and some experimental results are presented in Section IV. Finally, some conclusions are made in the last section.

SINUSOIDAL peak detector is a device that generates an output voltage proportional to the peak amplitude of a sinusoidal signal. Some systems require an ac voltage detector with a fast response characteristic in order to improve their transient performance. For example, it can be used in an automatic voltage regulation loop of an uninterruptible power supply (UPS) [I], or in an automatic line voltage regulator 121, or in a generator excitor systems 131. The transient response 11. THE PROPOSED PEAK DETECTOR time of the above equipment is usually required to be less than 50 ms. In a practical circuit, the response time of the ac voltage detector occupies a significant portion (about 20 ms) of this A. Basic Principle 50 ms. Hence if the response time of the ac voltage detector Assume the input three-phase signal is given as can be reduced, the transient performance can be improved v a ( t )= V, sin(wt) [6]. However, peak detection of conventional techniques is achieved by rectification and filtering. This usually requires w,(t) = V, sin(wt - 120") several cycles (about 20 ms for 60 Hz source) for the lowvc(t) = V,sin(wt 120") pass filter to settle to the corresponding average dc level. As a consequence, systems using conventional techniques cannot where achieve good transient performance and the detector portion V,: the unknown peak amplitude, usually becomes a bottleneck of the system. tu: angular frequency, Recently, some other methods [4]-161 were proposed by t: time variable. taking advantage of the mathematical characteristic of sinuIt is straightforward through some trigonometric operations soidal signals to improve the response time. However, these to get the following equation: methods can only be used for applications where the frequency is restricted to a single frequency or very narrow range to maintain the accuracy. Moreover, the above mentioned methods are not able to achieve instantaneous response.

+

Manuscript received April 30, 1993; revised August 16, 1993. The authors are with the Department of Electrical Engineering, National Tsing Hua University, Hsinchu 300, Taiwan, R.O.C. IEEE Log Number 9403301.

The result of (5) is obtained by using the characteristic of a balanced three-phase system. From the corresponding phasor diagram of (1) to (3), one can see the peak phasor of vb(t) - vc(t) is perpendicular to that of va(t) and has a

0278-0046/94$04.00 0 1994 IEEE

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PAN AND JIANG: QUICK RESPONSE PEAK DETECTOR

ACU

vx

W)

I

+I

1-

Fig. 1. The basic configuration of the proposed detector.

magnitude of fi times that of wa(t). It follows from (5) that it is possible to detect the peak value using the following relationship:

Although (6) can be used directly for hardware circuit implementation, however, it would take three multipliers. W O Fig. 2. A circuit diagram of the prototype detector. of the three multipliers are used for performing the square function and the third for taking the square root. In order to reduce the number of multipliers, (4) can be manipulated into from Fig. 2 one can observe that the circuit wiring is rather the following form: simple, since very few components are connected to each IC and only one variable resistor is used in the hardware circuit. The above results are derived by assuming an ideal balanced three-phase voltage. Next, consider some nonideal conditions Fig. 1 shows the basic configuration of the proposed detector. such as unbalanced phase voltage or with harmonic distortion. The analog computational unit (ACU) receives three inputs This is given in the next section.

V,, V,, and V, to generate the output V, = V,V,/V,. Due to the polarity requirement of the analog computational unit, two precision rectifiers are added to convert the signals into absolute values. From Fig. 1 one can see that Ve = I [ W b ( t ) - wc(t)]/fil and the output wo(t) indeed performs the same mathematical operation of (7). From Fig. 1 it is evident that implementation of the proposed method requires only one analog computational unit. B. Hardware Implementation Fig. 2 shows the detailed hardware circuit of the proposed detector. It is seen that only one analog computational unit, AD 538, and two operational amplifiers, TL 084, are used. The analog computational unit (ACU) is connected to perform the following function:

111. ANALYSIS OF EFFECTS OF NONIDEAL WAVEFORMS In practical utility power systems, due to the application of large balanced three-phase synchronous generators, the input signal of the detector is rather close to the previous ideal waveform, however, to understand the characteristic of the novel detector, effects of three-phase voltage unbalance and harmonic distortion will also be investigated. A. Eflect of Three-phase Unbalance

First consider the voltage magnitude unbalance. Suppose that the three-phase voltages take the following nonideal forms:

w a ( t ) = (V, In (8), V, is set equal to wo(t)+I[wa(t)-v,(t)]/fil, V, and V, is set equal to Iwa(t)l. It should be noted that the input signals of the analog computational unit must be positive. Hence, two precision full-wave rectifiers are added. From Fig. 2 one can see that no reactive component is used. Therefore, the time delay of the proposed detector is extremely short compared with that of the conventional detectors. In other words, the proposed detector is able to achieve instantaneous response. Also, due to absence of a reactive element the proposed detector can achieve a frequency independence characteristic. Furthermore,

Wb(t)

wc(t)

+ AVI) sin(wt)

+ AV2) sin(wt - 120') = (V, + AV3) sin(wt + 120') = (V,

(9) (10) (1 1)

where AV,, AV,, and AV3 represent small deviations of the three phases, respectively. Substituting (9) to (11) into (6) yields the following result

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 41, NO. 4, AUGUST 1994

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Similarly, an upper bound of the error can be obtained as follows:

where v,ll(t) = (261

+ 6;) sin2(wt),

v,13(t) = - C(-l)i-'Gisin[wt a=2

S. z -

r

(20)

(i - 1)120~1 ,

-

Av,

As can be expected from the above result, the influence of phase angle deviation is not significant in practical power systems.

~

VP .

B. Effect of Harmonic Distortion Therefore, one can see that the effect of the phase unbalance Suppose that the three-phase input voltages take the followis merely to add a small ripple component in the output v o ( t ) . In the literature [6], [8] there are different definitions used for ing form: indicating the output error of the detector. If the peak ripple (21) v a ( t ) V, sin(wt) ' ~ , h ( t ) error [6] is used, then an upper bound of the percentage error is obtained as follows: ' ~ b ( t2 ) V, sin(wt - 1200) w b h ( t ) (22)

+

I

max ~1

+ v , l l ( t ) + 21,12(t) + u,13(t) - 11 x 100%.

+

where 00

(13)

In case another definition of rms ripple factor [8] is used, then one has another version of the error expression

=

/(&y

- 1 x 100%

(14)

where V,,, and V& are the root mean square value and the average value, respectively, of the corresponding U' , ( t ) . Next, consider the effect of the phase angle unbalance. For reference, the following practical case is considered. Suppose that

+

va(t) = V,sin(wt (61) ' ~ b ( t= ) V, sin(wt - 120" 42) v,.(t), = V, sin(wt + 120" + 43)

+

(15) where (16) (17)

where 411(62, and ,fi3 are the phase angle deviations of each phase, respectively, and it is reasonably assumed that sin4i

S

&,

COS&

Z

1.

(18)

With the above approximation it is straightforward to obtain vo(t) "=

vpJ1 + 7)e21(t)+ 'Ue22(t) + ve23(t)

n = order of harmonics. Similarly, following the same procedure, one can get

(19)

v,gl(t) = 2 s i n ( w t ) m ( t ) w,32(t)

= &(t)

2 +cos(wt)[vch(t) - ~ b h ( t ) ] , fi

+ i1[ v c h ( t ) - vbh(t>l2.

Hence, a percentage error bound due to harmonics can be expressed in terms of either of the following forms: Eh,peak(%)

=

maxi,/-

- 11 x 100%

(25)

where

cos[wt - (i - 1)120°]

To illustrate the significance and facilitate the understanding of theoretical results obtained in preceding sections, a hardware circuit is constructed as shown in Fig. 2, where only

437

PAN AND JIANG: QUICK RESPONSE PEAK DETECTOR

-

theoreucal value expermental rewlt..

5

input peak voltage.

Fig. 3.

Linearity characteristic of the proposed amplitude detector.

one analog computational unit, AD 538, and two operational amplifiers, TL 084, are used. Five tests are given below for reference. The first test illustrates its linearity characteristic. The second test shows the effect of frequency variation. The third test is concerned with transient response, which shows how fast the novel detector will respond to a step change in amplitude. The fourth test deals with the effect of input voltage unbalance as well as comparison with the simulated result. The last test shows the impact of harmonic distortion. A. Linearity Characteristic

Linearity is one of the most important characteristics of any detectors. Fig, 3 shows a typical experimental result together with the theoretical value of the proposed peak detector. The source frequency is 60 Hz and the peak amplitude is varied from 0.1 V up to the full scale of 6.5 V. The worst case error is less than 1% near the zero amplitude region. One can see from Fig. 3 the excellent linearity characteristic and the close agreement between the theoretical values and the experimental ones. Results for other frequencies have also been tested. This is discussed in the next section.

B. Frequency Characteristic In general, the major source of measured error in power system applications is due to frequency drift. Most existing methods for fast amplitude detection were restricted by a single input frequency [4]-[6]. If a detector has frequency independent characteristic, naturally it can provide much better accuracy. Fig. 4 shows the frequency characteristic of the proposed detector. As can be expected from the previous theoretical basis and the implementation, Fig. 4(a) shows the frequency independence characteristic of the proposed detector. Due to the limited range of the available three-phase signal generator of the authors' laboratory, the frequency range under test is from 0.03 Hz to 3 KHz. For reference, Fig. 4(b) also shows a transient response of the proposed detector for a step frequency change from 500 Hz to 50 Hz. One can clearly observe the frequency independence characteristic as

(b) Fig. 4. (a) The frequency characteristic of the proposed detector. (b) The transient response for a step change of frequency from 500 Hz to 50 Hr.

well as the instantaneous response and the very low ripple characteristics of the detector. C. Trunsient Response

It is known that settling time of conventional peak detectors implemented by a rectifier and a second-order Butterworth low-pass filter may last up to 20 ms [6]. The proposed detector is able to achieve an almost instantaneous response. Fig. 5 shows some transient responses for different inception angles, namely 45", 90°, and 180", respectively. One can see from Fig. 5 the excellent transient response of the proposed detector. Also, the response is independent of the inception angle unlike the results in [6]. In addition, due to the attractive instantaneous response characteristic, the proposed detector can also be used for detecting some abnormal voltage conditions in power systems for supervising the system voltage quality. Fig. 6 shows an example of instantaneous voltage dip phenomenon where, for clarity, the duration of zero amplitude is chosen to be 0.3 ms. It is seen that the proposed peak detector indeed can instantaneously detect the abnormal voltage variation. D. Phase Voltage Unbalance Test

Since unbalanced load conditions cause unbalanced phase voltage on the three-phase system, for these applications, it

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 41, NO. 4. AUGUST 1994

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l4I

0-

12

0-

percentagedeviationof the b phase voltage magnitude,

(a)

I

I

0

0.

percentagedeviation of the b phase voltage magnitude (70)

(C)

(b)

Fig. 5. Transient responses of the proposed detector for different inception angles: (a) 45'; (b) 90'; (c) 180O.

::

*: experimentalresults

/ /

.

32-

Fig. 6. The transient response to a chopped 60 Hz sinusoidal signal where duration of zero amplitude is chosen to be 0.3 ms.

1-

.

/'

//' , '

____/_' deviation of the single-phaseangle

is necessary to know the influence of the phase unbalance to the proposed detector. Theoretical results have been derived in (13), (14), and (20) for magnitude and phase angle, respectively. For reference, Fig. 7 shows some experimental results of the b phase unbalance. The maximum error between the theoretical value and the experimental result is less than 2%. It is seen that the previously derived formulas are indeed valid

(C)

Fig. 7. Simulation and test results of single phase voltage unbalance. (a) k a k ripple emor, Eu.peak(%'E'), due to magnitude unbalance. (b) rms *P) , to magnitude unbalance. (c) Peak ripple error, ple factor, E " , ~ ~ ~ ( %due due to phase angle unbalance,

for predicting the effects of phase unbalance. Also, one can see from this result that due to application of all three-phase

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PAN AND JIANG: QUICK RESPONSE PEAK DETECTOR

harmonic contents (X) Cases 1 2

3 4 5 6 7 8 9 10

1 3 100.000 0.750 100.000 1.688 100.000 2.625 100.000 3.563 100.000 4.500 100.000 5.438 100.000 6.375 100.000 7.313 100.000 8.250 100.000 9.188

5 0.188 0.422 0.656 0.891 1.125 1.359 1.594 1.828 2.063 2.297

7 0.063 0.141 0.219 0.297 0.375 0.453 0.531 0.609 0.688 0.766

9 THD(%) 0.031 0.776 1.747 0.070 2.716 0.109 3.687 0.148 4.657 0.188 5.628 0.227 6.598 0.266 7.568 0.305 0.344 8.539 0.383 9.509

14

~

12

~

10

~

voltages the proposed detector is not so sensitive to the small unbalance as existing detectors.

1 8 10

6

E. Harmonic Distortion Test

To obtain an estimate of the impact of harmonics in the input signal, a versatile three-phase oscillator [7] is applied as the harmonic source of this test. The tested waveforms are chosen to consider practical applications. Since even harmonics can usually be neglected due to the power electronic system characteristic, hence they are not included. For higher order harmonics, they can either be eliminated easily using a prefilter or are already decayed to a negligible quantity. Hence, only lower order harmonics are tested. In fact, the data of Table I is similar to [6]. Fig. 8 shows the experimental results as well as the theoretical results of (25) and (26). The error is less than 2%. From the above experiments, one can see that the peak ripple error of the proposed detector is about 5% for a input signal with 5% of THD. This error is smaller than 8.5% error of the detector [6] for the same input signal. In case the rms ripple factor definition is used, then, the proposed detector has an error of 3.5%. Compared with the result of [8], namely 8%, the proposed detector has improved accuracy in addition to the instantaneous response and frequency independence characteristics. From the above experimental results one can see that the error between the theoretical and the experimental value is not very significant. The error sources are mainly due to the limited accuracy of the analog computational unit and the full-wave rectifier circuit, the nonzero offset voltage of the operational amplifier as well as the accuracy of the l / & gain. Finally, in case the total harmonic distortion is too large for some application, one can add a small prefilter to reduce the distortion to increase the accuracy at the sacrifice of a little time delay.

v.

CONCLUSION

In this paper, an instantaneous peak detector for variable frequency three-phase sinusoidal signals is proposed. Compared with existing analog peak detectors, only one analog computational unit is required and no reactive component is used in the novel detector. The proposed detector has excellent linearity as well as frequency independence characteristics. Because of its promising accuracy and excellent transient response performance, it can be used in many applications such as the voltage regulator of an unintermptible power

6t

-

--L

6

4

--8

10

total harmolllc &stomon(%)

(b) Fig 8 Simulation and test results of harmonic distortion (a) Peak npple error, Eh,peak(%), due to harmonic distortion (b) rms nppie factor, Eft ,,,,(%), due to harmonic distortion

supply (UPS), an automatic line voltage regulator, or electric generators, etc., to improve the system transient performance. Although due to application of all three-phase voltages, the proposed detector is not very sensitive to the small voltage unbalance and harmonic distortion of a normal power system, however, it may also be used to detect the system serious unbalance condition, poor total harmonic distortion, and the voltage dip phenomenon, etc., for supervising the voltage quality of power systems.

REFERENCES P. D. Ziogas, “Optimum voltage and harmonic control PWM technique for three-phase static UPS systems,” IEEE Trans. Ind. Appl., vol. IA-16, no. 4, pp. 542-546, Jul./Aug. 1980. J. E. Allos, M. K. Mahmood, and F. A. AI-qirimil, “Transient response of the modified variable-phase-shift automatic voltage regulator,” IEE Proc., vol. 3 , pt. G, pp. 10-16, Feb. 1984. A. J. Wood and B. F. Wllenberg, Power Generation, Operution, and Control. New York: Wiley, 1984, pp. 291-320. C. A. Karybakas and G. A. Micholitsis, “Fast amplitude detection for constant period sinusoidal signals,” Inr. J. Elecrron., vol. 49, no. I , pp. 67-72, 1980.

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[5] H. L. Jou, H. Y. Chu, C. L. Huang, and C. H. Chen, “A shortest data

window algorithm for detecting the peak value of sinusoidal signals,” IEEE Truns. Ind. Electron., vol. 37, no. 5, pp. 4 2 U 2 5 , Oct. 1990. [ 6 ] H. Y. Chu, H. L. Jou, and C. L. Huang, “Transient response of a peak voltage detector for sinusoidal signals,” IEEE Truns. Ind. Electron., vol. 39, no. I , pp. 74-79, Feb. 1992. [7] D. J. Clarke and P. C. Sen, “A versatile three phase oscillator,” IEEE Trans. Ind. Electron., vol. 24, no. I , pp. 57-60, Feb. 1977. [SI M. K. Mahmood, J. E. Allos, and M. A. H. Abdul-Karim, “Microproceasor implementation of a fast and simultaneous amplitude and frequency detector for sinusoidal signals,” IEEE Truns. Instrum. Meas., vol. 34, no. 3, pp. 4 1 3 4 1 7 , Sept. 1985.

Ching-Tsai Pan (M’88) was born in Taipei, Taiwan, Repubic of China, in October 1948. He received the B.S. degree in electrical engineering from the National Cheng Kung University, Tainan, Taiwan, in 1970, and the M.S. and Ph.D. degrees from Texas Tech University, Lubbock, in 1974 and 1976, respectively, all in electrical engineering. Since 1977, he has been with the Department of Electrical Engineering, National Tsing Hua University. Hsinchu, Taiwan, where he is currently Professor. From 1985 to 1986. he was a Visiting Professor at the Department of Electrical Engineering, Ecole Centrale de Lyon, France. He served as the Directors of University Computer Center and Computer Center, Ministry of Education from 1986 to 1989, and from 1989 to 1992, respectively. His research interests are in the areas of power electronics, control systems and numerical analysis. Dr. Pan has been twice the recipient of the Award for Excellence in Teaching, presented by the Minister of Ministry of Education and the University President, respectively. He also received Research Awards from the National Science Council in 1986-1993. He is a member of ICE, IEE, Phi Tau Phi, Eta Kappa Nu, and Phi Kappa Phi. ~~~~~

Maoh-Chin Jiang was born in I-Lan, Taiwan, Republic of China, in February 1963. He received the B.S.E.E. degree from National Taiwan Institute of Technology, Taipei, Taiwan, in 1988. He is currently working toward the Ph.D. degree at the National Tsing-Hua University, Taiwan. His field of interests are power electronics and electrical variables measurement.