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Letters to the Editor A New Circuit for Measuring Power Factor in Nonsinusoidal Load Current
in (2) can also be expressed as
p
iL (t) =
Kuen-Der Wu, Hurng-Liahng Jou, and Jhy-Shoung Yaung
Abstract—This letter presents a new method for measuring the power factor in nonsinusoidal load current. The proposed method is based on the technique of sampling and holding the amplitude of the real part of the load current. Because no Fourier or fast Fourier transform calculation is used, this method can be implemented by a simple electronic circuit. Index Terms— Nonsinusoidal load current, power factor, true power factor.
Power factor (PF) is an important index to evaluate the power efficiency of electric equipment or electric utility. The design of conventional PF measurement equipment is based on the assumption that the measured voltage and current signals are sinusoidal. Hence, the measured results of conventional PF measurement methods are not accurate under the distorted load current [1]–[4]. Unfortunately, nonlinear load, where current waveform is nonsinusoidal, is widespread due to the wide use of power-electronic-related equipment [5]–[7]. The commercial PF measurement equipment, which can measure the PF under the nonsinusoidal load current, is using the fast Fourier transform (FFT) analysis in the calculation process to calculate the real power, root mean value of voltage, and root mean value of current [8]. An electronic circuit for measuring the PF under the nonsinusoidal load current was propose in [9]. However, three power components I1 ; 1 , and Irms must be measured individually in that paper. In this letter, a new PF measurement method, based on the sample-and-hold technique, is proposed. The amplitude of the real part of load current can be measured directly. Hence, the proposed method is simpler.
0 1 ) +
p 1 2
n=2
In sin(n!t
0 n)
(3)
where In and n are the rms value and phase of the load current at the nth-order harmonic. The average power P is defined as
T
1
P =
T
0
p(t) dt =
T
1
T
0
v (t)iL (t) dt:
(4)
Using v (t) from (1) and iL (t) from (3), then P =
I. INTRODUCTION
2 I1 sin(!t
T
p
T
1
0
p 1
+
2
n=2
2 Vrms sin !t
In sin(n!t
p
0 n )
2 I1 sin(!t
0 1 )
dt
= Vrms I1 cos(1 ):
(5)
The apparent power S is the product of the rms voltage Vrms and the rms current Irms . It is represented as S = Vrms Irms :
(6)
The PF is defined as PF =
P : S
(7)
Using (5)–(7), the PF can be derived as [10] PF =
P I1 Vrms I1 cos(1 ) = cos(1 ) = S Vrms Irms Irms
(8)
II. POWER FACTOR DEFINITION
where cos(1 ) is defined as the displacement PF (DPF). DPF can be represented as
The voltage supplied from the power system can be assumed to be a sinewave. It is represented as
DPF = cos(1 ):
v (t) =
p
2 Vrms sin(wt):
(1)
Therefore, the PF in nonsinusoidal current is
If the nonlinear load current contains no dc component in the steady state, it can be represented as [10] iL (t) = iL1 (t) +
1
n=2
iLn (t)
(2)
where iL1 (t) is the fundamental component and iLn (t) is the component at the nth harmonic frequency. The load current components Manuscript received May 23, 1998; revised December 28, 1998. Abstract published on the Internet April 18, 1999. This work was supported by the National Science Council, Taiwan, R.O.C., under Contract NSC 86-2213-E151-002. The authors are with the Department of Electrical Engineering, National Kaohsiung Institute of Technology, Kaohsiung 807, Taiwan, R.O.C. (e-mail:
[email protected];
[email protected];
[email protected]). Publisher Item Identifier S 0278-0046(99)05627-0.
(9)
PF =
I1 DPF: Irms
(10)
The PF definition shown in (10) [10] is also named the “true PF” [11]. If the load is linear, the load current is a pure sinusoidal waveform. It is represented as iL (t) =
p
2 I1 sin(!t
0 1 ):
(11)
In this condition, I1 is equal to Irms . Then, the PF is equal to the DPF. It is written as PF = cos(1 ) = DPF:
(12)
Nevertheless, the PF definition written as (12) is accurate only under the condition that the waveform of load current is sinusoidal.
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999
(a)
(b)
(c) Fig. 1. Related diagrams for proposed method. (a) Relationships of related signals. (b) Block diagram. (c) Schematic diagram.
III. PROPOSED METHOD A. PF Measurement for Sinusoidal Current If the load is linear, the load current is a pure sinusoidal signal and I1 is equal to Irms . Then, the PF cos(1 ) is equal to the DPF. A pure sinusoidal reference signal with the phase of 90 lagging with the load current signal can be written as vr1 (t) =
p
2 I1 cos(wt
0 1 ):
(13)
B. PF Measurement for Nonsinusoidal Current
(14)
In a practical industrial power system, the load is frequently nonlinear. In this condition, the conventional PF definition is not suitable. For measuring the true PF, the measurement method must be modified.
The absolute value of vr1 (t) can be written as vr2 (t) =
p
j
2 I1 cos(wt
0 1 )j:
The phase relationships between the above signals are shown in Fig. 1(a). The points P1 and P2 are at the time of zero-crossing pointpof the input voltage. The value of vr2 (tp ) at P1 or P2 is just 2 I1 cos(1 ). By multiplying a factor 1= 2; I1 cos (1 ) is obtained. If the load current is sinusoidal, I1 is equal to Irms . PF can be obtained by dividing I1 cos(1 ) to Irms .
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999
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(a)
(b)
(c)
(d)
Fig. 2. Test results of the proposed detector. (a) Input voltage Vi (t). (b) Load current iL (t). (c) Absolute value of reference signal Vr2 (t). (d) Detected output voltage Vo (t) (channel (a): 5 V/div, 5 ms/div; channel (b): 10 V/div, 5 ms/div; channel (c): 5 V/div, 5 ms/div; channel (d): 0.5 V/div, 5 ms/div).
(a)
To obtain the fundamental component of load current, the load current is fed to a bandpass filter to eliminate the harmonic p component. Then, the fundamental component of load current, 2 I1 sin(!t 0 1 ), is gotten. Since the fundamental component of load current is obtained by using the bandpass filter, the following measurement process is similar to the condition of Section III-A. IV. HARDWARE IMPLEMENTATION Fig. 1(b) and (c) shows the block and schematic diagrams for implementing this method. The voltage signal is fed to a precision full-wave rectifier and a trigger pulse generator to generate a pulse every half cycle. The load current shown as (2) is divided into two paths. One is fed to an rms measurement circuit for measuring the rms value of the load current. The other is fed to a bandpass filter to extract its fundamental component. The output of the bandpass filter is fed to a 90 phaseshift circuit to generate the signal shown as (13). The output signal of the phase-shift circuit is fed to a precision full-wave rectifier. Then, the signal shown as (14) is obtained. The generated pulse and the signal shown as (14) are fed to a sample-and-hold circuit, then, p 2 I1 cos (1 ) is obtained. For getting I1 cos (1 ), p the output of the sample-and-hold circuit is multiplying a factor 1= 2. The rms of load current, Irms , and I1 cos(1 ) are fed to an analog divider to operate as a denominator and numerator, respectively. Then, the true PF shown as (10) is obtained. The value of PF is in the range from 0 to 1 in practice. For representing the PF as a dc voltage, the correction factor in this letter is designed as 1. For example, if the dc output voltage is 1 V, it represents that PF is unity.
(b)
V. TEST RESULTS The computer-based signal generator is used in the following test to generate the input voltage and the load current. The phase difference between two signals is defined as the same frequency in the normal condition. However, the frequency of the two input signals in Fig. 2 is different to intensify the transient performance of the proposed method clearly [9]. Fig. 2 shows the test results of this method under the pure sinewave. It shows that the proposed method can measure the PF as a dc voltage. To verify the performance of the proposed circuit under the nonsinusoidal load current, the nonlinear load current which contains a fixed fundamental component and the varied third-order harmonic is used. The nonsinusoidal load current used in the following test can
(c) Fig. 3. Simulation and test results. (a) Load current contains the third harmonic with the same phase and the variable amplitude. (b) Load current contains the third harmonic with the same amplitude and the variable phase. (c) Load current contains different harmonic order with fixed THD (30%).
be represented as iL (t) = sin(!t) + A sin(3!t + )
(15)
where A is the amplitude of harmonic and is the phase of the
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A Reduced Hysteresis Controller for a Four-Switch Three-Phase Bidirectional Power Electronics Interface
harmonic. The total harmonic distortion (THD) is defined as [10]
%THD = 100 3 IIdis1
(16)
where I1 is the rms of the fundamental component and Idis is the rms value of the total harmonic component. Fig. 3(a) shows the theoretical and test results of the proposed method under the load current which contains the third-order harmonic with the same phase ( ) and the variable amplitude (A). Both the theoretical and test results show that this method can measure the PF accurately. Fig. 3(b) shows the theoretical and test results of the proposed method under the load current which contains the third harmonic with constant amplitude (A) and the variable phase ( ). This figure also shows that the proposed method can measure the PF accurately. Fig. 3(c) shows the theoretical and test results of the proposed method under the load current with different harmonic order THD (30%). It shows that the proposed method can measure the PF accurately under the load current with different harmonic component. VI. CONCLUSION A new PF measurement method for nonlinear load current has been proposed and developed in this letter. This measurement method can be implemented by a simple electronic circuit. The output of the electronic circuit is a dc voltage. The amplitude of output dc voltage is proportional to the PF, regardless of whether the load current is sinusoidal or nonsinusoidal. ACKNOWLEDGMENT
Yu-Kang Lo, Huang-Jen Chiu, and Wen-Tsair Li
Abstract—A reduced hysteresis controller for a four-switch three-phase bidirectional power electronics interface is proposed in this letter. Polarity detection of the input voltages to determine the switching states is not required. The circuit is simple. Experimental results show unity input power factor operation and bidirectional power transfer capability. Index Terms—Hysteresis controller, three-phase bidirectional interface, unity power factor.
I. INTRODUCTION Many types of modern power electronics equipment utilize ac/dc rectifiers as front stages. Recently, switch-mode rectifiers have been proposed as substitutes for diode rectifiers for lower current harmonics contents and high power factors in single- or three-phase applications [1]–[4]. One novel three-phase bidirectional power electronics interface was presented in [4], which claims a high output voltage and the use of four active switches only. The hysteresis current control scheme was adopted for the novel three-phase topology. Besides two hysteresis comparators, there are, in addition, four comparators for detecting the polarities of the phase voltages. In this letter, a reduced hysteresis controller is proposed to reduce the cost of the circuit. Only two hysteresis comparators are required. Experimental results demonstrate the unity input power factor and bidirectional capabilities of the circuit.
The authors would like to acknowledge the valuable comments of the reviewers. REFERENCES [1] M. St¨ockl and K. H. Winterling, Electro Technical Measurement. Berlin, Germany: Springer-Verlag, 1973. [2] K. M. Jan and Y. Chang, “Measurement of watt-hour by digital conversion method,” in Proc. 8th Symp. Electrical Power Engineering, Kaohsiung, Taiwan, R.O.C., Dec. 1987, pp. 329–340. [3] R. M. Inigo, “An electronic energy and average power-factor meter with controllable nonuniform rate,” IEEE Trans. Ind. Electron. Contr. Instrum., vol. IECI-27, pp. 71–78, Nov. 1980. [4] M. T. Chen, H. Y. Chu, C. L. Huang, and L. W. Fei, “Power-component definitions and measurements for a harmonic-polluted power circuit,” Proc. Inst. Elect. Eng., vol. 138, pt. C, no. 4, pp. 299–306, July 1991. [5] H. L. Jou, H. Y. Chu, and J. C. Wu, “A novel active power filter for reactive power compensation and harmonic suppression,” Int. J. Electron., vol. 75, no. 3, pp. 577–587, 1993. [6] F. Z. Peng, H. Akagi, and A. Nabae, “A study of active power filter using quad-series voltage-source PWM converters for harmonic compensation,” IEEE Trans. Power Electron., vol. 5, pp. 9–15, Jan. 1990. [7] M. Takeda, K. Ikeda, A. Teramoto, and T. Ariitsuka, “Harmonic current and reactive power compensation with an active filter,” in Conf. Rec. IEEE PESC’88, 1988, pp. 1174–1179. [8] PM3000 User Manual, ed. 5, Voltech Instruments Ltd., Oxon, U.K., 1992. [9] J. C. Wu and H. L. Jou, “Fast response power factor detector,” IEEE Trans. Instrum. Meas., vol. 44, pp. 919–922, Aug. 1995. [10] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converter Applications and Design, 2nd ed. New York: Wiley, 1995. [11] K. Johonson and R. Zavadil, “Assessing the impacts of nonlinear loads on power quality in commercial building—An overview,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1991, pp. 1863–1869.
II. CIRCUIT DESCRIPTION A novel four-switch three-phase bidirectional interface is shown in Fig. 1. The phase-C source voltage is directly connected to the midpoint of two output capacitors through the filter inductor. In a balanced three-phase system, the current sum is zero. Thus, by controlling the input currents of phases A and B with the four switches, the phase-C current can be forced to remain within a hysteresis band. Under steady state, it can be deduced that
1ik = vk 0L Vk 1T 0
k
1ik = 0;
k = a; b; c
(1)
where vk is the source voltage, Vk0 is the voltage at the other side of the inductor, ik is the phase current, T is the duration of a switching state, and ik is the variation of each phase current in T . According to the polarities of va and vb , one can divide a period into four sections. There are four possible conducting paths in each section with different state combinations of the switches. Vk0 and ik can then be determined, as summarized in Table I. Whether a switch or its paralleled reverse diode is conducting depends on the direction of the phase current and, therefore, the polarity of the source voltage under unity power factor operation. In conducting path 1, S2 (or D2), and S4 (or D4) are carrying the currents. From (1), ia and ib increase, thus, ic must decrease. The maximum ripple of ic could
1
1
1
2
1
Manuscript received September 7, 1998; revised March 19, 1999. Abstract published on the Internet April 18, 1999. The authors are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C. Publisher Item Identifier S 0278-0046(99)05628-2.
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