Leonardo Electronic Journal of Practices and Technologies
Issue 6, January-June 2005
ISSN 1583-1078
p. 17-28
Instantaneous Active and Reactive Power Measuring Method in Three
Phase Power System
A. TAHRI, A. DRAOU
Applied Power Electronics Laboratory, Department of Electrotechnics,
University of Sciences and Technology of Oran
BP 1505 El Mnaouar (31000 Oran), ALGERIA, Fax:+213–41–421581
Contact author: Dr. Azeddine Draou, Senior member IEEE, Email: adraou@yahoo.com
Abstract
This paper describes an electronic means of measuring the instantaneous
active and reactive power absorbed by any electrical equipment. The
measurements are based on the Clark (α-β) and Park (d-q) transformations.
The system is useful to teach electrical machines in Park’s coordinates and it
allows also the study and control of some power electronics converters that
are connected to three phase power network, such as static VAR compensator.
The principle of the measuring method of the active and reactive power is
described, and analyzed for different tests. The effectiveness of the proposed
measuring method is confirmed by experimental investigation employing a
test system.
Keywords
Active power, Reactive power, SVC, Clark and Park, EPROM
17
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Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System
A. TAHRI, A. DRAOU
Introduction
Up to now, the reactive power doesn’t really have a physical significance, but it
remains recognized as an essential factor in the conception and the efficient operating of AC
electric network [1]. The application of Clark (α-β) and Park (d-q) transforms to three phase
system in order to calculate the instantaneous active and reactive power is a useful tool for
study and analysis of many electrical systems [2]. There are many industrial applications that
require the knowledge of the instantaneous value of the active and reactive power. In fact,
they are used to manage the economical aspect of their system [1, 3, 4].
The instantaneous active and reactive powers are also used in the control of converters
connected to electric network [5]. These converters can control the flow of active and reactive
power in the power system to improve voltage regulation, and increasing transient stability
margin [4, 5].
In this paper, an inexpensive electronic circuit that calculate Clark (α-β), Park (d-q)
components and the instantaneous active and reactive power for three phase AC system is
presented and discussed thoroughly.
The effectiveness of the proposed electronic method that calculates the instantaneous
active and reactive currents and power is confirmed by experimental results through a
laboratory prototype.
Theoretical Analysis
α-β transformation
Voltages and currents can be transformed from abc system to α-β coordinates as
follows, where X denotes voltage or current:
⎡ Xα ⎤
⎢X ⎥ =
⎢ β⎥
⎢⎣ X o ⎥⎦
⎡
⎢
⎢
2⎢
3⎢
⎢
⎢
⎣
1
0
1
2
−1
2
3
2
1
2
−1 ⎤
2 ⎥⎡ X ⎤
⎥ a
3 ⎥⎢ ⎥
−
Xb
2 ⎥⎢ ⎥
1 ⎥ ⎢⎣ X c ⎥⎦
⎥
2 ⎦
(1)
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Leonardo Electronic Journal of Practices and Technologies
Issue 6, January-June 2005
ISSN 1583-1078
p. 17-28
d-q transformation
From α-β transformation the d-q coordinates are given by:
⎡ X d ⎤ ⎡ cos ω t sin ω t 0⎤ ⎡ X α ⎤
⎢ X ⎥ = ⎢− sin ω t cos ω t 0⎥ ⎢ X ⎥
⎢ q⎥ ⎢
⎥⎢ β ⎥
⎢⎣ X o ⎥⎦ ⎢⎣ 0
0
1⎥⎦ ⎢⎣ X o ⎥⎦
(2)
Active and reactive power
The active and reactive power for three phase balanced system can be written in d-q
coordinates as follows, where V d , V q , I d and I q are the voltages and currents in d-q coordinates:
P = Vd I d + Vq I q
Q = Vd I q − Vq I d
(3)
Proposed Measuring System
General description
The block diagram of the proposed measuring system is presented in fig. 1. The whole
system is divided in three subsystems connected in cascade. The function of subsystem 1 is
to synchronize all of the system to the AC mains using PLL and to generate the adequate
addresses to generate sine and cosine functions which are stored in two EPROMS.
In the subsystem 2, the measured voltages and currents are transformed from abc to
Clark and Park coordinates. And in the third subsystem the instantaneous active and reactive
power are calculated.
Detailed description
Subsystem 1:
Subsystem 1 is frequency synthesizer. The clock frequency is 16.16.16.8.50Hz =
1.638 MHz synchronized to the AC main. This clock frequency is used to drive the address
generator. The address generator is composed of four 74HC161 synchronous pre-settable
binary counters and two 74HC245 buffers. The addresses obtained are suitable to read in
parallel two EPROMs of
215
= 32 Koctets , where sine and cosine functions are stored.
1024
19
Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System
A. TAHRI, A. DRAOU
Hence the obtained address generator is shown in fig. 2.
Subsystem 2:
The measured voltages and currents in abc frame are transformed in Clark and Park
coordinates. The Clark transform given by equation (1) is obtained using simple operational
amplifiers as shown in fig. 3.
AC
main
Clock
Address
Generator
PLL
A(0-14)
sin-cos
EPROMS
Reset
sin
voltage
sense
Va
Vb
Vc
current
sense
Ia
Ib
Ic
cos
Vd
Clark
Park
transform
Vq
Id
Iq
Active and
reactive
power
calculator
(P, Q)
P
Q
Load
Figure 1. Proposed measurement system
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Leonardo Electronic Journal of Practices and Technologies
Issue 6, January-June 2005
ISSN 1583-1078
p. 17-28
74HC161
74HC161
A 0 ( 8 1 9 .2 H z )
A 1 ( 4 0 9 .6 k H z )
A 2 (2 0 4 .8 k H z )
A 3 ( 1 0 2 .4 k H z )
A 4 (5 1 .2 k H z )
A 5 ( 2 5 .6 k H z )
A 6 (1 2 .8 k H z )
A 7 (6 .4 k H z )
74HC245
74HC161
74HC245
74HC161
C lo c k
( 1 .6 3 8 M H z )
A 8 (3 .2 k H z )
A 9 (1 .6 k H z )
A 1 0 (8 0 0 H z )
A 1 1 (4 0 0 H z )
A 1 2 (2 0 0 H z )
A 1 3 (1 0 0 H z )
A 1 4 (5 0 H z )
A 1 5 ( 5 0 H z P u ls e d )
b u ffe r s
R eset
c o u n te r s
Figure 2. Address generator
Figure 3. Clark transform Circuit
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Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System
A. TAHRI, A. DRAOU
Park coordinates are obtained from Clark coordinates by using equation (2).
The sine and cosine functions generated by the address generator and synchronized to
the AC mains are used to obtain the Park coordinates by using the analog multiplier
AD534JD as shown in fig. 4.
sin (ωt )
cos (ωt )
1
2
Xα
6
7
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
V-
4
1
12
2
11
6
10
7
X1
SF
X2
Q
Y1
Z1
Y2
Z2
14
V+
8
V-
AD534JD
4
12
Xd
11
10
14
8
AD534JD
Xβ
1
2
6
7
+15V
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
V-
-15V
4
1
12
2
11
6
10
7
14
8
AD534JD
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
V-
4
12
Xq
11
10
14
8
AD534JD
Figure 4. Park transform Circuit
Subsystem 3:
The instantaneous active and reactive power calculator is also obtained using the
analog multiplier AD534JD as shown in fig. 5.
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Leonardo Electronic Journal of Practices and Technologies
Issue 6, January-June 2005
ISSN 1583-1078
p. 17-28
Vd
1
2
Id
6
7
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
V-
4
12
11
10
14
8
AD534JD
Vq
1
2
Iq
6
7
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
V-
4
12
P
11
10
14
8
AD534JD
1
2
6
7
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
V-
4
12
11
10
14
8
AD534JD
1
2
6
7
+15V
X1
SF
X2
Q
Y1
Z1
Y2
Z2
V+
-15V
V-
4
12
Q
11
10
14
8
AD534JD
Figure 5. Instantaneous active and reactive power calculator
Experimental Results
To confirm the effectiveness of the proposed measuring method of instantaneous
active and reactive units, some experiments were carried out employing a test system with
23
Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System
A. TAHRI, A. DRAOU
different loads. Fig. 6 shows the direct and quadrature Park’s voltages of the AC mains. A
transient starting test of induction motor was carried at the laboratory with the proposed
system.
Fig. 7 shows the AC current absorbed by induction motor in transient starting. Fig. 8
shows the direct and quadrature currents of induction motor starting.
The active and reactive power absorbed by the induction motor in transient starting are
depicted in fig. 9. The measurement system was tested with induction motor without load, it is
clear that the active power absorbed by the motor is negligible but there is a little amount of
reactive power necessary to create the three phase rotating magnetic field in the stator of the
induction motor. Another test was carried out in the laboratory with three phase symmetric
thyristor rectifier. Fig. 10 shows the output DC voltage and input current of the rectifier for
the phase angle control α = 80 degree.
Fig. 11 shows the direct and quadrature currents absorbed by the three phase
symmetric rectifier for the phase angle control α = 80 degree, and the active and reactive
power are depicted in fig. 12.
Figure 6. Direct and quadrature voltages of the AC mains
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Leonardo Electronic Journal of Practices and Technologies
Issue 6, January-June 2005
ISSN 1583-1078
p. 17-28
Figure 7. AC current of induction motor at transient starting
Figure 8. Direct and quadrature currents of induction motor in transient starting
25
Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System
A. TAHRI, A. DRAOU
Figure 9. Active and reactive power absorbed by induction motor at transient starting
Figure 10. Output DC voltage and input current of three phase symmetric rectifier
with α = 80 degree
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Leonardo Electronic Journal of Practices and Technologies
Issue 6, January-June 2005
ISSN 1583-1078
p. 17-28
Figure 11. Direct and quadrature currents of three phase symmetric rectifier with α = 80°
Figure 12. Active and reactive power of three phase symmetric rectifier with α = 80 degree
27
Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System
A. TAHRI, A. DRAOU
Conclusions
In this paper an electronic measurement of the instantaneous active and reactive
power method has been presented. The proposed measurement system has thoroughly been
tested in steady and transient states. The measurement method can be used to study different
electrical equipment in laboratory as induction and synchronous machines and some
converters.
The steady state and transient measurement results obtained have confirmed the
applicability of the proposed scheme to design a simple and fast controller for active and
reactive power applications.
References
1. Miller T. J. E., Reactive Power Control in Electric Systems, John Wiley and Sons, Inc.
1982.
2. Paap C. G., Symmetrical Components in the Time Domain and Their Application to Power
Network Calculations, IEEE Trans. On Power Systems, Vol. 15, No. 2, May 2000.
3. Boisdon C., Drown G., Les systèmes de compensation statique rapide dans les réseaux
industriels, R.G.E. No. 12, Decembre 1984.
4. Tahri A., Draou A., Benghanem M., Power Stability Improvement of Power Utility grid
using a New Advanced Static Var Compensator, 23rd International Telecommunications
Energy Conference, INTELEC 2001, Edinburgh UK, 14-18 October 2001.
5. Tahri A., Draou M., Benghanem A., Fast Current Control Strategy of a PWM Inverter
used for Static Var Compensation, Proceedings of the 24th Annual Conference of the IEEE
Industrial Electronics Society IECON'98, Vol. 1, p. 450-455, Aachen - Germany, August
31 - September 4, 1998.
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