Instantaneous Active and Reactive Power Measuring Method in … · 2018-12-20 · thyristor rectifier. Fig. 10 shows the output DC voltage and input current of the rectifier for the

Leonardo Electronic Journal of Practices and Technologies

ISSN 1583-1078

Issue 6, January-June 2005

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: [email protected]

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 http://lejpt.academicdirect.org

mailto:[email protected]

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:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−

−−

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

c

b

a

o XXX

XXX

21

21

21

23

230

21

211

32

β

α

(1)

18


ISSN 1583-1078


p. 17-28

d-q transformation

From α-β transformation the d-q coordinates are given by:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

oo

q

d

XXX

tttt

XXX

β

α

ωωωω

1000cossin0sincos

(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 , , and are the voltages and currents in d-q coordinates: dV qV dI qI

dqqd

qqdd

IVIVQ

IVIVP

−=

+= (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 Koctets321024215

= , where sine and cosine functions are stored.

19


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.

PLL

Clock

Reset

AddressGenerator

sin-cosEPROMS

ClarkPark

transform

voltagesense

currentsense

Load

A(0-14)

ACmain

Va

VcVb

IaIbIc

Vd

Vq

IdIq

sin cos

Active andreactivepower

calculator(P, Q)

P

Q

Figure 1. Proposed measurement system

20


ISSN 1583-1078


p. 17-28

74HC

16174H

C161

74HC

16174H

C161

74HC

24574H

C245

C lo c k(1 .6 3 8 M H z )

R e s e t

b u ffe rs

c o u n te rs

A 3 (1 0 2 .4 k H z )

A 7 (6 .4 k H z )A 6 (1 2 .8 k H z )A 5 (2 5 .6 k H z )A 4 (5 1 .2 k H z )

A 2 (2 0 4 .8 k H z )A 1 (4 0 9 .6 k H z )A 0 (8 1 9 .2 H z )

A 9 (1 .6 k H z )A 8 (3 .2 k H z )

A1 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 )

Figure 2. Address generator

Figure 3. Clark transform Circuit

21


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.

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

cos ωt( )

sin ωt( )

Xα

Xβ

X

Xd

q

+15V

-15V

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.

22


ISSN 1583-1078


p. 17-28

Vd

+15V

-15V

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

X1

X2

Y1

Y2

SF

Q

Z1

Z2

V+

V-

AD534JD

1

2

6

7

4

12

11

10

14

8

Vq

Id

Iq

P

Q

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


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

24


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


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

26


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


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.

28

Documents

Instantaneous Active and Reactive Power Measuring Method in … · 2018-12-20 · thyristor rectifier. Fig. 10 shows the output DC voltage and input current of the rectifier for the