Научная статья на тему 'Monitoring of electrical energy quality on the traction substation input'

Monitoring of electrical energy quality on the traction substation input Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

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Ключевые слова
QUALITY / HIGHER HARMONICS / ELECTRICAL ENERGY / SUBSTATION / MONITORING / LOSSES

Аннотация научной статьи по электротехнике, электронной технике, информационным технологиям, автор научной работы — Gryb O.G., Gapon D.A., Ierusalimova T.S., Borodin D.V., Diachenko A.V.

For the implementation of measures to maintain the quality of the energy industrial enterprises have to spend a significant material and monetary assets. In this regard, significant is the feasibility study of the allocation of such funds and, primarily, the determination of the economic damage arising from low quality of electricity. The reliability of the electricity metering system, relay protection and automation of modern digital substations depends on the quality of electrical energy. At the present time to improve the reliability of the substation operation it is necessary to monitor indicators of quality of electric energy, allowing you to take organizational and technical solutions for their improvement. Monitoring the power quality at the input traction substation has shown that indicators such as the coefficient of the n-th harmonic component of the voltage does not meet the standards GOST 13109-97. The source of higher harmonics is a voltage Converter used on the locomotive. To eliminate higher harmonics in the supply network for traction substations will need to install power filters. Today, the USB-analyzer of power quality «Digital system for the measurement of electrical energy quality» type of DSMEEQ of accuracy class 0.2. Work energy requires reliable and quality electricity supply to consumers. The new model of balancing energy market are bilateral contracts. The main task of this market, it ensure the stable and reliable operation of the unified energy system of Ukraine, that is, transmission and supply of electricity of appropriate quality.For the implementation of measures to maintain the quality of the energy industrial enterprises have to spend a significant material and monetary assets. In this regard, significant is the feasibility study of the allocation of such funds and, primarily, the determination of the economic damage arising from low quality of electricity. The reliability of the electricity metering system, relay protection and automation of modern digital substations depends on the quality of electrical energy. At the present time to improve the reliability of the substation operation it is necessary to monitor indicators of quality of electric energy, allowing you to take organizational and technical solutions for their improvement. Monitoring the power quality at the input traction substation has shown that indicators such as the coefficient of the n-th harmonic component of the voltage does not meet the standards GOST 13109-97. The source of higher harmonics is a voltage Converter used on the locomotive. To eliminate higher harmonics in the supply network for traction substations will need to install power filters. Today, the USB-analyzer of power quality «Digital system for the measurement of electrical energy quality» type of DSMEEQ of accuracy class 0.2. Work energy requires reliable and quality electricity supply to consumers. The new model of balancing energy market are bilateral contracts. The main task of this market, it ensure the stable and reliable operation of the unified energy system of Ukraine, that is, transmission and supply of electricity of appropriate quality.

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Текст научной работы на тему «Monitoring of electrical energy quality on the traction substation input»

UDC 621.311

O.G. Gryb, D.A. Gapon, T.S. Ierusalimova, D.V. Borodin, A.V. Diachenko

MONITORING OF ELECTRICAL ENERGY QUALITY ON THE TRACTION SUBSTATION INPUT

For the implementation of measures to maintain the quality of the energy industrial enterprises have to spend a significant material and monetary assets. In this regard, significant is the feasibility study of the allocation of such funds and, primarily, the determination of the economic damage arising from low quality of electricity. The reliability of the electricity metering system, relay protection and automation of modern digital substations depends on the quality of electrical energy. At the present time to improve the reliability of the substation operation it is necessary to monitor indicators of quality of electric energy, allowing you to take organizational and technical solutions for their improvement. Monitoring the power quality at the input traction substation has shown that indicators such as the coefficient of the n-th harmonic component of the voltage does not meet the standards GOST 13109-97. The source of higher harmonics is a voltage Converter used on the locomotive. To eliminate higher harmonics in the supply network for traction substations will need to install power filters. Today, the USB-analyzer ofpower quality «Digital system for the measurement of electrical energy quality» type of DSMEEQ of accuracy class 0.2. Work energy requires reliable and quality electricity supply to consumers. The new model of balancing energy market are bilateral contracts. The main task of this market, it ensure the stable and reliable operation of the unified energy system of Ukraine, that is, transmission and supply of electricity of appropriate quality. References 4, tables 1, figures 10.

Key words: quality, higher harmonics, electrical energy, substation, monitoring, losses.

Надежность работы системы учета электроэнергии, релейной защиты и автоматики на современных цифровых подстанциях зависит от качества электрической энергии. В настоящее время для повышения надежности работы подстанции необходимо контролировать показатели качества электрической энергии, что позволяет принимать организационные и технические решения по его повышению. Библ. 4, табл. 1, рис. 10.

Ключевые слова: качество, высшие гармоники, электрическая энергия, подстанция, мониторинг, потери.

Introduction. In the process of the scientific and technological progress, novel technologies creation, increase of the energetic security of Ukraine the reliable and qualitative delivery of electrical energy to customers plays an important role. A new model of the electrical energy market which represents a market of bilateral contracts and a balancing market is introduced in Ukraine. One of tasks of the new market model is to create a market operating to guarantee stable and reliable operation of the consolidated power system of Ukraine, transmission and delivery of electrical energy of appropriate quality [1].

Problem definition. To carry out measures to hold the electrical energy quality, industrial enterprises are forced to spend huge material and financial means. Therefore, technical and economical assessment of such expenses is important, first of all to determine economical losses arising as a result of low electrical energy quality.

In conditions of the market economy, a network enterprise and a customer are equal partners, subjects of the indivisible process of the distribution and demand of electrical energy [2]. Change of the attitude of power supply companies as well as of customers to problems of electrical energy quality is determined, first of all, by losses sustained by the enterprise and the power network proper as a result of utilization of electrical energy of low quality. Losses which can arise as a result of low electrical energy quality should be divided into material, labor, financial, temporal, and special ones.

Material losses become apparent in unforeseen additional losses or direct ones of equipment, property, production, low materials, or energy. In industry material losses are directly connected with loss of fixed and circulating capital.

Labor losses represent working time losses caused by unforeseen circumstances. At the direct measurement labor losses are expressed in man-hours, man-days or just in hours of the working time. Translation of labor losses to cost or money equivalent is carried out by multiplication of man-hours by cost (price) of one hour.

Financial losses are direct money loss connected with unforeseen payments, penalties, additional taxes, losses of money and securities. Besides, financial losses can be resulted when they receive less or do not receive money from foreseen sources, by failure to return the debt, when purchaser does not pay for production supplied, by the decrease of receipts as a result of the decrease of prices for production and services.

Time losses exist when the process of the economical activity proceeds slowly than it was planned. Direct assessment of such losses is carried out in hours, days, weeks, months of delay in obtaining the result scheduled. To translate the time losses estimation to the cost quality it is necessary to determine in which losses of income and profit the time losses can result [2].

Losses because of 1 hour of downtime resulted by voltage deviations are the following:

• airlines booking centers - USD 67,000 - 112,000;

• commodity exchange - USD Mio 5.6 - 7.3;

• a network of automates and services - USD 12,00017,000;

• credit card sale - USD Mio 2,2 - 3,1;

• voltage undershoot at the paper mill stops the production for 1 day, losses are USD 250,000;

• cycling production interruption in the glass industry costs USD 200,000.

© O.G. Gryb, D.A. Gapon, T.S. Ierusalimova, D.V. Borodin, A.V. Diachenko

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When de-energization takes place enterprises loss:

• USD 1477 during 1 s of de-energization;

• USD 2107 during 3 min of de-energization;

• USD 7795 during 1h of de-energization.

By the data of more than 200 large commercial and industrial customers at the de-energization during 4 h without preliminary notification, average loss in the USA is about USD 75,000. During 1 h without notification -USD 40,000. During 1 h with notification - USD 23,000. Loss by the voltage drop of 10-20% is estimated as USD 7,500, loss of sudden outage during 2 s - USD 11,000..

Materials of investigations. Main integral indicator of the electrical energy quality is suitability calculated on the base of the measured values of the electrical energy quality indicators determined by the Standard GOST 13109-97: suitability of each electrical energy quality indicator is calculated as a ratio of numbers of measurements situating in normally permitted by GOST 13109-97 bounds, and total numbers of measurements for the period under review. If the value of the electrical energy quality indicator corresponds to GOST 13109-97, the value of the suitability is equal or more than 0.95: if not - less than 0.95. The suitability by the indicator which has passed out the maximum allowable values is supposed to equal zero and does not correspond the requirements of GOST 13109-97. The electrical energy quality is characterized by the following properties:

• voltage deviation;

• voltage oscillations;

• voltage undershoot;

• temporal overvoltage;

• voltage non-sinusoidality;

• non-symmetry of three-phase voltage system;

• frequency error;

• pulsed voltage.

In the correspondence with [1] the electrical energy quality indicator correspond these properties:

• steady-state voltage deviation 5Uy;

• voltage swing 5Ut;

• flicker doze Pt;

• distortion coefficient of the voltage curve sinusoidal-

ity KU;

• coefficient of the и-th voltage harmonic component

KU(n);

• coefficient of the voltage non-symmetry by the reverse sequence K2U;

• coefficient of the voltage non-symmetry by the zero sequence K0U;

• frequency error Af

• duration of the voltage undershoot Atn;

• pulsed voltage иимш

• coefficient of the temporal overvoltage KnepU.

Currently, an analyzer of the electrical energy quality «Digital system for the measurement of electrical energy quality» (DSMEEQ) of the accuracy class 0.2 is developed (see Fig. 1) [3, 4].

Experimental investigations of the electrical energy quality are carried out at the substation 330/110 kV from which a traction substation of mainline electrical transport by the line 110 kV is supplied (Fig. 2-4).

Fig. 1. Digital system for the measurement of electrical energy quality (DSMEEQ)

Averages values of voltage deviation for phase С, %

1 - average voltage deviation 2 - normal allowable upper bound

3 - normal allowable lower bound

Fig. 2. Steady-state voltage deviation for phases А, В, С

Average voltage of direct sequence, kV

1 - average voltage of direct sequence 4 - normal allowable lower bound

2 - maximum allowable upper bound 5 - maximum allowable lower bound

3 - normal allowable upper bound

Fig. 3. Average voltage of direct sequence

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Distortion coefficient of the voltage curve sinusoidality for phases А, В, С, %

B

A

С

1 - maximum allowable bound 2 - normal allowable bound

Fig. 4. Distortion coefficient of the voltage curve sinusoidality for phases А, В, С

In Fig. 5-10 graphic charts and test record sheets for coefficients of the n-th harmonic voltage component in phases A, B, C at the traction substation 330/110 kV of the line 110 kV are presented. Measurements are carried out at the bound of the balance belonging of the supplier and customer of electrical energy.

n Coeff! Kun) %

2 0 021

3 0.665

4 0.017

5 0.316

6 0 008

1 0.349

a 0.007

s 0 172

10 0.005

11 0.033

12 0.002

13 0.046

14 0.D02

15 0.026

16 0.002

17 0.055

10 0.001

19 0.026

20 0.001

21 0.019

22 0.001

23 0.014

24 0.001

25 0.025

26 0.002

27 0.017

2B 0.D01

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29 0.019

30 0.001

31 0.D23

32 0 001

33 0.014

34 0.D01

35 0 009

36 Q.0Q1

37 0.011

30 0.001

39 0.014

40 0 001

З * і

Fig. 5. Graphic chart for the n-th harmonic voltage component in the phase A

From the total record sheet for coefficients of the и-th harmonic voltage component in the phase A at the traction substation 330/110 kV of the line 110 kV in the phase A during 24 hours it is shown that the coefficient of the n-th harmonic voltage component corresponds the normative by GOST 13109-97(see Fig. 5, 6).

From the total record sheet for coefficients of the nth harmonic voltage component in the phase B at the traction substation 330/110 kV of the line 110 kV in the phase B during 24 hours it is shown that the coefficient of

No. of harmonic Allowable values No. of measurements No. of passes out Availability

normal % maximum % normal allowable values maximum allowable values

2 0.50 0.75 28799 0 0 1.000

3 1.50 2.25 28 799 0 0 1.000

4 0.30 0.45 28 799 0 9 1000

5 1.50 2.25 28799 0 0 1.000

6 □ 20 0.30 28 799 0 0 1 000

7 1.00 1.50 28 799 0 0 1.000

8 0.20 0.30 28 799 0 D 1.000

5І йМ • ■lit* 1

10 0.20 0.Э0 28799 0 0 1.000

11 1.00 1.50 28 799 0 0 1 000

12 020 0.30 28 799 0 0 1 000

13 0,70 1.05 28799 0 9 1,000

14 □.20 0.30 28 799 0 0 1.000

13 0.20 0.Э0 28 799 0 0 1.000

16 □ 20 0-30 28799 0 0 1 000

17 □ so 0.75 28 799 0 0 1 000

13 0.20 0.30 28 799 0 0 1.000

19 □.40 0.60 28 799 0 0 1.000

20 0.20 0.30 28 799 0 0 1000

21 0.20 0.30 28799 0 0 1.000

22 0.20 0.30 28 799 0 0 1 000

23 0.40 0.60 28 799 0 9 1000

24 0.20 0.30 28799 0 9 1,000

25 □.40 0.60 28 799 0 0 1.000

26 0.20 0.30 28 799 0 0 1.000

27 □ 20 0-30 28 799 0 0 1 000

28 0.20 0.30 28 799 0 0 1000

29 0,37 0.S6 28799 0 0 1.000

30 0.20 0.30 28 799 0 0 1.000

31 0.36 0.54 28 799 0 9 1000

32 0.20 0.30 28799 0 0 1.000

33 □.20 0.30 28 799 0 0 1.000

34 0.20 Q.30 28 799 0 0 1000

35 0,34 0.51 28799 0 0 1,000

36 0.20 0.30 28 799 0 □ 1 000

37 0.33 0.50 28 799 0 0 1.000

38 □.20 0.30 28 799 0 0 1.000

39 0.20 0.30 28 799 0 0 1000

40 0.20 0.30 28799 0 D 1.000

Fig. 6. Test record sheet for coefficients of the n-th harmonic voltage component in the phase A

the n-th harmonic voltage component does not correspond the normative by GOST 13109-97(see Fig. 7, 8). Let us analyze harmonics presented in the phase B.

Coeff.

n Ku(n> % - - ...

0.025

4 0018

5 0.449

6 0597 0.005

8

9 0.106

11 12 0.102 0.004

nmn

13 0.047

14 15 16 0.003 0.024 0.002

17 0.042

18 19 20 21 0.001 0.018 0.001 0.014

22 0.001

24 25 0.003 0.025

0.400

26 0.002

28 29 0.001 0.014

ЗО 0.001

31 0014

34 0002

35 36 37 38 0.012 0.001 0.011 0.002 - - - It

Г “

39 40 0.007 0.001 і

Fig. 7. Graphic chart for the n-th harmonic voltage component in the phase B

In this phase even and odd harmonics which passed out the maximum allowable values (mav) are presented: Harmonics 2 - mav (0.75) - 3.11; 3.12; 3.21; 3.34. Harmonics 6 - mav (0.30) - 0.36; 0.35.

Harmonics 10 - mav (0.30) - 0.34; 0.33; 0.32. Harmonics 3 - mav (2.25) - 8.59;8.61; 8.63; 10.03.

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No. of harmonic Allowable values No. of measurements No. of passes out Availability

normal % maximum % normal allowable values maximum allowable values

2 Q.5Q 075 28 799 0 100 0000

3 1 50 225 23 799 3 99 oooo

4 0,30 045 25 799 0 0 1.000

5 1.50 22b 28 799 0 99 oooo

6 0.20 030 28 799 0 99 DQOQ

7 1.00 1 SO 23 799 0 99 OOOO

6 0.20 0.30 25 799 0 0 VOOD

9 0.40 060 23 799 0 99 OOOO

ia 0.20 030 28 799 IS 84 oooo

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11 1.00 1.50 23 799 0 99 oooo

12 0.20 0.30 25 799 a 0 1.QQD

13 0.70 1 05 23 799 0 99 OOOO

14 D.2D 0 30 28 799 99 0 0 997

15 0.20 030 23 799 0 99 OOOO

16 D.2Q 0.30 25 799 99 0 0997

17 0.50 075 23 799 0 99 OOOO

1B 0.20 030 25 799 0 0 VOOD

19 0.40 060 28 799 0 99 OOOO

2D D.20 0.30 25 799 0 0 VOOD

21 0.20 030 23 799 0 99 OOOO

22 0.20 0.30 25 799 0 0 VOOD

23 0.40 0.60 23 79S 13 0 1.000

24 0.20 030 23 799 90 0 0997

25 0.40 060 25 799 0 0 1,000

26 0.20 0.30 25 799 0 0 VOOD

27 0.20 030 23 799 93 0 0997

28 0.20 0.30 25 799 0 0 VOOD

25 0,37 056 25 799 0 0 vooo

3D 0.20 0.30 25 799 0 0 VOOD

31 0.36 054 25 799 0 0 1 00Q

31 0.20 030 25 799 0 0 1 00D

33 0.20 030 25 799 44 0 0995

34 0.20 0.30 23 799 0 0 1.000

35 0.34 051 25 799 0 0 V00D

36 0.20 030 23 799 0 0 1QOO

37 0.33 0.50 25 799 a 0 VOOD

36 0.20 0.30 23 799 0 0 1.000

39 0.20 0.30 25 799 3 0 VOOD

40 0.20 0.30 23 799 0 0 VOOD

Fig. 8. Test record sheet for coefficients of the и-th harmonic voltage component in the phase B

Harmonics 5 - mav (2.25) - 2.65; 2.59; 2.56; 2.54. Harmonics 7 - mav (1.50) - 3.10; 3.08; 3.15. Harmonics 9 - mav (0.60) - 2.34; 2.36; 2.35; 2.48. Harmonics 11 - mav (1.50) - 1.93; 1.91; 1.88; 1.89. Harmonics 13 - mav (1.05) - 1.47; 1.46; 1.44; 1.43. Harmonics 15 - mav (0,30) -1.29; 1.28; 1.30; 1.35. Harmonics 17 - mav (0.75) - 0.93; 0.92; 0.97. Harmonics 19 - mav (0.60) - 0.73; 0.72; 0.70. Harmonics 21 - mav (0.30) - 0.53; 0.52; 0.51. Harmonics 23 - mav (0.40) - 0.40; 0.41; 0.42.

Fig. 9. Graphic chart for the и-th harmonic voltage component in the phase C

Besides, even and odd harmonics which passed out the normal allowable values ^av):

Harmonics 14 - иav (0.20) - 0.26; 0.25; 0.23. Harmonics 16 - иav (0.20) - 0.24; 0.23; 0.25. Harmonics 24 - иav (0.20) - 0.20; 0.21.

Harmonics 27 - иav (0.20) - 0.21; 0.22; 0.23. Harmonics 33 - иav (0.20) - 0.22; 0.21 Harmonics 39 - иav (0.20) - 0.21; 0.20.

No. of harmonic Allowable values No. of measurements No. of passes out Availability

normal , % maximum % normal allowable values maximum allowable values

2 0 50 0,75 26 799 0 0 1.000

3 150 2.25 26 799 0 0 1.000

4 0J0 0.45 26 799 0 0 1.000

S 1.50 2,25 26 799 0 0 1.000

6 020 0-30 28 799 0 0 1.000

7 1.00 1.S0 28 799 0 0 1.000

3 020 0.30 26 799 0 0 1.000

9 040 0.60 28799 38 9 0.000

1D 020 0.30 28 799 a 0 i.aoo

11 1.00 t.50 26 799 0 0 1.Q00

12 020 0.30 26 799 0 0 1.000

13 0.70 1-05 28 799 a 0 1.000

14 020 0.30 28 799 0 0 1.000

15 020 0.30 26 799 0 0 1.000

16 020 0.30 28 799 a 0 1.000

17 0.50 0.75 28 799 a 0 1.QOD

13 020 0.30 26 799 a 0 1.000

19 040 0.60 26 799 0 0 1.000

20 020 0-30 28 799 a 0 1.000

21 030 0.30 28 799 0 0 1.000

22 020 0.30 26 799 0 0 1.000

23 040 0.60 28 799 0 0 1.000

24 020 0.30 28 799 a 0 1.000

25 0.40 0.60 28 799 a 0 1.000

25 020 0.30 26 799 0 0 1.000

27 020 0-30 28 799 0 0 1.000

26 0:20 0.30 23 799 a 0 1.000

29 027 0.56 26 799 0 0 1.000

30 020 0.30 28 799 0 0 1.000

31 0.36 0.S4 28 799 a 0 1.Q0D

32 020 0.30 28 799 a 0 1.000

33 020 0.30 26 799 0 0 1.000

34 020 0.30 28 799 a 0 1.000

35 0.34 0.51 28 799 0 0 1.000

36 020 0.30 28 799 0 0 1.000

37 0 33 0.50 26 799 0 0 1.000

36 020 0.30 28 799 a 0 1.000

39 020 0.30 28 799 0 0 1.000

40 0 20 0.30 26 799 0 0 1.000

Fig. 10. Test record sheet for coefficients of the и-th harmonic voltage component in the phase C

From the total record sheet for coefficients of the и-th harmonic voltage component in the phase C at the traction substation 330/110 kV of the line 110 kV in the phase C during 24 hours it is shown that the coefficient of the и-th harmonic voltage component does not correspond the normative by GOST 13109-97(see Fig. 9, 10). Let us analyze harmonics presented in the phase C.

In this phase there is odd harmonic which passes out the normal allowable value: the 9-th harmonic - (0.40) -in the range 0.42; 0.45; 0.46; 0.43; 0.49.

In Table 1 the generalized results of measurements of the и-th harmonic voltage component C at the traction substation 330/110 kV on the feeder of the line 110 kV are presented.

Conclusions.

1. Operation of power engineering at modern conditions requires reliable and qualitative electrical energy supply to customers. The main new model of the balancing power energy market is bilateral contracts. The main task of this market is to guarantee stable and reliable operation of the consolidated power system of Ukraine, i.e. transmission and supply of electrical energy of appropriate quality.

2. The carried out monitoring of the electrical energy quality on the traction substation input is shown that such an indicator as the coefficient of the и-th voltage

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harmonic component does not correspond the normative by GOST 13109-97. The source of higher harmonics is a voltage changer used in the electric locomotive. To remove higher harmonics in the supply main it is necessary to install power filters at the traction substation.

Table 1

Traction substation 330/110 kV on the feeder of the line 110 kV

№ No. of harmonic No. of passes out the normal allowable values No. of passes out the maximum allowable values

1 2 0 100

2 3 8 99

3 5 0 99

4 6 0 99

5 7 0 99

6 9 145 108

7 10 15 84

8 11 0 99

9 13 0 99

10 14 99 0

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11 15 0 99

12 16 99 0

13 17 0 99

14 19 0 99

15 21 0 99

16 23 13 0

17 24 90 0

18 27 93 0

19 33 44 0

20 39 3 0

REFERENCES

1. GOST 13109-97. Elektricheskaya energiya. Sovmestimost' tehnicheskih sredstv elektromagnitnaya. Normy kachestva elek-tricheskoi energii v sistemah elektrosnabzheniya obschego naznacheniya [State Standard 13109-97. Electrical energy. Technical equipment electromagnetic compatibility. Quality standards for electrical energy in general use power systems]. Minsk, IPK Publishing house of standards, 1998. 30 p. (Rus).

2. Kachestvo elektricheskoy energii. Tom 1. Ekonomiko-pravovaya baza kachestva elektricheskoy energii v Ukraine i Evrosoyuze. Pod redaktsiei Griba O.G. [The quality of electric power. Vol.1. Economic and legal framework of quality of electric energy in Ukraine and the EU. Edited by Gryb O.G.]. Kharkiv, Monograph PP Graf-X, Publ., 2014. 300 p. (Rus).

3. Kachestvo elektricheskoy energii. Tom 2. Kontrol kachestva elektricheskoy energii. Pod redaktsiei Griba O.G. [The quality of electric power. Vol.2. Monitoring of power quality. Edited by Gryb O.G.]. Kharkiv, Monograph PP Graf-X, Publ., 2014. 244 p. (Rus).

4. Gryb O.G, Prahovnik A.V., Tesik Y.F., Zharkin A.F., Novskiy V.O., Kalinchik V.P., Karasinskiy O.L., Dovgalyuk

O.M., Lazurenko O.P., Hodakivskiy A.M., Vasilchenko V.I., Svetelik O.D. Avtomatyzovani systemy obliku ta yakosti elek-trychnoyi enerhiyi [The automated systems of the account and quality of electric energy. Edited by Gryb O.G.]. Kharkiv, Ranok-NT Publ., 2012. 516 p. (Ukr).

Received 16.10.2015

Gryb O.G.1, Gapon D.A.1, Ierusalimova T.S.1, Borodin D.V.2, Diachenko A.V.1

1 National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, 61002, Ukraine.

phone +38 057 7076551, e-mail: [email protected]

2 O.M. Beketov National University of Urban Economy in Kharkiv, 12, Revolution Str., Kharkiv, 61002, Ukraine.

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