Specific features of harmonic conditions at the node connecting a pulp-and-paper mill to a supply network Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

DOI: 10.17516/1999-494X-0204 yflK 621.311

Specific Features of Harmonic Conditions at the Node Connecting a Pulp-And-Paper Mill to a Supply Network

Lidiia I. Kovernikova*a'b, Van Chung luongb and Van Cuong Ngob

aEnergy System Institute named after L.A. Melentiev

Irkutsk, Russian Federation bIrkutsk National Research Technical University Irkutsk, Russian Federation

Received 27.12.2018, received in revised form 04.08.2019, accepted 21.01.2020

Abstract. The paper presents the results of the analysis on measured parameters of harmonics at the node of the high-voltage network. The measurements were made at the node connecting the pulp-and-paper mill to the 220 kV supply network. This load is nonlinear and has a large capacity. Particular attention is paid to the distributions of the current and voltage harmonics. The paper clearly shows probabilistic properties of the measured parameters of harmonics.

Keywords: power quality, harmonics, high-voltage network, measurement, statistical analysis.

Citation: Kovernikova L.I., Luong V.C., Ngo V.C. Specific features of harmonic conditions at the node connecting a pulp-and-paper mill to a supply network, J. Sib. Fed. Univ. Eng. & Technol., 2020, 13(1), 38-51. DOI: 10.17516/1999-494X-0204

© Siberian Federal University. All rights reserved

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). Corresponding author E-mail address: [email protected]

Особенности параметров режимов гармоник в узле присоединения целлюлозно-бумажного комбината к питающей сети

Л.И. ^Берникова3'5, В.Ч. Лыонг6, В.К. Нгоб

аИнститут систем энергетики имени Л.А. Мелентьева

Российская Федерация, Иркутск бИркутский национальный исследовательский технический университет Российская Федерация, Иркутск

Аннотация. В статье представлены результаты анализа измеренных параметров гармоник в узле сети высокого напряжения. Измерения сделаны в узле присоединения к питающей сети 220 кВ мощной нелинейной нагрузки - целлюлозно-бумажного комбината. Особое внимание уделено законам распределения величин гармоник тока и напряжения. Статья наглядно показывает вероятностные свойства параметров гармоник.

Ключевые слова: качество электрической энергии, гармоники, сеть высокого напряжения, измерения, статистический анализ.

Цитирование: Коверникова, Л.И. Особенности параметров режимов гармоник в узле присоединения целлюлозно-бумажного комбината к питающей сети / Л.И. Коверникова, В.Ч. Лыонг, В.К. Нго // Журн. Сиб. федер. ун-та. Техника и технологии, 2020. 13(1). С. 38-51. DOI: 10.17516/1999-494Х-0204

Introduction

It is well known that nonlinear loads cause non-sinusoidal conditions in electrical networks. Non-sinusoidal current and voltage containing sinusoidal components of other frequencies, that are multiples of the fundamental frequency of 50 Hz (harmonics), cause damage to both electrical energy consumers and electricity suppliers, which is reflected in a large number of publications. In [1] the focus is made on the additional losses of harmonic active power in electrical networks and equipment. The harmonic active power does not perform useful work, consequently, electricity is wasted, which contradicts the aim of energy saving in Federal Law of the Russian Federation No. 261-FZ of November 23, 2009 "On Saving Energy and Increasing Energy Efficiency and on Amendments to Certain Legislative Acts of the Russian Federation". In [2] the authors raise issues of financial losses related to payment of bills for consumers and electricity suppliers because electricity meters measure not only the active power of the 1-st harmonic but also of other harmonics including the active power of harmonics they do not produce. The results of measurements in the low- and medium-voltage networks are presented in the substantial number of publications [3-7]. Their authors present the results of research into the harmonic conditions in the network with different types of loads. In the last decade intensive measurements of harmonics parameters have been continued, which is explained by the emergence and widespread use of new nonlinear electric equipment and increase in the values of current and voltage harmonics in the networks. For example, the results of measurements at the network node supplying the nonlinear loads of the retransmission TV stations

are presented in [8]; the results of measured parameters of the harmonics generated by energy saving lamps are presented in [9]; the harmonics measured in the medical center and their impact on the work of the medical equipment are indicated in [10]; the results of large-scale measurements of power quality indices in the 110 kV networks of Siberia, which cover 23% of Russia's territory, are demonstrated in [11]; the results of the studies on parameters of harmonics for the complex loads connected to the nodes of the 110-220 kV networks are presented in [12]; the results of an analysis of harmonic active power of high-power nonlinear loads connected to the 110-220 kV networks are given in [13]. The measurements confirmed the presence of harmonics in the electrical networks. In many cases the voltage harmonic levels exceed the limits established in State standard 32144-2013 "Power quality limits in public power supply systems". In [14] the authors indicate that 5.4% of the cost of losses due to the poor quality of electrical energy falls on the losses caused by current and voltage harmonics.

Although the parameters of harmonic conditions in electrical networks have been studied for many years, the interest to this problem does not decrease due to the growing number of nonlinear loads in the networks of different voltages and specific features of their operating conditions. The main feature is the probabilistic nature of operating parameters.

This paper presents the results of an analysis of the current, voltage and active power harmonics at the node connecting the 220 kV supply network to the large capacity nonlinear load, i.e. the pulp-and-paper mill. The operating parameters were measured in phases A, B, C of the network over 24 hours with a time interval of 1 minute. After processing the measured information, we obtained series of voltages, currents and their phase angles for harmonics 1-40 each having 1440 elements.

The current harmonics generated by the pulp-and-paper mill flow to the supply network and cause voltage distortion at its nodes. The mill is located in the region where the large number of other large capacity enterprises generating harmonics, i.e. traction substations, aluminum smelters, etc., are connected to the 220 kV network. Their current harmonics are also distributed throughout the 220 kV network and contribute to the formation of the parameters of the harmonic conditions. Consequently, the voltages at the nodes of the electrical network result from the influence of many nonlinear loads. At each node the non-sinusoidal voltage is unique since it is determined by the current harmonics flowing to the node from all nonlinear loads in the network and by the impedance of the network node.

Characteristics of the pulp-and-paper mill

The mill receives electricity from the 220 kV network. The mill uses direct-current electric motors with an automatic speed control system that drive the main process equipment. The power of the motors reaches 300 kW. Thyristor converters that have nonlinear volt-ampere characteristics are used to supply the motors with direct current.

Fig. 1 shows the graphs of the fundamental frequency currents of the load for three phases. The mill has a shift schedule. In the daytime the load conditions are the maximum and at night the loads are the minimum as can be clearly seen from the graphs.

Fig. 2 presents the graphs of variation in the phase voltages at the node connecting the mill to the supply network. The voltage values lie within acceptable limits.

J

k

yL W 4

o t-. Ci o m O r- CI o r C> o m

00 —1 CO — 00 — 00 ■çf — CO —

ci 00 o fi ci — ci vi 00 Ch ci

—1 —1 —1 —' r-l IN r-l —1 —1

Time, hour

Fig. 1.Phasecurrents at the mill connection node

> M

tat-MI;-»!}' 1 - - ^ ui fi tu

Time, hour

O r- O t-

m t - to 1; -^t « oj a ri

Fig. g. Phase velta)es a- She mill cormeo388nnoT8

An analysis of voltage at the node connecting the pulp-and-paper mill to the supply network

Fig. 3 shows the oscillograms of three-phase voltages for the maximum and minimum load conditions. The voltage waveforms in both conditions slightly differ from sinusoidal, which is confirmed by the values of the total harmonic distortion Kv. In the maximum load conditions in phases A, B and C they are equal to 1.76%, 1.31% and 2.13% respectively for 95% of the measurement time; in the minimum load conditions - to 1.23%, 1.10% and 1.25%. The limit of 2% established in State standard 32144-2013 is exceeded in phase C in the maximum load conditions. There is also phase voltage unbalance. The maximum value of the negative sequence voltage unbalance factor recorded during the measurement was equal to 1.3% at the limit of 2%.

The analysis of the voltage harmonic values shows that some of them reach large values. Fig. 4 presents a diagram of the effective values of voltage harmonic that have the largest values in the conditions of the maximum (Umax) and minimum (Umin) loads.

An analysis of measured information involved an analysis of phase angles for ten voltage harmonics. It was found that the phase angles range from 0 to 2n but are unevenly distributed. Phase angles of the 5-th and 11-th voltage harmonics have special distributions (Fig. 5). The notations used in the diagrams are: Ua - an active voltage harmonic, Ur - a reactive voltage harmonic. The overwhelming number of phase angles of the 5-th voltage harmonic range from n/2 to 3n/2.

The analysis of the series of measured values of voltage harmonics involved the calculation of the following statistical parameters [15]: maximum value (max), minimum value (min), mathematical mean (aver) and standard deviation (sd). Table 1 presents the results of a statistical analysis for ten odd

---Ua

-Ub---Uc

---Ua

-Ub

Uc

200 160 120 80 > 40 0

e -40 -80 -120 -160 -200

V ■ / ■v— ■ ** y \ \j

\ A / f — \ t

î-y / J , —V =i-y T—if {

f tl : r i ^ ? c: J c 1 > / - y« X c

. =v C i' \ c 3 y i—

Time, second

a)

200 160 120 80 > 40 0

= -40 -80 -120 -160 -200

-

/ s /

S./

/ 1 /\

* f \

O* 1,

\ p s < 3 r 3 r J " c

5 t\ c i <

. • s s • C i > i / \< i

■ — -

Time, second b)

Fig. 3. Oscillogramsofvoltage in the conditionsofa)maximum loads, b)minimumloads

> M

1,6 1,4 1,2 1

0,5! 0,6 0,4 0,2 0

.III

I Umax

Umin

1

1 11V lili 111111

3 5 7 9

11 13 17 19 23 25 31 33 35 H armonic

Fig. 4. Diagram of voltage harmonics

Urs,

a a #5 s

[J,T-. — kv Sf

.5 - 2 -1 fe t 0

a) b)

Fig. 5. Diagramsof phaseanglesof a) 5-thand b)11-thvoltageharmonics

harmonics of one phase voltage at which the limits established in State standard 32144-2013 are most often exceeded at the network nodes. The voltage harmonic values vary in the range from several volts to severalkilovolts.

Histograms were constructed for the values of ten voltage harmonics given in Table 1. Then, using the Pearson criterion, they were checked for compliance with the laws of the Gaussian and Rayleigh distribution. The purpose of the check was to confirm or refute the statements made by the authors of [6] that the parameters of the har monic conditions are in most cases distributed in accordance with

Table 1. Statistical assessment of voltage harmonics of phase A, kV

Paramuter Harmonic

3 5 5 9 11 33 17 99 23 00

max 1.18 2.18 1.61 1.94 2.73 1.08 0.45 0.48 0.50 0.57

min 0.02 0.03 0.03 0.03 0.06 0.00 0.00 0.00 0.00 0.01

aver 0.49 0.79 0.68 0.79 1.09 0.39 0.14 0.17 0.14 0.23

uh 0.24 0. 38 0.25 0.35 0.38 0.18 0.08 0.09 0.03 0.09

a) b)

Fig. 6. a) Gaussian distribution of the 11-th voltage harmonic, b) Rayleigh distribution of the 19-th voltage har-

the laws of GaussorRayleigh.The checkshowedthat out of ten harmonics the lland25-thvoltage harmomcs hen thr Gou-sion dittribthaon.Thevottage ofthe 19sth hrrmonic obeys the Rayleigh distribution. The histograms of the remaining seven harmonics have forms representing mixtures of known distributions [15-18]. Fig. 6 shows the histograms and theoretical distribution curves of the 11-th voltage harmonic according to the Gauss law and the 19-th voltage harmonic according to the Rayleigh law.

An analysis of currents at the node connecting the pulp-and-paper mill to the supply network

Fig. 7 presents oscillograms of currents for the maximum and minimum load conditions. In the minimum load conditions the current waveforms are severely distorted.

[40

Changen inthamaonituUoa afthatotaf harmenicdirtortirn oteurreni KKf = | ^T I2 /11 -100% are

V n=2

presented in Fig. 8. Values K under the minimum loads at night reach severalhundredsofpercentage points. During the daytime in the maximum load conditions, when the main process equipment is in operation, the value K does not exceed 6%.

-la---lb

Ic

-la---lb

Ic

700 500 300 < 100 --100

-"00

N

A

\

\

; c ) « y f - c > \c o l »¡nft

5 C ; A < ? c 1 >

Time, second

a)

80 60 40 20 0 -20 -40 -60 - 80

1*

r

J 1

>

rlwt >sj № tt , N

e t ? >

i V, > '■- 5 / c 5 C j t ■N > v < 5 i

■"V \

Time, second b)

Fig. 7. Oscillograms of currents in )he a) maximum 1 oad conditions, b) minimum load conditions

Ths drngrum claariy shows a group of coeffitien)swhich is much higherinvalue thanthe others. These are ghe snsnalleO ontliataon abnormwl elements l 15, 16] tlet violats ilis siaOoonarity of iPs s. Not vlwayt and tags all ^gndtr^eil [laments can Ce dt^P^riviiaixg s^iauiilly. gpeaiat tests cnch meShoOaare use. loerarch Por them in a t urine of mevsured parameleri. The sie metho hsvea tlea Icwin method [19], the Von Oeumann test [20], Phe Darhyg rest [21) aod otoars.

Test^^ijoO tee3-rd current harmomcusing the Icwtn meSOodrhcwad that there are 4 elements in the array of the 3-rdcutrentharnmmc, nomely 862, 865, 86U ond Chi. On) of [hem, naivety 865, is significant^)O )urger eiiaa the cShe) demlnt), Fig, O ehlws o ^Oiei ht the r -rd m^isje^s^^ harmonic

on whirh cm(t abnorma1 atemente even be cuea

The otlirer taemomct aten llaat<i ebrnebmal curree:! taete ihaws thaliherurrentoffhal-st

harmomcwith abnoemd eknwnCs Isret1 valuea o[ Iles Vhan e1sl a1, a11) tye tima ^oill coreespondmg to meaturemonS 20o ^Jtil vahiv rVtOo CiSt auп•en] haemonk; tcsee 5.2 ah.1

Fig. 8. Scatterdiagram ofthe Ki

100

80 < 60 X 40 20 0

o t- C] o t- C] o t- ci o t- ci o f- m

00 t — 00 — 00 t — œ — 00 t —

Cl Vt 00 o c-i Cl -H rn 00 Q\ —

T—1 i—i — T—1 fM <N (N 1 1 1 1

Tnoe. hour

Fig. 9. Abnormal elementsofthe3-rdcurrentharmonic

The abnormal elements distort the real picture of operation therefore they should be excluded in many cases. The analysis involved a statistical assessment of harmonics for the current of phase A of ten odd harmonics whose voltage values exceed the limits established in State standard 32144-2013 most often. The results of the calculations are given in Table 2. As can be seen from the Table, the current harmonicvalues vary over a wide range. Compari son ofthemaximum and mi nimum values and standoad aeyiaaionsindrcatesiheirwadovaadaiioa

To analyze ihe phoae anglus nf ihe aonreni harmoaicr in thr compler plnnrtiic scatter diae-oms weri eanstauited (Fig. 10). Actine anh reactive nc^mj^^ne^Ss of coreec iirrmi^nras \ecso calzuiaten ating the expressions Ian = In cos yIn, Irn = In sin qIn for all 1440 measurements, where n - harmonic order. The analysis of the diagrams enables us to conclude that the phase nodes lie in the range from 0 to 2n, but are unevenly distributed across the quadrants of the complex plane, for example, in diagrams 10b) and 10c).

ffihtogramtshow^sfrsaributionof thevoluaa of the artive anil reantive coit^onenUs of the current harmomcswecn arnrtructeUand checked aucording to thn Pearson eriterdon foe Checoп•espondence of tdis drstubutiouttotheGsuseandRayleighlaws. happened. tU^atl^l^a; artivocomeonrui of She n-rd cur trot earmcniu is dostaibuted cccoadiiigio ihoGcura tie co^^esu^i^nSicc^^ai^e^i^t^ive

compeuentbotdrGeusi lgwwaa egtco nfirmed by checking with the Pearson criterion (Fig. 11b).

Table 3 presents the results of the analysis of the distribution laws for ten odd harmonics: current magnitude, active and reactive components. The notations used in the Table are: G is the Gaussian distribution law, M is a mixture of several distribution laws. All three values of the analyzed currents

Table 2.Stntiriiralssscscmenrof suwentharmonlrs of^aseA, A

Parameter Harmonic

3 i 7 e D it 17 19 23 25

max 15.12 3.11 4.65 1.94 6.01 4.3 7 2.34 1.75 2.14 4.68

min 0.07 0.06 0.07 0.01 ee>4 0.01 4.02 0.01 0.03 0.01

wec 2.16 1.10 1.17 e.7( 2.ie 1.48 1.3 6 6.39 0.70 1.06

do 2. il 0.78 0.91 0.41 m 0.67 1.717 e.35 0.40 0.63

s) C) C)

Fig. lO.Diagramr ewhechrteshiiranglo srorlliechrrenl carmoaics:a) 3-rd,b)7-cdt a) 25-th

- 45 -

□ Histogram

. - „ nnflfl IL„ „

Ch f c\ n \o c r'. rj

l> —. —. O O C\ O, CO 00 ÖÖ—: (N »/S ^

1rs, A

a) b)

Fig. 11. Distribution of values of the 3-rdcurrentharmonic: a)active,b) reactive

are distributed according to the Gauss law only at the 7 and 13-th harmonics. At the 5, 17-th and 23-rd harmonics all three currents have mixtures of different distribution laws. At the 3-rd, 9, 11, 19 and 25-th harmonics one or two of the three values are distributed according to the Gauss law and the rest have mixturesof the knowndistributio nlaws.

Toassesstheelfectofcurrent hnrmomct onvoltage haamonics, lmear correlabion coefficients (rUnIn) were oalcolated foe phaoe A il5]. The;1 are ptestnted in Tabled

The Che°oka acalewaauaed to esIimtle tht ^^tri^hgtlt oft. l-oe ar cr«^^^t^tonthoit belwten the t urrent and voltageharmo n^cs [2I\ .Tho onafys^estoMishedthefollowingdegae et efcoare lation: no correlation (if rUnIn = 0-O.a) at the7-th WaamoIhe; weak tofaelnaiantif oUro„ = (.I-OwS- atthe3-ad, 17 ana 19-th har^(^nooa;ncbde^£ifc ^ot^i^s^^^t^ic^ii (iftv^ = 0.3-0.a- - al a; ft, 13 tni 05-ah haamsmos; aoticeable correlhtioh (if-v^ = 0.5-0.7)at9-thnnd 23tadhoпnon-cs. TOeac itnostaongaelaaisnahip.

We can conclude that nonlinear loads connected to other nodes of the network also make a large contribution to the formation of voltage harmonics aC ahe node to which the mill is connected.

Table 3. Distribution law harmonics current

Current Harmonic

3 5 7 9 11 13 17 19 23 25

In M M G M G G M M M G

Ian G M G G M G M G M M

Irn M M G G M G M M M M

Table 4. Coefficients rUnIn for phase A

Correlation coefficient Harmonic

3 5 7 9 11 13 17 19 23 25

rUnln 0.29 0.34 -0.07 0.51 0.43 0.43 0.16 0.22 0.55 0.31

An analysis of active power harmonics at the node connecting thepulp-and-paperm illtothesupply network

Active powers at any harmonic were csdculatedas fpllows

Pnt = Unt Int cos 9nb (1)

where Unt, Int - effective values of voltage and current of the n-th harmonic measured on the interval of 1 minute, t - the number of ameasurement interval, a»r- phaseangle betweenthevectors of voltage and curreeh nit the snteharmonicon tlta n^enture:nree^g intervals, whieh is c^akn^iiePas

9nt = 9unt - Vint

Fig. 12 presents a plot of the active power of the 1-st harmonic. The maximum value of power rerghrd 4n.9g MW, thu minimum - 0.2 MW. The magnitudes of angles qnt enable the conclusion on the direction of active eowerflown wiih gcserctroihe nodeat wluchthemeasuremgnto were made. In thcrveot OhaVangles He wi^tUP^ tOeranaes ftran 0 to Jt/2or fromeht2to in iiienrhe activa r>nwnr of harmonics flow from the network to the load and the node for the n-th harmonic is a load node. If the angles ynt lie within the range from n/2 to 3n/2 active power is directed from the load to the network ann tge oMefor Ohen-thharmonic ^generating Thn angtes.v masi oftenha m the rangs frome to 2rc,but fo rnanch^rmo^raiec. Thenara Plenib^tit^d ira aomplex plave veryuncvrgty.

Fig. 13presenVs en exampir of a dannram of the ofthe 3-rU harmoiVc. tor

some part of the measurement time the active power of the 3-rd harmonic is directed from the network to the load and for the other part of the time from load to the network.

Tte meesrreb curiente, soUg^i ar- phase anglea towem them were ^edta eakatoe the activrncwerofhaemonier i-40. It was established that the directions of the active power flows for

50

40

g 30

s 20

Oh 10

0

y VU K/

VyAt \ \ / w/'

o t-- ci oo -rf —

o

00 ^r

o r-

00 Tj-

o 00

Time, hour

Fig. 1h. A jmlot ob tire asiva powec ofthe i-ss harrt^onic of the mi 11

I"- m

Tf 1 '

O 00 Q\

Tf 1 '

Fig. l3.AngledistoibutioneiMidf the 2-rdOarmonio

100 SO -60 40

£ 20

■5 -20

-40 -60 -SO -100

Harmonic

Fig. 14.Diagram of directions for the harmonic activepowers

Table 5.Statistical estimatesof P^- and Pn(+),kW

n Pn(-) Pn(+)

max min aver sd max min aver sd

3 11.5 0.0 0.8 0.7 1.7 0.0 0.2 0.2

5 1.0 0.0 0.2 0.1 17.3 0.0 0.4 0.7

7 1.9 0.0 0.4 0.4 1.8 0.0 0.6 0.3

9 1.0 0.0 0.2 0.1 2.2 0.0 0.3 0.2

11 0.2 0.0 0.1 0.1 25.2 0.0 22.0 1.5

23 0.2 0.0 0.0 0.0 8.7 0.0 0.5 0.4

all harmonics change during the measurement time. For some harmonics however the predominant direction, i.e. for more than 50% of the measurement time, is the direction from the load to the network, for the others - from the network to the load.

Fig. 14 demonstrates a diagram showing the amount of time during which the harmonic active power flows through the node connecting the mill to the supply network from the network to the load and vice versa. In the diagram the harmonic active power with the minus sign (Pn(-)) is directed from the mill load to the network and with the plus sign (Pn(+)) - from the network to the load. As can be seen from the diagram, the directions of power from the network to the load prevail.

The magnitudes of active power of the even harmonics in both directions are very small and do not exceed 0.1 kW. Significant flows of active power in both directions are observed at some odd harmonics. The statistical characteristics of the harmonics active power are given in Table 5. At the mill connection node the active power of the 3-rd harmonic directed to the network has a larger value, while in the direction from the network to the load the 11-th harmonic active power is larger. The magnitudes of powers of odd harmonics, which are not listed in Table 5, do not exceed 0.2 kW.

When power is supplied from a source with sinusoidal voltage, the load receives the active power of the 1-st harmonic Pn(+). Most of this power is consumed by electrical equipment to perform useful work PW. The remaining part is converted by nonlinear equipment to active powers of harmonics of orders n >1. Let us denote this power as Pn(-). Active power of the 1-st harmonic can be represented as

Table 6. Statistical estimates of Pdt

Parameter Pd„ kW Pdt, % PWt

max 17.25 6.59

aver 4.92 0.08

Pi(+) = Pw + P„(-). (2)

Together with the active power of the 1-st harmonic the load of the mill receives active powers of orders n >1 - Pn(+) from the network, which are created by nonlinear loads connected to other nodes in the network. Numbers of harmonics Pn(-) and Pn(+) can be different. Thus, the active powers P = P1(+) + Pn(+) flow to the load of the mill through the node connecting it to the network.

The total active power of the n-th harmonic for n >1, i.e. detrimental power as it is called in [2], is determined as follows

Pd = Pn(-) + Pn(+). (3)

Based on the expression obtained, we calculated the total values Pdt for harmonics 2-40 for all 1440 elements. Table 6 presents the statistical estimates of Pdt in the measurement units of active power and in the percentage of useful power PWt. As seen from the Table, the maximum magnitudes differ greatly from the average values. An analysis of arrays Pdt consisting of 1440 elements shows that some of the abnormal elements are several times larger in magnitude than the other elements of the array. They give the maximum power values. The abnormal elements were not excluded as they are taken into account by meters when measuring electrical energy. It also follows from the Table that the share of detrimental active power flowing through the node of the mill connection to the network is not large compared to the effective active power. However, it is worth noting that the Table demonstrates the results of calculations only for 24 hours of one phase of the mill electrical network.

Conclusions

1. The phase voltages at the mill connection node during the measurement time are within acceptable limits. The phase voltages are slightly unbalanced and their waveforms are distorted. The total harmonic distortion of voltage KU exceeds the limit only in phase C. The values of the voltage harmonics are in the range from several volts to several kilovolts. For most harmonics they have distributions that are mixtures of different distribution laws. Only the voltages of the 11 and 25-th harmonics are distributed according to the Gauss law and the 19-th harmonic is distributed according to the Rayleigh law. The phase angles of the voltage and current harmonics are in the range from 0 to 2n, however, their distribution across the quadrants of the complex plane is uneven.

2. Phase currents of the load during the measurement time change. They have the highest values during the daytime and the lowest - at night. At night the phase current waveforms are highly distorted. The total harmonic distortion of current K during operation of the main process equipment does not exceed 6%. There are abnormal elements in the arrays of current harmonics. They are much larger than the rest of the elements. A small number of magnitudes of the effective current harmonics and

their active and reactive components are distributed according to the Gauss law. The overwhelming majority of the distributions represent mixtures of different distribution laws.

3. The values of the coefficients rUnIn indicate that nonlinear loads connected to other network nodes influence the formation of voltage harmonics.

4. Harmonic active powers change the flow direction during the measurement time. For some part of the time they flow from the load to the supply network and for the other part -from the network to the load. Their values range from several watts to several tens of kilowatts. Harmonic active powers that are the canonical harmonics of nonlinear equipment have the highest values.

Список литературы / References

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[2] Czarnecki L.S. Working, reflected and detrimental active powers, IETGeneration, Transmission & Distribution, 2012, 6(3), 233-239.

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