Methods indemnification of reactive capacity in the electric network for increase of regime reliability of the power supply system Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

METHODS INDEMNIFICATION OF REACTIVE CAPACITY IN THE ELECTRIC NETWORK FOR INCREASE OF REGIME RELIABILITY OF THE POWER SUPPLY SYSTEM

Guliyev H.B., Zeynalova N.F.

Azerbaijan Scientific-Research and Design-Prospecting Power Institute AZ1012, Ave. H.Zardabi-94, E-mail: huseyngulu@mail.ru

ABSRACT

There are considered questions of a choice and placing of devices of the battery of static condensers in distributive electric networks of power supply systems for indemnification of reactive capacity, on the basis of technical and economic indicators and investment possibilities of a power supply system. Given results of settlement experiments of realization of an offered methods for the typical distributive network, characterizing technical and economic efficiency of the made decision are resulted.

Keywords: power supply systems, a distributive electric network, batteries of static condensers, indemnification of reactive capacity.

I. INTRODUCTION

Problems of rise of efficiency and regime reliability of electric power systems at the expense of decrease of losses of the electric power in electrical networks by means of a reactive power compensation (RPC) is the important provision on an energy conservation. Thus the all-round energy conservation can be observed as alternative in relation to the large-scale escalating of power powers on large power stations.

Methodically the problem of sampling and disposing of devices RPC dares as follows. The supply authority should install meaning of a reactive power which should be transmitted from an electric power system in a consumer web (an economic reactive power - Q3K), and a deficiency of a reactive power of consumer webs should become covered at the expense of its generation in webs at the expense of batteries of statistical capacitors (BSC) [1-4] or other modes, for example, by application of a thrystors radiant of a reactive power [5].

In the conditions of market economy electrical networks of electric power systems belong to various departments and consequently solving problems BSC it is represented as a complex technical and economic problem. Thus determination Q3K should dare on the basis of technical-and-economic indexes and investment possibilities of an electric power system, and consumer webs are obliged to realize local BSC ensuring set Q3K (tgp3K), or to them sanctions in the form of the allowance to the tariff for use by electric energy should be applied.

Practically the technique of sampling and disposing of operated compensating devices (CD) in electrical networks of electric power systems consists in definition of summarized power CD, and then their optimum disposing, with determination of sequence of their installation, in electric power system knots.

The sampling and disposing problem operated BSC in distributive electrical networks of electric power systems is in-process observed.

II. CRITERION FUNCTIONS AND ACCEPTED RESTRICTION AT CRC

On the basis of experience of the solution of the given problem and the developed economic mutual relations at the optimum complex solution of problem CRC the optimization equations in a following aspect [6] are used: 1. Criterion function

F = laaWmn = s(aw:: -aw::max

SE

y C ^ YAAW -B-y CD ^max

^^ ann ~

n ;

V c J

T C

T nu =-—--> min

pb yAAWann B

where: AAwann - annual economy of the electric power owing to compensation;

AW^, AW^c - annual losses of energy before and after compensation; B- the cost price of manufacture of the electric power in power supply system; y CCD - total expenses for CD installation; nc - serviceability of the capacitor battery.

2. The restriction equations:

y i Qc — max a , exs )

Q . — Q„ — non - adjustable CD Q < QH — adjustable CD

y Ccd = Q y Qadd < Cmv.

where

node;

region);

"'cd

Ukmin < Uk <Ukmax

^ Qadd - in addition necessary CD power; Pc max - the maximal power supply system; a - the equipment factor of the CD power supply system (a » 0,2) ; Qc ex s — capacity of existing CD;

Qci Qh i min Qh i max - necessary CD power, minimal and maximal reactive power in i Cc - specific cost of CD ( $ ^ ;

C [ MBAp )

Cmv - amount of the allocated investment on CD installation in a power supply system (in Umin, Uimax - the minimal and maximal values of the voltage in k node.

3. Constraint equation.

The program of calculation of the established mode of the electric network (CEMEN) - for definition Z^W =

= AAW - for definition of the sequence of CD installation

m' 9Qc

where ap, t - ctive power losses in a mode of the maximal loading, number of hours of use of the maximal losses (t= 4000-5000 hours).

mi - sensitivity of alteration of losses at changing of the CD power in i node. Economic benefit from CRP is achieved owing to: - reduction of energy losses in air and cable lines and in transformers.

AAW = AAP-t ; CAP = AAW-ß

- increase in throughput of lines and transformers, which is taken into account by corresponding shares of their cost, i.e.: for lines with admissible current ld

AKl = Kl(11 — I2)/Id

for transformers

AKT = Kj (Sj — Si)/ Sj

Here K and KT- cost of lines and transformers. Annual economic benefit

E = C — C / n

Eann = CAP CCD ' n

Pay-back period

Tpb = (ccd —AKT — AKl)/Cap

III. METHOD OF SAMPLING CD IN DISTRIBUTIVE ELECTRICAL NETWORKS

OF ELECTRIC POWER SYSTEMS

The principle of sampling CD in distributive electrical networks is based on security of an economic reactive power - Q3K or tgç3K. Thus CD, ensuring Q3K in a point of association of a

distribution net (DN) to an electric power system, it can be installed in various points [7-9].

At installation CD on buses of a high voltage of the feed source, i.e. in a point 4 power CD will be

Qk4 = Q4 - Qk = Q4 - P4 • tgç (1)

At installation CD on a low leg of substation on supply net buses, in a point 3 Qk3 it is had:

Q4flC = Q3 - Qk3 + AQTr = Qek = P4ac • tgç

Where pac, Qac, AQriac - active and reactive powers on buses 4 and reactive power losses in transformer T1 after compensation. Here

Qk3 = Q — Qek = Qг + AQt: — Pac • tgç = 03 + AQTlac — (P3 + &PTlac)tgç =

= Q3 — P3tgV +

P32 + (Q3- Qk 3)

U2

3T1

P32 + (Q3- Qk 3)2 ' U2

rT Jgv =

= Q3 — PJgV + xT: - rTltgç — 2Q3Qk3(Xt^TM) +

,f\2( XT 1 rT 1 tgP

+ Qk 3( U.2

) =Qk 4—[2Q3Qk 3 — Q«]

2 n XT 1 — rTjtgV

2

U2

(2)

In expression (2) 2Q3QB - QB2 > 0 , since Q > Qk3, hence, Q3 < Qk4 •

Meaning of power CD Qt3 we will discover from the following quadratic equation gained after transformation (2)

U

Q 2 ■

2 Qk 3

U

2 2Q3Qk3 -Qk3 + (P32 + Q2)Xti +rf+ Q3 -P3tgç=0

U

(3)

In observed case Qk3 it is defined according to U3,p, Q3, tgy, rn, xn.

From two roots of an equation (3) it is accepted 0 > Qt3 < Q which will ensure demanded tg^ on a substation high-tension side.

At desire of definition Qk3 it is direct according to p, Q in the formula (3) meanings p, Q3 are substituted from expressions:

p =pbc_ (Pbc)2 + (Qbc)2

U2

bc (P4bC)2 + (Q4C)2

Q3 = Qbc -

U2

Where, Pb Qb- meaning active and a reactive power before compensation.

P4-jQ4

rTl+JxTl

U4 ==

P3-jQ3

rl+jxl

Qi

k4

U3 = =

Qi

rT2+jxT2

U2 = =

Pi-jQi

U 1

Q

k2

Qi

2

X

r

Fig. 1. The typical circuit design of a supply net

Let's accept:

A =

xT 1 ~ rTltgV

U2

ß _ /xT1 ~ rT 1tg9

=( U

C = (P+Q2)

2 - 2Q3-1)

3

XT1 +

U

+Q3~ Ptgv

Then

AQI3 ~ BQk3 + C = 0

Apparently from (3) meaning of reactive power CD it is defined affiliated active both a reactive power of a knot and active and jet by resistance between a point of association of a supply net to an electric power system. Therefore at installation CD in a knot 2 to resistance rn and xn it is necessary to add r and x lines 2-3, and at installation CD in a knot 1 still rr2 and xr2, voltage led to one step, for example to voltage U .

In case the supply net is represented several departing from buses 3 (10 kV) lines it is expedient to define at first the general power which is necessary for installing in this supply net, and then it to distribute between knots of loadings to proportionally their reactive powers.

IV. RECOMMENDATIONS ABOUT DISPOSING BSC IN ELECTRIC POWER

SYSTEM NETS

In existing webs for definition of a place of disposing new CD it is necessary to have the information on reactive loadings on substation. The most authentic data are the winter and summer indications spent in an electric power system. On the basis of the indications spent in real electric power system in winter phase, the analysis of a relationship jet and an active-power (tgy) on all central substations 110 kV is made ^and knots with the greatest meanings of these relationships are revealed. For 7 substations where tgp > 0,4 powers CD are defined, adoption in limits (0,2-0,3)

P^ax and their effectiveness's are defined, at various meanings r, CCD resulted in table 1. In

association about volume of investments summarized power CD, and on it annual economic benefit Ea and pay-back period the Current is chosen.

For reaching of the greatest efficiency it is necessary to install also sequence of installation CD in the electrical network of electric power systems. The analysis on the basis of factor design of experiments can be for this purpose used. Thus in the capacity of factors powers CD in various, most probable load buses with the greatest factors of a reactive power can be used.

The regression equation will have the following appearance:

k

Y = f (X) = bo +X b,X, (4)

i=1

Where, Y - average meanings of the sized up parameter; X ~ current meanings of input parameters; b0, b - estimations of factors of the equation of a regression.

Table 1

Outcomes of accounts of sampling CD and performances of their efficiency _in PC electric power systems_

Qks QKi, MVAr AP MVt AAP MVt AAWyear, kVt.h CAAW, a dale

Qk i Qk ii Qk III Qk IV Qk v QkVI Qk VII x=4500 x=5000 1 2

0 0 0 0 0 0 0 0 127,38 - - - - -

142 18 18 18 25 19 20 24 123,78 3,60 16200000 18000000 810000 900000

158 20 16 16 30 16 30 30 123,53 3,85 17325000 19250000 866250 962500

180 20 20 20 30 20 40 30 123,16 4,22 18990000 21100000 949500 1055000

194 20 20 24 40 20 40 30 123,01 4,37 19665000 21850000 983250 1092500

235 25 25 25 45 25 45 45 122,09 5,29 23805000 26450000 1190250 1322500

255 35 30 30 50 25 50 35 122,05 5,33 23985000 26650000 1199250 1332500

Table 1 prolongation

Ccd, in USD Ey=CaaW-(Ccd/n), in USD Tpb=CcD/Caaw, year

15000 20000 1 2 3 4 1 2 3 4

- - - - - - - - - -

2130000 2840000 668000 758000 620667 710667 2,6 2,4 3,5 3,2

2370000 3160000 708250 804500 655583 751833 2,7 2,5 3,6 3,3

2700000 3600000 769500 875000 709500 815000 2,8 2,6 3,8 3,4

2910000 3880000 789250 898500 724583 833833 3,0 2,7 3,9 3,6

3525000 4700000 955250 1087500 876917 1009167 3,0 2,7 3,9 3,6

3825000 5100000 944250 1077500 859250 992500 3,2 2,9 4,3 3,8

The greatest and least meanings of factors can make (0,15-0,35)Pmx. Annual economic efficiency and pay-back period application CD will be responses (outcomes). The sequence will be defined on positive greatest regression coefficient for annual economic efficiency and on negative greatest factor for pay-back period. On these in factors it is possible to choose as sequence, and most an effective value of power CD.

For sampling of sequence of installation CD in the real electrical network 110 kV electric power systems have been carried out also researches on disposing CD in 12 knots resulted in table 2.

Table 2

Outcomes of indications on active and a reactive power for separate substations

№ SS Pmax MVt Qmax MVAr tg 9 Pmin MVt Qmin MVAr tg 9

1 SS № 17 121,15 76,86 0,63 104,86 47,01 0,45

2 SS № 162 111,72 57,25 0,51 32,38 9,01 0,28

3 SS № 9 252,86 85,75 0,34 38,03 87,57 2,30

4 SS № 195 159,34 72,48 0,45 49,16 17,32 0,35

5 SS № 298 87,44 44,17 0,51 67,88 37,12 0,55

6 SS № 290 194,31 81,89 0,42 43,97 16,82 0,38

7 SS № 99 163,63 52,33 0,32 29,37 13,94 0,47

8 SS № 26 194,41 64,72 0,33 28,06 46,51 1,66

9 SS № 23 93,19 36,78 0,39 28,5 31,13 1,09

10 SS № 112 73,92 32,14 0,43 12,24 5,05 0,41

11 SS № 31 64 32 0,50 25 14,07 0,56

12 SS № 21 106,3 81,97 0,77 139,6 40 0,29

THE SUM: 1378,05 572,23 0,42 599,05 365,55 0,61

12 8

The plot of a fractional factorial experiment of type 2 =16 is made. Following adequate equations of a regression are gained:

MP = 7,75 + 0,514X7 + 0,180X5 + 0,149X2 + 0,146X9 + 0,139X3 +

+ 0,131Xg + 0,110XU + 0,105X10 + 0,104X6 + 0,101X + 0,080X12 + 0,066X4 (MVt) MW = 38,753 + 2,571X7 + 0,903X5 + 0,746X2 + 0,734X9 + 0,696X3 + + 0,659X8 + 0,553Xn + 0,528X10 + 0,521X6 + 0,509X + 0,403X12 + 0,334X4 (mln.kVt.h)

Emn = 1,47 + 0,108X7 + 0,035XS + 0,024X2 + 0,023X9 + 0,021X3 +

+ 0,019X8 + 0,019X10 + 0,014XU + 0,012X + 0,006X6 + 0,006X12 + 0,003X4 (Mln.dol.)

Tpb = 3,587 + 0,100X6 + 0,062X12 + 0,050X: + 0,050X4 + 0,050Xn +

+ 0,037X + 0,037X3 + 0,037X8 + 0,025X9 + 0 ■ X10 - 0,012X5 - 0,087X7 (year)

From the analysis of equations Ea and the Current follows the following sequence of installation CD in knots: 7-5-2-9-3-10-8-11-1-12-4-6.

V. ANALYSIS CRC IN A TYPICAL SUPPLY NET

The typical electric radial supply net 110/10/0,4 kV is observed (fig. 2), in which buses 110 kV are a feeding knot of an electric-power supply, and transformer T1 (110/10 kV), a line 10 kV and transformer T2 (110/10 kV) belong to a supply net. Summarized loading of users makes

25+j11,5MVA, distributed between knots 1 (0,4 kV), 2 and 3 (10 kV). Equivalent parameters of lines and transformers are resulted in table 3.

I\ +jQ<

Zn =2,39 + j 43,35

a

T

Qki

Fig. 2. The circuit design observed typical SS

Table 3

Equivalent parameters of lines and trans: ormers

Net element Type, brand S, MVA I, A Rekv, Om Xekv, Om

Tr-r T1 2xTDN 16/110 2x16=32 2,19 43,35

Tr-r T2 8xTM 1,6/10 8x1,6=12,8 0,0875 0,41

Line 4xAC-120 4x390=1560 0,21 0,358

Loading

S1 10 - j6

S2 12 - j5,5

S3 3 - j1,5

Outcomes of account before and after CRC in the distributive electrical network of electric power systems are resulted in table 4.

Table 4

Outcomes of account before and after CRC in the distributive electrical network

Indexes Before compens ation After compensation Efficiency of compensation

1 2 3 4 1 2 3 4

APT2 0,119 0,119 0,119 0,119 0,088 0 0 0 0,031

^2t2 0,556 0,556 0,556 0,556 0,413 0 0 0 0,143

APti 0,157 0,121 0,118 0,119 0,117 0,039 0,038 0,038 0,04

AQti 3,115 2,388 2,33 2,358 2,32 0,727 0,785 0,757 0,795

APi 1,33 1,33 1,036 1,132 1,032 0 0,294 0,198 0,298

Aß 2,28 2,28 1,77 1,934 1,763 0 0,51 0,346 0,517

S 1 add 1560 1560 1560 1560 1560

S /. 1456 1456 1284 1342 1281 0 172 114 175

Ui 356 366 390 382 398 10 34 26 42

st1 32,66 27,68 27,7 27,51 27,28 4,98 4,96 5,11 5,38

st2 12,05 12,05 12,05 12,05 10,2 0 0 0 1,75

SAAP MVt 0,039 0,332 0,236 0,369

S aaw = S aaP •7 • 103 KVt.h. (t = 4500) 177,5 1494 1062 1660

CMW =Saa W • ß •• 103 dol. ^ = 0,07^ ] 12,42 104,58 74,34 116,2 3

Ccd = C„ • Q • 103 dol. [Co = 20 • 1103 Ivdoy 200 200 200 200

f c \ Эv = CAAW - CD -103 dol. (n = 10 year) 1 ni J -7,58 84,6 54,34 96,2

C rrr CD Tpb = year c aaw 1,93 2,6 1,72

It is observed following alternatives of disposing CD in knots:

1) QK3 = 10,5 MVAr

2) QK2 = 10 MVAr

3) QK3 = 5MVAr QK2 = 5MVAr

4) QK2 = 5MVAr QK1 = 5MVAr

From the analysis of outcomes of account follows, that in a typical supply net 10-0,4 kV on

everyone installed IMVAr BSC the economy on losses (100-160 thousand kVt.h is gained. The

electric power in a year, with pay-back period BSC 2-2,6 years. Thus, loading of transformers

decreases more than on 15 %, and lines on 12 %. Voltage levels in the most remote knot raises on

7-11 %. The Most effective is installation CD more close to users, especially on voltage 0,4 sq.

Installation CD in the accepted level will ensure system of an electric-power supply of a supply net

with necessary economic power in a knot of association of a supply net, with tgq=0,21 which

„j- , ™ , 10MVAr MVAr ,

before compensation made tgrn=0,6. Installed in supply net CD makes, -= 0,4-that

25MVt MVt

matches to an average value of equipment CD for supply nets.

VI. CONCLUSIONS

1. On the basis of technical-and-economic indexes and investment possibilities of an electric power system it is given a technique of sampling and disposing of devices a reactive power compensation in the distributive electrical network, raising effectiveness and regime reliability of electric power systems at the expense of decrease of losses of the electric power.

2. For reaching of the greatest efficiency it is installed sequence of installation CD in the electrical network of electric power systems with use of the analysis on the basis of factor design of experiments and the adequate equations of a regression for parameters of efficiency CRP are accordingly gained. From the analysis of the matching equations are defined sequence of installation CD in 12 knots of electric power systems.

3. Outcomes of implementation of the offered technique for a typical supply net has shown, that on everyone installed IMVAr BSC the economy on 100-160 thousand losses kVt.h is gained. The electric power in a year, with pay-back period BSC 2-2,6 years. Installed in supply net CD makes, 0,4 MVAr ¡MVt that matches to an average value of equipment CD for supply nets.

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