Reactive capacity compensation and voltage regulation multipurpose optimization method in power distribution networks Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

REACTIVE CAPACITY COMPENSATION AND VOLTAGE REGULATION MULTIPURPOSE OPTIMIZATION METHOD IN POWER DISTRIBUTION NETWORKS

Guliyev H.B. •

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

ABSTRACT

Using the most effective method of usefulness theory in multi-purpose optimization, algorithms and effective methods of reactive capacity compensations inside given technical restrictions of power network of electricity have been worked out.

Key words: power systems, electric network, reactive capacity compensation, voltage, optimization.

I. INSTRUCTION

With a big number of electric energy consumers and different characters electric energy quality depends on many factors in the modern power networks. It includes: power networks and working condition factors of consumers. One of them is the possibility of reactive power balances with an important reserve providing after emergency modes on the basic knots of the power system and voltage regulation on all networks.

As the length of networks of a power system increases in modern conditions, we can reduce the reactive power streams, as well as operational and capital expenses. Rational voltage mode brings to the front plan the technical - economic aspects of the power transmission EFFICIENCY. Analyses and economic calculations show that transferring the reactive power by short length lines means of a high voltage justifies. Therefore in most cases reduction of reactive power to the minimum is very effective for economically when the sources of reactive power settle down near the consumption centers.

The increase of consumer loading and its structure qualitative causes considerable increase of reactive power and constant reduction of a power factor in distributed power networks [1].

Thus, the tendency of modern power systems development is characterized by one side with the increase of reactive power consumption (in some systems to 1 kVAR/kVt), on the other side with decrease of power plant generators usage expediency and possibility for the reactive power compensation purpose [2-5]. In such conditions reactive power compensation attains a special urgency. Here the optimization's primary goal is optimum placing of reactive power sources and support of a necessary reserve of capacity Qrez for voltage regulation on loading knot. For example, Polish power engineers consider that capacity of compensators should be 50% of the established capacity of generators in power plants. In France, Sweden and Germany the capacity of compensators is 35% of active peak loading, in the USA and Japan this volume is 70%. In different power systems of the USA the established capacity of compensators is 100% of generators capacities [6-11].

II. PROBLEM STATEMENT

Reactive power compensation problem is a multidimensional problem on the technical and economic aspects and consequently it is resulted with the finding of a global extremum of criterion function with the set of local extreme. In this article the voltage support within the technical restrictions and definition of optimal placing of the reactive power sources with a technique of multi-purpose optimization of reactive power in the power system is considered. By the problem consideration as one-target optimization within restrictions the criterion function is a linear combination from several factors. The problem decision is a unique optimum version and has lacks of alternative versions, and there is not dependency of an end result from the initial data.

Thus, the purpose of reactive power sources optimal placing in a power system consists of increase the quality of voltage in all central points of a network, control the stability of the system, reduce the power losses and capacities in networks. As a result these will increase the economic efficiency in the power system. From the economic efficiency point of view the new compensating units intended for installation should be proved and given corresponding optimum recommendations.

Considering the aforesaid as conditions of technical restriction of optimization it is possible to accept the followings:

1. Voltage support in the set limits of the technical restrictions on considered knots of loading of a power system:

U. < U. < U.

i min i i max

PF ■ < PF < PF

min max

F ( x, u) = 0

where, Uimin, Umax - is respectively, admissible minimum and maximum values of voltage on ith knot; PF- power factor; F(...) -

2. Voltage deviation should be minimum:

ÔU =

z

f u - ï

\ 2

i w inom y Ui nom J

^ min

3. Power loss reduction maximization in power system networks

AAW, = (AAP r) = (APfe,c - APfl>c)r ^ max

where, AAP, APfec, APac - respectively, the change (reduction) by loss of active power in the

maximum loading mode, losses of active power before and after compensation, r - the loss time of maximum power.

4. Maximization of annual economic efficiency

E =

( C ^

AAWa ■ p

nk j

^ max

where, ¡3 - the cost price of electric energy, for a power system; Ck -general expense of compensating devices; nk - operating time of compensating devices.

5. Compensating devices expense outlay recovery time minimization:

C - C - C T0 = C Ct Cx ^ min

0 AAWtl ■ p

where, Ct and Cx -incomes formed from increase of throughput of transformers and lines as a result of compensation:

Ct,, = K,,

S,,1 - S,,2

^ TS Ii,1 Ii,2

C, = K

Ibi

Si, i, Si, 2 - total power of transformers before and after compensation respectively; ii, 1, ii, 2 -currents proceeding through lines before and after compensation; Snom - full rated power of the transformer; ia, i - an admissible current of a line; kt and kx-costs of lines and transformers.

For voltage regulation on loading knot the necessary reactive power reserve should be provided:

=(0,1 ■ 0,15)gy

In this case capacity of the compensating device on consumer balance border belonging and power supplying organization should satisfy the below-mentioned condition:

Qk >(1,1 ■ 1,15) Qy - Qekv

where, Qekv Qy - q is equivalent reactive power which is defined on the basis of the report; ^ Qy - the sum of reactive power demanded by the consumer; q - reactive power loss in a network.

The most effective method of efficiency for multi-purpose optimization is used. According to this method efficiency of each analyzed version is defined as below:

B =Z hi ■ N ^ max

where Ni - is coefficients of purposes importance, their sum should be equal to one; lik - the standardized values of optimization criteria. For minimization purpose

Y - Y

1 _ k max ik

—

Y - Y

k max k min

For maximization purpose

Y - Y

J _ ik k min

Y - Y

k max k min

In this problem decision the acceptance of Ni creates uncertainty and consequently its use creates difficulty. In the offered algorithm coefficients Ni are accepted in the below-mentioned form:

N 1 > N2 > Nk

N1 >(N2 + N3+... Nk ) = mt 2 Ni

i=2

N! >(nJ+1 + Nj+2 +...Nk)= mi 2

- Nj jj

J J+1

In the first case Ni is given by the researcher. And in the second case the change step is defined, and coefficients Ni are accepted as the least usage N (Nk « 0,01 - 0,05) :

1 + kN,,

a =

1 + 2 + ... (k -1)

k - number of criterion functions. For this case

Nk-1 = Nk + a ; N^ = N-1 + a = Nk + 2a ; N1 = Nk + (k - 1)a.

After definition Ni condition 2 Ni = 1 is checked and updating of coefficients to accuracy 0,001 is conducted.

In the third case for definition of Ni k number linear equations systems are constituted and from their decision Ni is found. For example, k=4 the following equation turns out

N1 + N2 + N4 = 1

m1 N1 =(N2 + N3 + N4 ) 3 + N4"

m2 N2 =(N3 + N4 )

m3 N3 = N4

or

N1 + N2 + N3 + N4 = 1 m1 N1 - N2 - N3 - N4 = 0 m2 N2 - N3 - N4 = 0 m3 N3 - N4 = 0

The problem decision in the matrix form is as following:

1 111 -1 1 N1

m1 -1 -1 -1 0 N2

0 m2 - 1 - 1 X 0 = N3

0 0 m3 - 1 0 N4

If coefficients mi, m2, m3 are not given m1 = m2 = • • • = mk-1 = 1 is accepted

III. PRACTICAL RESULTS

For defining of reactive power sources optimal voltages Vi values of coefficients efficiency for problem of four criterion optimizing have been accepted as Vi =0, 526; V2 =0, 263; V3=0, 158;

V4=0, 053. Criteria report values are given at the table 1 and optimal variants have been given at the table 2.

As caan be seen from the tables 1 (0,789), 10 (0,7084) va 11-ci (0,7037) versions are much more optimal with the maximal efficiency point of view. For the optimal versions selfpeyment terms are 3,9; 3,4; 3,4 yerars.

As an example a distribution power network which has sixteen nodes has given. Before the installation of the capacitor banks in the electric network the power flow and power losses for the maximum load case has been calculated and given in the table 3 and table 4. As can be seen from the voltage graphic (Fig. 1) in the most of the nodes voltage values are lower than the permittable minimum level (85 - 89%). The total losses of the network are 4, 37%.

Table 1

Standardizing and general efficiency

Variants F1(0,526) F2(0,263) F3(0,158) F4(0,053) General effeciency

1 2 3 4 5 6

1 1 1 0 0 0,789

2 0,311 0,3162 0,6735 0,5714 0,3834

3 0,3484 0,3959 0,5102 0,1429 0,3756

4 0,7097 0,6427 0,4898 0,7143 0,6576

5 0,6503 0,5964 0,5102 0,5714 0,6098

6 0,4271 0,455 0,4898 0,1429 0,4293

7 0,3806 0,4242 0,4898 0,1429 0,3967

8 0,6968 0,6272 0,5102 0,7143 0,6499

9 0,4142 0,4396 0,5102 0,1429 0,4217

10 0,7794 0,6889 0,4898 0,7143 0,7064

11 0,7755 0,6864 0,4898 0,7143 0,7037

12 0,4103 0,437 0,5102 0,1429 0,4189

13 0,5226 0,491 0,5714 0,5714 0,5246

14 0,6748 0,6401 0,4286 0,4286 0,6137

15 0,5406 0,4961 0,5918 0,7143 0,5462

16 0,3226 0,3033 0,7347 0,7143 0,4034

17 0 0 0 1 0,211

18 0,6413 0,5938 0,5 0,5714 0,6028

Table 2

Optimal variants

№ Variants General efficiency F1 (man) F2(MVt) F3 (man) F4 (year)

1 1 0,789 1758333 9,54 9400000 3,9

2 10 0,7084 1615833 8,33 7000000 3,4

3 11 0,7037 1613333 8,32 7000000 3,4

With the application of genetic algorithm eight nodes has been chosen for the optimal placement of the static capacitor banks.

The studied network with the allocation of capacitor banks (CB) in the nodes has been shown in fig.2. The voltage deviation from the nominal value has been given in the table 5. Also according to the power losses values of the static capacitor banks for which the electric network is considered as an optimal has been given in this table. After the allocation of the static capacitor banks the improvement of voltage quality and the decrease of power losses can be observed from the table 6. As can be seen the losses are decreased from 5,28% to 3,7%.

Table 3

The results of the flow distribution

Node Voltage Generation Power Node Power Flow Curr ent cos

Name K V % An gle MW MVA r MW MV Ar Name MW MVAr A Power faktor. %

404 35 96,56 -1,2 0 0 6,178 2,682 405 403 -11,34 5,169 -5,818 3,136 217,8 103,3 89 85,5

405 35 98,67 -0,6 0 0 2,434 1,46 Dubendi 404 -13,964 11,53 -7,53 6,07 265,2 217,8 88,0 88,5

Buzovna 35 85,46 -5,2 0 0 0,454 0,272 TS3 405 -0,454 14,071 -0,272 7,779 10,2 265,2 85,8 87,5

Dubendi 35 100,0 0,0 49,74 32,11 0 0 N432 TS1 8,511 27,154 5,385 18,941 166,1 546,1 84,5 82,0

N406 35 89,79 -3,8 0 0 4,031 2,419 TurkenII N408 3,298 -16,894 2,007 -10,456 70,9 365 85,4 85

N407 35 85,69 -5,2 0 0 2,754 1,653 TS2 TS3 -3,665 0,911 -2,200 0,547 82.3 20.4 85,7 85,7

N408 35 91,75 -3,0 0 0 2,104 1,263 TS1 N406 -19,222 17,118 -12,178 10,915 409,1 365,0 84,5 84,3

N432 35 97,71 -0,5 0 0 8,365 5,184 Dubendi -8,365 -5,184 166,1 85,0

N403 35 95,44 -1,5 0 0 5,124 3,074 404 -5,124 -3,074 103,3 85,8

TS1 35 95,59 -1,6 0 0 0 0 Dubendi Zire N408 -26,439 6,744 19,694 -17,395 4,197 13,197 546,1 137,1 409,1 83,5 84,9 83,1

TS2 35 87,13 -4,9 0 0 0 0 N406 N407 TurkenI -9,396 3,717 5,679 -5,667 2,252 3,415 207,7 82,3 125,4 85.6 85,5 85.7

TS3 35 85,57 -5,2 0 0 0 0 Buzovna N407 0,455 -0,910 0,273 -0,546 10,2 20,4 85,7 85,7

Seysm/st 35 85,51 -5,2 0 0 0,455 0,273 Seysm/st TS3 0,455 -0,455 0,273 -0,273 10,2 10,2 85.7 85.8

TurkenI 35 86,94 -5,0 0 0 5,670 3,402 TS2 -5,670 -3,402 125,4 85,8

TurkenlI Zire 35 35 89,13 95,04 -3,9 -1,7 0 0 0 0 3,278 6,716 1,987 4,162 N406 TS1 -3,278 -6,716 -1,987 -4,162 70,9 137,1 85,5 85

■Ulf OCP

HH|p

Fig. 1. The voltage profile in the nodes

Table 4

The losses in the branches

Line Flow -To Flow- From Losses Node Voltage , % Voltage drop %

Name МW МVАr МW МVАr kw KVAr To From

Line 5 -11,347 -5,818 11,530 6,070 183,3 252,1 96,6 98,7 2,11

Line 6 5,169 3,136 -5,124 -3,074 44,8 61,6 96,6 95,4 1,12

Line 2 -13,964 -7,530 14,071 7,779 106,7 248,5 98,7 100,0 1,32

Line51 -0,454 -0,272 0,455 0,273 0,5 0,5 85,5 85,6 0,12

Line 8 8,511 5,358 -8,365 -5,184 146,1 200,8 100,0 97,7 2,29

Line18 27,154 18,941 -26,439 -17,395 715,8 1546,2 100,0 95,6 4,41

Line41 9,565 6,030 -9,396 -5,667 168,3 363,5 89,8 87,1 2,65

Line44 3,298 2,007 -3,278 -1,897 20,3 20,5 89,8 89,1 0,65

Line58 -16,894 -10,456 17,118 10,915 223,8 458,8 89,8 91,8 1,96

Line47 -3,665 -2,200 3,717 2,252 52,2 52,6 85,7 87,1 1,44

Line52 0,911 0,547 -0,910 -0,546 1,1 1,1 85,7 85,6 0,12

Line56 19,222 -12,178 19,694 13,197 472,0 1019,5 91,8 95,6 3,84

Line19 6,744 4,197 -6,716 -4,162 27,9 35,1 95,6 95,0 0,54

Line48 5,679 3,415 -5,670 -3,402 9,3 12,7 87,1 86,9 0,19

Line54 0,455 0,273 -0,455 -0,273 0,3 0,3 85,6 85,5 0,06

Total 2172,4 4273,9

Table 5

The results of the optimal placement of capacitors

Information on the ca pacitors Cost, ($)

Node-Candidat Voltage Power Factor % Nom. KBAp/ bank Rat e, kV Num ber of bank s Total KVAr Install ation costs Pursach e, thousand Servi ce/ye

Name kV % Angle ar

404 35 96,998 -1,39 91,7

405 35 98,850 -0,65 85,8

Buzovna 35 92,124 -7,96 -70,4 1000 37 1 1000 1000 30 300

Dubendi 35 100,00 0,00 100,0 1000 37 1 1000 1000 30 300

N406 35 93,780 -5,35 85,8

N407 35 92,057 -7,71 85,8

N408 35 94,763 -4,21 85,8

N432 35 97,712 -0,53 85,0

N403 35 96,169 -1,80 97,1 1000 37 2 2000 1000 60 600

TS1 35 96,934 -2,11 100,0

TS2 35 93,028 -7,11 100,0 1000 37 4 4000 1000 120 1200

TS3 35 92,123 -7,86 100,0

Seysm/st 35 92,188 -7,95 -35,7 1000 37 2 2000 1000 60 900

TurkenI 35 92,885 -7,19 98,1 1000 37 3 3000 1000 90 900

TurkenlI 35 93,406 -5,64 -99,3 1000 37 3 3000 1000 90

Zire 35 96,385 -2,25 85,0

Total 16 16000 7000 480 4200

Table 6

Summary results of losses in the nodes (at maximum load)

Node Flow-To Flow-From Losses Node Voltage,% Voltage drop %

Name MW MVAr MW MVAr kW KVAr From To

Line 5 -11,471 -4,026 11,636 4,253 165,2 227,1 97,0 98,8 1,85

Line 6 5,238 1,320 -5,202 -1,272 35,4 48,7 97,0 96,2 0,83

Line 2 -14,079 -5,719 14,176 5,946 97,5 227,2 98,8 100,0 1,15

Line51 -0,528 0,532 0,529 -0,531 0,9 0,9 92,1 92,1 0,00

Line 8 8,511 5,385 -8,365 -5,184 146,1 200,8 100,0 97,7 2,29

Line18 29,294 8,636 -28,685 -7,320 609,1 1315,7 100,0 96,9 3,07

Line41 10,912 -1,794 -10,764 2,113 147,6 318,7 93,8 93,0 0,75

Line 44 3,616 -0,419 -3,599 0,436 16,6 16,7 93,8 93,4 0,37

Line 58 -18,925 -0,425 19,111 0,807 186,3 381,8 93,8 94,8 0,98

Line 47 -4,241 0,001 4,285 0,044 44,5 44,9 92,1 93,0 0,97

Line 52 1,063 -1,908 -1,059 1,912 3,9 4,0 92,1 92,1 0,07

Line 56 -21,356 -2,154 21,750 3,004 393,7 850,4 94,8 96,9 2,17

Line 19 6,935 4,316 -6,907 -4,280 28,7 36,1 96,9 96,4 0,55

Line 48 6,479 1,305 -6,471 -1,294 8,1 11,1 93,0 92,9 0,14

Line 54 0,530 -1,381 -0,528 1,383 1,8 1,8 92,1 92,2 0,07

Total 1885,4 3686,1

Power system 1500 MVA

Dubendi

35 kV —

N432 35 kV

18569 j5404

PL 60

PL 18

H2

TS.1

35 kv t

41115 j25964

+ 18475 j12782

405 35 kV

114071 j7779

PL 2

8.246 MVA @TS-2

I 8464 ^¡5245

PL 19

6946 j4323

PL 56 N408 35 kV T

X11200 j7747

404 35 kV

2434

|11530 If j1460

j6070 Vh1

0

j985

MW 3000

Zire 35 k

PL 58

If 8802 1+2247 ¡6072 Vj1348 H12

2.332 MVA

I

2.332 MVA

6917 ff j4267

H4 V

Turkan 2 "35 kv

6.997 MVA N406

35 kV

T

CB 30 0,9 MVar

Cabel 4

3000 |fj991

PL 6 N403 35 kV

If 5169 L j3136

6178 j2682

+614 j 1200 PL 44

I

3731 j2115

PL 41

f 3612 H7 ^j2189

3.859 MVA

X 4398 j2639

+5124 H3^3074 5.248 MVA

H5

5.778 MVA

WPS-1 4 MW

H6

4.665 MVA

Cabel 3

WPS-3 3 MW

«

3000

j0

±3451 j2900

PL 48 ' ' Turkan1 Cabel 2 If3000 If 6447

_|CB33 -JT.2 MVar

f0

=^j967

CB 29 0,9 MVar

h

j973 j3868

H8

I

V

6.997 MVA

PL 52

TS.3 35 kv

Seysmo/st 35 kv

PL 54

Buzovna 35 kv

525 -j739

I

H11 I*524 pc

H11Vj315 __j

P

j 1054

^j5

580KVA

^KB32 1 MVar

^524 j315

H10 580KVA

X 526 -j738

PL 51

0

j 1055

CB 31 1 MVar

N407

1054 4 -j 1475

35 kV

PL 47

3159T j1896

V H9 3.499 MVA

Fig. 2. The circuit of the network with the static capacitor banks

CONCLUSIONS

1. Methods and multi-purpose optimization compensations algorithms have been developed with support of a necessary reserve for preservation of normal level of voltage taking into account technical restrictions in knots of an electric network of a power system. Results of computerization to realization have shown speed and high efficiency the developed algorithm providing minimization of losses of active capacity in a net.

2. Based on genetic algorithm the power and installation locations of the static capacitor banks with the multicriteria optimization technique has given. In this case, as a criterion of optimality the minimum expenses for the installation and exploitation, the minimization of power losses during the required values of voltage and power factor and maximum saving and the minimum self-payment term are accepted.

3. The report of the real electricity network is given for two cases: operation without the CB; with optimal placement of CB. The application of the proposed method can reduce the average power losses approximately 13-14% in the electric network.

REFERENCES

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