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Л1НЕАР1ЗАЦ1Я МОДЕЛ1 КОМПЕНСАЦП РЕАКТИВНО! ПОТУЖНОСТ1 В ЕЛЕКТРИЧНИХ МЕРЕЖАХ
Лежнюк П.Д.
Втнщький нацюнальний техтчний ynieepcumem, д.т.н., проф., зав. кафедрою ЕСС, м. Втниця, Украта
Детое О.Д.
Втнщький нацюнальний теxнiчний ymiверситет, к.т.н., доц., доцент каф. ЕСЕЕМ, м. Вiнниця, Украта
Шенюк Ю.Ю.
Вiнницький нацюнальний теxнiчний yнiверситет, асистент кафедри ЕСС, м. Втниця, Украта
LINEARIZATION OF MODEL OF REACTIVE POWER COMPENSATION IN ELECTRIC NETWORKS
Lezhníuk P.D.
Vinnytsia National Technical University, Dr. Sc. (Eng.), Professor, Head of Department of Electric Power Stations and Systems, Vinnitsia, Ukraine
Demov O.D.
Vinnytsia National Technical University, PhD, Assistant Professor, Department of Electric Engineering Systems of Electro-Consumption and Power
management, Vinnitsia, Ukraine Pívníuk Yu.Yu.
Vinnytsia National Technical University, Assistant, Department of Electric Power Stations and Systems, Vinnitsia, Ukraine
АНОТАЦ1Я
n0Ka3aH0, що вщносш raa^ ranpyra e лшшними iнтегpaльними покaзникaми i дозволяють одночa-сно оцiнювaти втpaти a^^roi' потужносп в елекфичнш меpежi i raa^ Hanpyra Ha ïï дiлянкax. Ha основi цього зaпpопоновaно лшшну модель pозpaxyнкy компенсaцiï pеaктивноï потужносп в електpичниx меpе-жax i yпpaвлiння компенсуючими yстaновкaми, як дозволяють зaбезпечити мaксимaльне зниження втpaт i допyстимi piвнi нaпpyги в циx меpежax. Викоpистaння вiдносниx спaдiв нaпpyги дозволяе лiнеapизyвaти пpоцес оптимiзaцiï потокiв pеaктивноï потужносп в електpичниx меpежax, що, поpiвнюючи з вiдомими методaми, спpощye pозв'зaння вкaзaниx моделей.
ABSTRACT
Relative voltage drops are linear integral indicators and allow simultaneously evaluate both active power losses in electric network and voltage drops in its areas. On the basis of this linear mathematical model of calculation reactive power compensation in electric networks and control of compensating devices were proposed. These mathematical models allow provide maximum reduction of active power losses and allowable levels of voltage in these electric networks. Use of relative voltage drops allow to linearize the process of optimization with overflows of reactive power in electric networks.
Ключовi слова: лтеар1зацш моделi, електричт мережц eidHOCHi спади напруги, компенсуючiустановки.
Keywords: linearization of model, reactive power compensation, electric networks, relative voltage drops, compensating devices.
INTRODUCTION
Introduction of compensating devices (CD) and their control is one of the most effective ways to reduce losses of electricity in electric networks (EN). In accordance with existing methods [1-4] this task is carried out with two ways: maximum reduction of losses and providing allowable levels of voltage in load nodes EN. Complicated mathematical methods, nonlinear programming methods in particular and appropriate laws control of power of CD, are necessary to solve this problem [2].
Results of calculations, obtained by these methods, are difficult to be checked on compliance with both criteria, since they characterize different technical parameters. On the other hand in [5, 6] is shown that these criteria are caused by overflows of reactive power, have common physical nature which makes it possible to form the integral linear indicators evaluating both active power losses and levels of voltage in EN.
As a result of the above, the aim of this paper is to research integral linear indicators mode of operation EN by reactive power, which evaluate both active power losses and levels of voltage and their usage for reactive power compensation (RPC).
RESEARCH RESULTS Carry out appropriate research for area of EN (Fig. 1).
AUr
Active component of voltage drop can be written
P+jQ
Fig. 1. Equivalent scheme of area of electric network: S - power system; AUr - active component of voltage drop; R,X - active and inductive resistances; P, Q -active and reactive loads of network.
Active power losses during the transmission of reactive power Q are defined as
AP0 = AUR •0,
Q R U
(1)
where U is the voltage in load node. Find value AUr. Voltage drop in area of electrical network (Fig. 1)
AÙ = IR + jlX = AUr + jAUx, (2)
where I - full current load; AUx - reactive component of voltage drop.
as
AUR=IaR + jIrR = AUaR+jAUrR, (3)
where Ia , Ir - active and reactive component of full current load I; AUaR , AUr - active voltage drops caused by flow in accordance by active and reactive currents, on the resistance R.
In Fig.2 shown vectorial diagrams of voltages which allow to find voltage drops AUrR.
IZ
ll
IX
IrR=QR/U
IR
l=arctg X/R a)
IaR=PR/U 9=arctg Q/P
b)
Fig. 2 Vectorial diagrams voltage drop on full (Z) (a) and active (R) (b) resistances of area of electrical network
Voltage drops AUrR are defined as
AUrR = I • Z • sin cos ^ . (4)
Consider economic content of value AUrR. For this find active power losses AP, which is created by a reactive load Q
AP = AUrR •
rR U
or
AP = I • Z • sin ф- cos ф
0 u'
(5)
If consider that AU = AU is a relative voltage * U
drop, then (5) written as
AP = d • AU* • Q, (6)
where d = sin COS ^.
From formula (6) is seen that AU* =
AP d • Q
, i.e.
value AU. allows to evaluate not only voltage drop,
but the specific active power losses during the transmission Q.
It allows to use the value AU* in calculations
RPC in EN. During the calculation sequence of installation CD at the first place it is necessary to install them
in nodes with maximum value AU .
Consider optimization introduction of CD in EN by their step-by-step installation. We consider, that installation of CD is possible only on the side of low voltage transformer substation 10/0,4 kV.
We divide the process of optimization by g stages. Maximum reduction of losses on i stage installation of CD in EN is determined as trying out of all possible places (positioning) for installation of CD
au:
max
g maxiAU* ), i = 1, g (7)
J=1 J
where g - amount of stages installation of CD; n -amount of load nodes where installing CD.
During the positioning is carried out the checking implementation of next limitations:
1) impossibility of the reverse overflows by the reactive power
g
S Qkij < Qj (8) i=1
where Qkij - power of CD installed in j node on i stage calculating; QCj - calculated reactive load in j node.
2) the nodes with inadmissible values of voltage are excluded
U - Umax,
(9)
where Umax - maximum allowable value of voltage in j load node.
The expanded mathematical model of positioning of place for installing CD on i stage calculating (7) is
n
AUmax = *i
AU»j ,if AU»j > AU»2 ,AU»3 ,...., AU»n; AU»j - AU^ AU»2 ,if AU»i <AU»2 >AU»3 ,AU»4 ,...., AU»n; AU»2 <AU^ AU»3 ,if AUn ,AU»2 < AU»3 > AU»4 ,AU»5 ,...., AU»n; AU»3 - AUa;
, (10)
AU*n ,if AU*n_n ,...., AU*n_2 ,AU*n_1 < AU*n >AU*n+1 ,AU
*n+2
AU*n+„; AU*<AUa;
where AUa - allowable value of relative voltage voltage drops are AUa = 10% . On every stage cal-
drops in area of EN.
At all stages of positioning of place installing for CD is performed similarly. The amount of stages is defined as
n
!Qc
g=
j=1
Qkij
(ii)
This principle of RPC can be used during the control of input of the reactive power by the industrial enterprise. For automatic providing preset of the reactive power of the enterprise it is suggested to switch on the section of CD in j node EN of enterprise and it is offered to make according to the mathematical model (10). Such control of powers of CD provide maximum reduction of active power losses in this electrical network and allowable levels of voltage in its nodes [7].
eXAMPLE of CALCULATION
Carry out calculation step-by-step installation of CD in EN (Fig.3) and provide compensation 50% of reactive load EN. Solve the problem by two methods: existing [4] and proposed. Allowable values of relative
culating power of CD which installed is 100 kvar.
Solution. In accordance to parameters scheme of electrical distribution network (EDN) (Fig.3) the estimated parameters for the scheme substitution of EDN are defined (Fig.4).
Voltage losses on branches EN AU0j are defined in accordance with the existing method [3] as
_P- R0J+ Qj- X0j U '
AU0=-
(12)
where U0 - voltage starting point of branch. Voltages in load nodes of EDN are defined as
U
:U0 _AU0j.
(13)
Relative voltage drops in accordance with (4) are defined as
AU
..........(14)
AU = ^rR°J
AU*rRj
Reduction of active power losses in EDN after the installing of CD (power Qk) in j node on i stage of the calculating in accordance with the existing method are defined as
■»before * Tiafter
ô(AP^ = APbefore - AP = ■
U2
(15)
ATjbefore *T>after , accordance before a
where AP- , AP- - active power losses , , ..
ij ij calculating procces.
from overflows of reactive power to j node in EDN in
accordance before and after installing of CD on i stage
Buses 10 kV
S
1000/10 1
AAB 3x150
L=500m
AAB 3x150 ►-
HI
L=600m
AAB 3x150 ►-
630/10 2
HI
L=400m
AAB 3x150 ►-M
1000/10 3
HI
1000/10 4
L=300m
HI
- 1600+j800 kVA
■ 1700+j780 kVA
-1500+j750 kVA
•1200+j600 kVA
Fig. 3 Scheme of electrical distribution network
S
Uo =10,5 kV
Buses 10 kV
0,104 Ohm
0,039 Ohm 0,047 Ohm 5 0,032 Ohm 1 0,024 Ohm
11,22 Ohm
5,35 Ohm
±
0,125 Ohm
±
0,083 Ohm
I
0,062 Ohm
2,12 Ohm
8,5 Ohm
T
1,22 Ohm
5,35 Ohm
T
1,22 Ohm
5,35 Ohm
r^T^T^T«
1600+j800 kVA 1700+j780 kVA 1500+j750 kVA 1200+j600 kVA
Fig. 4 Scheme of substitution of electrical distribution network
On first stage of calculating in accordance with
At every next stage similarly calculate maximum
(12), (13) have received next values AU*j: values relative voltage drops AUmax and places for in-
AU*i=0,0583; AU*2=0,0951; AU.s=0,0543;
AU4=0 0432 stalling of CD. Results of calculations 1-3 stages are
, max shown in table 1. Results of calculations at all stages
In accordance with (9) determine AUm . On are shown on graphs (Fig. 5-7).
first stage of calculating: AU^ = AU = 0,0951. So CD will be installed in second node.
Table 1
Results of calculations
\ № \ node № \ stage \ 1 2 3 4 Place for installing CD 100 kvar (node)
U1/AU.1/ AUW 5(AP)1 U2/AU.2/ AUW 5(AP)2 U3/AU.3/ AUW 5(AP)b U4/AU.4/ AUW S(AP)4 max 5(AP) max AU*
1 9,8877 9,5016 9,9294 10,0464 2 2
0,0583 0,0951 0,0543 0,0432
0,0066 0,0111 0,0061 0,0047
2,0314 3,6306 1,8502 1,3972
2 9,8877 9,583 9,9294 10,0464 2 2
0,0583 0,0873 0,0543 0,0432
0,0066 0,009 0,0061 0,0047
2,0314 3,08 1,8502 1,3972
3 9,8877 9,6644 9,9294 10,0464 2 2
0,0583 0,0796 0,0543 0,0432
0,0066 0,0071 0,0061 0,0047
2,0314 2,5478 1,8502 1,3972
In result we receive that CD is expedient to install successively in such nodes: 2 - 2- 2 - 2- 1 - 3 - 1 - 3 - 2 - 1
- 4 - 3 - 1 - 4 - 2.
Fig. 5 Graph offunction reduction of active power losses S(AP) in EDNfrom total power of CD Ok
2 3 4
Numbers of nodes
Fig. 6 Graph of changes in values of voltages in nodes EDN before and after installing CD
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Total power of CD Qk, kvar
Fig. 7 Graph offunction reduction of relative voltage drops AU*rR in EDNfrom total power of CD Qk
Calculation results:
- sequences of installing CD which were defined by the existing and proposed methods are identical;
- proposed method provides allowable values of
relative voltage drop AUa.
CONCLUSIONS
1. It is shown that it is possible using relative voltage drops as integral indicators which allow simultaneously evaluate both active power losses during transmission reactive power and levels of voltage in load nodes EN.
2. Linear mathematical models for optimization introduction of CD and their control were developed and which allow simplify the processes of calculations of reactive power compensation and its control.
References
1. Karpov F.F. Reactive power compensation in distribution networks (Moscow: Energy, 1975), 184 p.
2. Melnikov N.A. Electric networks and systems (M.: Energy, 1969), 456 p.
3. Idelchik V. I. Electric systems and networks (M.: Energoatom Publishing house, 1989), 592 p.
4. Kovalev I. N. Selection of compensating devices in the design of electric networks (M.: Energoatom Publishing house, 1990), 200 p.
5. Zhelezko Yu. S. Loss of electricity. Reactive power. Power quality: A guide for practical calculations (M.: ENAS, 2009), 456 p.
6. Pirniak V. M., Lezhniuk P. D., Demov O. D., Pivniuk Yu. Yu. Economic equivalents of reactive power as relative voltage drops, Energy and electrification, 2013, №8(360), pp. 17-20.
7. Lezhniuk P. D., Demov O. D, Pivniuk Yu. Yu. Automatic regulator of capacitors, Patent for utility model № 98570, Ukraine, G05F 1/70, Publ. 27.04.2015, Bul. № 8.
ОСОБЕННОСТИ РЕАЛИЗАЦИИ ОДНОМЕРНОГО КЛЕТОЧНОГО АВТОМАТА В ПЛИС INTEL CYCLONE V
Пляскин С.А.
Аспирант кафедры ЭВМ Вятский государственный университет, Киров, Россия
FEATURES IN IMPLEMENTATION OF ELEMENTARY CELLULAR AUTOMATON IN INTEL FPGA CYCLONE V
Plyaskin S.A.
post-graduate student of the Department of Computer Science Vyatka State University, Kirov, Russia
АННОТАЦИЯ
Рассмотрен результат синтеза кода клетки элементарного клеточного автомата на языке описания аппаратуры Verilog в САПР Intel Quartus Prime 17.1 Lite Edition для ПЛИС Altera Cyclone V. Выявлен недостаток автоматического размещения примитивов ПЛИС при синтезе элементарного клеточного автомата.
