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Taslimov Abdurahim Dehkanovich, candidate of technical sciences, associate professor, Head of the Electric Supply Department of the Energy Faculty of the Tashkent State Technical University (Uzbekistan))
Melikuzeyev Mikromil Vohijon ugli, assistant of the Electric Supply Department of the Energy Faculty of the Tashkent State Technical University (Uzbekistan)
Rakhimov Farrux Movliddinovich, assistant of the Electrical power engineering Department of the Electromechanical Faculty of the Navoi State Mining Institute E- mail: ilider1987@yandex.ru
METHODOLOGY IN MULTICRITERIA PROBLEMS OPTIMIZATION AND UNIFICATION OF PARAMETERS OF POWER SUPPLY SYSTEMS
Abstract: The article deals with the General provisions of the method of formation, mathematical models used in multi-criteria optimization and unification of the parameters of power supply systems. The developed algorithm of multi-criteria harmonization of cross-sections of the lines method for vector optimization of additional criteria of energy losses and consumption of conductive metal and the particular value of an optimized (unificarea) parameters. Keywords: multicriteria analysis, simultaneity coefficient, unification, normalization, optimization.
The literature on the optimization and unification of large graphical conditions, etc. In one form or another, the technical
and economic model also takes into account the influence of the time factor (changes in economic and technical indicators, one-time or dispersion of investments, increase in loads, etc.).
Another part of the influencing factors and conditions, which can not be expressed in the monetary form of costs, but can be represented by certain technical characteristics, is introduced into the optimization process in the form of technical restrictions and, further, functionally associated with the optimized parameters of SES (for example, the electric field strength near substations, voltage losses, etc.). These constraints are included in the optimization mathematical model.
The application of certain methods of mathematical optimization and unification and the preparation of the SES model revealed:
a) extreme value of technical and economic model and the corresponding theoretical-optimum values of parameters of SES;
b) the area of technical and economic stability of the model and the equally optimal values of the considered parameters of the SES (within this area);
c) the sensitivity of the technical and economic function to changes in the initial information, as well as to the difference in the values of the parameters of The SES optimal;
g) if required by the terms of the task, it sets the optimal proportion of the above costs for individual subsystems, assemblies and sections of lines SES, etc.
energy systems describes possible methods for solving multi-criteria problems and the complexity of obtaining quite specific and reliable recommendations based only on the cognitive application of the necessary criteria or their use with "weight" coefficients, etc. [1].
In connection with these difficulties, the following briefly describes the proposed and used in subsequent works method of making recommendations for the optimal construction of power supply systems (SES). At the same time, the process of developing optimization solutions and recommendations consists of two stages:
1) the stage of formalized determination of the area of optimal solutions with possible full consideration of all influencing factors and conditions;
2) development of decisions and recommendations based on the results of a formalized decision and taking into account the effects of conditions and criteria that are not compatible with the forms of their fixation.
The basis of decisions at the first stage is the technical and economic model of SES (or its reasonably allocated part) in the form of costs. At the same time, all investments and costs of operation of SES facilities are determined taking into account their dependence on specific social and industrial conditions, construction and operation of electrical installations in the city, compliance with the requirements of environmental protection and human health, requirements of urban planning and urban architecture, the influence of climatic and geo-
METHODOLOGY IN MULTICRITERIA PROBLEMS OPTIMIZATION AND UNIFICATION OF PARAMETERS OF POWER SUPPLY SYSTEMS
Further, the analysis and synthesis of the complexes of the obtained results are carried out, which in most cases allow to formulate recommendations for planning the optimal development of the structure and parameters of SES, taking into account the influence of a significant (or decisive) part of all the above criteria.
It is obvious that in some cases, first of all, in specific conditions, the previous study does not give unambiguous answers to all the main parameters of electricity supply. However, the main task of planning the optimal development of SES will certainly be fulfilled: the areas of optimal values and the necessary laws of development of structures and parameters of these systems will be determined.
In cases where the influence of not all criteria can be taken into account in the form of technical limitations or characteristics of the main model of SES, the second stage of the study should be used. The latter consists in the secondary evaluation and selection of the solutions obtained by the formalized method on the basis of the system and hierarchical subordination of the criteria:
- socio-economic;
- environmental and human health protection;
- urban planning and urban engineering;
- technical and economic indicators;
- quality of implementation and functioning;
- geographical and climatic conditions.
Consistent application of these criteria is based on the
method of expert assessments and taking into account the specific objectives of the study or planning.
The significant stability of the technical and economic cost function (the main criterion) to the optimization parameters (for example, the cross-section of lines, the power of transformers, the number of applied cross-sections of lines, etc.) does not allow you to clearly select these parameters. In this case, it is necessary to take into account additional criteria for a certain choice of parameters. This means that when solving the optimization problem under consideration, it is necessary to perform taking into account additional criteria.
Vector optimization method can be used to solve the problem [1].
The developed algorithm of multi-criteria harmonization of cross-sections of the lines when using the method ofvector optimization for additional criteria of the energy loss DE(NF) and consumption of conductive metal G(NF).
The application of the vector optimization method to the selection of the number of applied line sections according to additional criteria of power loss and consumption of conductive metal is based on mathematical models of these criteria.
If the optimized parameter to consider the number of used cross-sections of the lines, the mathematical model of the ad-
ditional criteria of the energy loss DE(NF, N) and consumption of conductive metal G (NF, NB) for the PC has the form [2]:
AЭ(NPH ) = AÏNl'H G(NPH ) = Af + A?NF]H
T T1 jH _ \ 0H <j-0,46 02,46 i.f-1,21 T-.-1
Where: A7 - \ny)MHop)F2,hOp)
\H _ GH c-0,19 s 0,19 M 1>06 F A8 _ G(1)° STn(y)MH(ozp)F2,HOp) ,H _ GH °-1,38s1,38 MM-0.13 F A9 _ G(2)° STn(y)MHOp)F2,HOp)
Here: A3H^), GH(1), G^ - generalized constant coefficients, which are the initial data for this problem.
M F2H - accordingly, the number of lines departing from the TA and the cross section of the head section of the lines obtained subject to restrictions.
The main objective of the method is to optimize the additive scalar efficiency vector:
Y(Nf) = \A3(Nf) + \g(nf)
Where X, X2- accordingly, the coefficients of importance of the criteria of power loss and consumption of conductive metal.
When solving multi-criteria optimization problems, it is necessary to bring the criteria under consideration to a single measurement scale (normalization).
We define the normalized criteria ofpower losses A3'(Nf h) and the consumption of conductive metal G*(N H) for PC:
A3\Np h ) =
A3(Nfh ) - min A3(Nfh ) max A3(Nf h ) - min A3(NF H )
' F,H
N 03 -
F ,H (max)
:N°3 =
F ,H (max)
The following are accepted:
min ДЭ(Nf ,h ) = A7h при Nf ,h = 1
max A3>(Nfh ) = A7HN0,,3H(max) при Nf,h = NF,H(max)
The normalized flow criterion for conductor metal is:
G\Nfh ) =
N — N -1
F ,H F ,H (max)
1 — N
1 F ,H (max)
The maximum number of line sections (NF (max)) that can be applied to Rs is determined by the number of parcels in each line. In turn, the number of parcels is determined by the number of connections to the lines and is:
nc =
Sb
ksm (у )мс
Where KQ is the coefficient of simultaneous loading of
transformers for the network lines.
The choice of the optimality principle on the additive scalar vector of efficiency can be identify with the choice of the criterion of the best approximation of normalized values of criteria AЭ'(NF) and G'(Nf). The optimal solution is chosen according to the model [1]:
otherwise < X2}-2 ^ 4 sections of lines. At equal importance of criteria (A1 = X2), execution of RS is expedient with application of one or two standard sections, and RS - with application of two sections of lines in all range of density of electric load (5 mw/km2 and more).
The preferred importance of the energy saving factor is the principle, rather than the economy of conductor metal consumption. So one of the main provisions of the strategies of action for the further development of the Republic of Uzbekistan for 2017-2021 years is the implementation of active energy-saving policies in all directions, in particular reduction of electricity losses. In addition to the development of the national economy, the problem of saving natural energy resources will remain quite relevant.
Thus, it may be considered expedient (justified) to solve the problem at the preference of the criterion of loss of electricity (A1 > X2) or, in the extreme case, its solution at X1 = X2. The solution when X1 > X2 corresponds to the application of one section of cable living in Rs. It is recommended to use the section 150 mm2 in considered RS.
References:
1. Borisov R. I. Problems of vector optimization.- In the book.: Operation research.- M.: Science, 1972.
2. Taslimov A. D. a Comprehensive techno-economic model for the unification of sections of cables of electric networks. Journal "Mountain Bulletin of Uzbekistan",- No. 53. - Navoi, 2013.
N0 = F-1
min
N
y\nf )
= F-
min
N
(A, A3 (Nf ) + A G\Nf ))
where F-1 is the reverse conversion of j * to NF.
In this task, the most uncertain and, at the same time, essential is the choice of ratios of coefficients X1 and X2. Therefore, fundamentally calculations should be carried out for three possible ratios of coefficients: X1 > X2 - the loss of electricity is more important than the flow of conductor metal; X1 = X2 - they are of equal importance; X1 < X2 - The flow of conductor metal is more important than Loss of electricity.
Optimum values of number of applied sections of RS lines are obtained depending on the density of electric load for loopback and for two-beam circuits of networks. Thus the consideration of different degrees of importance of the considered criteria adverse a significant influence on the choice of the optimal number of applied sections of the RS lines. So at X1 > X2 Optimal is the application of only one section of lines,
