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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
Rakhimov Farrux Movliddinovich, Assistant of the Electrical power engineering Department of the Electromechanical Faculty of the Navoi State Mining Institute Mikromil Vohijon ugli Melikuzeyev, Assistant of the Electric Supply Department of the Energy Faculty of the Tashkent State Technical University, Uzbekistan E-mail: ilider1987@yandex.ru
OPTIMIZATION (UNIFICATION) OF PARAMETERS OF ELECTRICAL SUPPLY SYSTEMS UNDER THE CONDITIONS OF UNCERTAINTY OF LOAD DEVELOPMENT
Abstract. The problem of optimization (unification) of the parameters of power supply systems under conditions of uncertainty in the development of electric load is considered. The choice of the optimal number of cross sections is taken into account, taking into account the development of the load, and proves the expediency of using a very limited number of cross-sections in the power supply system (using one or two standard cross sections for a wide range load density).
Keywords: unification, optimization, cross-sections, factor, analysis, accounting, load growth.
When planning and forecasting the optimal development of power supply systems (PSS), it is necessary to take into account the technical and economic possibilities of broad optimization and unification of parameters (in particular, nominal cross-sections of the lines and power of transformers) with the development of electrical loads in fairly wide limits.
At the same time, based on the mathematical models of the PSS, the optimal parameters of the system are identified, corresponding to the series of changes in the initial information, and the optimal construction of the PSS for a number of parameters is revealed, which on a certain scale reflects the development of this system in time. The obtained sets ofoptimal parameters determine the rational construction of the system and the strategy for the development of structure and parameters [1].
It should be noted that the problem of optimization (unification) of PSS parameters is solved taking into account the uncertainty of the complex of factors characterizing the development of the load in the period under consideration. Such factors are: the laws of load growth in time; factors of annual load growth, year of achievement of the design load from the moment of commissioning, the period of time under consideration, for example, the estimated period of operation of the projected network before its reconstruction.
In addition, in the problems of optimization and unification of parameters, taking into account the development of
PSS, significant and at the same time uncertain are the development of the load in time. It is advisable to take into account the possibilities of various laws, namely, the growth of the load according to the laws of uniform and uneven load growth.
The use of the law ofuniform load growth allows one to conduct research for the conditions of a constant annual increase in the load. In this case, the function Y(i) is by following expression
*(t ) = fit-1 (1) The law of uneven load growth allows one to conduct research in conditions of decreasing the annual increase in the load. This law of load growth is close to the real operating conditions, when the load in the line reaches a certain limit (the design level) and remains subsequently constant due to its redistribution. This model of load growth corresponds to the modern principle of integrated urban development. In this case, the function x¥(t) can be determined from the expression:
v(t ) = i + (-1 -i)(-y,
k t„
(2)
where K = —— the load share of the first year of operation
1tp
(I1) from the load of the last year of the period under consideration
tp - is the considered period of time, v is the factor of the annual non-uniform growth of the load, v > 0.
Section 9. Technical sciences
In the technical and economic analysis, taking into account the change in the load in time, the initial load and design ratio(lnp), the year of achievement of the design load (tnp), etc. are significant.
The account of these characteristics allows to carry out the research also under conditions close to the actual ones, when in the first year of operation only a certain part of the designed design electric load of the distribution grids is observed. In this case, the load grows with an undetermined load growth factor (depending on the year of achievement of the design load) to the achievement of the design level, and then one or another of its further growth is observed until the end of the period under consideration.
In this study, the energy losses are determined by the currents (loads) of the head sections of the lines, which also vary with time. In view of the above, the problem of optimization or unification of parameters (number of sections) of SES distribution networks, taking into account the development of the load, can be solved by the following technical and economic model:
3 =SU +S2i+83NZ +8<Mt )N0;3 (3) The function f(t) is a resultant undefined factor, for which only the maximum values can be set:
0 .(t) < 0(t) < 0 (t)
mmy ' x ' maxx '
where
r , ^ ^mmCt) , V^mJ'p mm)
(O . (t) = K
t min \ ' ,
np
"1(1 + Kn ) (1 + EH .n.)
tp min
^2min(t )
¥2 (tp )
I max v p max '
(4)
(5)
^max(t) Knp —H n. ^ ■ max
t=1 (1 + EH .nJ (1 + EH .n.)
These boundary values of the function ^(t) are determined by the maximum and minimum values of the quantities v, fi and tp. The increment value is determined by the period tnp, at which the design load is reached. Usually in the design calculations of distribution electrical networks, the value of tp is assumed to be 5-7 years. However, as practice shows the operation of large urban distribution networks, often the design load is achieved much later, for example, after 10 years or more. Therefore, in our case, the deadline for achieving the project load of 2 and 10 years is adopted. In accordance with these, the values of load growth factors fi1 and v1 are chosen.
The growth rates of loads of distribution electric networks are in a very wide range from 0.5 to 6% per year. In our studies, the following limit values of the factor fi2 are considered for the period tn, under the law of uniform load growth: fi2(min) = 1.01, fi2(fmax) = 1.1.
Accordingly, the maximum and minimum values of the factor v2 are determined for the time (t ), for the law
of uneven load growth. In the calculations, the limit values of the calculation period Tp are Tp (min) = 10 years and Tp (max) = 25 years. To solve problems of optimization (unification) of parameters under conditions of uncertainty of the initial information, the method of zoning of the set of vectors of the "state of nature" [2] can be applied. This method provides specific optimization solutions and gives recommendations on the use of the solutions obtained.
With respect to the problem of choosing the number of line cross-sections used, the zoning method consists in splitting the set S of possible values of the resulting indeterminate factor 0 into regions in each of which the optimal strategy is optimal (in our case, a certain number of cross-sections of the lines from the set N).
The zoning method is based on the operation of dividing the set S for a subclass of the two strategies NF and NF + 1.
The equation of the pair boundary is determined by the equality of the optimization criteria for the strategy NF and NF + 1, that is
3(Nf ,0) = 3(Nf +1,0) (6)
If the pair boundary passes outside the field of state vectors, i.e.
max A3(0) <0 min A3(0) > 0
where
A3(0) = 3(NF ,0) - 3(NF +1,0), (7)
then one of the strategies cannot be optimal under any conditions and is excluded from consideration.
If the pair boundary intersects the field of state vectors of nature, i.e. max A3(0) > 0 min A3(0) < 0, then an equation of the pair boundary is constructed whose solution with respect to $ determines the optimality zone of some strategy, i.e.- some number of applied cross-sections of lines.
In the problem under consideration, due to the linear dependence of the optimization criterion on the resulting indefinite factor 0 outside the pair boundary, there is a strict optimality of one strategy over the other.
The equation for the pair boundary is: Sl +§2 +S3 N-1 +84 0napNF0,3 =
0,3
= 5, +S2 +S3(NF +1)-1 +SA ®nai (NF +1) Here 0 - characterizes the boundaries of the region in
nap O
an undefined factor, in which the optimal strategy is optimal.
By the solution, the equation for Fap is determined by the region of optimality of applying a certain number of cross-sections of the lines:
¿3 (Nf +1)-1 - N-
0 =
nap
84 №/ - (NF + 1)0J
(9)
With the help of the obtained formulas and with the accepted initial data, the zoning of the resultant indeterminate factor is carried out by the number of cross-sections of the RS lines. Here, for each value of the electric load density, an
uncertainty zone corresponding to the maximum and minimum values of the indeterminate factor is determined. The zones between the curves determine the optimal number of cross-section lines used.
If, however, in the zone of uncertainty Omin ^ Omax optimality zones of several numbers of line cross sections fall, then in this case it is impossible to obtain an unambiguous solution. Such a case arises at low load densities (S < 10 kW/km2), when loop networks are used. For example, at S = 5 MW/km2, three zones of optimality of different amounts of the cross sections of the NF = 1.2 and 3 lines enter the zone of uncertainty Omin = 2, Omax = 4(8). In such cases, it is recommended to partially or density to remove the uncertainty on based on additional information on the values of uncertainty based on additional information about the values of uncertain factors [2].
Sources of such information can serve as observations and measurements, expert assessments, etc.
Expertise is used as additional information on the values of uncertain factors.
With the help of expert assessments, the minimum and maximum values of the load growth factor j3(u), the values of the calculation period Tp and the value of the project load time tpr, are specified and their most probable values |?av = (u) = 1.02 (0.4), tp.sp. = 5 years, Tp = 25 years, then the value of the resulting undetermined factor is Oav = 2.7 (3.8).
For S < 10 kVT/km2, at Oav = 2.7, which corresponds to the uniform law of load growth, the application of one or two cross-sections of the lines is optimal. And at Oav = 3.8, which corresponds to the non-uniform law of load growth, one cross section of the lines is optimal. At high electric load densities (S > 10 kW / km2) over the entire range of the resulting uncertain factor, the use of one line section is optimal.
At the same time it is recommended at high load densities - to apply a section of150 mm2; at low load densities - one section of 150 mm2 or two sections of 185 and 95 mm2.
The obtained results on the number of applied line cross-sections in SES correspond to similar foreign solutions (France, Poland, Russia, etc.), which is a definite confirmation of the reliability of the results obtained.
References:
1. Taslimov A. D. Mathematical models of problems of optimization of parameters and structures of power supply systems of cities. Problems of energy and resource scarcity, 2017.- No. 3-4.
2. Belyaev L. S. Solving complex optimization problems in conditions of uncertainty. Novosibirsk: Science, Sib. Department, 1978.
