Technical and economic analysis of parameters of urban distribution electric networks 10 kV

. In the article, using the criterion analysis method, the analysis of the stability of total costs, the sensitivity of parameters to changes in the initial data (to the analysis of the influence of errors in the initial data) is carried out, and recommendations are given on the use of the obtained parameters for 10 kV distribution electrical networks.


Introduction
Solving the problem of choosing the parameters of electrical distribution networks (DET) requires the use of methods of mathematical and geometric programming. This method is the method of criterion analysis or programming [1][2][3], which makes it possible to solve a complex of problems of choosing parameters. An important advantage of the criterion analysis method is that some tasks of quantitative analysis (for example, the stability of the technical and economic function to parameters, the sensitivity of optimal solutions to the initial data) are solved without knowing the numerical values of the initial data [7][8][9][10][11].
Consider the total costs of 10 kV DET for one power source (PS), which, taking into account the total capital costs, operating costs and electricity losses, are determined by the expression [4][5]: Where ZС(i),initial data; NF,C, -number of standard cable cross-sections; FH,C, -cross-sections of the head sections of cable lines 10 kV, mm 2 ; MС,the number of lines outgoing from one PS; PS S -power PS, mVA; capacity of transformers, kVA;  -electrical load density, referred to as PS tires, mVA/km 2 .
On the basis of (1), using the criterion analysis method, the economic values of the DET parameters corresponding to the minimum total costs are determined. The calculation results and their analysis are given in [6].
It should be pointed out that the results obtained in [5] are intermediate, since they were obtained without taking into account the stability and the zone of equal efficiency of total costs. The study of the stability of the total costs of 10 kV DET in the area of its minimum involves an analysis of the applicability of discrete standard values of economic parameters in the area of equal efficiency of total costs and creates the prerequisites for further unification of these parameters [12][13][14][15][16][17][18][19].
To study economic sustainability based on (1), we write down the general criterion equation for a 10 kV network in the following form: Where «*» -means that all parameters are expressed in relative units from their economic values; π1e, π2e, π3e, π4esimilarity criteria for economic options. Similarity criteria in matrix form are determined by the formula (2): Here α Т -parameter exponent matrix; πEcolumnar matrix of similarity criteria; m -number of components of total costs; n -number of parameters.
For model (1), we compose the transposed matrix from the exponents of the parameters Т  and find the inverse matrix ( Т  ) -1 :      332  ,  0  664  ,  0  372  ,  0  79  ,  0   1  ,  0  199  ,  0  111  ,  0  763  ,  0   232  ,  0  464  ,  0  26  ,  1  553  ,  1   336  ,  0  327  ,  1  743  ,  1  579  ,  1 In this case, the economic values of the similarity criteria in matrix form are: Thus, the economic values of the similarity criteria are: Taking into account the values of the similarity criteria, the criterion equation takes the form:  (3) we obtain expressions that are directly used to study the economic sustainability of total costs: at The analysis of the economic sustainability of total costs to changes in parameters is carried out according to the dependences in Fig. 1 constructed according to criterion equations (4) -(6).  Fig. 1 allow to determine the degree of economic stability of the total costs for 10 kV DET to changes in individual parameters. Fig. 1  Thus, a significant equally economical zone of total costs for the parameters NF,i and F,H,i on the one hand, creates the preconditions for the unification of cable cross-sections, on the other hand, it does not allow to unambiguously select these parameters -the number and values of standard crosssections of 10 kV DET cables. In this case, additional criteria are used for the final selection of these parameters [20][21][22][23][24][25][26].
The obtained economic values of the parameters depend both on the initial data and on the completeness and accuracy of the total costs. When forming the total costs of 10 kV DET as a function of the number of cable cross-sections used, a number of assumptions and approximations were made, which affected the values of the generalized coefficients ZC(i) . In addition, the influence of the initial data error on the parameters of the 10 kV DET needs to be clarified for practical purposes. Therefore, it is necessary to investigate the influence of possible changes in the initial data (generalized coefficients) on the values of the parameters, that is, the sensitivity of the economic parameters NF,i ,F2,i and Mi . From (5) we get: Where i=n, c. Expressions (7)-(9) show how the possible ranges of variation of the error of generalized constants (initial data) affect the economic values of the parameters. By (7)÷(9) graphs of sensitivity were constructed (Fig. 2a, b, c). As can be seen from Fig. 2c the number of outgoing lines 10 kV MС (from PS) is most sensitive to a change in the generalized constants ZC(1), determined by the constant part of the unit cost of 10 kV cable lines МС respectively. With the growth of ZC(1) the economic values of the МС parameters decrease significantly [27][28][29][30][31][32].
The economic values of the cross-sections of the head sections of the 10 kV CL (FH,i) are most sensitive to changes in the generalized constants Zi(1),Zi(2) and the least to a change in the constants Zi(3) and Zi (4), that is, the economic value parameter FH,i is mainly determined by the cost characteristics of cable lines (Fig. 2b).
As can be seen from Fig.2a (4)) on the value of the unification parameter NF,i is insignificant (Fig. 2a, b, c). Thus, the reliability of determining the economic value of the parameter Mi depends to the greatest extent on the error of the constant component of the characteristic of the cost of 10 kV cable lines, and the accuracy of determining the parameters FH,i and NF,i depends to the greatest extent on the error in determining the cost characteristics of cable lines [33][34][35][36][37].

Conclusions
Thus, by analyzing the characteristics of a complex technical and economic model of 10 kV DET, it was found that the reliability of determining the economic value of the parameter Mi depends to the greatest extent on the error of the constant component of the characteristic of the cost of cable lines, and the accuracy of determining the parameters F2,i and NF,i depends to the greatest extent on the error determination of the cost characteristics of cable lines 10kV. The significant stability of the technical and economic function to the parameter of the number of cross-sections used creates a prerequisite for further unification of the crosssections of 10 kV DET cables.