Economic load intervals for selection of cable sections for agricultural purpose

The article is devoted to the issues of choosing the optimal cross-section of cables and their scales for the lines of rural electrical networks by the method of economic intervals for various laws of load growth, taking into account the restrictions on long-term permissible current loads and permissible voltage loss, and a comparison of the load boundary obtained on the optimization model with economic intervals is carried out load.


Introduction
Electrical distribution networks for agricultural purposes are characterized by a constant increase in loads. In these conditions, the correct choice of the parameters of power lines and, first of all, the cross-sections of wires of overhead lines and cables of cable lines is of great importance. To select the cross-sections of cable power lines, until now, the economic current density is widely used, which does not meet the condition of the minimum total costs [1][2][3][4][5][6][7][8]. In this regard, it became necessary to determine the economic load intervals for the selection of cable cross-sections and the solution of related problems, taking into account the dynamics of load growth.
In this case, the boundaries of economic intervals for adjacent sections for the case that does not take into account the dynamics of load growth are determined [9-10]: where ‫ܨ‬ and ‫ܨ‬ ାଵ are standard sections; ‫ܧ‬ мstandard efficiency ratio, ‫‬ -standard depreciation deduction ratio; ܷ н -Rated voltage; ‫ܭ‬ and ‫ܭ‬ ାଵvalues of capital costs; ܷ И -the cost of compensating for electricity losses.
The boundary values of the economic load intervals, taking into account the dynamics of load changes, are determined: where is the coefficient determined by the law of load growth.
To take into account the laws of load growth, the shear coefficient is convenient. In this case, the shift coefficient is determined: The shear factor does not depend on the cross-section of the cables and is determined by the factor relative to the load growth (multiplicity of load growth) and the design period.
To study the effect of various laws of load growth on the shear coefficients, appropriate calculations were made. The calculation results are shown in Fig. 1 and 2.
In all possible cases, the shift factor is always greater than one. At the same time, the boundaries of economic load intervals will always be large when choosing cable cross-sections for lines on which the load changes over time. Thus, having determined the boundaries of the economic intervals of the load without taking into account the change in the load over time and using the coefficients of the shift of the boundaries of the economic intervals, it is possible to determine the boundaries of the economic intervals for any laws of growth of the load. In all possible cases, the shift factor is always greater than one. At the same time, the boundaries of economic load intervals will always be large when choosing cable cross-sections for lines on which the load changes over time. Thus, having determined the boundaries of the economic intervals of the load without taking into account the change in the load over time and using the coefficients of the shift of the boundaries of the economic intervals, it is possible to determine the boundaries of the economic intervals for any laws of growth of the load [11 -13].
Comparison of the load boundaries obtained on the optimization model with the economic load intervals showed the following. When the restrictions on long-term permissible current loads and permissible voltage loss are removed, the load boundaries determined according to the proposed program practically coincide with the economic load intervals, the optimization model, determined taking into account the shear coefficient for any duration of the design period (Tables 1-3). Thus, for any settlement period, the boundaries of economic intervals coincide. Based on such a comparison, it can be concluded that the proposed optimization model is correct [14][15][16].
For calculated periods of 10 and 15 years, the boundaries of economic load intervals determined by the method of economic intervals and by the optimization model, taking into account the limiting conditions, practically coincide (the relative error does not exceed 1%, i.e. the discrepancy is explained by the accuracy of the calculations) [17][18][19][20][21][22]. With the duration of the calculation period of 20 years, the upper boundaries of the economic load intervals for the cross-section of cable conductors of 50, 120, 150 and 185 mm 2 do not coincide. However, for the rest of the sections, the boundaries of the economic load intervals practically coincide [23][24][25][26][27][28].  Table 1 The upper limits of economic load intervals, taking into account Section, mm2 Calculated period, years  10  15  20  30  16  269  310  363  513  25  441  507  594  839  35  569  655  767  1086  50  944  1087  1272  1798  70  1169  1346  1575  2227  95  1456  1675  1954  2772  120  2009  2312  2707  3826  150  2417  2782  3257  4604  185 2856 3291 3853 5445  Table 3 Economic load intervals according to the optimization model taking into account the limiting conditions Section, mm2 Calculated period, years  10  15  20  30  16  268  311  361  394  25  443  503  595  613  35  567  651  765  832  50  948  1095  1189  1269  70  1175  1346  1572  1751  95  1453  1672  1954  2145  120  -2308  2570  5122  150  -2781  3101  6347  185  --3674  7310 Thus, the boundaries of the loads determined by the proposed optimization model without taking into account the influence of the limiting conditions fully correspond to the boundaries of the economic intervals of the load, determined taking into account the shear coefficient, subject to the conditions of comparability. To select the cable sections of the lines, the relationships were established between the boundaries of the economic load intervals, the values of the load intervals themselves and the value of the total costs at the boundaries of the economic load intervals. The influence of the nature and dynamics of changes in the load on the boundaries of economic intervals is investigated and the shift coefficient is proposed.