On overhead networks transfer from 10 ( 6 ) kV to 20 kV

The expediency of preferential use of the rated voltage of 20 kV for the overhead networks of Russia is investigated. The feasibility study of the 20 kV voltage application areas based on the integrated parameters of the networks was performed. It is shown that due to the convergence of technical and economic characteristics of 10 and 20 kV equipment, 20 kV networks have more significant advantages in comparison with traditional 10 kV electrical installations.


Introduction
Feasibility of using 20 kV electric networks in our country has a long history.This voltage class was included into the list of rated voltage scale and then excluded again [1].It was alleged that "...the introduction of 20 ... kV voltage is not necessary...".There were other opinions [2, 3, etc.]: "... the overhead networks require significantly lower costs, non-ferrous metals and especially transformer capacities... for 110/20 kV system with a direct 20/0.4kV transformation...".When comparing alternatives of 10 and 20 kV networks it was assumed [3] that the cost parameters of overhead lines (OHL) and transformer substations (TS) of 20/0.4 kV exceed similar characteristics of 10 kV OHL and 10/0.4 kV TS in 1.1 and 1.25 times respectively.
The widespread construction of 20 kV electric networks in the country began after almost half a century, about five years ago in Moscow [4].To date, more than 1,000 km of 20 kV cable lines have been commissioned.The construction of cable networks of this voltage class is also carried out in St. Petersburg and Yekaterinburg.
20 kV overhead networks of suburban and agricultural areas have their own specifics and have not been used all-round the country.The grounds on technical and economic efficiency of 20 kV voltage class application in overhead networks are presented below.

Integral network parameters
The methods for solving such optimization problems are well-known.The first one is referred to as the method of idealized structures, the second one is analytical.An example of the first approach is presented in the paper [1].In this work, the network topology is given in the form of a lattice with a given step.TS are located in its nodes.Alternatives of the network are compared by the minimum cost through variation of initial data -load density, distances between nodes of the network, etc.In the second method, the cost indicators of OHL and TS are specified in the form of analytical (usually approximating) functions depending on their parameters (voltage, wire cross-section, line length, current, power, etc.).The extremum point is identified, for example, as in [5] -with the use of undetermined Lagrange multipliers.
The drawback of the first method is the divorcement from the actual structure and parameters of the network.The second method is even weaker, since it considers [5] the simplest configuration of the network: the power source -the load node.
We will analyse overhead networks of 10(6) kV in 18 districts of a large electric grid company from the European part of the country.In each district, typical network fragments were allocated according to the form shown in Fig. 1 [4].Network fragments are connected in a loop and sourced by two geo-graphically separated main substations (MS) of 110/10(6) kV and sectionalized by reclosers, i.e. automatic posts of OHL sectionalizing.Transformer substations of 10(6)/0.4 are connected to the backbone transmission line with a disconnector or recloser for long distance branches.Protection of 10(6)/0.4transformers is carried out by fuses on the 10(6) kV side.In normal operation mode, the network is separated by one of the reclosers with automatic load transfer (ALT).Mainly, one-transformer TS of pole-mounted (PTS, nominal transformer power S nom is 16-100 kV•A), mast (MTS, S nom =160-250 kV•A) and kiosk (KTS, S nom =400-1000 kV•A) types are installed.
In Table 1 the parameters relating to the linear part of the above-mentioned 18 network fragments are given: P max and P min -peak winter and summer load based on measurements of 2016; l OHL and l OHLP -the length of the line made of uninsulated wires and wires with a protective insulating sheath (OHLP); l CL -the same for cable lines; l total -the total length of the lines; l back -the length of the backbone transmission line between the PC (without regard for the branches); σ ld is the load density; σ n is the network density.The power supply area for assessing σ ld and σ n was determined on the assumption that the coverage radius of the 0.4 kV network of 10(6)/0.4kV TS composes not more than 0.5 km.Accordingly, the width of the corridor of 10(6) kV OHL is 1 km when determining the area.
In fact, the entire overhead network (Table 1) is made with a wire of 70 mm 2 , except fragments No. 5 and 17 where cross-section of 120 mm 2 is used for backbone transmission lines.
Table 2 shows the parameters relating to the TS of network fragments: S total -the total installed capacity of 10(6)/0.4kV step-down transformers; l TS -the average distance between the TS; σ TS -TS density; ITS -indoor TS.Analysis of data from Tables 1 and 2 allows to establish some statistical patterns: 1.
The length of the 10(6) kV backbone line between the MS varies from 12.9 to 41.3 km with an average value of 28.0 km, which shows a relative uniformity of the MS distribution in the region.

2.
The load density varies over a wide range from 8.2 to 157.3 kW/km 2 (average 76.1 kW/km 2 ).The range of average distances between TS in the fragments is 0.76-2.33km (average 1.14 km), which indicates a relatively uniform TS distribution over the territory.

3.
The installed capacity of 10(6)/0,4 kV TS is 2-9 times higher than the actual maximum load, which is clearly irrational.
For comparison, the authors of [1] in their conclusions relied on the following data on the load density: in industrial areas it reaches 30-40 kW/km 2 (average 20 kW/km 2 ), in electrified agricultural areasdoes not exceed 2-3 kW/km 2 .For the 70 years passed since, the load density has multiply increased, which is an incentive to increase the nominal voltage of the network.

Technical and economic aspects of using 20 kV OHL
When transferring from 10 to 20 kV, the phase-to-phase distances increase slightly (from 0.2 to 0.45 m) in case of uninsulated wires [6] and there is no difference (0.4 m) when using OHLP.However, the actual phase-to-phase distances for typical reinforced concrete supports are approximately 2.5 times larger [7].Therefore, for the same cross-section and wire type, the mechanical part of the 10 and 20 kV OHL is identical, except the number and rated voltage of the insulators in some cases, the cost of which is an insignificant part of the costs of OHL [8].Therefore, capital investments to 10 and 20 kV overhead lines differ by not more than 1%.
The cost of constructing a 10-20 kV OHL in the European part of the country (hereinafter in 2017 prices without VAT) is determined by the simplest linear dependencies in the range of nominal cross sections from 50 to 120 mm 2 with a maximum error of 1.4%: for uninsulated steel-aluminum wires С OHL =665.1+2.21s and С OHL =497.5+2.18sth.RUB/km in populated and unpopulated areas respectively.Similarly, for insulated wires: С OHLP =861.8+2.86s and С OHLP =665.8+2.86sth.RUB/km.
When calculating discounted costs, the cost of OHL construction must be multiplied by the increasing factor K=1+k 1 k 2 =1+0.0085·9.4=1.8,where k 1 stands for repairs and maintenance; k 2 =

n (1 E) 1 n E(1 E)
; E -discount factor; n is the design lifetime of the electrical installation calculated from the moment of commissioning.Thus, at E=0.1 and n=30 years, k 2 =9.4.
Moreover, it is necessary to take into account the cost of electric power losses for the design lifetime C ΔW =∆P max τC e k 2 , where ∆P max -the power losses in the peak loading conditions; τ -annual time of maximum losses; C e -the unit cost of electric power losses.As it is known, τ=f(T max ), where T max -the number of hours of maximum load.According to the current reporting data for the region under consideration, T max ≈6000 h (τ=3800 h) and C e =2.18 RUB/kWh.

Technical and economic aspects of using 20 kV TS
Currently, domestic factories produce all the range of 20 kV TS elements.Power transformer of TMG type, used in TS of 10 and 20 kV, has the same weight and dimensions.The main difference is the height of highvoltage bushings (for 20 kV 75 mm higher than for 10 kV).For actual air insulation gaps between the fuse block and the transformer in 10 kV PTS and MTS, such an increase in bushings is not critical.The same relates to KTS transformer chambers.
The cost of 20/0.4 kV PTS is approximately 20-25% higher than of 10/0.4 kV PTS.In general, the rise in price is due to the higher price of transformers and disconnectors.The cost of TS constructing is determined by the simplest linear dependencies at the highest error of 3.6%: for PTS С PTS =273+S nom +11.56U nom ; for MTS С MTS =178+1.16Snom +15.32U nom ; for KTS С KTS =401+1.29Snom +25.94U nom .
For the TS, K=1+k 1 k 2 =1+0.037·9.4=1.35.According to the factory data, the idling and short circuit losses of 10/0.4 and 20/0.4 kV transformers are the same and are further excluded from consideration.
The types of TS considered above have principal structural differences.Therefore, their costs are not jointly approximated with acceptable accuracy.

Comparison of the 10 and 20 kV network options
Table 3 shows the discounted costs (mln.RUB) for constructing networks fragments with the characteristics from Tables 1 and 2 at 10 and 20 kV: С TS -costs for TS while maintaining their installed capacities; С total =С L +C ΔW +С TS -total expenses of the electric network; Δ -the ratio of total expenses of the electrical networks of 10 and 20 kV.The wire cross-section was taken to be equal to the actual value (mainly 70 mm 2 -see above) and the same for the backbone sections and branches.The cost of OHL construction С L was estimated by the average value between the minimum and maximum estimates; the minimum -650 th.RUB/km at a voltage of 10 and 20 kV for uninsulated wires in unpopulated areas; the maximum -1070 th.RUB/km for insulated wire in the populated area; an average is 860 th.RUB/km without taking into account the factor K. When determining the cost of electric power losses in the overhead line, an annual load increase is taken to be equal to 2%.
It should be noted that the component C ΔW from Table 3 differs by more than four times for 10 and 20 kV voltages: when calculating steady-state modes, no restrictions on the minimum voltage values at the network nodes were imposed.Therefore, for the 10 kV network fragments No. 1, 9, 10 from Table 3, the voltage in the network nodes decreased significantly (more than 10%) in the normal mode, while in the alternative 20 kV network it was at the rated level.For fragments No. 3-5 there was no mode convergence for 10 kV network.Here the cost of electric power losses is determined formally, by a multiple increase in losses in the 20 kV network.
The required voltage quality should be provided in accordance with State regulations GOST 32144-2013 not only in normal, but also in continuous repair and post-emergency operation modes -voltage reduction cannot exceed 10% of the value.In the 10 kV network this requirement is not satisfied for fragments No. 1-6, 9, 10, 12-14 at the current loading conditions and all fragments, except No. 16, in the prospective.Thus, in the foreseeable future, a deep reconstruction of practically the entire 10 kV network will be required (disaggregation of the backbone sections due to their diversion to other power centers), which is not taken into account in Table 3.In the alternative 20 kV network, the required quality is not provided only in the fragment No. 3 at the current load conditions and also in the fragment No. 10 for the perspective load growth.Thus, when using 20 kV voltage, measures to increase the network capacity will be local and significantly less expensive.
The existing approach to the comparison of diagrams of electrical networks with different levels of rated voltages is to be referred to as [9]: "The criterion for choosing a voltage system is the total costs for networks of all classes of voltage.When comparing the options of electrical networks with different voltage classes having equal costs or costs, differing up to 10%, priority is given to the option of developing networks with a higher average voltage of the distribution network".There is a certain logic in this: 10% is the generally accepted engineering accuracy of calculations, especially under conditions of great uncertainty in decision-making.
In our case, with a fixed cross-section of the wire, the capacity of the 20 kV network is twice as high as at 10 kV, and with the same transmitted power, the power losses are approximately four times less.This is a significant advantage of the electrical network of 20 kV.As can be seen from Table 3, according to the indicated criteria the transfer from 10 kV to 20 kV is reasonable practically for all the variety of values of the network parameters from Tables 1 and 2.
For a cross section of conductors of 70 mm 2 , the current will be 0.6•70=42 A or power of S≈730 kV•A at a voltage of 10 kV.For the configurations in Fig. 1 and Table 1, the power of a typical network fragment is estimated as 2S≈1460 kV•A.This ratio is satisfied only by case studies No. 14-16 from Table 1, which indicates an imbalance: overloaded OHL with redundant excess of transformer capacity.
When transferring to a voltage of 20 kV at the same section of the OHL wires, there is 2S≈2920 kV•A.In this case, already more than half of network fragments have satisfactory indicators from the point of j0.For the remainder of the fragments, it is advisable to further increase the cross section of the conductors to 120 mm2 (2S≈5800 kV•A).However, this is clearly not enough for fragments No. 3 and 5 from Table 1.They should be disaggregated.Accounting for the growth of loads, which was not taken into account in (1), will lead to even more lowering of j0.
Such obvious distortions in the configuration of electrical networks force to return to the well-known problem of optimizing their rated voltage.The method of undetermined Lagrange multipliers, worked out in [5] for this class of problems, will be used.Assume that

Table 1 .
Parameters of the linear part of network fragments.

Table 2 .
Parameters of the transformer part of network fragments.

Table 3 .
Discounted costs for constructing network fragments.