Correction factors for the cable: temperature, ground, pipes and grouting

How to Recalculate the Permissible Current: A Brief Answer

The permissible continuous current of a cable from the PUE RK table is given for standardised conditions: air temperature of +25 °C or ground temperature of +15 °C, single laying, absence of additional heating from neighbouring cables. Under real conditions these parameters differ, therefore the tabulated current is multiplied by correction factors:

I_perm.actual = I_tab · k₁ · k₂ · k₃ · …

where k₁ is the temperature coefficient; k₂ is the grouped laying coefficient; k₃ is the coefficient for soil (when laying in the ground), and others. Each coefficient is less than or equal to one when cooling conditions worsen. If the actual permissible current after recalculation turns out to be lower than the design load current, the cross-section is increased and the recalculation is repeated.

What Data Is Needed for Recalculation

• Tabulated permissible current I_tab — from the PUE RK table for the selected cross-section, conductor material and insulation type under standardised conditions.
• Laying method — openly in air, in a pipe, in a tray, in the ground, in ducts.
• Actual ambient temperature — of air or soil at the laying depth.
• Insulation material — PVC (standardised conductor temperature +65 °C) or cross-linked polyethylene (XLPE, +80 °C or +90 °C).
• Number of loaded cables laid together and the distance between them.
• Soil thermal resistance — when laying in the ground, if it differs from the standardised 2.5 K·m/W according to IEC 60364-5-52 or from the PUE RK values.
• Laying depth — when buried deeper than the standardised depth, a separate coefficient is required.

Formula and Principle of Recalculation

I_perm.actual = I_tab · k₁ · k₂ · k₃ · … · k_n

I_tab — tabulated permissible continuous current for standardised conditions, A; k₁ — temperature coefficient; k₂ — grouped laying coefficient; k₃ — soil thermal resistance coefficient; k_n — other coefficients (laying depth, thermal insulation).

Selection condition: I_design ≤ I_perm.actual, where I_design is the design load current. If the condition is not met, the cross-section is increased and I_perm.actual is recalculated for the new cross-section.

Temperature Coefficient

The tabulated values of permissible currents in the PUE RK correspond to the standardised temperature: +25 °C for air and +15 °C for ground. When the actual temperature deviates, the correction coefficient k₁ from Table 1.3.3 of the PUE is introduced.

Source: Table 1.3.3 of the PUE, 6th edition (current version). Values for intermediate temperatures are interpolated.

For cables with cross-linked polyethylene (XLPE) insulation with a standardised conductor temperature of +90 °C, the coefficients are higher, since the permissible overheating is greater. The data are given in Table B.52.14 of IEC 60364-5-52 and in the corresponding tables of the PUE RK.

Soil and Thermal Resistance

When laying in the ground, cable cooling depends on the thermal resistance of the soil. The standardised value according to IEC 60364-5-52 is 2.5 K·m/W. If the actual thermal resistance of the soil is higher (dry sand, rocky soil), heat dissipation is worse and the permissible current is reduced.

The values are given for cables laid directly in the ground or in pipes in the ground (methods D1 and D2 according to IEC). For intermediate values the coefficient is interpolated.

Laying in Pipes

A pipe worsens heat dissipation compared with open laying, since the air inside the pipe is an additional thermal resistance. In the PUE RK, the permissible currents for laying in pipes are already taken into account in separate tables (for example, Table 1.3.4 for wires in pipes). If a table for open laying is used, an additional reducing coefficient is introduced.

When laying several cables in one pipe or in parallel pipes at a close distance, the grouped laying coefficient is introduced — see the next section.

For pipes in the ground, the soil thermal resistance and the soil temperature are additionally taken into account.

Grouped Laying

When several loaded cables are laid together, mutual heating occurs: the thermal field of one cable raises the temperature of the neighbouring ones. The more cables there are and the closer they are located, the more the permissible current of each is reduced.

Source: Table 1.3.26 of the PUE, 6th edition. Reserve cables are not taken into account in the calculation. When laying in air (in trays, ducts, in bundles), similar approaches are applied according to IEC 60364-5-52, Tables B.52.17–B.52.19.

If the cables are laid in a single row close to each other (for example, in a tray with a distance of less than 100 mm), the coefficient is taken according to the lower boundary of the corresponding row. For cables laid in a triangle close together, the values are lower than for single-row laying with a gap.

Step-by-Step Example: From Tabulated Current to Final Cross-Section

Initial data. A three-phase 380 V line supplies a group of loads with a design current I_design = 55 A. The cable has copper conductors, PVC insulation, and is laid in the ground in a pipe. The laying depth is 0.8 m. The actual soil temperature at the depth is +25 °C. The soil thermal resistance is 3.0 K·m/W. Next to it, in the same trench at a distance of 100 mm, two more loaded cables of the same group are laid.

Step 1. Preliminary selection by tabulated current.

According to the table of permissible currents for copper conductors with PVC insulation when laying in the ground (Table 1.3.6 or the corresponding table of the PUE RK), for I_design = 55 A, a cross-section of 16 mm² with a tabulated current I_tab = 90 A is suitable (standardised conditions: +15 °C, single cable, standardised soil thermal resistance).

Step 2. Temperature coefficient k₁.

The standardised ground temperature is +15 °C. The actual is +25 °C. According to Table 1.3.3 of the PUE, for a standardised conductor temperature of +65 °C and an ambient temperature of +25 °C, the coefficient k₁ = 0.89.

Step 3. Soil thermal resistance coefficient k₂.

The standardised resistance is 2.5 K·m/W. The actual is 3.0 K·m/W. According to Table B.52.16 of IEC 60364-5-52, the coefficient k₂ = 0.96.

Step 4. Grouped laying coefficient k₃.

Three loaded cables in the ground at a distance of 100 mm. According to Table 1.3.26 of the PUE, the coefficient k₃ = 0.85.

Step 5. Recalculation of the permissible current.

I_perm.actual = 90 · 0.89 · 0.96 · 0.85 ≈ 65.4 A.

The condition I_design = 55 A ≤ I_perm.actual = 65.4 A is met. The cross-section of 16 mm² passes.

Step 6. Voltage drop check.

For completeness of the calculation, the voltage drop is checked for the actual line length. If the length is significant, the decisive factor may be not heating but voltage drop. The design and characteristics of a power cable are described in a separate material.

Step 7. Result.

A 16 mm² cable with copper conductors and PVC insulation is accepted for this line. If the soil thermal resistance were higher and the soil temperature +35 °C, the recalculation would give I_perm.actual = 90 · 0.77 · 0.93 · 0.85 ≈ 54.7 A, which is lower than the design current of 55 A. In this case a cross-section of 25 mm² would be required, with recalculation of all coefficients for the new cross-section. A comparison of copper and aluminium conductors affects the choice of the table of permissible currents.

Typical Mistakes

• Multiplying coefficients without checking the condition I_design ≤ I_perm.actual. Recalculation for the sake of recalculation makes no sense if the resulting current is not compared with the design one.
• Applying the temperature coefficient from Table 1.3.3 of the PUE for cables with XLPE insulation. For cross-linked polyethylene, the standardised conductor temperature is higher, and the coefficients are different — tables for the corresponding insulation type must be used.
• Ignoring grouped laying when the distance between cables is more than 100 mm. Coefficients exist for distances up to 300 mm; at 300 mm and more, mutual heating can be neglected, but at 100–200 mm it cannot.
• Taking reserve cables into account when calculating the group coefficient. The PUE RK directly states: reserve cables are not taken into account.
• Neglecting soil thermal resistance. Dry sand has a resistance of 3.0–4.0 K·m/W, which gives a reducing coefficient of 0.93–0.85.
• Applying a coefficient for pipes in addition to a table where laying in pipes is already taken into account. If the tabulated current is taken from a table for laying in pipes, an additional coefficient for the pipe is not introduced — double counting underestimates the result.

Brief Recalculation Algorithm

1. Determine the design load current I_design.
2. Select a preliminary cross-section from the table of permissible currents, taking into account the laying method and conductor material.
3. Determine all applicable correction coefficients: temperature, soil, group, depth.
4. Recalculate the permissible current: I_perm.actual = I_tab · k₁ · k₂ · …
5. Check the condition I_design ≤ I_perm.actual. If it is not met — increase the cross-section and repeat the recalculation.
6. Check the voltage drop for the selected cross-section at the actual line length.
7. Accept the larger of the cross-sections obtained by heating and by voltage drop.
8. When choosing the cable type, take into account the installation conditions and insulation requirements. VVG or VVGng — a separate analysis by insulation. Single-core or multi-core cable — by design.

FAQ

What to do if the product of the coefficients gives a permissible current that is too low?

Increase the cross-section. The recalculation for the new cross-section is performed with the same coefficients, since the laying conditions have not changed. If increasing the cross-section to the next standard value does not satisfy the condition, a change of route is considered: laying at a greater distance from each other, replacing the soil, switching to open laying.

Can coefficients from the PUE RK and IEC be multiplied together?

Coefficients from different normative systems must not be mixed without justification. If the calculation is carried out according to the PUE RK, the PUE RK tables are used. If according to IEC 60364-5-52 — the IEC tables. Coefficients from different systems may have different base conditions, and their product will give an incorrect result.

How to take into account laying cables in different planes?

When laying in several rows (for example, on the shelves of a tray), the grouped laying coefficient is taken from the tables for the corresponding configuration. IEC 60364-5-52 provides separate tables for cables laid in a single layer on a wall, on a tray and in bundles. For multi-layer laying the coefficient is lower than for single-layer.

Does the laying method affect the temperature coefficient?

Yes. The standardised temperature for air is +25 °C, for ground — +15 °C. The same actual temperature regime will give different coefficients for air and underground laying. In addition, for cables in the ground, the soil thermal resistance is additionally taken into account.

Should the permissible current be recalculated if the cable is laid in thermal insulation?

Yes. Contact of the cable with thermal insulation material worsens heat dissipation. IEC 60364-5-52 provides Table B.52.21 for cables in contact with thermal insulation. The coefficient can be 0.5–0.8 depending on the thickness and type of insulation.

How to check the correctness of the recalculation?

The check includes: verifying the dimensions of all quantities, verifying the source of each coefficient, checking the condition I_design ≤ I_perm.actual and checking the voltage drop. If at least one coefficient is taken from a source that does not correspond to the laying method or insulation type, the result is considered unreliable.

Sources Used

• Electrical Installation Code of the Republic of Kazakhstan 2015, as amended by the order of the Minister of Energy of the Republic of Kazakhstan dated 31.10.2022 No. 340 — Committee for Technical Regulation and Metrology of the MIR RK — https://base.spinform.ru/show_doc.fwx?rgn=71151
• GOST R 50571.5.52-2011/IEC 60364-5-52:2009 Low-voltage electrical installations. Part 5-52. Selection and erection of electrical equipment. Wiring systems — Rosstandart — https://meganorm.ru/mega_doc/norm/gost-r_gosudarstvennyj-standart/4/gost_r_50571_5_52-2011_mek_60364-5-52_2009_natsionalnyy.html
• IEC 60364-5-52:2009 Low-voltage electrical installations — Part 5-52: Selection and erection of electrical equipment — Wiring systems — International Electrotechnical Commission — https://webstore.iec.ch/publication/1869
• Technical Regulation of the Customs Union TR CU 004/2011 “On the safety of low-voltage equipment” — EAEU — https://docs.eaeunion.org/docs/ru-ru/0145005