Result:

Proposal for a method

The above analyses will be grouped below into specific recommendations for action. Regardless of whether these procedures will ever be defined in standards on the energy efficiency of installations and systems in the same or a similar way as proposed here, it is urgently recommended with respect to determining, taking into account and minimising the life cycle costs of cables and lines that the following steps be included when dimensioning the conductor cross-sections.

Tariff customers

For electricity customers for whom standardised load profiles are available, proceed therefore as follows:

  1. The mean absorbed power is determined dividing the energy consumption [kWh] of the previous year by 8760 h. For new installations an estimated value, a typical value or a comparative value from a similar installation is used. Reactive power is not taken into consideration.
  2. The resultant mean power is divided equally across the whole year and across all existing / planned final circuits. Division by the mains voltage and by the number of final circuits yields the minimum current Imin for each final circuit. If final circuits with different current carrying capabilities are present, the total current is to be split up in such a way that all final circuits are evenly loaded in proportion to their maximum permissible current IZ (e.g. all at 20%). Hence, final circuits with different magnitudes of IZ will also have Imin magnitudes diverging by the same factor.
  3. It is now assumed that the current distribution over time in every final circuit be identical with that of the entire installation according to the respective official load profile of the respective plant. Hence, the maximum permissible current magnitude IZ will need to be reduced down to IZ_mean by the peak factor FP (Table 12), so that the maximum current IZ is actually reached some time or other during the year but never exceeded:
Table 12: Peak factors and form factors for official load profiles
Table 12: Peak factors and form factors for official load profiles
  1. Now this maximum permissible annual mean current IZ_mean is multiplied by the minimum continuous current Imin obtained from step 2 and the root drawn from the product. The obtained value is regarded as the equivalent mean operating continuous current Icalc for calculating the annual losses of all equivalent circuits in the system, i. e. those of equal cross sections and installation methods, but different lengths:
  1. For this current Icalc, the length-based values of the ohmic loss are determined, which still need to be multiplied by the peak factor FP (also given in Table 12) depending on the selected standard load profile and representing the fact that the discontinuity of the real current produces more heat than would the mean value (like TRMS vs AV when considering current waveforms). From the power loss, the annual lost energy and corresponding loss costs per unit length can be calculated. The respective line resistance per unit length to be used for calculating the ohmic losses is the maximum permissible value (cold value) according to IEC 60228. If no electricity prices are available, the values from Table 7 or Table 9, respectively, can be used as typical values.
  2. The conductor cross-section is now to be increased by one standard size and the calculation specified in point 5 repeated.
  3. For this measure (point 6) the payback period is determined by dividing the difference in loss costs (between point 5 and point 6) by the difference in cable prices (between point 5 and point 6). Like the length related values in point 5, the cable prices also relate to length. This calculation does not therefore depend on the length of the cable. If no cable prices are available for this bill, double the copper prices (market price at the time of the calculation of the conductor cross-sections compared) can be used as an approximation.
  4. If the payback period is shorter than the planned life cycle of the installation, the conductor cross-section is to be increased by another standard size and the calculation specified in point 5 repeated.
  5. This procedure is to be carried on until the payback period is longer than the planned life cycle of the installation. The conductor cross-section from the previous iterative step then matches the wanted conductor cross-section.

The load profiles no longer need to be taken into account for this procedure; they were merely used to derive the method and the values for the factors FF and FP given in Table 12.

While the result represents a mere hypothesis in so far as it was simply calculated with an assumed fictive load current Icalc, a number of safety factors have been employed:

  • For the length-related resistivities of the cables, the cold values were used, although a loaded conductor is warm.
  • Reactive current remained unconsidered, operating current being calculated from active power only.
  • The inclusion of load profiles (approach 2) is as such already a safety factor in its own right. One could have stuck to the first approach right from the start. Also the following assumptions would have yielded plausible results:

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Special contract customers

As stated, the above approach is unsuited to industrial customers. A large number of tests using the mathematical model presented here give as reference points the values from Table 13 – which were calculated conservatively. Installation method A2 allows the smallest loads, and installation method C the largest. These benchmark figures were therefore included here. All other values are in between.

It will generally suffice to estimate the load profile of a specific consumer or part of an installation and then, if necessary, over-dimension the cable in accordance with Table 13. If a more accurate figure is required, Table 13 can be used to estimate whether a more precise calculation is worthwhile.

This assumes currents requiring, for thermal reasons, a conductor cross section of 4 mm² applying the respective installation method. Under these assumptions, the table looks somewhat “unobtrusive”, but the following remains to be considered viewing it:

  • Within this range of the standardized conductor cross sections, an upgrade by 4 degrees already represents 6 times the cross section!
  • Towards larger conductor cross sections the tiers become less coarse; expressed in standard sizes, the lifetime optimisation would comprise an upgrade by even more sizes.
  • Anyhow, a single-case calculation will sooner be worthwhile towards larger cross sections. The generic approach presented here will be more adequate for smaller cross sections.
Table 13: So much upgrading of the conductor cross-section is worthwhile (copper base EUR 4.10/kg, operating life 10 years, cable prices from various price lists)
Table 13: So much upgrading of the conductor cross-section is worthwhile (copper base EUR 4.10/kg, operating life 10 years, cable prices from various price lists)