Attempt to develop a method

Both approaches, that of the geometric average between two theoretical extreme scenarios (Approach 1) and that of the transfer of standardised system load profiles to final circuits (Approach 2), point in the same direction, and give a sense of how far the “operate at highest permissible temperature” design can be away from the life cycle cost optimum. Only they are not sufficient to create a methodology for determining this optimum. However, the synthesis of the two can be developed further:

Example 1: The residential building

For customers in the range below 100 MWh/a the standardised load profiles are used for grid planning and to determine tariffs. From a qualitative point of view let us stay with simplifying approach 2, of transferring the load profile that is valid for the system in question to the final circuits. Deciding on a particular load profile determines by which “annual peak factor” FP the mean current Iz_mean is below the maximum permissible current Iz. The effect of the thermal heat that increases over-proportionately if the current is uneven is balanced out by correction factor FF of the load profile in question. It is also listed in the tables but has already been included in the calculation of the table.

The single-family home

Approach 1 now provides another factor by which the actual mean annual operating current IB_mean of the system falls below the maximum permissible annual average of the operating current IZ_mean. Let us call this “load factor” FL (it does not actually appear in the tables, but is implied in the calculations). According to Approach 1 (Table 3 or Table 4, respectively), this factor corresponds to the relevant geometric average between the smallest possible and the greatest possible current. In other words, this is the root from the quotient of the least uniform by the most uniform load distribution across the year and across the circuits that is at all possible. This arbitrary determination of the load factor FL follows the assumption that the effective thermal load of the final circuits is equal to that of a constant load current IB_mean with the current thus produced:

In the first example (Table 3) the factor FL is very high, since the junction box is only fully utilised on rare occasions on an annual average basis:

This therefore gives small annual peak currents IB_max = 1.50 A or IB_max = 1.33 A for two or three loaded conductors, respectively (Table 6). For the annual mean IB_mean of profile H0, dividing by the annual peak factor FP of profile H0 gives the respective values 0.64 A or 0.56 A. In (Table 7), lower section “Selected load” (the other columns provide invalid values here), a payback calculation is performed again in column H0 with these values in an analogous manner to the upper section “Permissible load” to upgrade the conductor cross-section from 1.5 mm² to 2.5 mm². We see that the payback periods – now for only one standard size up – rise to values of 30 or 25 years, respectively. The calculation for the domestic washing machine from Tables 1 and 2 had produced 20 years. Nonetheless, 142 kWh/a was also drawn at this socket, 4.6% of the total consumption of the property – and this on an extremely concentrated basis. This is therefore plausible, “fits in the range” and confirms the usability of the method currently proposed. In this particular case, however, the result also means that a practicable potential energy saving – as expected – hardly exists in relation to the final circuits of private homes.

The multi-family home

At least this is what things look like inside an apartment, independently on whether this apartment is located in a single-family building or in a condominium. But let us have one more look at the riser supplying a single home, a few or a multitude of homes. “Simultaneous” starts to be an ambiguous phrase here right from the start again, since of course not all of the apartments draw their maximum possible / permissible power from the mains at the same moment. Grid planning assumes that this will never ever happen, and so long “nothing has gone wrong”, so this procedure is perfectly fine with respect to safety and availability – but how about the losses?

Table 8: Values for Fig. 6, curve with electrical warm water supply
Table 8: Values for Fig. 6, curve with electrical warm water supply

Fortunately a helpful colleague had been prepared to restore the lost data underlying the diagram (Fig. 5) from DIN 18015-1 for the power ratings. The old restored table including the limit values of the maximum line lengths lmax (for the respective voltage drop ∆U) was used as a basis for Table 8 and Table 9 here. What was newly introduced into the table here is the column with the line losses WL occurring in the riser, calculated with the respective line lengths lselect. Due to the relatively coarsely tiered standard sizes and due to the abrupt leap of the voltage drop from 0.5% to 1%, lmax rises anything else but continuously with the number of flats supplied; here and there the values also leap back again.

Table 9: Values for Fig. 6, curve without electrical warm water supply
Table 9: Values for Fig. 6, curve without electrical warm water supply

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Regarding the quantification of line losses, this brings about the question which line length to assume. Using a relative indicator, e. g. referenced to a line length of 1 m, did not appear reasonable, since a bigger building with more apartments tends to have longer risers. Hence, an algorithm was “tinkered” leading to a continuous increase of the assumed line length lselect with the number of flats supplied, tolerating that – due to the excessive discontinuity – in some cases (red figures) the line lengths exceed their maximum limits. Cynics may claim this was common practice anyhow. A different approach, however, would have resulted in preposterously short line lengths in the top part of the table, which would have been just as unrealistic.

Bild 5: Auswahl der Leiterquerschnitte (Absicherungen) der Steigleitungen in Mehrfamilienhäusern nach DIN 18015-1
Bild 5: Auswahl der Leiterquerschnitte (Absicherungen) der Steigleitungen in Mehrfamilienhäusern nach DIN 18015-1Bild 5

Good as it is so far, but now how to arrive at the losses? A creative assumption is required again here, for so long already two calculation models are at hand: Of course, the same load profile as for the one and only flat in the first line of the table was also applied to the respective riser. Two homes were assumed as having 2% the load profile according to Approach 2 and 98% the load profile of Approach 1 as for a single dwelling and so on. At the end of the table, 100 dwellings were calculated as 99% infinitely many dwellings and only more 1% as 100 times one dwelling. After all, the official load profiles already apply to customers from 100 MWh/a onwards, and this corresponds to only 20 to 40 flats. Obviously, no relevant difference is seen by grid planners between this and an infinity of users.

Fig. 6: Maximum and selected cable lengths; annual losses with electrical warm water supply
Fig. 6: Maximum and selected cable lengths; annual losses with electrical warm water supply
Fig. 7: Maximum and selected cable lengths; annual losses without electrical warm water supply
Fig. 7: Maximum and selected cable lengths; annual losses without electrical warm water supply

With all care that has to be taken with respect to the assumptions and simplifications made, the following results become obvious:

  • An individual dwelling – in effect a single-family home – causes losses worth around 40 cents annually.
  • 100 homes cause losses not as high as 100 times, but only as 20 times as much, worth about EUR 8 in total, i. e. 8 cents per dwelling.
  • The dwellings “with electrical warm water supply for bath and shower purposes” exhibit lower losses (also see the plot Fig. 6) than the dwelling without (Fig. 7).

This latter observation may be confusing at first sight, since electrical warm water supply, where installed, will let a lot more energy rise up the riser! The calculation is based on a practical example (4796 kWh/a instead of 2903 kWh/a at a long-term average over 20 years) with an additional consumption of 65%, which means a plus of about 2/3 on top of the electricity bill of the home without electrical warm water supply. However, the “electrical warm water supply for bath and shower purposes” takes into regard the current intake of a direct instantaneous electric water heater (to be installed immediately at the construction stage or to be refurbished later on), which is capable of heating the water just as quickly as it flows. This requires installed capacities between 18 kW and 27 kW. While such a high power is needed for just a few minutes per day, the requirements for larger conductor cross sections are the same as would be for permanent load. Over the rest of the day, this larger cross section then reduces the losses.

As an overall result, it can be stated that the riser may just be missed out of this consideration right from the start. Even if the mentioned guesswork should be by a whole magnitude in error, this would not change anything about the result. This being so, the estimate is quite likely to be still too high, since all risers have been calculated as being loaded with the entire current drawn by the building. In fact, every storey takes away its part of the load, and the last section is loaded only more with the current of two flats. So one ought to calculate with half the load as a mean or, alternatively, with half the real length, neither of which was done here. Despite this inaccuracy, which lays the estimate “onto the safe side”, the riser losses turned out to be negligible here. Hence, the force to design the conductors to the peak of the occurring load is not really a cost driver but rather a piggy bank, viewed across the lifespan, adding erection and loss costs! The riser need not be optimized anymore because it has already been energy optimized, although not for energy efficiency but other – compelling – reasons.

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Example 2: The office

Table 10: Data underlying the calculations according to Table 11
Table 10: Data underlying the calculations according to Table 11

Applying the same procedure to the office from Table 4 turns the table straight away. But first of all, one encounters the problem that a standardized load profile “Office” is missing. So the profile G0 “Business General” is to be applied here (top of Table 11, profile G0). The installation method be B1 again. Calculating with these again as if all circuits were loaded with their maximum permissible load IZ at peak time, the average currents IZ_mean are already significantly greater with 8.35 A (two conductors) or 7.39 A (three conductors), respectively. The average loading of the floor sub-distribution panel of nearly 20% is significantly higher than the barely 1.5% at the junction box of the residential building. This leads to the relatively high values of 7.76 A and 6.87 A, respectively, for the annual peak value of the operating current IB_max (Table 10) and the respective mean operating currents IB_mean of 3.70 A and 3.28 A (bottom of Table 11 “Selected load”, profile G0 – the other columns present invalid values here).

Table 11: Annual losses of cables and lines depending on selected standard load profiles – in the upper half the maximum annual load = IZ of the relevant line and installation method to VDE 0298-4; in the lower half the mean annual load (for an office flat – column G0) was selected such that the peak load matches the geometric mean from Approach 1
Table 11: Annual losses of cables and lines depending on selected standard load profiles – in the upper half the maximum annual load = IZ of the relevant line and installation method to VDE 0298-4; in the lower half the mean annual load (for an office flat – column G0) was selected such that the peak load matches the geometric mean from Approach 1

These result in payback times of 7 and 6 years, respectively. Since the office has been in operation for 33 years already, an additional initial investment for conductors upsized to 2.5 mm² would have paid back 6 times by now. Despite all the uncertainty with this precise, but estimate-based calculation, the factor of 6, on the other hand, allows for quite a certain assumption that the additional investment would have paid off until today. Further arguments like resource savings and CO2 reduction would still come on top – if not then, now they would. This result is particularly astonishing if you consider that the 1.5 mm² cables installed are fused 10 A only – why ever this may have been done – and hence a part of the savings potential had already been tapped at the point where this calculation starts.

Anomalies, characteristics, further action

Analogous investigations should now be carried out for the other load profiles. If upgrading the conductor cross-section from 1.5 mm² to 2.5 mm² results in an “overly short” payback period, increase by a further step, etc. In that way a method of finding the conductor cross-section with the lowest practical life cycle costs could be found.

Regarding the “invalid” grey values at the bottom of Table 7 and Table 11, respectively, it should also be noted: These give the values obtained if the degree of loading of the meter from examples H0 or G0 is transferred to the other load profiles and taken into account.

Special contract customers

Special rates negotiated on a case-by-case basis apply to customers in the range from 100 MWh/a. The power drawn is generally recorded in the form of quarter-hour averages and used to calculate the amounts to be paid for power and energy (active energy / reactive energy). The advantage is that this produces a “genuine” load profile measured on this specific consumer.

The disadvantage is that this is of no use to us, since transferring the profile from the overall operation to these individual final circuits does not offer a solution. Not only do industrial companies of varying types differ fundamentally so much that such a generalisation would be meaningless; there are also cables within the company that are operated close to the maximum permissible load almost the entire year, and then there is the supply line to the yard gate, which is loaded with a current of 1 A for 10 minutes every day. Lumping all this together by means of a “watering can factor” does not lead anywhere. An assessment must be found for each individual cable. We must now look at how the expenditure required for this can be kept within reasonable limits.