Approach 1:

Average hypothesis

What is the average of e.g. 1 mm and 1 km? Unless otherwise specified, by the average of two values we usually mean the arithmetic mean. This would be equivalent to the value that has the same differences from the two values, in other words is equidistant from the two on a linear scale. In the present case that would be approximately 500 m, or quite precisely 500.0005 m. But “gut feeling” alone would suggest that this value is much too close to the upper and too far away from the lower limit of the range. In this example, however, the value of 1 m is more likely to suggest itself to the technician as an average between 1 mm and 1 km. This would correspond to the geometric mean. This refers to the value that is in the same ratio to the upper and lower limits of the specified range, in other words differs from the upper and lower limits of the range by the same factor and therefore would lie midway between the two on a logarithmic scale. In those cases, this average is much more practically relevant than the arithmetic, in which the smallest value is very small, i.e. is close to 0, and the larger one is a long way from 0. It is determined not by adding the two values together, but by multiplying them and then extracting the root from the product instead of dividing the total by the number of values. With three, four, five ... values the third, fourth, fifth ... root must be extracted from their product, but this is not relevant here.

Residential buildings

Connection for a terraced house (1983)
Connection for a terraced house (1983)

Although the standardised load profile H0 exists for homes this only allows the connection of the entire property to be assessed (Fig. 1), for instance from the distribution network operator to the meter. From there, however, the absorbed power is distributed to all final circuits in a very uneven manner in terms of both time and space.

 

 

An individual consumer

If, for example, we consider the socket in the laundry room that is intended solely for the washing machine on its own, a fairly accurate estimate can be made for this one circuit. It appears that during a two-hour wash cycle, even this “slowest washing machine in the world” – as the housewife grumbles – only consumes a current that represents an appreciable load for the installation cable for half an hour (Fig. 2). The length of the cable from the distribution box is estimated at 13 m. The resistance rise of the conductor material due to the temperature rise is neglected as insignificant and instead the ambient temperature in the cellar assumed as 20 C, which is too high. The measurement recording (Fig. 2) consists of active, reactive and apparent power recorded in 1-s intervals. From the apparent power and the rated mains voltage the respective instantaneous current value and from these the energy lost in the line during the respective second are calculated. The sum of the individual values per second then results in the energy loss for one wash. 125 washes a year yields a loss worth 70 cents (Table 1).

Fig. 2: Power consumption curve of a washing machine over one wash cycle
Fig. 2: Power consumption curve of a washing machine over one wash cycle
Table 1: Calculation of the annual line losses with standard cable 1.5 mm²...
Table 1: Calculation of the annual line losses with standard cable 1.5 mm²...

If the cable is upsized from 3*1.5 mm² to 3*2.5 mm², the loss costs can be reduced to 50 cents (Table 2) – a saving of 20 cents over the year. The length of 13 m of cable NYM-J 3*1.5 mm² assumed here costs around EUR 12.50. With 3*2.5 mm² it would have cost EUR 16.80. The payback period would then be more than 20 years.

Table 2: ... and with upgraded cross-section 2.5 mm²: 20 cents a year saved!
Table 2: ... and with upgraded cross-section 2.5 mm²: 20 cents a year saved!

The potential here is obviously very limited, since there is in fact only an appreciable load for around 60 hours a year. Nevertheless, the standard cable in the example with a peak value of 8.9 A is operating at only half-capacity. Because of the quadratic dependence of the heating on the current, even the thinner cable only reaches one quarter of its permissible temperature rise.

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The entire installation

Now it is comparatively easy to record the load profile of a washing machine over a wash cycle and assign appropriate line losses to the cable that only supplies this one load. The resolution could be refined further by making several recordings in different wash programmes and keeping a log for a year of how many of which wash cycles are run. The annual line loss costs could then well rise to 72 cents or fall to 68 cents. This can therefore be left as it is.

For other circuits that supply consumers with different load profiles, i.e. part-simultaneously, part-alternately, which is the norm, things become difficult. What helps in such cases, at least a little, is the comparative consideration of the most and least favourable cases. The truth should most likely be near the middle – of the previously described geometric average.

Thus, with its average annual consumption of 3110 kWh, a house connection for a terraced house chosen by way of example (built 1983, Table 3) is loaded with barely 1.5% of its rated capability of 3*35 A. The least favourable case (with the greatest possible line losses) would now be to draw the annual electricity consumption of the given household in the shortest possible time via as few circuits as possible. In the present case, this would correspond to a load of three circuits – one per phase conductor – of 17.6 A each via a circuit breaker B 16 A, since up to 1.1*In it is guaranteed that “nothing happens”. For the second three circuits – one per phase – a further 17.4 A is left over in each case in order to fully utilise the three 35 A main fuses, and the remaining 6 available final circuits stay unloaded. This load distribution would yield the greatest possible power loss across the residential distribution, and the annual electricity consumption of the chosen household would then run through the meter within 129 h. The annual energy loss would be around 29.6 kWh per phase, 88.7 kWh in total (Table 3).

Table 3: Extreme scenarios “most favourable case” and “least favourable case” and resulting geometric average for a private household; annual line losses for all three cases.
Table 3: Extreme scenarios “most favourable case” and “least favourable case” and resulting geometric average for a private household; annual line losses for all three cases.

It would correspond to the most favourable case (with the lowest line losses) to distribute the annual electricity consumption as evenly as possible, i.e. a constant load over the entire year and equal currents on all 12 final circuits. Then, each of the circuits would be loaded constantly with just 129 mA.

In the first scenario described, the energy loss is around 88.7 kWh/a, while in the second it is just 0.7 kWh/a. This approximately equals a factor of 100. The truth will then most likely lie above the minimum by the factor of 10 and below the maximum by the factor of 10, i.e. at the geometric mean between the two scenarios:

  • The best scenario causes hardly any losses – calculations reveal an amount of just 0.21 permille (210 ppm) of the annual consumption.
  • Even the least favourable scenario would only produce a loss amount of 2.83%.
  • The scenario of the geometric mean only gives a loss amount of around 0.245%, which would correspond to an efficiency of the house installation of 99.755%.

That does not necessarily look like an appreciable savings potential by increasing the conductor cross-sections.

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Office floor

An office building produces completely different values. In the example chosen (again built in 1983 – Table 4), a floor is protected with 3*100 A. Each phase conductor is split between 7 final circuits each of B 10 A (Fig. 3). If the annual consumption of 91,466 kWh in 2015 is divided according to the specified methods, this gives a mean utilisation of around 20%, which exceeds the corresponding value for the above-mentioned terraced house 13 times. An energy loss can therefore be calculated for the final circuits of minimum 401 kWh/a (0.44%) and maximum 2645 kWh/a (2.87%), corresponding to 1164 kWh/a in the geometric mean between the two:

Table 4: Corresponding calculation to Table 3, here for an office floor
Table 4: Corresponding calculation to Table 3, here for an office floor

That looks pretty clearly like a potential energy saving. Because of the significantly higher utilisation of the floor distribution, the spread between minimum and maximum scenarios – and therefore the uncertainty – is correspondingly less. Admittedly, here too the cable lengths could only be estimated and were used as a general “average”, but this does not impact the determination of a payback period (cf. Approach 2), since the costs for the required quantities are in the same proportion “off beam”.

The distribution is also different from those in residential buildings, in accordance with the purpose: The limiting factor is the number of circuits, which all together cannot ever fully load the main fuse. In residential buildings, the ubiquitous availability of electrical energy prevails over the volume actually used; as a result, the design there is different from those in the office under consideration: The main fuse does not provide anywhere near as much power as the final circuits could distribute. This was taken into account accordingly in the calculations of the tables reproduced here.

Fig. 3: Distribution panel of the office floor
Fig. 3: Distribution panel of the office floor

The potential energy saving that exists here had partially already been converted during the original planning of the office in question, in that although the final circuits had been provided with a conductor cross-section of 1.5 mm², they had only been fused 10 A. This is probably down to the limitation of the voltage drop on the cables, some of which are quite long. Incidentally, more stringent provisions and limits also enforce energy to be saved in the event of excessive voltage drop “as a by-product”. This must be taken into account as a pleasant side effect when designing systems and also in the current revision of standards on voltage drops.

Also worthy of note is the high power consumption, which suggests quite different potential savings in quite different places – in the place the electrical energy is being used as opposed to its distribution. This is especially true bearing in mind the fact that the share of the building's general consumption charged to the tenant still far exceeded the consumption on the floor: In total, the tenant was charged for a consumption of 250,869 kWh! If it is assumed that each of the 13 employees spends 2,000 hours in the office and 5,000 hours at home each year, each one has a “power consumption” of almost 10 kW during working hours! Converted to his presence, the employee from the household in Table 3, that (only) comprises 2 people, consumes just 300 W. One hour's office work therefore consumes 30 times as much electrical energy as one hour's leisure time! Does that have to be so? This will have to be clarified (from) elsewhere.

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Industrial company

Industrial load profiles can vary considerably, and therefore cannot be assessed all together. We should therefore begin from an assumption in the border area for continuous load, which is encountered with some degree of certainty in certain industrial companies:

Table 5: Initial values for the calculation shown in Fig. 4
Table 5: Initial values for the calculation shown in Fig. 4

A cable 5*4 mm² is loaded on a three-phase basis with a load profile close to its rated capacity – 14 hours a day at 100% and 10 hours a day at 50% of the permissible current. The load is symmetrical and free from harmonics, i.e. no current in the neutral conductor. In installation method A2 to VDE 0298-4, the current carrying capacity is then 23 A per conductor. This is the smallest value that occurs for this cross-section; all other installation methods allow higher values. Nevertheless, with an electricity tariff of just 11 ct/kWh: After 10 years of operation, the loss costs exceed the price of the cable by several times! In actual fact, the conductor cross-section has to be increased by no fewer than 4 standard steps, to four times the thermally required cross section, to achieve the economic optimum (Table 5, Fig. 4): 4 mm² is sufficient thermally, but the lowest overall costs are achieved with 16 mm²!

Peculiarities

Interestingly, there is a kink in the curve between 16 mm² and 25 mm². This is due to the fact that only a single “reasonable” price list could be found, but this only went as far as 16 mm². All others offer only “moonshine prices”, a sort of fictional accounting units that cannot be confirmed on the market – as if only the denomination was changed when switching from DM to euros. Furthermore, all the price lists that can be found are very old; publishing prices seems to have gone completely out of fashion. It is then, however, inconsistent that the old lists are also made available quite officially as “originals” – not, for instance, merely as historical left-overs from third parties – on providers' current websites.

Fig. 4: Cable prices, loss costs and overall costs of a cable for a typical industrial load profile over 10 years depending on conductor cross-section (only 4 mm² required)
Fig. 4: Cable prices, loss costs and overall costs of a cable for a typical industrial load profile over 10 years depending on conductor cross-section (only 4 mm² required)

Dealing with the peculiarities

In the end this does not play a decisive role in the case of larger conductor cross-sections, since their prices are largely determined by the metal price – and as a global market price this fluctuates significantly, but only over time and not from country to country or provider to provider. As a result, the cable prices are given in the lists as hollow prices, in other words without the metal, and the metal is billed subsequently at the daily price. An employee of the trade association for cables and insulated wires in the ZVEI involved with standardisation had even suggested only taking the cost of the copper into account; this would be sufficiently accurate for the present rough estimate. The kink would then not have occurred; however, with hollow prices and kinks, the accuracy is still somewhat better than with “cable price entirely without cable, just with copper”.

Only copper cable was taken into consideration. Aluminium would have given different results, but aluminium – with good reason – is rarely ever used in industrial networks.