Some helpers

are already at work

However, as already indicated, there are also design criteria that are defined by standards and used for entirely different reasons, but then “play into the hands”, as it were, as a “synergetic side effect” of energy efficiency:

Age-old helper: Reactive power compensation

An argument that is sometimes put forward against the over-dimensioning of conductor cross-sections, sometimes as a supplement to it, is that you should first ensure the conductor's load to be reduced through appropriate reactive power compensation; this could lead to equally high or even higher savings. Is that right? When is that right and when not? Or should you do the one without neglecting the other? The calculations given in Table 14 should help decide this.

Table 14: What pays back sooner – over-dimensioning of conductor cross-sections or reactive current compensation?
Table 14: What pays back sooner – over-dimensioning of conductor cross-sections or reactive current compensation?

Boundary conditions, restrictions and simplifications

As a comparison, three example loads were chosen that are commonly known to be of an ohmic-inductive nature: One small, one medium and one large three-phase asynchronous induction motor. The design values of the motors were chosen such that their normal operating currents utilised the relevant cables as fully as possible: The first case involved the thinnest (A = 1.5 mm²), the third the second-thickest (A = 500 mm² – i.e. with “air upwards” for upgrading to the thickest available with A = 630 mm²), for which the required data could be found in the manufacturers' technical data sheets. The second case was in the (geometric) middle in between (A = 35 mm² required, upgraded to 50 mm²). Besides the prices, the “required data” also included the inductances per unit length of each cable.

The operating temperature of the cable is assumed to be 70°C at full load. Here, unlike stated earlier, the effect of reducing the load through over-dimensioning or (complete) reactive current compensation (to cosφ = 1) is assumed to be linear to the change of temperature. The resistance R of the cable therefore decreases linearly with the load relief, leading to a slight reduction in losses and therefore to a minor improvement in the saving effect.

The cable prices given in Table 14 relate to the lengths specified in each case – without taking into account any bulk discounts on account of the different lengths in the individual examples.

A further inaccuracy arises because the inductances per unit length of the minimum cable with a 500 mm² conductor cross-section required for the large motor and the upgraded cross-section of 630 mm² were calculated as three-core cables, whereas the prices of 3 single conductors were used, since multicore cables of such dimensions do not exist. It is also somewhat confusing that the only supplier who specifies inductances per unit length for its cables also provides this data for single conductors, even though inductance is a system variable and cannot therefore be assigned to an individual conductor. Rather, the inductance of a conductor loop depends on the spacing between the outward and return paths. The decision here to minimise error was, however, to calculate the inductance values by means of a theoretical formula, assuming the single-core cables were installed in touch with each other. The results roughly match the data given by the cable supplier.

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Method

Fig. 8: 500 kW motor without compensation on the “adequate” 500 mm² line
Fig. 8: 500 kW motor without compensation on the “adequate” 500 mm² line

Because a specific three-phase asynchronous motor always displays a specific reactive power requirement Q at the nominal operating point, the design of a corresponding compensation system is fixed from the outset; not, however, the cable length l. Thus a decision was made here to choose a cable length in each case that kept the voltage drop ΔU of the uncompensated motor below 24 V (6% of the nominal voltage UN = 400 V). This produced the line losses PV shown in each case (Fig. 8).

Where no motor current rating IN could be found, it was calculated from the rated power PN, the power factor cosφ and the efficiency η. This data is always specified in the manufacturers' brochures. Table 14 is therefore split into a “motor section” and a “cable section”, each of which were further divided into a section with found data and a section with values calculated from these data. The compensation system was designed for a power factor λ = 1, and the grid was idealised as free from harmonics.

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Results

The results can be found at the bottom of Table 14, based on an electricity price of EUR 0.11/kWh and 10,000 full-load operating hours. It should be noted that the surcharge for the upgraded cross-section was already deducted from the saving, but not the set-up costs for the compensation system, since these systems cannot be supplied off the shelf at standard prices. The table (e.g. for the small motor) thus reads as follows:

A compensation system with Q = 4.7 kvar is required to reduce the loss costs per 10,000 h full-load operation by EUR 413. From here a payback period can easily be determined, if e.g. an offer exists. Increasing the cable cross-section by one standard size saves almost twice as much (EUR 751 per 10,000 h) as reactive power compensation.

It is best to combine the two – even though the overall saving will then be slightly less than the sum of the two economy measures each calculated individually. Thus, you might expect a saving of EUR 1164/10,000 h for the small motor, but in fact it is “only” EUR 1043/10,000 h. It is a general observation that the first improvement always has the greatest effect for the least cost. Each subsequent step will normally cost more and have less effect than the preceding one. In the present case, this becomes very clear, since due to the preceding setting up of the compensation system, the current had already been reduced and the difference in losses with the minimum cross-section against the cross-section upgraded by one size is correspondingly smaller. Or, looked at another way: If an over-dimensioned cross-section is already in use, the losses are already lower, and using compensation naturally does not bring about as big a reduction as if compensation were the first measure taken.

With the medium and large motors, the upgrade still saves more than compensation, but not as much as with the small motor. With this, increasing the cross-section produces a massive saving, and at EUR 29 the surcharge is minimal compared with the saving of EUR 1099 within 10,000 h – with the surcharge already deducted – which yields a payback period of just 261 h. With the medium and large motors, the differences in payback times, 2945 h or 2752 h, respectively, are less – which, however, is still remarkably short at significantly less than half a year of continuous service. In contrast, a compensation system

  • of 4.7 kvar would be required for EUR 18;
  • of 40.6 kvar would be required for EUR 1228;
  • of 253 kvar for EUR 2820

to achieve the same payback periods as the upgrading of the cross-sections. While the former seems absurd, the other two appear to be somewhere close to reality – albeit just about so.

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Further observations

One reason for the above observations is the larger cable lengths in the second and third cases. This is due to the greater permissible current densities at smaller cross-sections. The outer surface (relevant for cooling) increases linearly with the size, i.e. only linearly to the diameter, while the cross-sectional area grows by the square of the diameter.

A further surprising observation is the influence of the two loss reduction measures discussed here on the voltage drop ΔU in the line. These values are included in Table 14 for information. However, they were calculated using a new method, not according to the formula in IEC 60364-5-52, which is quite obviously not only simplified but factually incorrect. In principle, the methods of loss minimisation being debated here – compensation and cross-section increasing – both lead to a reduction in the voltage drop in the line in question. However, the following is rather surprising:

  • In the small motor the compensation only leads to a marginal reduction in the voltage drop. The advantage is disproportionate. Conversely, upgrading the cross-section has a disproportionately significant impact.
  • In the large motor, the opposite observation can be made: Increasing the cross-section has almost no effect on the voltage drop, but compensation is a revelation in this regard!
  • The medium motor lies somewhere in between.

How can this be explained? It is a matter of the phase angle between the voltage drops UC of the cable and UM of the motor. It should be noted with regard to the pointer diagram used here for clarification (Fig. 9) that this was presented in somewhat unorthodox fashion: The mains voltage UN was not used as a reference for the phase position, as is normally the case, but the ohmic proportion URM of the load voltage (at the motor). As a result, it becomes immediately apparent, when the arrow of the overall voltage UN is not vertical, that the total load – including the supply line – is not of a purely ohmic nature, i.e. is not or not completely compensated. An inclination to the right means an inductive phase position.

Cables with a small cross-section are of a practically ohmic nature. The inductive proportion UXC of the voltage drop along the cable falls far behind the ohmic proportion URC. However, the greater the cross-section, the smaller URC becomes, while UXC remains at the same order of magnitude. In theory, it should even become greater, since the centre distance between the outward and return current paths increases, but this does not appear in the corresponding catalogue data. Viewed as a load (under short circuit conditions, for instance) a cable presents an impedance with the following data (Table 15 – Example values):

Table 15: Constituents of cable impedances – three example values for small, medium and large conductor cross-sections
Table 15: Constituents of cable impedances – three example values for small, medium and large conductor cross-sections

Now if the phase angles and thus the power factors of both cable and load are the same, the full magnitude of the cable impedance contributes to the voltage drop (Fig. 9). However, the more they differ, the less “the load pulls the voltage down”. In an extreme case – in other words if a (predominantly) inductive cable feeds a capacitive load (a static var compensator, for instance) – the voltage drop even becomes negative, i.e. it turns into a voltage increase; the voltage is higher at the end of the line than at the beginning!

For only a slightly inductive load on a practically ohmic cable this means almost no improvement in voltage stability through compensation: While the compensation does reduce the current in the line, in other words both saves energy losses and also reduces the ohmic proportion URC of the voltage drop UC, the phase angle of the load due to compensation approximates the phase angle of the cable: UC becomes smaller, but has a greater impact on the vector sum of UC and UM.

Fig. 9: Scale pointer diagram of voltage drops across large motor (500 kW) and across connecting cable, uncompensated (left), load compensated (middle) and both load and cable compensated (right)
Fig. 9: Scale pointer diagram of voltage drops across large motor (500 kW) and across connecting cable, uncompensated (left), load compensated (middle) and both load and cable compensated (right)

For a heavily inductive load on a heavily inductive cable, the opposite is the case: The compensator only reduces the current by 10% (and therefore the line losses by 21%), but the voltage drop is reduced by 60%: Without compensation, the voltage vectors of UC and UM point in roughly the same direction, and their amounts therefore add up almost perfectly (Fig. 9 left). On the compensated motor, the inductive voltage drop UXM is missing, and the overall voltage drops UC and UM are more or less perpendicular to each other (Fig. 9 right). Increasing UC (i.e. URC and UXC in the same proportion) hardly increases the difference between UM and the (fixed) mains voltage UN = 400 V – but does increase the power loss in the cable! This aside, in high-current systems this can be a further reason for compensation.

It is of course assumed here that the compensator is placed at the end of the line, near the load. Otherwise, were it positioned at the start of the line path, at the feed-in point, it would not relieve the load on the line and therefore miss its intended purpose.

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Conclusions

Fig. 10: 500 kW motor on the same line – “over-compensated” to an amount so that the inductive voltage drop of the line is also compensated along
Fig. 10: 500 kW motor on the same line – “over-compensated” to an amount so that the inductive voltage drop of the line is also compensated along

A careful study of Table 14 and Fig. 9 shows that both methods considered, over-dimensioning of conductor cross-sections and reactive power compensation, help reduce losses in electrical systems. However, neither can be regarded as a replacement for the other. Rather, both must be considered independently of each other, and the outcome will generally be that both have a right to exist alongside one another. Neither renders the other superfluous.

It must be remembered that the actual reason why grid operators charge their customers for reactive energy lies in the unnecessary, avoidable losses reactive currents otherwise cause in this grid. The customary method of setting up a large central compensator at the main feed-in point reduces losses in the upstream grid, but not those that occur downstream in the consumer installation. The popularity of this practice is down to the fact that the external reactive energy drawn from the grid becomes visible on the electricity bill, but the internal reactive energy does not appear separately anywhere but is paid “blind”, as it were. Small compensators, decentralised and placed close to the individual inductive loads, improve this situation. Implementing this practice, but then abusing the reduced currents as an argument for downsizing the conductor cross-sections by one gauge negates the effect – easy come, easy go. This is therefore not to be recommended.

With large loads, compensation as well as loss reduction can have highly beneficial effects on voltage drop. Under certain conditions, the voltage drops can be reduced by more than half!

In view of the large inductive proportions of the impedances of thick conductors, in systems with corresponding current amplitudes it is worth considering installing a second compensator at the beginning of the cable – not to compensate the connected load, but directed at the reactive power of the cable.

Alternatively you might consider dimensioning the compensation system at the end of the line such that the load is “over-compensated”, in other words is actually designed for the image performance of line plus load:

  • The advantage would be in completely eliminating the inductive voltage loss along the line: Only 9.4 V would be lost to the ohmic resistance of the supply line, and 389.6 V would still reach the consumer. The inductive loss of 28.4 V would no longer be effective (Fig. 10; see also Section 5.2).
  • The power factor at the end of the line would, however, be slightly capacitive, while at the beginning it would be ohmic (Fig. 9). The current in the line would therefore be very slightly higher than with full compensation of the load (alone).
  • However, this minor disadvantage could very easily be (more than) offset by a correspondingly larger conductor cross-section. Since a “very small” increase in the cross-section is not possible, but the next standard size must be chosen, you are “involuntarily” acquiring a further advantage, as the line losses decrease even more than by simply compensating the load. It is reasonably certain that this would be a more cost-effective solution than splitting the reactive power compensation between a small system at the beginning of the line and a larger one at the end alongside the load, which would also be an option.

This is the proof: Upgrading conductor cross-sections and reactive current compensation work hand in hand; only together do they make sense!

It is irrelevant that in the schematic (Fig. 10) the load and the associated compensation capacity are switched in series, while of course a compensation system is normally connected in parallel to the load to be compensated. However, any interconnection of impedances can be shown as series or equivalent parallel wirings, i.e. as two-terminal element with the same properties. Since the capacitance is in fact also physically in series with the inductance of the line, the chosen form of representation is not at all so far-fetched.

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Helper 2: The voltage drop

The above representations showed that the voltage drop is a very welcome helper in implementing the energy-saving measure “upgrading conductor cross-sections”. Since it cannot or should not exceed specific values, if a particular length is exceeded the line must be selected with an additional thickness in proportion to the extra length. The voltage drop is (for cross-sections common in the construction sector) almost of a purely ohmic nature, and therefore a voltage drop of e.g. 3% – at a corresponding current – also represents an energy loss of 3%. If (for cross-sections that occur in industry) this ohmic drop is offset by inductive-capacitive “tricks”, the losses are not removed! They simply no longer appear with their side effect “voltage drop”.

However, both when designing systems and when standardising energy efficiency in buildings, the target should always be as low a voltage drop as possible, therefore: Do not criticise limit values that appear all too stringent, simply implement them!

Helper 3: The tripping conditions

The same applies to the tripping conditions, which may require a larger cross section to be used in order to get the short-circuit current high enough so that, for sure, the short-circuit protective device will trip. Hence: Do not simply select the protective device one grade “weaker”, but reinforce the performance of the installation by upgrading the conductors and save some energy along with this!

Helper 4: Selectivity

Selectivity is a very similar helper: If – as a protection against electric shock, against overload and in cases of short-circuit – a protective device trips, then only this protective device shall trip and not any other ones further upstream in the installation, so that no more “gets dark” than is necessary to avert the peril. As a rule of thumb, the nominal tripping currents of any two protective devices connected in series should never be any less than two standard sizes apart. In fact, it is quite a bit more sophisticated and represents a topic in its own right. Nevertheless, it may occur also here that a larger cross section will need to be selected, “only” because the protective device has to be dimensioned one size up in order to ensure selectivity. Again, what applies is: Do not remonstrate, but install! The larger cross section brings about nothing but advantages in practical use.

Helper 5: The load profiles

It could be claimed that the load profiles themselves “save energy”, since an almost non-existent profile (base load) means that a line can or must be permanently loaded with the maximum permissible current. As initially shown, this point is miles away from the life cycle cost optimum. If the load is characterised by brief peaks, this requires the line to be operated well below its maximum permissible current for the vast majority of the year (example: profile HZ0). Thus, a night storage heater with a power rating of 10 kW almost fully utilises a connection cable of 5*1.5 mm². However, if the heater draws its annual energy consumption (that is around 14,656 kWh according to load profile HZ0) continuously over the year, distributed over day and night at its mean power of 1.7 kW, in theory a line of 0.25 mm² would be sufficient (attention: do not imitate! Only heating was considered in this – hypothetical – operation; all other safety aspects “had to keep out”!). To put the cart before the horse, you could therefore say that the potential saving through the tenfold cross-section had already been exploited here, as it were – even if this is not objectively correct, because the larger cross-section is actually needed in this operating mode. The above-mentioned payback period of 13 years for an upgrade that goes even further is not absurdly long, but is within the range of the life cycle of such a system. This indicates that the factor 10 is not really absurdly high, but happens to represent the desired economic optimum. Therefore: Do not criticise demands in terms of design for continuous load, even for only sporadically utilised conductor cross-sections, simply implement them!

Helper 6: Harmonics and other system perturbations

IEC 60364-5-52 contains all sorts of limits for the current-carrying capacity for a variety of cables and a whole host of installation methods and grouping factors – although still only for two or three loaded wires. If harmonic currents occur with four loaded wires, the (now no longer very) new Supplement 3 to IEC 60364-5-52 gives further indications as to how to deal with these situations. However, it is extremely difficult to determine in advance how much of which harmonic current will actually flow. They do not all pile up in the neutral conductor. As a result, “fear factors” were incorporated into the guideline values in the supplement, so that under no circumstances “anything can happen”. The effect that the harmonics partially cancel each other out instead of adding up could not be taken into account, since the occurrence and possible extent of this effect cannot be predicted. In most cases, therefore, a thicker line will be chosen than is needed, although this certainly does not impair safety – and certainly not energy efficiency! We are again a little closer to the design based on lowest life cycle costs (instead of highest conductor temperature). Therefore: Do not criticise demands for designs with “fear factors” that appear excessive, simply implement them!

Helper 7: E-mobility and other sustained loads

Even the latest standards in the IEC 60364 series still contain statements such as: “The current I2 ensuring effective operation of the protective device shall be provided by the manufacturer. Protection in accordance with this clause may not ensure protection in certain cases, for example where sustained overcurrents less than I2 occur. In such cases, consideration should be given to selecting a cable with a larger cross-sectional area.” This means in effect that this standard says about itself: “Compliance with the requirements of this standard need not necessarily mean that your installation is safe.”

It is sentences such as these that now preoccupy many installation professionals and standard makers. Previously it simply did not happen that any building cable was exposed to its full current carrying capability for hours or even days. The background is that e.g. a circuit breaker B 16 A trips at the earliest at 17.6 A, at the latest at 23.2 A – and also not necessarily any earlier than after one hour. But what if an electric car is charged through such a connection? Because of this, special charging plugs have been developed instead of having recourse to familiar home plugs and CEE connectors. Whether CEE plugs are actually not suitable for continuous loads remains to be seen; the problem with the lines has therefore not yet been resolved. As always – sentences like the above should not need to appear in any standard. Remedy is long overdue – and could be so simple. You only have to look at other countries on this point (which otherwise look enviously at the high German standards) and

Fig. 11: How cheap can / should safety actually become?
Fig. 11: How cheap can / should safety actually become?
Fig. 12: Is it just the quantity that makes the 16 A MCB so “cheap”? Then any other one would also be affected in its place
Fig. 12: Is it just the quantity that makes the 16 A MCB so “cheap”? Then any other one would also be affected in its place
  • either generally use 2.5 mm² conductor cross-sections with final circuits fused 16 A – including single-phase
  • or generally fuse circuits designed with 1.5 mm² with 13 A. Feel free to install one more to offset any potential deficiencies.

We would be somewhat closer to a low-loss installation again. That the B 16 A circuit breaker is by far the cheapest (Fig. 11) is an objection that is often raised against this, but which is not improved by being repeated. Once again, cause and effect have been confused: The B 16 A circuit breaker can be offered so cheaply (Fig. 12) precisely because it is manufactured and sold in very large quantities. There are no technical grounds for this. If the focus shifts to another current rating, prices will follow. Prices are a matter of trade. Manufacturers think and act globally, and in other countries other sizes are the market leaders. For the manufacturers the piece numbers level out more or less.

Therefore: As long as the demands in the standards question the specification made in the same standard, do not wait for the protracted rectification of the deficiency, simply implement it!