Dimensions of the modeled cable arrangement.

## Abstract

The principal numerical and experimental results obtained by the authors on the harmonic power losses in low-voltage networks in the lighting area have been summarized in this review. Light-emitting diodes (LEDs) and compact fluorescent lamp (CFL) loads were considered. Four-core cables and four single-core cable arrangements were examined. The cables were modeled by using electromagnetic finite element analysis software. It was found that the cross section of the neutral conductor plays an important role in the derating of the cable ampacity due to the presence of a high level of triplen harmonics in the distorted current. In order to reduce the third-order harmonic currents in the neutral conductor, an experimental investigation of diversity factors for LED in combination with CFL and LED lamps was also performed. Attention was paid to the reduction of the third-order harmonic current, which is mainly responsible for the strong increase in power losses in the neutral conductor of low-voltage installations. The convenience of having LED lamps designed to operate as two-phase loads is suggested for certain applications.

### Keywords

- LED
- CFL
- non-linear lighting loads
- harmonic currents
- energy losses
- low-voltage networks

## 1. Introduction

Today, non-linear devices constitute a bigger part of the electrical load in industrial and commercial power systems. Non-linear devices generate harmonics in line currents, resulting in a large number of problems for electrical equipment, such as capacitors, circuit breakers, electronic equipment, metering, conductors and telephones [1, 2, 3]. The presence of harmonic currents in electric systems has increased in recent times due to several factors (increased use of solid-state energy conversion devices, industrial variable speed drive systems and cutting and welding equipment). Significant sources of harmonic currents in power systems also include electric devices such as compact fluorescent lamps (CFLs), power transformers operating near saturation and computer system installations [4, 5, 6].

Nowadays, with the technological advancement in semiconductors, light-emitting diode (LED) lamps are becoming a promising lighting technology due to its superior energy efficiency, longer lifetime and a better visual performance compared to most of the conventional light sources [7, 8, 9]. Due to these unique features, CFLs are now being replaced by LED, seeking a reduction in lighting costs and a lower impact on environment. In general lighting applications, a compact ac/dc (alternating current/direct current) converter should be used to supply dc current to LEDs, which introduces non-linearity to the system [10, 11, 12]. As non-linear loads, LEDs might produce highly distorted currents. Although the input power of a single LED is quite low, an incoming widespread use of them in lighting could create significant additional harmonic losses in the existing low-voltage lines [13]. Since several national standards allow for the neutral conductor reducing sizing with respect to the phase conductors, many of these existing low-voltage installations have the cross section of the neutral conductor approximately equal to half of the phase conductors.

A large number of works were conducted on LEDs as an energy-efficient lamp, but most of them have been devoted to the internal driver circuit design [10, 11, 12, 14, 15, 16, 17]. Several other works have concentrated on the light distribution and visual performance of LED lamps [18, 19, 20]. A few contributions focused on harmonic emissions of LED lamps [12, 21, 22, 23, 24].

When significant harmonic currents are present in low-voltage supply systems, additional Joule losses occur in the phase or line conductors as well as the neutral conductor. Significant harmonic currents may be present in secondary circuits of three-phase wye-connected transformers and single-phase transformers. Zero sequence harmonic currents flow in the phase conductors and are added in the neutral conductor, thus resulting in even higher harmonic current flow in the neutral conductor [25, 26]. Thus, the harmonic current flow in the neutral must be considered in the design of the supply system. The presence of harmonic currents in the supply conductors affects the ampacity of the supply system because of the additional ohmic losses [13, 26, 27, 28]. The determination of ohmic losses is complicated by the fact that the resistance of the cables is frequency dependent. Specifically, the resistance is increased with frequency because of the skin effect and proximity effect in the conductors and proximity effect from metallic conduit (if present) [26, 29]. The effects of harmonic currents in the neutral conductors can be evaluated with the same methods as for the phase or line conductors. However, the harmonic current magnitudes may be different in the neutral conductors due to non-cancelation of zero sequence harmonic currents and the cancelation of the positive and negative sequence harmonic currents. Thus, the neutral conductor becomes an additional heat-generating conductor and must be considered in the ampacity calculation for three-phase wye-connected and single-phase circuits [26, 27, 28]. Besides the knowledge of the increased losses due to harmonic currents, it is significant also for the economic evaluation of measures that attenuate harmonic currents. Such measures can be, for instance, passive or active harmonic filters [30, 31] or controlling the current unbalance in three-phase distribution systems by node reconfiguration [32].

A research on the diversity factor for combinations of LED lamps with powers in the range 3 to 8 W was presented in [33]. It was found that the diversity factor becomes smaller if a large number of lamps are combined. However, such a reduction was more significant for high-order harmonic currents. In particular, a diversity factor close to one for the third-order harmonic was found for the combinations studied. In [34] an investigation was presented on the diversity factor for combinations of LED and FCL lamps. The measurements showed a considerable reduction of the diversity factor for higher harmonic currents, but, on the other hand, the low-order harmonics did not show a significant decrease.

The principal numerical and experimental results obtained by the authors on the harmonic power losses in low-voltage networks feeding large LED and CFL loads have been summarized in this review. Attention was paid to the reduction of low-order harmonic currents, especially the third one, which is mainly responsible for the strong increase in power losses in the neutral conductor of low-voltage installations [13]. The convenience of having LED lamps designed to operate as two-phase loads is suggested for certain applications of significant power demand.

## 2. Harmonic losses in low-voltage networks

### 2.1. Harmonic emission of LED and CFL

Figure 1 shows the current in one phase and in the neutral conductor of a four-core cable that feeds a balanced load of three identical LEDs (one per phase). Specifically, Figure 1 was obtained by testing the Philips 8 W LED. It can be seen that the LED current is highly distorted with respect to a sinusoidal waveform and that the fundamental frequency of the current in the neutral conductor is 150 Hz (i.e. the frequency of the third harmonic). Because the third-order harmonic currents (and their multiples) are zero sequence, they are added to the neutral conductor. All experiments were done with an almost sinusoidal voltage waveform. The total harmonic distortion (THD) of the phase voltage waveform was relatively low (< 3%).

A frequency domain analysis of the current harmonics (_{pu}(* h*)) produced by several commercially available LEDs is presented in Figure 2. In this figure,

I

_{pu}(

*) was expressed in per unit of the fundamental current harmonic (*h

*= 1 corresponding to a harmonic frequency of*h

*= 50 Hz, with*f

*being the order of the harmonic).*h

The experimental data can be approximately described by the power law:

where * m* = − 1.2 ± 0.2. Eq. (1) (which is indicated by a solid line in Figure 2) defines the harmonic signature of the examined LED lamps. It is observed in Figure 2 that the amplitude of the harmonic currents decreases almost inversely with the order of the harmonic, thus indicating that the third-order one is usually the most significant one. Note that the data corresponded to LEDs from 3 to 120 W. FCLs also tend to present considerable amplitudes in their third-order harmonics [34]. Figure 3 shows the amplitude of the third harmonic current (expressed in per unit of the fundamental harmonic) of several commercially available LEDs and CFLs, with powers varying between 3 and 23 W. The red line (representing a constant value of 86%) indicates one of the criteria established by IEC 61000–3-2 [36] for the harmonic emission limits for lamps having an active input power < 25 W (i.e. that the third harmonic current should not exceed 86% of the fundamental one).

As it can be seen in Figure 3, the lamps tested meet the quoted emission limit imposed by IEC, except for one of them (LED 9 W Sica), which is slightly above it.

A power quality analyzer (Fluke 435-II) was used in the measurements presented here.

### 2.2. Numerical simulation of the harmonic losses in low-voltage networks

Two different types of cables were examined. The first type was an arrangement of four single-core cables in contact with each other, as they are specified by IEC 60502–1 [37]. The schematic of the used cable arrangement is shown in Figure 4, while its geometric dimensions are summarized in Table 1.

Nominal cable cross section [mm^{2}] | ||||
---|---|---|---|---|

Dimensions [mm] | 3 × 35 + 16 | 3 × 70 + 35 | 3 × 120 + 70 | 3 × 240 + 120 |

Phase conductor radius []_{p} | 3.3 | 4.7 | 6.2 | 8.8 |

Neutral conductor radius []_{n} | 2.3 | 3.3 | 4.7 | 6.2 |

Thickness of phase conductor insulation []_{p} | 2.6 | 2.8 | 3.1 | 4.0 |

Thickness of neutral conductor insulation []_{n} | 2.4 | 2.6 | 2.8 | 3.1 |

Distance [] | 8.4 | 10.6 | 13.1 | 18.0 |

Distance [] | 6.5 | 8.2 | 10.5 | 12.7 |

As the conductors in all cables were assumed solid in the modeling, the conductor dimensions showed in Table 1 are slightly smaller than the actual dimensions. This assumption leads to results that are on the conservative side. Cases where the conductors were copper and the cross section of the neutral conductor was approximately equal to half of phase conductors were modeled.

The second type corresponded to four-core cables as they were specified by CENELEC Standard HD603 [38]. In this case, a large cross-sectional sector-shaped cable, namely, 3 × 240 + 120 mm^{2}, was examined.

In a conductor where the conductivity is sufficiently high, the displacement current density can be neglected, and the conduction current density is given by the product of the electric field and the electrical conductivity (ohm’s law). With these simplifications, the Maxwell’s equations are

where * μ*is the magnetic permeability,

*is the conductor electrical conductivity and*σ

(where * V*is the electrostatic potential), and Eq. (2) becomes

The electromagnetic software [39] solved the diffusion equation (Eq. (5)) to obtain the spatial distribution of the total current density (* S*), having as input the measurable current in the conductor:

where * I*is the total current and

*is the dc conductor resistance (*R

_{dc}

(where * κ*is the conductor thermal conductivity and Λ =

*/2.4 and*R

*is the conductor radius) due to the non-uniform distribution of the Joule heat caused by the skin and proximity effects are very small because of the large value of the thermal conductivity.*R

At each harmonic frequency, the software calculates the losses per unit length in each conductor using the integral:

where * P*(

*) is the harmonic losses per unit conductor length and*h

*(*J

*) is the current density corresponding to the harmonic of order*h

*.*h

The cables were modeled in two dimensions assuming that at each harmonic frequency, balanced, three-phase and sinusoidal currents flow through them. The three-phase conductors were assumed carrying the following currents:

where * I*is the current peak value,

_{p}

*is the angle phase of the harmonic order*φ

_{h}

*and*h

*1,*L

*2 and*L

*3 are the three phases.*L

For non-triplen harmonic (* h*≠ 3

*, with*N

*= 1, 2, 3,…), the neutral conductor only carries the eddy currents calculated by the software. Notice that in this case,*N

*= 3*h

*+ 1 represents the direct sequence harmonics, while*N

*= 3*h

*– 1 represents inverse sequence harmonics. For triplen harmonics the current in the neutral conductor was assumed as*N

In order to obtain an accurate distribution of the current density over the conductor sections, it was checked that the size of the local numerical mesh was less than half the characteristic skin penetration length for each harmonic order.

The study domain for the cases of sector-shaped and four single-core cables, showing the non-uniform numerical grid (with up to about 4000 mesh cells), is presented in Figure 5. At the boundary of the domain (at a radius up to ten times the cable size), it was assumed that

The simulation results were obtained for * μ* = 4 π × 10

^{−7}H/m (non-magnetic material was considered). The copper electrical conductivity at 293 K was taken as

*= 5.8 × 10*σ

^{7}Ω

^{−1}m

^{−1}according to IEC 60028 [40]. The

*value was correspondingly corrected for other cable operating temperatures.*σ

Figure 6 illustrates the spatial distribution of the root-mean-square (rms) value of the total current density over the conductors of cables of large sections submitted to harmonic currents of different frequencies. Figure 6(a) corresponds to a 3 × 240 + 120 mm^{2} sector-shaped cable submitted to a 15 A (peak value) fifth-order harmonic current, while Figure 6(b) corresponds to an arrangement of four single-core cables (3 × 70 + 35 mm^{2}) submitted to a 30 A (peak value) third-order harmonic current. The magnetic field lines produced by the current are also shown in Figure 6. A noticeable reduction in the effective area of current circulation due to the skin and proximity effects is observed in Figure 6(a), thus causing a considerable increase of the ac conductor resistance (* R*ac) as compared to the dc resistance, (

*dc), which in turn results in high heat losses. In Figure 6(b) the neutral conductor is assumed to carry the algebraic sum of the phase currents.*R

To calculate the * L*1 and

*3 (Figure 4) are the same, but those in*L

*2 are different. The losses per unit length in the three-phase conductors, when a symmetrical current of rms value*L

*(*I

_{rms}

*) and of frequency*h

*1, L2 and*L

*3, respectively. The uneven heat generation inside the cable is a fact that also needs to be considered when calculating the derating of cable ampacity. According to [41], not only the average cable temperature but also the temperature at any point along the insulation of the cable should not exceed the maximum permissible one. Therefore, for derating of the cable ampacity, the maximum conductor losses should be considered and not their average. For non-triplen harmonic (*L

*≠ 3*h

*), the neutral conductor only carries the eddy currents calculated by the software, so the maximum cable losses can be represented by an effective conductor resistance per unit length*N

*(*R

_{eff}

*) for the harmonic order*h

*, which was defined as*h

where

When triplen harmonics are present, the neutral conductor picks up the current. An effective resistance that reflects the maximum losses of the phase conductors (

where

is the neutral conductor current for the harmonic current of order * h*. The resistances

^{2}four-core cable are shown in Figures 7(a) and (b), respectively. As expected, the ratio

This is mainly due to the increased losses in conductors * L*1 and

*3 when zero sequence currents flow in the phase conductors and thereby in the neutral conductors. The ratio*L

The simulation results corresponded to a conductor operating temperature of 343 K, which is the maximum conductor temperature for PVC-insulated cables according to IEC 60502–1 [12]. It was checked that large variations in this temperature value (in the range 283 to 343 K) only render slightly variations (less than 10%) in the conductor resistance ratio. The results of the employed electromagnetic model were validated by comparison to (a) the numerical model developed in [27] and (b) the formulae given in the standard IEC 60287–1-1 [42] for thee single-core cable arrangements. The differences in the calculated ratios

The cable losses can be approximately calculated by the following formula:

where the first term on the right-hand side represents the losses in the phase conductors and the second term is the losses in the neutral conductor. This second term is present only when triplen harmonics are considered (i.e. * h* = 3, 9, 15, 21, 29). The values of

were calculated by using the harmonic signature given by Eq. (1) for the cables described in Table 1 and for a 3 × 240 + 120 mm^{2} four-core cable as was specified by CENELEC Standard HD603 [38]. The results obtained for the upper bound of * m*(= − 1.0) are shown in Table 2. The assumption on the

*value leads to results that are on the conservative side.*m

Cable type | Nominal cable cross section [mm^{2}] | |
---|---|---|

Arrangement of four single-core cables | 3 × 35 + 16 | 2.1 |

3 × 70 + 35 | 2.1 | |

3 × 120 + 70 | 2.0 | |

3 × 240 + 120 | 2.3 | |

Four-core cable | 3 × 240 + 120 | 2.5 |

As it is observed in Table 2, for a four-core cable with a cross section of 3 x 240 + 120 mm^{2}, the power losses reach 2.5 times the value corresponding to an undistorted current of the same rms value of the first harmonic of the LED current. Even for cables with relatively small cross sections, such as 3 × 35 + 16 mm^{2}, this ratio reaches about 2.1. Furthermore, if the skin and proximity effects are neglected in the cable losses given by Eq. (18) (the conductor radius is small as compared to the characteristic skin penetration length and the distances of the nearby conductors are large as compared to the conductor radius) and thus * ξ*is not dependent on the cable cross section, the loss ratio still reaches 2.0 for

*= − 1.0. The increase in the losses is mainly due to the harmonic content of the distorted current.*m

As shown Table 2, large LED-like loads generate huge harmonic losses resulting in additional conductor heating. This heating will result in a higher-temperature rise of the cable which can exceed its rated temperature, thus requiring the derating of the cable ampacity.

## 3. Reduction of the harmonic losses in low-voltage networks

In order to reduce the third-order harmonic currents by properly combining lamps that have an important phase difference in their corresponding harmonic currents (rather than combining lamps in a random way), the phase angle (* φ*3) of the third-order harmonic currents was first measured (with respect to the fundamental harmonic voltage angle of the phase 1) for the CFL and LED lamps. The results are given in Table 3.

Lamp type | _{3} (degrees) | Lamp type | _{3} (degrees) |
---|---|---|---|

LED Alic 3 W | 95 | LED Philips 14 W | −33 |

LED Sylvania 5.5 W | −112 | LED TBC in 14 W | −126 |

LED Osram 8 W | −126 | LED Sica 15 W | −130 |

LED Philips 8 W | −77 | LED Philips 18 W | −125 |

LED Lumenac 8 W | −9 | CFL Sica 11 W | −114 |

LED Sica 9 W | −153 | CFL Osram 13 W | −111 |

LED Philips 9 W | −9 | CFL Philips 15 W | −111 |

LED GE 10 W | −49 | CFL Sylvania 20 W | −119 |

LED Philips 13 W | 2 | CFL Philips 23 W | −108 |

LED Sica 13 W | −129 |

Data in Table 3 correspond to time-averaged values over an interval of 5 minutes with a sampling rate of 1 S/s. The data were taken applying nominal voltage to the lamps once they acquired their stable working temperature. A power quality analyzer (Fluke 435-II) was used in the measurements. The experimental uncertainty (mainly due to statistical fluctuations) was within ±5°. In order to match the measuring range of the instrument used to the relatively small currents of the lamp combinations, the currents were measured by using low-inductance (around 0.1 mH) coils. It was verified during the measurements that the inductance introduced in the circuit by the coils does not appreciably affect the results. The uncertainty (± 2%) in the current measurement due to the position sensitivity of the used flexible current probe was accounted for. The information provided by the instrument was processed through the PowerLog 4.3.1 software.

During the measurements, the phase angles of the third-order harmonic currents were remarkably stable as shown in Figure 8. The corresponding experimental uncertainty (mainly due to statistical fluctuations) was within ±5°.

In order to achieve a considerable attenuation effect of the third-order harmonic currents for a given combination of lamps, they should not only fulfil with the condition that its third-order harmonic be strongly out of phase (as is the case of LED Alic 3 W and LED Philips 8 W), but also the amplitudes of each harmonic current should be similar, i.e. the ratio between the amplitudes of the third-order harmonic current of each lamp should be approximately united. Table 4 shows the results of the ratio between the amplitudes of the third-order harmonic currents for several selected combination types LED-LED and LED-CFL of the lamps used in this work. The corresponding experimental uncertainty (mainly due to statistical fluctuations) was within ±7%.

Lamp combination | Ratio between the amplitudes (rms) of the third-order harmonic current of each lamp of the combination |
---|---|

CFL Philips 23 W-LED Philips 18 W | 1.1 |

CFL Philips 15 W-LED Philips 13 W | 1.8 |

LED Lumenac 8 W-LED Sica 9 W | 1.9 |

LED Philips 13 W-LED Sica 13 W | 1.9 |

LED Osram 8 W-LED Lumenac 8 W | 2.3 |

CFL Sica 11 W-LED Philips 9 W | 2.6 |

LED Sica 9 W-LED Philips 9 W | 2.8 |

CFL Sica 11 W-LED Osram 8 W | 4.6 |

CFL Philips 15 W-LED Philips 14 W | 4.7 |

LED Philips 14 W-LED TBC in 14 W 114 W | 4.7 |

CFL Sica 11 W-LED GE 10 W | 6.7 |

CFL Sylvania 20 W-LED Philips 14 W | 6.8 |

To find the level of attenuation of the third-order harmonic currents as a consequence of the combinations of lamps, it is useful to define the diversity factor for the harmonic current, as the ratio between the vector sum (as measured) and the arithmetical sum (as calculated) of the third-order harmonic currents:

Note that a value of _{3} ≈ 1 indicates an inadequate combination of lamps, which generates a minimum attenuation of the third-order harmonic currents, whereas _{3} < < 1 implies an optimum combination, with a maximum attenuation of this harmonic current. Figure 9 shows the dependence of measured _{3} for selected lamp combinations on the difference between the corresponding phase angles of the third-order harmonic currents. The solid curves represent the diversity factor calculated for limit values of the ratio between the amplitudes of the third-order harmonic current of each lamp of the combination (values calculated for a ratio = 1 are indicated with a blue line while for a ratio = 7 with a red line). Note that these values are close to the minimum and maximum ratios obtained in the different combinations proposed, as it was indicated in Table 4.

It is seen in Figure 9 that a number of combinations of LED and CFL lamps lead to a considerably decrease in the content of the third-order harmonic current. As expected, the maximum attenuation of the third harmonic amplitude is achieved with harmonic ratios close to 1 and for harmonic phase angle differences close to 180°. These results are different from those reported by other studies [33, 34] where lower-order harmonics did not exhibit a very large reduction in amplitude. However, it should be noted that in [33, 34] random combinations of lamps were used.

Note that the results presented in Figure 9 were obtained combining two lamps; however, the same results could be obtained between two arbitrary sets of lamps, provided that each set is formed by the same number of elements. Currently, CFLs are being replaced by LEDs gradually, and in several lighting installations, the two technologies coexist. From the point of view of the reduction of the third harmonic, the combinations of lamps of different technologies are usually convenient. For the lamps evaluated, the change of technology (CFL to LED) not only improves the level of illumination and reduces the content of third harmonic but also decreases the active power demanded by the installation, reducing also the environmental impact.

In order to better show the contribution of the proposed solution, the measured spectrum of the harmonic currents (expressed in per unit of the fundamental harmonic current), both in one phase and in the neutral conductor of a four-core cable, feeding balanced single-phase loads formed by selected LED-LED combination is shown in Figures 10(a) and (b), respectively. The corresponding spectrums for the individual lamps are also shown. Harmonic currents up to the order * h* = 19 were measured. In addition, the rms value of the total current in both conductors is presented in Figures 10(a) and (b).

It is seen in Figure 10 that the selected LED combination leads to a significant decrease in the third-order harmonic content of the line current. Notice also that the RMS value of the total current of the combination is considerable lower than the corresponding value of the individual lamp having the higher harmonic content of the combination (LED Sica 9 W), being similar to that of the LED Lumenac 8 W.

As it can be seen in Figure 10, the RMS value of the total current of the combination is strongly reduced with respect to that of the LED Sica 9 W, mostly due to a decrease in the content of the third-order harmonic current, although some reduction is also observed for the high-order harmonics. It is important to note that the current of the LED Sica 9 W has a strong component of the third-order harmonic (exceeding the emission limit imposed by IEC as quoted in Section 1) and also of high-order harmonics (* h* = 9 and 15). As the overall harmonic power losses in the neutral conductor depend on the RMS value of the total current, a marked reduction in the harmonic losses with respect to that of the LED Sica 9 W (and even with respect to the LED Lumenac 8 W) is expected for the tested lamp combination.

Notice also the negligible small value of the first-order harmonic current in the neutral conductor due to the balanced loading of the cable. The small residuals observed are due in part to small asymmetries attributable to the constructive differences between the lamps tested.

The cable harmonic power losses can be approximately calculated by Eq. (18). To quantify the reduction in the harmonic power losses due to the lamp combination, it is useful to compare the above calculated cable losses with the losses produced in an identical cable but carrying an undistorted electric current of the same RMS value as the first harmonic current of the distorted current. To do this, the cable loss ratio defined as

(the first-order harmonic current in the neutral conductor is due to small asymmetries in the single-phase loads) was calculated on the basis of the measured data by neglecting the influence of the harmonic frequency on the resistance of the conductors (i.e. the conductor radius is small compared to the characteristic skin penetration length, and the distances of the nearby conductors are large compared to the conductor radius [29]). For a neutral conductor having a cross section equal to half of the phase conductor section [38], it results in a value of 9.6, 3.3 and 2.8 for the individual lamps LED Sica 9 W and LED Lumenac 8 W and for the combination, respectively, thus showing that the tested lamp combination leads to a significant decrease in the power harmonic losses. A similar result can be obtained for other lamp combination provided that the diversity factor for the third-order harmonic current of the arrangement is small enough.

Note that in lighting loads of substantial power demand such as those considered in this work, it would be convenient from the point of view of the reduction of the power losses to connect the LED lamps between lines (rather than between a line and the neutral conductor). In such case, the third-order harmonic currents (and their multiples) cannot flow through the network since the return path through the neutral conductor does not exist. This suggests the convenience of having LED lamps including ac/dc converters designed to operate as two-phase loads. As quoted before, a large number of the existing low-voltage installations present a neutral conductor with a reduced section (about half of the phase conductor) [38]. These installations when feeding LED loads could present more than twice the losses corresponding to a current without distortion of the same rms as the value of the first harmonic current of the lamps [13]; thus, a marked reduction (over ~ 50%) in the overall harmonic power losses can be expected if the LED lamps (having ac/dc converters designed to operate as two-phase loads) are connected between lines instead as single-phase loads.

## 4. Conclusions

Calculation of harmonic disturbances in low-voltage network installations having the neutral cross section approximately equal to half of the phase conductors when used for feeding large LED lighting loads was reported. The cables were modeled by using electromagnetic finite element analysis software. Four-core cables and four single-core cable arrangements (three phases and neutral conductor) of small, medium and large conductor cross sections were examined. This study has shown that:

The cross section of the neutral conductor plays an important role in the harmonic losses and thus in the derating of the cable ampacity, due to the presence of a high level of triplen harmonics in the distorted current.

An incoming widespread use of LED lamps in lighting could create significant additional harmonic losses in the supplying low-voltage lines, and thus more severely harmonic emission limits should be defined for LED lamps.

In order to reduce the third-order harmonic currents in the neutral conductor, an experimental investigation of diversity factors for LED in combination with CFL and LED lamps was also performed. An experimental investigation of diversity factors for LED (light emitting diode) in combination with CFL (compact fluorescent lamps) and LED lamps with nominal powers <25 W was presented. In contrast to other works, attention was paid to the reduction of low-order harmonics, especially the third one, which is mainly responsible for the strong increase in power losses in the neutral conductor of the low-voltage installations. The results showed that a number of selected combinations of LED and CFL lamps lead to a considerable decrease in the content of the third-order harmonic current. These results are different from those reported by other studies where lower-order harmonics did not exhibit a very large reduction in amplitude. However, it should be noted that in those studies random combinations of lamps were used. The convenience of having LED lamps designed to operate as two-phase loads is suggested for certain applications of significant power demand.

## Acknowledgments

N. M. and L. P. acknowledge financial support by the National Technological University (PID 3568). L. P. and M. A. L. are members of the CONICET. We have reused our own original work published in * Advanced Electromagnetic Journal*to write part of the presented chapter.