APPLICATION OF DIGITAL CELLULAR RADIO FOR MOBILE LOCATION ESTIMATION


IIUM Engineering Journal, Vol. 22, No. 1, 2021 Yudaev et al. 
https://doi.org/10.31436/iiumej.v22i1.1569 

THE HARMONIC COMPOSITION OF CURRENT IN 

ZERO-WORKING WIRE WITH NON-LINEAR LOAD 

IGOR V. YUDAEV1*,  EVGENY V. RUD2, MIKHAIL A. YUNDIN3,  

TAMARA Z. PONOMARENKO2 AND ALEKSANDRA M. ISUPOVA3

1
Department of Thermal Engineering and Information Management System, 

Azov-Black Sea Engineering Institute of Don State Agrarian University, 

Zernograd, Russian Federation 
2
ICPE “Energy Institute for Advanced Studies of the PJSC “Kubanenergo”, 

Krasnodar, Russian Federation 
3
Department of Electric Power and Electrical Engineering,  

Azov-Black Sea Engineering Institute of Don State Agrarian University, 

Zernograd, Russian Federation 

*
Corresponding author: yudaev5303@ubogazici.in 

     (Received: 4th August 2020; Accepted: 14th October 2020; Published on-line: 4th January 2021) 

ABSTRACT:   The purpose of this study was experimental investigations and a study of 

the nature of the change in the main harmonic components of the current in the neutral 

working wire of a three-phase four-wire network with a voltage of 0.38 kV. The study of 

the amplitude-phase-frequency characteristics of currents flowing in an electric network 

with a predominant non-linear load is one of the most urgent tasks, the solution of which 

will increase the efficiency of electric power transmission and eliminate the negative 

consequences due to the current flow in a zero-working wire in the network at 0.38 kV. 

To study the effect of load changes on the amplitude-phase-frequency characteristics of 

currents in the linear and zero working wires at the input of the load node, measurements 

were carried out by certified electrical measuring instruments namely, the “Resource-

UF2M” and “Hioki 3196”. With these devices, the phase voltages at the input to the load 

node were measured. The analysis of the results obtained for the load node whose power 

was formed mainly by a lighting system with fluorescent and LED lamps and a system of 

office electrical receivers (computers, copiers, printers, scanners, etc.) was performed. It 

can be concluded that a current comparable to the currents of the linear wires of the 

network flows from the load node with the predominant nonlinear power receivers through 

the zero-working wire. At the same time, in the zero-working wire of the network, the 

third harmonic current prevails over the main frequency currents.  

ABSTRAK: Tujuan kajian ini adalah penyelidikan eksperimental dan kajian mengenai 

sifat perubahan komponen harmonik utama arus dalam wayar kerja neutral rangkaian 

empat wayar tiga fasa dengan voltan 0.38 kV. Kajian mengenai ciri-ciri frekuensi-

amplitud-fasa arus yang mengalir dalam rangkaian elektrik dengan beban bukan linear 

yang dominan adalah salah satu tugas yang paling mendesak, penyelesaiannya akan 

meningkatkan kecekapan penghantaran tenaga elektrik dan menghilangkan akibat negatif 

yang disebabkan ke arus semasa dalam wayar sifar bekerja di rangkaian pada 0.38 kV. 

Untuk mengkaji kesan perubahan beban pada ciri frekuensi-fasa frekuensi arus dalam 

wayar linier dan sifar pada input nod beban, pengukuran dilakukan oleh alat pengukur 

elektrik yang disahkan iaitu, "Resource-UF2M" dan "Hioki 3196". Dengan peranti ini, 

voltan fasa pada input ke simpul beban diukur. Analisis hasil yang diperoleh untuk simpul 

beban yang kekuatannya dibentuk terutama oleh sistem pencahayaan dengan lampu 

pendarfluor dan LED dan sistem penerima elektrik pejabat (komputer, mesin fotokopi, 

pencetak, pengimbas, dll.). Dapat disimpulkan bahawa arus yang setanding dengan arus 

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wayar linier rangkaian mengalir dari nod beban dengan penerima kuasa bukan linier yang 

dominan melalui wayar sifar. Pada masa yang sama, dalam wayar sifar rangkaian, arus 

harmonik ketiga berlaku berbanding arus frekuensi utama. 

KEYWORDS: three-phase four-wire network; zero working wire of the network; harmonic 

currents; non-symmetry; non-linear power receiver 

1. INTRODUCTION  

The main reasons for current appearance in the zero-working wire of a three-phase four-

wire network are the asymmetry of the loads in the phases and presence of nonlinear power 

receivers. When flowing through a zero-working wire, the components of the currents of 

higher harmonics and asymmetries cause additional losses of voltage and electricity; 

reduction in the service life of cable lines; increase the resistance of grounding devices of 

electrical installations; and interference in low-voltage communication lines [1-6]. 

The study of the amplitude-phase-frequency characteristics of currents flowing in an 

electric network with a predominant non-linear load is one of the most urgent tasks, the 

solution of which will increase the efficiency of electric power transmission and eliminate 

the negative consequences due to the current flow in a zero-working wire in the network at 

0.38 kV [7]. 

Since the spectral composition of currents in real electric networks is influenced by a 

large number of simultaneously influencing factors (the composition of power receivers in 

the load node, their connection diagram, switching frequency, etc.), the study of the 

harmonic composition of currents of the most common typical consumers is of practical 

interest. The power of the load node under study was formed mainly by a lighting system 

with fluorescent and LED lamps and a system of office electrical receivers (computers, 

copiers, printers, scanners, etc.) [8]. 

To study the effect of load changes on the amplitude-phase-frequency characteristics 

of currents in linear and zero working wires at the input of the load node, measurements 

were carried out by certified electrical measuring instruments [9]. The “Resource-UF2M” 

and “Hioki 3196” devices controlled currents in linear and zero working (“Hioki 3196”) 

wires. At the same time, the same devices measured the phase voltages at the input to the 

load node. 

2.   CHARACTERISTICS OF THE DISTORTION COEFFICIENT OF 

THE SINE CURVE IN ACCORDANCE WITH DAILY CHANGES 

The change in the total active power at the input of the load node during the day is 

shown in Fig. 1. The range of changes in the total active power is large – from 5 kW at night 

up to 68 kW during the day. The greatest loads were during daylight hours from 7:30 to 

17:00 hours. The minimum value of the total active power, as seen in Fig. 1, was recorded 

in the morning (from 5:00 to 7:00 hours), and the maximum – in the daytime from 12:00 to 

13:32 hours. As can be seen from Fig. 1, the power consumption of the load node occurred 

according to a two-stage schedule. 

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Fig. 1: Schedule of changes in total active power at the input of the load node. 

Moreover, the change in active capacities during the day is very asymmetric in the 

network phases (Fig. 2). The active power P1 of the first phase L1 during the day turned out 

to be the smallest most of the time. Separate bursts of active power P1 of phase L1 were 

clearly observed in the period from 5:00 to 6:00 hours, when the load was the greatest. Most 

of the day, the greatest load fell on the L3 phase with an active power of P3. Only in the 

period from 14:00 to 16:32 hours the active power of P2 exceeded P3. 

 
Fig. 2: Daily graphs of changes in active powers for the phases of the network  

0.38 kV at the input of the load node. 

Due to the asymmetric load of the phases, the voltage asymmetry coefficients in the 

zero and reverse sequences of the fundamental frequency were significant (Fig. 3). So, for 

example, the voltage asymmetry coefficient in the zero sequence of the fundamental 

frequency (K0U) did not fall during the day, even with a minimum (below 2%) load. During 

periods of greatest power consumption (from 8:00 to 17:00 hours), the voltage unbalance 

coefficient in the zero sequence of the fundamental frequency often exceeded 5%. 

The voltage asymmetry coefficient in the reverse sequence of the fundamental 

frequency (K2U) during the day had lower values. Moreover, it turned out to be more stable 

than the coefficient K0U. The range of variation of K2U ranged from 2% to 4%. The results 

of these studies, as well as an analysis of literature [10-15] indicate that the active use of 

switching power supplies in electrical appliances leads to an increase in harmonic distortions 

of voltages and currents in the electrical network. Moreover, the distortion coefficients of 

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the sinusoidality of the voltages have lower values than the distortion coefficients of the 

sinusoidality of the load currents. 

 

Fig. 3: Diagrams of daily changes in the voltage asymmetry coefficients in the zero 

and reverse sequence at the input of the load node with the prevailing non-linear 

power receivers. 

Figure 4 shows graphs of daily changes in the distortion coefficients of the sinusoidality 

of the voltage curves in the phases of the network at the input of the load node 0.38 kV. It 

should be noted that in none of the phases at the input of the load node, the distortion 

coefficient of the sinusoidality of the voltage curves did not exceed the minimum allowable 

value – 8%. 

 

Fig. 4: Diagrams of daily changes in the distortion coefficients of the sinusoidality 

of the phase voltage curves at the input of the load node with predominant non-

linear power receivers. 

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During periods of maximum load (from 8:00 to 17:00 hours), the distortion coefficient 

of the sinusoidality of the voltage curve in the first phase KU1 was the largest, more than 6% 

(see Fig. 4). During load shedding, the distortion coefficients of the sinusoidality of the 

voltage curves in phases became the same (over 2%). The average amplitude-frequency 

characteristic of the most significant average daily coefficients of the 3rd, 5th, 7th, 9th and 

11th voltage harmonics in the phases of the network 0.38 kV at the input to the load node 

(Fig. 5) clearly show that the odd harmonic voltage components prevail over even ones. 

Among the odd higher voltage harmonics, the 3rd, 5th, and 9th harmonics had the 

largest amplitudes. It should be noted that the largest amplitudes of the 3rd and 5th voltage 

harmonics were recorded in the first phase, and the 9th voltage harmonic was the largest in 

the second phase of the network 0.38 kV (Fig. 5). The coefficients of the 3rd voltage 

harmonic by phase at the input to the load node varied from 4.7% to 5.5%, the coefficients 

of the 5th voltage harmonic, respectively, from 1.4% to 2.5%, and the coefficients of the 9th 

voltage harmonic, respectively, from 1.0% to 1.4% (Fig. 5). 

 
Fig. 5: Frequency response of the most significant daily average coefficients of the 

n-th harmonic components of the phase voltage at the input of the load node. 

3.   CHANGES IN CURRENT PARAMETERS AT VARIOUS LOADS 

OF THE POWER RECEIVER 

To assess the degree of distortion of currents sinusoidality during the period of the 

highest loads, the waveforms of the phase currents and in the zero-working wire at the input 

of the load node were recorded using the “Hioki 3196” instrument (Fig. 6). 

The current waveforms correspond to the time interval on the daily graph of the change 

in the total active power at the highest load (from 11:40 to 12:00 hours according to the 

schedule of Fig. 1). An analysis of the current shape in the zero-working wire i4(t) on the 

waveform shows (Fig. 6) that it is not substantially sinusoidal. The waveforms of currents 

in the linear wires of the load node i1(t), i2(t) and i3(t) are also significantly distorted by 

higher harmonics. 

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Fig. 6: A fragment of the waveforms of the phase currents and the zero-working 

wire at the input of the load node with the prevailing non-linear power receivers. 

Using the “Hioki 3196” software package, the amplitudes and phases of the currents 

were determined for seven significant harmonic components not equal to zero (odd 

harmonics from the 1st to the 13th). For compact recordings, these transformations are 

presented in the form of Fig. 7, which also shows mathematical models (expressions) of 

instantaneous current values at the input to the load node.  

In Fig. 7, the Fourier expansion is performed up to the 50th harmonic of the current. 

This allows us to justify the selection of the seven most significant harmonic components 

of the current by comparison. The sinusoidal distortion coefficients of the curves (see Fig. 

7) are denoted by THD (Total Harmonic Distortions) and are called the “total current 

harmonic distortion coefficient”. 

As can be seen from Fig. 5, the values of the sinusoidality distortion coefficients of the 

current curves THDI1, THDI2 and THDI3 significantly exceed the similar voltage 

coefficients. In the first linear wire L1 at the input of the load node, the total THDI current 

distortion factor for the considered time was 23.7%, in the second wire L2 – 15.98%, in the 

third wire L3 – 36.18%, and in the neutral wire – 138.35%, respectively. 

The analysis of the harmonic composition of the current of the zero-working wire i4(t) 

is of interest. As can be seen from Fig. 1, in the working (mean square) current I4, the 

proportion of the main harmonic of the current is 6.77 A. The proportion of the third 

harmonic components of the currents flowing in the linear wires of the network 0.38 kV, in 

the zero working wire for the considered time point, is 8.9 A, in 5th harmonic current, 

respectively, 2.33 A, 7th – 0.79 A, 9th – 1.13 A, 11th – 0.51 A and 13th – 0.58 A. In this 

case, the total current load of the zero-working wire for the considered time was equal to 

12.48 A.  

With this load mode, the current values in the linear wires of the network 0.38 kV were 

as follows: I1 = 16.63 A; I2 = 13.54 A; I3 = 18.8 A. That is, the current load of the zero 

working wire is commensurate with the load of the linear wires. Obviously, the third and 

ninth current harmonics make the main contribution to the increase in the current load of 

the zero-working wire to the values of the currents flowing in the linear wires of the network 

0.38 kV. 

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Fig. 7: Vector diagrams of currents and voltages at a frequency of 150 Hz at the 

input of a load node with predominant nonlinear power consumers: 

(a) (b) 

(c) (d) 

(e) (f) 

(g) (h) 

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a), b) – 𝑖1(𝑡) = √2 ∙ (

15,26 𝑠𝑖𝑛(𝜔𝑡 + 2°) + 3,14 𝑠𝑖𝑛(3𝜔𝑡 − 163°) +

+1,31 𝑠𝑖𝑛(5𝜔𝑡 + 16°) + 0,19 𝑠𝑖𝑛(7𝜔𝑡 − 44°) + 0,78 𝑠𝑖𝑛(9𝜔𝑡 − 165°) +

+0,59 𝑠𝑖𝑛(11𝜔𝑡 + 27°) + 0,30 𝑠𝑖𝑛(13𝜔𝑡 − 153°)
)А 

c), d) – 𝑖2(𝑡) = √2 ∙ (

13,34 𝑠𝑖𝑛(𝜔𝑡 − 130°) + 1,34 𝑠𝑖𝑛(3𝜔𝑡 − 173°) +

+1,22 𝑠𝑖𝑛(5𝜔𝑡 + 88°) + 0,86 𝑠𝑖𝑛(7𝜔𝑡 + 2°) + 0,47 𝑠𝑖𝑛(9𝜔𝑡 − 42°) +

+0,09 𝑠𝑖𝑛(11𝜔𝑡 + 116°) + 0,30 𝑠𝑖𝑛(13𝜔𝑡 − 0°)
) А 

e), f) – 𝑖3(𝑡) = √2 ∙

(

17,63 𝑠𝑖𝑛(𝜔𝑡 + 115°) + 5,20 𝑠𝑖𝑛(3𝜔𝑡 + 156°) +

+3,26 𝑠𝑖𝑛(5𝜔𝑡 − 177°) + 1,08 𝑠𝑖𝑛(7𝜔𝑡 − 137°) + 0,72 𝑠𝑖𝑛(9𝜔𝑡 + 164°) +

+0,68 𝑠𝑖𝑛(11𝜔𝑡 + 167°) + 0,69 𝑠𝑖𝑛(13𝜔𝑡 + 162°)
)А 

g), h) – 𝑖4(𝑡) = √2 ∙ (

6,77 𝑠𝑖𝑛(𝜔𝑡 − 82°) + 8,90 𝑠𝑖𝑛(3𝜔𝑡 − 7°) +

+2,33 𝑠𝑖𝑛(5𝜔𝑡 − 37°) + 0,79 𝑠𝑖𝑛(7𝜔𝑡 + 103°) + 1,13 𝑠𝑖𝑛(9𝜔𝑡 + 17°) +

+0,51 𝑠𝑖𝑛(11𝜔𝑡 − 73°) + 0,59 𝑠𝑖𝑛(13𝜔𝑡 − 10°)
)А 

 

 

Fig. 8: Vector diagrams of currents and voltages at a frequency of 50 Hz at the input 

of a load node with predominant nonlinear power consumers. 

Figure 8, obtained using the “HIOKI 3196” instrument software, shows the logical 

vector diagrams of currents and voltages at the input of the load node with prevailing 

nonlinear power receivers at time 11:42 (see Fig. 1). Along with this, the amplitude of the 

third harmonic of the current i4(t) is greater than the amplitude of the fundamental harmonic.  

In addition to the current values of voltage and current, the phase shifts of each value 

are also indicated here. For the first harmonic (frequency 50 Hz) the components of the 

direct (Positive), reverse (Negative) and zero (Zero) sequences of voltages and currents are 

given. With these components, real three-phase voltage and current systems can be balanced 

to a symmetrical system. Similar characteristics for the considered time and frequency of 

150 Hz are presented in Fig. 9. 

A distinctive feature of the vector diagrams of voltages and currents of the third 

harmonic (Fig. 9) is the lack of common mode between the vectors of different phases. 

Along with the lack of phase matching of vectors, they are also characterized by inequality 

in magnitude. So, for example, the effective current of the third harmonic in the first phase 

is 3.14 A, in the second phase is 1.34 A, and in the third phase is 5.2 A (see Fig. 1). This is 

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explained by the nature of the formation of these currents in the load node in case of 

accidental switching on of various power consumers under different voltages. 

 

Fig. 9: Vector diagrams of currents and voltages at a frequency of 150 Hz at the  

input of a load node with predominant nonlinear power consumers. 

4.   CONCLUSIONS 

The research contribution of this work lies in the fact that an experimental study was 

carried out, the nature of the change in the fundamental harmonic components of the current 

in the zero-working wire of a three-phase four-wire network with a voltage of 0.38 kV was 

studied. The results obtained during the work will increase the efficiency of electric power 

transmission and eliminate the negative consequences due to the current flow in a zero-

working wire in the network 0.38 kV. 

The analysis of the research results shows that in the presence of non-linear power 

receivers, the current in the zero-working wire of a three-phase four-wire network is 

comparable with the currents in linear wires. So, in the maximum load mode, with the 

current value of the zero working wire current 12.48 A, the currents of the linear wires were 

I1 = 16.63 A, I2 = 13.54 A, and I3 = 18.8 A, respectively. 

Based on the obtained results of the study, it can be argued that the currents of the third 

harmonic component, which dominate in the neutral working wire of the network 0.38 kV, 

are not in-phase in the linear wires. The results obtained are of great practical importance 

when designing technical means that provide current unloading of the zero-working wire of 

the network 0.38 kV and, ultimately, reduce energy losses during transmission. 

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