Harmonic present in Neutral Current for 3Phase 4Wire

Star Connected Balanced Power System

Faculty of Electrical Engineering

Abstract- When we have a balanced 3 phase 4 wire system, there will not be any current
flowing in the neutral in a balanced 3 phase 4 wire system unless there is a presence of
harmonic current in the system. This assignment shows us when the harmonic current is
occurring in the system, there will be a current in the neutral. When we have the 3phase 4
wire star connected source with single phase full wave (uncontrolled) rectifiers connected in
each phase has a severe neutral current due to harmonics present in the line current. The
system will have the main sources of harmonics present in the line current. These
harmonics will have affect currents at the neutral wire with excessive heating of the line. In
this report we have done simulation for two different cases. These cases are 3 phase 4 wire
with two sources induction and 3 phase 4 wire with three sources induction. The simulation is
done by use of PSpice; we compare the results obtained from theoretical analysis with that comes from
simulation. We will see that they are close to each other and there is no much error.

Keyword-Harmonic content, 3-phase balanced system, neutral current, 3rd harmonic current, conductor size

I. INTRODUCTION

A balanced 3 phase 4 wire power system does not have any neutral current present. On the
other hand, if we have 3 phase unbalanced system, the system will have heavily neutral current.
This current will transfer high level of heating. By using of many electronic devices in electrical
distribution systems has raised the level of concern about the effects of “non-linear” loads on these
systems. Three phase non-linear loads such as motor drives, silicon controlled rectifier (SCR)
controllers, large uninterruptible power systems (UPS), and other similar devices can create their
own set of distinct problems, but do not contribute to neutral current. Of special concern are single
phase devices with rectifier front-end power supplies such as computers, electronic lighting ballasts,
and other similar electronic devices. When these types of loads are connected line to neutral in a
three phase wye-connected power system, the neutral conductors in the three phase feeders can
carry surprising levels of current, even with the loads balanced on the three phases. In this case the
magnitude of neutral current is based on the triplen harmonics in the line current. Due to these
effects, the neutral cable will be de-rated, and this will result in the overloading and heating of the
cable and eventually the cable fails. This work analyses the effect of harmonic present in the system
for neutral wire of 3phase 4 wire star connected source with full wave uncontrolled rectifiers
1
 connected between each phase and neutral. The analysis is done using PSpice software and all
results are captured and presented here for analysis. The line current and neutral currents are
measured from output waveforms. Both time domain transient analysis and frequency domain Fast
Fourier Transform (FFT) analysis are performed. Also, proposes the suitable size of conductor to be
used for the considered application based on the IEC 60364-5-52 guidelines [1].

Contrary to traditional thinking, efforts made to balance loads on the three phases that are
under high current distortion conditions, may even contribute to increased neutral current. Since
the IEEE has prohibited neutral conductor overcurrent protection, proper sizing of neutral
conductors is a concern when supplying large numbers of single phase non-linear loads. (An
exception is when the overcurrent device opens all conductors of the circuit including the neutral.)
To realistically evaluate the need for neutral oversizing, it’s important to differentiate between the
types of single phase electronic loads.

II. NEUTRAL CURRENT AND HARMONICS

A. Analysis of Neutral Current in Balanced 3-Phase System due to Harmonics because the
three phase star connection have the neutral line.

Fig. 1 shows the schematic diagram of a 3 Phase 4 Wire Start connected Source with Full wave rectifier
in each Phase as considered in [2].

The individual single-phase rectifier system is connected to each phase and neutral as shown in the
Fig.2. In ideal case, the neutral current will be zero. When there is harmonic present in the system there
will be current flowing in the neutral due to the triplen harmonic present in the system.

Fig. 3 shows the neutral line current wave form for such a system.

2
We can calculate the line current in terms of fundamental current and harmonic currents as below;

Where k = 1,2, 3…….

Assuming a balances 3-phase supply and identical loads, the currents phase “b” and “c” are shifted by
1200 and 2400.

i n=i a +i b +i c
∞ ∞
ia =ia1 + ∑ iah = √2 I s1 sin (ω1 t−ϕ1 )+ ∑ √2 I sh sin (ωh t−ϕh )
h=2 k+1 h=2k+1
∞
ib =√ 2 I s 1 sin(ω 1 t−ϕ 1−120 )+ o
∑ √2 I sh sin( ωh t−ϕh−120 0 )
h=2 k+1
∞
ic= √2 I s1 sin(ω1 t−ϕ1 −240 o )+ ∑ √ 2 I sh sin(ωh t−ϕh−2400 )
h=2 k +1

When we add up all the above equations for line currents, non-triplen harmonics and fundamental
frequency components will be cancelled out and the neutral current becomes,
∞
in =3 ∑ √ 2I sh sin(ωh t−ϕh )
h=3(2 k−1)

( )
∞ 1/2
in=3 ∑ I 2
h=3(2k−1) sh

3
When the value of ‘h’ increases, the magnitude of harmonic current decreases. Therefore, considering
the most significant harmonic component of h=3,

i n =3 I s3

Wherei n is the RMS neutral current and I s 3 is the third harmonic current. Through
mathematical analysis, it can be shown that the high neutral current is approximately three
times the third harmonic component in the line current.
Using the Pspice simulation program, the issue described at the beginning of our discussion will
be addressed above. The circuit below is a three-phase star connection voltage source
connected to the neutral line. Each phase is connected to a full wave rectifier which in turn
feeds a 20-ohm resistance load and capacitive load 5 mF. A resistance of 1 ohm was added to
the neutral line to facilitate measurement of the neutral current.

B. Neutral Cable/Wire Sizing

Cable or wire is used to transfer energy or current continuously. Cables will be sized for the
maximum current carrying capacity without increasing its rated temperature. Here we need to find out
the current flowing in the neutral from the simulation output due to the harmonics in the system and
size the cable/wire accordingly. The continuous current carrying capacity will be arrived by considering
the de-rating factors for ampacity [3] apart from other factors like ambient temperatures and laying
methods. Here we have considered the guidelines of IEC 60364- 5-52 standard [1] for cable current de-
rating factor due to the harmonics. As per [1], the neutral conductor shall be sized according to any one
of the suitable methods below;

1. Size of neutral conductor shall be at least equal to line conductors if;

- Single phase circuits using two conductors

- Multi-phase circuits with line conductor size less than or equal to 16mm2 copper or 25mm2
aluminum.

- Three phase circuits carrying 3rd harmonic currents and odd multiples of 3rd harmonic currents and
total harmonic distortion is between 15% to 33%.

2. Where the third harmonic and odd multiples of third harmonic currents is higher than 33 %, total
harmonic distortion, it may be necessary to increase the cross-sectional area of the neutral conductor;

- For multi-core cables, the cross-sectional area of the line conductors is equal to the cross-sectional
area of the neutral conductor, this cross-sectional area being chosen for the neutral to carry 1,45 design
current of the line conductor;

- For single-core cables, the cross-sectional area of the line conductors may be lower than the neutral
crosssectional area, the calculation being made:

a) for the line: at design current of circuit

b) for the neutral: at a current equal to 1,45design current of the line.

4
 3. For polyphaser circuits where the size of line conductors is greater than 16 mm2 copper or 25 mm2
aluminum, the size of the neutral conductor may be lower than the size of the line conductors if the
following conditions are fulfilled simultaneously:

- the load carried by the circuit in normal service is balanced between the phases and the third
harmonic and odd multiples of third harmonics currents do not exceed 15 % of the line conductor
current;

- the neutral conductor is protected against overcurrent

- the cross-sectional area of the neutral conductor is not less than 16 mm2 copper or 25 mm2
aluminum. Also, there is a guideline for rerating factor in association with heating effect. In Table E.52.1
of Annexure E, IEC [1] provides the effect of harmonic current on balanced 3-phase system based on 3rd
harmonic content. The same data has been reproduced here for easy reference in Table-1 below.

The values of 3rd harmonic current and fundamental line currents can be measured from the simulation
output. Based on which the percentage of 3rd harmonic line current to the fundamental line current
can be calculated. Based on the value of the above, the de-rating factor needed for neutral and phase
conductors shall be selected from TableI and to be considered for conductor sizing.

II. SYSTEM DESCRIPTION

As discussed, the below fig show us 3 phase 4 wire two sources induction star connection
simulation circuit. The presence of power electronic equipment in the system will contribute to the
harmonic content in the system. In this work a 400Vrms, 3Ph, 50Hz, 4 wire start connected source
with neutral solidly grounded has been considered. Full wave three phase uncontrolled rectifier
with capacitance of 5mF and load resistance of 20 Ohm is connected across each phase and neutral
to simulate a 3-phase 4 wire star connected balanced system [2]. Each neutral is connected back to
the source neutral via adequately sized wire. Fig.3 shows the schematic diagram of the overall
circuit arrangement.

5
 Fig. 3. Schematic Diagram of 3Phase source with Full wave rectifiers

III. RESULTS AND DISCUSSIONS

A 230V, 50Hz, 4 wire star connected source with full wave rectifiers connected to each phase and
neutral is simulated using OrCAD Capture – Lite version 17.2 software and generated various output
waveforms. Also, Harmonic analysis using Fast Fourier Transform (FFT) is conducted for the circuit
using the same software. Various graphs and output data are analyzed here. The neutral current for
the above set up is calculated from the neutral current wave form and it has been validated with
the calculations in terms of 3rd harmonic current in the line current. Upon finding the neutral
current of the system, a proper wire size shall be selected to carry the current without increasing
the rated conductor temperature.

A. Simulation Output

Fig. 3 Shows Present of harmonic in Line1

6
 Fig. 3 harmonic in Line1

Fig. 4 shows the current at R2.

Fig. 4 current at R2

Fig. 5 shows the current at each phases.

Fig. current at each phases

Fig.6 shows the waveform for phase “a” voltage of input sinusoidal source voltage.

7
 Fig.6. Source Voltage, Va

Table-II gives the exported simulation output data of FFT analysis of line current Ia.

TABLE-II

FFT COMPONENTS OF LINE CURRENT, IA

Fig. 7 shows the waveform for Line current, Ia with harmonic content present.

8
 Fig.5. Line Current, Ia

Fig. 7 is the FFT analysis plot of Fig. 6 above. It is evident that only odd harmonics are present in the line
current. Also, it shows that the major contribution is from 3rd harmonic content other than
fundamental component as analyzed in the other section of this document.

Fig.7. Line Current, Ia in Frequency domain (FFT)

From the frequency domain plot, the 3rd harmonic current of Ia is Ia3 = 139.6A and Fundamental
current is Ia = 1176.6A.

Fig.8. Neutral Current, In

Fig. 8 shows Neutral current in Frequency domain (FFT). It clearly shows that only triplen harmonics are
present in the neutral current.

IV. RESULTS AND DISCUSSIONS

A 230V, 50Hz, 4 wire star connected with three sources induction with full wave rectifiers
connected to each phase and neutral is simulated using OrCAD Capture – Lite version 17.2 software
and generated various output waveforms. Also, Harmonic analysis using Fast Fourier Transform
(FFT) is conducted for the circuit using the same software. The software gives us many different
graphs such as neutral current, source voltage, harmonic for each phase and three phase current
with 3 phase 4 wire three sources induction simulation circuit. Various graphs and output data are
analyzed here. The neutral current for the above set up is calculated from the neutral current wave
form and it has been validated with the calculations in terms of 3rd harmonic current in the line
current. Upon finding the neutral current of the system, after analyzed and calculation of system we
achieved neutral conductor wire with specific cross section area to capable transfer current with
limit temperature.

9
 Fig, 9 Schematic Diagram of 3Phase and three induction sources with Full wave rectifiers

Fig 10 show us the three phase harmonic which give us by simulation for the 3 phase 4 wire star
connection with three sources induction;

Fig 12(Harmonic at three Phases measured at Ls)

10
Fig 13 show us the phase one harmonic which give us by simulation for the 3 phase 4 wire star
connection with three sources induction;

Fig 13(Harmonic at Phase 1 measured at Ls1)

Fig14 show us the phase two harmonic which give us by simulation for the 3 phase 4 wire star
connection with three sources induction

Fig 14(Harmonic at Phase 2 measured at Ls2)

Fig 15 show us the phase three harmonic which give us by simulation for the 3 phase 4 wire star
connection with three sources induction;

11
 Fig 15( Harmonic at Phase 3 measured at Ls3)
Fig, 16 show the three phase harmonic current

Fig 16(Harmonic at Neutral measured at R1) Show measured harmonic current 3 x phase 1(harmonic)
3rd harmonic

Conclusion
For balanced 4wire 3phase power system the should be no or minimum current flow in
neutral wire. Basically, the neutral wire thickness is less then phase cable since the return current
will be very low compare to phase wires. This true is earlier days during power system design
not much of no linear or power electronic devices present. Power Electronic very obvious cause
severe harmonic present in neutral wire and at line wire. When ever harmonic present in line
wire either of phase it can be observed harmonic in neutral wire. Simulation verifies this
situation that main cause of harmonic in neutral is 3 rd harmonic. All other non triplen harmonic
contents are added to zero. Present of harmonic at phase and neutral wires will reduce current
capacity of the wire. Harmonic increase with THDi increases and this will increase the present
12
of harmonic current in neutral wire. The present of harmonic in the neutral wire need derated the
size of cable. Considering all the factors the suitable size of cable will be 300mm 2 for copper
conductor.

Result

references

13