1

Abstract-- The increased penetration of renewable and alternative

energy systems such as wind turbines and photovoltaic cells upon

the distribution network has led to a new concept called

“Microgrid”. The renewable/alternative generation systems upon

the microgrid are sometimes referred to as Distributed Energy

Resource (DER) system and are usually interfaced with the grid

using power electronic converters. However, as the power

converter switch at high frequencies, harmonic voltages and

currents are generated at the converter terminals and these

harmonics are further transmitted to the microgrid/grid.

This paper presents and evaluates different factors that may

affect the produced harmonics and reduce the quality of supply

including the switching frequency, modulation index and the

converter topology. It clearly shows in detail the relation between

these factors and the harmonics generated by the converters.

Moreover, it introduces a generic model of a DER grid

interfacing Voltage Source Converter (VSC). The paper also

presents methods that can be used to mitigate these harmonics.

The simulation was modelled and the results are presented using

MATLAB SimulinkTM and PlecsTM simulation tools.

Index Terms—Current Mode Control, Filters, Harmonics,

Microgrid, Plecs Modeling, Sinusoidal Pulse Width Modulation,

Voltage Source Converters.

I. INTRODUCTION

he ever increasing demand for electrical energy, the need

to conserve fuel sources due to its depletion and the

environmental challenges being faced by the world have

led to the use of renewable and alternative energy sources in

the generation of electrical energy [1], [2].

The increased penetration of renewable and alternative

energy systems such as wind turbines and photovoltaic cells

upon the distribution network has led to a new concept called

“Microgrid” [3]. The microgrid can be described as a close

assemblage of small controllable generators, energy storage

systems and loads in order to optimize the use of renewable

and/or alternative energy generation sources [3], [4]. An

advantage of the microgrid is that it can be connected to the

The authors are with the George Green Institute of Electromagnetic

Research (GGIEMR), Electrical Systems and Optics Research Division,

The University of Nottingham, NG7 2RD, Nottingham, UK.

(email: eexpmiv@nottingham.ac.uk, mrawa@kau.edu.sa,

dave.thomas@nottingham.ac.uk).

grid to meet the grids electrical energy demand or in a stand-

alone mode be used to supply energy to its immediate locality

[3], [4].

The renewable/alternative generation systems in the

microgrid are sometimes referred to as Distributed Energy

Resource (DER) system, and they are usually interfaced with

the grid using power electronic converters [3], [4]. Recently,

most of the DER system converters are Voltage Source

Converters (VSC) which consists of Insulated Gate Bipolar

Transistors (IGBTs) for superior controllability and very fast

switching responses [5].

As the DER system grid interfacing VSC converter switch

at high frequencies, harmonic voltages and currents are

generated upon the VSC converter terminals and are further

transmitted to the microgrid/grid [5], [6], [7].

The generated harmonics can have adverse effects on the

microgrid/grid as it causes sensitive loads and equipment to

trip or malfunction, voltage flickers, reduction of equipment

life span, overheating of distribution transformer [8]. For these

reasons it has become necessary to investigate the harmonics

generated by VSC converters on microgrids and establish ways

to mitigate these harmonics and ensure best quality of power.

This paper presents a generic DER grid interfacing VSC

converter (as shown in Fig. 1) whose switching strategy is

based on the Sinusoidal Pulse Width Modulation (SPWM)

technique and the control scheme is achieved using the current

control method. The controllers are the conventional

Proportional Integral (PI) controllers.

The factors that affect the harmonics produced by VSC

converters have been researched and discussed in various

literatures [5]-[7], [9], however, they have not clearly shown

the exact impact of these factors on the generated harmonics.

Therefore the aim of this paper is to present and clearly

evaluate important factors that affect harmonics generated on

this microgrid system by a VSC converter.

GSVSC

Edc

Idc

Rg Lg

Grid

Vgabc

Igabc

Distributed

SourceC

Vgcabc

IL

Ic

Fig. 1. A single line diagram of a grid interfacing DER system VSC

converter (GSVSC).

Factors Affecting the Harmonics Generated by a

Generic Voltage Source Converter within a

Microgrid

Preye M. Ivry, Muhyaddin J. Rawa, and D. W. P. Thomas

Electrical Systems and Optics Research Division,

The University of Nottingham, UK

T

2

The paper also presents some methods that can be used to

mitigate these harmonics and design procedure for an LCL

filter was given.

Matlab SimulinkTM

[10] and PlecsTM

[11] simulation tools

are used to model the system. The measured harmonics were

quantified using the Individual Harmonic Distortion (IHD) and

THD indices.

II. VSC CONVERTER SWITCHING AND CONTROL

Understanding the switching pattern and control of the

IGBTs in the VSC is necessary as they can affect the generated

harmonics produced by a VSC converter [12].

A. Sinusoidal Pulse Width Modulation (SPWM)

The simplest and most common switching strategy adopted

for IGBTs of VSC converters is the SPWM [6], [13].

The SPWM compares a high frequency triangular wave

known as the carrier wave with a slow varying power

frequency sinusoidal signal that is referred to as the

modulating signal as shown in Fig. 2a. The points of

intersection between the triangular carrier wave and the

sinusoidal modulating signal determines the switching pattern

of the VSC converter IGBTs [5], [6], [13].

Fig. 2a. Sinusoidal Pulse Width Modulation (SPWM) Scheme.

The ratio of the peak amplitude of the modulating signal Vm

and the peak amplitude of the carrier signal Vtri gives the

amplitude modulation index ma [6]:

dc

a

tri

m

a

V

V

V

Vm

1)ˆ(2

ˆ

ˆ

(1)

where 1

)ˆ(a

V is the peak amplitude of the fundamental voltage,

Vdc is the DC voltage and ma ≤ 1.

Fig. 2b. 2-level VSC Terminal Voltage wrt DC Voltage.

The resulting voltage output fluctuates between two values

Vdc/2 and –Vdc/2 as shown in Fig. 2b.

The triangular carrier wave frequency determines the

switching frequency of the VSC converter [6] and the

frequency modulation index is:

m

sw

m

tri

f

f

f

f

fm (2)

where ftri is the frequency of the triangular carrier wave and is

equal to the switching frequency fsw of the VSC and fm is the

frequency of the sinusoidal modulating signal and is equal to

the fundamental frequency of the generated voltage waveform.

Fig. 2c. 2-level VSC Terminal Voltage Harmonic Performance.

It can be seen from Fig. 2c that the voltage contains

harmonics and mf is calculated using (2).

4050

2000

Hz

Hzm

f

The frequency, fh at which the harmonic voltage occurs is

given as [6]:

mfhfkjmf )( (3)

and the harmonic order, h corresponds to the kth sideband of j

times the frequency modulation index mf

kmjhf

)( (4)

j is the group index and k is the sideband harmonic index from

each group. When j is odd k is even and when j is even k is

odd [6], [13].

Fig. 2c shows that the dominant harmonics are at the

switching frequency and multiples of the switching frequency

having negative and positive sidebands. The frequencies at

which the harmonic occur are calculated using (3). For the first

set of harmonics around fsw, the harmonics appear at frequency

fh = 1900Hz, 2000Hz and 2100Hz and they correspond to the

orders, h = 38, 40, 42 using (4). The THD of the VSC terminal

voltage with respect to the DC voltage is 159.8%.

B. Control Technique

The conventional active and reactive current control

technique is employed to control the instantaneous active (P)

and reactive (Q) power of the VSC converter using a PI vector

controller. This is chosen as it is simple to design, less

complex to implement and has a robust control response in a

balanced system [12].

In the current control technique, the active and reactive

power flow in the microgrid is regulated by controlling the

3

active current component Igd and the reactive current

component Igq. The PI controllers forces Igd and Igq to track

certain reference commands Igdref and Igqref, respectively. Igdref

and Igqref are provided from a reference signal generator block.

Utilizing the instantaneous power theory [5]:

acdcPP (5)

)(2

3

gqgqgdgdgIVIVP (6a)

)(2

3

gqgdgdgqgIVIVQ (6b)

where Pdc is the DC source power and Pac is the active power

on the grid (Pg), Qg is the reactive power on the grid.

Since the phase voltage of the grid is aligned to the d-axis

reference frame then Vgq = 0 [5], so the equation can be further

reduced to:

)(2

3

gdgdgIVP (7a)

)(2

3

gqgdgIVQ (7b)

If Igd = Igdref and Igq = Igqref then Pg and Qg can be controlled by

Pgref and Qgref [5]. So that:

gref

gdref

gdrefP

VI

3

2 (8a)

gref

gdref

gqrefQ

VI

3

2 (8b)

Fig. 3 shows the control scheme utilized in the control of

the active and reactive power on the microgrid. GSVSC

Edc

Rg Lg

Grid

Vgabc

IgabcC

Vgcabc

Qg

weLgweLg

Id Current

Controller

Iq Current

Controller

Angle

Calculator

abc

αβ

abc

αβ

abc

αβ

αβ

dq

αβ

dq

dq

αβ

PWM Scheme

Iqref Signal

Generator

Iq*

Id*

Id

Iq

Vabc

Iabc

Mabc

Vd’

θ

Vq’

Vd

-

-

+

-

-

+-

+

-

+

Idref Signal

GeneratorPg

Fig. 3. P and Q Control Scheme for the grid interfacing VSC converter.

The PI controller design is based on the plant of the system

which is [5]:

gggq

gq

gd

gd

c

sLRsV

sI

sV

sIsG

1

)(

)(

)(

)()( (9)

where Rg is the resistance of the grid line (Ω) and Lg is the

inductance of the grid line (mH).

The DC side voltage would not require a controller since we

are considering a constant DC voltage source.

III. PROPOSED MICROGRID SYSTEM

The analysed microgrid system which is shown in Fig. 4

comprises a DC voltage source, a grid interfacing VSC

converter, converter and grid line reactors and a 3-phase grid

voltage.

Fig. 4. Generic VSC Converter Microgrid Modelled in Plecs.

A microgrid system having a 3-phase 2-level VSC converter

with Va = 240V and Vdc = 640V, ma = 0.75, fm = 50Hz, fsw =

2000Hz, converter interfacing reactor Lcabc = 3.25mH, grid

inductance Lgabc = 0.75mH, converter and grid resistance Rcabc

= Rgabc = 0.1Ω has been considered and the system harmonic

performance is shown in Figs. 5 and 6.

Fig. 5a. 2-level VSC Phase Current Iga at PCC.

Fig. 5b. 2-level VSC Phase Current Harmonic Performance (Iga1/10).

It is clear from Figs. 5 and 6 that both the current and

voltage at the Point of Common Coupling (PCC) contains

harmonics. In Fig. 5b the 2-level VSC microgrid has a current

THD of 7.13% and in Fig. 6b the PCC phase voltage has a

voltage THD of 14.89%.

4

Fig. 6a. 2-level VSC Voltage at PCC Vga.

Fig. 6b. 2-level VSC Voltage at PCC Harmonic Performance (Vga1/10).

IV. FACTORS AFFECTING THE HARMONICS GENERATED BY A

GENERIC VSC CONVERTER ON A MICROGRID

The major factors that affect the generated harmonics by an

SPWM VSC converter are:

The Switching Frequency (fsw)/Frequency Modulation

Index (mf)

The Amplitude Modulation Index (ma)

The Converter Topology

A. The Switching Frequency/ Frequency Modulation Index

For a SPWM VSC grid interfacing converter, the generated

harmonics would appear at fsw, and its multiples. There would

also be positive and negative sidebands centred around the

switching frequency and its multiples. This is true for all

values where ma range is from 0 – 1 [6], [13]. In this case mf

defines the frequency at which the harmonic voltage or current

would occur. The frequency, fh at which the harmonic would

occur is given by (3) and the harmonic order by (4).

Fig. 7a. 2-level VSC Phase Current Iga at PCC at fsw = 4kHz.

The fsw can be increased to reduce the harmonics but

considerations should be given to the VSC switching losses, as

increasing fsw to reduce harmonics is done at the expense of

increasing the VSC converter switching losses [5].

To evaluate the effect of the fsw and mf we would increase fsw

from 2kHz to 4kHz and then 8kHz.

Fig. 7b. 2-level VSC Phase Current Harmonic Performance (Iga1/10) at fsw =

4kHz.

Fig. 8. Voltage at PCC Harmonic Performance (Vga1/10) at fsw = 4kHz.

Fig. 9a. 2-level VSC Phase Current Iga at PCC at fsw = 8kHz.

Fig. 9b. 2-level VSC Phase Current Harmonic Performance (Iga1/10) at fsw =

8kHz.

5

Fig. 10. Voltage at PCC Harmonic Performance (Vga1/10) at fsw = 8kHz.

Increasing fsw to 4kHz and 8kHz reduces the impact of the

generated harmonics on the microgrid at the systems frequency

[7]. Figs. 7–10 show that when the frequency of the converter

increases the order at which the harmonic appears increases

and hence would have a lesser impact on the microgrid at the

system frequency [7]. The voltage THD (14.9%) is similar for

all cases this is due to the fact that the IGBTs still switch

through 640V, but as shown in Figs. 7b and 9b the current

THD reduces with the increase of fsw. The current THD

reduces from 7.13% to 3.69% at fsw = 4kHz and when fsw is

further increased to 8kHz the current THD is reduced to

2.12%. The maximum current IHD reduces from 1.1A to

0.25A at 8kHz. The THD is calculated over the entire range of

harmonics on the system using (10). The harmonic groups are

still present, only that they now appear after every 4000Hz as

in Figs. 7b and 8 and after every 8000Hz as shown in Figs. 9b

and 10. Where:

%100

1

1

2max

I

I

THD

h

h h (10)

I1 is the fundamental current component (A), Ih is the

individual current harmonic (A) and hmax is the maximum

harmonic order. This formula can be used for both current and

voltage harmonic calculations.

B. The Amplitude Modulation Index (ma)

The amplitude modulation index determines the amplitude of

the generated current/voltage harmonics at the switching

frequency and its multiples having positive and negative

sidebands. The amplitude of the harmonic is independent of the

modulation frequency index [6], [9], [13]. In practice, ma for an

SPWM VSC converter is usually between 0.6–0.9. Figs. 11–14

show the harmonic performance for the 2-level VSC microgrid

system when the ma is varied from 0.75 to 0.6 and 0.91.

Fig. 11. 2-level VSC Phase Current Harmonic Performance (Iga1/10) at ma =

0.6.

Fig. 12. Voltage at PCC Harmonic Performance (Vga1/10) at ma=0.60.

Fig. 13. 2-level VSC Phase Current Harmonic Performance (Iga1/10) at

ma=0.91.

Fig. 14. Voltage at PCC Harmonic Performance (Vga1/10) at ma=0.91.

In Fig. 11 ma was 0.6 and current THD was 7.84% when ma

was 0.75 in Fig. 5b current THD was 7.13% but as ma was

increased to 0.91 current THD became 6.70%. For a microgrid

with a fixed system phase voltage of 240V, a lower ma implies

a higher DC voltage. This means the VSC IGBTs are made to

switch between a higher DC voltage thus generating higher

amplitudes of the IHD on the voltage. From the above results

in Figs. 12 and 14 it is clearly seen how the amplitude

modulation index, ma affects the voltage harmonics generated

by the VSC. As the ma increased from 0.6 – 0.91 it is observed

that maximum amplitude of the individual harmonic voltages

reduces from 22.5V to 11V thus reducing the voltage THD at

PCC from 18.26% to 12.01%.

C. The Converter Topology

The converter topology determines the maximum voltage a

single IGBT would be required to switch through [9].

Conventionally, the 2-level VSC converter topology has been

extensively used in low and medium power systems. In the

6

case of the 2-level VSC, the IGBTs are made to switch

through the full DC voltage Vdc. In series connection of these

devices the maximum voltage an IGBT is required to switch

through reduces and this has led to the introduction and use of

multilevel VSC converters in medium and high voltage level

applications and in HVDC links [9].

To illustrate how the converter topology affects the

generated harmonics, a 2-level VSC and a 3-level Neutral

Point Clamped (NPC) VSC as shown in Figs. 15a and 15b

respectively would be considered.

Fig. 15a. Generic 2-level VSC Converter Modelled in Plecs.

Fig. 15b. Generic 3-level VSC Converter Modelled in Plecs

In a microgrid system the 3-level VSC would be connected

to a 3-phase low voltage grid via line reactors and this would

help filter the generated current and voltage harmonics, thus

improving the VSC harmonic performance as seen in Figs. 16-

17.

Fig. 16a. 3-level VSC Phase Current Iga at PCC.

Fig. 16b. 3-level VSC Phase Current Harmonic Performance (Iga1/10).

It is clear from Fig. 16a that the current waveform of the 3-

level VSC is cleaner and more sinusoidal to that of the 2-level

VSC in Fig. 5a. Fig. 16b shows the current harmonic

performance is better than that of the 2-level VSC in Fig. 5b. It

has a reduced current IHD, the highest amplitude of the IHD is

0.48A at 1600Hz, whereas, the highest IHD for the 2-level

VSC microgrid system is about 1.1A at 1800Hz and there are

also high values of IHD above 0.8A at frequency 3950Hz and

4050Hz as seen in Fig. 5b. The 3-level VSC current THD is

3.28% while that of the 2-level VSC is 7.13%.

Fig. 17a. 3-level VSC Phase Voltage Vga at PCC.

Fig. 17b. 3-level VSC Voltage at PCC Harmonic Performance (Vga1/10).

The 3-level VSC terminal voltage IHD is much less than

that of the 2-level VSC as shown in Figs. 17b and 6b. The 3-

level VSC has a maximum voltage IHD of 4.2V, while that of

the 2-level VSC has a maximum IHD of 17V. In Fig. 17a it

can be seen that the 3-level VSC waveform is more sinusoidal

than that of the 2-level VSC in Fig. 6a.

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It could also be seen that the harmonics of the 3-level VSC

contains more sidebands, which is due to the increased number

of switching within the 3-level NPC VSC converter IGBTs.

V. HARMONIC MITIGATION OF THE MICROGRID SYSTEM

Having analysed the major factors that affect harmonics

generated on a microgrid by a VSC converter, it would be

proper to investigate some of the techniques or methods used

in attenuating harmonics. The conventional way of attenuating

harmonics to meet the IEEE 519 harmonic standard [14] or

any other harmonic standards is by the use of filters. In

microgrids the filter most commonly used to mitigate ac

voltage/current harmonics are the L, LC or LCL filter [15].

The L filter provides little attenuation of −20dB/decade. Its

attenuation is based on the size of the filter inductance and is

dependent on the switching frequency [16], [17]. The LC filter

provides an attenuation of −40dB/decade but in a stiff grid

system the LC filter operates like an L filter whereby the shunt

element becomes ineffective and the attenuation is based on

the size of L [16].

The LCL filter provides a better attenuation of

−60dB/decade for frequencies in excess of the resonant

frequency. It achieves the harmonic attenuation with lower

switching frequencies [16], [17]. Notwithstanding, the LCL

filter has been known to cause lots of instability on the system

due to resonance [18]. To overcome this, a damping passive

element is used. An LCL filter is used and designed according

to the procedure shown below and their results are compared

with a system with no filter [16] - [19].

max

1 ˆ8

1

Lsw

dc

f

If

VL

(11)

ratedLII %20ˆ

max (12)

21 ffLL (13)

223

%15

ratedm

rated

f

Vf

PC

(14)

fff

ff

res

CLL

LL

21

21

(15)

fres

d

CR

3

1 (16)

Lf1 and Lf2 are filters inductances 1 and 2, max

ˆL

I is the peak

inductor maximum current ripple (A), α is a limiting factor for

Lf2, Cf is the filter capacitance (mF), ωres is the resonant

frequency (rad/s) and Rd is the damping resistance (Ω).

Using an LCL filter of Lf1 = 5mH, Cf = 18.49µF, Lf2 =

1.5mH, Rd = 2.81Ω for the 2-level VSC microgrid having an

initial system result as shown in Figs. 5 and 6, will achieve an

attenuation of the current and voltage harmonics to be within

the required IEEE 519 standard, that is below 5%.

Fig. 18a. 2-level VSC LCL Filtered Phase Current Iga at PCC.

Fig. 18b. LCL Filtered Phase Current Harmonic Performance (Iga1/10).

Fig. 19a. 2-level VSC LCL Filtered Voltage at PCC.

Fig. 19b. LCL Filtered Voltage at PCC Harmonic Performance (Vga1/10).

Figs. 18a and 19a shows a cleaner and more sinusoidal grid

current and voltage waveform at the point of common coupling

as compared to Figs. 5a and 6a. In Fig. 18b it can be clearly

seen that the current harmonics are successfully attenuated to

2.06% from 7.13% with the help of an LCL filter and Fig. 19b

shows that the voltage THD is reduced to 4.78% from 14.89%

(as shown in Figs. 5b and 6b respectively).

8

VI. CONCLUSIONS

In conclusion, knowing the factors that affect the generated

harmonic by a VSC converter on a microgrid affects a

designer’s choice in selecting optimum operating parameter

values (as in Table 1) for the converter to meet the required

harmonic standard in [14]. This paper has clearly analysed and

stated the factors affecting the harmonics generated by a

generic VSC converter within a microgrid. Where the VSC

converter switching is achieved by using SPWM and the

converter is current controlled. The microgrid system was

simulated using Matlab SimulinkTM

and PlecsTM

simulation

tools and the harmonic effects were quantified using the IHD

and THD indices.

Harmonic attenuation methods and design procedure was

also given and the use of an LCL filter to further attenuate the

harmonics in the microgrid was demonstrated.

TABLE I

COMPARISON OF FACTORS THAT AFFECT HARMONICS GENERATED BY A VSC

CONVERTER ON THE MICROGRID

VII. ACKNOWLEDGMENT

The authors would like to acknowledge The Petroleum

Technology Development Fund (PTDF), Nigeria for funding

this PhD research.

VIII. BIOGRAPHIES

Preye M. Ivry received his BEng. degree in

Electrical and Electronics Engineering (Second

Class Upper Division (Hons)) from the Niger Delta

University, Nigeria in 2006. In 2010, he received his

MSc degree in Electrical Engineering and graduated

with distinction at the University of Nottingham

where he is currently working towards a PhD degree.

His research interests include power system analysis,

power quality, power system transients/harmonics,

power system converters and control, integration of

renewable energy systems to the grid.

Muhyaddin Jamal Rawa was born in Makkah,

Saudi Arabia on August 03 1977. He received a BSc

degree in Electrical and Computer Engineering from

Umm Al-Qura University and an MSc degree in

Electrical and Computer Engineering, Power and

Machines, from King Abdulaziz University in 2000

and 2008, respectively. He has more than 6 years

experience in Saudi Electricity Company before

joining the Department of Electrical and Computer

Engineering at King Abdulaziz Univeristy as a

Lecturer in 2008. Currently, he is a PhD student at the University of

Nottingham. His research interest includes power quality and system

reliability. Mr Muhyaddin is a member of the IET and IEEE.

David W. P. Thomas (M’94–SM’09) received the

B.Sc. degree in physics from Imperial College of

Science and Technology, London, U.K., the M.Phil.

degree in space physics from Sheffield University,

Sheffield, U.K., and the Ph.D. degree in electrical

engineering from Nottingham University,

Nottingham, U.K., in 1981, 1987, and 1990,

respectively. In 1990, he joined the Department of

Electrical and Electronic Engineering, University of

Nottingham, Nottingham, as a Lecturer, where he is

currently an Associate Professor and Reader. His research interests include

power system transients, power system protection, electromagnetic

compatibility, and electromagnetic simulation. Dr. Thomas is a member of

CIGRE and a Convenor for CIGRE JWG 4.207. He is also vice-chair for

IEEE EMC Technical committee 7 “Low frequency EMC”.

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