MODELLING OF THREE-PHASE SHUNT HYBRID ACTIVE POWER FILTERshodhganga.inflibnet.ac.in/bitstream/10603/9782/6/chapter-3.pdf · Chapter 3 Modelling of Three-Phase Shunt Hybrid active

Chapter 3 Modelling of Three-Phase Shunt Hybrid active Power filter 77

Ph.D Thesis submitted to Jawaharlal Nehru Technological University Anantapur, Anantapur

CHAPTER 3

MODELLING OF THREE-PHASE SHUNT HYBRID

ACTIVE POWER FILTER

3.1 INTRODUCTION

The three-phase Shunt hybrid APF topology for harmonic mitigation in low

and medium voltage power distribution systems consists of a VSI based three phase

shunt active filter (SAF) and tuned passive filters (TPF) connected in parallel with the

load. This chapter discusses the modelling of shunt active filter and design of filter

interfacing inductor, DC bus capacitor, tuned passive filters. It also presents the

analysis of synchronous reference frame theorem to estimate the compensation

reference current and hysteresis current controller for switching signal generation for

SAF. In addition the principle of operation of asymmetric cascaded multilevel inverter

used as SAF in medium voltage power distribution system and modulation strategy of

MLI is also presented.

3.2 OPERATION PRINCIPLE OF THE PROPOSED SHUNT

HYBRID APF TOPOLOGY

The operation principle of the proposed shunt hybrid APF topology is

illustrated in Fig. 3.1. It consists of a shunt active filter and tuned passive filters

(TPFs) connected in parallel with the nonlinear load which is connected to ac source.

The two TPFs are designed to absorb 5th

and 7th

harmonic currents with the principle

of series resonance and SAF compensates remaining harmonics. The SAF generates

compensation current (if) equal to harmonic load current (iLh) but in opposite phase to



it and injects in to the point of common coupling (PCC) through an interfacing

inductor. Therefore source current (is) is desired to be sinusoidal and in phase with the

source voltage (vs) to yield maximum power factor. The SAF is a VSI and a capacitor

connected on the DC side acts as storage element.

Fig. 3.1 Operation principle of the proposed Shunt Hybrid APF.

3.3 THREE PHASE SHUNT ACTIVE FILTER MODEL

The basic SAF scheme considered is depicted in Fig. 3.2. Practically, it is a

three phase AC/DC boost converter, where the main energy storage element is

provided by the capacitor C and the inductors L are used to control the filter currents

by means of the converter voltages. Conversely to the case of a pure voltage

converter, the focus for such type of device is on the currents injected into the line

which have to compensate for harmonics generated by nonlinear loads. The capacitor

voltage has to be constrained into a safe range while it is unimportant the shape of its



wave. The definitions, assumptions and preliminary design considerations are ;

1. In Fig. 3.2, Vsa, Vsb, Vsc are the mains voltages, isa, isb, isc are the mains

currents, ila, ilb, ilc are the load currents, ifa, ifb, ifc are the filter currents and

Vdc is the capacitor voltage (DC bus) and all currents and voltages are

balanced i.e. Vsa+ Vsb+Vsc=0,

isa + isb + isc =0,

ifa + ifb + ifc =0. (3.1a)

2. The mains voltages Vsa(t), Vsb(t), Vsc(t) are co-sinusoidal of frequency fm,

balanced and equilibrated.

Vsa(t) = Vm Cos (2π fmt)

Vsb(t) = Vm Cos (2π fmt-2 π/3)

Vsc(t) = Vm Cos (2π fmt+2 π/3) (3.1b)

3. The sampling frequency fs and the PWM frequency fPWM are supposed

already chosen.

4. The load currents ila, ilb, ilc are balanced and periodic of frequency fm.

5. Mains voltages, mains currents, filter currents are balanced.

6. The six-switches-bridge is supposed ideal.

7. The maximum current of the devices implementing the bridge switches is

Ifmax.

8. The steady-state capacitor voltage must be kept inside the range

[Vdc min,Vdc max]. The upper bound Vdc max depends on the kind of capacitor

chosen and on the number of series connected capacitor banks. Hence, it

can be assumed chosen before starting the design procedure. The lower



bound Vdc min depends on the controllability constraints.

Fig. 3.2 Three phase shunt active filter scheme.

Let , Vs(t)=[Vsa(t) Vsb(t) Vsc(t)]T mains voltage vector;

VfK(t)=[Vfxk(t) Vfyk(t) Vfzk(t)]T voltage vector between leg

centers and the node K;

Vabc(t)=VfN(t)=[VfxN(t) VfyN(t) VfzN(t)]T voltage vector

between leg centers and the node N;

ifabc (t) = [ifa(t) ifb(t) ifc(t)] filter current vector;

isabc (t) = [isa(t) isb (t) isc(t)] source current vector;

ilabc (t) = [ila(t) ilb (t) ilc(t)] load current vector;

Uxyz(t)=[ux(t) uy(t) uz(t)]T control inputs of the six-

switches-bridge, where ux є {0,1}, x = a,b,c. (3.2)

By means of Kirchoff laws it is possible to express the vector Vabc as



Va = Vsa- L 𝑑𝑖𝑎

𝑑𝑡 - Ria = SaVdc - VNK (3.3a)

Vb = Vsb- L 𝑑𝑖𝑏

𝑑𝑡 – Rib = SbVdc - VNK (3.3b)

Vc = Vsc- L 𝑑𝑖𝑐

𝑑𝑡 – Ric = ScVdc - VNK (3.3c)

C dV dc

dt = Saifa + Sbifb + Scifc (3.3d)

where Sa , Sb , Sc are the logic states of the switches, whose value is 1 when the

positive switch is on and 0 when negative switch is conducting. Therefore the

following relations hold good.

Sa = 0 → Vak = 0

= 1 = Vdc

Sb = 0 → Vbk = 0

= 1 = Vdc

Sc = 0 → Vck = 0

= 1 = Vdc

Also L and C are the inductors and capacitor values while R is the parasitic

resistance. Summing the first three scalar equations of (3.3) and considering equation

(3.1a) the value of VNK can be recovered as:

VNK = Sa +Sb +Sc

3 Vdc (3.4)

By means of equations (3.4), the above equations (3.3) can be rearranged as:

di a

dt = -

R

L ia -

Vdc

L (Sa -

Sa +Sb +Sc

3 ) +

1

L Vsa

di b

dt = -

R

L ib -

Vdc

L (Sb -

Sa +Sb +Sc

3 ) +

1

L Vsb



di c

dt = -

R

L ic -

Vdc

L (Sc -

Sa +Sb +Sc

3 ) +

1

L Vsc

dV dc

dt =

1

C [Saifa + Sbifb + Scifc] (3.5)

Looking at the previous equation (3.5) it is quite natural to define three new control

functions ua, ub and uc as:

ua = Sa - Sa +Sb +Sc

3 =

2

3 Sa -

1

3 Sb -

1

3 Sc

ub = Sb - Sa +Sb +Sc

3 = -

1

3 Sa -

2

3 Sb -

1

3 Sc

uc = Sc - Sa +Sb +Sc

3 =-

1

3 Sa -

1

3 Sb -

2

3 Sc (3.6)

It is worth to point out that the previous logic functions Sj represent the

normalized voltages VjK with respect to the DC-link voltage Vdc while the new control

functions represents the normalized voltages Vj that are referred to node N. Looking

at the previous equation it is possible to express the relation between logic functions

and control functions in a more compact way as:

uabc = uTS Sabc with

uabc =

ua

ub

uc

; Sabc =

sa

sb

sc

; uTS =

−

2

3−

1

3−

1

31

3

2

3−

1

3−1

3−

1

3

2

3

By means of equations (3.6), elaborating equations (3.5) it can be readily obtained:

di a

dt = -

R

L ia -

Vdc

L ua+

1

L Vsa

di b

dt = -

R

L ib -

Vdc

L ub +

1

L Vsb

di c

dt = -

R

L ic -

Vdc

L uc +

1

L Vsc



dV dc

dt =

1

C [uaifa + ubifb + ucifc] (3.7)

Substantially this last model differs from the previous one for the different definitions

of the control vector u instead of logic one S.

3.4 PROPOSED SHAF FOR HARMONIC COMPENSATION IN

LV POWER DISTRIBUTION SYSTEM

The low voltage power distribution system of interest consists of a three

phase, 2000 V (r.m.s), 50 Hz sinusoidal AC voltage source. The source inductor is

considered as Ls. A full-bridge diode rectifier with R-L load is selected as the

nonlinear load as shown in Fig. 3.3.

Fig. 3.3 System configuration with the proposed SHAPF.

This type of load can be found in most power electronics applications, i.e.



switch-mode power supply, uninterruptible power supply (UPS), AC motor drive and

DC servo drive. It is used to convert the input AC to DC in an uncontrolled manner. It

is well known that this nonlinear load draws highly distorted current from the

distribution source, thus a major source of harmonic distortion [9]. The proposed

shunt hybrid APF is connected with the distribution line at the PCC through an

interfacing inductor (Lf). This interfacing inductor provides isolation from the

distribution line. A large interfacing inductor is preferable because it results in small

switching ripple. However, the large interfacing inductor limits the dynamic response

of the compensation current. Therefore, there is a compromise involved in sizing the

interfacing inductor. This VSI uses DC-bus capacitor (Cdc) as the supply source and

switches at high-frequency to generate a compensation current that follows the

estimated reference current. Therefore the voltage across the DC-bus capacitor (Vdc)

must be maintained at a constant value that is higher than the amplitude of the source

voltage.

3.4.1 Power Circuit

The power circuit used in the proposed hybrid APF is an universal full-bridge

VSI as shown in Fig. 3.3. The VSI consists of six transistors, each connected to an

anti-parallel diode. The transistors are the metal oxide semiconductor field effect

transistors (MOSFETs). They are selected due to their superior performance

characteristics, i.e. low forward voltage drop, fast switching times and high power

handling capability. The logic inverters ensure that each MOSFET on the same leg

complement each other avoiding short circuit problem of the DC-bus capacitor (Cdc).

3.4.2 Interfacing Inductor

The desired compensation current waveform is obtained by controlling the



switching of the MOSFETs in the VSI. The switching ripple (isw) of the compensation

current is determined by the size of the interfacing inductor, available driving voltage

across the interfacing inductor, and switching frequency. In the proposed scheme, the

driving voltage is the DC-bus voltage (Vdc). The bipolar DC-bus voltage across the

interfacing inductor determines the peak-to-peak switching ripple (∆Isw,p−p).The

minimum interfacing inductor (Lf ,min) can be calculated as

Lf.min =Vdc

2. ΔIsw .p−p .fsw ,max (3.8)

where f sw,max is the maximum frequency of switching ripple and ∆Isw, p− p is the peak-

to-peak switching ripple of compensation current. The detailed derivation of (3.8) is

presented in Appendix A.

3.4.3 DC-Bus Capacitor

The DC-bus capacitor (Cdc) is used as a temporary energy storage element in

the proposed hybrid APF as shown in Fig. 3.3. Under steady state condition, the

reactive and harmonic load currents will charge and discharge the DC-bus capacitor

during the source voltage period. The total reactive and harmonic load current to be

compensated is the principle factor that causes the DC-bus capacitor voltage

fluctuation. To get a good compensation performance, serious voltage fluctuations

must be avoided. In such cases the capacitor may have to supply real power demand

of the load during one cycle of the utility voltage. This can be achieved by proper

sizing of the DC-bus capacitor. The size determination of the DC-bus capacitor is

based on the energy-balance principle which means that the stored energy of the

capacitor should be equal to sudden change in the load energy for one cycle of supply

voltage.



Let Vdc(t) be the DC-bus voltage at that instant(maximum or minimum), Vdc,ref

is the DC-bus reference voltage, Vsmax is the peak value of the source voltage, ∆IL is

the change in peak value of the harmonic load current and T is the time period of

source voltage. Then change in energy due to change in load per one cycle is

ΔEL(t) = 1

2. Vsmax . ΔIL.T

and stored energy in the capacitor is given by

ΔEc(t) = 1

2Cdc Vdc .ref

2 − Vdc (t) 2

Therefore stored energy of the capacitor should supply change in load energy for one

time period.

∴ ΔEc(t) = ΔEL(t)

1

2Cdc Vdc .ref

2 − Vdc (t) 2 =1

2. Vsmax . ΔIL.T (3.9)

Therefore three capacitor voltage values are obtained on the basis of the following

three situations:

i) When there is a sudden increase in the fundamental load current (Cdc1):

1

2Cdc Vdc .ref

2 − Vdc ,min 2 =

1

2. Vsmax . ΔIL1. T

where Vdc,min is the minimum value of DC bus voltage.

ii) When there is a sudden decrease in the fundamental load current (Cdc2):

1

2Cdc Vdc .max 2 − Vdc ,ref

2 =

1

2. Vsmax . ΔIL2 T

iii) Reactive and harmonic currents of load current during steady state(Cdc3):

1

2Cdc ΔVdc .

2 − Vdc ,ref 2 =

1

2. Vsmax . ΔIL3 T

where ΔVdc is the maximum or minimum value of Vdc.

The largest value of Cdc1, Cdc2, Cdc3 will be selected. For compensating



harmonics and reactive power Cdc3 is selected in this thesis. Therefore the

size of DC-bus capacitor is determined by

Cdc ≥ Vsmax ΔIL T

ΔVdc 2− Vdc ,ref 2 (3.10)

3.4.4

The objective the control strategy of the proposed three-phase shunt hybrid

active filter is to produce appropriate gating signals for the switching transistors of

VSI. The control system consists of synchronous reference frame theorem based

compensation current estimator, hysteresis current controller for gate signal

generation and a Fuzzy logic controller to maintain the DC bus voltage constant.

3.4.4.1 Compensation Current Reference Estimation Using d-q-0

Theory

In this work synchronous reference frame (SRF) theory is employed to obtain

compensating current reference signal. In this control strategy three phase load

currents are sensed and transformed from a-b-c reference frame to d-q coordinates

which are DC components using park‟s transformation. Passing these d-q components

of load currents through low pass filter, the low frequency fundamental components

only will be passed through and harmonic component is stopped. By subtracting

fundamental component from non-filtered signal will result in harmonic component in

load current. Control signal from Fuzzy logic controller is added to this signal to

obtain the reference compensating signal in d-q reference frame. By transforming

these components in d-q reference to a-b-c reference frame using inverse Park‟s

transformation, the information about harmonic current component in a-b-c reference

frame is obtained.



Suppose the three phase source currents are Isa, Isb, Isc, the nonlinear load

currents are ILa, ILb, ILc and active filter compensating currents are Ifa, Ifb, Ifc for phases

A,B,C respectively. The load currents in a-b-c synchronous reference frame

components can be converted in to d-q reference frame components using Park‟s

transformation as shown in equation (3.11).

Id

Iq =

2

3 cos θ cos θ −

2π

3 cos θ +

2π

3

sin θ − sin θ −2π

3 − sin θ +

2π

3

ILa

ILb

ILc

(3.11)

These currents can be decomposed into fundamental and harmonic components as

shown in equations (3.12).

Id =Iddc + Idh, Iq = Iqdc + Iqh (3.12)

The fundamental component of load current will appear as DC quantity in d-q

reference frame. Therefore Iddc = Id1 and Iqdc = Iq1. The harmonic component of load

current is obtained by subtracting high frequency harmonic current signal from total

load current.

Idh = IL-LPF( Id), Iqh = IL-LPF(Iq) (3.13)

These reference currents are transformed into a-b-c coordinates by applying

Inverse Park‟s transformation to obtain reference currents in a-b-c coordinates.

Ifa∗

Ifb∗

Ifc∗ =

2

3

cos θ sin θ

cos θ −2π

3 − sin θ −

2π

3

cos θ +2π

3 − sin θ +

2π

3

Idh

Iqh (3.14)

These reference currents are applied to hysteresis current controller which

produces required gating pulses to switching devices of VSI. Since it deals with



mainly DC quantities and computation is instantaneous this theory is considered in

this thesis for estimating reference compensating current.

3.4.4.2 Hysteresis Current Control (HCC) for Switching Signal

Generation

Fig. 3.4(a) shows a single phase VSI with terminal voltage (Vf)

connected to a sinusoidal voltage source (Vs) through an equivalent

inductance L and resistance R. Fig. 3.4(b) shows it‟s HCC.

Fig. 3.4 (a) Single phase VSI and ( b ) Its hysteresis current controller.

To control APF output current (if) and to track certain reference current if*,

according to Fig. 3.4(a), the instantaneous voltage equation is:

L di f

dt + if R = Vf - Vs (3.15)

When the APF output current is equal to reference current if∗, the corresponding

equation will be

L di f

∗

dt + if

∗ R = Vf∗ - Vs (3.16)

where Vf∗ is the reference VSI terminal voltage corresponding to if

∗. If APF current

tracking error Δif = if∗ - if , then it is clear that when R = 0,



L ∆if

dt = Vf

∗ −Vf (3.17)

where VSI terminal voltage Vf = Vdc

2 when S=1

= - Vdc

2 when S=0

Here Vdc is the DC bus voltage o f VSI and S is switching state of the

solid-state switches. When Δif is greater than 0 and beyond the tolerance, S is

controlled to be at lower level i.e S = 0 and therefore (Vf - Vf∗) < 0 which

makes Δif to reduce (Eqn.(3.17)). In the same way if Δif < 0 and beyond the

tolerance, S is controlled to be at higher level i.e S=1 and therefore (Vf - Vf∗) > 0

which makes Δif to increase. The corresponding Hysteresis current control block

diagram is shown in Fig. 3.4(b).

3.4.4.3 Fuzzy Logic based DC Bus Voltage Control

Fuzzy logic has become more popular during past four decades due to its

advantages of robustness against parameter variation, popularity, customization, etc.

When system is too complex or too poorly understood to be described in precise

mathematical terms, fuzzy modeling provides the ability to linguistically specify

approximate relationships between the input and desired output. The relationships are

represented by a set of fuzzy If–then rules in which the antecedent is an approximate

representation of the state of the system and the consequent provides a range of

potential responses. In this thesis fuzzy logic controller is used to maintain DC bus

voltage constant at a reference value. Fuzzy logic uses fuzzy set theory, in which a

variable is a member of one or more sets, with a specified degree of membership.

Fuzzy logic allows emulating the human reasoning process in computers, quantifying

imprecise information, making decision based on vague and in complete data, yet by



applying a “defuzzification” process, arriving at definite conclusions. The block

diagram representation of a fuzzy logic controller (FLC) is shown in Fig. 3.5.

The FLC mainly consists of three blocks

• Fuzzification

• Inference

• Defuzzification

The details of the above processes are given below.

Fig. 3.5.Block diagram of FLC

A. Fuzzification

The fuzzy logic controller requires that each input/output variable which

define the control surface be expressed in fuzzy set notations using linguistic labels.

The membership values of each input and output variable divide its universe of

discourse into adjacent intervals to form the membership functions. The membership

value denotes the extent to which a variable belong to a particular level. The process

of converting input/output variable to linguistic levels is termed as fuzzification.



B. Inference

The behavior of the control surface which relates the input and output

variables of the system is governed by a set of rules. A typical rule would be

If x is A Then y is B

When a set of input variables are read, each of the rule that has any degree

of truth in its premise is fired and contributes to the forming of the control

surface by approximately modifying it. When all the rules are fired, the resulting

control surface is expressed as a fuzzy set to represent the constraints output. This

process is termed as inference.

C. Defuzzification

Defuzzification is the process of conversion of fuzzy quantity into crisp

quantity. There are several methods available for defuzzification. The most prevalent

one is centroid method, which utilizes the following formula:

μ x x dx

μ x dx where μ is the membership degree of output x.

3.4.5 Tuned Passive Filter Design

The proposed shunt hybrid active power filter consists of tuned passive filters

connected in parallel with the load to absorb specified harmonic currents. The

common types of passive harmonic filters include single tuned, double tuned and high

pass filters. However for simplicity single tuned filters are considered in this work.

The basic shunt passive filtering principle is to trap harmonic currents in LC circuits,

tuned up to the harmonic filtering frequency, and to eliminate from power system. A

single tuned 1st order filter configuration consists of RLC elements in series as shown



in Fig. 3.6.

Fig. 3.6 Design of Tuned Passive Filters.

In single-tuned passive filter, the reactance of inductor is equal to that of

capacitor at resonant frequency fn. The relationship among L, C, R, Q values are

given in Eqn.(3.18)[4].

Cn = 1/Ln(2πfn)2

,

Rn=Ln(2 πfn)/Q , 𝑄 = 𝑅𝑛

𝐶𝑛

𝐿𝑛 (3.18)

where fn=frequency of harmonic component, n=order of harmonic,

Q=Quality factor, Rn=Resistance of nth

harmonic filter, Ln=inductance of nth

harmonic

filter. In the proposed hybrid filter the shunt passive filters are tuned to absorb 5th

and

7th

harmonic currents and other higher order harmonics are to be suppressed by SAF.

Hence burden on SAF is reduced resulting in reduced rating of SAF and effective

filtering of higher order harmonics. Therefore source needs to supply only

fundamental component of load current.



Fig. 3.7 Simplified model of the proposed shunt hybrid APF.

Fig. 3.7 presents an equivalent circuit of the proposed shunt hybrid APF for

harmonic filtering, where ZTP is the equivalent impedance of TPF and Zs is the

equivalent impedance of distribution source assumed to be a simple inductor (Ls). The

shunt APF is assumed to act as an ideal current source which produces the

compensation current that follows the compensation current reference, while the

nonlinear load is considered as a harmonic currents source. Since we are only

interested in the system performance with the harmonic components, the source

voltage can be neglected. This is because the source voltage is assumed to contain

only the fundamental frequency component.

3.5 ACSLI BASED SHAPF FOR HARMONIC MITIGATION IN

MV POWER DISTRIBUTION SYSTEM

The proposed SHAF configuration for compensating harmonics in medium

voltage system uses ACSLI as shunt active filter and single tuned passive filters as

shunt passive filters. The design of shunt passive filter is explained in section 3.4.5.

The operation of ACSLI SAPF is discussed in this section. The basic structure of a

three-phase Y-configured multilevel inverter with „n‟ series-connected H-bridge cells



per phase is shown in Fig. 3.8.

Fig. 3.8 Circuit diagram of a three-phase cascaded multilevel inverter.

A phase voltage waveform is obtained by summing the output voltages of the inverter

cells as in Eqn.(3.19).

Va(t) = Va1(t)+Va2(t)+…..+Van(t) (3.19)

If DC voltage sources of all H-bridge cells are equal, the maximum number of levels

(m) of phase voltage is given by Eqn.(3.20).

m = 2n + 1 (3.20)

On the other hand, if at least one of the DC voltage sources is different of the

other ones, the multilevel inverter can be called as asymmetric multilevel inverter.

Thus, considering the lowest DC voltage source (V1) as base value for the p.u.

notation (Vbase =V1), the normalized values of all DC voltage sources must be natural

numbers to obtain a uniform step multilevel inverter, i.e.:

Vj є N , j = 1, 2, ..., n. Vj=normalized voltage of DC source j. (3.21)



Moreover, to obtain a uniform step multilevel inverter, the DC voltage sources

of the H-bridge cells must also respect the following relation given in Eqn.(3.22):

Vj ≤ 1+2 𝑉𝑘𝑗−1𝑘=1 , 𝑗 = 2,3, …… . . , 𝑛 (3.22)

It is also considered that the DC voltage sources are arranged in an increasing

way as in Eqn.(3.23).

V1≤ V2≤ V3≤ ...≤ Vn (3.23)

Therefore, the maximum number of levels of output phase voltage waveform

can be given by Eqn.(3.24).

M= 2σn + 1 where σn = Vjnj=1 (3.24)

From Eqns.(3.20) and (3.24), it is possible to verify that asymmetric multilevel

inverters can generate a larger number of levels with the same number of cells. Hence

in this thesis asymmetric cascaded inverter with two H-Bridge cells (LV cell and HV

cell) in cascade is used as shunt active power filter for harmonic mitigation in medium

voltage distribution system. On the DC side of HV cell 3kV DC supply is connected

and on LV cell a capacitor is connected as storage device. Fuzzy logic controller is

used for maintaining LV cell capacitor voltage constant. The FLC design is explained

in section 3.4.4.3.

Carrier switching frequency subharmonic PWM is used for producing

switching signals for ACSLI. For m-level inverter this technique uses (m-1) triangular

carrier signals with the same frequency, same peak-to-peak amplitude and same phase

which are disposed such that the bands they occupy are contiguous. The sinusoidal

modulation waveform is centered in the middle of the carrier set and is continuously

compared with each of the carrier signals. If the reference is greater than a carrier



signal, then the active device corresponding to that carrier is switched on, and if the

reference is less than a carrier signal, then the active device corresponding to that

carrier is switched off. This method is also known as sinusoidal pulse width

modulation. D-q-0 theory is used for estimating reference compensating current of

SAPF which is described in section 3.4.4.1.

Multilevel Inverter Modulation Strategy

A generalized modulation strategy has been presented in [62], which

incorporates stepped voltage waveform synthesis in higher power H-bridge cells in

conjunction with high frequency variable pulse width modulation (PWM) in the

lowest power H-bridge cell. However, to synthesize a voltage waveform modulated at

high frequency among all adjacent voltage steps, switching at high frequency only the

lowest power inverter, the DC voltage sources must satisfy the following equation:

Vj ≤ 2 𝑉𝑘𝑗−1𝑘=1 , 𝑗 = 2,3, … … . . , 𝑛 (3.25)

Therefore, if eqn.(3.25) is satisfied, the output voltage harmonics will be

concentrated around the frequencies multiples of the switching frequency of the

inverter with the lowest DC voltage source. Consequently, with this topology and this

modulation strategy, the spectral response of the output voltage depends on the

switching frequency of the lowest power inverter, while the power processing

depends basically on the inverter with the highest DC voltage source. Fig. 3.9 shows

that the reference signal of the hybrid multilevel inverter is the command signal of the

H-bridge cell with highest DC voltage source (Vn). This signal is compared with a

voltage level corresponding to the sum of all smaller DC voltage sources of the hybrid

multilevel inverter (σn-1). If the command signal is greater than this level, the output

of the inverter with the highest DC voltage source must be equal to Vn. In addition, if



the command signal is less than the negative value of σn-1, the output of this cell must

be equal to −Vn, else the output of this cell must be zero. The command signal of the

jth

cell is the difference between the command signal of the inverter j+1 and the output

voltage of the inverter j+1. In this way, the command signal of the jth

cell contains

information about the harmonic content of the output voltage of all higher voltage

cells.

Fig. 3.9 Modulation strategy of hybrid multilevel inverters [62].

This command signal is compared with a voltage level corresponding to the

sum of all voltage sources until the inverter j–1 (σj-1). In the same way that presented

for the inverter n, the output voltage of this cell is synthesized from the comparison of

these two signals. Finally, the command signal of the first inverter (lowest power

inverter) is compared with a high frequency triangle carrier signal with amplitude V1,

resulting in a high frequency output voltage. Consequently, the frequency modulation

index (mf) of the hybrid multilevel inverter is defined as the ratio between the

switching frequency of the lowest power inverter (fs) and the frequency of the

reference signal (fr).



3.6 CONCLUSION

This chapter explained the principle of operation of proposed SHAF topology

and modelling of basic three phase shunt active filter in detail. The overall topology is

highlighted to give an overview of the work. Then, the design of each main block

namely power source, interfacing inductor and DC bus capacitor followed by tuned

passive filter. It also presented ACSLI based SHAF operation, component design and

its control strategy. A larger number of levels can be obtained with the same number

of power devices of the conventional cascaded multilevel inverter, minimizing the

THD of output voltage with ACSLI.

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MODELLING OF THREE-PHASE SHUNT HYBRID ACTIVE POWER FILTERshodhganga.inflibnet.ac.in/bitstream/10603/9782/6/chapter-3.pdf · Chapter 3 Modelling of Three-Phase Shunt Hybrid active