ABSTRACT

A Shunt Active Power Filter(APF) is a device that is connected in parallel to group

of loads.APF cancels the reactive and harmonic currents drawn by the load so as to make

supply current sinusoidal. Active Power Filter play a vital role in present day liberalized

energy market. Active Power Filter are explored for executing different power conditioning

function simultaneously along with harmonic elimination due to increase in nonlinear and

unbalanced load, at the point of common coupling. The aim of present dissertation is to

study different control strategies for Active Power Filter. More importantly to study

instantaneous power theory based Shunt Active Power Filter which is predominantly used in

present scenario. The shunt active power filter is investigated through Matlab/Simulink

simulation under different load conditions. Simulation results are discussed in depth. Then

the design issues of Active Power Filter for different load conditions are also discussed.

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CHAPTER 6SIMULATION DESIGN

The p-q theory based shunt APF is implemented for Harmonic compensation and power

factor correction. Logic utilized for shunt APF is discussed in chapter 5 and is summarized

in fig.5.2

6.1 Specification of the design:

Simulation is performed on 2 types of Three phase Balanced Non –Linear Load as

fallows:

System Parameters

Source Voltage V Sa , V Sb ,V Sc 220 V rms(line- line)

System Frequency f 60 Hz

APF

Dc-link voltage V dc 800V

Dc side capacitance C 1100μF

Ac side inductance Lc 3.75mH

Ac side resistance Rc 0.01 Ω

(Rating of APF is generally decided by peak voltage and RMS Current)

Load 1 Thyristor Rectifier (of rating 4 KVA)supplying to DC motor equivalent of 2.5KW

AC side inductance LLac 1mH

AC side resistance RLac 0.01 Ω

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DC side Resistance RLdc 18 Ω

DC side Inductance LLdc 85mH

Load2 Diode rectifier (of rating around 3KVA) supplying to purely resistive load

AC side inductance LLac NA

AC side resistance RLac NA

DC side Resistance RLdc 18 Ω

DC side Inductance LLdc NA

(NOTE: Rating of APF is generally decided by peak voltage and RMS Current[14]

APF rating for Load1 is V peak=312 v∧Irms=3 A will result in rating of

1

√2×312 ×3=0.661 KVA .Thus in practical cases can be assumed to be around 1-1.5KVA}.

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Fig 6.1 p-q theory based control block diagram of three-phase shunt APF system.

220

V rm

s L-L

3-ph

ase

Sour

ce

PI co

ntro

ller

Low

Pass

FIlte

r

Curre

nt m

easu

rem

ent

Volta

ge m

easu

rem

ent

RcLc

Conti

nuou

spo

wer

gui

A B C

non-

linea

r loa

d

curre

nt m

easu

rem

ent1

v+-

v+-

VcVbVa

Valph

a

Vbet

a

pdc

ploss

Isalf

a

Isbe

taIn

1

In2

Out1

Load

Cur

rent

mea

sure

men

t

Isalp

ha

Isbe

ta

Ia*

Ib*

Ic*

Inve

rse T

rans

form

atio

n

Isa*

Isb*

Isc*

Isa

Isb

Isc

A1 A2 B1 B2 C1 C2Hy

steris

is Ba

nd C

urre

nt C

ontro

ller

[Vdc

]Go

to7

[isc]

[Vsc

][V

sb]

[isb]

[isa]

[Vsa

]

[Vdc

]

[isc]

[isb]

[isb][is

a]

[isc]

[Vsb

]

[Vsa

]

[Vsc

]

[isa]

i+

-

i+

-

i+ -

i+ -

i+ -

i+

-

i+

-

i+

-i+

-

800

g11

g12

g21

g22

g31

g32

Vdc

a b cCo

mpe

nsat

or

Vsa

Vsb

Vsc

Isa

Isb

Isc

Valph

a

Vbet

a

p

Clar

ke T

rans

form

atio

n

Capa

citor

volta

ge

butte

r

v+-

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6.2 Clark Transformation:

is done in accordance with section 4.2.2

3

p

2

Vbeta

1

Valpha

Vbeta

Ibeta

Valpha

Ialpha

p

Subsystem5

a

b

c

alpha

beta

Subsystem2

a

b

c

alpha

beta

Subsystem1

6

Isc

5

Isb

4

Isa

3

Vsc

2

Vsb

1

Vsa

Fig 6.2 Block Diagram for Clark Transformation and p calculation

2

beta

1

alpha

Sum ofElements1

Sum ofElements

-K-

K=sqrt(2/3)

-K-

K=sqrt(2/3)

-K-

K=-1/2

-1

1

1

-K-

K=-1/2

3

c

2

b

1

a

Fig 6.3 Clark transformation block diagram for both V ∝ , V β , I α∧I β

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6.3 Calculation of p

According p-q theory real and imaginary power can be separated into two parts:

Real power: p=p+~p

Imaginary power: q=q+~q (from eq)

w h ere p and qare average power due to component iap∧iaq respectively

~p and ~q are oscillating power due to components i~ap∧i~aq respectively.

And i−(i~ap+i~aq) will produces a purely sinusoidal waveform. But in order to

achieve unity power factor APF must compensate for qfrom component iaq. Thus,

i−(i~ap+i~aq+iaq) will produce purely sinusoidal waveform with unity power factor.

Thus, inverse transformation iap will produce reference current iS¿ for each phase.iap

can deduced from p which is filtered out using low pass filter from p.

1

p

Product1

Product

4

Ialpha

3

Valpha

2

Ibeta

1

Vbeta

Fig 6.4 Block diagram for calculation of p

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Fig 6.5 p fromp using Low Pass filter

6.4 DC-Bus Voltage Control

Under a loss free situation, the shunt APF need not provide any active powerto cancel the reactive and harmonic currents from the load. These currents show up as reactive power. Thus, it is indeed possible to make the DC-bus capacitor delivers the reactive power demanded by the proposed shunt APF. As the reactive power comes from the DC-bus capacitor and this reactive energy transfers between the load and the DC-bus capacitor (charging anddischarging of the DC-bus capacitor), the average DC-bus voltage can be maintained at a prescribed value.

However, due to switching loss, capacitor leakage current, etc., the distribution source must provide not only the active power required by the load but also the additional power required by the VSI to maintain the DC-bus voltage constant. Unless these losses are regulated, the DC-bus voltage will drop steadily.

A PI controller used to control the DC-bus voltage is shown in Figure6.6. Its transfer function can be represented as

H (s )=K p+K I

swhere K p is the proportional constant that determines the dynamic response of theDC-bus voltage control, and K I is the integration constant that determines its settling time.

1

ploss

Subtract

PID

PID Controller

2

constant

1

Vdc

Fig 6.6 PI controller for DC-bus voltage control(Note:Kd=0∈above PID cotroller)

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p p

It can be noted that if K p and K I are large, the DC-bus voltage regulation is dominant, and the steady-state DC-bus voltage error is low. On the hand, if K p and K I are small, the real power unbalance give little effect to the transient performance. Therefore, the proper selection of K p and K I is essentially important to satisfy above mentioned two control performances.

6.5Reference Current Calculation:

Reference Currents are calculated from inverse clark transformation.

2

Isbeta

1

Isalfa

Product3

Product2

Product1

Product

Divide1

Divide

4

ploss

3

pdc

2

Vbeta

1

Valpha

Fig 6.7 Block diagram for calculation of I s∝∧I sβ

3

Ic*

2

Ib*

1

Ia*

Subtract

-K-

Gain3

-K-

Gain2

-K-

Gain1

-K-

Gain

2

Isbeta

1

Isalpha

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Fig 6.8 Reference Current calculation I a¿ , I b

¿∧I c¿

6.6 Hysteresis Band Current Controller:

It is introduced in chapter 3 section 3.5.2

6

C2

5

C1

4

B2

3

B1

2

A2

1

A1

Subtract3

Subtract2

Subtract1

Relay3

Relay2

Relay1

NOT

LogicalOperator2

NOT

LogicalOperator1

NOT

LogicalOperator

6 Isc

5 Isb

4 Isa

3

Isc*

2

Isb*

1

Isa*

Fig 6.9 Hysteresis Band Current Controller

Actual source currents (iSa ,iSb , I Sc) are compared with the reference currents iSa¿ ,iSb

¿ , I Sc¿

generated by the control algorithm in the hysteresis-band current controller. Three

hysteresis-band current controllers generate the switching pattern of the VSI. The switching

logic is formulated as follows

If iSa< (iSa¿

HB) higher switch is OFF and lower switch is ON for leg “A” (QA=1)

If iSa> (iSa¿

+ HB) higher switch is ON and lower switch is OFF for leg “A” (QA=0).

The switching functions of QB and QC for legs ‘‘B’’ and ‘‘C’’ are determined similarly,

using corresponding reference and measured currents and hysteresis bandwidth (HB). The

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hysteresis-band current control is the fastest control method with minimum hardware and

software but variable switching frequency is its main drawback

6.7 Compensator:

Switching is done according to gating signals from Hysteresis Band Current Controller.

Capacitor Voltage is continuously measured and fed to PI controller as explained earlier.

1

Vdc

3

c

2

b

1

a

v+-

Voltage Measurement3

gm

12

gm

12

gm

12

gm

12

gm

12

gm

12

C

6 g32

5 g31

4 g22

3 g21

2 g12

1 g11

Fig 6.10 Compensator

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6.8 Non-Linear Loads

Case:1 Thyristor Converter Supplying to DC motor equivalent

Synchronization Voltages

DC motor equivalent circuit

PI Curent Regulator

LlacRlac

3 C

2 B

1 A

v+-

Vca

v+-

Vbc

v+-

Vab

g

A

B

C

+

-

Thyristor Converter

alpha_deg

AB

BC

CA

Block

pulses

Synchronized6-Pulse Generator

1s

Id_Refence

i+ -

Id

5

100

90

0

Fig6.11 Block Diagram for Thyristor Converter controlled DC motor

Using PI controller DC motor current value is maintained at 20 Amps. PI controller varies

alpha of thyristor until motor current matches reference current. Pulse width is takes as 15°.

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case2:Diode Rectifier supplying to pure resistive load

3 C

2 B

1 A

Diode5

Diode4

Diode3

Diode2

Diode1

Diode

Fig 6.12 Block diagram for Diode rectifier supplying to pure Resistive Load

A pure resistive load is taken in order to APF performance. As in this load phase current

varies in abrupt manner on the contrary to RL load where load phase current is smooth

varying curve.

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CHAPTER 7 SIMULATION RESULTS

7.1 Case 1: Thyristor converter supplying to DC motor Equivalent(R-L Type Load)

FiFig 7.1 Source Voltages and Load Currents with APF(Case 1)

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V Sa

I Lb

I La

V Sb

I Lc

V Sc

Fig 7.2 Harmonic Analysis of Load Current with APF(Case 1)

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I Sa¿

Fig 7.3 Reference Current I Sa¿

(Case 1)

Fig 7.4 Source Current with APF(Case 1)

Fig 7.5 Compensating Current and Load Current(Case 1)

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I CaI La

I Sa

Fig 7.6 Source Voltage and Source Current with APF(Case 1)

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I Sb

V Sb

V Sa

I Sa

V Sc

I Sc

Fig7.7 Harmonic Analysis of Source Current (Case 1)

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Fig7.8 DC Capacitor Voltage for three-phase APF(Case 1)

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V c

7.2 Case 2: Diode Rectifier supplying to pure resistive

Fig 7.9 load Source Voltage & Load Current with APF

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V Sa

I La

V Sb

I Lb

V Sc

I Lc

Fig 7.10 Harmonic Analysis of Load Current

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Fig 7.11 Source Current after Compensation(Case 2)

Fig 7.12 Compensating Current and Load Current(Case 2)

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I Sa

I Ca I La

Fig 7.13 Source Voltages and Source Current(Case 2)

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V Sa

I Sa

V Sb

I Sb

V Sc

I Sc

Fig 7.14 Harmonic analysis of Source Current(Case 2)

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Fig 7.15 DC Capacitor voltage for three-phase APF(Case 2)

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7.3 Simulation Result Discussion:

As the source current and voltage are in phase,also the source current is almost

sinusoidal(very low THD) it can be said that source is providing only active power required

by the circuit. In instantaneous power theory view, source current is providing only average

real power component(p) while remaining components i.e real oscillating power(~p),

imaginary average power(q) and imaginary oscillating power(~q), is being provided by

Shunt APF.(see Discussion in section 6.3 )

From source currents and THD in case1 (RL load) and case 2 (purely resistive

load )it can be said that the effectiveness of the active filter in compensating for harmonic

components of the load current depends on the specific load current waveform involved.

Two different waveforms may have the same rms harmonic content but the active filter may

do a better job of compensating for one of the waveforms because of the waveshapes

involved. Source current has very less THD in case of RL load compared to purely resistive

one. Thus it can be inferred performance of shunt APF with RL load is much better than

purely resistive load.

In general, the current waveform of an ac regulator with resistive load is an example

of the waveshape that poses the severest challenge for an active filter. The problem is the

high di/dt that is required of the filter to compensate for the high di/dt at turn on of the

regulator. The problem is most severe when the regulator is turned on with a firing angle

close to 90 degrees because this is when the available driving voltage stored on the dc

capacitor is at a minimum. The output di/dt capability can be raised either by increasing the

dc voltage setting or by reducing the size of the interfacing inductance. The limiting factor

for increasing the dc voltage is the voltage withstand capability of the IGBT devices. The

limiting factors for reducing the interfacing inductance include the IGBT di/dt withstand

capability, control requirements, the interface passive filter requirement, and overall system

stability. If the interfacing inductance becomes too small, the dc voltage cannot be kept

constant for normal operation.

From harmonics analysis of Source Current it can be seen due to uneven switching

of compensator large number of interharmonics are introduced. But,it should be noted that

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those components have very less magnitude.(Maximum magnitude of interharmonic is 0.11

% in case 1)

Using PI Controller DC capacitor is maintained at reference value. It was seen that

Settling time improved drastically using PI controller.

It is worth to also to note that p-q based APF can be used for complete harmonic

elimination not selective harmonic elimination.

7.4 Future Scope

As p-q theory can be implemented in three-phase with excellent results in terms of

THD, transient response, reference current generation. The work on extending use of p-q

theory in single phase APF is being done[13].

Switching required in APF is very high in order of 10 kHz. Resulting in appreciable

amount of power. Thus, one can further work on to reduce switching frequency and to

switching losses.

One can also work on linear control technique to replace hysteresis band

controller .So, that irregular switching in compensator can be removed.

Study of Control system of APF is also a possibility n order to get lesser steady state

error and improved settling time. Most importantly to study various APF techniques and

comparing them in terms of dynamic response, performance under various type of load, total

harmonic compensation is to be done.

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CHAPTER 8CONCLUSION

The validity in terms of eliminating p-q theory in terms of eliminating harmonics and power

factor improvement is confirmed from low THD source current which is in phase with source

voltage. But p-q theory utilizes large number of sensors and reference current calculation block.

Large number of calculation in p-q theory demands higher processing power. Resulting in utility to

be complex and expensive. The p-q theory base APF is predominantly utilized in three phase circuits

thus can not be used at remote single phase customer. As a result, Harmonics are present in large part

of system. From source currents of the both cases (i.e. RL Load and purely resistive load) it can be

inferred that APF is most effective when the load current waveform does not have abrupt changes.

The overall filtering effectiveness depends significantly on the types of loads being compensated. As

a result, it is very effective for most voltage source inverter-type loads, even when the distortion is

high.

From comparing reference current and source waveforms it can be concluded that hysteresis

band current controller done the compensation at the cost of high switching frequency. Which can

result in high switching losses in practical high power APF applications. PI controller performance is

also validated from the DC-bus capacitor voltage which shows decreased settling time.

In theoretical view p-q theory has some shortcomings which need to be addressed. Like

mathematical expression of instantaneous power does not fallow power conservation and real and

imaginary power needed to be more accurately defined as zero sequence instantaneous power can

not be defined by the theory. In practical approach also it can be noted that p-q theory is incapable of

providing selective harmonic elimination and specific power factor compensation.

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References

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483-490

2.Power Quality C.Sankaran

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4. Das, J. C. Passive Filters – Potentialities and Limitations. IEEE Trans. On Industry

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5. Power Electronics Handbook CRC PRESS

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IEEE

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12.Instanteneous Power Theory and applications to power conditioning, IEEE Press, H.

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