19

CHAPTER 2

CONSTANT FREQUENCY HYSTERESIS CURRENT

CONTROL OF SHUNT ACTIVE FILTER

The active filters are used to suppress harmonic distortion in power

system. The active filters use power electronic converters in order to inject

harmonic components to the system that cancel out the harmonics in the

supply current caused by non-linear loads. The shunt active filter is a pulse

width modulated voltage source inverter that is connected in parallel with the

load. The switches of the voltage source inverter in the active power filter are

switched such that proper compensation is achieved. Various current control

strategies have been proposed to control the inverter. Among the various

current control techniques, hysteresis current control technique is the most

commonly used approach due to its simplicity in implementation and fast

response. But, the current control technique with a fixed hysteresis band has

poor compensation performance with large current ripple which leads to

inadequate tracking performance. Moreover, the switching frequency varies a

lot even for fixed load condition. This chapter presents a novel constant

frequency hysteresis current control technique for shunt active power filter

which maintains a constant switching frequency. In this technique, the

hysteresis bandwidth need not be specified in the entire control algorithm.

The operating principles of the proposed technique and mathematical

derivation of the switching functions are presented in this chapter. The

proposed control scheme is validated through computer simulation in three

phase three-wire shunt active filter with non-linear load.

20

2.1 OPERATION OF SHUNT ACTIVE FILTER

Figure 2.1 shows the schematic representation of a Shunt Active

Filter connected in a three phase system feeding a non-linear load.

Figure 2.1 Schematic representation of Active Power Filter with the

proposed control technique

Voltages Va, Vb, Vc and current Ia, Ib, Ic indicate the phase voltages

and currents at the load side respectively. The active filter is connected in

parallel with the load to suppress the harmonics. The shunt active filter

generates the compensating currents Ifa, Ifb, Ifc to compensate the load currents

Ia, Ib, Ic so as to make the current drawn from the source as sinusoidal and

balanced. The performance of the active filter mainly depends on the

technique used to compute the reference current and the control strategy

followed to inject the desired compensation current into the line (Pericle

Zanchetta et al 2009). In this work, the instantaneous p-q theory is used to

determine the current references (Ifa*, Ifb*, Ifc*).

21

Another important task in the development of active filter is the

maintenance of constant DC voltage across the capacitor connected to the

inverter. This is necessary because there is energy loss due to conduction and

switching power losses associated with the diodes and IGBTs of the inverter

in Active power filter, which tend to reduce the value of voltage across the

DC capacitor.

2.1.1 Reference Current Extraction

Derivation of compensation current is the important part of active

filter control. The time domain methods are mainly used due to its speed with

less calculation compared to the frequency domain methods. Instantaneous

p-d theory (Joao Afonso et al 2000), one of the time domain methods is

followed in this work. The details of instantaneous p-q theory are presented

here.

The p-q theory is based on the transformation, and is known as

the Clarke Transformation. It transforms the three phase voltage and current

into stationary reference frame using the following equations:

c

b

a

V

V

V

V

V

2

3

2

30

2

1

2

11

3

2 (2.1)

c

b

a

I

I

I

I

I

2

3

2

30

2

1

2

11

3

2 (2.2)

22

Since in a balanced three-phase three wire system, neutral current is

zero, the zero sequence current does not exist. The power components p and q

are related to the voltages and currents, and can be written as,

I

I

VV

VV

q

p(2.3)

where p is the instantaneous real power and q is the instantaneous imaginary

power. The instantaneous real power includes AC and DC values and can be

expressed as follows:

~

ppp (2.4)

where p~ is the alternating value of the instantaneous real power which is

exchanged between the source and load and p is the average real power.

The alternating (AC) value of instantaneous real power is calculated

back to a-b-c frame which represents the harmonic distortion, given as

reference for the current controller. The mean (DC) value of the

instantaneous real power is usually the only desirable power component. The

other quantities have to be compensated using the shunt active filter. To

calculate the reference compensation currents in the coordinates, the

expression (2.3) is inverted as given below,

q

p

VV

VV

i

i

c

c

~

*

*

(2.5)

23

where p~ is the alternating value of the instantaneous real power which is

exchanged between the source and load and q is the instantaneous imaginary

power corresponding to the power that is exchanged between the phases of

the load.

In order to obtain the reference compensation currents in the a-b-c

coordinates the inverse of the transformation is applied to eqn 2.2 and is given

as

*

*

*

*

*

2

3

2

1

2

3

2

1

01

c

c

cc

cb

ca

i

i

i

i

i

(2.6)

The eqn 2.6 gives the reference compensation current to be injected

to the system.

2.1.2 Hysteresis Current Control

The current control strategy plays an important role in the

development of shunt active filter. The hysteresis-band current control

method (Anshuman shukla et al 2007) is popularly used because of its

simplicity in implementation.

Hysteresis current controller derives the switching signals of the

inverter power switches in a manner that reduces the current error. The

switches are controlled asynchronously to ramp the current through the

inductor up and down so that it follows the reference. The current ramping up

and down between two limits is illustrated in Figure 2.2. When the current

24

through the inductor exceeds the upper hysteresis limit, a negative voltage is

applied by the inverter to the inductor. This causes the current through the

inductor to decrease. Once the current reaches the lower hysteresis limit, a

positive voltage is applied by the inverter through the inductor and this causes

the current to increase and the cycle repeats. The current controllers of the

three phases are designed to operate independently. They determine the

switching signals to the respective phase of the inverter.

Figure 2.2 Hysteresis Current Control Operation Waveform

This method has the drawbacks of variable switching frequency,

heavy interference between the phases in case of three phase active filter with

isolated neutral and irregularity of the modulation pulse position (Simone et al

2000). These drawbacks result in high current ripples, acoustic noise and

difficulty in designing input filter. In this chapter, a constant frequency

hysteresis current controller is proposed for shunt active filter applications.

The details of the proposed current control strategy are presented in the next

section.

25

2.1.3 DC Voltage Control

In shunt Active power filter, the output voltage of the inverter is

controlled by changing the switching pulses. This causes a flow of

instantaneous power into the inverter which charges/discharges the inverter

DC bus capacitor. Despite the resultant DC bus voltage fluctuations, its

average value remains constant in a lossless active filter. However, the

converter losses and active power filter exchange causes the capacitor voltage

to vary. Hence the DC bus capacitor must be designed to achieve two goals,

i.e., to comply with the minimum ripple requirement of the DC bus voltage

and to limit the DC bus voltage variation during load transients. In this work,

a PI controller is developed to control the DC bus voltage.

The input to the PI controller is DC voltage error e(t), which isgiven by

22)(ccref VVte (2.7)

Figure 2.3 shows the block diagram of the proposed PI Controller. In this

work, the value of pK and i

K are tuned by Zicholar Nihols method. The real

power requirement for voltage regulation is directly proportional to the square

of the dc voltage. Hence, square of the dc voltage is considered for calculating

the required real power to maintain constant voltage across the dc bus.

Figure 2.3 Block diagram of the DC voltage control using a PI controller

The controller adjusts the real power (Preg) requirement for voltage

regulation to keep the constant voltage across the capacitor.

26

2.2 PROPOSED CURRENT CONTROL TECHNIQUE

A constant frequency hysteresis current control strategy (CFHCC)

is proposed in this work for the current control of voltage source inverter. The

switching time for the inverter is determined by referring the method used by

Carl Ngai-Man Ho et al (2009). The proposed current control strategy is

explained through the circuit diagram shown in Figure 2.4. As shown in

figure, the active filter consists of three phase VSI which is needed to

compensate the three phase currents. Higher order harmonic current generated

by the switching of the power semiconductor devices of the inverter is filtered

by using the inductance Lf. Figure 2.5 shows the output waveform from the

inverter in one switching cycle for phase A. In this figure, *

fai is the reference

current for phase A and fai is the actual current which flows through the

coupling inductance Lf. The current controller guides the inductor current to

track the reference current. The conventional hysteresis control technique uses

the current ripple band to limit the inductor current between upperfai ,

and lowerfai , . When the inductor current reaches the upper band, a turn-OFF

command is given to switch S1. Similarly, when the inductor current reaches

the lower band, a turn-ON command is given.

In the CFHCC strategy proposed in this work, no physical band is

involved to limit the increasing or decreasing inductor current. The CFHCC

predicts the values of the two current signals, namely, *

fi and fi in the

inverter, based on the circuit parameters, namely coupling inductance, dc

voltage, and instantaneous feedback signals to determine the switching

actions.

27

Figure 2.4 Circuit diagram of voltage source inverter based Shunt

Active Filter

Figure 2.5 Output Waveform of Inverter

28

As shown in Figure 2.5, the current waveform has been divided into

two sections namely, positive half cycle (t0–t2) and negative half cycle (t2–t4),

in one switching period. The controller determines the time for turn-ON and

turn-OFF actions to achieve the desired half switching period, T/2, in positive

and negative sections. At the same time, the controller predicts the value of

*

fi as well. The system is operated with bipolar pulse width modulation

switching. The development of control algorithm for CFHCC which drives

the inverter at a constant switching frequency is described below.

Figure 2.6 Equivalent Circuit (a) Turn ON b) Turn OFF

Figure 2.6 (a) shows the equivalent circuit of the inverter when the

switches S1 and S6 are in turn-ON condition. From the figure, the loop

equation can be written as,

0)( aON

fa

fdc Vdt

diLV (2.8)

29

From eqn (2.8),

f

adc

ON

fa

L

VV

dt

di)( (2.9)

Figure 2.6 (b) shows the equivalent circuit of the inverter when the switch S4

and S5 are in turn-ON condition. In this case the loop equation can be written

as,

0)(aOFF

fa

fdcV

dt

diLV (2.10)

From eqn (2.10)

f

adc

OFF

fa

L

VV

dt

di)( (2.11)

wheredc

V is the dc link voltage,a

V is the instantaneous grid voltage, and Lf is

the output inductance. The voltage drop across internal resistance of the

coupling inductor is neglected. To predict the value of *

fai an assumption has

to be made that is *

fai changes linearly over one switching cycle. Then, the

controller can predict the crossover point by considering the instantaneous

slope of *

fai .

2.2.1 Turn-OFF Criteria

At 1t , the inductor current and reference current can be expressed as

)()( ,1 ofaON

ON

fa

fa titdt

diti (2.12)

30

)()(*

,

*

1

*

ofaON

fa

fa titdt

diti (2.13)

From equations (2.12) and (2.13)

)()()()(*

*

,11

*

ofaofa

ON

fafa

ONfafa titidt

di

dt

dittiti (2.14)

In Figure 2.5, at t0,

)()(*

ofaofatiti (2.15)

Hence, in the positive section ( )20 tt , the instantaneous slope of

*

fai is given by

ON

fafa

ON

fafa

t

titi

dt

di

dt

di

,

11

*** )()(

(2.16)

Using the value of slope OFFt , is estimated as given below.

At 2t , the inductor current and reference current are expressed as

)()( 1,2 titdt

diti

faOFF

OFF

fa

fa (2.17)

)()( 1

*

,

*

2

*tit

dt

diti faOFF

fa

fa (2.18)

From equations (2.17) and (2.18)

)()()()( 22

**

,11

*titi

dt

di

dt

dittiti fafa

OFF

fafa

OFFfafa (2.19)

31

In Figure 2.5, at t0,

)()( 22

*titi fafa

)]/()/[(

)()(

*

11

*

,dtdidtdi

titit

faOFFfa

fafa

OFF (2.20)

By using eqns (2.8) to (2.11)

1

,1

*

1

,

1

)]()(([

2

ONfafaf

dcOFF

ttitiL

Vt (2.21)

The turn-OFF time is estimated using (2.21) with instantaneous

feedback signals. The turn-OFF criterion is the time of *

fafa ii in positive that

is equal to half switching cycle as shown in Figure 2.5. Thus

2,,

Ttt ONOFF and 0

*

fafa ii (2.22)

where T is the switching period. Based on eqns (2.20) and (2.21), the

controller can determine the turn-OFF action at the most suitable time.

2.2.2 Turn-ON Criteria

In the negative section )( 42 tt , the instantaneous slope of *

fai is

given by

OFF

fafa

OFF

fafa

t

titi

dt

di

dt

dif

,

33

**

)()((2.23)

32

Based on the slope, ONt , is predicted as

)]/()/[(

)()(*

33

*

,dtdidtdi

titit

faONfa

fafa

ON(2.24)

By using (2.8), (2.9), (2.23) and (2.24)

1

,33

*,

1

)]()(([

2

OFFfafaf

dc

ONttitiL

Vt (2.25)

From eqn 2.25 the turn-ON time is estimated with instantaneous

feedback signals. The turn-ON criterion is the time of *

fafa ii in negative that

is equal to half switching cycle as shown in Figure 2.5. Thus

2,,

Ttt

ONOFF and 0*

fafa ii (2.26)

It is the same as positive section. Based on eqns (2.22) and (2.26),

the controller can be designed. The gate pulses (g1 and g4) for the inverter

(Phase A) using the proposed control logic can be derived using the circuit

shown in Figure 2.7.

33

Figure 2.7 Implementation of proposed control strategy

[

The switching function (g3 g6 and g2 g5) for the other two legs of

the inverter is derived by calculating the ON/OFF time using the reference

currents *

fbi and *

fci respectively.

2.3 SIMULATION RESULTS

This section presents the details of the simulation carried out on a

test system. The test system consists of a three phase voltage source, and an

uncontrolled rectifier with RL loads connected through circuit breakers

(CB1 and CB2) as shown in Figure 2.8. The active filter with proposed

control strategy is connected to the test system through an inductor Lf. The

values of the circuit elements used in the simulation are given in Table 2.1.

The design steps to determine system parameters are given in Appendix 2.

34

MATLAB/SIMULINK is used to simulate the test system and the proposed

shunt active filter. The active filter performance is evaluated under steady

state and transient system conditions. The comprehensive simulation results

are presented below.

Figure 2.8 Test System

35

Table 2.1 System Parameters

Parameter Specification

Supply phase to phase voltage,

frequency415 V (rms), 50 Hz

Line Parameters (Rs, Ls) 1 , 1mH

Load Resistance (R1,R2) 70 , 50

Load Inductance (L1,L2) 37 mH, 3mH

Filter coupling Inductance (Lf) 3 mH, 0.5

Inverter DC bus capacitor 1mF

Vdc (reference) 700V

Sampling Time sec102 6

Switching Frequency 16 kHz

No of samples taken for FFT

calculation10000

A. Steady State Performance

First the system is simulated without the filter. In this case the

circuit breaker 1 is closed and circuit breaker 2 is opened. The three phase

source current waveform in this case is shown in Figure 2.9(a). Figure 2.9(b)

shows the harmonic spectrum of the distorted waveform. The total harmonic

distortion of the distorted line current is 26.34%. The methodology of

calculating THD is given in Appendix 1. From the harmonic spectrum, it is

evident that, the source current is distorted due to the dominancy of fifth and

seventh harmonic spectral components.

36

(a) Distorted three phase source current

(b) Harmonic Spectrum of the source current

Figure 2.9 Distorted line current and harmonic spectrum caused by

three phase uncontrolled rectifier

Next, an active filter with proposed control strategy is connected in

parallel with the load. A PI controller is used to maintain the constant voltage

across the DC side capacitor. Figure 2.10 shows the source current along with

the frequency spectrum in the presence of the active power filter with the

CFHCC scheme. The performance of the active filter with the proposed

control algorithm is found to be excellent, and the source current is practically

sinusoidal and it is in phase with the supply voltage as shown in Figure 2.11.

The THD of current in Phase A, B and C has reduced to 3.87%, 3.89% and

3.39%. It shows that the THD is very much reduced after connecting the

filter.

THD = 26.34%

37

During the filtering process, the inverter charges/discharges the

inverter DC bus capacitor. Despite the resultant DC bus voltage fluctuations,

its average value remains constant in a lossless active filter. However, the

converter losses and active power filter exchange cause the capacitor voltage

to vary. Hence, the DC bus capacitor must be designed to achieve two goals,

i.e., to comply with the minimum ripple requirement of the DC bus voltage

and to limit the DC bus voltage variation during load transients. A

proportional and integral controller is implemented to control the DC bus

voltage. By controlling the real power, the dc bus voltage can be varied.

Hence, the error between the actual voltage and the reference is given as input

to the PI controller. The controller generates an output value corresponding to

the error value. The output of the controller is the real power required to

maintain the reference dc voltage. The calculated Figure 2.12 shows the

constant voltage (700V) maintained by the PI controller across the capacitor.

Figure 2.10 Harmonic current filtering with proposed CFHCC

Technique

38

Figure 2.11 Waveform of Source voltage and Current in Phase A

Figure 2.12 DC Bus Voltage Maintenance using PI Control

For comparison, next the active filter is simulated with fixed

hysteresis band current control technique. The hysteresis current controller

with fixed band (HB=0.1A) has been used to generate the gate pulses for the

inverter. Figure 2.13 shows the performance of the shunt active filter with

fixed hysteresis current control technique. In this case, the THD has reduced

to 4.1% which is high compared to the THD obtained using the proposed

technique. Also, the distortion in the supply current is high due to high ripple.

Table 2.2 gives the comparison of the individual harmonic level of source

current and voltage between the proposed technique and the FHBCC

technique. From this comparison, it is clear that the source voltage and current

39

harmonics have greatly reduced in the proposed technique compared to the

FHBCC.

Table 2.2 Harmonic Contents of the supply current and voltage

Harmonic

Order

Individual Harmonic Content (% of fundamental)

Without

Filter

Filter with

FHBCC

Filter with

CFHCC

Current Voltage Current Voltage Current

3 0 0.01 0.5 0 0.03

5 23 0.12 1.5 0.11 1.27

7 12 0.12 1.52 0.13 1.03

9 0 0.01 0.12 0.01 0.07

11 9 0.3 1.61 0.28 1.34

13 7 0.23 1.45 0.23 1.1

15 0 0.02 0.26 0.01 0.15

17 5 0.39 1.33 0.39 1.0

19 4 0.25 0.9 0.25 0.2

THD(%) 26.34 3.3 4.1 2.91 3.89

40

Figure 2.13 Fixed HBCC Technique – Source Current with its

Harmonic Spectrum

Figure 2.14 Average Switching Frequency of the Inverter

41

Figure 2.15 Current Ripple Band

In order to demonstrate the switching performance of the proposed

CFHCC, the average switching frequency is calculated over the time period of

0.5 sec which is given in Figure 2.14 (a). In the fixed hysteresis current

control technique, the switching frequency of the voltage source inverter

varies from 14kHz to 18kHz as shown in Figure 2.14 (b). In order to convert

the varying switching frequency to constant switching frequency, the width of

current ripple band must be varying in a line cycle. Hence, the CFHCC

determines the switching actions cycle by cycle to keep constant switching

frequency. It leads to different ripple current peak values in every switching

cycle. The ripple current is given in Figure 2.15. It is clear from the figure that

the ripple current is being enveloped by the current bands. Hence the

switching frequency is maintained constant. .

42

The proposed controller maintains the switching frequency at 16kHz

since it is designed for the switching period (ton+toff=T/2) of 1/16000/2 sec.

The periodogram of the inductor current is shown in Figure 2.16. From this

figure, it is evident that the switching frequency sharply concentrates at one

frequency, 16kHz.

Figure 2.16 Periodogram of Inductor Current

B. Transient Performance

To observe the transient characteristics of the proposed control

strategy, a step change in load current was applied. For this, the load I is

connected to the source upto 0.3 sec through circuit breaker I after that CB1

disconnect the load I from the source and CB2 connects the load II to the

source. Figure 2.17 (a) and (b) show the source current without shunt active

filter and with SAF respectively. The transient behavior of CFHCC is same as

that of the conventional fixed hysteresis control as shown in Figure 2.17(c).

But, unlike fixed hysteresis control, the proposed CFHCC is able to keep the

43

constant switching frequency after the transient period. But at transient time

(at 3 sec) there is a big current dip before the current returns to steady state as

shown in Figure 2.18. The reason for this is that the CFHCC predicts the

crossover point in each half switching period based on the instantaneous

current reference signal. When the current reference change occurs before the

command, the controller estimates incorrect turn-ON time since the initial

values of reference and actual current are same at the initial condition of the

timer.

Figure 2.17 Load and Source current waveform during step change in

load

44

cu

rren

t (A

)

Reference

Current

Actual Current

Time(sec)

Figure 2.18 Transient Response of the proposed Controller

2.4 CONCLUSION

This chapter has presented a Constant frequency hysteresis Current

Control Technique for developing the active filter. Instantaneous p-q theory

was employed for effectively computing the reference. The active filter was

simulated using MATLAB/ SIMULINK and the performance was analyzed in

a sample power system with a source and non-linear loads. The shunt active

filter is found to be effective to meet IEEE 519-1992 standard

recommendation on harmonic levels under ideal source voltage condition

with constant switching frequency. The proposed control technique has fast

dynamic response similar to conventional hysteresis control but it overcomes

the drawback of having variable switching frequency.