SMC_ActiveFilter

7/31/2019 SMC_ActiveFilter

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SLIDING-MODE CONTROL FOR A SINGLE-PHASE

ACTIVE POWER FILTER

IU KHIN TRT B LC CNG SUT TCH CC MT PHA

Son.T.Nguyen, Thanh.V.NguyenHanoi University of Science and Technology

ABSTRACTThis paper presents the method of designing a non-linear controller for a single-phase active

power filter (APF) that is connected power electronic loads in parallel. In particular, a controller withsliding-mode control is developed for this application. A single-phase APF has the topology of an H-bridge with four MOSFET switches connected the load via an inductor and connected a capacitor inthe DC bus. With the structure like this, the model of the APF can be seen as a variable structuremodel and is well suited with the sliding-mode control. In this application, the sliding mode controlalways guarantees the shape of the main current to be sinusoidal and coincide with the phase of themain voltage. The simulation results show that the sliding-mode control always maintains the goodperformance of the APF when working at different conditions. Moreover, the control algorithm is easilydeployed on low-cost digital control systems.

TM TT

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1. INTRODUCTION

The wide application of power electronic

devices causes the distortion of the main currentdue to the power electronic devices work asnon-linear loads. One of the methods foreliminating the harmonic distortion of thesingle-phase load is using the active powerfilter (APF) connected with the load in parallel.The function of the active filtere is generating aharmonic compensation current that is able toeliminate harmonic components generated bythe load.

Recently, there have been some methodsof designing the single-phase APF. Most ofthese methods include two following steps:

Step 1: Determining the compensationcurrent for the active fitlter with the linefrequency of the non-linear load.

Step 2: Designing the controller for ACcurrent of the filter computed in step 1.

Essentially, the compensation current isthe inverse of the harmonic current via the load.According to [1, 2], there are some methods ofdetermining the harmonic current such as Fast

Fourier Transform (FFT), instantaneous powertheory, synchronous d q theory, instantaneous

p q

theory. For FFT method, the exactcomputation method requires two cycles of thewave needed to be analysed: the first cycle fordata acquisition and another cycle for analyzingdata. For other method, the implementation isquite complicated. Recently, the use of adaptivelinear neural networks can be seen one of themethods for determining the compensationcurrent [3]. However, this method requirescostly hardware such as digital signal processor(DSP) or specific digital control systems.

This paper decribes a simple method thatis able to combine two steps when designing

the single-phase APF. In particular, a sliding-mode control is developed to guarantee themain current to be sinusoidal and coincide withthe phase of the main voltage. The mainadvantage of this method is that it has the fastcomputation and is easy to be deployed oncheap digital control systems.

This paper is organized as follows.Section 2 summarizes the model of a single-phase APF. In section 3, the authors mention


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the development of sliding-mode control forthis application. Section 4 are simulation resultsobtained by using Matlab/Simulink. Finally,Section 5 is the conclusion of this research.

2. MODEL OF A SINGLE-PHASE APF

The single-phase APF is connected witha non-linear load in parallel as shown inFigure.1. The power of the resistive load ischanged by adjusting the firing angle of theTriac. The APF has four controllable switches

1 2 3, ,S S S and S and is connected with thenon-linear load via an inductor L andconnected with a capacitor Cin the DC bus.The values of the inductor L and the capacitorCdepend on the maximum power of theresistive load.

In order to guarantee the APF workingcorrectly, the switches in the same legs of theH-bridge have to work in reverse order. Thismeans that if 1S is closed then 2S is open, if

3S is closed then S is open. Therefore, thecontrol of the H-bridge is essentially controllingtwo switches 1S and S .

Fig.1. A single-phase APF is connected with a

power electronic load in parallel.

The model of the single-phase APF is avotage source inverter with the DC votage isformed on the capacitor Cdepending onswitching status of the swiches on the H-bridgeas shown in Figure.2. Another matter is that the

law of switching 1S and S has to guaranteethe voltage on the capacitor greater than themaximum voltage of the AC source at anymoment. Therefore, the control law has to besatified the first condition as follows:

( )0 2c sV V V> (1)

whereC

V is the voltage on the capacitor C, 0V

is the reference voltage andS

V the r.m.svotlage of the AC source.

Fig.2. The APF is developed by the principle of

a voltage-source inverter

If 1u and u are called logic signals (0 or 1)

for closing and opening the switches 1S and S with the rule below:

If 1 1u = then 1S is closed, if 1 0u = then1S is open.

If 4 1u = then S is closed, if 4 0u = thenS is open.

Two equations of the inverter have thefollowing forms:

( )1 41

1L s ci V u u V L

= + i

(2)

( )1 41

1c LV u u iC

= + i

(3)

According to equations (2) and (3), thecurrent Li is governed by the voltage on thecapacitor and the switching status of 1S and S .

3. SLIDING-MODE CONTROL

In control theory, sliding-mode control(SMC) is a control form that has variablestructure. This is a non-linear control methodthat changes the dynamics of a non-linearsystem by high-frequency switching control.SMC is concerned with forcing one or moreforce variables (often, but not necessary, statevariables) to follow a specific trajectory. Thetrajectory is known as the sliding surface. Thelocation of the variables relative to the slidingsurface governs the control law which isapplied to the system. As the system variablesof interest pass through the sliding surface, thecontrol law changes. The nonlinear control lawis chosen so that regardless of where the systemis with respect to the sliding surface, controlactions always drive the system toward the


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sliding surface. Power electronic systems arenatural candidates for sliding-mode controlbecause topologies of power electronic circuitsalways change with the operation ofsemiconductor switches.

The starting point with the sliding modecontrol is the defination of a sliding surface. For

the single-phase APF, we are interseted inforcing the source current to be the same shapeas, and in phase with, the source voltage.Therefore, the trajectory for the line current isdefined as follows:

s si kV = (4)

where k is a scaling factor based on the realpower demand of the loads. In the standardform, the sliding surface is written as follows:

0s ss i kV = = (5)when the source current is on the slidingsurface. In order to guarantee the system on thesliding surface, the following condition has tobe satisfied at any moment:

0s s i

(6)In order to have condition (6) to be

always satisfied, the sign of si

has to becontrolled approximately. At any time, the APF

can make the sign of sii

positive or negative

due to the switching status of the switches onthe H-bridge. In addition, the procedure ofdesigning a correct power circuit will always

guarantees s

i kV>i i

. Therefore, we can control

si

following the non-linear control law asshows in Table.1.

In other words, we have:

s ss i kV = i i i

(7)The source current

si is the sum of the

determinationLi and the load current i . When

si is on the sliding surface, from (7) we have:

( )1 4

11 0ss ci V u u V kV

L+ + =

i i

(8)

According to Table.1, we can use logic value ofswitch 4 as follows:

( )4

1

2s

sgn V u

+= (9)

where ( ) 1ssgn V = if 0sV > and ( ) 1ssgn V = if

0sV < .

Substitute (9) into (8) and solve equation(8) with variable 1u we have:

( )1

1 sgn

2ss

s

s c

VVLu i kV

V V

= + +

i i

(10)

Equation (10) is popularly used in

inverter simulations.

Table.1 The non-linear control law used to

implement the sliding mode control for the APF

s si kV<

s si kV>

1u 0 1

2u 1 0

0sV < 0sV >

3u 1 0

u 0 1

4. SIMULATION AND RESULTS

In this part, the control algorithm of theAPF was tested in Matlab/Simulinkenvironment. The simulation procedureincludes four following steps: Step 1: Determining the maximum power

of the load. In this case, we assume that theresistive power of the load is adjustable bychanging the firing angle of the Triac. Themaximum resistive power is 10kW. The

r.m.s value of the source voltage is 220V . Step 2: Determining the values of the

inductor L and the capacitor C. In thiscircumstance, 0.001L H= and

1000C F= are suitable for compensatingthe minimum to the maximum power.

Step 3: Choosing the parameter for the non-linear controller. For the convenience, wechoose 1

sk = .

Step 4: Choosing the parameters for the PIcontroller including the reference voltageon the DC bus 0V , the proportional

coefficient pK , the integral coefficient iK and the saturation output of the PIcontroller M . In this case, thosecoefficients are chosen as shown in Table.2.


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Table.2 The coefficients of the PI controller

used to stabilize the voltage on the capacitor C

pK iK M 0,001 0,08 5

In order to verify the control algorithm at

different conditions, the load was supplied bythe source voltage with different firing anglesof the Triac 0 0 030 , 60 ,90 and 0120 . Theswitching frequency of the DFETs on the H-bridge is 50 Hz

Figure 3, 4, 5 and 6 are waveforms ofcurrents without and with the use of the APF.Table.3 is the summary of the total harmonicdistortion (THD) of the source current whenusing the APF. The THD of the source currentafter the compensation reduces to half of THDof the source current before filtering

0 0. 01 0. 02 0. 03 0. 04 0. 05 0 .06 0. 07 0. 08 0 .0 9 0 .1-100

-50

0

50

100

i

time(s)

0 0. 01 0. 02 0. 03 0. 04 0. 05 0 .06 0. 07 0. 08 0 .0 9 0 .1-100

-50

0

50

100

is

time(s)

Fig.3. Waveforms of the currents when firing

angle of Triac0

30 = : load current (abovecurve) and grid side current (below curve).

0 0.0 1 0. 02 0. 03 0. 04 0. 05 0 .06 0. 07 0. 08 0. 09 0. 1-100

-50

0

50

100

i

time(s)

0 0.0 1 0. 02 0. 03 0. 04 0. 05 0 .06 0. 07 0. 08 0. 09 0. 1-200

-100

0

100

is

time(s)


angle of Triac 060 = : load current (abovecurve) and grid side current (below curve).

0 0. 01 0. 02 0. 03 0 .04 0. 05 0. 06 0. 07 0. 08 0. 09 0 .1-100

-50

0

50

100

i

time(s)

0 0. 01 0. 02 0. 03 0 .04 0. 05 0. 06 0. 07 0. 08 0. 09 0 .1-100

-50

0

50

100

is

time(s) Fig.5. Waveforms of the currents when firing


0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 0. 1-100

-50

0

50

100

i

time(s)

0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 0. 1-100

-50

0

50

100

is

time(s)



0 0. 01 0.02 0. 03 0.04 0. 05 0.06 0. 07 0. 08 0. 09 0. 1-100

-50

0

50

100

is

time(s)

0 0. 01 0.02 0. 03 0.04 0. 05 0.06 0. 07 0. 08 0. 09 0. 10

100

200

300

400

Vc

time(s)

Fig.7. Source current after filtering (abovecurve) and the voltage on the capacitor

C(below curve) when the firing angle of Triac090 = .


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Table.3 THD of the source current according to

different working schemes of the loadFiring

angle ( )

THD (%)

without filter

THD (%)

with filter030 15.12 7.890

60 37.75 15.49

090 65.06 33.690120 102.6 63.27

4. CONCLUSIONS

The simulation results obtained show thatthe advantage of sliding-mode control for thisapplication is simple. Therefore, the controlalgorithm is easily deployed on low-cost digitalcontrol systems. The THD of the source current

after the compensation reduces to half of THDof the source current before filtering.

REFERENCES

[1] M.Rukonuzzaman and M.Nakaoka, "Single-phase shunt APF with Adaptive Neural NetworkMethod for Determining Compensating Current," The 27th Annual Conference of the IEEEIndustrial Electronics Society, pp. 2032 - 2037, 2001.

[2] J.-Q. W. Shu-Guang Sun, Shun-Quan Shi, "Study on Two Detection Methods for Harmonics andReactive Currents," Proceedings of the Seventh International Conference on Machine Learningand Cybernetics, Kunming, 12-15 July 2008, pp. 1445 - 1449, 2008.

[3] P. Salmern and J. R. Vzquez, "Practical Design of a Three-Phase Active Power-LineConditioner Controlled by Artificial Neural Networks," IEEE Transactions on Power Delivery,Vol. 20, No. 2, April 2005, vol. 20, pp. 1037 - 1044, 2005.

[4] David A. Torrey and A. M. A. M. Al-Zamel, "Single-phase Active Power Filters for MultipleNonlinear Loads," IEEE Transactions on Power Electronics, Vol. 10, No. 3, May 1995, vol. 10,pp. 263 - 272, 1995.

[5] D. Ibrahim,Microcontroller Based Applied Digital Control: Wiley, 2006.

Authors address: Nguyen Thanh Son Tel: (+844) 3869.2511,Email: [email protected] of Electrical EngineeringHanoi University of Science and TechnologyNo. 1, Dai Co Viet Str., Ha Noi, Viet Nam

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