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Comparison of Three Phase Shunt Active Power Filter Algorithms Under Non-Ideal Mains

Voltages

S.H.Salleh, M.Z.Omar, J.Syarif, A.G.Jaharah, S.Abdullah and M.J.Ghazali

Department of Mechanical and Material EngineeringNational University of Malaysia, Malaysia.

ABSTRACT

The control of an active filter comprises two major parts: the reference current computation and thecurrent control. There are two fundamental methods of generating the reference current: (i)

frequencydomain methods, based on the Fourier analysis and (ii) time-domain analyze, based on the

theory of instantaneous imaginary power in the three-phase circuits, often called p-q theory. In this

work of p-q theory,(d-q) current method, modified p-q, synchronous detection methods , SynchronousReference Frame, Self-Tuned Vector Filter andFrequency Domain Control, are investigated for determining

the reference compensation currents of shunt APF with respect to balanced, unbalanced - distorted

source voltage conditions. The simulation is done on a three-phase system with a three-phase diode

rectifier(load1) and a thyristor converter controlled DC motor (load2)are taken as the nonlinearloads.. simulations using Matlab/Simulink andthe results are used for comparison

Key words : Active filters, current reference, compensation, harmonic,comparison

INTRODUCTION

Because of the use of more nonlinear loads, especially more power electronic equipments, alarge number of harmonic and reactive currents have been introduced into power grid, resulting in

some problems such as voltage flicker, frequency variation, imbalance of three-phase problem,

etc [1]. In order to suppress the harmonics, passive filters have been used in the past years [2],while recently Active Power Filter (APF) has been developed rapidly.

This research discusses the performances of APF systems using p-q theory,(d-q) current method,modified p-q, synchronous detection methods , Synchronous Reference Frame, Self-Tuned Vector Filter andFrequency Domain Control method for the control of current harmonics.

CONTROL OF APF SYSTEM

Principle of operation: Basically an APF system[6] is used for current compensation. The

compensation currents are generated by properly controlling the voltage source inverter (VSI)in the current control mode. It has been observed that for the successful operation of APF

system the capacitor voltage of the inverter system should be 1.5 times the maximum line-

to-line voltage[6]. A booster inductor could be used to convert the VSI in the current control

mode. In this research VSI is assumed to be instantaneous and infinitely fast to track thecompensation currents, hence it is modeled as a current amplifier with unity gain and the simulink

model of the inverter sub system used is shown in Fig. 1[7]. Seven different control

algorithms namely p-q, id - iq, modified p-q, synchronous detection methods , SynchronousReference Frame, Self-Tuned Vector Filter and Frequency Domain Control, are discussed to generate

the compensation currents.Conventional p-q method

Fig1. shows the block diagram of a typical APF system. The instantaneous reactive-power (p-q)theorem is proposed by Akagi et al. [57]. This theorem is based on 0 transformation which

transforms three-phase voltages and currents into the 0 stationary reference frame [14], [45], [58].

From this transformed quantities, the instantaneous active and reactive power of the nonlinear load is

calculated, which consists of a DC component and an AC component. The AC component is extractedusing HPF and taking inverse transformation to obtain the compensation reference signals in terms of

either currents or voltages. This theorem is suitable only for three-phase system and its operationtakes place under the assumption that three-phase system voltage waveforms are symmetrical and

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purely sinusoidal. If this technique is applied to contaminated supplies, the resulting performance isproven to be poor [59]. In order to make the p-q theorem applicable for single-phase system, some

modifications in the original p-q theorem were proposed and implemented by Dobrucky et al. [27].

Assume that the source voltage (v ) and load current (iL ) of a single-phase system are defined asvt= 2v sin( t) ; iLt = 2iL sin(t + )After complementing by fictitious imaginary phase (shifted by 90), the complemented source voltage

(v and load current (iL ) are defined asvt= 2v sin( t 90o ) ) ; iL t= 2iLsin(t +- 90)the orthogonal co-ordinate system is obtained, whereasv= vt and v vt i iLt and i iL tThus, the instantaneous active power of the load can be derived as

p = vi + vi= p + pThe instantaneous reactive power of the load can be derived as

q = vi vi = q + qFrom the obtained instantaneous active and reactive power, the AC components (pand q) areextracted using HPF. The extracted AC components are then used for compensation reference signalestimation.

Modified p-q method

Under non-ideal supply conditions, the mains voltage Vs can be unbalanced and/or distorted byharmonics. As shown in [3], the fundamental load current now can combine with the fundamental

negative sequence and harmonics in the voltage to produce extra ac-values inPL

andCiL'

Further, theharmonic currents and voltages which have the same order can produce extra de-power in PL and qL'Thus the instantaneous active and reactive load powers calculated in (2) will be distorted and the APFcannot compensate successfully the harmonic and/or reactive currents from the load.

To improve the performance of p-q method, Ozdemir et al. [6] proposed the use of fundamentalpositive sequence of voltage vs (hereinafter denoted as v;) in (2) and (5) to calculate PL, qL and theniF. The key point of this modified p-q method is to extract instantaneously v; from the three-phasemains voltage. Different from the method used in [6] which requires a rotating d-q frame, this paperproposes a new algorithm to detect v; in the stationary frame. Therefore, a PLL will not be requiredfor this algorithm.

-3 Self-Tuned Vector Filter

A. Time-domain expressions

The Self-Tuned Vector Filter (STVF) is, basically, a sequence filter that extracts one particularcomponent, of a given frequency, from a vector signal. The filter frequency may also be adjusted,or self- tuned. In Fig. 1, the structure of the filter is shown. As it can be seen, the filter is a first-order, two inputs, two outputs, coupled system. In the figure, (Ya, Yb) are the components of thevector to be filtered, and Yfa, Yfb the components of the filtered vector.The equations of thisfilter are, in time domain, as shown in (1)

i i. k . i ;

i i. k . i

where i, and ip represents the components of the filtered vector, i, and ip are the components of

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the input vector, kf is the filter constant, and ois the center frequency for the lilter.B. Frequency-domain expressionsEquation 1 could be represented in a vectorial form, in the frequency domain (2)

Also, the central frequency could be self-tuned, using aniterative process, being o proportional to

the modulus of vectorial product of the vector filtered and the input vector, asshown in (3). Thatfeature gives its name to this filter (self-tuned), although is not used in the present application, asthefrequency is a known constant (50Hz).

. .

-4 Synchronous-Reference-Frame Theorem

This theorem relies on the Parks Transformations to transform the three phase system voltage and

current variables into a synchronous rotating frame [13], [15],[17], [18], [40], [43], [44], [50]. The

active and reactive components of the three-phase system are represented by the direct and quadrature

components respectively. In this theorem, the fundamental components are transformed into DCquantities which can be separated easily through filtering. This theorem is applicable only to three-

phase system. The system is very stable since the controller deals mainly with DC quantities. Thecomputation is instantaneous but incurs time delays in filtering the DC quantities [54].

-5 Control of APF system using SDM:Synchronous-detection theorem [59], [61] is very similar to p-q theorem. This technique is suitableonly for three phase system and its operation relies in the fact that the three-phase currents are

balanced. It is based on the idea that the APF forces the source current to be sinusoidal and in phase

with the source voltage despite the load variations. The average power is calculated and divided

equally between the three-phases. The reference signal is then synchronised relative to the sourcevoltage for each phase. Although this technique is easy to implement, it suffers from the fact that it

depends to a great extent on the harmonics in the source voltage [10].-6 frequency domain based on Fourier analysis

for the control of shunt active power filter. It compensates harmonics and reactive power requirement

of nonlinear loads, and maintains similar distortion in the compensated current as present in the mains

voltage.Therefore, load behaves as a linear/resistive load, and the resultant source current will have

the same waveform as that of the supply voltage.The non-sinusoidal utility voltage and current signal

can be expressed as a sum of sinusoidal signal of various frequencies as :

sin 1, sin

2

Where, and , are the phase difference oforder voltage and current waveform. The referencecurrent drawn from the source is the portion of the current, which retains the same level of distortion

as of the voltage, while at the same time accounts for the entire fundamental frequency component.

The reference current has the same graphical pattern of variation as the voltage. It might have a time

leg or lead or may be in phase with the voltage, depending on the harmonic or harmonic and reactive

power compensation capability. Thus the fundamental frequency component of the reference current

will equal to the fundamental frequency component of load current (plus loss component) forharmonic compensation, and cos(plus loss component) [12] for both harmonic and reactivepower compensation respectively. All other frequency components will be in the same proportion as

their counterparts in the voltage, which can be mathematically expressed as:

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Load1

a) p-q theory

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b) id-iq method

c) modified pq theory

d) sdm method

e) srf method

f) stvf method

j) fdc method

Load2

a) p-q theory

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b) id-iq method

c) modified pq theory

d) sdm method

e) srf method

f) stvf method

j) fdc method

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CONCLUSION

The paper presents a comparative study of seven compensation methods for three phase shunt active

filters under balanced, unbalanced - distorted mains voltage conditions. In the simulation study, it is

shown that the p-q method has poorer performance than the id-

iq

method under unbalanced and

distorted mains voltage conditions. However the solution based on using a PLL circuit for better

performance of the p-q theory works well under unbalanced and distorted mains voltage but it has the

disadvantage of its fairly complex algorithm and requirement of a PLL circuit. The synchronous

detection methods performance is poor in respect to the voltage distortion but good at unbalanced

condition and demands less calculations due to the needlessness of reference frame transformation.

Another disadvantage of this method is that it assumes equal currents in every phase which meaning

balanced load conditions.

Although the historically important p-q theory is limited to balanced voltage conditions, the

modified version of it is the most effective method for all voltage conditions.

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REFERENCES