performance investigation of fractional-order pi …

PERFORMANCE INVESTIGATIONOF FRACTIONAL-ORDER PI BASED

UNIFIED POWER QUALITYCONDITIONER

Dr.M.Ramesh1, Dr.T.Anil Kumar2,1Professor and HOD,1Professor

1Vaageswari college of Endineering,Karimnagar,Telengana

2Anurag Group of Institutions(CVSR),Venkatapur(V),Ghatkesar(M)[email protected]

October 12, 2018

Abstract

To improve power quality parameters of distribution sys-tem consisting of nonlinear loads, a UPQC (Unified PowerQuality Conditioner) is introduced. This UPQC shall ad-dress well known power quality issues. In this proposedwork to make the performance of UPQC more roust by in-troducing novel control strategy known as Fractional Or-der PI (FOPI) controller. The performance of FOPI basedUPQC demonstrated over PI based UPQC.

Index Terms: Unified Power Quality Conditioner (UPQC),power quality (PQ), proportional integral (PI), fractionalorder PI (FOPI), voltage source inverter (VSI), Active Powerfilter (APF).

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International Journal of Pure and Applied MathematicsVolume 120 No. 6 2018, 473-493ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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1 INTRODUCTION

The unified power quality control conditioner was widely studied bymany as an eventual method to improve power quality of electricaldistribution system [1-3]. It has been viewed as a combination ofseries and shunt active filter in [2-3]. In [3] it has been shown thatit can be used to attenuate current harmonics by inserting a seriesvoltage proportional to the line current. Alternatively, the insertedseries voltage is added to the voltage at the point of common cou-pling such that the device can provide a buffer to eliminate anyvoltage dip or flicker. It is also possible to operate it as a combi-nation of these two modes. In either case, the shunt device is usedfor providing a path for the real power to flow to aid the operationof series connected VSI. Also included in this structure is a shuntpassive filter to which all the relatively low frequency harmonics aredirected. The performance of UPQC depends upon the accuracyof the reference signals derived. From the distorted signal, a suit-able dc-link current regulator is used to derive the actual referencesignals. Various approaches, such as PI, PID, Fuzzy logic, Artifi-cial Neural network, sliding mode controller, etc., are used in [4-5].Similar to the PI control, the PID controller requires precise lin-ear mathematical models, which are difficult to obtain, and hencefails to perform satisfactorily under sensitive load disturbance, etc.In recent past authors proposed Modern control theory-based con-trollers are state feedback controllers, self-tuning controllers, andmodel reference controllers, etc.In this proposed work a controlleris designed based on fractional order calculus(i.e. Fractional or-der PI controller) for the control of UPQC. These controllers alsoneed mathematical models and are therefore sensitive to parametervariations.A basic system configuration of a general UPQC con-sisting of the combination of a series active power filter and shuntactive power filter are connected back to back to a common dc-link bus [8]. A simple configuration of a typical UPQC is shown inFig.1.Isolation of harmonics between sub transmission system anddistribution system can be done by series active power filter. Thisfilter mitigates sag, swell and harmonic compensation at Point ofCommon Coupling (PCC).The current harmonics are compensatedby shunt active power filter. The DC link to regulate DC voltagebetween two filters.

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International Journal of Pure and Applied Mathematics Special Issue

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Fig.1. Unified Power Conditioner configuration.

A. Series active power filter control algorithm The series activepower filter control algorithm used here is based on the conceptof unit vector template (UVT) as proposed in [8]. The UVT isextracted from the distorted supply. The extraction process andcontrol algorithm is shown in Fig.2.

Fig.2. Control System block diagram of Series APF

B. Shunt active power filter control algorithm Instantaneous re-active power theory (p-q theory) used for the control of active powerfilters. Transformation of three phase voltages and currents froma-b-c coordinates to d-q coordinates by utilizing these modellingequations.

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Active and reactive components are obtained by the given rela-tion in equation-3.Where Active and reactive components are func-tion of load current and phase voltages.

Isd,ref and Isq,ref are reference currents of shunt active powerfilter in d-q coordinates. These current are transformed to three-phase system as shown in equation -7

The reference current in the three-phase system (Ica,ref , Icb,ref , Icc,ref )are calculated in order to compensate neutral, harmonic and reac-tive current in the load. Hysteresis band current control algorithm[9]is used to generate switching signal by comparing actual signalwith reference signal, depending on speed and accuracy of referencesignal the performance of UPQC can be improved.

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Fig.3. Control System block diagram of Shunt APF

2 Design of Fractional Order Control

Before defining the FOPI controller, it is important to understandthe fractional order derivative operator. Once the fractional op-erator was mathematically defined, the use of fractional calculusin control system became widespread. The mathematical form ofFOPI is

Where can take any value in the range (0, 2). If 2 the controller istransformed to a higher-order structure which is of different formin comparison to convention PI controller. The fractional ordercontroller described in (8) may be regarded as the general case ofthe conventional PI controller.

3 DESIGN OF FILTER USING FRAC-

TIONAL ORDER CONTROLER

In the development of fractional-order calculus, there appeared dif-ferent definitions of fractional-order differentiations and integra-tions. Some of the definitions extend directly form integer- order

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calculus. The well-established definitions include the Cauchy inte-gral formula, the Grunwald-Letnikov definition etc., gives good fit-ting to the fractional-order derivatives. However, in control systemanalysis and design, the definition is not useful, since the samplesof the function should be known. Online real-time fractional-orderdifferentiation may be required in control systems. Using filters isone of the best way to solve the problems.Some continuous filters have been summarized in [12]. Among thefilters, the well-established refined recursive filter has a very goodfitting to the fractional-order differentiators [13]. Assuming the ex-pected fitting range is (ωb, ωh), the fractional-order operator sλ canbe approximated by the fractional-order transfer function or filtercan be written as,

In the frequency range ωb < ω < ωh by using a Taylor series ex-pansion, we obtain

It is then found that

Truncating the Taylor series to leads to

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Thus, the fractional-order differentiator is defined as

Equation (14) is stable if and only if all the poles are left-hand sideof the complex s-plane. The poles of the above expression is

• One of the pole is located at −bωh/d which is negative realpole since ωh > 0, b > 0, d > 0;

• The two other poles are the roots of the equation

Whose real parts are negative since 0 < λ < 1. Thus, all the poles of(14) are stable within the frequency range (ωL, ωH). The irrationalfractional-order part of expression (14) can be approximated by thecontinuous-time rational model.

According to the recursive distribution of real zeros and poles, thezero and pole of rank k can be written as

Thus, the continuous rational transfer function model can be ob-tained [107] as

Through confirmation by experimentation and theoretical analysis,this synthesis approximation can obtain the good effect when b =10 and d = 9. Through the approximation method, the fractional-order system may be approximated as the very high integer-ordersystem. The high integer-order rational transfer function could bevery tedious. A fractional-order integration can be obtain chang-ing the sign of order (λ). Hence, the range of λ for integration is

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−1 < λ < 0. The structure of FOPI controller is shown in Fig.4. To design a controller the proportional element, the fractionalintegrator are individually designed and place in the structure showin Fig. 4.

Fig-4: Structure of FOPI controller

4 SIMULAITON RESULTS

Simulations are performed using MATLAB-SIMULINK.The pa-rameters used to simulate UPQC are given in Table-I.

Table-1: UPQC system parameters

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Fig-5 (a). UPQC Configuration

Fig-5 (b). Shunt Control block

Fig-5 (c). Series Control block

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Fig-5 (d). Series and Shunt filter block

Fig-5 (e). Series Transformer block

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Fig-5(f). Non-Linear Load

A.Voltage and current harmonics Compensation In the conven-tional and proposed control algorithm, the simulation results loadcurrent (ILabc), source current (ISabc), and compensating current(ICabc) waveforms are shown in Fig. 8, before and after the UPQCis operation with PI control and FOPI control for λ = 0.5.Fig. 9 shows the simulation results for load voltage harmonics miti-gation with UPQC based PI and FOPI controller when introductionof 5th (20%) and 7th (14%) order voltage at 0.2 sec for a durationof 0.2 sec into the source voltage as shown in Fig. 9(a). The seriesAPF injects an out-of-phase voltage with 5th and 7th harmonicswhich is difference between the desired load voltage and actual sup-ply.

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Fig-88(a). With UPQC based PI control

Fig-8(b) With UPQC based FOPI control for λ=0.5Fig. 8. Load, source and compensating current before and after

UPQC operation.

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Fig. 9. Mitigation of load voltage harmonics with UPQC based PIcontrol and FOPI control

Simultaneously, shunt APF with PI control and FOPI controlregulates the dc-link voltage to the reference dc-link voltage asshown Fig. 10. Fig. 9(b) and Fig. 9(c) shows the operationof UPQC with PI control and FOPI control which mitigates loadvoltage harmonics to %THD = 0.86 and 0.82 respectively from thesource voltage with %THD = 24.62.

Fig. 10. Regulation of DC-Link voltage for harmonics in sourcevoltage

B.Voltage sag and current harmonic compensation The simula-tion results of voltage sag and current harmonics compensation for

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UPQC based PI control and FOPI control is observed in Fig.11 and12 respectively.A sag of 25% is introduced into the supply voltageat 0.7 sec and lasts till 1.3 sec, can be seen in Fig. 11(a).

Fig. 11 Mitigation of Load voltage sag and current compensationby UPQC based PI control

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Fig. 12 Mitigation of Load voltage sag and current compensationby UPQC based FOPI control

The series APF injects the voltage in phase to the load voltageas shown in Fig. 11(c) and Fig. 12(b) into the system in order tomitigate the load voltage sag can be seen in Fig. 11(b) and Fig.12(a). In doing this, series filter demands active power which isdrawn from the source through shunt APF via dc-link, by drawingextra current component as in Fig. 11(d) and Fig. 12(c) in orderto keep this DC link voltage at fixed level as shown in Fig. 13. If itis not maintained, the DC link voltage will drop to very low valueand UPQC fails.

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Fig. 13. Regulation of DC-Link voltage for Voltage sag

C.Voltage swell and current harmonics compensation The sim-ulation results of voltage swell compensation by UPQC based PIcontrol and FOPI control is shown in Fig. 14 and Fig. 15 respec-tively. A swell of 25% is introduced to the supply voltage at 1.7sec and lasts till 2.3 sec as shown in Fig .14(a). The voltage sagand swell conditions are opposite to each other.Therefore, during asource side voltage swell, the series active filter injects out-ofphasevoltage with a certain magnitude as shown in Fig. 14(c) and Fig.15(b) such that there is a desired magnitude at load side with mini-mum harmonics as shown in Fig 14(b) and Fig 15(a).Hence, UPQCcancels the increased source voltage that may appear at the loadside.The increase in source voltage reflects that the utility is sup-plying some extra power to the load which may damage equipmentsand loads due to the increase in current drawn by them.

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Fig. 14 Mitigation of Load voltage swell and currentcompensation by UPQC based PI control

Fig. 15 Mitigation of Load voltage swell and currentcompensation by UPQC based FOPI control

At the same time, rise in source voltage results in the increase

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in DC-link voltage and is regulated by shunt APF by respectivecontroller as shown in Fig. 16. Reduced supply current under theaforesaid condition as shown in Fig. 14(d) and Fig. 15(c).

Fig. 16 Regulation of DC-Link voltage for Voltage swell

From Fig. 10, 13 and 15, it is observed that the FOPI controllerregulates the dc-link voltage faster than PI control which showsthat proposed controller calculates the reference current more effi-ciently and quickly than conventional controller. Table II gives theharmonic comparison of UPQC based FOPI controller with UPQCbased PI controller. Here, Load current is constant throughout thesimulation for all controllers with %THD = 25.68. From Table II,the performance is found to be in close approximation with that ofthe PI controller; however, there is considerable improvement canbe observed which shows the FOPI controller has good performancewith the extra parameter included into the controller.

Table II Comparison of %THD in voltage and current for UPQCbased PI and FOPI controller.

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5 CONCLUSION

In this proposed work a FOPI based UPQC is proposed to addressthe well known power quality issues, popularly known as harmoniccompensation and load voltage sag. The performance of UPQC isdemonstrated on power distribution system consisting of nonlinearloads. The UPQC with FOPI controller is quite capable of miti-gating power quality issues compared to UPQC with PI controller.

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