PI, PID and Fuzzy logic controller for Reactive Power and Harmonic Compensation

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This article describes the proportional integral
(PI), proportional integral derivative (PID) and fuzzy logic
controller (FLC) based three phase shunt active power line
conditioners (APLC) for the power-quality improvement such
as reactive power and harmonic current compensation
generated due to nonlinear loads. PI, PID controller requires
precise linear mathematical model and FLC needs linguistic
description of the system. The controller is capable of
controlling dc capacitor voltage and generating reference
source currents. Hysteresis current controller is used for
current control in PWM voltage source inverter. Extensive
simulation studies under transient and steady states are
conducted, the simulation result analysis reveal that the
APLC performs perfectly in conjunction with PI, PID and
FLC. A comparative assessment of the three different
controllers is brought out.

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PI, PID and Fuzzy logic controller for Reactive Power and Harmonic Compensation

  1. 1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 PI, PID and Fuzzy logic controller for Reactive Power and Harmonic Compensation Karuppanan P and Kamala Kanta Mahapatra Dept of ECE, National Institute of Technology-Rourkela, India-769008 Email: karuppanan1982@gmail.com, kmaha2@rediffmail.comAbstract— This article describes the proportional integral under both steady state and transient conditions. The(PI), proportional integral derivative (PID) and fuzzy logic operation of APLC is demonstrated in details. The methodscontroller (FLC) based three phase shunt active power line of extracting reference current(s) and dc capacitor voltageconditioners (APLC) for the power-quality improvement such is also presented. The results are also presented thatas reactive power and harmonic current compensation validates the concept and a comparative assessment isgenerated due to nonlinear loads. PI, PID controller requiresprecise linear mathematical model and FLC needs linguistic done.description of the system. The controller is capable ofcontrolling dc capacitor voltage and generating reference II. DESIGN OF SHUNT APLCsource currents. Hysteresis current controller is used for The active power line conditioner comprises of sixcurrent control in PWM voltage source inverter. Extensivesimulation studies under transient and steady states are power transistors six power diodes, a dc capacitor , threeconducted, the simulation result analysis reveal that the filter inductor. Reduction of current harmonics is achievedAPLC performs perfectly in conjunction with PI, PID and by injecting equal but opposite current harmonicFLC. A comparative assessment of the three different components at the point of common coupling (PCC), thiscontrollers is brought out. facilitates improving the power quality on the connected power system. The APLC additionally supplies the reactiveIndex Terms—Proportional Integral (PI) controller, current component of the load current. The block diagramProportional Integral Derivative (PID) controller Fuzzy logic of APLC is shown in fig 1. The output voltage of thecontroller (FLC), Hysteresis current controller (HCC), Active inverter is controlled with respect to the voltage at the pointpower line conditioners (APLC). of common coupling. The design of the DC side capacitor is based on the principle of instantaneous power flow. The I. INTRODUCTION selection of C DC can be governed by reducing the voltage AC power supply feeds different kind of linear and ripple.non-linear loads in utilities and industrial applications. The The instantaneous current can be written as [4]non-linear loads produce harmonics. The harmonic and is (t ) = iL (t ) − ic (t ) (1)reactive power cause poor power factor and distort the Source voltage is given bysupply voltage at the common coupling point or customer vs (t ) = Vm sin ωt ( 2)service point [1-3]. Passive L-C filters are used tocompensate the lagging power factor of the reactive load, If a nonlinear load is applied, then the load current willbut there are drawbacks such as resonance, large size, have a fundamental component and harmonic components,weight, etc., the alternative solution, are an active power which can be represented as ∞line conditioner (APLC) that provides an effective solutionfor harmonics elimination and reactive power iL (t ) = ∑I n =1 n sin( nωt + Φ n )compensation. The controller is the most important part ofthe APLC and currently lot of research is being conducted ⎛ ∞ ⎞in this area. PI and PID controllers have been used to = I1 sin(ωt + Φ1 ) + ⎜ ⎜ ∑ I n sin( nωt + Φ n ) ⎟ ⎟ (3)extract the fundamental component of the load current(s) ⎝ n=2 ⎠and simultaneously control dc capacitor voltage of the The instantaneous load power can be given asshunt APLC [1-2]. Recently, fuzzy logic controllers (FLC) p L (t ) = is (t ) * vs (t )are used in power electronic system [3-5] as it can handle = Vm sin 2 ωt * cos φ1 + Vm I1 sin ωt * cos ωt * sin φ1nonlinearity, and it is more robust than conventionalnonlinear controllers. ⎛ ∞ ⎞ This paper explores the potential and feasibility of PI, + Vm sin ωt * ⎜ ⎜∑ I n sin(nωt + Φ n ) ⎟ ⎟PID and FLC schemes that are suitable for extracting the ⎝ n=2 ⎠fundamental component of the load current(s) and = p f (t ) + pr (t ) + p h (t ) (4)simultaneously controlling dc capacitor voltage of the From the equation the real (fundamental) power drawn byshunt APLC. The performance of APLC with different the load iscontrollers are evaluated through computer simulations 54© 2010 ACEEEDOI: 01.IJEPE.01.03.134
  2. 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 3-Phase Source isa,isb, isc Non-Linear Load A ILa,iLb, iLc A B RL B C C LL Ica,icb, icc vsa,vsb, vsc Rs,Ls Rc,Lc Active Power Filter A B VDC C G PWM-VSI inverter g1 g2 g3 g4 g5 g6 Active Power Controller isa* Proportional Integral Hysteresis Current isb* Reference current (Or) VDC Controller Generator Proportional-Integral Derivative isc* (Or) Fuzzy Logic Controller VDC ref isc isb isa vsc vsb vsa Fig 1 Block diagram of the Proposed APLC based on Fuzzy logic controller or Proportional-Integral controllerp f (t ) = Vm I1 sin 2 ωt * cos φ1 = vs (t ) * is (t ) (5) PID-ControllerFrom this equation the source current supplied by the PI-Controllersource, after compensation is Gain p f (t ) Vdc,ref is (t ) = = I1 cosφ1 sin ωt = I sm sin ωt (6) vs (t ) Integrator Gain Saturationwhere, I sm = I1 cos φ1 (7) Derivative Gain VdcThe total peak current supplied by the source is LPF isa* I sp = I sm + I sl (8) Vs Gain XIf the active filter provides the total reactive and harmonic isb*power, then is(t) will be in phase with the utility voltage Vs Gain Xand purely sinusoidal. At this time, the active filter must isc*provide the following compensation current: Vs X Gain ic (t ) = iL (t ) − is (t ) (9)The desired source currents, after compensation, can be Fig 2 PI and PID- controller for reference current generatorgiven Its transfer function can be represented as isa * = I sp sin ωt (10) K isb * = I sp sin(ωt − 1200 ) (11) H ( s) = K P + I (13) s isc * = I sp sin(ωt + 1200 ) (12) where, K P is the proportional constant that determines the dynamic response of the DC-bus voltage control and K I isWhere I sp = I sm + I sl is the amplitude of the desired the integration constant that determines it’s settling time. PIsource current. controller to eliminate the steady state error in dc voltage.A. Proportional Integral (PI) Controller: The proportional gain [ K P =0.3] and integral gain [ K I =9] Figure 2 shows the block diagram of the proposed PI are set such way that Vdc across capacitor is nearly equal tocontrol scheme of an APLC. The DC side capacitor voltage the reference value of Vdc .is sensed and then compared with a reference value. Theobtained error e = Vdc ,ref − Vdc at the nth sampling instant is B. Proportional Integral Derivative (PID) Controller:used as input for PI controller. PI controller used to control The PID controller works on the principle of the PIthe DC-bus voltage. controller(refer fig 2), its control gain is a linear combination of the error itself representing the present, the integral of the error representing the past and the derivative of the error representing the future/trend. 55© 2010 ACEEEDOI: 01.IJEPE.01.03.134
  3. 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 KI D. Hysteresis Band Current Control: H ( s) = K P + + K D ( s) (14) s emax +Vdc/2The controller is tuned with proper gain parameters iactual(t) vout e (t) L[ K P =0.7, K I =23, K D =0.01]. ioutC. Fuzzy Logic Controller (FLC): Fuzzy logic control is derived from fuzzy set theory, emin -Vdc/2 iref (t)the transition between membership and non-membershipcan be gradual. Therefore, boundaries of fuzzy sets can bevague and ambiguous, making it useful for approximate Fig 4 Block diagram of hysteresis current controllersystems [4-5]. In fig.1 shows the APLC compensationsystem with fuzzy control scheme. In order to implement A hysteresis current controller (Fig. 4) is implementedthe control algorithm of a shunt active power line to control the switches in the inverter [6-8] to control theconditioner in a closed loop, the dc capacitor voltage current within the inverter.VDC is sensed and then compared with the reference III. SIMULATION RESULT AND ANALYSISvalue VDC , ref . The results of the proposed PI, PID and fuzzy logic controlled shunt APLC is investigated using SIMULINK/ Rule Base MATLAB. The system parameters values are; source voltage (Vs) is 230 Vrms, System frequency (f) is 50 Hz, e(n) Source impedance of RS, LS is 1 Ω; 0.1mH respectively,Vdc,ref Rule Evaluator Filter impedance of Rc, Lc is 1 Ω; 2.7 mH, Load impedance + Fuzzification (Decision Defuzzification of RL, LL of diode rectifier RL load in Steady state: 20 Ω; - making) ce(n) 200 mH and Transient: 10 Ω; 100 mH respectively, DC Vdc link capacitance (CDC) is 1600 μF, Reference Voltage (VDC) is 400 V and Power devices used are IGBT/Diode. Data Base Case 1: Proportional Integral controller: Fig 3 Fuzzy logic controller PI-controlled APLC system comprises of a three-phase Table 1 Rule base table source, a nonlinear load (six pulse diode rectifier bridge feeding an RL load) and a PWM voltage source inverter ce(n) NB NM NS ZE PS PM PB e(n) with a dc capacitor input. The simulation time T=0 to T=0.5s with diode rectifier and R L load parameter values NB NB NB NB NB NM NS ZE of 20 ohms and 200 mH respectively. The source current NM NB NB NB NM NS ZE PS after compensation is presented in fig. 5 (a) that indicates NS NB NB MN NS ZE PS PM the current becomes sinusoidal. The load current is shown ZE NB NM NS ZE PS PM PB in (b) for a particular phase (phase a). The actual reference PS NM NS ZE PS PM PB PB currents for phase (a) are shown in fig. 5(c). This wave is obtained from our proposed PI controller. The APLC PM NS ZE PS PM PB PB PB supplies the compensating current that is shown in Fig. PB ZE PS PM PB PB PB PB 5(d). The current after compensation is as shown in (a) which would have taken a shape as shown in (b) without In case of a fuzzy logic control scheme, the error ( ) e = VDC , ref − VDC and integration of error signal APLC. It is clearly visible that this waveform is sinusoidal with some high frequency ripples. We have additionally (∫ e) are used as inputs for fuzzy processing shown in fig achieved power factor correction as shown in Fig. 5(e), phase (a) voltage and current are in phase. The time3. The output of the fuzzy controller after a limit is domain response of the PI controller is shown in Fig. 5(f)considered as the magnitude of peak reference current I max . that clearly indicates the controller output settles after a few cycles.The switching signals for the PWM inverter are obtained 100 Isaby comparing the actual source currents (isa , isb , isc ) with 80 60 40 (a) 20 0 -20 (isa *, isb *, isc *) in -40 -60 -80the reference current templates the 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 50 iLa 40 30 (b) 20hysteresis current controller. The output pulses are then 10 0 -10 -20given to the switching devices of the PWM converter.The -30 -40 -50 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5rules used in this paper are shown in table 1. 80 Isaref 60 40 (c) 20 -20 0 -40 -60 -80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 56© 2010 ACEEEDOI: 01.IJEPE.01.03.134
  4. 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 The real and reactive power measured using PID 80 Ica 60 40 20 (d) -20 -40 -60 0 controller, shown in fig 9. 9000 -80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 8000 7000 200 Isa 6000 Real Power Vsa 150 Reactive Power 5000 100 (e) 50 4000 0 3000 -50 2000 -100 1000 -150 0 -200 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1   Fig 9 Active and Reactive power at diode rectifier RL load under the 700 Vdc 600 500 (f) 400 300 200 100 steady state condition (P=7.34 KW, Q=0.034 KW) 0 -100 Total Harmonic distortion measurement (THD) of the 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Fig.5 Simulation results for PI-controlled three-phase APLC under the APLC in the transient condition by proportional-integral steady state condition (a) Source current after APLC, (b) Load currents, (c)Reference currents by the Proportional-integral algorithm, (d) derivative controller, shown in fig 10. Compensation current by APLC, (e) source voltage per current for unity 20 Mg it d b s do " a eP a "-P r mt r aa ee 18 16 power factor and (f) DC capacitor voltage 14 a nu e a e n Bs e k (a) 12 10 8 The active power P and reactive power Q associated 6 4 2with a periodic voltage-current pair that can contain 0 0 2 4 6 8 10 12 14 16 18 Order of Harmonic 30harmonics. P and Q are calculated by averaging the Mg it d b s do " a e e k -Pr mt r a nu e a e n Bs Pa " aa e e 25 20voltage-current product with a running average window (b) 15 10over one cycle of the fundamental frequency (refer fig 6). 5 0 0 2 4 6 8 10 Order of Harmonic 12 14 16 18 t 1 ∫ V (ωt ) × I (ωt )dt Fig 10 PID-controlled under the Transient condition (a) FFT analys of P= (15) Source current without APLC(THD=24.96%) (b) with T t −T APLC(THD=2.96%). t 1 Q= T ∫ v(ωt ) × i(ωt − π / 2)dt (16) Case 3: Fuzzy logic controller: t −T Simulation time T=0 to T=0.5s with load of rectifier with RL parameter values of 20 ohms and 200mH9000800070006000 Real Power5000 Reactive Power respectively in the steady state and the load with R L value4000300020001000 of 10 ohms and 100 mH under transient condition. The 0-1000 0 0.1 0 .2 0.3 0 .4 0.5 0 .6 0.7 0 .8 0.9 1 Fig 6 Active and Reactive power at diode rectifier RL load under the simulated waveforms are presented in figures 11, 12 and steady state condition (P=7.34 KW, Q=0.04 KW) 13. 100 Isa 80 Total Harmonic distortion (THD) is measured of the 60 40 (a) 20 0APLC in the PI controller, shown in fig 7. -20 -40 -60 -80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 16 M iu b eo"a Pk- amr a e a t d a dn s e " P e r t 50 14 iLa 40 12 30 Be a 10 20 (a) 10 8 (b) 0 g e s 6 -10 4 -20 n -30 2 -40 0 0 2 4 6 8 10 12 14 16 18 -50 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Order of Harmonic 30 80 a e e a - r tr M iu be n a Pk P m a td ad " s e" a e Ica 25 60 20 (b) 40 g e s oB 15 20 10 (c) 0 n 5 0 -20 0 2 4 6 8 10 12 14 16 18 Order of Harmonic -40 -60Fig 7 PI-controlled under the steady state (a) FFT analys of Source current -80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 600 without APLC (THD=25.58%) (b) with APLC(THD=1.98%). Vdc 500 400 300 (d) 200Case 2: Proportional Integral Derivative controller: 100 -100 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 ID controlled simulation waveforms are verified Fig.11 Simulation results for Fuzzy Logic Controlled 3-phase APLCsimilarly PI-controller, PID controller waveform presented under the steady state condition (a) Source current after APLC, (b) Loadin figures 8, 9 and 10. currents, (c) Compensation current by APLC, and (d) DC capacitor voltage 100 Isa 80 60 40 (a) The summarized DC voltage settling time compared 20 0 -20 -40 PI, PID and Fuzzy logic controller, shown in table 2 -60 -80 -100 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 50 iLa 40 30 20 Table 2 comparison of PI, PID and FLC for DC voltage settling time 10 (b) 0 -1 0 -2 0 -3 0 -4 0 -5 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 80 Ica Diode VDC settling time in seconds 60 40 (c) 20 rectifier 0 -20 -40 PI PID Fuzzy logic RL load -60 -80 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 700 vdc controller controller controller 600 500 (d) 400 300 200 Steady State 0.37s 0.26s 0.22s 100 0 -100 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Fig.8 Simulation results for PID controlled 3-phase APLC under the Transient 0.39s 0.28s 0.23s steady state condition (a) Source current after APLC, (b) Load currents, (c) Compensation current by APLC, and (d) DC capacitor voltage The real and reactive power measured using fuzzy logic controller, shown in fig 12. 57© 2010 ACEEEDOI: 01.IJEPE.01.03.134
  5. 5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010 9000 8000 7000 CONCLUSIONS 6000 Real Power PI, PID and fuzzy logic controllers are implemented for 5000 Reactive Power 4000 3000 three phase shunt active power line conditioner to obtain dc 2000 1000 0 capacitor voltage and the reference currents. This facilitates -1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fig 12 Active and Reactive power at diode rectifier RL load under the to improve the power quality parameters such as reactive steady state condition (P=7.33 KW, Q=0.04 KW) power and harmonic compensation due to nonlinear load. The summarized Real (P) and Reactive (Q) power The performance of a PI, PID and fuzzy logic controlledcalculation compared with PI, PID and Fuzzy logic APLC is verified and compared under steady state andcontroller, shown in table 3. transient in various disciplines. The fuzzy logic controller reduces ripples in the dc capacitor voltage and needs less Table 3 comparison of PI, PID and FLC for Real and Reactive power settling time compared to PI and PID-controller. The THD Controller Condition Real (P) and Reactive (Q) power of the source current after compensation is less than 5% in measurement case of all the controllers, the harmonic limit imposed by Without APLC With APLC the IEEE-519 standard. Apparently it seems that the fuzzy PI Steady state P=3.90 KW P=7.34 KW Q=0.12 KW Q=0.04 KW logic controller is an effective candidate for active power Transient P=4.85 KW P=7.34 KW line conditioner to solve power quality issues as this would Q=0.16 KW Q=0.07 KW also facilitate easy implementation. PID Steady state P=3.90 KW P=7.34 KW Q=0.12 KW Q=0.03 KW ACKNOWLEDGEMENTS Transient P=4.85 KW P=7.34 KW Q=0.16 KW Q=0.07 KW The authors would like to acknowledge to Ministry ofFuzzy logic Steady state P=3.91 KW P=7.33 KW Q=0.13 KW Q=0.04 KW Communication and Information Technology, Govt. of Transient P=4.83 KW P=7.35 KW India for the financial support. Q=0.17 KW Q=0.08 KW REFERENCES Total Harmonic distortion measurement of the APLCin the fuzzy logic controller, shown in fig 13. [1] Bimal Abdelmadjid Chaoui, Jean Paul Gaubert, Fateh Krim, 30 Gerard Champenois “PI Controlled Three-phase Shunt aa e r M g itu eb s do " a eP a " -P r m te Active Power Filter for Power Quality Improvement”- 25 (a) an d ae n Bs ek 20 15 Electric Power Components and Systems, 35:1331–1344, 2007 10 5 0 0 2 4 6 8 10 Order of Harmonic 12 14 16 18 [2] Yu Chen and Bo Fu Qionglin Li “Fuzzy Logic Based Auto- 30 modulation of Parameters PI Control for Active Power aa e r M g itu eb s do " a eP a " - P r m te Filter”- World Congress on Intelligent Control and 25 a n d ae n Bs e k 20 (b) 15 Automation June 25 - 27, 2008 [3] S. Saad, L. Zellouma “Fuzzy logic controller for three-level 10 5 0 0 2 4 6 8 10 Order of Harmonic 12 14 16 18 shunt active filter compensating harmonics and reactive power” Electric Power Systems Research, Elsevier, page no Fig 13 Fuzzy logic controlled FFT analys of Source current with APLC 1337–1341 May-2009 under the (a) steady state (THD=1.98%) (b) transient (THD=2.98%) [4] S.K. Jain, P. Agrawal and H.O. Gupta “Fuzzy logic The summarized Total harmonic distortion (THD) controlled shunt active power filter for power qualitycompared PI, PID and Fuzzy logic controllers, under steady improvement”-IEE proc.electr.power.appl,Vol 149, No.5, Sept-2002state and transient conditions, shown in table 4. [5] V. S. C. Raviraj and P. C. Sen “Comparative Study of Table 4 THD comparison of PI, PID and FLC Techniques Proportional–Integral, Sliding Mode, and Fuzzy Logic Controllers for Power Converters” IEEE Tran Industry Vol Diode Source Source Current(IS) with APLC 33, No. 2, March/Appl-1997. rectifier Current(IS) [6] K. K. Mahapatra, Arindam Ghosh and S.R.Doradla PI PID Fuzzy logic RL load without APLC “Simplified model for control design of STATCOM using Steady State 25.258% 1.98% 1.82% 1.98% Three-Level Inverter”- IEEE Conference vol. 2, pp. 536-539- 1998 Transient 24.96% 2.96% 2.96% 2.98% [7] Brod D.M, Novotny D.M “Current control of VSI-PWM Inverter”-IEEE Trans on Industry Appl, Vol.21, pp.562-570- The obtained result shows small variation in steady state July/Aug. 1985. [8] Malesani, L., L. Rosetto, G. Spiazzi and A. Zucatto “An acand transient conditions. FFT analysis of the active filter power supply with sliding mode control”-IEEE Industrybrings the THD of the source current into compliance with Appl Magazine Vol.2, page(s): 32-38 Sep/Oct 1996IEEE-519 standards. 58© 2010 ACEEEDOI: 01.IJEPE.01.03.134

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