Control of a 3-phase 4-leg active power filter under non-ideal mains voltage condition

Transcription

1 Available online at Electric Power Systems Research 78 (008) Control of a 3-phase 4-leg active power filter under non-ideal mains voltage condition Mehmet Ucar, Engin Ozdemir Kocaeli University, Technical Education Faculty, Electrical Education Department, Umuttepe, Turkey Received 9 August 005; received in revised form October 006; accepted 13 December 006 Available online 5 January 007 Abstract In this paper, instantaneous reactive power theory (IRP), also known as p q theory based a new control algorithm is proposed for 3-phase 4-wire and 4-leg shunt active power filter (APF) to suppress harmonic currents, compensate reactive power and neutral line current and balance the load currents under unbalanced non-linear load and non-ideal mains voltage conditions. The APF is composed from 4-leg voltage source inverter (VSI) with a common DC-link capacitor and hysteresis band PWM current controller. In order to show validity of the proposed control algorithm, compared conventional p q and p q r theory, four different cases such as ideal and unbalanced and balanced-distorted and unbalanced-distorted mains voltage conditions are considered and then simulated. All simulations are performed by using Matlab-Simulink Power System Blockset. The performance of the 4-leg APF with the proposed control algorithm is found considerably effective and adequate to compensate harmonics, reactive power and neutral current and balance load currents under all non-ideal mains voltage scenarios. 006 Elsevier B.V. All rights reserved. Keywords: 4-Leg shunt active power filter; Instantaneous power theory; Non-ideal mains voltage; Unbalanced load 1. Introduction The widespread increase of non-linear loads nowadays, significant amounts of harmonic currents are being injected into power systems. Harmonic currents flow through the power system impedance, causing voltage distortion at the harmonic currents frequencies. The distorted voltage waveform causes harmonic currents to be drawn by other loads connected at the point of common coupling (PCC). The existence of current and voltage harmonics in power systems increases losses in the lines, decreases the power factor and can cause timing errors in sensitive electronic equipments. The harmonic currents and voltages produced by balanced 3-phase non-linear loads such as motor drivers, silicon controlled rectifiers (SCR), large uninterruptible power supplies (UPS) are positive-sequence harmonics (7th, 13th, etc.) and negative-sequence harmonics (5th, 11th, etc.). However, harmonic currents and voltages produced by single phase non-linear loads such as switch-mode power supplies in computer equip- Corresponding author. Tel.: ; fax: address: eozdemir@kou.edu.tr (E. Ozdemir). ment which are connected phase to neutral in a 3-phase 4-wire system are third order zero-sequence harmonics (triplen harmonics 3rd, 9th, 15th, 1st, etc.). These triplen harmonic currents unlike positive and negative-sequence harmonic currents do not cancel but add up arithmetically at the neutral bus. This can result in neutral current that can reach magnitudes as high as 1.73 times the phase current. In addition to the hazard of cables and transformers overheating the third harmonic can reduce energy efficiency. The traditional method of current harmonics reduction involves passive LC filters, which are its simplicity and low cost. However, passive filters have several drawbacks such as large size, tuning and risk of resonance problems. On the contrary, the 4-leg APF can solve problems of current harmonics, reactive power, load current balancing and excessive neutral current simultaneously, and can be a much better solution than conventional approach. The IRP theory introduced by Akagi et al. [1,] has been used very successfully to design and control of the APF for 3-phase systems. This theory was extended by Aredes et al. [3], for applications in 3-phase 4-wire systems. The IRP theory was mostly applied to calculate the compensating currents assuming ideal mains voltages. However, mains voltage may be /$ see front matter 006 Elsevier B.V. All rights reserved. doi: /j.epsr

2 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 1. The basic compensation principle of the shunt APF. unbalanced and/or distorted in industrial systems. Under such conditions, control of the 4-leg APF using the p q theory does not provide good performance. For improving the APF performance under non-ideal mains voltage conditions, new control methods are proposed by Komatsu and Kawabata [4], Huang et al. [5], Chen and Hsu [6], Haque et al. [7], Lin and Lee [8], Chang and Yeh [9] and Kim et al. [10]. This paper presents a new control algorithm for the shunt 4-leg APF even for all non-ideal mains voltage and unbalanced non-linear load condition. Performance of the proposed scheme has been found feasible and excellent to that of the p q theory under unbalanced non-linear load and various non-ideal mains voltage test cases.. The 4-leg shunt active power filter Fig. 1 shows the basic compensation principle of the shunt APF. A shunt APF is designed to be connected in parallel with the load, to detect its harmonic current and to inject into the system a compensating current, identical with the load harmonic current. Therefore, the current draw from the power system at the coupling point of the filter will result sinusoidal as shown in Fig. and Eq. (1). Fig. shows load current (i L ), compensating current reference (i C ) and desired sinusoidal source current (i S ) waveform, respectively. i S = i L + i C (1) Fig.. Load, APF and source current waveforms. In 3-phase 4-wire systems, two kinds of VSI topologies such as 4-leg inverter and 3-leg (split capacitor) inverter are used. The 4-leg inverter uses 1-leg specially to compensate zerosequence (neutral) current. The 3-leg inverter is preferred for due to its lower number of switching devices, while the construction of control circuit is complex, huge DC-link capacitors are needed and balancing the voltage of two capacitors is a key problem. The 4-leg inverter has advantage to compensation for neutral current by providing 4th-leg and to need for much less DC-link capacitance and has full utilization of DC-link voltage. Fig. 3 shows the power circuit of a 4-leg shunt APF connected in parallel with the 1-phase and 3-phase loads as an unbalanced and non-linear load on 3-phase 4-wire electrical distribution system. The middle point of each branch is connected to the power system through a filter inductor. The APF consists of 4-leg VSI, 3-legs are needed to compensate the 3-phase currents and 1-leg compensates the neutral current [11]. The 4-leg VSI has 8 IGBT switches and an energy storage capacitor on hysteresis band current controllers is used to obtain the VSI control pulses for each inverter branch. High order harmonic currents generated by the switching of the power Fig. 3. Power circuit of the 4-leg shunt APF.

3 60 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) semiconductor devices of the PWM inverter is filtered by using a small RC high-pass filter, as shown in Fig The p q theory based control strategy The p q theory based control algorithm block diagram for the 4-leg APF is shown in Fig. 4. Form the Eqs. () and (3), the p q theory consist of an algebraic transformation (clarke transformation) of the measured 3-phase source voltages (v Sa,v Sb,v Sc ) and load currents (i La, i Lb, i Lc )inthea b c coordinates to the α β 0 coordinates, followed by the calculation of the instantaneous power components (p, q, p 0 ) [,3]. v 0 v α v β i 0 i α i β = = v Sa v Sb v Sc i La i Lb i Lc () (3) Instantaneous real power (p), imaginary power (q) and zerosequence power (p 0 ) are calculated as Eq. (4). p 0 v i 0 p = 0 v α v β i α (4) 3 q 0 v β v α i β The total instantaneous power (p 3 ) in 3-phase 4-wire system is calculated as sum of instantaneous real and zero-sequence power. p 3 =p + p 0 = v 0 i 0 + v α i α + v β i β = v a i a + v b i b + v c i c (5) The instantaneous real and imaginary powers include AC and DC values and can be expressed as follows: p = p + p = p + p ω + p h q = q + q = q + q ω + q h (6) DC values ( p, q) ofthep and q are the average active and reactive power originating from the positive-sequence component of the load current. AC values ( p, q) ofthep and q are the ripple active and reactive power originating from harmonic (p h, q h ) and negative sequence component (p ω, q ω ) of the load current [1,13]. For harmonic, reactive power compensation and balancing of unbalanced 3-phase load currents, all of the imaginary power ( q and q components) and harmonic component ( q) of the real power is selected as compensation power references and compensation current reference is calculated as Eq. (7). [ ] [ ][ ] i Cα 1 vα v β p + p i = Cβ v α + (7) v β v β v α q Since the zero-sequence current must be compensated, the reference compensation current in the 0 coordinate is i 0 itself: i C0 = i 0 (8) The additional average real power ( p) is equal to the sum of p loss, to cover the VSI losses and p 0, to provide energy balance inside the active filter. p = p 0 + p loss (9) The signal p loss is used as an average real power and is obtained from the voltage regulator. DC-link voltage regulator is designed to give both good compensation and an excellent transient response. The actual DC-link capacitor voltage is compared by a reference value and the error is processed in a PI controller, which is employed for the voltage control loop since it acts in order to zero the steady-state error of the DC-link voltage [3]. Eqs. (7) and (8) represent the required compensating current references (i C0,i Ca,i Cβ )inα β 0 coordinates to match the demanded powers of the load. Eq. (10) is valid to obtain the compensating phase currents (i Ca,i Cb,i Cc )inthea b c axis in terms of the compensating currents in the α β 0 coordinates: i Ca i Cb i Cc = i C0 i Ca i Cβ (10) Finally, neutral reference current is calculated as follows: i Cn = i Ca + i Cb + i Cc (11) 4. The p q r theory based control scheme Fig. 4. The p q theory based control algorithm block diagram for the 4-leg APF. The p q r theory proposed by Kim et al. [10] with reference current control method, which can control the system currents balanced and sinusoidal even when mains voltages are unbalanced or distorted. But, the calculation steps become rather high as can be defined following equations. After a transformation of 3-phase source voltages (v Sa,v Sb, v Sc ) and load currents (i La, i Lb, i Lc ) from a b c coordinates to

4 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) α β 0 coordinates, according to Eqs. () and (3), the currents are transformed from α β 0 coordinates to p q r coordinates (i p, i q, i r ) as follows: i p i q i r = 1 v 0αβ v 0 v α v β 0 v 0αβv β v 0αβ v α v αβ v αβ v αβ v 0v α v 0v β v αβ v αβ i 0 i α i β (1) where v 0αβ = v 0 + v α + v β, v αβ = v α + v β. Therefore, to get the source currents balanced and sinusoidal, the reference compensation currents (i Cp,i Cq,i Cr ) are selected as Eq. (13). i Cp = ĩ p i Cq = i q i Cr = i r + i pv 0 v αβ (13) The compensation currents in p q r coordinates are inversely transformed to α β 0 coordinates (i C0,i Cα,i Cβ )aseq.(14) and then to a b c coordinates (i Ca,i Cb,i Cc )aseq.(10). i v 0 0 v αβ C0 i Cα = 1 v α v 0αβv β v 0v α i Cp i v v αβ v αβ 0αβ v 0αβ v α Cβ v β v i Cq (14) 0v β i Cr v αβ v αβ The neutral reference current is determined as Eq. (11). 5. The proposed control algorithm The p q theory is suitable for ideal 3-phase systems but is inadequate under non-ideal mains voltage cases. In fact, under non-ideal mains voltage conditions, the sum of components (v α + v β ) will not be constant and alternating values of the instantaneous real and imaginer power have current harmonics and voltage harmonics. Consequently, the APF does not generate compensation current equal to current harmonics and gives to mains more than load harmonics than required. To overcome these limitations, the p q theory based a new control algorithm to decrease total harmonic distortion for desired level is proposed; the instantaneous reactive and active powers have to calculate after filtering of mains voltages. The proposed theory is designed for 3-phase 3-leg inverter system under non-ideal cases by Kale and Ozdemir [14]. In this paper the control theory is evaluated for 3-phase 4-wire 4-leg inverter system. The proposed method has a simple algorithm, which allows compensating harmonics, reactive power, neutral current and imbalance load currents under unbalanced non-linear load and non-ideal mains voltage cases. The proposed p q theory based method block diagram for the 4-leg APF is shown in Fig. 5. Since the mains voltages, applied to control algorithm of the 4-leg APF is to be balanced and sinusoidal, proposed voltage harmonics filter block diagram is shown in Fig. 6. Fig. 5. The proposed p q theory based method block diagram for the 4-leg APF. In the proposed method, instantaneous voltages are first converted to synchronous d q coordinates (Park transformation) as Eq. (15). [ ] [ ] vd sin(ωt) sin(ωt 10 ) sin(ωt + 10 ) = v q 3 cos(ωt) cos(ωt 10 ) cos(ωt + 10 ) v a (15) v b v c The produced d q components of voltages are filtered by using the 5th order low-pass filters (LPF) with a cut-off frequency at 50 Hz. These filtered d q components of voltages are reverse converted α β coordinates as expressed in Eq. (16). These α β components of voltages are used in conventional IRP theory. Hence, the non-ideal mains voltages are converted to ideal sinusoidal shape by using LPF in d q coordinate. [ ] [ ] vα sin(ωt) cos(ωt) ][ vd = (16) v β sin(ωt) cos(ωt) v q So, the mains voltages are assumed to be an ideal source in the calculation process. Since the APF input voltages have no zero-sequence components, zero-sequence power is (p 0 )tobe always zero. These reference currents calculated by the control algorithm equations should be supplied to the power system by switching of the IGBT of the inverter. The method for generation of the switching pattern is achieved by the instantaneous current control of the 4-leg APF line currents. The actual 4-leg APF line currents are monitored instantaneously, and then compared to the reference currents generated by the control algorithm. A hysteresis band PWM current control is implemented to generate the switching pattern of the VSI. The hysteresis band PWM current control is the fastest control method with minimum hard- Fig. 6. Voltage harmonics filtering block diagram.

5 6 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 7. Matlab-Simulink simulation block diagram of the 4-leg APF. ware and software but variable switching frequency is its main drawback [15]. Matlab-Simulink simulation block diagram of the proposed method controlled the 4-leg APF is shown in Fig Simulation results Harmonic current filtering, reactive power compensation, load current balancing and neutral current elimination performance of the 4-leg APF with the proposed method, the p q and p q r theory have been examined under four mains voltage cases, including ideal mains voltage, unbalanced mains voltage, balanced-distorted mains voltage and unbalanced-distorted mains voltage cases. The purpose of the designed case studies is to show the validity and performance of the proposed APF control strategy, even if the mains voltages are highly distorted and unbalanced. The presented simulation results were obtained by using Matlab-Simulink Power System Toolbox for a 3-phase 4-wire power distribution system with a 4-leg shunt APF. 3-Phase thyristor rectifier and 1-phase diode rectifier nonlinear loads are connected to the power system, in order to produce an unbalance, harmonic and reactive current in the phase currents and zero-sequence harmonics in the neutral current. The 4-leg APF is switched on 0.15 s later. After 0. s, a single-phase diode bridge rectifier load is connected to phase c to evaluate the dynamic performance of the 4-leg APF. Firing angle of 3-phase thyristor rectifier is α =30 and RL load is connected on the DC side. DC side of 1-phase diode rectifiers is connected RC filtered ohmic load. Since reactive power compensation performance of the 4-leg APF is showed clearly, load and source current are enlarged to two times in phase c. The comprehensive simulation results are discussed below Ideal mains voltage case Fig. 8 shows the harmonic current filtering and load current balancing simulation results with the p q, the p q r theory and proposed method for the 4-leg APF under ideal mains voltages. 3-Phase source currents are balanced and sinusoidal after compensation in three control methods for this case. The neutral current is successfully cancelled with three control methods as shown in Fig. 9. The reactive power compensation simulation results with the p q, the p q r theory and proposed method are shown in Fig. 10. Compensated source currents are in phase with 3-phase mains voltages. Harmonic spectra of i Lc load and i Sc source current under ideal mains voltage case is shown in Fig. 11. Detailed summary of load currents, source currents and their total harmonic distortion (THD) levels are shown in Table 1. The proposed method, the p q and the p q r theory are feasible under ideal mains voltages case. 6.. Unbalanced mains voltage case Unbalanced loads or 1-phase loads that are not evenly distributed between the phases of a 3-phase system will cause voltage unbalance. Excessive voltage unbalance can cause motor overheating and failure of power conversion components and increases the stresses of power electronics. When 3-phase power system is not balanced, effective values of phase voltages is not equal and there will be fundamental negative-sequence voltage component in the mains voltage. Voltage unbalance can be quantified using the following definition according to IEEE Std as shown below Eq.

6 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 8. (a e) Harmonic currents filtering under ideal mains voltage case. Fig. 9. (a d) Neutral current elimination under ideal mains voltage case.

7 64 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 10. (a d) Reactive power compensation under ideal mains voltage case. Fig. 11. Harmonic spectra of (a) i Lc load current and (b) i Sc source current under ideal mains voltage case. Table 1 Detailed summary of load currents, source currents and their THD levels under ideal mains voltage case 3-Phase and neutral Load currents Source currents t < 0. (s) t > 0. (s) p q theory p q r theory Proposed method 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) THD (%) A-phase B-phase C-phase Neutral RMS (A) A-phase B-phase C-phase Neutral

8 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 1. (a e) Harmonic currents filtering under unbalanced mains voltage case. (17) [16]. voltage unbalance (%) = maximum deviation from average 100 (17) average of three phase phase voltages An alternative way of calculating voltage unbalance is defined as the ratio of negative to positive-sequence voltage. voltage unbalance (%) = V (18) V 1+ 3-Phase unbalanced mains voltage is given in Eq. (19) [5]. v da v 1a+ v 1a = + (19) v db v dc v 1b+ v 1c+ v 1b v 1c For this case, the unbalanced 3-phase mains voltages are shown Eq. (0). The power system has not zero-sequence voltage component. v da = 311 sin(ωt) + 31 sin(ωt) v db = 311 sin(ωt 10 ) + 31 sin(ωt + 10 ) v dc = 311 sin(ωt + 10 ) + 31 sin(ωt 10 ) (0) Harmonic current suppression and load current balancing simulation results with the p q, the p q r theory and proposed method for the 4-leg APF under unbalanced mains voltages are shown in Fig. 1. While the load current THD level is 45.49% before 0. s, 56.54% after 0. s in phase c. Since compensation current references of the 4-leg APF have negative-sequence component, the 3-phase compensated source currents are not sinusoidal with the p q theory is shown in Fig. 1(c). The THD value of source current after compensation is 10.0% during 0.15 < t < 0. s and 10.3% after 0. s in phase c with the p q theory. Since negative-sequence component of mains voltage with the proposed method is eliminated, after compensation 3- phase source currents are balanced and sinusoidal as shown in Fig. 1(e). After compensation, THD level of source current is 3.49% during 0.15 < t < 0. s and 3.63% after 0. s in phase c with the proposed method. The neutral current elimination and reactive power compensation is successfully done with three control methods as shown in Figs. 13 and 14, respectively. Harmonic spectra of i Lc load and i Sc source current under unbalanced mains voltage case is shown in Fig. 15. Detailed summary of load currents, source currents and their THD levels are shown in Table. The unbalanced mains voltage in a 3-phase 4-wire power system will not affect the 4-leg APF performance with proposed algorithm Balanced-distorted mains voltage case When 3-phase mains voltages are balanced-distorted, mains voltages contain harmonic voltage components except

9 66 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 13. (a d) Neutral current elimination under unbalanced mains voltage case. fundamental component. 3-Phase balanced-distorted mains voltage is expressed as Eq. (1) [5]. v ba v bb v bc = v 1a+ v 1b+ v 1c+ + v ah v bh v ch (1) The 3-phase 4-wire distribution system with unbalanced 3- phase and 1-phase loads, the voltage disturbances (especially unbalanced and even harmonics) are very common especially in Turkey [17]. In order to simulate a real case distortion level, mains voltages are measured with a power harmonic analyzer. The measured real mains voltage waveform, THD level and its harmonic spectrum is shown in Fig. 16. The mains voltage have Fig. 14. (a d) Reactive power compensation under unbalanced mains voltage case.

10 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 15. Harmonic spectra of (a) i Lc load current and (b) i Sc source current under unbalanced mains voltage case. Table Detailed summary of load currents, source currents and their THD levels under unbalanced mains voltage case 3-Phase and neutral Load currents Source currents t < 0. (s) t > 0. (s) p q theory p q r theory Proposed method 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) THD (%) A-phase B-phase C-phase Neutral RMS (A) A-phase B-phase C-phase Neutral dominant 5th harmonic component and also have 3rd, 7th, 11th harmonic component. For this case, the distorted 3-phase mains voltages are expressed as below Eq. (). THD level of source current after compensation is 7.61% during 0.15 < t < 0. s and 6.79% after 0. s in phase c with the p q theory. The performance of the p q theory for this case is v ba = 311 sin(ωt) sin(3ωt) sin(5ωt 10 ) sin(7ωt) sin(11ωt 10 ) v bb = 311 sin(ωt 10 ) sin(3ωt) sin(5ωt) sin(7ωt 10 ) sin(11ωt) v bc = 311 sin(ωt + 10 ) sin(3ωt) sin(5ωt + 10 ) sin(7ωt + 10 ) sin(11ωt + 10 ) () Fig. 17 shows that the harmonic current filtering and load current balancing simulation results with the p q, the p q r theory and proposed method for the 4-leg APF under balanceddistorted mains voltages. While the load current THD level is 40.41% before 0. s, 50.9% after 0. s in phase c. The shown not qualified. 3-Phase source currents are balanced and sinusoidal after compensation with the proposed method and THD level of source current after compensation is 3.64% during 0.15 < t < 0. s and 3.39% after 0. s in phase c. Figs. 18 and 19 show the neutral current elimination and Fig. 16. The measured real mains voltage waveform, THD level and its harmonic spectrum.

11 68 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 17. (a e) Harmonic currents filtering under balanced-distorted mains voltage case. reactive power compensation performance with three control methods for the 4-leg APF, respectively. At the same time, the 4-leg APF compensates reactive current of the load and improves power factor and eliminates zero-sequence current components. Harmonic spectra of i Lc load and i Sc source current under balanced-distorted mains voltage case is shown in Fig. 0. Detailed summary of load currents, source currents and their THD levels are shown in Table 3. There is a significant Fig. 18. (a d) Neutral current elimination under balanced-distorted mains voltage case.

12 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 19. (a d) Reactive power compensation under balanced-distorted mains voltage case. Fig. 0. Harmonic spectra of (a) i Lc load current and (b) i Sc source current under balanced-distorted mains voltage case. Table 3 Detailed summary of load currents, source currents and their THD levels under balanced-distorted mains voltage case 3-Phase and neutral Load currents Source currents t < 0. (s) t > 0. (s) p q theory p q r theory Proposed method 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) THD (%) A-phase B-phase C-phase Neutral RMS (A) A-phase B-phase C-phase Neutral

13 70 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 1. (a e) Harmonic currents filtering under unbalanced-distorted mains voltage case. reduction in harmonic distortion level with the proposed technique. Therefore, the performance of the proposed method is better than that of the conventional p q theory. The balanceddistorted mains voltage in a 3-phase 4-wire power system will not affect the 4-leg APF performance by using the propose method Unbalanced-distorted mains voltage case When 3-phase mains voltage are unbalanced and distorted, mains voltage contains negative-sequence component and harmonic voltage components. In this case, 3-phase balanceddistorted mains voltage is expressed as Eq. (3). v dba v 1a+ v 1a v ah = + + (3) v dbb v dbc v 1b+ v 1c+ v 1b v 1c For this case, the unbalanced 3-phase mains voltages are shown Eq. (4). v bh v ch and proposed method for the 4-leg APF under unbalanceddistorted mains voltages. While the load current THD level is 4.31% before 0. s, 54.8% after 0. s in phase c. The THD level of source current after compensation is 11.99% during 0.15 < t < 0. s and 10.75% after 0. s in phase c with the p q theory. The performance of the p q theory for this case is shown not qualified. After compensation the source currents become sinusoidal and balanced with the proposed method and THD level of source current after compensation is 3.86% during 0.15 < t < 0. s and 3.57% after 0. s in phase c. The neutral current elimination and reactive power compensation is successfully done with three control methods as shown in Figs. and 3, respectively. Harmonic spectra of i Lc load and i Sc source current under unbalanced-distorted mains voltage case is shown in Fig. 4. Detailed summary of load currents, source currents and their THD levels are shown in Table 4. The unsymmetrical distorted voltage system is the most severe condition. However, good results can be obtained by the proposed theory. v dba = 311 sin(ωt) + 31 sin(ωt) sin(3ωt) sin(5ωt 10 ) sin(7ωt) sin(11ωt 10 ) v dbb = 311 sin(ωt 10 ) + 31 sin(ωt + 10 ) sin(3ωt) sin(5ωt) sin(7ωt 10 ) sin(11ωt) v dbc = 311 sin(ωt + 10 ) + 31 sin(ωt 10 ) sin(3ωt) sin(5ωt + 10 ) sin(7ωt + 10 ) sin(11ωt + 10 ) Fig. 1 shows the harmonic current filtering and load current balancing simulation results with the p q, the p q r theory (4) The design specifications and the main parameters of the system used in the simulation study are indicated in Table 5. From

14 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig.. (a d) Neutral current elimination under unbalanced-distorted mains voltage case. the 4-leg APF control block diagram in simulation study, it can be seen that the hardware of the proposed algorithm is simpler than that of the conventional p q theory and earlier the proposed algorithms [4 10] and that in addition its compensation performance is better. All figures show that the actual currents are almost agrees with the reference currents. The waveforms indicate that after compensation the mains currents are still sinusoidal even when the mains voltages are distorted and/or unbalanced. In an unsymmetrical or distorted voltage system, the results obtained by the p q theory are not good. However, the proposed theory gives good results for both non-ideal and distorted voltage system. The results obtained by simulations with Matlab-Simulink Power System Blockset show that the proposed approach is more flex- Fig. 3. (a d) Reactive power compensation under unbalanced-distorted mains voltage case.

15 7 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) Fig. 4. Harmonic spectra of (a) i Lc load current and (b) i Sc source current under unbalanced-distorted mains voltage case. Table 4 Detailed summary of load currents, source currents and their THD levels under unbalanced-distorted mains voltage case 3-Phase and neutral Load currents Source currents t < 0. (s) t > 0. (s) p q theory p q r theory Proposed method 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) 0.15 < t < 0. (s) t > 0. (s) THD (%) A-phase B-phase C-phase Neutral RMS (A) A-phase B-phase C-phase Neutral ible than conventional approaches for compensating reactive power and harmonic, neutral current of the load, even if the mains voltages are severely distortion and/or unbalanced. In the proposed method, the distorted mains voltages do not affect the compensated mains current. Table 5 System parameters used in simulation Parameter Value Source Voltage (V Sabc ) 0 V rms /phase-neutral Frequency (f) 50Hz Impedance (R S, L S ) 10m, 50 H 4-Leg shunt APF DC-link voltage (V C ) 800 V DC capacitor (C DC ) 1500 F Switching frequency (f S ) 1 khz/average AC side filter (R C, L C ), (R F, C F ) (0.1, 1 mh), (, 0 F) Load 3-Phase thyristor rectifier (R L1, L L1 ), (R DC1, L DC1 ) (0.1, 3 mh), (1, 0 mh) Firing angle 30 1-Phase diode rectifier (R L, L L ), (R DC, L DC, C DC1 ) (0.1, 1 mh), (15, 1 mh, 470 F) (R L3, L L3 ), (R DC3, L DC3, C DC ) (0.1, 1 mh), (15, 1 mh, 470 F) 7. Conclusion In this paper, a new 3-phase 4-wire and 4-leg shunt APF control algorithm has been proposed to improve the performance of the 4-leg APF under unbalanced non-linear loads and non-ideal mains voltage cases. The new control theory has been presented, which is suitable for 4-wire shunt APF design under unbalanced and distorted mains voltage cases. The computer simulation has verified the effectiveness of the proposed control scheme. The simulation results prove that the following objectives have been successfully achieved even if under unbalanced load and non-ideal mains voltage conditions. (I) Current harmonics filtering. (II) Reactive power compensation. (III) Load current balancing. (IV) Elimination of excessive neutral current. (V) High performance under both dynamic and steady state operations. The 4-leg inverter based shunt APF is found effective to meet IEEE Std standard recommendations on harmonic levels in all of the non-ideal voltage conditions [18]. The studied control approach compensates neutral current, reactive power and harmonics as well as unbalanced and reactive

16 M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (008) current components, and this will be really appreciated by the distribution system. Acknowledgement This research is supported by TUBITAK Research Fund (No.: 103E034-AY-57). Appendix A. List of symbols C DC C F i Cabc DC capacitor switching harmonics filter capacitor capacitance instantaneous compensation currents i Ca,i Cb,i Cc instantaneous compensation current references in the a b c coordinates i C0,i Cα,i Cβ instantaneous compensation current references in the α β 0 coordinates i Cp,i Cq,i Cr instantaneous compensation current references in the p q r coordinates i Labc instantaneous load currents i Sabc instantaneous source currents i α, i β, i 0 instantaneous currents in the α β 0 coordinates i p, i q, i r instantaneous currents in the p q r coordinates L C APF filter inductance L S source inductance L L load filter inductance n neutral p instantaneous real power p average real power p oscillating part of real power p loss average real power loss p 0 instantaneous zero-sequence power p ω negative sequence part of real power p 3 3-phase total instantaneous real power p h harmonic part of real power p average real power q instantaneous imaginary power q average imaginary power q oscillating part of imaginary power q ω negative-sequence part of imaginary power q h harmonic part of imaginary power R C APF filter resistance R F switching harmonics filter resistance R S source internal resistance R L load filter resistance v ah,v bh,v ch harmonic parts of mains voltage v ba,v bb,v bc balanced-distorted instantaneous mains voltages v d,v q instantaneous mains voltages in the d q coordinates v da,v db,v dc unbalanced instantaneous mains voltages v dba,v dbb,v dbc unbalanced-distorted instantaneous mains voltages v Sabc instantaneous mains voltages v α,v β,v 0 instantaneous mains voltages in the α β 0 coordinates v 1a+,v 1b+,v 1c+ fundamental positive-sequence part of mains voltage v 1a,v 1b,v 1c fundamental negative-sequence part of mains voltage References [1] H. Akagi, Y. Kanazawa, A. Nabae, Instantaneous reactive power compensators comprising switching devices without energy storage elements, IEEE Trans. Ind. Appl. 1A-0 (1984) [] J. Afonso, C. Couto, J. Martins, Active filters with control based on the p q theory, IEEE Ind. Electron. Soc. Newslett. 47 (3) (000) [3] M. Aredes, J. Hafner, K. Heumann, Three-phase four-wire shunt active filter control strategies, IEEE Trans. Power Electron. 1 () (1997) [4] Y. Komatsu, T. Kawabata, A control method for the active power filter in unsymmetrical voltage systems, Int. J. Electron. 86 (10) (1999) [5] S.J. Huang, et al., A study of three-phase active power filters under non-ideal mains voltages, Electr. Power Syst. Res. 49 (1999) [6] C.C. Chen, Y.Y. Hsu, A novel approach to the design of a shunt active filter for an unbalanced three-phase four-wire system under nonsinusoidal conditions, IEEE Trans. Power Delivery 15 (4) (000) [7] M.T. Haque, T. Ise, S.H. ve Hosseini, A novel control strategy for active filters usable in harmonic polluted and/or imbalanced utility voltage case of 3-phase 4-wire distribution systems, in: Proceedings of Ninth International Conference on Harmonics and Quality of Power, 000, pp [8] B.R. Lin, Y.C. Lee, Three-phase power quality compensator under the unbalanced sources and nonlinear loads, IEEE Trans. Ind. Electron. 51 (5) (004) [9] G.W. Chang, C.M. Yeh, Optimisation-based strategy for shunt active power filter control under non-ideal supply voltages, IEE Proc. Electr. Power Appl. 15 () (005) [10] H. Kim, F. Blaabjerg, B. Bak-Jensen, J. Choi, Instantaneous power compensation in three-phase systems by using p q r theory, IEEE Trans. Power Electron. 17 (5) (00) [11] A.N. Segura, G.M. Aguilar, Four branches inverter based active filter for unbalanced 3-phase 4-wires electrical distribution systems, in: Proceedings of the IEEE-IAS 000 Annual Meeting, Rome, Italy, 000, pp [1] F.Z. Peng, G.W. Ott, D.J. Adams, Harmonic and reactive power compensation based on the generalized instantaneous reactive power theory for 3-phase 4-wire systems, IEEE Trans. Power Electron. 13 (6) (1998) [13] E.H. Watanabe, R.M. Stephan, M. Aredes, New concepts of instantaneous active and reactive powers in electrical systems with generic loads, IEEE Trans. Power Delivery 8 () (1993) [14] M. Kale, E. Ozdemir, Harmonic and reactive power compensation with shunt active power filter under non-ideal mains voltage, Electric Power Syst. Res. 77 (005) [15] L. Malesani, P. Mattavelli, P. ve Tomasin, High-performance hysteresis modulation technique for active filters, IEEE Trans. Power Electron. 1 (5) (1997) [16] The New IEEE Standard Dictionary of Electrical and Electronics Terms, IEEE Std [17] Uçar, M., Design and implementation of 3-phase 4-wire shunt active power filter, Master Thesis, Kocaeli University, Turkey, 005. [18] IEEE Recommended Practice and Requirements for Harmonic Control in Electrical Power Systems, IEEE Std