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Real time simulation and experimental validation of active power filter operation and control
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Original articles
Real time simulation and experimental validation of active power filter operation and control M. Haddad a,b , S. Ktata a,b , S. Rahmani a,b,∗ , K. Al-Haddad a a Canada Research Chair in Energy Conversion and Power Electronics CRC-ECPE, Ecole ´ de Technologie Sup´erieure, 1100 notre-dame,
Montr´eal, Qu´ebec H3C 1K3, Canada b Laboratory of Biophysics and Medical Technology (BMT), ISTMT of the University of Tunis El-Manar, Tunisia, 9, Av. Dr. zouhaier essafi 1006,
Tunisia Received 13 October 2014; received in revised form 31 July 2015; accepted 14 September 2015
Abstract Nonlinear loads inject harmonics into electric power systems distribution network, which deteriorate power quality and affect the sensitivity of connected electronic equipment. Shunt active power filter (APF) is an important piece of depolluting equipment that is used in power systems to cancel current harmonics, compensate reactive power and balance supply loads. In this paper an APF setup is studied and analyzed using RT-Lab real-time simulator and controller. A simple control method is used to extract the harmonic contents of the supply currents. The pulse width modulation (PWM) technique is therefore applied to command the power switches to generate the reference current for the APF. Experimental results validate the real time model and the control method is used to properly compute and track the reference current, results show efficient filtering of the load harmonics and load balancing is also successfully achieved. c 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights ⃝ reserved. Keywords: Shunt active power filter; Real-time simulation; Reactive power compensation; Harmonic elimination; Power quality
1. Introduction Voltage and current harmonics are matter of concern in most research on power networks. Power quality issues are attractive for most researchers in power engineering. Use of nonlinear loads is increased significantly which generates harmonic and reactive power that is not acceptable due to high power losses. Rectifiers are the most existed nonlinear loads that change the drawn current waveform shape due to harmonic components leading to power losses and resonance problems. The harmonic components are the sinusoidal currents with the frequencies different from
∗ Corresponding author at: Canada Research Chair in Energy Conversion and Power Electronics CRC-ECPE, Ecole ´ de Technologie Sup´erieure, 1100 notre-dame, Montr´eal, Qu´ebec H3C 1K3, Canada. Tel.: +1 514 396 8874, +216 71 260 400; fax: +1 514 396 8684, +216 71 260 426. E-mail addresses: [email protected] (M. Haddad), [email protected] (S. Ktata), [email protected] (S. Rahmani), [email protected] (K. Al-Haddad).
http://dx.doi.org/10.1016/j.matcom.2015.09.007 c 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights 0378-4754/⃝ reserved.
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the system frequency. Therefore the sum of these waveforms is periodic while there is not any similarity to sinusoidal wave which is desirable in power systems [1,12]. Active power filter is composed of an inverter and the associated controller. It can generate the harmonic content of the load current. When the APF is connected in parallel to the load, it can inject the harmonic current to the system, therefore the source just need to produce the sinusoidal current and active power [3,4,13]. APF performs this action using the appropriate controller to calculate the reference current that includes harmonic part of the load current [8,10,9]. APF is widely used in power network to eliminate the harmonics, compensate the reactive power and balance unbalanced loads in order to reduce the power losses of the power sources [11,12]. In this paper, an indirect current control method has been used to extract the load harmonic current. The Proportional Integral (PI) controller is tuned to fix the DC bus voltage even in a disturbance condition. The later section describes the system configuration. The control method has been clarified in Section 3. The practical results are illustrated and discussed in Section 4. The experimental results are discussed comprehensively to demonstrate the operation of the APF. The results containing the currents and voltages as well as the Total Harmonic Distortion (THD) prove the efficiency of controller. The prototype can be used to test many controllers and switching techniques for analyzing the APF in power system. 2. Three-phase shunt active power filter configuration As mentioned former, APF contains an inverter with DC storage device (capacitor) connected in parallel to the load to eliminate the current harmonics and compensate the reactive power [6,11]. Fig. 1 shows a three-phase APF connected to the power system in parallel with a nonlinear load. The inverter can convert DC to AC by various switching states. In this paper, a three-phase two-level voltage source inverter (VSI) has been used to produce the reference current. Recently various multilevel inverter topologies have been introduced that can be employed in APF applications. 3. Indirect current control method To compensate the current harmonics of a nonlinear load in power systems, the source currents (i s123 (t)) should ∗ (t)). be extracted. The fundamental content of source currents will be used to calculate the reference currents (i 123 The derived reference current should be modulated to generate the associated pulses that order the inverter switches to inject the appropriate currents (i F123 (t)) into the system which can compensate the load harmonics [6,5,7]. The controller used in this case has two parts: first, the current extraction part and second; the PI controller which is used to balance the inverter DC link voltage. Fig. 2 shows the overall view of the control process. As it is clear in Fig. 2, the DC bus voltage (Vdc ) is sensed and compared with the reference value (Vdcref ). The PI controller plays an important role to fix the DC voltage and balance it during any disturbance in the system parameters such as load. The output value of the PI is multiplied by a sinusoidal unit wave which is in phase with the source voltage. This step is done to make the source current in phase with the source voltage which leads to unit power factor of the three-phase supply. The source current must track this reference current, therefore the difference of these currents for three phases is sent to the PWM modulation block to produce the appropriate pulses. The conventional PWM method is used to compare the reference wave with the carrier wave and modulate the input signal. The firing pulses command the switches to generate calculated reference current which is injected to the system to suppress the source harmonic current and make it sinusoidal in phase with the voltage waveform. Eq. (1) is the output of the PI controller. ∗ Imax = K p (Vdcref − Vdc ) +
Ki (Vdcref − Vdc ) S
(1)
∗ where Imax is the output of the PI controller which determines the peak value of the reference current. K p and K i are the proportional and integral coefficients that are tuned to regulate the DC bus voltage against deviation. Fixing the DC voltage is an important part of the controller in APF applications which requires accurate design and tuning. If the DC voltage changes during the time, the filtering aim would not be performed well and undesired harmonics are injected into the grid that increases the power losses. Besides, there are unwanted disturbances in the system such
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Fig. 1. A Three-phase shunt APF connected to the power system.
as load change or voltage sag and swell that affect the DC bus voltage. All in all, the PI controller is responsible in balancing and fixing the DC voltage close to the reference value. To distinguish the current harmonics, the reference current should be subtracted from the source current. In order to make a sinusoidal reference waveform the magnitude and the frequency of the waveform is needed. Since the source voltages and currents must be in phase to have a unit power factor, unit sine waveforms are derived from the phase 1 source voltage with the same angle and multiplied by reference current peak value calculated from last step and can be written as follows: vs1 (t) u 1 (t) = = sin (ωt) Vsmax 2π u 2 (t) = sin ωt − (2) 3 u 3 (t) = sin ωt − 4π 3
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Fig. 2. APF controller block diagram.
where u 123 (t) are the unit sine waves and vs1 (t) is the source voltage with maximum value of Vsmax . Finally, the reference currents can be shown as: ∗ ∗ ∗ i (t) = Imax × u 1 (t) = Imax sin (ωt) 1 2π ∗ ∗ ∗ i 2 (t) = Imax × u 2 (t) = Imax sin ωt − (3) 3 4π i ∗ (t) = I ∗ × u 3 (t) = I ∗ sin ωt − max max 3 3 ∗ (t) are the reference currents which are sinusoidal with the frequency of ω. i 123 While the source current should be same as the reference current, the difference between these two currents waveforms is calculated. The deducted waveform is a periodic wave including the harmonics which will be generated and injected by the inverter through the point of common coupling. PWM technique is widely used to fire the inverter switches in most power electronics equipment [2,6,5,7]. As it is clear in Fig. 1, the three-phase inverter has three legs that each leg has two switches. The switches in one leg work in complementary. For instance, if the upper switch in a leg is ON, the lower switch must be OFF and vice versa. This rule should be obeyed regarding the DC source short circuit damages. Hence, three reference currents shifted by 120◦ are compared with one carrier waveform to produce three firing pulses for upper switches of each leg. The lower switches receive the reverse pulses generated by a NOT logic block of the corresponding upper switches. The firing pulses command the switches to generate calculated reference current which is injected to the system to suppress the source harmonic current and make it purely sinusoidal in phase with the voltage waveform.
4. MATLAB model of shunt active power filter Fig. 3 shows the MATLAB model of the shunt active power filter system. The nonlinear load is modeled using a three-phase diode bridge converter connected to ac mains. At the dc bus of diode bridge converter, a resistor–inductor filter combination is employed. The unbalanced load is realized through connecting a single phase diode bridge converter between phase-1 and phase-2. The active filter is modeled as depicted in Fig. 3. The three-phase voltage source inverter (VSI) with dc link capacitor uses IGBTs as switches. The inverter block contains three-phase-bridge and dc bus measurement block. This figure also depicts an inductor ripple filter to crunch current ripples generated by the VSI. The size of the inductor is determined on the basis of required bandwidth of desired current compensation. The simulation is carried out in a discrete mode at 1.5 ∗ 10−5 step size with ode23s (stiff/Mod. Rosenbrock) solver. 5. Experimental procedure and results During this experimentation OPAL-RT platform has been used which is a flexible and powerful tool which allows real-time control through FPGA-based cards for I/Os and CPUs to solve the simulation equations. RT-LAB software
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Fig. 3. MATLAB-based model of the APF system.
Fig. 4. OPAL-RT real-time simulator and signal conditioning interface.
uses Matlab/Simulink models which will be built and compiled in order to be executed on OPAL-RT platform. It runs real-time simulation of Simulink model on multi-CPU computer with shared memory. It builds parallel tasks from the original Simulink model and runs them on each CPU of the multi-CPU computer. Data are exchanged though shared-memory that has ultra-low latency in the same order of the CPU system memory and thus permits the parallel simulation of electrical systems at time step below 10 µs. The software allows also viewing results and monitoring control parameters in real time by computer through UDP/IP protocols. The RT-Lab used in this project contains real-time controller and measurement box which are shown in Fig. 4. The real-time controller produces pulses based on the control strategy and sends them to the inverter switches. The measuring box is used to sense the source voltage and current as well as the DC voltage for the controller to calculate the reference current. The system parameters are listed in Table 1. As it is clear in Table 1, the prototype has been built to use in normal condition of the main power network using rated voltage and frequency. Many tests have been carried out on the prototype of the APF for harmonic compensation, power-factor correction and load balancing. Test results on the APF are shown in Figs. 5–11. The experimental results have been discussed as follows. At first the filtering process has been illustrated in Fig. 5. It shows the source voltage, source current, filter current and the load current for one phase of the system, respectively. The two upper waveforms are the phase 1 source voltage (vs1 (t)) and current (i s1 (t)) in blue and green, respectively. These two waveforms are in phase that proves the proficiency of the controller in power factor correction.
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Table 1 System parameters used for experimentation. Vs (peak) = 208 V(rms), f s = 60 Hz L s = 0.5 mH, Rs = 0.1 L L = 10 mH, R L = 26.6 , 40 Cdc = 2200 µF, L F = 5 mH, Vdc = 350 V 5 kHz
Line voltage, and frequency Line impedance Nonlinear load DC capacitance, filter inductance (L F ) and DC bus voltage of APF Switching frequency
Fig. 5. Steady state results showing vs1 , i s1 , i F1 and i L1 . 100 90 80 70 60 50 40 30 20 10 0
1
5
10
15
20
25
30
35
40
45
50
35
40
45
50
Fig. 6. Load current THD. 100 90 80 70 60 50 40 30 20 10 0
1
5
10
15
20
25
30
Fig. 7. Source current THD after compensation.
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Fig. 8. Dynamic response for a sudden change of load current. (The load is decreased and then increased.)
Moreover, the sinusoidal wave of the source current validates the proper filtering performance of the APF. The source voltage has some harmonic which is due to the inductance of the autotransformer used for generating three-phase source voltage. Phase 1 filter current (i F1 (t)) is the middle violet waveform and the phase 1 load current (i L1 (t)) is in the lower light blue one. The illustrated currents waveforms clear the fact that the reference current has been calculated by the controller appropriately. Then, the reference current has been modulated by PWM technique and the inverter has generated and injected the filter current into the network to eliminate the source current harmonics. The filter current shown in Fig. 5 contains harmonics which are required for the load. The load current is the combination of main sequence and harmonic current. The harmonic content is supplied by the filter; therefore the main sinusoidal current is produced by the source. The source and load currents THDs have been measured using the Fluke power analyzer. Figs. 6 and 7 show the THD results.
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Fig. 9. Dynamic response for a sudden change of load current. (The load is increased and then decreased.)
The source current THD has been reduced from 26% without APF to 2.3% with APF connected. The THD results show the efficiency of the controller and the APF in eliminating the current harmonics. In order to show the stability of the system and the controller robustness in making the DC voltage fixed, two kinds of load changes have been investigated. Three 80 resistive loads are prepared. By paralleling three of them, a 26.6 resistor will be achieved. In first case, the third 80 load has been disconnected therefore the equal resistor value increases to 40 . As it is clear in Fig. 8, decreasing and increasing the load have not affected the DC bus voltage. Moreover, the load increasing and reducing result have been measured and illustrated in Fig. 9. The DC voltage has
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Fig. 10. Steady-state performance of APF under nonlinear load unbalances.
not also changed during the load reduction from 40 to 26.6 . These results clarify the controller performance in fixing the DC voltage due to any disturbance. All in all, the experimental results show that APF prototype works well with acceptable results in eliminating the source current harmonics. It also proves the performance of the setup. This test aims to evaluate the active power filter capability to balance unbalanced loads. The load consists of a threephase and a single-phase diodes rectifiers. The single-phase rectifier is connected between phases 1 and 2 as shown in Fig. 1. Fig. 10 shows the three-phase source voltages (vs123 ), three-phase source currents (i s123 ), unbalanced threephase load currents (i L123 ), and three-phase active power filter currents (i F123 ). Fig. 11 illustrates the THD spectrum of load currents and source currents after compensation. The source currents THDs have been reduced respectively from 13.08%, 14.06% and 25.94% without APF to 2.62%, 3.31% and 3% with APF connected. It may be observed that the source currents after compensation are balanced, sinusoidal and in-phase with the source voltages, which confirm the capability of the APF to correct power-factor, compensate harmonic currents and balance the source currents. 6. Conclusion APFs are widely used in power distribution systems to remove the harmonics, compensate the reactive power and balance unbalanced loads. In this project, a prototype of the APF has been built, which the described controller has been implemented on Opal-RT platform. Source, load and filter currents have been illustrated to validate the proper filtering procedure. As well, the DC voltage of the inverter has been kept constant by the controller during the load changes. The dynamic response of the APF has been observed to be fast and it is able to keep the THD of the source current well below the limit specified by the IEEE 519 standards. Experimental results prove the performance of the active power filter to eliminate harmonics, compensate reactive power and balance loads. Many control methods can be surveyed using this flexible prototype to develop the APF controllers in least time.
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Fig. 11. Harmonics spectrum of load and source currents during load unbalance.
Acknowledgment The authors gratefully thank the Canada Research Chair in Energy Conversion and Power Electronics (grant no. ´ CRC-950-209162) at the Ecole de Technologie Sup´erieure for their financial support. References [1] H. Akagi, New trends in active filters for power conditioning, IEEE Trans. Ind. Appl. 32 (7) (1996) 1312–1322. [2] L. Asiminoaei, P. Rodriguez, F. Blaabjerg, M. Malinowski, Reduction of switching losses in active power filters with a new generalized discontinuous-PWM strategy, IEEE Trans. Ind. Electron. 55 (1) (2008) 467–471. [3] A. Bhattacharya, C. Chakraborty, S. Bhattacharya, Parallel-connected shunt hybrid active power filters operating at different switching frequencies for improved performance, IEEE Trans. Ind. Electron. 59 (11) (2012) 4007–4019. [4] Z. Chen, Y. Luo, M. Chen, Control and performance of a cascaded shunt active power filter for aircraft electric power system, IEEE Trans. Ind. Electron. 59 (9) (2012) 3614–3623. [5] S. Rahmani, K. Al-Haddad, H.Y. Kanaan, A comparative study of shunt hybrid and shunt active power filters for single-phase applications: Simulation and experimental validation, Math. Comput. Simul. 71 (2006) 345–359. [6] S. Rahmani, K. Al-Haddad, H. Kanaan, Two PWM techniques for single-phase shunt active power filters employing a direct current control strategy, IET Power Electron. 1 (2008) 376–385. [7] S. Rahmani, K. Al-Haddad, H.Y. Kanaan, B. Singh, Implementation and simulation of modified PWM with two current control techniques applied to single-phase shunt hybrid power filter, IEE Proc. Electr. Power Appl. 153 (2006) 317–326. [8] S. Rahmani, A. Hamadi, K. Al-Haddad, A Lyapunov-function-based control for a three-phase shunt hybrid active filter, IEEE Trans. Ind. Electron. 59 (2012) 1418–1429. [9] S. Rahmani, Ab. Hamadi, K. Al-Haddad, A combination of shunt hybrid power filter and thyristor controlled reactor for power quality enhancement, IEEE Trans. Ind. Electron. 61 (5) (2014) 2152–2164. [10] S. Rahmani, A. Hamadi, N. Mendalek, K. Al-Haddad, A new control technique for three-phase shunt hybrid power filter, IEEE Trans. Ind. Electron. 56 (2009) 2904–2915. [11] S. Rahmani, N. Mendalek, K. Al-Haddad, Experimental design of a nonlinear control technique for three-phase shunt active power filter, IEEE Trans. Ind. Electron. 57 (2010) 3364–3375.
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[12] B. Singh, K. Al-Haddad, A. Chandra, A review of active filters for power quality improvement, IEEE Trans. Ind. Electron. 46 (1999) 960–971. [13] Y. Tang, P.C. Loh, P. Wang, F.H. Choo, F. Gao, F. Blaabjerg, Generalized design of high performance shunt active power filter with output LCL filter, IEEE Trans. Ind. Electron. 59 (3) (2012) 1443–1452.
ScienceDirect Mathematics and Computers in Simulation (
)
– www.elsevier.com/locate/matcom
Original articles
Real time simulation and experimental validation of active power filter operation and control M. Haddad a,b , S. Ktata a,b , S. Rahmani a,b,∗ , K. Al-Haddad a a Canada Research Chair in Energy Conversion and Power Electronics CRC-ECPE, Ecole ´ de Technologie Sup´erieure, 1100 notre-dame,
Montr´eal, Qu´ebec H3C 1K3, Canada b Laboratory of Biophysics and Medical Technology (BMT), ISTMT of the University of Tunis El-Manar, Tunisia, 9, Av. Dr. zouhaier essafi 1006,
Tunisia Received 13 October 2014; received in revised form 31 July 2015; accepted 14 September 2015
Abstract Nonlinear loads inject harmonics into electric power systems distribution network, which deteriorate power quality and affect the sensitivity of connected electronic equipment. Shunt active power filter (APF) is an important piece of depolluting equipment that is used in power systems to cancel current harmonics, compensate reactive power and balance supply loads. In this paper an APF setup is studied and analyzed using RT-Lab real-time simulator and controller. A simple control method is used to extract the harmonic contents of the supply currents. The pulse width modulation (PWM) technique is therefore applied to command the power switches to generate the reference current for the APF. Experimental results validate the real time model and the control method is used to properly compute and track the reference current, results show efficient filtering of the load harmonics and load balancing is also successfully achieved. c 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights ⃝ reserved. Keywords: Shunt active power filter; Real-time simulation; Reactive power compensation; Harmonic elimination; Power quality
1. Introduction Voltage and current harmonics are matter of concern in most research on power networks. Power quality issues are attractive for most researchers in power engineering. Use of nonlinear loads is increased significantly which generates harmonic and reactive power that is not acceptable due to high power losses. Rectifiers are the most existed nonlinear loads that change the drawn current waveform shape due to harmonic components leading to power losses and resonance problems. The harmonic components are the sinusoidal currents with the frequencies different from
∗ Corresponding author at: Canada Research Chair in Energy Conversion and Power Electronics CRC-ECPE, Ecole ´ de Technologie Sup´erieure, 1100 notre-dame, Montr´eal, Qu´ebec H3C 1K3, Canada. Tel.: +1 514 396 8874, +216 71 260 400; fax: +1 514 396 8684, +216 71 260 426. E-mail addresses: [email protected] (M. Haddad), [email protected] (S. Ktata), [email protected] (S. Rahmani), [email protected] (K. Al-Haddad).
http://dx.doi.org/10.1016/j.matcom.2015.09.007 c 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights 0378-4754/⃝ reserved.
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the system frequency. Therefore the sum of these waveforms is periodic while there is not any similarity to sinusoidal wave which is desirable in power systems [1,12]. Active power filter is composed of an inverter and the associated controller. It can generate the harmonic content of the load current. When the APF is connected in parallel to the load, it can inject the harmonic current to the system, therefore the source just need to produce the sinusoidal current and active power [3,4,13]. APF performs this action using the appropriate controller to calculate the reference current that includes harmonic part of the load current [8,10,9]. APF is widely used in power network to eliminate the harmonics, compensate the reactive power and balance unbalanced loads in order to reduce the power losses of the power sources [11,12]. In this paper, an indirect current control method has been used to extract the load harmonic current. The Proportional Integral (PI) controller is tuned to fix the DC bus voltage even in a disturbance condition. The later section describes the system configuration. The control method has been clarified in Section 3. The practical results are illustrated and discussed in Section 4. The experimental results are discussed comprehensively to demonstrate the operation of the APF. The results containing the currents and voltages as well as the Total Harmonic Distortion (THD) prove the efficiency of controller. The prototype can be used to test many controllers and switching techniques for analyzing the APF in power system. 2. Three-phase shunt active power filter configuration As mentioned former, APF contains an inverter with DC storage device (capacitor) connected in parallel to the load to eliminate the current harmonics and compensate the reactive power [6,11]. Fig. 1 shows a three-phase APF connected to the power system in parallel with a nonlinear load. The inverter can convert DC to AC by various switching states. In this paper, a three-phase two-level voltage source inverter (VSI) has been used to produce the reference current. Recently various multilevel inverter topologies have been introduced that can be employed in APF applications. 3. Indirect current control method To compensate the current harmonics of a nonlinear load in power systems, the source currents (i s123 (t)) should ∗ (t)). be extracted. The fundamental content of source currents will be used to calculate the reference currents (i 123 The derived reference current should be modulated to generate the associated pulses that order the inverter switches to inject the appropriate currents (i F123 (t)) into the system which can compensate the load harmonics [6,5,7]. The controller used in this case has two parts: first, the current extraction part and second; the PI controller which is used to balance the inverter DC link voltage. Fig. 2 shows the overall view of the control process. As it is clear in Fig. 2, the DC bus voltage (Vdc ) is sensed and compared with the reference value (Vdcref ). The PI controller plays an important role to fix the DC voltage and balance it during any disturbance in the system parameters such as load. The output value of the PI is multiplied by a sinusoidal unit wave which is in phase with the source voltage. This step is done to make the source current in phase with the source voltage which leads to unit power factor of the three-phase supply. The source current must track this reference current, therefore the difference of these currents for three phases is sent to the PWM modulation block to produce the appropriate pulses. The conventional PWM method is used to compare the reference wave with the carrier wave and modulate the input signal. The firing pulses command the switches to generate calculated reference current which is injected to the system to suppress the source harmonic current and make it sinusoidal in phase with the voltage waveform. Eq. (1) is the output of the PI controller. ∗ Imax = K p (Vdcref − Vdc ) +
Ki (Vdcref − Vdc ) S
(1)
∗ where Imax is the output of the PI controller which determines the peak value of the reference current. K p and K i are the proportional and integral coefficients that are tuned to regulate the DC bus voltage against deviation. Fixing the DC voltage is an important part of the controller in APF applications which requires accurate design and tuning. If the DC voltage changes during the time, the filtering aim would not be performed well and undesired harmonics are injected into the grid that increases the power losses. Besides, there are unwanted disturbances in the system such
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Fig. 1. A Three-phase shunt APF connected to the power system.
as load change or voltage sag and swell that affect the DC bus voltage. All in all, the PI controller is responsible in balancing and fixing the DC voltage close to the reference value. To distinguish the current harmonics, the reference current should be subtracted from the source current. In order to make a sinusoidal reference waveform the magnitude and the frequency of the waveform is needed. Since the source voltages and currents must be in phase to have a unit power factor, unit sine waveforms are derived from the phase 1 source voltage with the same angle and multiplied by reference current peak value calculated from last step and can be written as follows: vs1 (t) u 1 (t) = = sin (ωt) Vsmax 2π u 2 (t) = sin ωt − (2) 3 u 3 (t) = sin ωt − 4π 3
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Fig. 2. APF controller block diagram.
where u 123 (t) are the unit sine waves and vs1 (t) is the source voltage with maximum value of Vsmax . Finally, the reference currents can be shown as: ∗ ∗ ∗ i (t) = Imax × u 1 (t) = Imax sin (ωt) 1 2π ∗ ∗ ∗ i 2 (t) = Imax × u 2 (t) = Imax sin ωt − (3) 3 4π i ∗ (t) = I ∗ × u 3 (t) = I ∗ sin ωt − max max 3 3 ∗ (t) are the reference currents which are sinusoidal with the frequency of ω. i 123 While the source current should be same as the reference current, the difference between these two currents waveforms is calculated. The deducted waveform is a periodic wave including the harmonics which will be generated and injected by the inverter through the point of common coupling. PWM technique is widely used to fire the inverter switches in most power electronics equipment [2,6,5,7]. As it is clear in Fig. 1, the three-phase inverter has three legs that each leg has two switches. The switches in one leg work in complementary. For instance, if the upper switch in a leg is ON, the lower switch must be OFF and vice versa. This rule should be obeyed regarding the DC source short circuit damages. Hence, three reference currents shifted by 120◦ are compared with one carrier waveform to produce three firing pulses for upper switches of each leg. The lower switches receive the reverse pulses generated by a NOT logic block of the corresponding upper switches. The firing pulses command the switches to generate calculated reference current which is injected to the system to suppress the source harmonic current and make it purely sinusoidal in phase with the voltage waveform.
4. MATLAB model of shunt active power filter Fig. 3 shows the MATLAB model of the shunt active power filter system. The nonlinear load is modeled using a three-phase diode bridge converter connected to ac mains. At the dc bus of diode bridge converter, a resistor–inductor filter combination is employed. The unbalanced load is realized through connecting a single phase diode bridge converter between phase-1 and phase-2. The active filter is modeled as depicted in Fig. 3. The three-phase voltage source inverter (VSI) with dc link capacitor uses IGBTs as switches. The inverter block contains three-phase-bridge and dc bus measurement block. This figure also depicts an inductor ripple filter to crunch current ripples generated by the VSI. The size of the inductor is determined on the basis of required bandwidth of desired current compensation. The simulation is carried out in a discrete mode at 1.5 ∗ 10−5 step size with ode23s (stiff/Mod. Rosenbrock) solver. 5. Experimental procedure and results During this experimentation OPAL-RT platform has been used which is a flexible and powerful tool which allows real-time control through FPGA-based cards for I/Os and CPUs to solve the simulation equations. RT-LAB software
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Fig. 3. MATLAB-based model of the APF system.
Fig. 4. OPAL-RT real-time simulator and signal conditioning interface.
uses Matlab/Simulink models which will be built and compiled in order to be executed on OPAL-RT platform. It runs real-time simulation of Simulink model on multi-CPU computer with shared memory. It builds parallel tasks from the original Simulink model and runs them on each CPU of the multi-CPU computer. Data are exchanged though shared-memory that has ultra-low latency in the same order of the CPU system memory and thus permits the parallel simulation of electrical systems at time step below 10 µs. The software allows also viewing results and monitoring control parameters in real time by computer through UDP/IP protocols. The RT-Lab used in this project contains real-time controller and measurement box which are shown in Fig. 4. The real-time controller produces pulses based on the control strategy and sends them to the inverter switches. The measuring box is used to sense the source voltage and current as well as the DC voltage for the controller to calculate the reference current. The system parameters are listed in Table 1. As it is clear in Table 1, the prototype has been built to use in normal condition of the main power network using rated voltage and frequency. Many tests have been carried out on the prototype of the APF for harmonic compensation, power-factor correction and load balancing. Test results on the APF are shown in Figs. 5–11. The experimental results have been discussed as follows. At first the filtering process has been illustrated in Fig. 5. It shows the source voltage, source current, filter current and the load current for one phase of the system, respectively. The two upper waveforms are the phase 1 source voltage (vs1 (t)) and current (i s1 (t)) in blue and green, respectively. These two waveforms are in phase that proves the proficiency of the controller in power factor correction.
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Table 1 System parameters used for experimentation. Vs (peak) = 208 V(rms), f s = 60 Hz L s = 0.5 mH, Rs = 0.1 L L = 10 mH, R L = 26.6 , 40 Cdc = 2200 µF, L F = 5 mH, Vdc = 350 V 5 kHz
Line voltage, and frequency Line impedance Nonlinear load DC capacitance, filter inductance (L F ) and DC bus voltage of APF Switching frequency
Fig. 5. Steady state results showing vs1 , i s1 , i F1 and i L1 . 100 90 80 70 60 50 40 30 20 10 0
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Fig. 6. Load current THD. 100 90 80 70 60 50 40 30 20 10 0
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Fig. 7. Source current THD after compensation.
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Fig. 8. Dynamic response for a sudden change of load current. (The load is decreased and then increased.)
Moreover, the sinusoidal wave of the source current validates the proper filtering performance of the APF. The source voltage has some harmonic which is due to the inductance of the autotransformer used for generating three-phase source voltage. Phase 1 filter current (i F1 (t)) is the middle violet waveform and the phase 1 load current (i L1 (t)) is in the lower light blue one. The illustrated currents waveforms clear the fact that the reference current has been calculated by the controller appropriately. Then, the reference current has been modulated by PWM technique and the inverter has generated and injected the filter current into the network to eliminate the source current harmonics. The filter current shown in Fig. 5 contains harmonics which are required for the load. The load current is the combination of main sequence and harmonic current. The harmonic content is supplied by the filter; therefore the main sinusoidal current is produced by the source. The source and load currents THDs have been measured using the Fluke power analyzer. Figs. 6 and 7 show the THD results.
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Fig. 9. Dynamic response for a sudden change of load current. (The load is increased and then decreased.)
The source current THD has been reduced from 26% without APF to 2.3% with APF connected. The THD results show the efficiency of the controller and the APF in eliminating the current harmonics. In order to show the stability of the system and the controller robustness in making the DC voltage fixed, two kinds of load changes have been investigated. Three 80 resistive loads are prepared. By paralleling three of them, a 26.6 resistor will be achieved. In first case, the third 80 load has been disconnected therefore the equal resistor value increases to 40 . As it is clear in Fig. 8, decreasing and increasing the load have not affected the DC bus voltage. Moreover, the load increasing and reducing result have been measured and illustrated in Fig. 9. The DC voltage has
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Fig. 10. Steady-state performance of APF under nonlinear load unbalances.
not also changed during the load reduction from 40 to 26.6 . These results clarify the controller performance in fixing the DC voltage due to any disturbance. All in all, the experimental results show that APF prototype works well with acceptable results in eliminating the source current harmonics. It also proves the performance of the setup. This test aims to evaluate the active power filter capability to balance unbalanced loads. The load consists of a threephase and a single-phase diodes rectifiers. The single-phase rectifier is connected between phases 1 and 2 as shown in Fig. 1. Fig. 10 shows the three-phase source voltages (vs123 ), three-phase source currents (i s123 ), unbalanced threephase load currents (i L123 ), and three-phase active power filter currents (i F123 ). Fig. 11 illustrates the THD spectrum of load currents and source currents after compensation. The source currents THDs have been reduced respectively from 13.08%, 14.06% and 25.94% without APF to 2.62%, 3.31% and 3% with APF connected. It may be observed that the source currents after compensation are balanced, sinusoidal and in-phase with the source voltages, which confirm the capability of the APF to correct power-factor, compensate harmonic currents and balance the source currents. 6. Conclusion APFs are widely used in power distribution systems to remove the harmonics, compensate the reactive power and balance unbalanced loads. In this project, a prototype of the APF has been built, which the described controller has been implemented on Opal-RT platform. Source, load and filter currents have been illustrated to validate the proper filtering procedure. As well, the DC voltage of the inverter has been kept constant by the controller during the load changes. The dynamic response of the APF has been observed to be fast and it is able to keep the THD of the source current well below the limit specified by the IEEE 519 standards. Experimental results prove the performance of the active power filter to eliminate harmonics, compensate reactive power and balance loads. Many control methods can be surveyed using this flexible prototype to develop the APF controllers in least time.
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Fig. 11. Harmonics spectrum of load and source currents during load unbalance.
Acknowledgment The authors gratefully thank the Canada Research Chair in Energy Conversion and Power Electronics (grant no. ´ CRC-950-209162) at the Ecole de Technologie Sup´erieure for their financial support. References [1] H. Akagi, New trends in active filters for power conditioning, IEEE Trans. Ind. Appl. 32 (7) (1996) 1312–1322. [2] L. Asiminoaei, P. Rodriguez, F. Blaabjerg, M. Malinowski, Reduction of switching losses in active power filters with a new generalized discontinuous-PWM strategy, IEEE Trans. Ind. Electron. 55 (1) (2008) 467–471. [3] A. Bhattacharya, C. Chakraborty, S. Bhattacharya, Parallel-connected shunt hybrid active power filters operating at different switching frequencies for improved performance, IEEE Trans. Ind. Electron. 59 (11) (2012) 4007–4019. [4] Z. Chen, Y. Luo, M. Chen, Control and performance of a cascaded shunt active power filter for aircraft electric power system, IEEE Trans. Ind. Electron. 59 (9) (2012) 3614–3623. [5] S. Rahmani, K. Al-Haddad, H.Y. Kanaan, A comparative study of shunt hybrid and shunt active power filters for single-phase applications: Simulation and experimental validation, Math. Comput. Simul. 71 (2006) 345–359. [6] S. Rahmani, K. Al-Haddad, H. Kanaan, Two PWM techniques for single-phase shunt active power filters employing a direct current control strategy, IET Power Electron. 1 (2008) 376–385. [7] S. Rahmani, K. Al-Haddad, H.Y. Kanaan, B. Singh, Implementation and simulation of modified PWM with two current control techniques applied to single-phase shunt hybrid power filter, IEE Proc. Electr. Power Appl. 153 (2006) 317–326. [8] S. Rahmani, A. Hamadi, K. Al-Haddad, A Lyapunov-function-based control for a three-phase shunt hybrid active filter, IEEE Trans. Ind. Electron. 59 (2012) 1418–1429. [9] S. Rahmani, Ab. Hamadi, K. Al-Haddad, A combination of shunt hybrid power filter and thyristor controlled reactor for power quality enhancement, IEEE Trans. Ind. Electron. 61 (5) (2014) 2152–2164. [10] S. Rahmani, A. Hamadi, N. Mendalek, K. Al-Haddad, A new control technique for three-phase shunt hybrid power filter, IEEE Trans. Ind. Electron. 56 (2009) 2904–2915. [11] S. Rahmani, N. Mendalek, K. Al-Haddad, Experimental design of a nonlinear control technique for three-phase shunt active power filter, IEEE Trans. Ind. Electron. 57 (2010) 3364–3375.
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