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Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and High-Frequency Harmonics

Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching... Hindawi Publishing Corporation Advances in Power Electronics Volume 2011, Article ID 397872, 6 pages doi:10.1155/2011/397872 Review Article Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and High-Frequency Harmonics 1 2 3 Hani Vahedi, Abdolreza Sheikholeslami, Mohammad Tavakoli Bina, and Mahmood Vahedi Department of Electrical Engineering, Islamic Azad University, Sari Branch, Sari, Iran Department of Electrical Engineering, Babol University of Technology, Babol, Iran Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran Correspondence should be addressed to Hani Vahedi, hani.vahedi@gmail.com Received 1 February 2011; Accepted 2 May 2011 Academic Editor: Francesco Profumo Copyright © 2011 Hani Vahedi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Hysteresis Current Control (HCC) is widely used due to its simplicity in implementation, fast and accurate response. However, the main issue is its variable switching frequency which leads to extraswitching losses and injecting high-frequency harmonics into the system current. To solve this problem, adaptive hysteresis current control (AHCC) has been introduced which produces hysteresis bandwidth which instantaneously results in smoother and constant switching frequency. In this paper the instantaneous power theory is used to extract the harmonic components of system current. Then fixed-band hysteresis current control is explained. Because of fixed-band variable frequency disadvantages, the adaptive hysteresis current control is explained that leads to fixing the switching frequency and reducing the high-frequency components in source current waveform. Due to these advantages of AHCC, the switching frequency and switching losses will be diminished appropriately. Some simulations are done in MATLAB/Simulink. The Fourier Transform and THD results of source and load currents and the instantaneous switching frequency diagram are discussed to prove the efficiency of this method. The Fourier Transform and THD results of source and load currents are discussed to prove the validity of this method. 1. Introduction behavior. On the other hand, conventional hysteresis method includes some undesirable results, such as variable switching In recent years, shunt active power filters have being applied frequency that causes audio noises, high switching losses by many industries and researchers to remove the current and injection of high-frequency current components to the harmonics caused by nonlinear loads [1–3]. An APF as can source current that makes it difficult to design suitable filters be seen in Figure 1 is a parallel power inverter with loads to remove these high-frequency harmonics. that can remove large amounts of current harmonics through Many switching methods are used to produce switching the injection of reference current to the power system pulse which leads to generate reference current. Hysteresis that contains harmonic components of the source current. current control (HCC) has been noticed more than other Complete compensation occurs when the APF produces the current control techniques, due to simplicity and quicker same current as harmonic current with the same amplitude dynamic response [5–8]. and opposite in sign. The main problem of HCC is its variable switching fre- Hysteresis current control is one of the most appropriate quency which leads to variable high-frequency components PWM switching methods to produce reference current in in source current waveform, audio noises and increase APFs [4]. Hysteresis current control has desirable charac- switching losses. One of performed methods that can solve teristics such as high stability, fast and accurate dynamic this problem is the AHCC method that builds variable band 2 Advances in Power Electronics for current tracking, hence the switching speed becomes i (t) i (t) L s l l smooth and the frequency switching will be fixed consider- 3φ AC R ably. source i (t) Furthermore, different frequency components in current f waveform will appear due to different switching frequencies Rectifier that make it difficult to design appropriate filters to elimi- f v (t) i (t) nate these components and make noises affects measuring l l devices. To overcome this problem, an adaptive hysteresis Harmonic extraction current control (AHCC) has been introduced. Using this method, variable hysteresis bandwidth is calculated instan- Current controller taneously, which leads to reducing the switching frequency V /2 dc variation, thus the fixed-band HCC issues will be amended. Voltage source In this paper, in Section 2, the instantaneous power the- Switching pulses inverter V /2 ory has been explained to extract the harmonics components dc of current waveform. Then in Section 3, the fixed-band HCC and AHCC have been clarified. Finally, some simulations Figure 1: Power System Diagram with APF. have been done with MATLAB/Simulink, and the results consisting of switching frequency diagrams and current THD in high-frequency range have been discussed in Section 4. By comparing the results of simulations, the advantages in order to compensate the harmonics and the instantaneous of AHCC in fixing switching frequency and modifying the reactive power, compensation reference currents can be above-mentioned problems, especially reducing the high- extracted as follows: frequency components in source current waveform and ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ −1 i (t) v (t) v (t) −p (t) α β fα switching losses, have been proved. ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ = ,(4) i (t) −v (t) v (t) −q(t) fβ β α 2. Instantaneous Power Theory t t ∗ ∗ ∗ ∗ ∗ −1 i (t) i (t) i (t) 0 i (t) i (t) = C . (5) fa fb fc fα fβ One of the popular compensation reference current extrac- tion methods is the instantaneous reactive power theory (p-q 3. Hysteresis Current Control theory). Although there are some problems with this theory, it is well established and simple in implementation. The p-q Hysteresis current control is used for generating the switch- theory could be briefly reviewed as follows [8]. ing pulses. Among the various current control techniques, Assume a three-phase load with the instantaneous volt- t HCC is the most extensively used technique because of the ages as v(t) = [v (t) v (t) v (t)] and the instantaneous a b c t noncomplex implementation, outstanding stability, absence currents as i (t) = [i (t) i (t) i (t)] (Figure 1). Using (1), l la lb lc of any tracking error, very fast transient response, inherent v(t)and i (t)can be convertedto0-α-β coordination where limited maximum current, and intrinsic robustness to load C is matrix (2): parameters variations. As indicated in [6, 7]areview of t t used current control techniques for PWM converters reveals t t v (t) = C[v (t)] , i (t) = C[i (t)],(1) 0αβ abc 0αβ abc that HCC shows certain superiority for active power filter applications. HCC provides a better low-order harmonic ⎡ ⎤ suppression than PWM control, which is the main target of 1 1 1 √ √ √ ⎢ ⎥ the active power filter. It is easier to realize with high accuracy 2 2 2 ⎢ ⎥ ⎢ ⎥ and fast response. However, as a disadvantage its switching −1 −1 ⎢ ⎥ C = ⎢ 1 ⎥ . (2) frequency might fluctuate. ⎢ ⎥ 2 2 ⎢ ⎥ √ √ In the HCC technique the error function is centered in ⎣ ⎦ 3 − 3 a preset hysteresis band. When the error exceeds the upper 2 2 or lower hysteresis limit the hysteretic controller makes an Let’s assume that the zero sequence current (i (t)) is appropriate switching decision to control the error within l0 null. Thus, the instantaneous active (p(t)) and reactive (q(t)) the preset band and send these pulses to VSI to produce the powers can be calculated as reference current as shown in Figure 2. The outputs of the hysteresis blocks are directly fed as the ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ p(t) v (t) v (t) i (t) α β lα firing pulse of VSI switches. ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ = ;(3) q(t) −v (t) v (t) i (t) β α lβ 3.1. Fixed-Band Hysteresis Current Control. In fixed-band p(t)and q(t) can be decomposed to the average parts HCC, the hysteresis bandwidth (HB) has been taken as (p(t), q(t)) and the oscillating parts (p (t), q (t)). It is notable a small portion related to system current, and in many that p(t) is produced by the fundamental harmonics of the researches it has been taken as 5% of main current which will positive sequence component of the load current. Therefore, be HB = 0.9A, here. Advances in Power Electronics 3 Table 1: APF simulation parameters. i (t) i (t) f Switching pulses f APF Supply phase voltage 155 V Grid frequency 50 Hz i (t) Load resistance R 10 Ω Hysteresis l block Inverter side inductance L 4mH Rectifier side inductance L 3mH Figure 2: Fixed-band hysteresis current control loop. APF dc-link voltage V 500 V dc Fixed hysteresis bandwidth 0.9 A i (t) V /2 i (t) dc v (t) i (t) L f f i (t) HB HB V /2 dc V /2 dc Figure 3: Single-phase diagram of a power system with APF. −V /2 dc Figure 4: The upper and lower bands of the reference compensa- 3.2. Adaptive Hysteresis Current Control (AHCC). As men- tion current. tioned above, the crucial concern with the fixed band hysteresis current control is producing a varying modulation + − where i (t)and i (t) are the rising current and the falling frequency of the power converter which, in turn, results f f in increasing the switching losses. To avoid this situation, current, respectively. Furthermore, the following relations can be extracted: adaptive hysteresis current controller methods with the variable hysteresis band have been recommended in the + ∗ di (t) di (t) f f literature [6, 7]. Hence, a variable hysteresis band is defined × t − × t = 2HB, 1 1 dt dt for each phase so that the switching frequency remains (10) − ∗ almost constant. di (t) di (t) f f × t − × t =−2HB, 2 2 The variable hysteresis band (HB) formula can be dt dt calculated based on Figures 1 and 3. The following KVL equation can be easily achieved: f = , (11) t + t 1 2 di (t) f 1 where t and t are switching intervals and f is the switching 1 2 = V − v (t),(6) f s dt L frequency. By substituting (8), (9), and (11)in(10), the hysteresis where V is the inverter-side voltage and can be elaborated band (HB) can be achieved as follows: as below: ⎧ ∗ di (t) V L V f v (t) f ⎪ dc dc s the upperswitchisON, ⎪ HB = − + . (12) 2 8fL 2fV L dt f dc f V = (7) ⎪ −V dc the lower switch is ON. The adaptive HB should be derived instantaneously during each sample time to keep the switching frequency Having paid attention to Figure 4, the following relations constant. can be obtained: 4. Simulation Results di (t) f 1 = V − v (t),(8) f s dt L To verify validity of the proposed method some simulations are done using MATLAB/Simulink (Table 1). The nonlinear di (t) −1 f load consists of a three-phase diode rectifier with a DC-side = V + v (t),(9) f s resistive load. It should be mentioned that the nonlinear dt L f 4 Advances in Power Electronics Fixed-band HCC Adaptive HCC 50 50 −50 −50 0.12 0.14 0.16 0.12 0.14 0.16 Time (s) Time (s) (a) (b) 20 20 −20 −20 0.12 0.14 0.16 0.12 0.14 0.16 Time (s) Time (s) (c) (d) 50 50 0 0 −50 −50 0.12 0.14 0.16 0.12 0.14 0.16 Time (s) Time (s) (e) (f) Figure 5: The currents for phase (a). load is connected to the grid via inductances (L = 4 mH). Table 2: THD% value of load and source currents. Besides, the load voltages have an rms value of 155 V-50 Hz Source current THD% Load current THD% which leads to a rms value of 18 A for system current. Phase Phase Phase Phase Phase Phase The source voltage has been remained sinusoidal and (a) (b) (c) (a) (b) (c) does not contain any harmonics. Figure 5 shows comparative Fixed- diagrams of load current, filter current, and source current, 2.15 2.59 2.83 24.42 24.31 24.55 band respectively, for fixed-band HCC and AHCC methods sim- AHCC 3.73 3.81 3.53 24.42 24.21 24.55 ulation. These diagrams show a good filtering which leads to eliminate the source current harmonics, so the source current contains just the main component. The THD results in Table 2 show that AHCC method Figure 6 shows the instantaneous switching frequency for works properly to track the reference current, and there the fixed-band HCC and AHCC. It is obvious that the switch- was a good filtering process. But the following figures show ing frequency in fixed-band HCC varies in vast range (in this the difference between fixed-band and AHCC. The AHCC case it changed from 15 KHz to 25 KHz) and causes audio distinction will be proved by Figures 5 and 6. noises and injects high-frequency components in source Source current (A) Load current (A) Filter current (A) Filter current (A) Load current (A) Source current (A) Advances in Power Electronics 5 Fixed-band HCC ×10 Fixed-band HCC 2.5 0.8 0.6 1.5 0.4 0.2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) 0 0.5 1 1.5 2 2.5 (a) 4 ×10 Frequency (Hz) (a) ×10 Adaptive HCC 2.5 Adaptive HCC 0.8 1.5 0.6 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.4 Time (s) 0.2 (b) 0 0.5 1 1.5 2 2.5 Figure 6: Instantaneous switching frequency. ×10 Frequency (Hz) (b) Figure 7: FFT analysis of the source current in high frequency current that makes it difficult to design appropriate filters range. for eliminating them. In AHCC method, the instantaneous switching frequency remains constant with little deviation contrary to conventional fixed-band hysteretic current con- trol method. In practical application, it is necessary to keep 5. Conclusion switching frequency to certain limits, in order to determine switching device and decrease its switching losses [9]. Shunt active power filters are the most suitable devices in Figure 7 proves that many high-frequency components power networks which eliminate the current harmonics and have been injected to the source current due to variable compensate the reactive power. Instantaneous power theory switching frequency, but in Figure 7, the AHCC results is one of the effective methods which have been explained prove the fact that this method has worked properly which in this paper. Afterwards, the hysteresis current control results in fixing switching frequency (12 KHz to 15 KHz). has been clarified with two modes: fixed-band and AHCC. This result influences the source current THD especially in The simulation results proved that AHCC technique made high-frequency range. Since the variation range of switching the fixed switching frequency that results in reducing the frequency has been limited to small domain, the high- high-frequency components of source current and switching frequency components of source current have been reduced losses. to a narrow range which is apparent in Figure 7. As the variable switching frequency causes audio noises, References the AHCC fixes this problem by constant switching fre- quency, too. [1] B. Singh and J. Solanki, “An implementation of an adaptive The vast range of high-frequency components of current control algorithm for a three-phase shunt active filter,” IEEE harmonic is just a source for audio noises as well as Transactions on Industrial Electronics, vol. 56, no. 8, pp. 2811– producing switching losses due to the switch resistance. Each 2820, 2009. harmonic order should be multiplied by the square of the [2] M. Tavakoli Bina and E. Pashajavid, “An efficient procedure switch resistor to obtain the power losses so in fixed-band to design passive LCL-filters for active power filters,” Elsevier method this value is higher than AHCC. Journal Electric Power Systems Research, vol. 79, no. 4, pp. 606– Besides, calculating the number of switching on-off 614, 2009. pulses proves the fact that fixing switching frequency [3] A. Emadi, A. Nasiri, and S. B. Bekarov, Uninterruptable Power decreases the switching number and the switching number Supplies and Active Filters, Illinoise Institute of Technology, has a direct relation with the switching losses. In this simulation for 0.2 sec, the switching number has been [4] M. P. Kazmierkowski and L. Malesani, “Current control changed from approximately 11000 to 6000, respectively, techniques for three-phase voltage-source pwm converters: a from fixed-band to AHCC method. So the switching losses survey,” IEEE Transactions on Industrial Electronics, vol. 45, are reduced by about 50%. no. 5, pp. 691–703, 1998. Frequency (Hz) Frequency (Hz) Mag (% of fundamental) Mag (% of fundamental) 6 Advances in Power Electronics [5] B. K. Bose, “An adaptive hysteresis band current control technique of a voltage feed PWM inverter for machine drive system,” IEEE Transactions on Industrial Electronics, vol. 37, no. 5, pp. 402–408, 1990. [6] H. Vahedi and A. Sheikholeslami, “Variable hysteresis current control applied in a shunt active filter with constant switching frequency,” in Proceedings of the Power Quality Conference (PQC’ 10), pp. 1–5, 2010. [7] H. Vahedi and A. Sheikholeslami, “The source-side inductance based adaptive hysteresis band current control to be employed in active power filters,” International Review on Modeling and Simulation Journal, vol. 3, no. 5, pp. 840–845, 2010. [8] H. Akagi, Y. Kanazawa, and A. Nabae, “Instantaneous reactive power compensators comprising switching devices without energy storage components,” IEEE Transactions on Industry Applications, vol. 20, no. 3, pp. 625–630, 1984. [9] G. Vazquez, ´ P. Rodriguez, R. Ordonez, ˜ T. Kerekes, and R. Teodorescu, “Adaptive hysteresis band current control for transformerless single-phase PV inverters,” in Proceedings of the 35th Annual Conference of the IEEE Industrial Electronics Society (IECON ’09), pp. 173–177, November 2009. 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Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and High-Frequency Harmonics

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Copyright © 2011 Hani Vahedi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Publishing Corporation Advances in Power Electronics Volume 2011, Article ID 397872, 6 pages doi:10.1155/2011/397872 Review Article Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and High-Frequency Harmonics 1 2 3 Hani Vahedi, Abdolreza Sheikholeslami, Mohammad Tavakoli Bina, and Mahmood Vahedi Department of Electrical Engineering, Islamic Azad University, Sari Branch, Sari, Iran Department of Electrical Engineering, Babol University of Technology, Babol, Iran Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran Correspondence should be addressed to Hani Vahedi, hani.vahedi@gmail.com Received 1 February 2011; Accepted 2 May 2011 Academic Editor: Francesco Profumo Copyright © 2011 Hani Vahedi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Hysteresis Current Control (HCC) is widely used due to its simplicity in implementation, fast and accurate response. However, the main issue is its variable switching frequency which leads to extraswitching losses and injecting high-frequency harmonics into the system current. To solve this problem, adaptive hysteresis current control (AHCC) has been introduced which produces hysteresis bandwidth which instantaneously results in smoother and constant switching frequency. In this paper the instantaneous power theory is used to extract the harmonic components of system current. Then fixed-band hysteresis current control is explained. Because of fixed-band variable frequency disadvantages, the adaptive hysteresis current control is explained that leads to fixing the switching frequency and reducing the high-frequency components in source current waveform. Due to these advantages of AHCC, the switching frequency and switching losses will be diminished appropriately. Some simulations are done in MATLAB/Simulink. The Fourier Transform and THD results of source and load currents and the instantaneous switching frequency diagram are discussed to prove the efficiency of this method. The Fourier Transform and THD results of source and load currents are discussed to prove the validity of this method. 1. Introduction behavior. On the other hand, conventional hysteresis method includes some undesirable results, such as variable switching In recent years, shunt active power filters have being applied frequency that causes audio noises, high switching losses by many industries and researchers to remove the current and injection of high-frequency current components to the harmonics caused by nonlinear loads [1–3]. An APF as can source current that makes it difficult to design suitable filters be seen in Figure 1 is a parallel power inverter with loads to remove these high-frequency harmonics. that can remove large amounts of current harmonics through Many switching methods are used to produce switching the injection of reference current to the power system pulse which leads to generate reference current. Hysteresis that contains harmonic components of the source current. current control (HCC) has been noticed more than other Complete compensation occurs when the APF produces the current control techniques, due to simplicity and quicker same current as harmonic current with the same amplitude dynamic response [5–8]. and opposite in sign. The main problem of HCC is its variable switching fre- Hysteresis current control is one of the most appropriate quency which leads to variable high-frequency components PWM switching methods to produce reference current in in source current waveform, audio noises and increase APFs [4]. Hysteresis current control has desirable charac- switching losses. One of performed methods that can solve teristics such as high stability, fast and accurate dynamic this problem is the AHCC method that builds variable band 2 Advances in Power Electronics for current tracking, hence the switching speed becomes i (t) i (t) L s l l smooth and the frequency switching will be fixed consider- 3φ AC R ably. source i (t) Furthermore, different frequency components in current f waveform will appear due to different switching frequencies Rectifier that make it difficult to design appropriate filters to elimi- f v (t) i (t) nate these components and make noises affects measuring l l devices. To overcome this problem, an adaptive hysteresis Harmonic extraction current control (AHCC) has been introduced. Using this method, variable hysteresis bandwidth is calculated instan- Current controller taneously, which leads to reducing the switching frequency V /2 dc variation, thus the fixed-band HCC issues will be amended. Voltage source In this paper, in Section 2, the instantaneous power the- Switching pulses inverter V /2 ory has been explained to extract the harmonics components dc of current waveform. Then in Section 3, the fixed-band HCC and AHCC have been clarified. Finally, some simulations Figure 1: Power System Diagram with APF. have been done with MATLAB/Simulink, and the results consisting of switching frequency diagrams and current THD in high-frequency range have been discussed in Section 4. By comparing the results of simulations, the advantages in order to compensate the harmonics and the instantaneous of AHCC in fixing switching frequency and modifying the reactive power, compensation reference currents can be above-mentioned problems, especially reducing the high- extracted as follows: frequency components in source current waveform and ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ −1 i (t) v (t) v (t) −p (t) α β fα switching losses, have been proved. ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ = ,(4) i (t) −v (t) v (t) −q(t) fβ β α 2. Instantaneous Power Theory t t ∗ ∗ ∗ ∗ ∗ −1 i (t) i (t) i (t) 0 i (t) i (t) = C . (5) fa fb fc fα fβ One of the popular compensation reference current extrac- tion methods is the instantaneous reactive power theory (p-q 3. Hysteresis Current Control theory). Although there are some problems with this theory, it is well established and simple in implementation. The p-q Hysteresis current control is used for generating the switch- theory could be briefly reviewed as follows [8]. ing pulses. Among the various current control techniques, Assume a three-phase load with the instantaneous volt- t HCC is the most extensively used technique because of the ages as v(t) = [v (t) v (t) v (t)] and the instantaneous a b c t noncomplex implementation, outstanding stability, absence currents as i (t) = [i (t) i (t) i (t)] (Figure 1). Using (1), l la lb lc of any tracking error, very fast transient response, inherent v(t)and i (t)can be convertedto0-α-β coordination where limited maximum current, and intrinsic robustness to load C is matrix (2): parameters variations. As indicated in [6, 7]areview of t t used current control techniques for PWM converters reveals t t v (t) = C[v (t)] , i (t) = C[i (t)],(1) 0αβ abc 0αβ abc that HCC shows certain superiority for active power filter applications. HCC provides a better low-order harmonic ⎡ ⎤ suppression than PWM control, which is the main target of 1 1 1 √ √ √ ⎢ ⎥ the active power filter. It is easier to realize with high accuracy 2 2 2 ⎢ ⎥ ⎢ ⎥ and fast response. However, as a disadvantage its switching −1 −1 ⎢ ⎥ C = ⎢ 1 ⎥ . (2) frequency might fluctuate. ⎢ ⎥ 2 2 ⎢ ⎥ √ √ In the HCC technique the error function is centered in ⎣ ⎦ 3 − 3 a preset hysteresis band. When the error exceeds the upper 2 2 or lower hysteresis limit the hysteretic controller makes an Let’s assume that the zero sequence current (i (t)) is appropriate switching decision to control the error within l0 null. Thus, the instantaneous active (p(t)) and reactive (q(t)) the preset band and send these pulses to VSI to produce the powers can be calculated as reference current as shown in Figure 2. The outputs of the hysteresis blocks are directly fed as the ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ p(t) v (t) v (t) i (t) α β lα firing pulse of VSI switches. ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ = ;(3) q(t) −v (t) v (t) i (t) β α lβ 3.1. Fixed-Band Hysteresis Current Control. In fixed-band p(t)and q(t) can be decomposed to the average parts HCC, the hysteresis bandwidth (HB) has been taken as (p(t), q(t)) and the oscillating parts (p (t), q (t)). It is notable a small portion related to system current, and in many that p(t) is produced by the fundamental harmonics of the researches it has been taken as 5% of main current which will positive sequence component of the load current. Therefore, be HB = 0.9A, here. Advances in Power Electronics 3 Table 1: APF simulation parameters. i (t) i (t) f Switching pulses f APF Supply phase voltage 155 V Grid frequency 50 Hz i (t) Load resistance R 10 Ω Hysteresis l block Inverter side inductance L 4mH Rectifier side inductance L 3mH Figure 2: Fixed-band hysteresis current control loop. APF dc-link voltage V 500 V dc Fixed hysteresis bandwidth 0.9 A i (t) V /2 i (t) dc v (t) i (t) L f f i (t) HB HB V /2 dc V /2 dc Figure 3: Single-phase diagram of a power system with APF. −V /2 dc Figure 4: The upper and lower bands of the reference compensa- 3.2. Adaptive Hysteresis Current Control (AHCC). As men- tion current. tioned above, the crucial concern with the fixed band hysteresis current control is producing a varying modulation + − where i (t)and i (t) are the rising current and the falling frequency of the power converter which, in turn, results f f in increasing the switching losses. To avoid this situation, current, respectively. Furthermore, the following relations can be extracted: adaptive hysteresis current controller methods with the variable hysteresis band have been recommended in the + ∗ di (t) di (t) f f literature [6, 7]. Hence, a variable hysteresis band is defined × t − × t = 2HB, 1 1 dt dt for each phase so that the switching frequency remains (10) − ∗ almost constant. di (t) di (t) f f × t − × t =−2HB, 2 2 The variable hysteresis band (HB) formula can be dt dt calculated based on Figures 1 and 3. The following KVL equation can be easily achieved: f = , (11) t + t 1 2 di (t) f 1 where t and t are switching intervals and f is the switching 1 2 = V − v (t),(6) f s dt L frequency. By substituting (8), (9), and (11)in(10), the hysteresis where V is the inverter-side voltage and can be elaborated band (HB) can be achieved as follows: as below: ⎧ ∗ di (t) V L V f v (t) f ⎪ dc dc s the upperswitchisON, ⎪ HB = − + . (12) 2 8fL 2fV L dt f dc f V = (7) ⎪ −V dc the lower switch is ON. The adaptive HB should be derived instantaneously during each sample time to keep the switching frequency Having paid attention to Figure 4, the following relations constant. can be obtained: 4. Simulation Results di (t) f 1 = V − v (t),(8) f s dt L To verify validity of the proposed method some simulations are done using MATLAB/Simulink (Table 1). The nonlinear di (t) −1 f load consists of a three-phase diode rectifier with a DC-side = V + v (t),(9) f s resistive load. It should be mentioned that the nonlinear dt L f 4 Advances in Power Electronics Fixed-band HCC Adaptive HCC 50 50 −50 −50 0.12 0.14 0.16 0.12 0.14 0.16 Time (s) Time (s) (a) (b) 20 20 −20 −20 0.12 0.14 0.16 0.12 0.14 0.16 Time (s) Time (s) (c) (d) 50 50 0 0 −50 −50 0.12 0.14 0.16 0.12 0.14 0.16 Time (s) Time (s) (e) (f) Figure 5: The currents for phase (a). load is connected to the grid via inductances (L = 4 mH). Table 2: THD% value of load and source currents. Besides, the load voltages have an rms value of 155 V-50 Hz Source current THD% Load current THD% which leads to a rms value of 18 A for system current. Phase Phase Phase Phase Phase Phase The source voltage has been remained sinusoidal and (a) (b) (c) (a) (b) (c) does not contain any harmonics. Figure 5 shows comparative Fixed- diagrams of load current, filter current, and source current, 2.15 2.59 2.83 24.42 24.31 24.55 band respectively, for fixed-band HCC and AHCC methods sim- AHCC 3.73 3.81 3.53 24.42 24.21 24.55 ulation. These diagrams show a good filtering which leads to eliminate the source current harmonics, so the source current contains just the main component. The THD results in Table 2 show that AHCC method Figure 6 shows the instantaneous switching frequency for works properly to track the reference current, and there the fixed-band HCC and AHCC. It is obvious that the switch- was a good filtering process. But the following figures show ing frequency in fixed-band HCC varies in vast range (in this the difference between fixed-band and AHCC. The AHCC case it changed from 15 KHz to 25 KHz) and causes audio distinction will be proved by Figures 5 and 6. noises and injects high-frequency components in source Source current (A) Load current (A) Filter current (A) Filter current (A) Load current (A) Source current (A) Advances in Power Electronics 5 Fixed-band HCC ×10 Fixed-band HCC 2.5 0.8 0.6 1.5 0.4 0.2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time (s) 0 0.5 1 1.5 2 2.5 (a) 4 ×10 Frequency (Hz) (a) ×10 Adaptive HCC 2.5 Adaptive HCC 0.8 1.5 0.6 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.4 Time (s) 0.2 (b) 0 0.5 1 1.5 2 2.5 Figure 6: Instantaneous switching frequency. ×10 Frequency (Hz) (b) Figure 7: FFT analysis of the source current in high frequency current that makes it difficult to design appropriate filters range. for eliminating them. In AHCC method, the instantaneous switching frequency remains constant with little deviation contrary to conventional fixed-band hysteretic current con- trol method. In practical application, it is necessary to keep 5. Conclusion switching frequency to certain limits, in order to determine switching device and decrease its switching losses [9]. Shunt active power filters are the most suitable devices in Figure 7 proves that many high-frequency components power networks which eliminate the current harmonics and have been injected to the source current due to variable compensate the reactive power. Instantaneous power theory switching frequency, but in Figure 7, the AHCC results is one of the effective methods which have been explained prove the fact that this method has worked properly which in this paper. Afterwards, the hysteresis current control results in fixing switching frequency (12 KHz to 15 KHz). has been clarified with two modes: fixed-band and AHCC. This result influences the source current THD especially in The simulation results proved that AHCC technique made high-frequency range. Since the variation range of switching the fixed switching frequency that results in reducing the frequency has been limited to small domain, the high- high-frequency components of source current and switching frequency components of source current have been reduced losses. to a narrow range which is apparent in Figure 7. As the variable switching frequency causes audio noises, References the AHCC fixes this problem by constant switching fre- quency, too. [1] B. Singh and J. Solanki, “An implementation of an adaptive The vast range of high-frequency components of current control algorithm for a three-phase shunt active filter,” IEEE harmonic is just a source for audio noises as well as Transactions on Industrial Electronics, vol. 56, no. 8, pp. 2811– producing switching losses due to the switch resistance. Each 2820, 2009. harmonic order should be multiplied by the square of the [2] M. Tavakoli Bina and E. Pashajavid, “An efficient procedure switch resistor to obtain the power losses so in fixed-band to design passive LCL-filters for active power filters,” Elsevier method this value is higher than AHCC. Journal Electric Power Systems Research, vol. 79, no. 4, pp. 606– Besides, calculating the number of switching on-off 614, 2009. pulses proves the fact that fixing switching frequency [3] A. Emadi, A. Nasiri, and S. B. Bekarov, Uninterruptable Power decreases the switching number and the switching number Supplies and Active Filters, Illinoise Institute of Technology, has a direct relation with the switching losses. In this simulation for 0.2 sec, the switching number has been [4] M. P. Kazmierkowski and L. Malesani, “Current control changed from approximately 11000 to 6000, respectively, techniques for three-phase voltage-source pwm converters: a from fixed-band to AHCC method. So the switching losses survey,” IEEE Transactions on Industrial Electronics, vol. 45, are reduced by about 50%. no. 5, pp. 691–703, 1998. Frequency (Hz) Frequency (Hz) Mag (% of fundamental) Mag (% of fundamental) 6 Advances in Power Electronics [5] B. K. Bose, “An adaptive hysteresis band current control technique of a voltage feed PWM inverter for machine drive system,” IEEE Transactions on Industrial Electronics, vol. 37, no. 5, pp. 402–408, 1990. [6] H. Vahedi and A. Sheikholeslami, “Variable hysteresis current control applied in a shunt active filter with constant switching frequency,” in Proceedings of the Power Quality Conference (PQC’ 10), pp. 1–5, 2010. [7] H. Vahedi and A. Sheikholeslami, “The source-side inductance based adaptive hysteresis band current control to be employed in active power filters,” International Review on Modeling and Simulation Journal, vol. 3, no. 5, pp. 840–845, 2010. [8] H. Akagi, Y. Kanazawa, and A. Nabae, “Instantaneous reactive power compensators comprising switching devices without energy storage components,” IEEE Transactions on Industry Applications, vol. 20, no. 3, pp. 625–630, 1984. [9] G. Vazquez, ´ P. Rodriguez, R. Ordonez, ˜ T. Kerekes, and R. Teodorescu, “Adaptive hysteresis band current control for transformerless single-phase PV inverters,” in Proceedings of the 35th Annual Conference of the IEEE Industrial Electronics Society (IECON ’09), pp. 173–177, November 2009. 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