Review Article  Open Access
Hani Vahedi, Abdolreza Sheikholeslami, Mohammad Tavakoli Bina, Mahmood Vahedi, "Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and HighFrequency Harmonics", Advances in Power Electronics, vol. 2011, Article ID 397872, 6 pages, 2011. https://doi.org/10.1155/2011/397872
Review and Simulation of Fixed and Adaptive Hysteresis Current Control Considering Switching Losses and HighFrequency Harmonics
Abstract
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 highfrequency 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 fixedband hysteresis current control is explained. Because of fixedband variable frequency disadvantages, the adaptive hysteresis current control is explained that leads to fixing the switching frequency and reducing the highfrequency 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
In recent years, shunt active power filters have being applied by many industries and researchers to remove the current harmonics caused by nonlinear loads [1โ3]. An APF as can be seen in Figure 1 is a parallel power inverter with loads that can remove large amounts of current harmonics through the injection of reference current to the power system that contains harmonic components of the source current. Complete compensation occurs when the APF produces the same current as harmonic current with the same amplitude and opposite in sign.
Hysteresis current control is one of the most appropriate PWM switching methods to produce reference current in APFs [4]. Hysteresis current control has desirable characteristics such as high stability, fast and accurate dynamic behavior. On the other hand, conventional hysteresis method includes some undesirable results, such as variable switching frequency that causes audio noises, high switching losses and injection of highfrequency current components to the source current that makes it difficult to design suitable filters to remove these highfrequency harmonics.
Many switching methods are used to produce switching pulse which leads to generate reference current. Hysteresis current control (HCC) has been noticed more than other current control techniques, due to simplicity and quicker dynamic response [5โ8].
The main problem of HCC is its variable switching frequency which leads to variable highfrequency components in source current waveform, audio noises and increase switching losses. One of performed methods that can solve this problem is the AHCC method that builds variable band for current tracking, hence the switching speed becomes smooth and the frequency switching will be fixed considerably.
Furthermore, different frequency components in current waveform will appear due to different switching frequencies that make it difficult to design appropriate filters to eliminate these components and make noises affects measuring devices. To overcome this problem, an adaptive hysteresis current control (AHCC) has been introduced. Using this method, variable hysteresis bandwidth is calculated instantaneously, which leads to reducing the switching frequency variation, thus the fixedband HCC issues will be amended.
In this paper, in Section 2, the instantaneous power theory has been explained to extract the harmonics components of current waveform. Then in Section 3, the fixedband HCC and AHCC have been clarified. Finally, some simulations have been done with MATLAB/Simulink, and the results consisting of switching frequency diagrams and current THD in highfrequency range have been discussed in Section 4. By comparing the results of simulations, the advantages of AHCC in fixing switching frequency and modifying the abovementioned problems, especially reducing the highfrequency components in source current waveform and switching losses, have been proved.
2. Instantaneous Power Theory
One of the popular compensation reference current extraction methods is the instantaneous reactive power theory ( theory). Although there are some problems with this theory, it is well established and simple in implementation. The  theory could be briefly reviewed as follows [8].
Assume a threephase load with the instantaneous voltages as and the instantaneous currents as (Figure 1). Using (1), and can be converted to  coordination where is matrix (2):
Let's assume that the zero sequence current is null. Thus, the instantaneous active and reactive powers can be calculated as and can be decomposed to the average parts and the oscillating parts . It is notable thatis produced by the fundamental harmonics of the positive sequence component of the load current. Therefore, in order to compensate the harmonics and the instantaneous reactive power, compensation reference currents can be extracted as follows:
3. Hysteresis Current Control
Hysteresis current control is used for generating the switching pulses. Among the various current control techniques, HCC is the most extensively used technique because of the noncomplex implementation, outstanding stability, absence of any tracking error, very fast transient response, inherent limited maximum current, and intrinsic robustness to load parameters variations. As indicated in [6, 7] a review of used current control techniques for PWM converters reveals that HCC shows certain superiority for active power filter applications. HCC provides a better loworder harmonic suppression than PWM control, which is the main target of the active power filter. It is easier to realize with high accuracy and fast response. However, as a disadvantage its switching frequency might fluctuate.
In the HCC technique the error function is centered in a preset hysteresis band. When the error exceeds the upper or lower hysteresis limit the hysteretic controller makes an appropriate switching decision to control the error within the preset band and send these pulses to VSI to produce the reference current as shown in Figure 2.
The outputs of the hysteresis blocks are directly fed as the firing pulse of VSI switches.
3.1. FixedBand Hysteresis Current Control
In fixedband HCC, the hysteresis bandwidth () has been taken as a small portion related to system current, and in many researches it has been taken as 5% of main current which will be โA, here.
3.2. Adaptive Hysteresis Current Control (AHCC)
As mentioned above, the crucial concern with the fixed band hysteresis current control is producing a varying modulation frequency of the power converter which, in turn, results in increasing the switching losses. To avoid this situation, adaptive hysteresis current controller methods with the variable hysteresis band have been recommended in the literature [6, 7]. Hence, a variable hysteresis band is defined for each phase so that the switching frequency remains almost constant.
The variable hysteresis band () formula can be calculated based on Figures 1 and 3. The following KVL equation can be easily achieved: where is the inverterside voltage and can be elaborated as below:
Having paid attention to Figure 4, the following relations can be obtained: where ) and are the rising current and the falling current, respectively. Furthermore, the following relations can be extracted: where and are switching intervals and is the switching frequency.
By substituting (8), (9), and (11) in (10), the hysteresis band () can be achieved as follows:
The adaptive should be derived instantaneously during each sample time to keep the switching frequency constant.
4. Simulation Results
To verify validity of the proposed method some simulations are done using MATLAB/Simulink (Table 1). The nonlinear load consists of a threephase diode rectifier with a DCside resistive load. It should be mentioned that the nonlinear load is connected to the grid via inductances (โmH). Besides, the load voltages have an rms value of 155โV50โHz which leads to a rms value of 18โA for system current.

The source voltage has been remained sinusoidal and does not contain any harmonics. Figure 5 shows comparative diagrams of load current, filter current, and source current, respectively, for fixedband HCC and AHCC methods simulation. These diagrams show a good filtering which leads to eliminate the source current harmonics, so the source current contains just the main component.
(a)
(b)
(c)
(d)
(e)
(f)
The THD results in Table 2 show that AHCC method works properly to track the reference current, and there was a good filtering process. But the following figures show the difference between fixedband and AHCC. The AHCC distinction will be proved by Figures 5 and 6.

(a)
(b)
Figure 6 shows the instantaneous switching frequency for the fixedband HCC and AHCC. It is obvious that the switching frequency in fixedband HCC varies in vast range (in this case it changed from 15โKHz to 25โKHz) and causes audio noises and injects highfrequency components in source current that makes it difficult to design appropriate filters for eliminating them. In AHCC method, the instantaneous switching frequency remains constant with little deviation contrary to conventional fixedband hysteretic current control method. In practical application, it is necessary to keep switching frequency to certain limits, in order to determine switching device and decrease its switching losses [9].
Figure 7 proves that many highfrequency components have been injected to the source current due to variable switching frequency, but in Figure 7, the AHCC results prove the fact that this method has worked properly which results in fixing switching frequency (12โKHz to 15โKHz). This result influences the source current THD especially in highfrequency range. Since the variation range of switching frequency has been limited to small domain, the highfrequency components of source current have been reduced to a narrow range which is apparent in Figure 7.
(a)
(b)
As the variable switching frequency causes audio noises, the AHCC fixes this problem by constant switching frequency, too.
The vast range of highfrequency components of current harmonic is just a source for audio noises as well as producing switching losses due to the switch resistance. Each harmonic order should be multiplied by the square of the switch resistor to obtain the power losses so in fixedband method this value is higher than AHCC.
Besides, calculating the number of switching onoff pulses proves the fact that fixing switching frequency decreases the switching number and the switching number has a direct relation with the switching losses. In this simulation for 0.2โsec, the switching number has been changed from approximately 11000 to 6000, respectively, from fixedband to AHCC method. So the switching losses are reduced by about 50%.
5. Conclusion
Shunt active power filters are the most suitable devices in power networks which eliminate the current harmonics and compensate the reactive power. Instantaneous power theory is one of the effective methods which have been explained in this paper. Afterwards, the hysteresis current control has been clarified with two modes: fixedband and AHCC. The simulation results proved that AHCC technique made the fixed switching frequency that results in reducing the highfrequency components of source current and switching losses.
References
 B. Singh and J. Solanki, โAn implementation of an adaptive control algorithm for a threephase shunt active filter,โ IEEE Transactions on Industrial Electronics, vol. 56, no. 8, pp. 2811โ2820, 2009. View at: Publisher Site  Google Scholar
 M. Tavakoli Bina and E. Pashajavid, โAn efficient procedure to design passive LCLfilters for active power filters,โ Elsevier Journal Electric Power Systems Research, vol. 79, no. 4, pp. 606โ614, 2009. View at: Publisher Site  Google Scholar
 A. Emadi, A. Nasiri, and S. B. Bekarov, Uninterruptable Power Supplies and Active Filters, Illinoise Institute of Technology, 2005.
 M. P. Kazmierkowski and L. Malesani, โCurrent control techniques for threephase voltagesource pwm converters: a survey,โ IEEE Transactions on Industrial Electronics, vol. 45, no. 5, pp. 691โ703, 1998. View at: Google Scholar
 B. K. Bose, โAn adaptive hysteresis band current control technique of a voltage feed PWM inverter for machine drive system,โ IEEE Transactions on Industrial Electronics, vol. 37, no. 5, pp. 402โ408, 1990. View at: Publisher Site  Google Scholar
 H. Vahedi and A. Sheikholeslami, โVariable hysteresis current control applied in a shunt active filter with constant switching frequency,โ in Proceedings of the Power Quality Conference (PQC' 10), pp. 1โ5, 2010. View at: Google Scholar
 H. Vahedi and A. Sheikholeslami, โThe sourceside inductance based adaptive hysteresis band current control to be employed in active power filters,โ International Review on Modeling and Simulation Journal, vol. 3, no. 5, pp. 840โ845, 2010. View at: Google Scholar
 H. Akagi, Y. Kanazawa, and A. Nabae, โInstantaneous reactive power compensators comprising switching devices without energy storage components,โ IEEE Transactions on Industry Applications, vol. 20, no. 3, pp. 625โ630, 1984. View at: Google Scholar
 G. Vázquez, P. Rodriguez, R. Ordoñez, T. Kerekes, and R. Teodorescu, โAdaptive hysteresis band current control for transformerless singlephase PV inverters,โ in Proceedings of the 35th Annual Conference of the IEEE Industrial Electronics Society (IECON '09), pp. 173โ177, November 2009. View at: Publisher Site  Google Scholar
Copyright
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.