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Active power filter for three-phase four-wire electric systems using neural networks
Electric Power Systems Research 60 (2002) 179– 192 www.elsevier.com/locate/epsr
Active power filter for three-phase four-wire electric systems using neural networks Chakphed Madtharad, Suttichai Premrudeepreechacharn * Power Electronic Research Laboratory, Department of Electrical Engineering, Chiang Mai Uni6ersity, Chiang Mai, Thailand Received 5 February 2001; received in revised form 12 September 2001; accepted 5 October 2001
Abstract This paper presents the design of neural networks compared with the conventional technique, a hysteresis controller for active power filter for three-phase four-wire electric system. A particular three-layer neural network structure is studied in some detail. Simulation and experimental results of the active power filter with both controllers are also presented to verify the feasibility of such controller. The simulation and experimental result show that both controller techniques can reduce harmonics in three-phase four-wire electric systems drawn by nonlinear loads and can reduce neutral current. The advantage of the neural network controller technique over hysteresis controller technique are less voltage ripple of d.c. bus, and less switching loss. Furthermore, the neural networks controller has better fault tolerance than the hysteresis controller. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Active power filter; Power quality; Neural networks
1. Introduction There has been a continuous proliferation of nonlinear type of loads due to the intensive use of electronics control in all branches of industry as well as by general consumers. Conventional rectifiers are harmonic polluters of the power distribution system. Non-linear loads, especially power electronics loads, create phase displacement and harmonic currents in the main three-phase power distribution system. Both make the power factor of the system worse. The presence of harmonic currents can also lead to some special problems in three-phase systems. In a three-phase four-wire systems, harmonic currents can lead to large currents in the neutral conductors, which may easily exceed the conductor rms current rating. Harmonic currents tend to flow through shunt-connected power
* Corresponding author. E-mail address: [email protected] (S. Premrudeepreechacharn).
factor correction capacitors. The capacitors may overheat and fail when they are exposed to significant harmonic currents. The active approaches have proven to be very effective [1–5]. Three single-phase active power filters (APF) can be used for this propose. However, a conventional three-phase, three-wire APF cannot be used in a three-phase four-wire system to eliminate harmonics on the neutral wire. The process of filtering is done in the time domain which is based on the principle of holding the instantaneous source voltage or current within some reasonable tolerance of a sine wave. The harmonic components are compensated instantaneously using current control technique. The past decade had seen a dramatic increase in interest in neural network systems. The application of neural networks promises high computation rate provided by the massive parallelism, a great degree of robustness or fault tolerance due to the distribution representation, and an ability for adaptation, learning, and generalization to improve performance. Today neural networks are actively explored in artificial
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Fig. 1. An APF and nonlinear loads considered in this paper.
Fig. 2. A controller for APF.
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Fig. 3. Neural network structure for APF.
intelligence, psychology, engineering, and physics. The neural networks can be applied to power electronics areas such as power converter control, current regulation control, motor speed regulation, etc. [6– 8]. Neural networks controllers are proposed in this paper as a mean to solve the problems introduced by non-linearities in APF. This paper presents the application of neural networks controllers for APF for three-phase four-wire distribution systems. The system considered in this paper is shown in Fig. 1. Section 2 of this paper provides the fundamentals of APF. In Section 3, the structure of the controller is discussed. In this paper, back-propagation neural networks is considered. The proposed neural network controllers are presented. Finally, simulation results verifying the concept are also presented.
Table 1 Training pattern for neural network controller Input pattern
Desired pattern
i*ca−ica
i*cb−icb
i*cc−icc
Va
Vb
Vc
1 1 1 1 −1 −1 −1 −1
1 1 −1 −1 1 1 −1 −1
1 −1 1 −1 1 −1 1 −1
1 1 1 1 −1 −1 −1 −1
1 1 −1 −1 1 1 −1 −1
1 −1 1 −1 1 −1 1 −1
Table 2 The system parameters used in simulating the system shown in Fig. 1 Utility source
Voltage source (Vs) Frequency (F) Source resistance (Rs) Source inductance (Ls)
75 Vrms 50 Hz 2.5 V 0.4 mH
Non-linear load
Load capacitance (Cl) Load resistance (Rl)
1500 mF 27 V
Active power filter (APF)
APF resistance (Rc) APF inductance (Lc) APF capacitance (Cc)
1.6 V 12.2 mH 2200 mF
2. Active power filter system The main objective of the APF is to compensate harmonics, reactive power, neutral current and unbalancing of non-linear loads locally such that a.c. mains supplies only unity power-factor sinusoidal balanced three-phase currents. The APF draws the required cur-
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Fig. 4. The system performance of APF: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa).
C. Madtharad, S. Premrudeepreechacharn / Electric Power Systems Research 60 (2002) 179–192
rents from the a.c. mains to feed harmonics, reactive power, and neutral current for balancing of load currents locally and causes balanced sinusoidal unity power-factor supply currents under all operating conditions. Fig. 1 shows the basic APF scheme including a set of non-linear loads on a three-phase four-wire distribution systems. In this paper, the APF consists of
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three single phase inverters. The switches of APF must support unipolar voltage and bipolar current, an IGBT with antiparallel diode is needed to implement each switch. The current which must be supported by each switch is the maximum inductor current. The maximum voltage which must be supported by controllable switches is the maximum d.c. bus voltage. The load may be either single phase, two phase or
Fig. 5. The frequency spectra for the system: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa).
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Fig. 5. (Continued)
three phase and non-linear in nature. In this paper, we consider three single phase uncontrolled diode bridge rectifiers with resistive– capacitive loading as non-linear unbalanced loads. This load draws a non-sinusoidal current from the utility. The controller for APF is comprised of an inner current loop which actively shapes the line currents and an outer voltage control loop which regulates the magnitude of the line currents as shown in Fig. 2. The inner current loop can use a current regulator scheme such as hysteresis to shape the line current. Among the various current control techniques, hysteresis current control is the simplest and most extensively used technique. However, a fixed-band hysteresis current control has drawbacks on various switching frequencies and has large ripple current. In this paper, we use the neural networks controllers as current regulator for APF. The outer voltage loop regulates the average capacitor voltage by using a proportional-integral (PI) controller. In addition, the magnitude of the line current is dictated by the outer voltage control loop. The current references for each of the three phase APF are derived by sensing the load currents and removing from their source references current which is sinusoidally waveshaped as shown in Eq. (1).
I*cx = I*sx − Ilx
(1)
where I*cx is the APF current for phase x; I*sx, source current for phase x; Ilx, load current for phase x. Thus, the current references consist of the harmonic current components drawn by load. By forcing the filter output current to follow the reference, only a fundamental frequency sinusoidal current is drawn from the utility or distribution transformer. Hence, undesirable harmonic current components are removed from the utility side of the system. Nominal d.c. bus voltage must be at least 2Vrms in order to assure control over the shape of the APF current at all times [3]. Since the compensating currents should be cyclic with the line frequency, the capacitor voltage will contain ripple but its average will be stable provided that there is an appropriate balance of power. Therefore, we are not concerned with the voltage ripple as long as the voltage is always at least 2Vrms. To charge and maintain adequate charge on the d.c. side capacitor, a PI regulator will be used to control the flow of real power from the a.c. side towards the d.c. side of the converter. Since the converter is designed only to compensate harmonics, which does not include the fundamental, this real power transfer merely compensates the losses in the
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Fig. 6. The system performance of APF: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa); (d) The neutral of nonlinear load current (Inl); (e) The neutral of source current using hysteresis controller (Inl); (f) The neutral of source current using neural networks controller (Inl); (g) The ac component of DC bus voltage using hysteresis controller (Vdc); and (h) The ac component of DC bus voltage using neural networks controller (Vdc).
various filter components, switches and interconnections. Hence, the outer voltage control loop uses the PI controller to sense the average voltage across the capacitor and adjust the gain of reference currents to maintain the desired bus voltage. If the gain of reference current is too large, power flow dictates that the average capacitor voltage must increase as the capacitor absorbs the excess power delivered by the source or vice versa.
The choice of capacitance value and capacitor type depends on both the minimum necessary d.c. bus voltage that it must support and also the rms and harmonic components of the current that pass through it. The capacitor must be capable of handling the required rms current without overheating and the harmonic components should not cause excessive ripple on the d.c. bus voltage. This knowledge is utilized in rating the converter switches.
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Fig. 6. (Continued)
3. Neural networks Neural networks have the potential to provide an improved method of deriving non-linear models which is complementary to conventional techniques. Neural networks have self-adapting capabilities which make them well suited to handle non-linearities, uncertainties
and parameter variations which may occur in a controlled plant. In this paper, back-propagation neural networks are utilized as pattern classifier. Back-propagation neural networks are an example of nonlinear layered feed-forward networks. It is a universal approximator [9,10]. The structure of the proposed neural networks used
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Fig. 6. (Continued)
for APF is shown in Fig. 3. The neural networks were trained using MATLAB software. We trained the neural networks with a learning rate of 0.25 until the error function was less than 5×10 − 5. The proposed neural network controllers are based on hysteresis current control. The neural network controller requires the training patterns to learn the desired control mapping. The training patterns should have
sufficient information to cover the essential characteristic of entire control mapping. Table 1 summarizes the eight training patterns for the neural network controller. The gating signal for controllable switches is the output of the neural networks passed through the hard limiter given by If Vx \ 0, gating signal= 1, else gating signal=0 (2)
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Fig. 6. (Continued)
4. Simulation results This section discusses the operation of the system shown in Fig. 1. The system was simulated and evaluated to learn more about the operation of the APF. The system components of Fig. 1 that are used in the simulation are described in Table 2. Simulation studies are carried out to predict the performance of the proposed APF using MATLAB.
Fig. 4 documents the performance of the system for one operating point. Fig. 4(a) show the nonlinear load current. The source current using hysteresis with hysteresis band is 0.01 A and neural network controllers have been shown in Fig. 4(b,c), respectively at a maximum switching frequency of 5.2 kHz. Fig. 5 shows the spectral performance of the system. The total harmonic distortion (THD) is based on the 1st–35th odd harmonic of current waveform
C. Madtharad, S. Premrudeepreechacharn / Electric Power Systems Research 60 (2002) 179–192
and a pure sinewave for the voltage. That means the distortion voltages present in the source voltage have not been considered with regard to the calculation of THD. Fig. 5 shows the significant reduction in the harmonics drawn from the utility by using APF. The APF is effectively used to reduce its THD of nonlinear load current as shown in Fig. 5(a) from 69.76 to 11.73% and 9.60% using hysteresis and neural network controllers in Fig. 5(b,c), respectively at a maximum switching frequency of 5.2 kHz.
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5. Experimental results This section discusses the operation of the system shown in Fig. 1. The system was experimental and evaluated to learn more about the operation of the APF. The system components of Fig. 1 that are used in the experiment are described in Table 2 at a maximum switching frequency of 5.2 kHz. Fig. 6 documents the performance of the system for one operating point. Fig. 6(a) shows the nonlinear load
Fig. 7. The frequency spectra for the system: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa).
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Fig. 7. (Continued)
current. The source current using hysteresis and neural network controllers have been shown in Fig. 6(b) and (c), respectively. Fig. 6(d– f) show the neutral current of nonlinear load, neutral source current using hysteresis and neural network controllers, respectively. Fig. 6(g) and (h) show the a.c. components of the d.c. bus capacitor of APF using hysteresis and neural network controllers, respectively. Since the compensating currents should be cyclic with the line frequency, the capacitor voltage will contain ripple but its average will be stable provided that there is an appropriate balance of power. As previously discussed, we are not con-cerned with the voltage ripple as long as the voltage always at least 2Vrms. The small amount of ripple on the d.c. bus voltage suggests that a smaller bus capacitor may be used if we are not concerned with transient operation. Fig. 7 shows the spectral performance of the system. The APF is effective in reducing its THD of nonlinear load current as shown in Fig. 7 (a) from 69.33 to 11.47% and 12.79% by using hysteresis and neural networks controllers in Fig. 7(b) and (c), respectively at a maximum switching frequency of 5.2 kHz. In the case of having some error in phase A of controller, neural networks controller can work effectively all of the three phase but hysteresis controller
cannot, as shown in Fig. 8(a,b). That is, the neural network controller has a better fault tolerance than the hysteresis controller. The THD of source in different conditions is shown in Fig. 9. Fig. 9(a) shows that the higher the switching frequency, the lower the THD of the source. The higher the THD of the load, the higher the THD of the source as shown in Fig. 9(b). Fig. 9(a,b) shows that the hysteresis and neutral network controllers can reduced harmonics in almost the same capacity under different conditions.
6. Conclusion This paper has focused on applying back-propagation neural networks to control the three single-phase APF compared with hysteresis controller at a maximum switching frequency of 5.2 kHz. The simulation and experimental results with the same parameters have shown that the APF with both controllers is able to compensate the distortion and reactive power drawn by the nonlinear loads. In addition, the APF also helps to reduce the undesirable current that flows in the neutral line of a three-phase four-wire distribution system. By simulation, the APF is effectively used to reduce its THD of nonlinear load current
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Fig. 8. The system performance of APF when there is an error in phase A of the controller: (a) The source current using hysteresis controller (Isa); and (b) The source current using neural networks controller (Isa).
from 69.76 to 11.73% and 9.60%, and by experiment, from 69.33 to 11.47% and 12.79% using hysteresis and neural networks, respectively. The advantages of the neural network controller technique over hysteresis controller technique are less voltage ripple of d.c. bus, and less switching loss. Furthermore the neural networks controller has better fault tolerance than the hysteresis controller.
Acknowledgements The authors would like to thank The Shell Centenary Scholarship Fund and Graduated School Fund of Chiang Mai University who supported this research. This paper was written when the first author studied in Chiang Mai University under the support of Provincial Electricity Authority (PEA).
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Fig. 9. The THD of source under different conditions: (a) The relationship between switching frequency and THD of source; and (b) The relationship between THD of load and THD of source.
References [5] [1] C.L. Chen, C.E. Lin, C.L. Huang, An active filter for unbalanced three-phase system using synchronous detection method, IEEE Power Electron. Specialists Conf. Record (1994) 1451 – 1455. [2] P. Enjeti, W. Shireen, P. Packebush, I. Pitel, Analysis and design of a new active power filter to cancel neutral current harmonics in three phase four wire electric distribution systems, Conf. Record of IEEE Ind. Appl. Society (IAS) Annual Meeting (1993) 939 – 946. [3] C.A. Quinn, N. Mohan, Active filtering of harmonic currents in three phase, four-wire systems with three-phase and single-phase non-linear loads, Proceedings of Applied Power Electron. Conf. (APEC) (1992) 829 –835. [4] B. Singh, K. Al-Haddad, A. Chandra, Harmonic elimination, reactive power compensation and load balancing in three-phase,
[6]
[7]
[8] [9] [10]
four-wire electric distribution systems supplying non-linear loads, Electr. Power Syst. Res. 44 (1998) 93 – 100. S. Saetieo, R. Devaraj, D.A. Torrey, The design and implementation of a three-phase active power filter based on sliding mode control, IEEE Trans. Ind. Appl. 31 (5) (1995) 993 – 1000. F. Harashima, Y. Demizu, S. Kondo, H. Hashimoto, Application of neural networks to power converter control, Conf. Record of IEEE Ind. Appl. Society IAS Annual Meeting (1989) 1086 – 1091. B.R. Lin, R.G. Hoft, Power electronics converter control based on neural network and fuzzy logic methods, IEEE Power Electron. Specialists Conf. Record (1993) 900 – 906. H.M. Tai, J. Wang, K. Ashenayi, Motor Speed Regulation Using Neural Networks, Proc. of the IECON (1990) 1215 –1220. S. Haykin, Neural Networks, Macmillan, New York, 1994. F.V. Laurene, Fundamentals of Neural Networks: Architectures, Algorithms, and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1994.
Active power filter for three-phase four-wire electric systems using neural networks Chakphed Madtharad, Suttichai Premrudeepreechacharn * Power Electronic Research Laboratory, Department of Electrical Engineering, Chiang Mai Uni6ersity, Chiang Mai, Thailand Received 5 February 2001; received in revised form 12 September 2001; accepted 5 October 2001
Abstract This paper presents the design of neural networks compared with the conventional technique, a hysteresis controller for active power filter for three-phase four-wire electric system. A particular three-layer neural network structure is studied in some detail. Simulation and experimental results of the active power filter with both controllers are also presented to verify the feasibility of such controller. The simulation and experimental result show that both controller techniques can reduce harmonics in three-phase four-wire electric systems drawn by nonlinear loads and can reduce neutral current. The advantage of the neural network controller technique over hysteresis controller technique are less voltage ripple of d.c. bus, and less switching loss. Furthermore, the neural networks controller has better fault tolerance than the hysteresis controller. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Active power filter; Power quality; Neural networks
1. Introduction There has been a continuous proliferation of nonlinear type of loads due to the intensive use of electronics control in all branches of industry as well as by general consumers. Conventional rectifiers are harmonic polluters of the power distribution system. Non-linear loads, especially power electronics loads, create phase displacement and harmonic currents in the main three-phase power distribution system. Both make the power factor of the system worse. The presence of harmonic currents can also lead to some special problems in three-phase systems. In a three-phase four-wire systems, harmonic currents can lead to large currents in the neutral conductors, which may easily exceed the conductor rms current rating. Harmonic currents tend to flow through shunt-connected power
* Corresponding author. E-mail address: [email protected] (S. Premrudeepreechacharn).
factor correction capacitors. The capacitors may overheat and fail when they are exposed to significant harmonic currents. The active approaches have proven to be very effective [1–5]. Three single-phase active power filters (APF) can be used for this propose. However, a conventional three-phase, three-wire APF cannot be used in a three-phase four-wire system to eliminate harmonics on the neutral wire. The process of filtering is done in the time domain which is based on the principle of holding the instantaneous source voltage or current within some reasonable tolerance of a sine wave. The harmonic components are compensated instantaneously using current control technique. The past decade had seen a dramatic increase in interest in neural network systems. The application of neural networks promises high computation rate provided by the massive parallelism, a great degree of robustness or fault tolerance due to the distribution representation, and an ability for adaptation, learning, and generalization to improve performance. Today neural networks are actively explored in artificial
0378-7796/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 7 7 9 6 ( 0 1 ) 0 0 1 8 5 - 7
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Fig. 1. An APF and nonlinear loads considered in this paper.
Fig. 2. A controller for APF.
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Fig. 3. Neural network structure for APF.
intelligence, psychology, engineering, and physics. The neural networks can be applied to power electronics areas such as power converter control, current regulation control, motor speed regulation, etc. [6– 8]. Neural networks controllers are proposed in this paper as a mean to solve the problems introduced by non-linearities in APF. This paper presents the application of neural networks controllers for APF for three-phase four-wire distribution systems. The system considered in this paper is shown in Fig. 1. Section 2 of this paper provides the fundamentals of APF. In Section 3, the structure of the controller is discussed. In this paper, back-propagation neural networks is considered. The proposed neural network controllers are presented. Finally, simulation results verifying the concept are also presented.
Table 1 Training pattern for neural network controller Input pattern
Desired pattern
i*ca−ica
i*cb−icb
i*cc−icc
Va
Vb
Vc
1 1 1 1 −1 −1 −1 −1
1 1 −1 −1 1 1 −1 −1
1 −1 1 −1 1 −1 1 −1
1 1 1 1 −1 −1 −1 −1
1 1 −1 −1 1 1 −1 −1
1 −1 1 −1 1 −1 1 −1
Table 2 The system parameters used in simulating the system shown in Fig. 1 Utility source
Voltage source (Vs) Frequency (F) Source resistance (Rs) Source inductance (Ls)
75 Vrms 50 Hz 2.5 V 0.4 mH
Non-linear load
Load capacitance (Cl) Load resistance (Rl)
1500 mF 27 V
Active power filter (APF)
APF resistance (Rc) APF inductance (Lc) APF capacitance (Cc)
1.6 V 12.2 mH 2200 mF
2. Active power filter system The main objective of the APF is to compensate harmonics, reactive power, neutral current and unbalancing of non-linear loads locally such that a.c. mains supplies only unity power-factor sinusoidal balanced three-phase currents. The APF draws the required cur-
182
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Fig. 4. The system performance of APF: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa).
C. Madtharad, S. Premrudeepreechacharn / Electric Power Systems Research 60 (2002) 179–192
rents from the a.c. mains to feed harmonics, reactive power, and neutral current for balancing of load currents locally and causes balanced sinusoidal unity power-factor supply currents under all operating conditions. Fig. 1 shows the basic APF scheme including a set of non-linear loads on a three-phase four-wire distribution systems. In this paper, the APF consists of
183
three single phase inverters. The switches of APF must support unipolar voltage and bipolar current, an IGBT with antiparallel diode is needed to implement each switch. The current which must be supported by each switch is the maximum inductor current. The maximum voltage which must be supported by controllable switches is the maximum d.c. bus voltage. The load may be either single phase, two phase or
Fig. 5. The frequency spectra for the system: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa).
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Fig. 5. (Continued)
three phase and non-linear in nature. In this paper, we consider three single phase uncontrolled diode bridge rectifiers with resistive– capacitive loading as non-linear unbalanced loads. This load draws a non-sinusoidal current from the utility. The controller for APF is comprised of an inner current loop which actively shapes the line currents and an outer voltage control loop which regulates the magnitude of the line currents as shown in Fig. 2. The inner current loop can use a current regulator scheme such as hysteresis to shape the line current. Among the various current control techniques, hysteresis current control is the simplest and most extensively used technique. However, a fixed-band hysteresis current control has drawbacks on various switching frequencies and has large ripple current. In this paper, we use the neural networks controllers as current regulator for APF. The outer voltage loop regulates the average capacitor voltage by using a proportional-integral (PI) controller. In addition, the magnitude of the line current is dictated by the outer voltage control loop. The current references for each of the three phase APF are derived by sensing the load currents and removing from their source references current which is sinusoidally waveshaped as shown in Eq. (1).
I*cx = I*sx − Ilx
(1)
where I*cx is the APF current for phase x; I*sx, source current for phase x; Ilx, load current for phase x. Thus, the current references consist of the harmonic current components drawn by load. By forcing the filter output current to follow the reference, only a fundamental frequency sinusoidal current is drawn from the utility or distribution transformer. Hence, undesirable harmonic current components are removed from the utility side of the system. Nominal d.c. bus voltage must be at least 2Vrms in order to assure control over the shape of the APF current at all times [3]. Since the compensating currents should be cyclic with the line frequency, the capacitor voltage will contain ripple but its average will be stable provided that there is an appropriate balance of power. Therefore, we are not concerned with the voltage ripple as long as the voltage is always at least 2Vrms. To charge and maintain adequate charge on the d.c. side capacitor, a PI regulator will be used to control the flow of real power from the a.c. side towards the d.c. side of the converter. Since the converter is designed only to compensate harmonics, which does not include the fundamental, this real power transfer merely compensates the losses in the
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Fig. 6. The system performance of APF: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa); (d) The neutral of nonlinear load current (Inl); (e) The neutral of source current using hysteresis controller (Inl); (f) The neutral of source current using neural networks controller (Inl); (g) The ac component of DC bus voltage using hysteresis controller (Vdc); and (h) The ac component of DC bus voltage using neural networks controller (Vdc).
various filter components, switches and interconnections. Hence, the outer voltage control loop uses the PI controller to sense the average voltage across the capacitor and adjust the gain of reference currents to maintain the desired bus voltage. If the gain of reference current is too large, power flow dictates that the average capacitor voltage must increase as the capacitor absorbs the excess power delivered by the source or vice versa.
The choice of capacitance value and capacitor type depends on both the minimum necessary d.c. bus voltage that it must support and also the rms and harmonic components of the current that pass through it. The capacitor must be capable of handling the required rms current without overheating and the harmonic components should not cause excessive ripple on the d.c. bus voltage. This knowledge is utilized in rating the converter switches.
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Fig. 6. (Continued)
3. Neural networks Neural networks have the potential to provide an improved method of deriving non-linear models which is complementary to conventional techniques. Neural networks have self-adapting capabilities which make them well suited to handle non-linearities, uncertainties
and parameter variations which may occur in a controlled plant. In this paper, back-propagation neural networks are utilized as pattern classifier. Back-propagation neural networks are an example of nonlinear layered feed-forward networks. It is a universal approximator [9,10]. The structure of the proposed neural networks used
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Fig. 6. (Continued)
for APF is shown in Fig. 3. The neural networks were trained using MATLAB software. We trained the neural networks with a learning rate of 0.25 until the error function was less than 5×10 − 5. The proposed neural network controllers are based on hysteresis current control. The neural network controller requires the training patterns to learn the desired control mapping. The training patterns should have
sufficient information to cover the essential characteristic of entire control mapping. Table 1 summarizes the eight training patterns for the neural network controller. The gating signal for controllable switches is the output of the neural networks passed through the hard limiter given by If Vx \ 0, gating signal= 1, else gating signal=0 (2)
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Fig. 6. (Continued)
4. Simulation results This section discusses the operation of the system shown in Fig. 1. The system was simulated and evaluated to learn more about the operation of the APF. The system components of Fig. 1 that are used in the simulation are described in Table 2. Simulation studies are carried out to predict the performance of the proposed APF using MATLAB.
Fig. 4 documents the performance of the system for one operating point. Fig. 4(a) show the nonlinear load current. The source current using hysteresis with hysteresis band is 0.01 A and neural network controllers have been shown in Fig. 4(b,c), respectively at a maximum switching frequency of 5.2 kHz. Fig. 5 shows the spectral performance of the system. The total harmonic distortion (THD) is based on the 1st–35th odd harmonic of current waveform
C. Madtharad, S. Premrudeepreechacharn / Electric Power Systems Research 60 (2002) 179–192
and a pure sinewave for the voltage. That means the distortion voltages present in the source voltage have not been considered with regard to the calculation of THD. Fig. 5 shows the significant reduction in the harmonics drawn from the utility by using APF. The APF is effectively used to reduce its THD of nonlinear load current as shown in Fig. 5(a) from 69.76 to 11.73% and 9.60% using hysteresis and neural network controllers in Fig. 5(b,c), respectively at a maximum switching frequency of 5.2 kHz.
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5. Experimental results This section discusses the operation of the system shown in Fig. 1. The system was experimental and evaluated to learn more about the operation of the APF. The system components of Fig. 1 that are used in the experiment are described in Table 2 at a maximum switching frequency of 5.2 kHz. Fig. 6 documents the performance of the system for one operating point. Fig. 6(a) shows the nonlinear load
Fig. 7. The frequency spectra for the system: (a) The nonlinear load current (I1a); (b) The source current using hysteresis controller (Isa); and (c) The source current using neural networks controller (Isa).
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Fig. 7. (Continued)
current. The source current using hysteresis and neural network controllers have been shown in Fig. 6(b) and (c), respectively. Fig. 6(d– f) show the neutral current of nonlinear load, neutral source current using hysteresis and neural network controllers, respectively. Fig. 6(g) and (h) show the a.c. components of the d.c. bus capacitor of APF using hysteresis and neural network controllers, respectively. Since the compensating currents should be cyclic with the line frequency, the capacitor voltage will contain ripple but its average will be stable provided that there is an appropriate balance of power. As previously discussed, we are not con-cerned with the voltage ripple as long as the voltage always at least 2Vrms. The small amount of ripple on the d.c. bus voltage suggests that a smaller bus capacitor may be used if we are not concerned with transient operation. Fig. 7 shows the spectral performance of the system. The APF is effective in reducing its THD of nonlinear load current as shown in Fig. 7 (a) from 69.33 to 11.47% and 12.79% by using hysteresis and neural networks controllers in Fig. 7(b) and (c), respectively at a maximum switching frequency of 5.2 kHz. In the case of having some error in phase A of controller, neural networks controller can work effectively all of the three phase but hysteresis controller
cannot, as shown in Fig. 8(a,b). That is, the neural network controller has a better fault tolerance than the hysteresis controller. The THD of source in different conditions is shown in Fig. 9. Fig. 9(a) shows that the higher the switching frequency, the lower the THD of the source. The higher the THD of the load, the higher the THD of the source as shown in Fig. 9(b). Fig. 9(a,b) shows that the hysteresis and neutral network controllers can reduced harmonics in almost the same capacity under different conditions.
6. Conclusion This paper has focused on applying back-propagation neural networks to control the three single-phase APF compared with hysteresis controller at a maximum switching frequency of 5.2 kHz. The simulation and experimental results with the same parameters have shown that the APF with both controllers is able to compensate the distortion and reactive power drawn by the nonlinear loads. In addition, the APF also helps to reduce the undesirable current that flows in the neutral line of a three-phase four-wire distribution system. By simulation, the APF is effectively used to reduce its THD of nonlinear load current
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Fig. 8. The system performance of APF when there is an error in phase A of the controller: (a) The source current using hysteresis controller (Isa); and (b) The source current using neural networks controller (Isa).
from 69.76 to 11.73% and 9.60%, and by experiment, from 69.33 to 11.47% and 12.79% using hysteresis and neural networks, respectively. The advantages of the neural network controller technique over hysteresis controller technique are less voltage ripple of d.c. bus, and less switching loss. Furthermore the neural networks controller has better fault tolerance than the hysteresis controller.
Acknowledgements The authors would like to thank The Shell Centenary Scholarship Fund and Graduated School Fund of Chiang Mai University who supported this research. This paper was written when the first author studied in Chiang Mai University under the support of Provincial Electricity Authority (PEA).
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Fig. 9. The THD of source under different conditions: (a) The relationship between switching frequency and THD of source; and (b) The relationship between THD of load and THD of source.
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