Electrical Power and Energy Systems 44 (2013) 219–226 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes A novel hysteresis band current controller scheme for three phase AC chopper Murat Kale a,⇑, Murat Karabacak b, Bilal Saracoglu a a b Duzce University, Faculty of Technology, Electrical and Electronics Engineering Department, Konuralp, Duzce, Turkey Duzce University, Duzce Higher Vocational School, Department of Electronics Technology, Duzce, Turkey a r t i c l e i n f o Article history: Received 2 August 2011 Received in revised form 13 June 2012 Accepted 5 July 2012 Available online 26 September 2012 Keywords: Three phase PWM AC chopper Hysteresis band current control Pulse width modulation (PWM) a b s t r a c t This paper presents the application of the hysteresis band current controller (HBCC) technique to the three phase pulse width modulation (PWM) AC chopper used for the purpose of controlling the magnitude of the sinusoidal currents and voltages applied to an AC load. If the HBCC technique used in the inverters is directly employed in the three phase PWM AC chopper, it causes the AC chopper to fail to provide balanced three phase sinusoidal currents for a three phase AC load. In return, this situation leads some unavoidable and serious faults to occur in the hardware of the three phase PWM AC chopper. In respect to this case, the detailed analysis expressing the related faults is presented. Consequently, for the first time, a novel HBCC technique overcoming these faults is proposed for the three phase PWM AC chopper. The proposed method is tested under various operating conditions and a very precise control performance is achieved. Simulation results prove the feasibility and validity of the proposed method. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction In order to obtain regulated AC supply, AC choppers are widely used in the applications such as lightening control, industrial heating and soft starting of induction motors. The simplest way to control an AC chopper consisting of a pair of triacs is the phase angle control (PAC) because of its simplicity and the ability of controlling a large amount of power economically [1,2], which is called the conventional AC chopper. However, it has several limitations due to the inherent characteristics of the PAC. That is, a lagging power factor appears at the supply side even for a resistive load [3,4]. As a result of PAC, the harmonic content of the output voltage and current of the AC chopper is large, where requires a relatively large filtering stage [5]. Moreover, a discontinuity of power flow appears at both the supply and load sides of the AC chopper as well, which leads to another serious drawback in driving dynamic loads such as electric motors [1]. In order to eliminate these drawbacks arising from the inherent characteristics of these controllers, linecommutated conventional AC controllers can be replaced by PWM AC choppers having better overall performance such as sinusoidal supply current with unity power factor, fast dynamics and significant reduction in filter size [1]. Using the high frequency switching devices such as IGBT and MOSFET, the supply voltage can be chopped by changing the duty ratio of the PWM modulation signal so as to regulate the load voltage [6]. ⇑ Corresponding author. Tel.: +90 380 5421133x2248; fax: +90 380 5421134. E-mail addresses: muratkale@duzce.edu.tr (M. Kale), muratkarabacak@duzce .edu.tr (M. Karabacak), bilalsaracoglu@duzce.edu.tr (B. Saracoglu). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.07.013 Downloaded from http://www.elearnica.ir In the inverters, in order to control the load current, HBCC among the various PWM techniques is widely used because of its inherent simplicity and fast dynamic response [7–14]. In [15,16], the AC load current is controlled by using HBCC in the single phase AC chopper. In [17], an adaptive HBCC technique is proposed for the three phase PWM AC chopper. In that study, the HBCC technique is established based on the claim that ‘‘the operation principle of the HBCC technique of a three-phase AC chopper is the same one as that of the three-phase inverter’’ [17]. In contrast to this claim, the HBCC technique employed in a three phase PWM AC chopper has to be structurally different from its counterparts in an inverter and/or a single phase PWM AC chopper. Otherwise, it is inevitable for the power switches such as IGBT or MOSFET of three phase PWM AC chopper to be subject to some unavoidable and serious faults since the continuity of load currents is not ensured. Therefore, in [17], the HBCC technique proposed for the three phase PWM AC chopper lacks theoretical validation and so it is not possible to be implemented experimentally. In the literature, there is not any study that proposes and evidently proves the application of HBCC technique to a three phase PWM AC chopper. As a result, this case formed the motivation of this study. The novelty of this study is to present a detailed analysis interested in the faults mentioned above and accordingly propose a novel HBCC technique eliminating them. The proposed HBCC technique for three phase PWM AC chopper, which is seen in Fig. 1, is simulated in Matlab/Simulink and detailed results are obtained for various operating points that also contain the case of unbalanced supply voltages. Since all the faults are eliminated, it is guaranteed 220 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 Voltage Measurement vSa vSb vSc Current Measurement R L S1 R L S2 R L S3 vSabc S3* S2* iLabc S1* Fig. 1. The power scheme of the three phase PWM AC chopper. the load voltages and currents are stably remained balanced in all the operating conditions. Table 1 Possible switching states for three phase inverter and AC chopper. 2. The HBCC used in the inverters In the inverter, the HBCC is only based on that the switching signals are obtained by means of comparing the desired sinusoidal reference currents at the desired frequency and amplitude with the actual load currents, which is clearly seen in Fig. 2. Where iLa ; iLb and iLc are the reference three phase currents aimed at applying to a three phase inductive AC load, iLa, iLb and iLc are the actual three phase load currents. R and L are also resistance and inductance of the AC load respectively. Thanks to the fact that the three phase current errors maintain within a hysteresis band, it is ensured the actual load current vector follows the reference trajectory. Due to the inherent nature of the HBCC, the switching signals of each phase are exactly independent of each other [18]. This implies that all the switching states given in Table 1 are possible to be performed at any moment in time according to the dynamics of the load driven. Moreover, including all the initial conditions of the load currents, the continuity of the load currents are provided on account of the inverse parallel diodes of the IGBTs. In this context, there is no possible fault to be able to occur as regards the switching sequence. In this technique, the DC-bus voltage of the inverter and the phase angle of the load are not required to be measured and/or calculated. Besides, the width of the hysteresis band has a direct influence on the switching frequency and peak to peak ripples in the load currents. In the literature, there are many studies about adaptively selecting the width of hysteresis band and thereby keeping the switching frequency constant, called adaptive hysteresis band. However, this is out of the scope of this study. 2.1. Analysis of thepossible faults interested in application of the HBCC to the three phase PWM AC chopper At this stage, we aim at applying the HBCC to the three phase PWM AC chopper. In this respect, the HBCC technique used in HB controller iLa* iLa iLb + - NOT iLc + - NOT iLc* 1 2 3 4 5 6 7 8 S2 S3 S1 S2 S3 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 the three phase inverter is directly applied to the three phase PWM AC chopper feeding a load with isolated neutral without any modification or improvement. Correspondingly, it is inevitable that some important and serious faults occur. In terms of analysis of the faults, we assumed the assumption below is valid. A1 In the course of the time t0, randomly selected polarities of the phase A, phase B and phase C load currents are negative, positive and positive respectively. In this moment, the initial values of phase A, phase B and phase C currents are iLa(0) = 9A, iLb(0) = 6A and iLc(0) = 3A respectively. It should be noted that, according to the dynamics of the load driven, any of the eight possible switching states listed in Table 1 is possible to immediately be in effect as soon as the time t0 passes. The general formulation of the phase voltages is given in the following: 2 3 2 32 3 2 L1 0 ia 0 54 ib 5 þ 4 0 r3 0 ic 3 2 32 1 1 1 v Sa 1 þ 4 1 1 1 54 v Sb 5 3 v Sc 1 1 1 r1 v Sa 4 v Sb 5 ¼ 4 0 v Sc 0 0 r2 0 0 L2 0 32 diLa 3 0 6 dt 7 0 54 didtLb 5 diLc L3 dt ð1Þ Therefore, after an infinitely small time following the time t0, we assumed the switching states given below are put into effect in order. Switching Signals for IGBTs + - iLb* State State State State State State State State S1 NOT Three Phase Two Level Voltage Fed Inverter iLa R L iLb R L iLc R L Fig. 2. The HBCC in the three phase inverters. Isolated Neutral 221 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 (a) (b) (c) (d) (e) (f) (g) (h) Fig. 3. The phase current path relations in connection with the application of the HBCC to the AC Chopper. 2.1.1. Switching state 1 S1, S2 and S3 are off, which the form of the phase current paths is given in Fig. 3a, then the load phase voltages are equal to zero as the following: 2 3 2 3 2 0 1 v La 6 7 6 7 16 4 v Lb 5 ¼ 4 0 5 4 1 3 0 1 v Lc 32 3 2 3 0 0 1 1 76 7 6 7 1 1 54 0 5 ¼ 4 0 5 0 0 1 1 ð2Þ It is clear that there is no fault. 2.1.2. Switching state 2 S1 and S2 are off and S3 is on. The form of the phase current paths is given in Fig. 3b, which implies no fault. 2 3 2 3 2 v La v Sa 1 6 7 6 7 16 4 v Lb 5 ¼ 4 0 5 4 1 3 1 v Lc v Sc 1 1 32 v Sa 3 76 7 1 1 54 0 5 1 1 v Sc 2.1.3. Switching state 3 S1 and S3 are off and S2 is on. That means there is no fault. The form of the phase current paths is given in Fig. 3c. 2 2 3 2 1 32 3 v Sa 76 7 1 54 v Sb 5 1 1 1 1 ð4Þ 0 2.1.4. Switching state 4 S1 is off and S2 and S3 are on. The form of the phase current paths is given in Fig. 3d. There is no fault and resulting equation yields: 2 ð3Þ 3 1 v La v Sa 7 16 6 7 6 4 v Lb 5 ¼ 4 v Sb 5 4 1 3 1 v Lc 0 3 2 3 2 1 v La v Sa 6 7 6 7 16 4 v Lb 5 ¼ 4 v Sb 5 4 1 3 1 v Lc v Sc 1 1 32 3 v Sa 76 7 1 54 v Sb 5 1 v Sc 1 1 ð5Þ 222 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 2.1.5. Switching state 5 In the previous modes, the overall three phase system is in the closed loop, the way all three phase currents have a return path. Therefore continuity of the load currents is ensured, since they follow their references as the three phase current errors maintain within the hysteresis band. For first four switching states, it is therefore clear that all inductive components of the three phase load have a certain stored energy in the magnetic field and the fact that no current path is broken prevents them from the instantaneous discharge, thus no voltage spike comes into existence in the phases. As for the switching state 5, the switches S1, S2 and S3 are on, off and off respectively, which means the AC chopper encounters an unavoidable fault. Namely, when the state 5 is put into practice, the current conduction path for phase A is broken. The form of the phase current paths related to this situation is given in Fig. 3e. This implies the phase A current will immediately be fallen equal to zero and, in turn, a very high reverse voltage spike is generated by the sharp change in the phase A current. In other words, from the viewpoint of the laws of magnetic induction, an instantaneous discharge of the inductance of phase A occurs, which leads to the voltage spike in phase A. In this case, the instantaneous variation in phase A current is iBRa = 9A. Furthermore, the phase B and C have been in the closed loop, which has no connection with supply, thus, the both currents induce a new current. Its amplitude is equal to the difference between them and the direction is same as the higher one, which cause the instantaneous partial charge and discharge of the inductance of phase B and C. Similarly, this also leads to voltage spikes in phase B and C. If we call it iBRb-c (the breakdown current between phase B and C), its amplitude will be |ib–ic| = 3A and direction will be same as ib, which is being reverse direction to the phase C current. Then, it is clear the phase B and C currents sharply change from ib = 6A and ic = 3A to iBRb = (ib–ic) and iBRc = (ib–ic) respectively, where iBRb and iBRc are the instantaneous variations in phase B and C currents. Since the magnetic field is a function of electrical current, by definition, the voltage spikes occurred in phase A, B and C can be expressed through the instantaneous rate of change of the phase currents passing through the phase inductances over an infinitely small time interval following the course of switching state5: 2 3 2 r1 v La 6 7 6 4 v Lb 5 ¼ 4 0 0 v Lc 0 r2 0 32 3 2 L1 0 7 6 76 0 54 ðiLb iLc Þ 5 þ 4 0 r3 ðiLb iLc Þ 0 0 0 L2 0 32 iBRa 3 0 Dt 76 iBRb 7 7 0 56 4 Dt 5 iBRc L3 ð6Þ Dt iBRa, iBRb and iBRc are the sharp variations in the phase currents during the course of the time Dt that is the infinitely small time interval. These voltage spikes can be supposed to be equal to infinite since Dt can be approximately identical to zero and, in consequence, probably brings about the fault causing a severe damage to the components in the AC chopper, especially power switches. 2 3 2 r1 v La 4 v Lb 5 ¼ 4 0 0 v Lc 2 0 r2 0 3 þ1 ffi 4 1 5 1 3 2 32 L1 0 0 0 54 ðiLb iLc Þ 5 þ 4 0 r3 ðiLb iLc Þ 0 0 L2 0 32 9 3 0 0 0 54 30 5 L3 60 ð7Þ 2.1.6. Switching state 6 S1, S2 and S3 are on, off and on respectively. The form of the phase current paths is given in Fig. 3f; the phase B current path is broken. The phase A and C have been in the closed loop; however, this closed loop is different from that in the switching state 5 since it has a connection to supply. In parallel with this case, the formulation of the load phase voltages appears slightly different from the general formulation given before. 3 2 32 L1 0 0 ðiLa iLc Þ 4 5þ4 0 5 r2 0 0 0 r3 0 ðiLa iLc Þ 3 3 2 32 1 1 1 v Sa v Sa 1 þ 4 0 5 4 1 1 1 54 0 5 3 v Sc v Sc 1 1 1 2 3 þ1 ffi 4 1 5 þ1 2 3 2 r1 v La 4 v Lb 5 ¼ 4 0 0 v Lc 2 0 L2 0 32 3 3 0 0 0 54 60 5 9 L3 0 ð8Þ 2.1.7. Switching state 7 S1, S2 and S3 are on, on and off respectively. The form of the phase current paths is given in Fig. 3g; the phase C current path is broken. This is another variant of the fault expressed in the switching state 6. The phase voltages are given in the following: 3 2 32 L1 0 0 ðiLa iLb Þ 4 5 r2 0 ðiLa iLb Þ 5 þ 4 0 0 r3 0 0 3 3 2 32 1 1 1 v Sa v Sa 1 þ 4 v Sb 5 4 1 1 1 54 v Sb 5 3 0 0 1 1 1 2 3 þ1 ffi 4 þ1 5 1 2 3 2 r1 v La 4 v Lb 5 ¼ 4 0 v Lc 0 2 0 L2 0 32 6 3 0 0 0 54 90 5 30 L3 ð9Þ 2.1.8. Switching state 8 S1, S2 and S3 are on. The form of the phase current paths is given in Fig. 3h. There is no fault and the phase voltages are: 2 3 2 3 2 1 v La v Sa 6 7 6 7 16 4 v Lb 5 ¼ 4 v Sb 5 4 1 3 1 v Lc v Sc 32 3 1 1 v Sa 76 7 1 1 54 v Sb 5 1 1 v Sc ð10Þ As seen from the analysis above, if the HBCC technique used in the inverters is directly applied to a three phase AC chopper and any of the switching states 5, 6 or 7 occurs at any moment in time according to dynamics of the load driven, it is inevitable that a serious damage to power switches of the chopper takes place. 3. The proposed HBCC for the three phase AC chopper Our task in this stage is to develop a HBCC technique for the three phase PWM AC chopper which eliminates the faults mentioned in the previous section. The main difference of the AC chopper from the inverter is that the currents and the voltages at the supply side of the AC chopper are AC signals. The AC chopper is obliged to produce output currents at only the same frequency and the same waveform as supply voltages. Besides, there is a load phase angle between the voltage and the current space vectors of the supply according to the characteristic of load. Consequently, the reference currents in the AC chopper have to be same frequency as the supply voltages and phase angle as the load [15]. The fact that the HBCC used in the inverters cannot be used for the AC chopper was expressed quite clear in the previous section. However, it can be modified to be applied to the AC chopper, which requires two certain modifications. These modifications are carried out by obtaining the reference currents and providing the continuity of the load current conduction paths. 223 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 3.1. Obtaining the reference currents vSa The reference currents can be generated in two steps. First, the frequency and the angle of the space vector of the supply voltages are obtained via employing the synchronous reference frame PLL. Second, it is required transforming the three phase load currents into synchronous reference frame using Park Transformation in order to calculate the load phase angle, which is revealed in Eqs. (11) and (12). It follows that d and q axis currents are passed through first order low pass filters (LPF) to obtain the angle of the fundamental component of the load currents. Then, the phase difference between the supply voltages and the load currents can be computed as shown in Eq. (13). The load phase angle and the angle of the space vector of the supply voltages are added, which enables the three phase reference currents at the same phase as the load currents and the same frequency as the supply voltages to be produced. The maximum value of the reference currents is determined by the user randomly, which is not in connection with the theory of the proposed HBCC. vSb vSc SHBA S1 S1* Fig. 5. Phase A switching signals obtained by minimum voltage algorithm. Table 2 Possible switching states when the phase A voltage is minimum. iLa ¼ Im sinðwt þ uÞ iLb ¼ Im sinðwt ð2p=3Þ þ uÞ ð11Þ iLc ¼ Im sinðwt þ ð2p=3Þ þ uÞ iLd iLq 2 3 iLa 2 sinðxtÞ sinðxt 2p=3Þ sinðxt þ 2p=3Þ 6 7 ¼ 4 iLb 5 3 cosðxtÞ cosðxt 2p=3Þ cosðxt þ 2p=3Þ iLc ð12Þ I u ¼ tan1 Lq ILd ð13Þ where Im is maximum value of the load currents, iLx (x = a, b, c) is the load currents, iLd and iLq are the d and q components of the load currents respectively, ILd and ILq are the filtered d and q components of iLd and iLq respectively, xt is the angle of the space vector of the supply voltages, u is the load phase angle. 3.2. Producing switching signals and providing the continuity of current paths It is possible to ensure the continuity of current conduction paths through the diodes parallel connected to the IGBTs in the inverters, but this situation is not sufficient for the AC chopper. There are some techniques to guarantee continuity of the current paths in the literature for the AC chopper [19,20]. Among them, the algorithm called as ‘turns on the switches of the phase with minimum voltage’ which is proposed in [19] is adapted for the HBCC proposed in this study. It is then ensured that the right power switch can be triggered according to the instantaneous values of the supply voltages, which eliminates the faults as guaranteeing the continuity of the current paths. Otherwise, it is inevitable that the faults mentioned in the previous section occur. vSa vSb vSc 1 2 3 4 S2 S3 S1 S2 S3 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 The measured load currents are subtracted from the reference currents as in Eq. (11), with the result that the current errors of each phase are acquired. The switching signals (SHBA, SHBB and SHBC) of each phase are formed through applying the HBCC to these current errors. After the switching signals (SHBA, SHBB and SHBC) are passed through the ‘Minimum Voltage Algorithm’, they can be applied to the switches in the AC chopper seen in Fig. 4. The output signals of the HBCC (SHBA) and the switching signals (S1 and S1 ) obtained by the ‘Minimum Voltage Algorithm’ are shown in Fig. 5. As two switches of the phase having minimum voltage are kept in ‘on’, the current control of three phase is implemented by the switches of the other two phases. Since the current passing through the phase having minimum voltage consists of sum of the currents of the other two phases, it is indirectly controlled by the currents of the other two phases that remain within the hysteresis band. In this way, HBCC of three phase currents can be achieved due to the fact that all the current errors are maintained within the hysteresis band. The two modifications applied to the HBCC used in the inverters are clearly shown in Fig. 4, which also depicts the real time implementation scheme of the proposed controller. 3.3. Analysis of application of the proposed HBCC to the AC chopper In order to analyze the proposed HBCC, the following assumption is supposed to be valid. The analyses can be expanded all initial conditions and all operating points. iLa iLb iLc ϕ + Im* iLd abc dq iLa + − * ωt + PLL ωt iLa iLb iLc State State State State S1 iLq LPF LPF Calculation of the Reference Currents (Equation 11) iLb* iLc* + − + − HB Controller ILd ILq Load Angle Calculation (Equation 13) Fig. 4. Real time implementation scheme of the proposed HBCC. SHBA SHBB SHBC Minimum Voltage Algorithm S1 S2 S3 S1* S2* S3* 224 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 R L vSa vSb vSc S1 R L S2 S3 R L S1* S2* R L vSa vSb vSc S1 R L S2 R L S3 S3* S1* (a) vSc R L vSa S1 R L vSb S2 R L vSc S3 S1* S2* S3* (b) vSa vSb S2* R L S1 R L S2 R L S3 S3* S1* S2* S3* (d) (c) Fig. 6. The phase current path relations in connection with the application of the proposed HBCC to the AC Chopper. 3.3.2. Switching state 2 S1, S3, S1 and S2 are on, S2 and S3 are off. The form of the phase currents is given in Fig. 6b. The load phase voltages follow: Table 3 The system parameters used in the simulations. Parameters Supply Voltage (phase-neutral) Frequency 3-Phase Load Inductances 3-Phase Load Resistors Load 2 Value VSabc f L R 220 Vrms 50 Hz 20 mH 10 O A2 The assumption A1 is valid here as well. For these initial values, the analysis results of the switching’s states given in Table 2 can be concluded in the following. After an infinitely small time following the time t0, we assumed the switching states given below are put into effect in accordance with the dynamics of the proposed HBCC. When the phase A voltage is minimum, all the switching states given in Table 2 are possible to be performed at any moment in time according to the dynamics of the load driven. 3.3.1. Switching state 1 S1, S1 , S2 and S3 are on, S2 and S3 are off. The form of the phase current paths is given in Fig. 6a. It follows that: 2 3 2 3 2 1 0 v La 6 7 6 7 16 4 v Lb 5 ¼ 4 0 5 4 1 3 1 0 v Lc 32 3 2 3 0 0 76 7 6 7 1 1 54 0 5 ¼ 4 0 5 0 0 1 1 1 1 iLa ð14Þ iLb 3 2 3 2 1 v La v Sa 6 7 6 7 16 4 v Lb 5 ¼ 4 0 5 4 1 3 1 v Lc v Sc 1 1 32 v Sa 3 76 7 1 1 54 0 5 1 1 v Sc ð15Þ 3.3.3. Switching state 3 S1, S2, S1 and S3 are on, S3 and S2 are off. The form of the phase current paths is given in Fig. 6c. The load phase voltages are: 2 3 2 3 2 1 v La v Sa 7 16 6 7 6 4 v Lb 5 ¼ 4 v Sb 5 4 1 3 1 v Lc 0 32 3 1 1 v Sa 76 7 1 1 54 v Sb 5 1 1 0 ð16Þ 3.3.4. Switching state 4 S1, S2, S3 and S1 are on. The form of the phase current paths is given in Fig. 6d. In this state, the load phase voltages can be expressed as follow: 2 3 2 3 2 v La v Sa 1 6 7 6 7 16 4 v Lb 5 ¼ 4 v Sb 5 4 1 3 1 v Lc v Sc iLc Fig. 7. The three phase load currents in the case of Im ¼ 20A. 1 1 32 3 v Sa 76 7 1 54 v Sb 5 1 v Sc 1 1 ð17Þ 225 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 25 Currents [A] 20 15 10 5 0 0 5 10 15 20 25 30 35 40 45 50 Harmonic Order Fig. 8. Harmonic spectra of the phase A current. Im* iLa Fig. 9. Dynamic responses of the phase A current for step changes in the amplitude of the reference currents. vSa vSb vSc iLa iLb iLc Fig. 10. The load currents under unbalanced supply voltages. 226 M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226 With the proposition of the ‘turn on all the switches of the phase with minimum voltage’, the instantaneous discharge of the inductive components of the load is avoided and thus the continuity of three phase load current paths are accordingly ensured, which is verified the analysis results above as well. 4. Simulation results The simulation results are obtained by the Matlab/Simulink on the basis of the parameters given in Table 3. In order to examine the behaviors of the proposed HBCC, the simulations are carried out for three different cases. 4.1. Case 1 In the case of the reference currents with constant amplitude, 20A, and balanced supply voltages, the load currents produced with the proposed HBCC is shown in Fig. 7. The harmonic spectra of the phase A current is shown in Fig. 8, which reveals the THD is % 2.15. As can be concluded from the Figure, the THD of the currents is quite low and complies with the IEC 1000-3-2 Harmonic Standards. 4.2. Case 2 In the case of the step changes in the amplitude of the reference currents (Im ), from 15A to 10A and then to 20A, the dynamic responses of the load currents are plotted in Fig. 9 under balanced supply voltages. It is clearly concluded from Fig. 9 that the load currents follow the references with high performance and accuracy. 4.3. Case 3 In the case of the reference currents with constant amplitude, 20A, the load currents are given in Fig. 10 under unbalanced supply voltages. Since the PLL method used in the proposed HBCC can correctly track the angle of the voltage space vector of the supply even in the case of unbalanced supply voltages, the reference currents can be easily generated and thus the load side currents are stably remained balanced at their reference values. The unbalances in the supply voltages are chosen as VSa = 220 V, VSb = 240 V and VSc = 205 V. 5. Concluding remarks and discussion The direct application of the HBCC to three phase PWM AC chopper leads to some serious and unavoidable faults which especially damage to the power switches of the chopper. In order to eliminate these faults, a novel HBCC for the three phase PWM AC chopper is proposed. The contributions obtained in the study can be given in the following order: 1. The related faults interested in direct application of HBCC technique used in the three phase inverter to the three phase PWM AC chopper are analyzed in detail. 2. Due to the two certain modifications in the HBCC technique used in the three phase inverter, the related faults are eliminated and the application of the HBCC technique to the three phase PWM AC chopper is achieved. 3. 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