96 IEEE POWER ELECTRONICS LETTERS, VOL. 3, NO. 3, SEPTEMBER 2005 Low-Harmonic, Three-Phase Rectifier That Applies Current Injection and a Passive Resistance Emulator Predrag Pejović, Predrag Božović, and Doron Shmilovitz Abstract A new three-phase diode bridge rectifier that provides low harmonic distortion of the input currents applying current injection technique is proposed in this paper. The rectifier applies a novel passive resistance emulator consisting of four diodes and a transformer with the volt-ampere rating of 3.57% of the rectifier-rated power. Optimization of the transformer turns ratio is performed in order to minimize the input current total harmonic distortion (THD). It is shown that with the optimal turns ratio the input current THD equals 3.72%. Dependence of the input current THD on the load current is analyzed, and it is shown that at low load currents the rectifier operates in the discontinuous conduction mode with the THD of 7.79%. The analytical results are experimentally verified on a 2 kw rectifier, indicating that the input current THD lower than 8% is provided within a wide range of the load current variations applying simple circuitry. Index Terms AC DC power conversion, converters, harmonic distortion, power conversion harmonics, power quality, rectifiers. I. INTRODUCTION THE third-harmonic current injection is a method to reduce harmonic content of input currents in three-phase diode bridge rectifiers. The method became popular after simple circuits proposed in [1] and [2] appeared. A detailed theoretical analysis of the method is given in [3], where it is shown that a part of the input power has to be taken by the current injection network in order to improve the input current THD. That power could be dissipated on resistors, as it is done explicitly in [1], or restored applying resistance emulation techniques. Another result of [3] is a comparison of the circuits proposed in [1] and [2], which showed that the circuit of [1] provides lower input current THD values than the circuit proposed in [2], due to the harmonic components at sixth multiples of the line frequency that flow between the diode bridge output terminals. In the case of the circuit proposed in [2], this harmonic content is significantly higher, resulting in the higher THD values. On the other hand, the circuit proposed in [2] requires only one inductor, in contrast to the circuit proposed in [1] that requires two inductors. To overcome the problem with the harmonic components at the sixth multiples of the line frequency, an application in the current injection network of a 1:1 transformer that completely Manuscript received January 15, 2005; revised August 8, 2005. This paper was recommended by Associate Editor V. G. Agelidis. P. Pejović is with the Faculty of Electrical Engineering, University of Belgrade, 11120 Belgrade, Serbia and Montenegro (e-mail: peja@el.etf.bg.ac.yu). P. Božović is with the Pupin Telecom DKTS, 11080 Belgrade, Serbia and Montenegro (e-mail: pbozovic@dkts.co.yu). D. Shmilovitz is with the Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978 Israel (e-mail: shmilo@eng.tau.ac.il). Digital Object Identifier 10.1109/LPEL.2005.858411 removes the harmonic components at sixth multiples of the line frequency is proposed in [4]. Volt-ampere rating of the introduced transformer is only 0.16% of the rectifier-rated power, and besides a significant reduction of the input current THD, it allows design of the current injection network applying only one inductor. The approach of [4] is applied in [5], where recovery of the power taken by the current injection network is focused. The result of [5] is a current injection network with a passive resistance emulator that provides self adjustment to the load current. The circuit proposed in [5] suffers from complexity, since the current injection network is a system of the fourth order, and it has to satisfy two resonance constraints. The power taken by the current injection network is restored at the rectifier output by increasing the output voltage. This requires circuitry to be added in series with the load, where a huge output current flows. In this paper, another approach to restore the power taken by the current injection network is analyzed. The current injection network proposed in [4] is applied, but in contrast to [5], the power taken by the current injection network is restored at the rectifier output by increasing the output current. This results in lower current ratings of applied semiconductor components, and even more important, the current injection network is of the second order, and only one resonance constraint has to be satisfied. Although self adjustment to the load current variations is not as straightforward as in [5], even better results are obtained experimentally. II. RECTIFIER TOPOLOGY The rectifier proposed in this paper is presented in Fig. 1. It consists of a three-phase diode bridge (diodes D1 to D6, the diodes not being labeled according to their conduction sequence), a current injection device which is realized as a zigzag autotransformer, a current injection network (consisting of two capacitors, an inductor, and a 1:1 transformer), and a passive resistance emulator ( transformer and diodes DR1 to DR4). Resistor models losses in the current injection network and the current injection device. The current injection network is the same as the one proposed in [4], but the resistance emulator is completely different in comparison to the one proposed in [5]. The injected current flows through the primary of the transformer, which is applied to adjust the voltage level. The transformer secondary is connected to the ac side of a single-phase diode bridge, which is supplied by a current originating from transformed. This current, after being rectified, is added to the output current. In this manner, the power taken by the current injection network is restored at the rectifier output. 1540-7985/$20.00 2005 IEEE
PEJOVIĆ et al.: LOW-HARMONIC, THREE-PHASE RECTIFIER 97 Fig. 1. The rectifier. III. OPERATION OF THE RECTIFIER The rectifier presented in Fig. 1 differs from the rectifier proposed in [4] in the resistance emulator section. Its function is to restore the power taken by the current injection network. The waveforms relevant to describe operation of the resistance emulator are presented in Fig. 2. The resistance emulator provides a link between the injected current, presented in Fig. 2(a), and the rectifier output voltage, whose waveform is presented in Fig. 2(b). Since the resistance emulator diode bridge (diodes DR1 to DR4) is current-fed, states of the diodes are determined by the direction of, such that DR1 and DR4 conduct when is positive, while DR2 and DR3 conduct when is negative. This results in the waveform of the voltage at the transformer primary, as presented in Fig. 2(c). The power is restored at the rectifier output by current, presented in Fig. 2(d). This current contains spectral components at sixth multiples of the line frequency, and it modifies the current that loads the threephase diode bridge. Applying the same nomenclature as in [5], spectral components of and at the triple of the line frequency are the same, equal to as given by (4) and (5) of [5]. Assume that the injected current is (1) Since the spectral component of at the triple of the line frequency, derived by applying Fourier analysis of the waveform of Fig. 2(c), is and the resonance of the reactive elements of the current injection network is tuned to the triple of the line frequency, i.e., (2) (3) Fig. 2. Waveforms of the rectifier voltages and currents, n =10., applying the method of equivalent circuits of [3], we obtain (4)
98 IEEE POWER ELECTRONICS LETTERS, VOL. 3, NO. 3, SEPTEMBER 2005 Fig. 3. Waveform of the input current for n =10and k =30=(7). Thus, and, in the ideal case of, gives the turns ratio of the resistance emulator transformer. Volt-ampere rating of this transformer is computed as of the input power. The diodes DR1 to DR4 are exposed to the maximum blocking voltage equal to the maximum instantaneous value of the output voltage, 1.73, the same as for the diodes in the main three-phase diode bridge. Average current of each of these diodes is equal to one half of the average value of, presented in Fig. 2(d), and equals 4.34%. This is significantly lower than the current rating for the diodes in the three-phase bridge. In this manner, applying one small transformer and four moderately-sized diodes, the resistance emulation is realized without a requirement for high frequency switching. Amplitude of the injected current affects the input current THD. Analyzing the waveform of the input current, assuming constant output current, negligible losses (, ), and the injected current waveform specified by (2), dependence of the input current THD on the amplitude of the injected current is obtained as where is normalized amplitude of the injected current, as defined by (2). This result is negligibly dependent on in the area of interest. The minimum of the THD is reached for in comparison to 1.5 obtained in [3], and results in the THD value of in comparison to 5.12% in [3]. These results are different from [3], since the current alters the waveform of the diode bridge load current, now, and thus affects the input current. This technique is similar to the one utilized in [6] to completely remove harmonics of the input currents. The obtained waveform of the input current for the optimal value of is presented in Fig. 3. The optimal amplitude of the injected current can be obtained precisely by adjusting the turns ratio of the resistance emulator (5) (6) (7) (8) Fig. 4. Experimentally obtained waveforms of the input voltage and the input current at the first phase. transformer according to (5), but this can provide the optimal current injection for only one value of the output current. At low loads, the injected current amplitude is limited by the discontinuous conduction of the diode bridge [7], while at high output currents the injected current amplitude will be independent on the load current, being determined by (4). Thus, it is of vital importance for the rectifier applicability to analyze the dependence of the input current THD on the output current in the suboptimal modes. The discontinuous conduction mode of the diode bridge occurs when the diode bridge load currents and reach zero [7]. Starting from these conditions and assuming the injected current waveform given by (2), the amplitude of the injected current in the discontinuous conduction mode is obtained as, resulting in for and. This gives the THD value of In the case where the resistance emulator is not applied, the discontinuous conduction mode occurs at, resulting in the input current THD of 10.43% [7]. It should be noted here that (9) is an approximation obtained assuming high filtering of the current injection network and negligible losses, resulting in the waveform given by (2). However, simulation and experimental experience justify these approximations. IV. EXPERIMENTAL RESULTS In order to validate the theoretical predictions, an experimental rectifier with rated power of 2 kw was built, applying mh and F. The rectifier operated with input voltage amplitude of V and output current up to 10 A. Fixing the turns ratio of the transformer according to (2), (5) and (7), it was chosen to be, in order to provide the optimal current injection at A; the parasitic resistance of the current injection system is measured as. Waveforms of the input current and the input voltage at the first phase, recorded for A, are presented in Fig. 4. This situation corresponds to the rectifier operation close to the optimal current injection. Measured THD of the input current is 4.48%, while the THD of the voltage waveform is 3.59%. To provide further comparison of the analytical and the experimental results, the waveforms presented in Fig. 2 were recorded (9)
PEJOVIĆ et al.: LOW-HARMONIC, THREE-PHASE RECTIFIER 99 Fig. 6. Dependence of the input current THD on the output current: (a) with the resistance emulator; (b) without the resistance emulator. THD. For the output current above 5.5 A, the rectifier operates in the continuous conduction mode with the injected current amplitude A, which no longer depends on the output current. To analyze the effects brought by the resistance emulator, dependence of the input current THD on the output current was measured on the same rectifier with the resistance emulator excluded. These results are presented by curve (b) of Fig. 6. The curve indicates that application of the resistance emulator improved the input current THD within a wide range of the output current. V. CONCLUSIONS Fig. 5. Experimentally recorded waveforms of the rectifier voltages and currents, n =17:6. on the experimental rectifier for the optimal current injection case, i.e., A, and the recorded waveforms are presented in Fig. 5 in the same form as the theoretical waveforms of Fig. 2. In the first diagram, Fig. 5(a), slight pollution of the injected current with the higher order harmonics could be observed. This effect was neglected in the analysis by the assumption of (2). The waveform of the output voltage, presented in Fig. 5(b), is close to the analytical predictions. A minor discrepancy was caused by commutation effects in the diode bridge and the distortions of the input voltages. However, the waveform of the voltage at the resistance emulator transformer primary, presented in Fig. 5(c), exposes a significantly lower amplitude than the corresponding waveform of Fig. 2(c), although the waveform shape matches the theoretical expectations. This discrepancy is caused by the transformer turns ratio, increased to to compensate for the losses in the current injection system. (Compare the lossless case where, which is used to generate the waveforms of Fig. 2.) The same situation applies for the diagram of the resistance emulator output current presented in Fig. 5(d). Dependence of the input current THD on the output current is presented in Fig. 6, curve (a). For the output current lower than 5.5 A, the rectifier operates in the discontinuous conduction mode. In the output current range from 1 A to 5.5 A, (9) is proven to be a good estimate of the input current A three-phase diode bridge rectifier that applies the current injection technique and a novel resistance emulator is proposed in this paper. The resistance emulator consists only of passive elements, four diodes and a transformer, and it restores the power taken by the current injection network at the rectifier output. The output current of the resistance emulator alters the diode bridge load current, and it contains some amount of harmonic components at sixth multiples of the line frequency. In the case of the optimal current injection, this results in the input current THD of 3.72%, a slight improvement over the input current THD of 5.12% obtained by pure third-harmonic current injection. The rectifier discontinuous conduction mode occurs when the amplitude of the injected current equals 5/3 of the output current, in comparison to the double of the output current in the case of pure third-harmonic current injection. In this manner, the THD of the input current in the discontinuous conduction mode is reduced from 10.43% to 7.79%. The proposed rectifier provides an input current THD lower than 8% in a wide range of the rectifier load current variations. The volt-ampere rating of the resistance emulator transformer is 3.57% of the rectifier rated power, while the resistance emulator diodes are exposed to the average current of 4.34% of the output current. Analytical results are verified on a 2 kw experimental rectifier. REFERENCES [1] W. B. Lawrance and W. Mielczarski, Harmonic current reduction in a three-phase diode bridge rectifier, IEEE Trans. Ind. Electron., vol. 39, no. 6, pp. 571 576, Dec. 1992.
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