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1. In an effort to comply with the stringent harmonic requirements set by North American and European standards such as IEEE Standard 519-1992, major high-power drive manufacturers around the world are increasingly using multi-pulse diode rectifiers in their drives as front-end converters. The rectifiers can be configured as 12-, 18- and 24-pulse rectifiers, powered by a phase shifting transformer with a number of secondary windings. Each secondary winding feeds a six-pulse diode rectifier. The dc output of the six-pulse rectifiers is connected to a voltage source inverter. The main feature of the multi-pulse rectifier lies in its ability to reduce the line current harmonic distortion. This is achieved by the phase shifting transformer, through which some of the low-order harmonic currents generated by the six-pulse rectifiers are canceled. In general, the higher the number of rectifier pulses, the lower the line current distortion is. The rectifiers with more than 30 pulses are seldom used in practice mainly due to increased transformer costs and limited performance improvements. The multipulse rectifier has a number of other features. It normally does not re quire any LC filters or power factor compensators, which leads to the elimination of possible LC resonances. The use of the phase-shifting transformer provides an effective means to block common-mode voltages generated by the rectifier and inverter in medium voltage drives, which would otherwise appear on motor terminals, leading to a premature failure of winding insulation. The multipulse diode rectifiers can be classified into _ Series-type multipulse rectifiers, where all the six-pulse rectifiers are connected in series on their dc side. In the medium-voltage drives, the series-type rectifier can be used as a front end for the inverter that requires a single dc supply such as three-level neutral point clamped (NPC) inverter and multi level flying-capacitor inverter. _ Separate-type multipulse rectifiers, where each of the six-pulse rectifiers feeds a separate dc load. This type of rectifier is suitable for use in a multi level cascaded H-bridge inverter that requires a multiple units of isolated dc supplies. This section starts with an introduction to the six-pulse diode rectifier, followed by a detailed analysis on the series- and separate-type multipulse rectifiers. The rectifier input power factor and line current THD are investigated, and results are summarized in a graphical format. The phase-shifting transformer required by the multipulse rectifiers will be dealt with in Section 5. 2. 2.1 Introduction The circuit diagram of a simplified six-pulse diode rectifier is shown in FIG. 2-1, where va, vb, and v_c are the phase voltages of the utility supply. For medium-voltage applications, each diode in the rectifier may be replaced by two or more diodes in series. To simplify the analysis, all the diodes are assumed to be ideal (no power losses or on-state voltage drop). FIG. 2-2 shows a set of voltage and current waveforms of the rectifier. The phase voltages of the utility supply are defined by v_a = _2 _ V_PH sin(omega t) v_b = _2 _ V_PH sin(omega t - 2 pi /3) v_c = _2 _ V_PH sin(omega t - 4 pi /3) (eqn. 2-1)
where VPH is the rms value of the phase voltage and _ is the angular frequency of the utility supply, given by _ = 2_f. The line-to-line voltage vab can be calculated by vab = va - vb = _2 _ VLL sin(_t + _/6) (eqn. 2-2) where VLL is the rms value of the line-to-line voltage relating to the phase voltage by VLL = _3 _VPH. The waveform of the line current i_a has two humps per half-cycle of the supply frequency. During interval I, vab is higher than the other two line-to-line voltages. Diodes D1 and D6 are forward-biased and thus turned on. The dc voltage vd is equal to vab, and the line current i_a equals vab/Rd. During interval II, D1 and D2 conduct, and i_a = vac/Rd. Similarly, the waveform of i_a in the negative half-cycle can be obtained. The other two line currents, ib and ic, have the same waveform as ia, but lag i_a by 2_/3 and 4_/3, respectively. The dc voltage vd contains six pulses (humps) per cycle of the supply frequency. The rectifier is, therefore, commonly known as a six-pulse rectifier. The average value of the dc voltage can be calculated by
2.2 Capacitive Load FIG. 2-3a shows the circuit diagram of the six-pulse rectifier with a capacitive load, where Ls represents the total line inductance between the utility supply and the rectifier, including the equivalent inductance of the supply, the leakage inductances of isolation transformer if any, and the inductance of a three-phase reactor that is often added to the system in practice for the reduction of the line current THD. The dc filter capacitor Cd is assumed to be sufficiently large such that the dc voltage is ripple-free. Under this assumption, the capacitor and dc load can be replaced by a dc voltage source Vd as shown in FIG. 2-3b. The value of Vd varies slightly with the loading conditions. When the rectifier is lightly loaded, Vd is close to the peak of the ac line-to-line voltage and the dc current id may be discontinuous. With the increase in dc current, the voltage across the line inductance Ls increases, causing a reduction in Vd. When the dc current increases to a certain level, it becomes continuous and thus the rectifier operates in a continuous current mode.
(1) Discontinuous Current Operation. FIG. 2-4 illustrates the voltage and current waveforms of the rectifier operating under the light load conditions. Each of the three-phase line currents, ia, ib, and ic, contains two pulses per half-cycle of the supply frequency. The rectifier operates in a discontinuous current mode since the dc current id falls to zero six times per cycle of the supply frequency. For the convenience of discussion, FIG. 2-5 shows the expanded voltage and current waveforms of the rectifier. During interval _1 _ _t < _2, the line-to-line voltage vab is higher than the dc voltage Vd, which turns D1 and D6 on. The dc cur rent id increases from zero, and energy is stored in Ls. At _2, vab is equal to Vd, the voltage across the line inductance Ls becomes zero, and id reaches its peak value i_p. When _t > _2, vab is lower than Vd, and Ls starts to release its stored energy to the load through D1 and D6. Both diodes remain on until _t = _3, at which id falls to zero and the energy stored in Ls is completely discharged. During interval _4 _ _t < _5, vac is higher than Vd, and D1 is turned on again together with D2. Obviously, each diode conducts twice per cycle of the supply frequency. The diode conduction angle is given by [...]
(eqn. 2-5) (eqn. 2-6) (eqn. 2-7) (eqn. 2-8) (eqn. 2-9) (eqn. 2-10) (eqn. 2-11) from which _3 can be calculated for a given VLL and Vd. It is interesting to note that the angles _1, _2, and _3 are a function of VLL and Vd only, irrelevant to the line inductance Ls. (2) Continuous Current Operation. As discussed earlier, the dc voltage Vd of the rectifier decreases with the increase in dc load current. The decrease in Vd makes _3 and _4 in FIG. 2-5 move toward each other. When _3 and _4 start to over lap, the dc current id becomes continuous. FIG. 2-6 shows the waveforms of the rectifier operating with a continuous dc current. During interval I, a positive i_a keeps D1 conducting while a negative ic keeps D2 on. The dc current is given by id = i_a = -ic. Interval II is the commutation period, during which the current flowing in D1 is commutated to D3. The commutation is initiated by a forward-biased voltage on D3, which turns it on. Due to the presence of the line inductance Ls, the commutation process cannot complete instantly. It takes a finite moment for current ib in D3 to build up and current i_a in D1 to fall. During this period, three diodes (D1, D2 and D3) conduct simultaneously, and the dc current id = i_a + ib = -ic. The commutation period ends at the end of interval II, at which i_a decreases to zero and D1 is turned off. During interval III, diodes D2 and D3 are on, and the dc current is id = ib = -ic. The diode conduction angle _c is 2_/3 + _, where _ is the commutation interval. Compared with discontinuous current operation, the rectifier operating under a continuous current mode draws a line current with less harmonic distortion. The details of the line current distortion are discussed in the following sections.
2.3 Definition of THD and PF Assume that the phase voltage va of the utility supply is sinusoidal va = _2 _Va sin _t (eqn. 2-12) The line current i_a drawn by a rectifier is generally periodical but nonsinusoidal. The line current can be expressed by a Fourier series (eqn. 2-13) where n is the harmonic order, Ian and _n are the rms value and angular frequency of the nth harmonic current, and _n is the phase displacement between Va and Ian, respectively. The rms value of the distorted line current i_a can be calculated by
where Ia1 is the rms value of the fundamental current. The per-phase average power delivered from the supply to the rectifier is….
(eqn. 2-17) where _1 is the phase displacement between Va and Ia1. The per-phase apparent power is given by
(eqn. 2-19) where DF is the distortion factor and DPF is the displacement power factor, given by:
For a given THD and DPF, the power factor can also be calculated by PF = (eqn. 2-21) 2.4 Per-Unit System It is convenient to use per-unit system for the analysis of power converter systems. Assume that the converter system under investigation is three-phase balanced with a rated apparent power SR and rated line-to-line voltage VLL. The base voltage, which is the rated phase voltage of the system, is given by
The base current and impedance are then defined as IB = and ZB = (eqn. 2-23) The base frequency is: _B = 2_f (eqn. 2-24) where f is the nominal frequency of the utility supply or the rated output frequency of an inverter. The base inductance and capacitance can be found from LB = and CB = (eqn. 2-25) Consider a three-phase diode rectifier rated at 4160 V, 60 Hz, and 2 MVA. The base current IB of the rectifier is 277.6 A and the base inductance LB is 22.9 mH. Assuming that the rectifier has a line inductance of 2.29 mH per phase and draws a line current of 138.8 A, the corresponding per unit value for the inductance and cur rent is 0.1 per unit (pu) and 0.5 p_u, respectively. 2.5 THD and PF of Six-Pulse Diode Rectifier Two typical waveforms of the line current drawn by the six-pulse diode rectifier are shown in FIG. 2-7. When the rectifier operates under the light load conditions with the fundamental line current Ia1 = 0.2 p_u, the line current waveform is somewhat spiky. The line current waveform contains two separate pulses per half-cycle of the supply frequency, which makes the dc current discontinuous. With the rectifier operating at the rated condition (Ia1 = 1.0 pu), the two current pulses are partially over lapped, which leads to a continuous dc current. The harmonic spectrum of the line current waveform is shown in FIG. 2-7c. The line current i_a does not contain any even-order harmonics since the current waveform is of half-wave symmetry, defined by f(_t) = -f(_t + _). It does not contain any triplen (zero sequence) harmonic currents either due to a balanced three-phase system. The dominant harmonics, such as the 5th and 7th, usually have a much higher magnitude than other harmonics. The line current THD is a function of the fundamental current Ia1, which is 75.7% at Ia1 = 0.2 p_u and 32.7% at Ia1 = 1.0 pu.
The THD and PF curves of the six-pulse diode rectifier are shown in FIG. 2-8, where the fundamental current Ia1 varies from 0.1 p_u to 1 p_u and the line inductance Ls changes from 0.05 p_u to 0.15 pu. With the increase of the line current, its THD decreases while the overall power factor (PF) of the rectifier increases. The increase in PF is mainly due to THD reduction, which improves the distortion power factor of the rectifier. For a given value of THD and PF, the displacement power factor DPF can be found from:
As mentioned earlier, the low-order dominant harmonics in the line current are of high magnitude. An effective approach to reducing the line current THD is, there fore, to remove these dominant harmonics from the system. This can be achieved by using multipulse rectifiers. 3. In this section, the configuration of 12-, 18-, and 24-pulse series-type rectifiers is introduced. The THD and PF performance of these rectifiers are investigated through simulation and experiments. 3.1 12-Pulse Series-Type Diode Rectifier (1) Rectifier Configuration. FIG. 3-1 shows the typical configuration of a 12-pulse series-type diode rectifier. There are two identical six-pulse diode rectifiers powered by a phase-shifting transformer with two secondary windings. The dc outputs of the six-pulse rectifiers are connected in series. To eliminate low-order harmonics in the line current iA, the line-to-line voltage vab of the wye-connected secondary winding is in phase with the primary voltage vAB while the delta-connected secondary winding voltage v_ã
The rms line-to-line voltage of each secondary winding is (eqn. 3-2) from which the turns ratio of the transformer can be determined by = 2 and = (eqn. 3-3) The inductance Ls represents the total line inductance between the utility supply and the transformer, and Llk is the total leakage inductance of the transformer referred to the secondary side. The dc filter capacitor Cd is assumed to be sufficiently large such that the dc voltage Vd is ripple-free. FIG. 3-1b shows the simplified diagram of the 12-pulse diode rectifier. The transformer winding is represented by sign "Y" or " " enclosed by a circle, where 'Y' denotes a three-phase wye-connected winding while _ represents a delta-connected winding. (2) Current Waveforms. FIG. 3-2 shows a set of simulated current wave forms of the rectifier operating under the rated conditions. The line inductance Ls is assumed to be zero, and the total leakage inductance Llk is 0.05 p_u, which is a typi cal value for a phase-shifting transformer. The dc current id is continuous, containing 12 pulses per cycle of the supply frequency. At any time instant (excluding commutation intervals), the dc current id flows through four diodes simultaneously, two in the top six-pulse rectifier and two in the bottom rectifier. The dc current ripple is relatively low due to the series connection of the two six-pulse rectifiers, where the leakage inductances of the secondary windings can be considered in series. The waveform of the line current i_a in the wye-connected secondary winding looks like a trapezoidal wave with four humps on the top. The waveform of i_ã in the delta-connected winding is identical to i_a except for a 30° phase displacement and is therefore not shown in the figure. The currents i_a and i_ã in FIG. 3-2b are the secondary line currents i_a and i_ã referred to the primary side. Since both primary and top secondary windings are connected in wye, the waveform of the referred current i_a is identical to that of i_a except that its magnitude is halved due to the turns ratio of the two windings. When i_ã is referred to the primary side, the referred current i_ã does not keep the same waveform as i_ã. The changes in waveform are caused by the phase displacement of the harmonic currents when they are referred from the delta-connected secondary winding to the wye-connected primary winding. It is the phase displacement that makes certain harmonics, such as the 5th and 7th, in i_ã out of phase with those in i_a. As a re sult, these harmonic currents are canceled in the transformer primary winding and do not appear in the primary line current, given by: i_a = ia + iã (eqn. 3-4)
FIG. 3-3 shows the harmonic spectrum of the rectifier currents in FIG. 3-2, where I_an, Iã_n, and I_An are the nth order harmonic currents (rms) in ia, iã, and iA, respectively. The harmonic content of the referred currents ia and iã is identical, although their waveforms are quite different. This is understandable since the harmonic content should not alter when a secondary current is referred to the primary side. The magnitude of the 5th and 7th harmonics is 18.6% and 12.4%, respectively, which are much higher than other harmonics. The THD of the primary line current i_a is only 8.38% in comparison to 24.1% of the secondary line current ia. The substantial reduction in THD is owing to the elimination of dominant harmonics by the phase-shifting transformer. The principle of harmonic cancellation by the phase shifting transformer will be discussed in Section 5.
FIG. 3-4 shows the waveforms measured from a 12-pulse diode rectifier operating under the rated conditions. The phase-shifting transformer has a total leak- age inductance of 0.045 p_u and a voltage ratio of: VAB/Vab = VAB/Vã ~ b = 2.05. The line inductance Ls between the utility supply and the transformer is negligible due to the high capacity of the supply and low power rating of the rectifier. The measured secondary currents, i_a and i_ã, are of a quasi-trapezoidal wave with a 30° phase displacement. The harmonic spectrum in FIG. 3-4b indicates that i_a and i_ã contain the 5th and 7th harmonics, but these harmonics are canceled by the transformer and do not appear in iA. It should be pointed out that the amplitudes of the fundamental component in i_a and i_a are not exactly the same. They would be identical if the voltage ratio of the transformer were equal to 2 instead of 2.05.
(3) THD and Power Factor. FIG. 3-5 shows the calculated line current THD and input power factor versus the fundamental line current IA1. The leakage inductance Llk is typically 0.05 p_u, while the line inductance Ls usually varies with the capacity and operating conditions of the power system. To investigate the effect of Ls, three typical values, Ls = 0, 0.05 p_u and 0.1 p_u, are selected. The THD of the line current i_a decreases with the increase of IA1 and Ls. Compared with the six pulse rectifier, the 12-pulse rectifier can achieve a substantial reduction in the line current THD. Its input power factor PF is also improved thanks to the lower line current THD and higher displacement power factor. Generally speaking, the THD of the line current in the 12-pulse rectifier does not meet the harmonic requirements set by IEEE Standard 519-1992. In practice, a line side filter is normally required to reduce line current THD.
3.2 18-Pulse Series-Type Diode Rectifier (1) Rectifier Configuration. The block diagram of an 18-pulse series-type diode rectifier is shown in FIG. 3-6. The rectifier has three units of identical six pulse diode rectifiers fed by a phase shifting transformer. The sign "Z" enclosed by a circle represents a three-phase zigzag-connected winding, which provides a required phase displacement between the primary and secondary line-to-line volt ages. The detailed analysis of the zigzag transformer is given in Section 5. The 18-pulse rectifier is able to eliminate four dominant harmonics (the 5th, 7th, 11th, and 13th). This can be achieved by employing a phase-shifting transformer with a 20° phase displacement between any two adjacent secondary windings. The typical values of are 20°, 0°, and -20° for the top, middle, and bottom secondary windings, respectively. Other arrangements for are possible, such as = 0°, 20°, and 40°. The turns ratio of the transformer for the 18-pulse rectifier is usually selected such that the line-to-line voltage of each secondary winding is one third that of the primary winding. (2) Waveforms. Assume that the 18-pulse diode rectifier in FIG. 3-6 operates under the rated conditions with Ls = 0 and Llk = 0.05 pu. A set of simulated wave forms for the rectifier are shown in FIG. 3-7, where i… _ are the primary current components referred from the secondary side of the transformer. The wave forms of these currents are all different due to the phase displacement of harmonic currents when they are transferred from the secondary to the primary winding. The waveforms of the secondary currents ia, i_ã, and i_a _ are not given in the figure, but they have the same shape as that of i_ã. The harmonic content of the primary and secondary line currents are given in FIG. 3-7c. The secondary line current has a THD of 23.7%, while the THD of the primary line current is only 3.06% due to the elimination of four dominant harmonics. The waveforms measured from an 18-pulse diode rectifier under the rated operating conditions are shown in FIG. 3-8. The phase-shifting transformer has a leak age inductance of 0.05 p_u and a voltage ratio of VAB/Vab = VAB/Vã ~ b = VAB/Va __ b = 2.95. The waveforms of the secondary line currents ia, i_ã, and ia _ has a 20° phase displacement between each other. The harmonic spectrum illustrates that the primary line current i_a does not contain the 5th, 7th, 11th, or 13th harmonics and therefore is nearly sinusoidal.
(3) Line Current THD and Input Power Factor. FIG. 3-9 shows the calculated primary line current THD and input power factor of the 18-pulse diode rectifier. Compared with the 12-pulse rectifier, the 18-pulse rectifier has lower line current THD and better power factor. For instance, when the 18-pulse operates under the rated load conditions (IA1 = 1 pu) with Ls = 0.05 p_u, the THD of i_a is reduced from 6.4% of the 12-pulse rectifier to 2.3% and the power factor is slightly increased as well. 3.3 24-Pulse Series-Type Diode Rectifier The configuration of a 24-pulse series-type diode rectifier is shown in FIG. 3-10, where a phase-shifting transformer is used to power four sets of six-pulse diode rectifiers. To eliminate six dominant current harmonics (the 5th, 7th, 11th, 13th, 17th, and 19th), the transformer should be arranged such that there is a 15° phase displacement between the voltages of any two adjacent secondary windings. The line to-line voltage of each secondary winding is usually one fourth that of the primary winding. FIG. 3-11 shows the current waveforms in the 24-pulse diode rectifier operating under rated conditions, where i_ a are the primary currents referred from the secondary side of the transformer. Each of these currents has a THD of 24%. The primary line current i_a is virtually a sinusoid with only 1.49% total harmonic distortion.
The calculated THD of the line current i_a and input power factor of the 24-pulse rectifier is shown in FIG. 3-12. It can be observed that the rectifier has an excellent THD profile, which meets the harmonic requirements specified by IEEE Standard 519-1992. 4. In the previous section, we have discussed series-type multipulse diode rectifiers, where the dc outputs of all the six-pulse diode rectifiers are connected in series. This section focuses on the separate-type multipulse rectifiers, where each of its six-pulse rectifiers feeds a separate dc load. 4.1 12-Pulse Separate-Type Diode Rectifier The block diagram of a 12-pulse separate-type diode rectifier is shown in FIG. 4-1. The rectifier configuration is essentially the same as that of the 12-pulse series-type rectifier except that two separate dc loads are employed instead of a single dc load. FIG. 4-2 illustrates an application example of the 12-pulse separate-type rectifier as a front end for a cascaded H-bridge multilevel inverter-fed drive. The phase-shifting transformer has six secondary windings, of which three are wye-connected with = 0 and the other three are delta-connected having a of 30°. Each of the secondary windings feeds a six-pulse diode rectifier. Since all wye-connected secondary windings are identical and so are the delta-connected windings, it is essentially a 12-pulse transformer. The six-pulse rectifiers provide isolated dc volt ages to H-bridge inverters, whose outputs are connected in cascade, providing a three-phase ac voltage to the motor.
FIG. 4-3 shows the current waveforms of the 12-pulse separate-type rectifier operating with a rated line current. The waveform of the secondary line current i_a is similar to that of the "stand-alone" six-pulse rectifier. This is due to the fact that with the line inductance Ls assumed to be zero, the 12-pulse rectifier is essentially composed of two units of stand-alone six-pulse rectifiers. The dc currents in the two rectifiers, i and i~ , contain a higher ripple component compared with that in the 12-pulse series-type rectifier where the dc load sees the leakage inductances of the two secondary windings in series. The currents ia and iã in FIG. 4-3b are the secondary line currents i_a and i_ã referred to the primary side. For the reasons discussed earlier, the 5th and 7th harmonic currents in ia and iã are out of phase and therefore are canceled in the primary winding of the transformer. It is interesting to note that although the waveforms of i_a and i_ã differ significant ly from those in the 12-pulse series-type rectifier, the primary line current i_a in both rectifiers has a similar waveform, and so does its THD. This is mainly due to the 12-pulse configuration, where the two most detrimental harmonics, the 5th and 7th, are eliminated. The remaining harmonics have less influence on the line current waveform and its THD. FIG. 4-4 shows the waveforms measured from a 12-pulse separate-type rectifier operating under the rated conditions. The phase shifting transformer has a leakage inductance of 0.045 p_u and a voltage ratio of VAB/Vab = VAB/Vã~ b = 2.05. The waveform of the secondary line currents, i_a and i_ã, has two humps per half-cycle while the primary current i_a is close to sinusoidal due to the elimination of the 5th and 7th harmonics as shown in FIG. 4-4b.
The THD of the line current i_a in the 12-pulse separate-type rectifier shown in FIG. 4-5 is somewhat lower than that of the series type. This is mainly due to the differences in harmonic distribution. The secondary line currents in the separate type rectifier contain higher 5th and 7th harmonics but lower 11th and 13th harmonics than those in the series type. When they are reflected to the primary side, the 5th and 7th harmonics are canceled, and thus the lower magnitude of the 11th and 13th harmonics makes a reduction in the line current THD. The power factor profile is also different from that of the 12-pulse series-type rectifier. A notch occurs approximately at IA1 = 0.22 p_u, which signifies a boundary be- tween continuous and discontinuous current operation of the rectifier. The discontinuous current operation normally does not occur in the series-type rectifiers since the dc load sees the leakage inductances of the secondary windings in series, making the dc current continuous over almost the full operation range. The power factor of the separate type is slightly lower than the series type. This is mainly due to the dc load connection, which affects the equivalent inductance seen by the utility supply. 4.2 18- and 24-Pulse Separate-Type Diode Rectifiers The configuration of the 18-pulse separate-type diode rectifier is shown in FIG. 4-6. It is essentially the same as that of the 18-pulse series-type diode rectifier except for the dc side connection. The waveforms of the 18-pulse separate-type rectifier are shown in FIG. 4-7. Due to the elimination of four dominant harmonics, the line current i_a is close to sinusoidal with THD of 3.05%. FIG. 4-8 shows the line current THD and input power factor of the 18- and 24-pulse separate-type rectifiers, respectively. In general, the THD profile of the separate-type rectifiers is somewhat better, and the power factor profile is slightly worse than their series-type counterparts.
5. This section provides a comprehensive analysis on the multipulse diode rectifiers widely used in high-power medium voltage drives as front-end converters. The main issues discussed in the section are summarized below. Systematic analysis on 12-, 18- and 24-pulse diode rectifiers. The line current THD and input power factor of the multipulse rectifiers are analyzed. The line current THD of the 12-pulse diode rectifiers normally do not satisfy the harmonic requirements specified by IEEE Standard 519-1992. The 18 pulse rectifiers have a better harmonic profile, while the 24-pulse rectifiers provide excellent harmonic performance. The input power factor of the multi pulse rectifiers is also analyzed. Rectifiers with more than 30 pulses are rarely used in practice mainly due to increased transformer costs and limited performance improvements. _ Comparison between series- and separate-type rectifiers. The multipulse rectifiers can be classified into series and separate types for use in various multilevel voltage source inverters. In general, the line current THD profile of the separate-type rectifiers is somewhat better, and the input power factor is slightly worse than their series-type counterparts. |

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