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1. INTRODUCTION
The multipulse diode rectifiers presented in the previous section are normally used in voltage source inverter (VSI)-fed drives, while the multipulse SCR rectifiers to be discussed in this section are mainly for current source inverter (CSI) based drives. The SCR rectifier provides an adjustable dc current for the CSI which converts the dc current to a three-phase PWM ac current with variable frequencies.
This section starts with an overview of six-pulse SCR rectifier, which is the building block for the multipulse SCR rectifiers, followed by an analysis on 12-, 18-, and 24-pulse rectifiers. The line current THD and input power factor of these rectifiers are investigated, and the results are summarized in a graphic format.
2. SIX-PULSE SCR RECTIFIER
Fig. 2-1 shows a simplified circuit diagram for the six-pulse SCR rectifier, where RC snubber circuits for the SCR devices are omitted. The line inductance Ls represents the total inductance between the utility supply and the rectifier, including the equivalent inductance of the supply, the total leakage inductance of isolation transformer if any, and the inductance of a three-phase line reactor that is often added to the system for the reduction of line current THD. On the dc side of the rectifier, a dc choke Ld is used to smooth the dc current. The choke is normally constructed with a single magnetic core and two coils, one coil in the positive dc bus and the other in the negative bus. Such an arrangement is preferable in medium-voltage drives since it helps to reduce the common-mode voltage imposed on the motor without increasing the manufacturing cost of the choke [1]. To simplify the analysis, it is assumed that the inductance of the dc choke Ld is sufficiently high such that the dc current Id is ripple-free. The dc choke and the load can then be replaced by an adjustable dc current source as shown in Fig. 2 1b.
2.1 Idealized Six-Pulse Rectifier
Let's consider an idealized six-pulse SCR rectifier, where the line inductance Ls in Fig. 2-1 is assumed to be zero. Fig. 2-2 shows typical waveforms of the rectifier, where va, vb, and v_c are the phase voltages of the utility supply, ig1 to ig6 are the gate signals for SCR switches S1 to S6, and _ is the firing angle of the SCRs, respectively.
During interval I (_/6 + __ _t < _/2 + _), va is higher than the other two phase voltages (vb and vc), making S1 forward-biased. When S1 is fired at _t = _/6 + _ by its gate signal ig1, it is turned on. The positive dc bus voltage vP with respect to ground G is equal to va. Assuming that S6 was conducting prior to the turn-on of S1, it continues to conduct until the end of interval I, during which the negative bus voltage vN is equal to vb. The dc output voltage can be found from vd = vP - vN = vab.
The dc current Id flows from va to vb through S1, the load, and S6. The three-phase line currents are i_a = Id, ib = -Id, and ic = 0 as shown in Fig. 2-2.
During interval II (_/2 + __ _t < 5_/6 + _), v_c is lower than the other two phase voltages (va and vb), making S2 forward-biased. At the moment the gate sig nal ig2 arrives, S2 is switched on. The conduction of S2 makes S6 reverse-biased, forcing it to turn off. The dc current Id is then commutated from S6 to S2, which leads to ib = 0 and ic = - Id. The commutation process in this case completes instant ly due to the absence of the line inductance. The dc output voltage is given by vd vP - vN = vac. Following the same procedure, all the current and voltage waveforms in other intervals can be obtained.
The average dc output voltage can be determined by:
(eqn. 2-1)
Fig. 2-1 Simplified circuit diagram of a six-pulse SCR rectifier.
…where vab = _2 _VLL sin(_t + _/6). The equation illustrates that the rectifier dc out put voltage Vd is positive when the firing angle _ is less than _/2 and becomes negative for an _ greater than _/2. However, the dc current Id is always positive, irrelevant to the polarity of the dc output voltage.
When the rectifier produces a positive dc voltage, the power is delivered from the supply to the load. With a negative dc voltage, the rectifier operates in an inverting mode, and the power is fed from the load back to the supply. This often takes place in a CSI drive during rapid speed deceleration where the kinetic energy of the rotor and its mechanical load is converted to the electrical energy by the inverter and then sent back to the power supply by the SCR rectifier for fast dynamic braking. The power flow in the SCR rectifier is, therefore, bidirectional, which also enables the CSI drive to operate in four quadrants, an important feature provided by the SCR rectifier.
The line current i_a in Fig. 2-2 can be expressed in a Fourier series as:
(eqn. 2-2)
where phi_1 is the phase angle between the supply voltage va and the fundamental-frequency line current ia1.
The rms value of i_a can be calculated by:
from which the total harmonic distortion for the line current i_a is:
(eqn. 2-4)
where Ia1 is the rms value of ia1.
To find the displacement power factor (DPF), we can refer to 1 and 2 in Fig. 2-2. Since 1 is fixed to _/6 and 2 is equal to _/6 + _, the displacement power factor angle is:
(eqn. 2-5)
Fig. 2-2 Waveforms of the idealized six-pulse SCR rectifier operating at _ = 30°.
The overall power factor for the six-pulse SCR rectifier can be obtained from PF = DPF × DF = = 0.955 cos _ (eqn. 2-6) where DF is the distortion factor defined in Section 3.
Fig. 2-3 Voltage waveforms of the idealized six-pulse SCR rectifier
operating at various firing angles.
Fig. 2-3 shows the voltage waveforms of the rectifier with various firing angles. The average dc output voltage Vd is positive at _ = 45°, falls to zero at _ cos _1 = 90°, and becomes negative when _ = 135°. It reaches its maximum negative value at _ = 180°. In a practical rectifier where the line inductance Ls is present, the firing angle _ should be less than 180° to prevent SCR commutation failure.
2.2 Effect of Line Inductance
With the presence of the line inductance Ls, the commutation of the SCR devices will not complete instantly. Consider a case where the dc output current Id is com mutated from S5 to S1 as shown in Fig. 2-4. Assuming that S5 and S6 are conducting prior to the turn-on of S1, the dc current flows through both devices. The com mutation process is initiated by turning S1 on at _. At the moment the incoming device S1 is gated on, its current i_a starts to rise from zero, but cannot jump to Id instantly due to the line inductance Ls. In the meantime, the current i_c in the outgoing device S5 starts to decrease since i_c = Id - ia. As a result, three SCR devices, S1, S5 and S6, conduct simultaneously. The commutation completes at the end of the com mutation interval , at which the current i_a in S1 reaches Id whereas the current i_c in S5 falls to zero.
Fig. 2-4 Voltage and current waveforms during commutation (_ = 45°).
The commutation causes a reduction in the average dc voltage Vd. Since both S1 and S5 conduct simultaneously during the interval, the positive bus voltage vP with respect to ground G can be expressed as
(eqn. 2-7)
(eqn. 2-8)
(eqn. 2-9)
(eqn. 2-10)
The waveform of vP during the interval is also shown in Fig. 2-4. The shaded area A , representing the amount of voltage reduction caused by the commutation, can be found from
(eqn. 2-11)
(eqn. 2-12)
(eqn. 2-13)
(eqn. 2-14)
Taking the effect of the line inductance Ls into account, the average dc output volt age of the six-pulse SCR rectifier is
(eqn. 2-15)
(eqn. 2-16)
Fig. 2-5 Commutation angle versus firing angle alpha.
Fig. 2-5 shows the relationship between the commutation angle and the firing angle _. For a given _, the lower the value for Ls and Id, the smaller the commutation angle is. The input power factor is affected by the line inductance Ls as well.
Assuming that i_a and ic shown in Fig. 2-4 varies linearly over time during the commutation interval, 1 is equal to _/6. The displacement power factor angle _1 can be calculated by:
(eqn. 2-17)
(eqn. 2-18)
(eqn. 2-19)
Fig. 2-6 Line current waveforms in the six-pulse SCR rectifier with
Ls = 0.05 p_u.
2.3 Power Factor and THD
Fig. 2-6 shows the simulated waveforms for the line current i_a when the rectifier operates with the rated line current (Ia1 = 1 p_u). The line inductance Ls is assumed to be 0.05 p_u, and the firing angle _ is 0° in Fig. 2-6a and 30° in Fig. 2-6b, respectively. It is interesting to note that waveform of i_a during the interval varies with _. It rises nonlinearly when _ = 0° and looks somewhat like linear for _ = 30°. This is because the line current i_a is a function of _ during com mutation, given by i_a = (cos _ - cos(_t + _)),0 _ _t _
(eqn. 2-20)
Fig. 2-6c shows the line current harmonic content for the six-pulse SCR rectifier. Its THD is more than 20%, which is not acceptable in practice, especially when the rectifier is for high-power applications.
Fig. 2-7 shows the line current THD versus Ia1 with Ls and _ as parameters.
The THD reduces with the increase of Ia1 and Ls as shown in Fig. 2-7a. It also de creases with the firing angle _ as illustrated in Fig. 2-7b.
Fig. 2-8 shows the input power factor profile of the six-pulse SCR rectifier as a function of Ia1 and _. The power factor varies slightly with the line current Ia1.
Fig. 2-7 Line current THD of the six-pulse SCR rectifier.
However, it reduces substantially with large values of _. This is, in fact, the main drawback of the SCR rectifier.
Fig. 2-8 Power factor of the six-pulse SCR rectifier.
Fig. 3-1 Block diagram of a 12-pulse SCR rectifier.
3. 12-PULSE SCR RECTIFIER
The block diagram of a 12-pulse SCR rectifier is shown in Fig. 3-1. It is com posed of a phase-shifting transformer and two identical six-pulse SCR rectifiers.
The transformer has two secondary windings, one connected in wye and the other in delta. The line-to-line voltage of the secondary windings is normally half of its primary line-to-line voltage. The dc outputs of the two SCR rectifiers are connected in series for a single dc load. The dc choke Ld is assumed to be sufficiently large and the resultant dc current Id is ripple-free.
As shown in Fig. 3-2, the 12-pulse SCR rectifier can be used as a front end for a CSI-fed drive. The inverter converts the dc current Id to a three-phase PWM cur rent iw. The magnitude of i_w is proportional to Id, and thus it can be adjusted by the rectifier through firing angle control. The details of the CSI drive will be discussed in the later sections.
Fig. 3-2 A CSI-fed drive using the 12-pulse SCR rectifier as a front
end.
Fig. 3-3 Current waveforms of the 12-pulse SCR rectifier (Ls = Llk = 0).
3.1 Idealized 12-Pulse Rectifier
Consider an idealized 12-pulse rectifier where the line inductance Ls and the total leakage inductance Llk of the transformer are assumed to be zero. The current wave forms in the rectifier are shown in Fig. 3-3, where i and i are the secondary line currents, i_a and iã are the primary currents referred from the secondary side, and i_a is the primary line current given by i_a = ia + iã, respectively.
The secondary line current i_a can be expressed as
(eqn. 3-1)
where _ = 2_f1 is the angular frequency of the supply voltage. Since the waveform of i_a is of half-wave symmetry, it does not contain any even-order harmonics. In addition, i_a does not contain any triplen harmonics either due to the balanced three phase system.
The other secondary current i leads i by 30°, and its Fourier expression is
(eqn. 3-2)
The waveform for the referred current ia in Fig. 3-3 is identical to i_a except that its magnitude is halved due to the turns ratio of the Y/Y-connected windings. The cur rent ia can be expressed in Fourier series as
(eqn. 3-3)
When the current i_ã is referred to the primary side, the phase angles of some harmonic currents are altered due to the Y/ -connected windings. As a result, the referred current iã does not keep the same wave shape as i_ã. The Fourier expression for iã is
(eqn. 3-4)
(eqn. 3-5)
where the two dominant current harmonics, the 5th and 7th , are canceled in addition to the 17th and 19th.
The THD of the secondary and primary line currents i_a and i_a can be determined by ....
The THD of the primary line current i_a in the idealized 12-pulse rectifier is reduced approximately by 50% compared with that of the secondary line current i_a.
Fig. 3-4 Typical current waveforms and harmonic contents of the
12-pulse SCR rectifier with Ls = 0 and Llk = 0.05 pu.
3.2 Effect of Line and Leakage Inductances
Fig. 3-4 shows typical current waveforms for the 12-pulse rectifier taking into account the transformer leakage inductance Llk. The rectifier operates under the condition of _ = 0°, IA1 = 1 p_u, Ls = 0 and Llk = 0.05 pu. The waveform for the secondary line current i_a is close to a trapezoid and contains the 5th and 7th harmonics with a magnitude of 18.8% and 12.7%, respectively. However, these two harmonics are canceled by the phase-shifting transformer, and thus they do not appear in the primary line current iA. Due to the effect of the leakage inductance, the THD of i_a is reduced from 15.3% in the idealized rectifier to 8.61%.
Fig. 3-5 Primary line current THD and input PF of the 12-pulse SCR
rectifier.
3.3 THD and PF
The THD of the primary line current i_a as a function of IA1 and Ls is illustrated in Fig. 3-5a. Compared with the six-pulse SCR rectifier, the 12-pulse rectifier has a much better THD profile. However, it generally does not meet the harmonic guide lines set by IEEE Standard 519-1992. The input power factor of the rectifier varies greatly with the firing angle as shown in Fig. 3-5b.
4. 18- AND 24-PULSE SCR RECTIFIERS
The block diagram of an 18-pulse SCR rectifier is depicted in Fig. 4-1. Similar to the 18-pulse diode rectifiers, the rectifier employs a phase-shifting transformer with three secondary windings feeding three identical six-pulse SCR rectifiers. The con figuration of the 24-pulse SCR rectifier can be easily derived and thus is not shown.
Fig. 4-2 shows the typical current waveforms of the 18-pulse SCR rectifier operating under the condition of _ = 0°, IA1 = 1 p_u, Ls = 0, and Llk = 0.05 p_u, where ia, iã and ia_ are the primary currents referred from the transformer secondary side. All these currents have the same THD of 24.6%, although their waveforms are all different. The primary line current i_a does not contain the 5th, 7th, 11th, or 13th harmonics, resulting in a nearly sinusoidal waveform with a THD of only 3.54%.
Fig. 4-3 shows the primary line current THD for the 18- and 24-pulse SCR rectifiers versus IA1 with the line inductance Ls as a parameter. As expected, the 18 pulse rectifier has better line current THD profile than the 12-pulse SCR rectifier while the 24-pulse rectifier is superior to the 18-pulse rectifier. The input power factor of the 18- and 24-pulse rectifiers is similar to that of the 12-pulse and there fore is not presented.
Fig. 4-1 Block diagram of an 18-pulse SCR rectifier.
Fig. 4-2 Current waveforms and harmonic contents of the 18-pulse
SCR rectifier with Ls = 0 and Llk = 0.05 p_u.
5. SUMMARY
In this section, the operation of the six-pulse SCR rectifier is introduced and its performance is analyzed. The six-pulse rectifier is the building block for the multipulse SCR rectifiers, and therefore it is discussed in detail. The line current THD of the 12-pulse SCR rectifier normally does not satisfy the harmonic guidelines set by IEEE Standard 519-1992. The 18-pulse SCR rectifier has a better line current harmonic profile, while the 24-pulse rectifier provides a superior harmonic performance. The input power factor of the SCR rectifiers varies with the firing angle, which is the major disadvantage of the rectifiers.
The multipulse SCR rectifiers are naturally suited for use in medium-voltage CSI-fed drives. Over the last decade, the 18-pulse SCR rectifier has been a preferred choice for the CSI drive as a front end due to its good performance to price ratio. However, the SCR rectifier starts to be replaced by PWM GCT current source rectifiers for higher input power factor and better dynamic performance.
Fig. 4-3 THD of the primary line current i_a in the 18- and 24-pulse
SCR rectifiers.