v o v an i L v bn V d Load L v cn D 1 D 3 D 5 i a i b i c D 4 D 6 D 2 Lecture 7 - Uncontrolled Rectifier Circuits III
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1 Lecture 7 - Uncontrolled Rectifier Circuits III Three-phase bridge rectifier (p = 6) v o n v an v bn v cn i a i b i c D 1 D 3 D 5 D 4 D 6 D d i L R Load L Figure 7.1 Three-phase diode bridge rectifier Diode 1, 3 and 5, whichever has a more positive voltage at its anode, conducts. Similarly, diode, 4 and 6, whichever has a more negative voltage at its cathode, returns the load current. With the numbering of diodes as indicated above, the conduction patterns is for a positive voltage sequence a-b-c. For the negative voltage sequence a-c-b, the pattern is When any of the diodes connected with the top (+ve) rail conducts, the potential of the rail is the corresponding AC line voltage. When any of the diodes connected with the bottom (-ve) rail conducts, the potential of the rail is the corresponding AC line voltage. The voltage across the load is the difference between the +ve and the -ve rail potentials. Lecture 7 Uncontrolled 7-1 F. Rahman
2 Assuming that the load current is continuous (i.e., non zero) at all times, each diode conducts for 10 in each half cycle of the ac waveform, followed by 40 of non conduction. The supply current is bipolar, conducting for 10 in each half cycle, followed by 60 of non conduction. Clearly, there is no dc component in the supply current to the rectifier. The output voltage waveform contains harmonics of order 6, 1, 18, 4 and so on. Assuming ripple-free, smooth load current, the input current harmonics are of orders 5, 7, 11, 13, 17, 19, 3, 5, 9, 31 and so on. Form the symmetry of the output voltage waveform, π 1 6 3max l l d = π maxl l ω ω = π π 6 cos td( t) (7.1) 6 where max l l is the peak value of the line-line voltage. Lecture 7 Uncontrolled 7- F. Rahman
3 v an v bn v cn v o -π/6 π/6 0 Figure 7. Lecture 7 Uncontrolled 7-3 F. Rahman
4 Figure 7. contd. Lecture 7 Uncontrolled 7-4 F. Rahman
5 Bridge rectifiers with 1 higher pulse numbers 6-pulse, three-phase bridge rectifier circuits can be connected in series or parallel to obtain rectifier circuits with 1, 4 or higher pulse numbers. The input voltages to each of these 6-pulse rectifier groups must be displaced by π/6n degrees, where n is the number of 6-pulse rectifiers used to obtain a rectifier of pulse number 6n. The figures below show typical connections for a 1-pulse rectifier. The series connection is preferred for high-voltage applications, while the parallel connection using an interphase reactor is preferable for lower voltage, high current applications. 3-phase AC Supply I d / I d / I d d Load Figure 7.3 Twelve-pulse rectifier: parallel connection Lecture 7 Uncontrolled 7-5 F. Rahman
6 + d / _ I d 3-phase AC Supply + d / d Load Figure 7.4. Twelve-pulse rectifier: series connection v o v an sec i R1 i R i R Waveforms of a 1-pulse diode bridge rectifier Lecture 7 Uncontrolled 7-6 F. Rahman
7 Input displacement factor of a diode rectifier v L i L v o i p i s v D 1 D 3 C d Load N:1 D D 4 Figure 7.5. Diode rectifier with LC output filter The filter capacitor at the output, in conjunction with the AC source inductance or filter inductance if any, makes the input current waveform i s as indicated in the figure below. v s v L i L i s i 1 φ π sec π 3π rad Figure 7.6. Waveforms in the circuit of figure 7.5. Lecture 7 Uncontrolled 7-7 F. Rahman
8 The source current waveform can be rather peaky if the inductance L is small and the filter capacitor C is large. In many applications, a resistor replaces the filter inductance. It limits the large peak of the input current, while at the same time damping the resonant inrush current when the AC input is first switched on. This resistance is normally shorted by a mechanical relay once the capacitor charges up to a reasonable voltage. Note that the fundamental of the input current now lags the AC input voltage by angle φ. The input displacement factor is thus cosφ. The input power factor of the rectifier is given by PF input power I s 1cosφ I1 = = = cosφ input A I I (7.) s s s = Input Distortion Factor Input Displacement Factor where the input displacement angle φ is as indicated in figure 7.6. Rectifier Output Filter The rectifier output DC voltage is usually filtered to remove some of the ripples, before supplying it to load circuits. L-, RC- and LC filters are usually considered. Inductive filters are normally considered for inductive loads such as, electromagnet coil, motor field supplies and so on. Reduction of audible noise, machine torque and Lecture 7 Uncontrolled 7-8 F. Rahman
9 voltage ripple by reducing the ripples in the load currents are normally concerns behind reducing ripples in load voltage and current. Capacitive filters are normally required to limit fluctuations in the DC voltage during the period of capacitor discharge to some predefined limit, (e.g., to 5% of the nominal value. This factor can be used to determine the required value of the filter capacitance). The resistor may not be used at all in very low power circuits. An LC filter allows both load voltage and current ripples to be reduced. Consider the LC filter circuit shown below where the rectifier is represented by a harmonic voltage source n(nω), where n is the harmonic order of the rectifier output voltage at the filter terminals. L f n (nω) ~ X L = jnωl f 1 jnωc f C f R L Figure 7.7. Harmonic representation of rectifier with LC filter Lecture 7 Uncontrolled 7-9 F. Rahman
10 For good filtering, the impedance of the load to the n-th harmonic voltage should be large in comparison to the impedance offered by the filter capacitor to this harmonic. { R (nω L) } Thus, + >> 1 nωc f (7.3) { R (nω L) } + = 10 nωc f (7.4) Using voltage divider rule, the RMS value of the n-th harmonic voltage across the load is on = nω L f ωc f n 1 (7.5) 1 n ( nωcf ) = 1 (n ω ) L C f f 1 n (7.6) Cf can be found from 7.4. If the total ripple in the output (ac) is specified, having found Cf form 7.4, Lf can be found. The total harmonic ripple voltage across the load is ac = ( ) on (7.7) n=,4,6,... Lecture 7 Uncontrolled 7-10 F. Rahman
11 Example: Output filter design for a single-phase rectifier The above computation can be simplified by specifying the performance of the filter to certain dominant (low order) harmonics of the rectifier. Consider the single-phase bridge rectifier in which the dominant output harmonic is of order. For this case dc = 4 max 3π (7.8) max = π (7.9) 1 = ( ω ) L C 1 (7.10) o f f 10 + = From (7.4), { R ( ωl) } ω (7.11) C f C f = 10 Thus 4πf { R + ( ωl) } (7.1) Neglecting all higher order terms except the dominant ( nd order) ripple, 4 RF (7.13) max ac = o = = dc 3π ( ω) LfCf 1 If the ripple factor RF is specified, and C f has already been found from (7.11), L f can be then be found from (7.13). Lecture 7 Uncontrolled 7-11 F. Rahman
12 Rectifier load regulation characteristic The filter inductance introduces a voltage regulation characteristic to the rectifier as shown in figure 7.8. When the load is an open circuit, i.e. with no load, the rectifier output voltage, or the capacitor voltage, is at the peak of the AC supply voltage to the rectifier. The inductor current is then zero at all times. As load current is drawn, the capacitor discharges into the load and the inductor current starts to increase. After the load current exceeds a certain value, the inductor current will become continuous. Thereafter, the mean capacitor voltage will not drop with load current. Before the onset of continuous conduction, the mean capacitor voltage drops significantly with load. The drop in the mean capacitor voltage with load DC current can be found as described below. Let us assume that Cf is sufficiently large so that the output voltage is ripple-free. We also assume that the diode currents fall to zero before the anode voltages become positive. In other words, discontinuous conduction is assumed. The angle at which conduction begins is then θ b 1 d = sin (7.14) max The voltage across the filter inductance is then di = ω = (7.15) vl max sin t d Lf dt Lecture 7 Uncontrolled 7-1 F. Rahman
13 ωt 1 i = [ max sinωt d ] d( ωt) L ω (7.16) f θb At ωt = β, i = 0, which allows us to find β. Once β is found, we can determine the mean inductor current, Id, for the d chosen. These then define two points on the d I d characteristic. By repeating the above procedure for a number of load DC voltages, d, the complete regulation characteristic of a rectifier-filter circuit can be found. The above analysis is approximate in assuming that the capacitor voltage remains constant. It also assumes no source inductance, which causes additional output voltage drop. Note that at light load, d is close to the peak of the input AC voltage and the filter inductor current is discontinuous. Note also that with discontinuous inductor current, d falls more with increase with load current (poor voltage regulation). When the inductor current becomes continuous, d does not fall with load current (ideal rectifier behaviour). Lecture 7 Uncontrolled 7-13 F. Rahman
14 i L L f I d v o C f d v o d I d i L t l-l d 1.35 l-l Discontinuous conduction Continuous conduction Figure 7.8 Rectifier voltage regulation with LC filter I d Lecture 7 Uncontrolled 7-14 F. Rahman
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