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AMAZON multi-meters discounts AMAZON oscilloscope discounts These devices convert a single or a three-phase AC power supply to a smooth DC voltage and current. Simple bi-stable devices, such as the diode and thyristor, can effectively be used for this purpose. Assumptions While analyzing power electronic circuits, it’s assumed that bi-stable semiconductor devices, such as diodes and thyristors, are the ideal switches, with no losses and minimal forward voltage drop. It will also be assumed that the reactors, capacitors, resistors, and other components of the circuits have ideal linear characteristics with no losses. Once the operation of a circuit is understood, the imperfections associated with the practical components can be introduced to modify the performance of the power electronic circuit. In power electronics, the operation of any converter is dependent on the switches being turned ON and OFF in a sequence. The current passes through a switch when it’s ON and is blocked when it’s OFF. Commutation is the transfer of current from one switch turning OFF, to another turning ON. In a diode rectifier circuit, a diode turns ON and then starts to conduct current when there is a forward voltage across it, i.e., the forward voltage across it becomes positive. This process usually results in the forward voltage across another diode becoming negative, which then turns off and stops conducting current. In a thyristor rectifier circuit, the switches additionally need a gate signal to turn them on and off. The factors affecting the commutation are illustrated in the idealized diode circuit, which shows two circuit branches, each with its own variable DC voltage source and circuit inductance. Assume, initially, that a current I is flowing through the circuit and that the magnitude of the voltage V1 is larger than V2. Since V1 > V2, diode D1 has a positive forward voltage across it and it conducts a current I1 through its circuit inductance L1. Diode D2 has a negative forward voltage that blocks and carries no current. Consequently, at time t1 ... ++++6 ---- Simple circuit to illustrate commutation from diode D1 to D2 Suppose the voltage V2 is increased to a value larger than V1, the forward voltage across diode D2 becomes positive, and it starts to turn on. However, the circuit inductance L1 prevents the current I1 from changing instantaneously and diode D1 won’t immediately turn off. Therefore, both the diodes D1 and D2 remain ON for an overlap period called the commutation time c . When both the diodes are turned on, a closed circuit is established which involves both branches. The effective circuit voltage c21 V= (V V), - called the commutation voltage, drives a circulating current c I , called the commutation current, through the two branches which have a total circuit inductance of c12 L= (L+L). In this idealized circuit, the voltage drop across the diodes and the circuit resistance has been ignored. From the basic electrical theory of inductive circuits, the current c I increases with time at a rate dependant on the circuit inductance. The magnitude of the commutation current may be calculated from the following equations: [...] It’s clear from the equation that the commutation time t_c depends on the overall circuit inductance (L1 + L2) and the commutation voltage. From this we can conclude the following: • A large circuit inductance will result in a long commutation time. • A large commutation voltage will result in a short commutation time. In practice, a number of deviations from this idealized situation occur. The diodes are not ideal and don’t turn off immediately when the forward voltage becomes negative. When a conducting diode is presented with a reverse voltage, some reverse current can still flow for a few microseconds. The current I1 continues to decrease beyond zero to a negative value before returning to zero. This is due to the free charges that must be removed from the PN junction before blocking is achieved. ++++7 The currents in each branch during commutation. Even if the commutation time is very short, the commutation voltage of an AC-fed rectifier bridge does not remain constant but changes slightly during the commutation period. An increasing commutation voltage will tend to reduce the commutation time. Three-phase commutation with six-diode bridge In practical power electronic converter circuits, the commutation follows the same basic sequence outlined above. ++++8 shows a typical six-pulse rectifier bridge circuit to convert three-phase AC currents IA, IB, and IC, to a DC current ID. ++++8 Three-phase commutation with a six-pulse diode bridge. This type of circuit is relatively simple to analyze because only two of the six diodes conduct current at any one time. The idealized commutation circuit can easily be identified. In this example, the commutation is assumed to be taking place from diode D1 to D3 in the positive group, while D2 conducts in the negative group. In power electronic bridge circuits, it’s conventional to number the diodes D1 to D6 in the sequence in which they are turned ON and OFF. When VA is the highest voltage and VC the lowest, D1 and D2 are conducting. Similar to the idealized circuit, when VB rises to exceed VA, D3 turns on and commutation transfers the current from diode D1 to D3. As before, the commutation time is dependent on the circuit inductance (L) and the commutation voltage (VB - VA). As can be seen from the six-pulse diode rectifier bridge, the commutation is usually initiated by external changes. In this case, the three-phase supply line voltages control the commutation. In other applications, the commutation can also be initiated or controlled by other factors, depending on the type of converter and the application. Therefore, converters are often classified in accordance with the source of the external changes that initiate commutation. In the above example, the converter is said to be line-commutated because the source of the commutation voltage is on the mains supply line. A converter is said to be self commutated if the source of the commutation voltage comes from within the converter itself. Gate-commutated converters are typical examples of this. ++++9 Line-commutated diode rectifier bridge. Line-commutated diode rectifier bridge One of the most common circuits used in power electronics is the three-phase line- commutated six-pulse rectifier bridge, which comprises of six diodes in a bridge connection. Single-phase bridges won’t be covered here because their operation can be deduced as a simplification of the three-phase bridge. Assumptions:
These assumptions are made to gain an understanding of the circuits and to make estimates of currents, voltages, commutation times, etc. In addition, the limiting conditions that affect the performance of the practical converters and their deviation from the ideal conditions will be examined to bridge the gap from the ideal, to the practical. In the diode bridge, the diodes are not controlled from an external control circuit. Instead, the commutation is initiated externally by the changes that take place in the supply line voltages, hence the name line-commutated rectifier. According to convention, the diodes are labeled D1 to D6 in the sequence in which they are turned ON and OFF. This sequence follows the sequence of the supply line voltages. The three-phase supply voltages comprise three sinusoidal voltage waveforms, 120° apart, which rise to their maximum value in the sequence A-B-C. According to convention, the phase-to-neutral voltages are labeled VA, VB, and VC and the phase-to phase voltages are VAB, VBC and VCA, etc. These voltages are usually shown graphically as a vector diagram, which rotates counter-clockwise at a frequency of 50 times per second. A vector diagram of these voltages and their relative positions and magnitudes. The sinusoidal voltage waveforms, of the supply voltage, may be derived from the rotation of the vector diagram. ++++10 Vector diagram of the three-phase mains supply voltages The output of the converter is the rectified DC voltage VD, which drives a DC current ID through a load on the DC side of the rectifier. In the idealized circuit, it’s assumed that the DC current ID is constant and completely smooth and without ripple. The bridge comprises of two commutation groups, one connected to the positive leg, consisting of diodes D1-D3-D5, and one connected to the negative leg, consisting of the diodes D4-D6- D2. The commutation transfers the current from one diode to another in sequence and each diode conducts the current for 120º of each cycle. In the upper group, the positive DC terminal follows the highest voltage in the sequence VA-VB-VC via diodes D1-D3-D5. When VA is near its positive peak, the diode D1 conducts and the voltage of the positive DC terminal follows VA. The DC current flows through the load and returns via one of the lower group diodes. With the passage of time, VA reaches its sinusoidal peak and starts to decline. At the same time, VB rises and eventually reaches a point, when it becomes equal to and starts to exceed VA. At this point, the forward voltage across diode D3 becomes positive and it starts to turn on. The commutating voltage in this circuit, VB-VA starts to drive an increasing commutation current though the circuit inductances and the current through D3 start to increase, as the current in D1 decreases. In a sequence of events similar to that described above, the commutation takes place and the current is transferred from diode D1 to diode D3. At the end of the commutation period, the diode D1 is blocked and the positive DC terminal follows VB until the next commutation takes place, to transfer the current to diode D5. After the diode D5, the commutation transfers the current back to D1 and the cycle is repeated. In the lower group, a similar sequence of events takes place, but here the negative voltages and the current flow from the load back to the mains. Initially, D2 is assumed to be conducting when VC is more negative than VA. As time progresses, VA becomes equal to VC and then becomes more negative. The commutation takes place and the current is transferred from diode D2 to D4. Diode D2 turns off and D4 turns on. The current is later transferred to diode D6, then back to D2 and the cycle is repeated. The conducting periods of the diodes in the upper and lower groups are shown over several cycles of the three-phase supply. This shows that only two diodes conduct current at any time (except during the commutation period, which is assumed to be infinitely short) and that each of the six diodes conduct for only one portion of the cycle in a regular sequence. The commutation takes place alternatively in the top group and the lower group. The DC output voltage VD is not a smooth voltage and consists of portions of the phase to-phase voltage waveforms. For every cycle of the 50 Hz AC Waveform (20 ms), the DC voltage VD comprises portions of six voltage pulses, VAB, VAC, VBC, VBA, VCA, VCB, etc., hence the name, six-pulse rectifier bridge. The average magnitude of the DC voltage may be calculated from the voltage waveform. The average value is obtained by integrating the voltage over one of the repeating 120º portions of the DC voltage curve. This integration yields an average magnitude of the voltage VD as follows: D RMS D = 1.35 × (RMS phase; Phase voltage) = 1.35 × V V V ++++11 Voltage and current waveforms during commutation ---Phase voltage Output voltage. For example, if VRMS = 415 V, then VD = 560 V DC. When there is a sufficient inductance in the DC circuit, then DC current ID will be steady and the AC supply current will comprise of segments of DC current from each diode in sequence. As an example, the current in the A-phase. The non-sinusoidal current that flows in each phase of the supply mains can affect the performance of any other AC equipment connected. In practice, to ensure that the diode reverse blocking voltage capability is properly specified, it’s necessary to know the magnitude of the reverse blocking voltage that appears across each of the diodes to the supply line that is designed to operate with sinusoidal waveforms. Theoretically, the maximum reverse voltage across a diode is equal to the peak of the phase-phase voltage. For example, the reverse voltage VCA and VCB appear across diode D5 during the blocking period. In practice, a safety factor of 2.5 is commonly used for specifying the reverse-blocking capability of diodes and other power electronic switches. On a rectifier bridge fed from a 415 V power supply, the reverse blocking voltage V_rb of the diode must be higher than 2.5 × 440 V = 1100 V. Therefore, it’s common practice to use diodes with a reverse-blocking voltage of 1200 V. The line-commutated thyristor rectifier bridge The output DC voltage and the operational sequence of the diode rectifier, is dependent on the continuous changes in the supply line voltages and is not dependent on any control circuit. Therefore, it’s called an uncontrolled diode rectifier bridge because the DC voltage output is uncontrolled and is fixed at 1.35 × VRMS. If the diodes are replaced with thyristors, it then becomes possible to control the point at which the thyristors are triggered and therefore, the magnitude of the DC output voltage can be controlled. This type of a converter is called a controlled thyristor rectifier bridge. This requires an additional control circuit, to trigger the thyristor, at the right instant. A typical six-pulse thyristor converter. Based on the previous section, the conditions required for a thyristor to conduct current in a power electronic circuit are given below:
If each thyristor were triggered at the instant when the forward voltage across it tends to become positive, then the thyristor rectifier operates in the same way as the diode rectifier described above. All voltage and current waveforms of the diode bridge apply to the thyristor bridge. ++++12 Six-pulse controlled thyristor rectifier bridge. A thyristor bridge operating in this mode is said to be operating with a zero delay angle and gives a voltage output of: DRMS 1.35 V = V × The output of the rectifier bridge can be controlled, by delaying the instant at which the thyristor receives a triggering pulse. This delay is usually measured in degrees, from the point at which the switch CAN turn on, due to the forward voltage becoming positive. The angle of delay is called the delay angle, or sometimes the firing angle, and is designated by the symbol a. The reference point, for the angle of delay, is the point where a phase voltage wave crosses the voltage of the previous phase and becomes positive, relative to it. A diode rectifier can be thought of as a converter with a delay angle of a = 0º. The main purpose of controlling a converter is to control the magnitude of the DC output voltage. In general, the larger the delay angle, the lower the average magnitude of the DC voltage. Under the steady state operation, of a controlled thyristor converter, the delay angle for each switch is the same. ++++ the voltage waveforms, where the triggering of the switches has been delayed by an angle of a degrees. Operation: In the positive switch group, the positive DC terminal follows the voltage associated with the switch, which is in conduction in the sequence VA-VB-VC. Assume initially, that thyristor S1 associated with voltage VA is conducting and S3 is not yet triggered. The voltage on the positive bus on the DC side follows the declining voltage VA because, in the absence of an S3 conduction, there is still a forward voltage across S1 and it will continue to conduct. When an S3 is triggered after a delay angle = a, the voltage on the positive bus jumps to VB, whose value it then starts to follow. At this instant, with both S1 and S3 conducting, a negative commutation voltage equal to VB-VA appears across the switch S1 for the commutation period, which then starts to turn off. With the passage of time, VB reaches its sinusoidal peak and starts to decline, followed by the positive DC terminal. Simultaneously, VC rises and when S5 is triggered, the same sequence of events is repeated and the current is commutated to S5. ++++13 Voltage waveforms of a controlled rectifier. As with the diode rectifier, the average magnitude of the DC voltage VD can be calculated, by integrating the voltage waveform over a 120º period, representing a repeating portion of the DC voltage. At a delay angle a, the DC voltage is given by the following equation: This formula shows that the theoretical DC voltage output of the thyristor rectifier with a firing angle a = 0 is the same as that for a diode rectifier. It also shows that the average value of the DC voltage will decrease as the delay angle is increased and is dependant on the cosine of the delay angle. When a = 90º, then cos a = 0 and VD = 0, which means that the average value of the DC voltage is zero. The instantaneous value of the DC voltage is a saw-tooth voltage. If the delay angle is further increased, the average value of the DC voltage becomes negative. In this mode of operation, the converter operates as an inverter. It’s interesting to note that the direction of the DC current remains unchanged because the current can only flow through the switches in one direction. However, with a negative DC voltage, the direction of the power flow is reversed, and the power flows from the DC side to the AC side. A steady state operation, in this mode, is only possible, if there is a voltage source on the DC side. The instantaneous value of the DC voltage for a > 90º. In practice, the commutation is not instantaneous and lasts for a period dependant on the circuit inductance and the magnitude of the commutation voltage. As in the idealized case, it’s possible to estimate the commutation time, from the commutation circuit inductance and an estimate of the average commutation voltage. ++++14 DC output voltage for delay angle a = 90º ++++15 DC voltage when the delay angle a > 90º As in the diode rectifier, the steady DC current ID comprises segments of current from each of the three phases on the AC side. On the AC side, the current in each phase comprises of non-sinusoidal blocks, similar to those associated with the diode rectifier and with similar harmonic consequences. In the case of the diode bridge, with a delay angle of a = 0, the angle between the phase current and the corresponding phase voltage on the AC side is approximately zero. Consequently, the power factor is unity and the converter behaves like a resistive load. For the controlled rectifier, with a delay angle of a, the angle between the phase current and the corresponding phase voltage is also a, and called the power factor angle. This angle should be called the displacement factor because it does not really represent the power factor. Consequently, when the delay angle of the thyristor rectifier is changed to reduce the DC voltage, the angle between the phase current and voltage also changes by the same amount. The converter then behaves like a resistive-inductive load with a displacement factor of cos _. f It’s well known that the power factor associated with a controlled rectifier falls, when the DC output voltage is reduced. A common example of this is a DC motor drive controlled by a thyristor converter. As the DC voltage is reduced, to reduce the DC motor speed, at a constant torque, the power factor drops and more reactive power is required at the supply line to the converter. Delay Angle | Converter Behavior a = 0º Behaves like a Resistive load 0º < a < 90º Behaves like a Resistive/Inductive load and absorbs active power a = 90º Behaves like an Inductive load with no active power drawn a > 90º Behaves like an Inductive load but is also a source of active power. As speed is reduced below the base speed, the reactive power requirement keeps increasing. Speed p.u. Base speed Reactive power (kVAR) Proportional to sin _a 00.51.0 ++++16 Reactive power requirements of a DC motor drive with a constant torque load fed from a line-commutated converter. Practical limitations of line-commutated converters: The above analysis covers the theoretical aspects of both uncontrolled and controlled converters. In practice, the components are not ideal and the commutations are not instantaneous. This results in certain deviations from the theoretical performance. One of the deviations is that the DC load current is never completely smooth. Reasons: • Accepting that the instantaneous DC voltage VD can never be completely smooth, if the load is purely resistive, the DC load current cannot be completely smooth because it will linearly follow the DC voltage. • Also, at delay angles a > 60º, the DC output voltage becomes discontinuous and, consequently, so would the DC current. Remedy: In an effort to maintain a smooth DC current, practical converters usually have some inductance LD in series with the load on the DC side. For complete smoothing, the value of LD should theoretically be infinite, which is not practical. The practical consequence of this is that the theoretical formula for the calculated value of DC voltage (VD = 1.35 VRMS cos a) is not completely true for all values of the delay angle a. Practical measurements confirm that it only holds true for delay angles of up to 75º, but this depends on the load type and in particular, the DC load inductance. Experience shows that for a particular delay angle a > 60º, the average DC voltage will be higher than the theoretical value. Inductive load; Resistive-inductive load; Resistive load 0306090120 a (Degrees) VD (Volts) cos_a ++++17 Deviation of DC voltage from theoretical vs delay angle Applications for line-commutated rectifiers: An important application of the line-commutated converter is the DC motor drive. --- shows a single controlled line-commutated converter connected to the armature of a DC motor. The converter provides a variable DC voltage VA to the armature of the motor. This is how the control circuit of the converter is used to change the motor speed. Rectifier IA IF VA VF M ++++18 Converter-fed DC motor drive When the delay angle is less than 90º, the DC voltage is positive and a positive current IA flows into the armature of the DC motor, to deliver active power to the load. The drive system is said to be operating in the 1st quadrant, where the motor runs in the forward direction, with a transfer of active power from the supply to the motor and its mechanical load. The motor field winding is separately excited from a simple diode rectifier and carries a field magnetizing current IF. For a fixed field current, the speed of the motor is proportional to the DC voltage at the armature. The speed can be controlled by varying the delay angle of the converter and its output armature voltage VA. If the delay angle of the converter is increased to an angle greater than 90º, the voltage VD will become negative and the motor will slow to a standstill. The current ID also reduces to zero and the supply line can be disconnected from the motor without breaking any current. ++++19 Operating quadrants for VSD --- Reverse braking; Forward driving; Reverse driving; Forward braking. Consequently, to stop a DC motor, the delay angle must be increased to a value sufficiently larger than 90º to ensure that the voltage VD becomes negative. With VD negative and ID still positive, the converter transiently behaves like a generator and produces a braking torque. In addition, this acts as a brake to slow the motor and its load quickly to a standstill. In this situation, the drive system is said to be operating in the 2nd quadrant where the motor is running in the forward direction. The converters discussed so far have been single converters, which can only operate with a positive DC current (ID = +ve), which means that the motor can only run in the forward direction but an active power can be transferred in either direction. Single DC converters can only operate in quadrants 1 and 4 and are known as second quadrant converters. Quadrant thyristor-controlled rectifier The concept of the four operating quadrants is illustrated below. It shows the four possible operating states of any drive system and shows the directions of VD and ID for the DC motor drive application. To operate in quadrants 3 and 2, it must be possible to reverse the direction of ID. This requires an additional converter bridge connected for current to flow in the opposite direction. This type of converter is known as a four-quadrant DC converter, and is sometimes called a double or back-to-back six-pulse rectifier. ++++20 Four-quadrant line-commutated rectifier ---Forward Reverse IA IF VA VF M With a DC motor drive fed from a four-quadrant DC converter, the operation in all four quadrants is possible with a speed control in either the forward or reverse direction. Operation: A change of direction of the motor can quickly be achieved. Converter-1 is used as a controlled rectifier for speed control in the forward direction of rotation, while converter 2 is blocked, and vice versa in the reverse direction. Assume initially, that the motor runs in the forward direction, under the control of Converter-1, with a delay angle of <90º and Converter-2 is blocked. The changeover sequence from running in the forward direction to the reverse direction is as follows: • Converter-1 delay angle increased to a > 90º. So, DC voltage VD < 0 and DC current ID is decreasing. • When ID = 0, Converter-1 is blocked and thyristor firing is terminated. • After a small delay, Converter-2 is unblocked and starts in the inverter mode with a firing angle greater than 90º. • If the motor is still turning in the forward direction, converter-2 DC current ID starts to increase in the negative direction and the DC machine acts as a generator and is broken to standstill, returning energy to the supply line. • As the firing angle is reduced to a < 90º, converter-2 changes from the inverter to the rectifier mode, and as voltage VD increases, the motor starts to rotate in the opposite direction. In a DC motor drive, the reversal rotation direction can also be achieved by using a single converter and by changing the direction of the excitation current. This method can only be used where there are no special drive requirements for changing over from the forward to the reverse operation. In this case, using switches in the field circuit do the changeover mechanically during a period at standstill. Considerable time delays are required during a standstill, to demagnetize the field in the reverse direction. There are many practical applications for both the uncontrolled and the controlled line commutated rectifiers. Some of the more common applications include the following: • DC motor drives with variable speed control • DC supply for variable voltage-variable frequency inverters • Slip-energy recovery converters for wound rotor induction motors • DC excitation supply for machines • High-voltage DC converters. |
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