24

Uncontrolled and Controlled Rectifiers

Mahesh M. Swamy

Yaskawa America Incorporated

24.1    Introduction

24.2    Uncontrolled Rectifiers

Mechanics of Diode Conduction • Single-Phase Half-Wave Rectifier Circuits • Full-Wave Rectifiers • Three-Phase Rectifiers (Half Wave and Full Wave) • Average Output Voltage • Influence of Three-Phase Rectification on the Power System • Why VFDs Generate Harmonics? • Harmonic Limit Calculations Based on IEEE 519-1992 • Harmonic Mitigating Techniques • Addition of Inductive Impedance • Capacitor-Based Passive Filters • Multi-Pulse Techniques

24.3    Controlled Rectifiers

Gate Circuit Requirements • Single-Phase H-Bridge Rectifier Circuits with Thyristors • Three-Phase Controlled AC to DC Rectifier Systems • Average Output Voltage • Use of Thyristors for Soft Charging DC Bus of Voltage Source Inverters • HVDC Transmission Systems • Power System Interaction with Three-Phase Thyristor AC to DC Rectifier Systems

24.4    Conclusion

References

24.1  Introduction

Rectifiers are electronic circuits that convert bidirectional voltage to unidirectional voltage. This process can be accomplished either by mechanical means employing commutators or by static means employing semiconductor devices. Static means of rectification is more efficient and reliable compared to rotating commutators. In this chapter, we will discuss rectification of electric power for industrial and commercial use. In other words, we will not be discussing small signal rectification that generally involves low power and low voltage signals. Static power rectifiers can be classified into two broad groups. They are (a) uncontrolled rectifiers and (b) controlled rectifiers. Uncontrolled rectifiers make use of power semiconductor diodes while controlled rectifiers make use of thyristors (SCRs), gate turn Off thyristors (GTOs), and MOSFET controlled thyristors (MCTs).

Rectifiers, in general, are widely used in power electronics to rectify single-phase as well as three-phase voltages. DC power supplies used in computers, consumer electronics, and a host of other applications typically make use of single-phase rectifiers. Industrial applications include, but are not limited to industrial drives, metal extraction processes, industrial heating, power generation and transmission, etc. Most industrial applications of large power rating typically employ three-phase rectification processes.

Uncontrolled rectifiers in single-phase and in three-phase circuits will be discussed in Section 24.2. Section 24.3 will focus on controlled rectifiers. Application issues regarding uncontrolled and controlled rectifiers will be briefly discussed within each section. Section 24.4 will conclude this chapter.

24.2  Uncontrolled Rectifiers

Simplest uncontrolled rectifier use can be found in single-phase circuits. There are two types of uncontrolled rectification. They are (a) half-wave rectification and (b) full-wave rectification. Half-wave and full-wave rectification techniques have been used in single-phase as well as in three-phase circuits. As mentioned earlier, uncontrolled rectifiers make use of diodes. Diodes are two terminal semiconductor devices that allow flow of current in only one direction. The two terminals of a diode are known as the anode and the cathode.

24.2.1  Mechanics of Diode Conduction [4]

Anode is formed when a pure semiconductor material, typically Silicon, is doped with impurities that have fewer valence electrons than Silicon. Silicon has an atomic number of 14, which according to Bohr’s atomic model means that the K and L shells are completely filled by 10 electrons and the remaining 4 electrons occupy the M shell. The M shell can hold a maximum of 18 electrons. In a Silicon crystal, every atom is bound to four other atoms, which are placed at the corners of a regular tetrahedron. The bonding, which involves sharing of a valence electron with a neighboring atom, is known as covalent bonding. When a group-3 element (typically boron, aluminum, gallium, and indium) is doped into the Silicon lattice structure, three of the four covalent bonds are made. However, one bonding site is vacant in the Silicon lattice structure. This creates vacancies or holes in the semiconductor. In the presence of either thermal field or an electrical field, electrons from neighboring lattice or from external agency tend to migrate to fill this vacancy. The vacancy or hole can also be said to move toward the approaching electron thereby creating a mobile hole and hence current flow. Such a semiconductor material is also known as lightly doped semiconductor material or p type. Similarly, cathode is formed when Silicon is doped with impurities that have higher valence electrons than Silicon. This would mean elements belonging to group 5. Typical doping impurities of this group are phosphorus, arsenic, and antimony. When a group 5 element is doped into the Silicon lattice structure, it oversatisfies the covalent bonding sites available in the Silicon lattice structure, creating excess or loose electrons in the valence shell. In the presence of either thermal field or an electrical field, these loose electrons easily get detached from the lattice structure and are free to conduct electricity. Such a semiconductor material is also known as heavily doped semiconductor material or n type.

The structure of the final doped crystal even after the addition of acceptor impurities (group 3) or donor impurities (group 5) remains electrically neutral. The available electrons balance the net positive charge and there is no charge imbalance.

When a p-type material is joined with an n-type material, p-n junction is formed. Some loose electrons from the n-type material migrate to fill the holes in the p-type material and some holes in the p-type migrate to meet with the loose electrons in the n-type material. Such a movement causes the p-type structure to develop a slight negative charge and the n-type structure to develop some positive charge. This slight positive and negative charges in the n-type and p-type areas, respectively, prevent further migration of electrons from n-type to p-type and holes from p-type to n-type areas. In other words, an energy barrier is automatically created due to the movement of charges within the crystalline lattice structure. Keep in mind that the combined material is still electrically neutral and no charge imbalance exists.

When a positive potential greater than the barrier potential is applied across the p-n junction, then electrons from the n-type area migrate to combine with the holes in the p-type area and vice versa. The p-n junction is said to be forward biased. Movement of charge particles constitutes current flow. Current is said to flow from the anode to the cathode when the potential at the anode is higher than the potential at the cathode by a minimum threshold voltage also known as the junction barrier voltage. The magnitude of current flow is high when the externally applied positive potential across the p-n junction is high.

FIGURE 24.1  Typical v-i characteristic of a semiconductor diode and its symbol.

When the polarity of the applied voltage across the p-n junction is reversed compared to the case described previously, then the flow of current ceases. The holes in the p-type area move away from the n-type area and the electrons in the n-type area move away from the p-type area. The p-n junction is said to be reverse biased. In fact, the holes in the p-type area get attracted to the negative external potential and similarly the electrons in the n-type area get attracted to the positive external potential. This creates a depletion region at the p-n junction and there is almost no charge carriers flowing in the depletion region. This phenomenon brings us to an important observation that a p-n junction can be utilized to force current to flow only in one direction depending on the polarity of the applied voltage across it. Such a semiconductor device is known as a diode. Electrical circuits employing diodes to convert ac voltage to unidirectional voltage across a load are known as rectifiers. The voltage-current characteristic of a typical power semiconductor diode along with its symbol is shown in Figure 24.1.

24.2.2  Single-Phase Half-Wave Rectifier Circuits

A single-phase half-wave rectifier circuit employs one diode. Typical circuit, which makes use of a halfwave rectifier, is shown in Figure 24.2. A single-phase ac source is applied across the primary windings of a transformer. The secondary of the transformer consists of a diode and a resistive load. This is typical since many consumer electronic items including computers utilize single-phase power.

Typically, the primary side is connected to a single-phase ac source, which could be 120 V, 60 Hz, 100 V, 50 Hz, 220 V, 50 Hz, or any other utility source. The secondary side voltage is generally stepped down and rectified to achieve low dc voltage for consumer applications. The secondary voltage, the voltage across the load resistor and the current through it is shown in Figure 24.3. For a purely resistive V_o = √2 ⋆ V_sec/π.

FIGURE 24.2  Electrical schematic of a single-phase half-wave rectifier circuit feeding a resistive load. Average output voltage is V_o.

FIGURE 24.3  Typical waveforms at various points in the circuit of Figure 24.2.

When the voltage across the anode-cathode of diode D1 in Figure 24.2 goes negative, the diode does not conduct and no voltage appears across the load resistor R. The current through R follows the voltage across it. The value of the secondary voltage is chosen to be 24Vac and the value of R is chosen to be 2Ω. Since, only one-half of the input voltage waveform is allowed to pass onto the output, such a rectifier is known as half-wave rectifier. The voltage ripple across the load resistor is rather large and in typical power supplies, such ripples are unacceptable. The current through the load is discontinuous and the current through the secondary of the transformer is unidirectional. The ac component in the secondary of the transformer is balanced by a corresponding ac component in the primary winding. However, the dc component in the secondary does not induce any voltage on the primary side and hence it is not compensated for. This dc current component through the transformer secondary can cause the transformer to saturate and is not advisable for large power applications. In order to smoothen the output voltage across the load resistor R and to make the load current continuous, a smoothing filter circuit comprising either a large dc capacitor or a combination of a series inductor and shunt dc capacitor is employed. Such a circuit is shown in Figure 24.4 and the resulting waveforms are shown in Figure 24.5.

It is interesting to see that the voltage across the load resistor has very little ripple and the current through it is smooth. However, the value of the filter components employed is large and is generally not economically feasible. For example, in order to get a voltage waveform across the load resistor R that has less than 25% peak-peak voltage ripple, the value of inductance that had to be used is 3 mH and the value of the capacitor is 20,000 μF. Increasing the value of inductance does reduce the peak-to-peak ripple across the load. However, the voltage drop across the inductor increases and the average voltage across the resistor reduces significantly.

FIGURE 24.4  Modified circuit of Figure 24.2 employing smoothing filters.

FIGURE 24.5  Voltage across load resistor R and current through it for the circuit in Figure 24.4.

24.2.3  Full-Wave Rectifiers [1]

In order to improve the performance without adding bulky filter components, it is a good practice to employ full-wave rectifiers. The circuit in Figure 24.2 can be easily modified into a full-wave rectifier. The transformer is changed from a single secondary winding to a center-tapped secondary winding. Two diodes are now employed instead of one. The new circuit is shown in Figure 24.6.

The waveforms for the circuit of Figure 24.6 are shown in Figure 24.7. The voltage across the load resistor is a full-wave rectified voltage. The current has subtle discontinuities but it can be improved by employing smaller size filters. For a purely resistive load, V_o = 2 ⋆ √2 ⋆ V_sec/π.

FIGURE 24.6  Electrical schematic of a single-phase full-wave rectifier circuit. Average output voltage is V_o. For balanced operation, V_sec1 = V_sec2 = V_sec.

FIGURE 24.7  Typical waveforms at various points in Figure 24.6. Vscale: 1/10 of actual value.

FIGURE 24.8  Voltage across the load resistor and current through it with only capacitor filter. Vscale: 1/10 of actual value.

A typical filter for the circuit of Figure 24.6 may include only a capacitor. The waveforms are shown in Figure 24.8. Adding a capacitor filter distorts the secondary voltage due to discontinuous and pulsating current flowing through the secondary windings.

Another way of reducing the size of the filter components is to increase the frequency of the supply. In many power supply applications similar to the one used in computers, a high frequency ac supply is achieved by means of switching. The high frequency ac is then level translated via a ferrite core transformer with multiple secondary windings. The secondary voltages are then rectified employing a simple circuit as that shown in Figure 24.4 or 24.6 with much smaller filters. The resulting voltage across the load resistor is then maintained to have a peak-peak voltage ripple of less than 1%.

Full-wave rectification can be achieved without the use of center-tap transformers. Such circuits make use of four diodes in single-phase circuits and six diodes in three-phase circuits. The circuit configuration is typically referred to as the H-bridge circuit. A single-phase full-wave H-bridge topology is shown in Figure 24.9. The main difference between the circuit topology shown in Figures 24.6 and 24.9 is that the H-bridge circuit employs four diodes while the topology of Figure 24.6 utilizes only two diodes. The VA rating of the center-tap transformer, however, is higher than that of the transformer needed for H-bridge rectifier. The voltage and current stresses in the diodes of Figure 24.6 is also greater than that in the diodes of Figure 24.9.

FIGURE 24.9  Schematic representation of a single-phase full-wave H-bridge rectifier.

In order to highlight the basic difference in the two topologies, it will be interesting to compare the component ratings for the same power output. To make the comparison easy, let both topologies employ very large filter inductors such that the current through R is constant and ripple free. Let this current through R be denoted by I_dc. Let the power being supplied to the load be denoted by P_dc. The output power and the load current are then related by the following expression:

$P_{dc}=I_{dc}^2\star R$

(24.1)

The rms current flowing through the first secondary winding in the topology in Figure 24.6 will be I_dc/√2. This is because the current through a secondary winding flows only when the corresponding diode is forward biased. This means that the current through the secondary winding will flow only for one-half cycle. If the voltage at the secondary is assumed V, the VA rating of the secondary winding of the transformer in Figure 24.6 will be given by

$\begin{array}{l}V{A}_1=V\star \frac{I_{dc}}{\sqrt{2}}\hfill \\ V{A}_2=V\star \frac{I_{dc}}{\sqrt{2}}\hfill \\ VA=V{A}_1+V{A}_2=\sqrt{2}\star V\star I_{dc}\hfill \end{array}$

(24.2)

This is the secondary-side VA rating for the transformer shown in Figure 24.6.

For the isolation transformer shown in Figure 24.9, let the secondary voltage be V and the load current be of a constant value, I_dc. Since, in the topology of Figure 24.9, the secondary winding carries the current I_dc when diodes D1 and D2 conduct as well as when diodes D3 and D4 conduct, the rms value of the secondary winding current is I_dc. Hence, the VA rating of the secondary winding of the transformer shown in Figure 24.9 is given by VA = V ⋆ I_dc and is less than that needed for the topology of Figure 24.6. Note that the primary VA rating for both cases remain the same since in both cases, the power being transferred from the source to the load remains the same.

When diode D2 in the circuit of Figure 24.6 conducts, the secondary voltage of the second winding V_sec2 (=V) appears at the cathode of diode D1. The voltage being blocked by the diode D1 can thus reach two times the peak secondary voltage (=2 ⋆ V_pk) (Figure 24.7). In the topology of Figure 24.9, when diodes D1 and D2 conduct, the voltage V_sec (=V), which is same as V_sec2, appears across D3 and D4 in series. This means that the diodes have to withstand only one time the peak of the secondary voltage, V_pk. The rms value of the current flowing through the diodes in both topologies is the same. Hence, from the diode voltage rating as well as from the secondary VA rating points of view, the topology of Figure 24.9 is better than that of Figure 24.6. Further, the topology in Figure 24.9 can be directly connected to a single-phase ac source since it does not need a center-tapped transformer. The voltage waveform across the load is similar to that shown in Figures 24.7 and 24.8.

In many industrial applications, the topology shown in Figure 24.9 is used along with a dc filter capacitor to smoothen the ripples across the load resistor. The load resistor is simply a representative of the active part of the load. It could be an inverter system or a high-frequency resonant link. In any case, the diode rectifier bridge would see a representative load resistor. For the same output power and the same peak-to-peak ripple voltage across the load, the dc filter capacitor in case of single-phase source will need to be much larger compared to that for a three-phase source connected to a six diode rectifier bridge circuit.

When the rectified power is large, it is advisable to add a dc link inductor. This can reduce the size of the capacitor to some extent and reduce the current ripple through the load. When the rectifier is turned ON initially with the capacitor at zero voltage, large amplitude of charging current will flow into the filter capacitor through a pair of conducting diodes. The diodes D1 ~ D4 should be rated to handle this large surge current. In order to limit the high inrush current, it is a normal practice to add a charging resistor in series with the filter capacitor. The charging resistor limits the inrush current but creates a significant power loss if it is left in the circuit under normal operation. Typically, a contactor is used to short-circuit the charging resistor after the capacitor is charged to a desired level. The resistor is thus electrically nonfunctional during normal operating conditions. A typical arrangement showing a single-phase full-wave H-bridge rectifier system for an inverter application is shown in Figure 24.10. The charging current at time of turn ON is shown in a simulated waveform in Figure 24.11. Note that the contacts across the soft-charge resistor are closed under normal operation. The contacts across the soft-charge resistor are initiated by various means. The coil for the contacts could be powered from the input ac supply and a timer or it could be powered ON by a logic controller that senses the level of voltage across the dc bus capacitor or senses the rate of change in voltage across the dc bus capacitor. A simulated waveform depicting the inrush with and without a soft-charge resistor is shown in Figure 24.11a and b, respectively.

The value of soft-charge resistor used is 6Ω. The dc bus capacitor is about 1200 μF. To show typical operation, at start-up, there is no load and resistor R represents only the bleed-off resistor of approximately 4.7 kΩ present across the capacitor. The peak value of the charging current for this case is observed to be approximately 50 A.

Next, simulation result is given in Figure 24.11b for the case with no soft charge resists. The current is limited by the system impedance and by the diode forward resistance. The peak current is seen to be about 175 A for the same parameters as that chosen for the simulation shown in Figure 24.11a. Note that the dc bus capacitor gets charged to a value almost twice the input peak voltage and this is due to the resonance type of condition set in by the input impedance of the ac source that includes the leakage inductance of the input transformer. The high voltage across the dc bus takes a long time to bleed off through the bleed resistor. The high voltage can damage the inverter IGBTs if the load is an inverter and hence charging the dc bus capacitor without soft-charge resistors is not recommended and should always be avoided.

FIGURE 24.10  Single-phase H-bridge circuit with soft-charge resistor-contactor arrangement.

FIGURE 24.11  (a) Charging current and voltage across capacitor for the circuit of Figure 24.10. Vscale: 1/2 of actual value. (b) Charging current and voltage across capacitor for no soft-charge resistor. Vscale: Actual voltage.

For larger power applications, typically above 1.5 kW, it is advisable to use a power source with a higher voltage. In some applications, two of the three phases of a three-phase power system are used as the source powering the rectifier of Figure 24.9. The line-line voltage could be either 240 or 480 Vac. Under those circumstances, a load of up to 4 kW can be powered using single-phase supply before adopting a full three-phase H-bridge configuration. Beyond 4 kW, the size of the capacitor becomes too large to achieve a peak-peak voltage ripple of less than 10%. Further, the strain that the pulsating current will put on the power system can become unacceptable. Hence, it is advisable to employ three-phase rectifier configurations for loads typically rated at 4 kW and higher.

24.2.4  Three-Phase Rectifiers (Half Wave and Full Wave)

Similar to the single-phase case, there exist half-wave and full-wave three-phase rectifier circuits. Again, similar to the single-phase case, the half-wave rectifier in the three-phase case also has dc components in the source current. The source has to be large enough to handle this. It is thus not advisable to use three-phase half-wave rectifier topology for large power applications. The three-phase half-wave rectifier employs three diodes while the full-wave H-bridge configuration employs six diodes. Typical three-phase half-wave and full-wave topologies are shown in Figure 24.12.

FIGURE 24.12  Schematic representation of three-phase rectifier configurations. (a) Half-wave rectifier needing a neutral point, N; and (b) full-wave rectifier.

In the half-wave rectifier shown in Figure 24.12a, the shape of the output voltage and current through the resistive load is dictated by the instantaneous value of the source voltages, A, B, and C. These source voltages are phase shifted in time by 120 electrical degrees, which corresponds to approximately 5.55 ms for a 60 Hz system. This means that if A phase reaches its peak value at time t₁, B phase will achieve its peak 120 electrical degrees later (t₁ + 5.55 ms), and C will achieve its peak 120 electrical degrees later than B (t₁ + 5.55 ms + 5.55 ms). Since all three phases are connected to the same output resistor R, the phase that provides the highest instantaneous voltage is the phase that appears across R. In other words, the phase with the highest instantaneous voltage reverse biases the diodes of the other two phases and prevents them from conducting which consequently prevents those phase voltages from appearing across R. Since a particular phase is connected to only one diode in Figure 24.12a, only three pulses, each of 120° duration, appears across the load resistor, R. Typical output voltage across R and current through it for the circuit of Figure 24.12a is shown in Figure 24.13a.

A similar explanation can be provided to explain the voltage waveform across a purely resistive load in the case of a three-phase full-wave rectifier shown in Figure 24.12b. The output voltage that appears across R is the highest instantaneous line-line voltage and not simply the phase voltage. Since there are six such intervals, each of 60 electrical degrees duration in a given cycle, the output voltage waveform will have six humps in one cycle—Figure 24.13b. Since a phase is connected to two diodes (diode pair), each phase conducts current out and into itself thereby eliminating dc component in one complete cycle.

The waveform for a three-phase full-wave rectifier with a purely resistive load is shown in Figure 24.13b. Note that the number of humps in Figure 24.13a is only three in one ac cycle while the number of humps in Figure 24.13b is six in one ac cycle. Further, the peak-to-peak ripple in the voltage as well as in the current is significantly lower in the full-bridge configuration compared to the half-bridge configuration.

In both the configurations shown in Figure 24.12, the load current does not become discontinuous due to three-phase operation. Comparing this to the single-phase half-wave and full-wave rectifier, the output voltage ripple is much lower in three-phase rectifier systems compared to single-phase rectifier systems. Hence, with the use of moderately sized filters on the DC side, three-phase full-wave rectifiers can be operated at hundred to thousands of kilowatts. The only limitation would be the size of the diodes used and power system harmonics, which will be discussed next. Since there are six humps in the output voltage waveform per electrical cycle, the three-phase full-wave rectifier shown in Figure 24.12b is also known as a six-pulse rectifier system.

FIGURE 24.13  (a) Typical output voltage across a purely resistive load and current through it for the half-wave rectifier shown in Figure 24.12a. Vscale: 0.5 of actual value. (b) Typical output voltage across a purely resistive load and current through it for the full-wave rectifier shown in Figure 24.12b. Vscale: 0.5 of actual value.

24.2.5  Average Output Voltage

In order to evaluate the average value of the output voltage for the two rectifiers shown in Figure 24.12, the output voltages in Figure 24.13a and b have to be integrated over a cycle. For the circuit shown in Figure 24.12a, the integration yields the following:

$\begin{array}{l}{V}_O=\frac{3}{2\pi }{\displaystyle \underset{\pi /6}{\overset{5\pi /6}{\int }}\sqrt{2}}{V}_{L-N}\sin \left(\omega t\right)d\left(\omega t\right)\hfill \\ V_O=\frac{3\star \sqrt{3}\star \sqrt{2}\star V_{L-N}}{2\star \pi }\hfill \end{array}$

(24.3)

Similar operation can be performed to obtain the average output voltage for the circuit shown in Figure 24.12b. This yields

$\begin{array}{l}{V}_O=\frac{3}{\pi }{\displaystyle \underset{\pi /3}{\overset{2\pi /3}{\int }}\sqrt{2}}{V}_{L-L}\sin \left(\omega t\right)d\left(\omega t\right)\hfill \\ V_O=\frac{3\star \sqrt{2}\star V_{L-L}}{\pi }=\frac{3\star \sqrt{2}\star \sqrt{3}\star V_{L-N}}{\pi }\hfill \end{array}$

(24.4)

In other words, the average output voltage for the circuit in Figure 24.12b is twice that of the circuit in Figure 24.12a.

24.2.6  Influence of Three-Phase Rectification on the Power System

Events over the last several years have focused attention on certain types of loads on the electrical system that result in power quality problems for the user and utility alike. Equipment which has become common place in most facilities including computer power supplies, solid state lighting ballast, adjustable speed drives (ASDs), and uninterruptible power supplies (UPSs) are examples of nonlinear loads. Nonlinear loads are loads in which the current waveform does not have a linear relationship with the voltage waveform. In other words, if the input voltage to the load is sinusoidal and the current is nonsinusoidal then such loads will be classified as nonlinear loads because of the nonlinear relationship between voltage and current. Nonlinear loads generate voltage and current harmonics, which can have adverse effects on equipment that are used to deliver electrical energy to them. Examples of power delivery equipment include power system transformers, feeders, circuit breakers, etc. Power delivery equipments are subject to higher heating losses due to harmonic currents consumed by nonlinear loads to which they are connected. Harmonics can have a detrimental effect on emergency or standby power generators, telephones and other sensitive electrical equipment. When reactive power compensation in the form of passive power factor improving capacitors is used with nonlinear loads, resonance conditions can occur that may result in even higher levels of harmonic voltage and current distortion thereby causing equipment failure, disruption of power service, and fire hazards in extreme conditions.

The electrical environment has absorbed most of these problems in the past. However, the problem has now reached a magnitude where Europe, the United States, and other countries have proposed standards to responsibly engineer systems considering the electrical environment. IEEE 519-1992 [5] and IEC 555 have evolved to become a common requirement cited when specifying equipment on newly engineered projects. Various harmonic filtering techniques have been developed to meet these specifications. The present IEEE 519-1992 document establishes acceptable levels of harmonics (voltage and current) that can be introduced into the incoming feeders by commercial and industrial users. Where there may have been little cooperation previously from manufacturers to meet such specifications, the adoption of IEEE 519-1992 and other similar world standards now attract the attention of everyone.

24.2.7  Why VFDs Generate Harmonics?

The current waveform at the inputs of a variable frequency drive (VFD) is not continuous. It has multiple zero crossings in one electrical cycle. The dc bus capacitor draws charging current only when it is discharged due to the motor load. The charging current flows into the capacitor when the input rectifier is forward biased, which occurs when the instantaneous input voltage is higher than the dc voltage across the dc bus capacitor. The pulsed current drawn by the dc bus capacitor is rich in harmonics because it is discontinuous as seen in Figure 24.1.

The voltage harmonics generated by VFDs are due to the flat-topping effect caused by weak ac source charging the dc bus capacitor without any intervening impedance. The distorted voltage waveform gives rise to voltage harmonics and this is of a more important concern than current harmonics. The reason is simple. Voltage is shared by all loads and it affects all loads connected in an electrical system. Current distortion has a local effect and pertains to only that circuit that is feeding the nonlinear load. Hence, connecting nonlinear loads like VFDs to a weak ac system requires more careful consideration than otherwise.

The discontinuous, nonsinusoidal current waveform as shown in Figure 24.1 can be mathematically represented by sinusoidal patterns of different frequencies having a certain amplitude and phase relationship among each other. By adding these components, the original waveform can be reconstructed. The amplitude of the various sinusoidal components that need to be used to reconstruct a given nonsinusoidal waveform is expressed in terms of a mathematical expression called total harmonic distortion. The total harmonic current distortion is defined as: $TH{D}_I=\sqrt{{\displaystyle {\sum }_{n=2}^{n=\infty }{I}_n^2}}/I_1;I_1$ is the rms value of the fundamental component of current; and I_n is the rms value of the nth harmonic component of current.

The reason for doing this is that it is easier to evaluate the heating effect caused by continuous sinusoidal waveforms of different frequencies and corresponding amplitudes than to estimate the heating effects caused by discontinuous nonsinusoidal waveforms.

The order of current harmonics produced by a semiconductor converter during normal operation is termed as characteristic harmonics. In a three-phase, six-pulse converter with no dc bus capacitor, the characteristic harmonics are nontriplen odd harmonics (e.g., 5th, 7th, 11th, etc.). In general, the characteristic harmonics generated by a semiconductor converter is given by

$h=kq\pm 1$

(24.5)

where

h is the order of harmonics

k is any integer

q is the pulse number of the semiconductor converter (six for a six-pulse converter)

When operating a six-pulse rectifier-inverter system with a dc bus capacitor (voltage source inverter or VSI), harmonics of orders other than those given by the previous equation may be observed. Such harmonics are called noncharacteristic harmonics. Though of lower magnitude, these also contribute to the overall harmonic distortion of the input current. The per unit value of the characteristic harmonics present in the theoretical current waveform at the input of the semiconductor converter is given by 1/h where h is the order of the harmonics. In practice, the observed per unit value of the harmonics is much greater than 1/h. This is because the theoretical current waveform is a rectangular pattern made up of equal positive and negative halves, each occupying 120 electrical degrees. The pulsed discontinuous waveform observed commonly at the input of a VFD (Figure 24.14) digresses greatly from the theoretical waveform.

24.2.8  Harmonic Limit Calculations Based on IEEE 519-1992 [5]

The IEEE 519-1992 relies strongly on the definition of the point of common coupling or PCC. The PCC from the power utility point of view will usually be the point where power comes into the establishment (i.e., point of metering). However, the IEEE 519-1992 document also suggests that, “within an industrial plant, the point of common coupling (PCC) is the point between the nonlinear load and other loads” [1]. This suggestion is crucial since many plant managers and building supervisors feel that it is equally if not more important to keep the harmonic levels at or below acceptable guidelines within their facility. In view of the many recently reported problems associated with harmonics within industrial plants [2], it is important to recognize the need for mitigating harmonics at the point where the nonlinear load is connected to the power system. This approach would minimize harmonic problems, thereby reducing costly downtime and improving the life of electrical equipment. If harmonic mitigation is accomplished for individual nonlinear loads or a group of nonlinear loads collectively, then the total harmonics at the point of the utility connection will in most cases meet or better the IEEE recommended guidelines. In view of this, it is becoming increasingly common for project engineers and consultants to require nonlinear equipment suppliers to adopt the procedure outlined in IEEE 519-1992 to mitigate the harmonics to acceptable levels at the point of the offending equipment. For this to be interpreted equally by different suppliers, the intended PCC must be identified. If not defined clearly, many suppliers of nonlinear loads would likely adopt the PCC to be at the utility metering point, which would not benefit the plant or the building but rather the utility.

FIGURE 24.14  Typical pulsed current waveform as seen at input of a VFD.

Having established that it is beneficial to adopt the PCC to be the point where the nonlinear load connects to the power system, the next step is to establish the short circuit ratio. Short circuit ratio calculations are key in establishing the allowable current harmonic distortion levels. For calculating the short circuit ratio, the available short circuit current at the input terminals of the nonlinear load needs to be determined. If the short circuit value available at the low-voltage side of the utility transformer feeding the establishment (building) is known, and the cable and other series impedances in the electrical circuit between the low-voltage side of the transformer and the input to the nonlinear load are known, then the available short circuit at the nonlinear load can be calculated. In practice, it is common to assume the same short circuit current level as at the secondary of the utility transformer feeding the nonlinear load. The next step is to compute the fundamental value of the rated input current into the nonlinear load. In case the nonlinear load is a VFD operating an induction motor, the NEC amp rating for induction motors can be used to obtain this number. NEC amps are fundamental amps that a motor draws when connected directly to the utility supply. An example is presented here to recap the previous procedure.

A 100 hp ASD/motor combination connected to a 480-V system being fed from a 1500-kVA, 3 ph transformer with an impedance of 4% is required to meet IEEE 519-1992 at its input terminals. The rated current of the transformer is: 1500 ⋆ 1000/(√(3) ⋆ 480), which is calculated to be 1804.2 A. The short circuit current available at the secondary of the transformer is equal to the rated current divided by the per unit impedance of the transformer. This is calculated to be: 45,105.5 A. The short circuit ratio, which is defined as the ratio of the short circuit current at the PCC to the fundamental value of the nonlinear current, is computed next. NEC rating for a 100 hp, 460 V induction motor is 124 A. Assuming that the short circuit current at the VFD input is practically the same as that at the secondary of the utility transformer, the short circuit ratio is calculated to be: 45,105.5/124 which equals 363.75. On referring to the IEEE 519-1992 Table 10.3 [1], the short circuit ratio falls in the 100–1000 category. For this ratio, the total demand distortion (TDD) at the point of VFD connection to the power system network is recommended to be 15% or less. For reference, Table 10.3 [5] is reproduced hereafter.

Current Distortion Limits for General Distribution Systems (120 through 69,000 V)

Even harmonics are limited to 25% of the odd harmonic limits mentioned earlier.

a All power generation equipment is limited to these values of current distortion, regardless of actual I_SC/I_L, where I_SC is the maximum short circuit current at PCC and I_L is the maximum demand load current (fundamental frequency) at PCC. TDD is total demand distortion and is defined as the harmonic current distortion in percent of maximum demand load current. The maximum demand current interval could be either a 15 min or a 30 min interval.

24.2.9  Harmonic Mitigating Techniques

Various techniques of improving the input current waveform are discussed hereafter. The intent of all techniques is to make the input current more continuous to reduce the overall current harmonic distortion. The different techniques can be classified into three broad categories:

1.  Passive techniques

2.  Active techniques

3.  Hybrid technique—combination of passive and active techniques

There are three different options in the passive configuration. They are as follows:

1.  Addition of inductive impedance—line reactors and/or dc link chokes

2.  Capacitor based harmonic filters—tuned as well as broadband type

3.  Multi-pulse techniques (12 pulse, 18 pulse, etc.)

This chapter will concentrate only on the passive techniques. Each of the mentioned passive option will be briefly discussed with their relative advantages and disadvantages.

24.2.10  Addition of Inductive Impedance

24.2.10.1  Three-Phase Line Reactors

A line reactor makes the current waveform less discontinuous resulting in lower current harmonics. Since the reactor impedance increases with frequency, it offers larger impedance to the flow of higher order harmonic currents.

On knowing the input reactance value, the expected current harmonic distortion can be estimated. A table illustrating the expected input current harmonics for various amounts of input reactance is shown as follows:

Percent Harmonics Versus Total Line Impedance

Input reactance is determined by the series combination of impedance of the ac reactor, input transformer (building/plant incoming-feed transformer), and power cable. By adding all the inductive reactance upstream, the effective line impedance can be determined and the expected harmonic current distortion can be estimated from the previous chart. The effective impedance value in % is based on the actual loading and is

$Z_{eff\left(pu\right)}=\frac{\sqrt{3}\star 2\star \pi \star f\star L_T\star I_{act\left(fnd.\right)}}{V_{L-L}}\star 100$

(24.6)

where

I_act(fnd.) is the fundamental value of the actual load current

V_L–L is the line-line voltage

L_T is the total inductance of all reactance upstream. The effective impedance of the transformer as seen from the nonlinear load is

$Z_{eff,x\text{-}mer}=\frac{Z_{x\text{-}mer}\star I_{act\left(fnd.\right)}}{I_r}$

(24.7)

where

Z_eff,x-mer is the effective impedance of the transformer as viewed from the nonlinear load end

Z_x-mer is the nameplate impedance of the transformer

I_r is the nameplate rated current of the transformer

The reactor also electrically separates the dc bus voltage from the ac source so that the ac source is not clamped to the dc bus voltage during diode conduction. This feature reduces flat topping of the ac voltage waveform caused by many VFDs when operated with weak ac systems.

However, introducing ac inductance between the diode input terminal and the ac source causes overlap of conduction between outgoing diode and incoming diode in a three-phase diode rectifier system. The overlap phenomenon reduces the average dc bus voltage. This reduction depends on the duration of the overlap in electrical degrees, which in turn depends on the value of the intervening inductance used and the current amplitude. The duration of overlap in electrical degrees is commonly represented by μ. In order to compute the effect quantitatively, a simple model can be assumed. Assume that the line comprises inductance L in each phase. Let the dc load current be I_dc and let it be assumed that this current does not change during the overlap interval. The current through the incoming diode at start is zero and by the end of the overlap interval, it is I_dc. Based on this assumption, the relationship between current and voltage can be expressed as

$\begin{array}{l}{v}_{ab}=\sqrt{2}\star V_{L-L}\star \sin \left(\omega t\right)=2\star L\star \left(\frac{di}{dt}\right)\hfill \\ \sqrt{2}\star V_{L-L}\star {\displaystyle \underset{\left(\pi /3\right)}{\overset{\left(\pi /3\right)+\mu }{\int }}\sin \left(\omega t\right)d\left(t\right)=2\star L\star {\displaystyle \underset{0}{\overset{I_{dc}}{\int }}di}}\hfill \\ I_{dc}=\frac{\sqrt{2}\star V_{L-L}\star \left(\cos \left(\pi /3\right)-\cos \left(\pi /3+\mu \right)\right)}{2\omega L}=\frac{\sqrt{2}\star V_{L-L}\star \sin \left(\pi /3+\mu /2\right)\star \sin \left(\mu /2\right)}{\omega L}\hfill \end{array}$

(24.8)

For small values of overlap angle μ, sin(μ/2) = μ/2 and sin(π/3+(μ/2)) = sin(π/3). Rearranging the preceding equation yields

$\mu =\frac{2\star \sqrt{2}\star \omega L\star I_{dc}}{V_{L-L}\star \sqrt{3}}$

(24.9)

From the preceding expression, the following observations can be made:

1.  If the inductance L in the form of either external inductance or leakage inductance of transformer or lead length is large, the overlap duration will be large.

2.  If the load current, I_dc is large, the overlap duration is large.

The average output voltage will reduce due to the overlap angle as mentioned before. In order to compute the average output voltage with a certain overlap angle, the limits of integration have to be changed. This exercise yields the following:

$\begin{array}{l}{V}_O=\frac{3}{\pi }{\displaystyle \underset{\mu +\left(\pi /3\right)}{\overset{\mu +\left(2\pi /3\right)}{\int }}\sqrt{2}}{V}_{L-L}\sin \left(\omega t\right)d\left(\omega t\right)\hfill \\ V_O=\frac{3\star \sqrt{2}\star V_{L-L}\star \cos (\mu )}{\pi }=\frac{3\star \sqrt{2}\star \sqrt{3}\star V_{L-N}\star \cos (\mu )}{\pi }\hfill \end{array}$

(24.10)

Thus, it can be seen that the overlap angle contributes to the reduction in the average value of the output dc bus voltage. Unfortunately, higher values of external inductive reactance, increases the overlap angle, which in turn reduces the average output voltage as seen from the previous equation.

24.2.10.2  DC Link Choke

Based on the earlier discussion, it can be noted that any inductor of adequate value placed in between the ac source and the dc bus capacitor of the VFD will help in making the input current waveform more continuous. Hence, a dc link choke, which is electrically present after the diode rectifier bridge and before the dc bus capacitor, can be used to reduce the input current harmonic distortion. The dc link choke appears to perform similar to the three-phase line inductance. However, on analyzing the behavior of the dc link choke, it can be seen that the dc link choke behaves similar to the input ac line inductor only from current distortion point of view but has a completely different influence on the average output voltage.

An important difference is that the dc link choke is after the diode rectifier block and so they do not contribute to the overlap phenomenon discussed earlier with regards to external ac input reactors. Hence, there is no dc bus voltage reduction similar to the way as experienced when ac input reactors are used. The dc link choke increases the diode conduction duration. There is a critical dc link choke inductance value, which when exceeded will result in complete 60° conduction of a diode pair. Any value of dc link inductance beyond this critical value is of no further importance and thus introducing a very large dc link inductor will have no further benefit. A larger inductance value will only be associated with a higher winding resistance and cause marginally extra voltage drop across the winding resistance, resulting in higher power loss without altering the input current distortion or the average output dc voltage significantly. The critical dc link choke that is needed to achieve complete 60° conduction is derived next.

It is assumed that the source is ideal with zero impedance. The forward voltage drop across the conducting diodes is also neglected. When no dc link inductance is used, the dc bus charges up to the peak of the input ac line and since the source is assumed ideal and the voltage drop across the diode is neglected, the average dc bus voltage remains at the peak of the input ac line-line voltage even under loaded condition. This assumption is not true and corrections for this will be made later. The critical inductance is that value that will result in the average dc bus voltage to drop from its peak value to the average 3 ph rectified value. The voltage across the dc link inductor absorbs the difference. Mathematically, the following is true:

$\begin{array}{ll}{L}_{cr}\hfill & \star \frac{\Delta i}{\Delta t}=V_m-V_{3\text{-}ph\text{-}avg}=V_m-\frac{3\star V_m}{\pi }\hfill \\ \hfill & L_{cr}=\frac{\pi -3}{\pi }\star V_m\star \frac{\Delta t}{\Delta i}=\frac{\pi -3}{\pi }\star V_m\star \frac{T/6}{I_{dc}}\hfill \end{array}$

(24.11)

where

L_cr is the critical value of the dc link choke

I_dc is the load current

The change in current Δi in Equation 24.11 is the difference from noload condition to rated load condition. Hence, Δi is the rated average dc link current that flows continuous for a 60° conduction interval. T is the period of the input ac supply. In Equation 24.11, it should be pointed out that if continuous current conduction for 60° duration is desired at a lower value of dc load current, a dc link inductor of a large value is required.

From the expression for the critical dc link inductance, it is seen that the value depends on the load condition, frequency of the input ac supply and the peak value of the input ac line-line voltage, V_m. It is also interesting to note that the value of the critical dc link inductor for a 240 V system for the same load is 1/4th the value for a 480 V system.

24.2.10.3  AC Reactor versus DC Link Choke

Often, application engineers are asked the question regarding the choice between input ac reactors and dc link chokes. As mentioned, the dc link choke appears to have an advantage over the input ac reactor from size, cost, and performance points of view. The ac reactor increases overlap duration of the diodes and reduces the overall dc link voltage, whereas the dc link choke does not have such effect on the dc bus. Variation of dc bus voltage with respect to different values of ac reactor and dc link choke have been studied and plotted in Figure 24.15. The dc bus voltage is seen to keep reducing for increasing values of input ac reactor, while it remains flat when dc link choke of value greater than the critical value is employed.

In spite of some shortcomings, the ac reactor does provide reasonable attenuation to switching noise riding on the input ac line due to disturbance in the input ac source. The reason for the disturbance could be switching in and out of power factor correcting capacitors, often done by utilities to improve the overall power factor or the disturbance caused by lightning and other weather related events. Hence, an optimal solution would be to use a small percent input ac reactor (0.02 pu or lower) and a standard dc link choke, as shown in Figure 24.16.

On knowing the input reactance (both ac reactor and dc choke values), the expected current harmonic distortion can be estimated. A graph illustrating the expected input current harmonics for various amounts of reactance is shown in Figure 24.17.

FIGURE 24.15  Variation of dc bus voltage with increasing value of ac reactor/dc link choke for a 460 V, 7.5 hp VFD.

FIGURE 24.16  Commonly used inductive filters.

FIGURE 24.17  Performance with ac line reactor and dc link choke. Note the slope of current in the two cases.

24.2.11  Capacitor-Based Passive Filters

Passive filters consist of passive components like inductors, capacitors, and resistors arranged in a predetermined fashion either to attenuate the flow of harmonic components through them or to shunt the harmonic component into them. Passive filters can be of many types. Some popular ones are series passive filters, shunt passive filters, and low-pass broadband passive filters. Series and shunt passive filters are effective only in a narrow proximity of the frequency at which they are tuned. Low-pass broadband passive filters have a broader bandwidth and attenuate a larger range of harmonics above their cutoff frequency.

24.2.11.1  Series Passive Filter

One way to mitigate harmonics generated by nonlinear loads is to introduce a series passive filter (Figure 24.18) in the incoming power line so that the filter offers high impedance to the flow of harmonics from the source to the nonlinear load. Since the series passive filter is tuned to a particular frequency, it offers high impedance at only its tuned frequency. Depending on the physical property of L and C chosen, typically there exists a narrow band around the tuned frequency where the impedance remains high.

Series passive filters have been used more often in 1 ph applications where it is effective in attenuating the third-harmonic component. The series pass filter is generally designed to offer low impedance at the fundamental frequency. A major drawback of this approach is that the filter components have to be designed to handle the rated load current. Further, one filter section is not adequate to attenuate the entire harmonic spectrum present in the input current of a nonlinear system. Multiple sections may be needed to achieve this, which makes it bulky and expensive.

24.2.11.2  Shunt Passive Filter

The second and more common approach is to use a shunt passive filter, as shown in Figure 24.19. The shunt passive filter is placed across the incoming line and is designed to offer very low impedance to current components corresponding to its tuned frequency. Another way of explaining the behavior of a shunt filter is to consider the energy flow from source to the nonlinear load via the shunt filter. Energy at fundamental frequency flows into the shunt passive filter and the energy at the filter’s tuned frequency flows out of the shunt filter since it offers lower impedance for flow of energy at its tuned frequency compared to the source. In other words, the harmonic component needed by the nonlinear load is provided by the shunt filter rather than the ac source.

FIGURE 24.18  Single-phase representation of a series filter configuration.

FIGURE 24.19  Single-phase representation of a shunt-tuned filter configuration.

FIGURE 24.20  Fifth harmonic tuned filter with input and output reactors.

The fundamental frequency energy component flowing into the shunt filter is the reason for leading VARs and can cause overvoltage at the filter terminals. This can create problems with VFDs that are vulnerable to higher than normal voltage and under light-load condition can encounter overvoltage trips. Similar to the series tuned filter, the shunt-tuned filter is effective only at and around its tuned frequency and only one section of the filter alone is inadequate to provide for all the harmonic energy needed by a typical nonlinear load (VFD). Multiple sections are needed, which makes them bulky and expensive.

The commonly used 3 ph shunt filter sections comprise individual sections tuned for the 5th, the 7th, and perhaps a high-pass section typically tuned near the 11th harmonic. Unfortunately, if care is not taken, the shunt filter will try to provide the harmonic energy needed by all nonlinear loads connected across its terminals. In this process, it can be overloaded and be damaged if unprotected. In order to avoid import of harmonics, it is important to use series line reactors, which impede the harmonic energy flow from other sources into the shunt-tuned filter sections.

A popular type of passive filter (Figure 24.20) comprises a shunt filter tuned to the fifth harmonic along with series impedance to limit import of harmonics from other sources. One more reactor is placed in between the filter section and the VFD to further reduce the current distortion. This type of filter is bulky, expensive, inefficient, and can cause dc bus overvoltage. All passive filters are associated with circulating current that cause unnecessary power loss. Circulating current in capacitor filters causes high voltage at VFD input terminals. Passive filters can also cause system resonance. Given these disadvantages, it is best to avoid them.

The addition of extra line inductance can aggravate the overvoltage condition experienced by inverter drive systems at light-load conditions. The over voltage tolerance margin would be compromised and the VFD could be more vulnerable to fault out on over voltage thereby causing nuisance trips.

24.2.11.3  Low-Pass Broadband Filter

The low-pass broadband filter is similar to the circuit configuration of Figure 24.20. To improve the filtering performance, the inductor Lf is removed and placed in place of the 5% input ac reactor. By removing Lf from the shunt path, the filter configuration changes from tuned type to broadband type. One advantage of the low-pass broadband harmonic filter is that unlike the shunt and series type filters, the broadband filter need not be configured in multiple stages or sections to offer wide spectrum filtering. In other words, one filter section achieves the performance close to the combined effect of a fifth, seventh, and a high-pass shunt-tuned filter section. A typical broadband filter section is shown in Figure 24.21. The series inductor L_f offers high impedance to limit import and export of harmonics from and to other nonlinear loads on the system [6].

However, by removing L_f from the shunt branch and moving it to the series branch, aggravates the overvoltage problem experienced by VFDs. Autotransformers have been used in the past to address this problem. Since the overvoltage is a function of the load current, the correction offered by autotransformer works only at one operating point at best and is inadequate to handle wide range of operating conditions. In addition, the size and cost of the total filter configuration becomes high and less appealing. The leading VAR problem is not resolved and in fact has been found to interfere with power measurement and monitoring systems. These unfavorable features are serious enough to limit use of such filters for VFD applications.

FIGURE 24.21  Broadband filter section with autotransformer.

24.2.12  Multi-Pulse Techniques

As discussed earlier, the characteristic harmonics generated by a semiconductor converter is a function of the pulse number for that converter. Higher the pulse number, lower is the total harmonic distortion since the order of the characteristic harmonics shifts to a higher value. Pulse number is defined as the number of diode-pair conduction intervals that occur in one electrical cycle. In a three-phase, six-diode bridge rectifier, the number of diode-pair conduction intervals is six and such a rectifier is known as a six-pulse rectifier. By using multiple six-pulse diode rectifiers in parallel and phase shifting the input voltage to each rectifier bridge by a suitable value, multi-pulse operation can be achieved.

24.2.12.1  12-Pulse Techniques

A 12-pulse rectifier operation can be achieved by using two six-pulse rectifiers in parallel with one rectifier fed from a power source that is phase shifted with respect to the other rectifier by 30 electrical degrees. The 12-pulse rectifier will have the lowest harmonic order of 11. In other words, the fifth, and the seventh harmonic orders are theoretically nonexistent in a 12-pulse converter. Again, as mentioned in Section 24.2.7, the amplitude of the characteristic harmonic is typically proportional to the inverse of the harmonic order. In other words, the amplitude of the 11th harmonic in a 12-pulse system will be 1/11 of the fundamental component and the amplitude of the 13th harmonic will be 1/13 of the fundamental component. There are many different ways of achieving the necessary phase shift to realize 12-pulse operation. Some popular methods are

1.  Three winding isolation transformer

2.  Hybrid 12-pulse method

3.  Autotransformer method

24.2.12.1.1    Three Winding Isolation Transformer Method

A three winding isolation transformer has three different sets of windings. One set of winding is typically called the primary, while the other two sets are called secondary windings. The primary winding can be connected in delta or in wye configuration. One set of secondary winding is connected in delta while the other set is connected in wye configuration. This arrangement automatically yields a 30° phase shift between the two sets of secondary windings. A traditional 12-pulse arrangement using a three winding isolation transformer is shown in Figure 24.22. The realization of 12-pulse operation in the circuit of Figure 24.19 is discussed next.

The current flowing out of the secondary windings, viewed independently, is similar to that observed in a six-pulse rectifier. However, since the voltages are phase shifted by 30 electrical degrees, the currents are also phase shifted by the same amount. In other words, if i₁ is the fundamental current through one set of secondary windings, and i₂ is the 30° phase-shifted current in the other set of secondary windings, then i₁ and i₂ can be expressed as follows:

FIGURE 24.22  Typical schematic of a 12-pulse configuration using a three winding isolation transformer. DC link choke improves performance.

$\begin{array}{l}{i}_1=I_m\star \sin \left(\omega t\right)\hfill \\ i_2=I_m\star \sin \left(\omega t-\frac{\pi }{6}\right)\hfill \end{array}$

(24.12)

The fifth harmonic component of the current in one of the secondary windings will be phase shifted with respect to its corresponding phase in the other set. However, it should be noted that the phase shift will get multiplied by the harmonic number as well. The fifth harmonic component in the two sets of windings can be represented as follows:

$\begin{array}{l}{i}_{5\left(1\right)}=I_{5m}\star \sin \left(5\star \omega t\right)\hfill \\ i_{5\left(2\right)}=I_{5m}\star \sin \left(5\star \omega t-\frac{5\star \pi }{6}-\frac{\pi }{6}\right)=-I_{5m}\star \sin \left(5\star \omega t\right)\hfill \end{array}$

(24.13)

Similar expressions can be written for the seventh harmonic currents in each set of the secondary windings. From the previous expressions, it can be said that the flux pattern formed by the fifth and seventh harmonic components by one set of secondary windings are theoretically equal and opposite to the fifth and seventh harmonic flux components produced by the second set of secondary windings. Consequently, there is no fifth and seventh harmonic component reflected on to the primary windings and so the fifth and seventh harmonic components do not theoretically exist in the input ac supply feeding the primary windings.

Based on the previous explanation, it can be said that in a three winding isolation transformer arrangement, magnetic flux coupling plays an important role in assuring the elimination of low order current harmonics. Any departure from the ideal scenario assumed earlier will yield suboptimal flux cancellation and higher total current harmonic distortion. Leakage flux and the primary magnetizing flux create nonideal conditions and are responsible for the existence of noncharacteristic harmonics in the input current of a typical 12-pulse system. Minor winding imbalance between the two sets of secondary windings also contributes to suboptimal performance.

Advantages

Some important advantages of the three winding isolation transformer configuration to achieve 12-pulse operation is listed as follows:

•  12-pulse operation yields low total current harmonic distortion.

•  Three winding arrangement yields isolation from the input ac source, which has been seen to offer high impedance to conducted EMI.

•  It offers in-built impedance due to leakage inductance of transformer. This smoothes the input current and helps further reduce the total current harmonic distortion.

•  It is ideally suited for voltage level translation. If the input is at a high voltage (3.2 or 4.16 kV), and the drive system is rated for 480 V operation, it is ideal to step down and to achieve the benefits of 12-pulse operation.

Disadvantages

In spite of its appeal, the three winding isolation transformer configuration has a few shortcomings listed as follows:

•  The three winding transformer has to be rated for full power operation, which makes it bulky and expensive.

•  Leakage inductance of the transformer will cause reduction in the dc bus voltage, which will require the use of taps in the primary winding to compensate for this drop. Addition of taps will increase cost.

•  Due to minor winding mismatch, leakage flux, and nontrivial magnetizing current, the total current harmonic distortion can be higher than expected.

•  Needs the VFD to be equipped with two six-pulse rectifiers that increases the cost of the VFD.

24.2.12.1.2    Hybrid 12-Pulse Method

One disadvantage of the three winding arrangement mentioned earlier is its size and cost. On reexamining the circuit of Figure 24.22, it can be noted that one set of winding does not have any phase shift with respect to the primary winding. This is important because it allows one 6-pulse rectifier circuit to be directly connected to the ac source via some balancing inductance to match the inductance in front of the other 6-pulse rectifier circuit to achieve 12-pulse operation.

The resulting scheme has one six-pulse rectifier powered via a phase shifting isolation transformer, while the other six-pulse rectifier is fed directly from the ac source via matching impedance. Such a 12-pulse arrangement is called a hybrid 12-pulse configuration and is shown in Figure 24.23. The phase shifting transformer feeding one of the two six-pulse rectifiers is sized to handle half the rated power. Similarly, the matching inductor is sized to carry only half the rated current. This arrangement results in the overall size of the transformer and matching inductor combination to be smaller and less expensive than the three winding arrangement.

FIGURE 24.23  Schematic of a typical hybrid 12-pulse arrangement.

Advantages

Some important advantages of the hybrid 12-pulse is listed as follows:

•  Size and cost of the hybrid 12-pulse configuration are much less than the three winding arrangement.

•  12-pulse operation is achieved with low total current harmonic distortion.

•  Unlike three winding method, in this method the current (instead of flux in the core) in the two bridges are combined at the source to cancel the low order harmonics. Leakage flux and winding mismatch problems are reduced by adjusting the matching inductor to effectively cancel the fifth and seventh harmonic currents.

Disadvantages

The hybrid version also has some important disadvantages that need to be pointed out. They are as follows:

•  The impedance mismatch between the leakage inductance and the external matching inductance can never be accomplished for all operating conditions because the leakage inductance is a function of current through the transformer while the external inductance is in the form of self inductance, which is constant till its rated current value.

•  In order to minimize the effect of mismatch, an input ac line inductor may need to be used sometimes to comply with the harmonic levels recommended in IEEE 519(1992).

•  The use of extra inductance ahead of the transformer-inductor combination can cause extra voltage drop that cannot be compensated for.

•  The arrangement of Figure 24.23 cannot be used where level translation is needed.

•  The advantage of high impedance to conducted EMI as offered by the three winding arrangement is reduced on using the hybrid arrangement of Figure 24.23.

•  Similar to the three winding configuration, this method also requires the VFD to have two six-pulse rectifiers.

It should be pointed out that in spite of the previously listed shortcomings the hybrid 12-pulse method is gaining in popularity primarily because of size and cost advantage. The transformer leakage inductance and the external matching inductance are matched to perform at rated current so that low harmonic distortion is achieved at rated operating conditions. Tests conducted at 75 hp along with the associated harmonic spectrum are shown in Figure 24.24.

24.2.12.1.3    Autotransformer Method

The phase shift necessary to achieve multi-pulse operation can also be achieved by using autotransformers. Autotransformers do not provide any isolation between the input and output but can be used to provide phase shift. Autotransformers are typically smaller compared to regular isolation transformers because they do not need to process the entire power. Majority of the load current passes directly from the primary to the secondary terminals and only a small amount of VA necessary for the phase shift is processed by the autotransformer. This makes them small, inexpensive, and attractive for use in multi-pulse systems.

Though autotransformers are appealing for multi-pulse applications, they are not well suited for single VFD load. In all ac to dc rectification schemes, the diode pair that has the highest voltage across the input terminals conducts to charge the dc bus. When parallel rectifiers are used as in multi-pulse techniques, it is important to maintain sharing of current among the multi-pulse rectifiers. If current sharing is compromised, then the amplitudes of lower order harmonics between the two rectifiers in a 12-pulse scheme will not cancel completely and this will result in poor harmonic performance. By electrically isolating one rectifier from the other in the two schemes discussed thus far, acceptable 12-pulse performance was possible. However, when autotransformers are employed, such isolation is lost and current from one set of phase-shifted windings can flow into the other set thereby compromising the equal distribution of current between the phase-shifted sets of windings. One way to force the rectifiers to share correctly is to introduce inter-phase transformer (IPT) in between the outputs of the two diode rectifier units as shown in Figure 24.25. A zero sequence blocking transformers (ZSBT) in between the rectifier and one of the phase-shifted outputs of the autotransformer also helps in reducing noncharacteristics triplen harmonics from flowing into the ac system. The autotransformer of Figure 24.8 has phase-shifted outputs of ±15°.

FIGURE 24.24  75 hp hybrid 12-pulse waveforms. THD = 6.7% with 5% input ac reactor and 8.8% with no input ac reactor.

The use of ZSBT and IPT makes the overall system bulky and expensive and the choice of autotransformer less appealing. However, in many cases, the VFD is not equipped with two rectifier units and so none of the 12-pulse schemes can be really used in such cases. In such applications, if multiple VFDs are being employed and they can be paired into approximately equal ratings then the delta-fork autotransformer shown in Figure 24.25 can be effectively implemented. Instead of isolating the two diode rectifier units in one VFD, it is possible to use two different VFDs operating two independent loads of approximately equal rating and supplying them power from the phase-shifted outputs of the delta-fork transformer. This type of matched pair possibilities exists in a given system and is ideal for VFDs that do not have two independent six-pulse rectifier units. One such scheme of distributing the load between the phase-shifted outputs of a delta-fork autotransformer is shown in Figure 24.26. This arrangement has been seen in the field to achieve low total current harmonic distortion even with load imbalance in the neighborhood of 20%–25%.

FIGURE 24.25  Delta-fork autotransformer with ZSBT and IPT for 12-pulse applications.

FIGURE 24.26  Use of low-cost autotransformer for 12-pulse operation in case of isolated and balanced loads.

Advantages

Some important advantages of the autotransformer connection shown in Figure 24.22 are listed as follows:

•  VFDs do not need to have multiple rectifier units to achieve benefits of 12-pulse operation.

•  Size and cost of autotransformer is small and unlike the circuit of Figure 24.21, there is no need for IPTs and ZSBTs.

•  The three-phase input ac reactor in front of each VFD helps in making the current more continuous. These may be replaced by dc link chokes.

Disadvantages

The circuit of Figure 24.22 has a few shortcomings and the reader should be aware of these. They are

•  Better harmonic performance is achieved if the loads are balanced. Since the loads are independent, many times it is not possible to guarantee balance and this may reduce the overall harmonic performance.

•  Input ac line inductors or dc link chokes may be necessary to get better harmonic performance.

•  VFDs need to be isolated to prevent crosscurrent flow between the two sets of windings and to assure good sharing.

24.2.12.2  18-Pulse Techniques

Harmonic distortion concerns are serious when the power ratings of the VFD load increases. Large power VFDs are gaining in popularity due to their low-cost and impressive reliability. The use of large power VFDs increases the amplitude of low order harmonics that can impact the power system significantly. In many large power installations, current harmonic distortion levels achievable using 12-pulse technique is insufficient to meet the levels recommended in IEEE 519(1992). In view of this, lately, quite a lot of interest has been shown in developing 18-pulse VFD systems to achieve much superior harmonic performance compared to the traditional 12-pulse systems.

18-pulse systems have become economically feasible due to the recent advances in autotransformer techniques that help reduce the overall cost and achieve low total current harmonic distortion. As mentioned earlier, when employing autotransformers, care should be taken to force the different rectifier units to share the current properly. The 18-pulse configuration lends itself better in achieving this goal compared to the 12-pulse scheme. Some popular 18-pulse autotransformer techniques are discussed next.

For 18-pulse operation, there is need for three sets of three-phase ac supply that are phase shifted with respect to each other by 20 electrical degrees. Traditionally, this is achieved using a four winding isolation transformer that has one set of primary windings and three sets of secondary windings. One set of secondary winding is in phase with the primary winding, while the other two sets are phase shifted by +20 electrical degrees and −20 electrical degrees with the primary. This arrangement yields three phase-shifted supplies that allow 18-pulse operation as shown in Figure 24.27.

The use of dc link choke as shown in Figure 24.27 is optional. The leakage inductance of the transformer may be sufficient to smooth the input current and improve the overall current harmonic distortion levels.

The primary disadvantage of the scheme shown in Figure 24.27 is that the phase shifting isolation transformer is bulky and expensive. A common disadvantage with all 18-pulse schemes is that all of them need three independent three-phase rectifier units. Many VFD manufacturers do not provide this feature and the additional rectifier units needed may have to be provided external to the VFD.

FIGURE 24.27  Schematic representation of 18-pulse converter circuit fed from phase-shifted isolation transformer.

Instead of using ±20° phase-shifted outputs from isolation transformer for 18-pulse operation, a 9-phase supply where each phase lags the other by 40 electrical degrees can be used. Autotransformers have been developed that implement this idea and are widely used [3]—Figure 24.28. Due to the nature of autotransformers, the size, weight, and cost can be reduced compared to the conventional technique shown in Figure 24.27.

Figure 24.28a shows a nine-phase ac supply using wye-fork with a tertiary delta winding to circulate triplen harmonics. The size of the autotransformer is big and there is need for additional series impedance to smoothen the input ac currents. The rating of the transformer is about 70% of the rating of the load. If the series inductance is not used, then the output dc voltage is about 4.3% higher than that achieved when a standard six-pulse rectifier is used.

FIGURE 24.28  Autotransformer methods of achieving 18-pulse operation. (a) A 3-phase to 9-phase wye fork with closed delta autotransformer. (b) A differential delta autotransformer with three sets of outputs phase shifted to 40 electrical degrees. (c) A 3-phase to 9-phase differential data type autotransformer. (d) A polygon autotransformer with three sets of windings phase displaced by 20 electrical degrees.

Figure 24.28b shows a nine-phase ac supply using delta-fork that does not require additional delta winding. In this configuration, the average dc output voltage is about 14% higher than that obtained using a standard six-pulse rectifier scheme. This can potentially stress the dc bus capacitors and the IGBTs in the inverter section of a VFD. In order to overcome this, additional teaser windings are used as shown. These windings not only add cost and increase the overall rating of the transformer, they also cause imbalance that results in higher than normal circulating currents in the delta windings, which need to be accommodated. The harmonic performance is good but the overall size is large with rated current flow through the teaser windings.

In order to overcome the 14% higher average dc bus voltage observed in the previous configuration, a modification of the configuration was proposed in the patent cited in Figure 24.28c. The harmonic performance is equally good and the average dc bus voltage is equal to that observed in six-pulse rectifiers. Similar to the previous configuration, the stub winding currents are high and the teaser winding needs to carry rated load current making the overall transformer big in size and expensive to wind.

In autotransformer configurations using stub and/or teaser windings shown in Figure 24.28a through c, the overall size and rating of the autotransformer is higher than the optimal value. The use of stub windings typically results in poor utilization of the core and involves more labor to wind the coils. Polygon type of autotransformer is better than stub type autotransformer from size and core utilization points of view. A polygon type autotransformer is shown in Figure 24.28d. It should be pointed out that the configuration of Figure 24.28d needs the use of IPTs and input ac inductors to achieve low total current harmonic distortion. The reason is that the outputs are not equally spaced to achieve a nine-phase ac supply as in the previous configurations. The polygon autotransformer of Figure 24.28d provides ±20° phase-shifted outputs to achieve 18-pulse operation.

One of the widely used 18-pulse autotransformer configurations is that shown in Figure 24.29. This configuration is a modified version of the configuration shown in Figure 24.28a and was proposed by the same author. In the configuration of Figure 24.29, the delta-connected tertiary winding is included in the wye fork. This construction is called the windmill construction. Initially the windmill structure was present in each phase and the size of the transformer was still big. The kVA rating was about 60%. By intelligently removing the windmill structure from two of the three phases, it was shown that the performance remained equally good. By adopting the modified structure of Figure 24.29, the kVA rating of the autotransformer was reduced from 60% to 55%.

FIGURE 24.29  Schematic of the modified windmill construction of the 18-pulse autotransformer configuration used with VFDs.

In all the 18-pulse autotransformer methods, the change of current from one conducting diode pair to the other is quite sudden. Though the rms current rating may not exceed the current rating of the diode, attention should be given to the di/dt of the current through the diodes. Since the use of autotransformer method of 18-pulse operation is recent, there is not much statistical data available to comment on the di/dt issue with diodes when used in conjunction with 18-pulse autotransformer techniques.

24.2.12.3  Summary of Drawbacks with Autotransformers

From the discussion on autotransformers thus far, some important shortcomings of the autotransformer based topology are summarized as follows:

1.  The leakage and magnetizing inductances of many auto transformers in the market is far lower than that in isolation transformers. Powering up an autotransformer typically results in an inrush current that is much higher than that observed in systems with isolation transformer. This requires careful fuse selection and coordination so that nuisance trips are avoided and fuse protection is still available.

2.  In all the 18-pulse autotransformer methods, the change of current from one conducting diode pair to the other is quick. Though the rms current rating may not exceed the current rating of the diode, attention should be given to the di/dt of the current through the diodes. One solution is to use additional inductors in between the autotransformer and the input rectifier to lower the di/dt. This makes the overall scheme bulky and expensive. The rectangular current through the windings also increases losses, prompting the need to use fans to keep the size of the transformer small.

3.  Due to the sudden change in current and lack of sufficient leakage inductance in autotransformers, such topologies require significant input impedance (shown as L_IN in Figure 24.29) to smooth the current and reduce the overall input current distortion. All the autotransformer configurations discussed here do not operate well without a significant amount of input inductance ahead of the autotransformer.

4.  Autotransformer techniques utilize complex winding structures, either of the stub type or the polygon type. These transformers are labor intensive to manufacture and result in poor core utilization. Even the polygon type shown in Figure 24.28d is labor intensive to wind.

5.  Autotransformer topologies that convert a three-phase system to a nine-phase output create an aberration in the dc bus ripple content of a VFD. When one or two of nine output phases have a bad rectifier, the increase in dc bus ripple is hardly noticeable and this reduces the chance for detection of failure. The power flow is now shared by existing rectifiers that can eventually fail.

Given the previous shortcomings, it is clear that there is room for improvement in multi-pulse rectification schemes. Similar to the idea shown in Figure 24.23, a new 18-pulse scheme that has two 6-pulse rectifiers powered via a phase shifting isolation transformer, and a third 6-pulse rectifier fed directly from the ac source via a matching impedance was proposed in [8]. Such an 18-pulse arrangement will be referred to as hybrid 18-pulse configuration and is shown in Figure 24.30. The phase shifting zigzag isolation transformer feeding two of the three six-pulse rectifiers is sized to handle 2/3 the rated load power. Similarly, the matching inductor is sized to carry only 1/3 the rated input load current. This arrangement results in the overall size of the transformer and matching inductor combination to be smaller and less expensive than the four winding arrangement of Figure 24.27. As an example, a 50 hp conventional 18-pulse transformer without input inductor L_IN was recently quoted to be 42″(H) × 36″(W) × 24″(D) with an estimated weight of 880 lb, while the hybrid 18-pulse structure (without L_IN) to handle the same load was quoted to be 24″(H) × 26″(W) × 14″(D) with an estimated weight of 550 lb. The topology requires a matching inductor to perform comparably, which will add 12 lb, for a total weight of 562 lb. Both these structures are naturally cooled.

The phase shift in the transformer shown in Figure 24.30 is achieved by winding extra teaser windings on appropriate limbs of a transformer. The teaser windings are marked “T” with subscript denoting the phase that they are wound on. For example, T_H21 denotes a teaser winding that is wound on the H2 winding of the primary side of the isolation transformer and is used in the first set of secondary winding to yield a phase shift of +20°.

FIGURE 24.30  Schematic of proposed hybrid 18-pulse topology [8].

The required phase shift could have been achieved using an autotransformer, but due to the reasons mentioned earlier, it is not the choice topology.

24.2.12.4  Harmonic Mitigation Technique Summary

This section discussed generation of current harmonics by nonlinear loads and the IEEE-519-1992 standard to limit the quantity of these harmonics. A methodology of applying this standard to a practical industrial site has been described. Different harmonic mitigating techniques presently available in the industry have been highlighted. Multi-pulse techniques to achieve low total current harmonic distortion have been discussed. Relative advantages and disadvantages of the techniques presented have also been discussed. Based on the materials presented in this report, the following important conclusions can be drawn:

1.  Passive techniques involving capacitors are associated with circulating current, leading power factor, and high dc bus voltage at light load condition and hence should be avoided as far as possible. They are also associated with the possibility of causing network resonance and hence if they are installed, care should be taken to monitor resonance conditions and avoid them.

2.  DC link chokes are a better alternative than ac line reactors for harmonic mitigation since they do not cause additional voltage drop if the value is greater than the critical inductance.

3.  To handle transients and surges on the ac line, a combination of small value of ac inductance and dc link choke is preferred.

Multi-pulse techniques offer the best passive solution to handle harmonics. The hybrid 18-pulse technique and the hybrid 12-pulse technique are attractive for medium power applications, while distributing the load on phase-shifted outputs of an autotransformer for small power application is an interesting alternative.

24.2.12.5  Active Harmonic Compensation

Most passive techniques discussed earlier aim to cure the harmonic problems once nonlinear loads have created them. However, motor-drive manufacturers are developing rectification techniques that do not generate low order harmonics. These drives use active front ends. Instead of using diodes as rectifiers, the active front end ASDs make use of active switches like IGBTs along with antiparallel diodes. In such active front-end rectifiers, power flow becomes bidirectional. The input current can be wave shaped and made sinusoidal to have low values of low-order harmonics.

Apart from the active front ends, there also exists shunt active filters used for actively introducing a current waveform into the ac network which when combined with the harmonic current, results in an almost perfect sinusoidal waveform.

Interesting and effective combinations of passive tuned and active components have been proposed by many researchers and quite a few of them are reportedly in use in the steel, rail, and power utility industries. Such topologies are commonly referred to as hybrid structures and have been extensively researched by authors of reference [7].

Most active filter topologies are cost-effective in high power ratings but require high initial investment. Hybrid filters also have large bandwidth and good dynamic response. Control is accomplished using digital signal processing (DSP) chips. The hybrid structures also need current and voltage sensors and corresponding analog to digital (A/D) converters.

Manufacturers of smaller power equipment like computer power supplies, lighting ballast, etc., have successfully employed single-phase active circuits, employing boost converter topologies.

Detailed discussions on active harmonic compensation and related topics can be found in literature. Since it is beyond the scope of this section, the topic on active harmonic compensating circuits is not dealt in detail here.

24.3  Controlled Rectifiers

Controlled rectifier circuits make use of controlled switches. One such device is the “thyristor.” A thyristor is a four-layer (p-n-p-n), three-junction device that conducts current only in one direction similar to a diode. The junction marked J3 in Figure 24.26 is utilized as the control junction and consequently the rectification process can be initiated at will provided the device is favorably biased and the load is of favorable magnitude. The operation of a thyristor can be explained by assuming it to be made up of two transistors connected back-to-back as shown in Figure 24.31.

Let α₁ and α₂ be the ratio of collector to emitter currents of transistors Q₁ and Q₂, respectively. In other words, α₁ = I_c1/I_e1; α₂ = I_c2/I_e2; Also, from Figure 24.26, I_e1 = I_e2 = I_A where I_A is the anode current flowing through the thyristor. From transistor theory, the value of I_e2 is equal to I_c2 + I_b2 + I_lkg, where I_lkg is the leakage current crossing the n1-p2 junction. From Figure 24.26, I_b2 = I_c1. Hence the anode current can be rewritten as

FIGURE 24.31  Virtual representation of a thyristor to explain its operation. (a) Semiconductor layer representation for a thyristor, (b) step towards deriving an equivalent model for a thyristor, and (c) equivalent model of a thyristor.

$I_A=I_{c1}+I_{c2}+I_{lkg}$

(24.14)

Substituting the collector currents by the product of ratio α and emitter current, the anode current becomes

$\begin{array}{l}{I}_A=\left({\alpha }_1\star I_{e1}\right)+\left({\alpha }_2\star I_{e2}\right)+I_{lkg}\hfill \\ I_A=\left({\alpha }_1+{\alpha }_2\right)I_A+I_{lkg}\hfill \\ I_A=\frac{I_{lkg}}{1-\left({\alpha }_1+{\alpha }_2\right)}\hfill \end{array}$

(24.15)

If the ratio of the collector current to base current (gain) of the transistors is assumed to be β₁ and β₂ respectively, then the relationship between to β₁, β₂ and α₁, α₂ can be written as

${\alpha }_1=\frac{{\beta }_1}{1+{\beta }_1};{\alpha }_2=\frac{{\beta }_2}{1+{\beta }_2}$

(24.16)

Substituting for α₁ and α₂ in the expression for I_A yields the following expression:

$I_A=\frac{\left(1+{\beta }_1\right)\left(1+{\beta }_2\right)I_{lkg}}{1-{\beta }_1{\beta }_2}$

(24.17)

If the values of α₁ and α₂ are low (low gains) then the anode current is low and comparable to the leakage current. Under this condition, the thyristor is said to be in its OFF state. However, if the effective gain of the transistor is such that the product of the gains are close to 1 (i.e., sum of the ratios of α₁ and α₂ are close to 1), then there is large increase in anode current and the thyristor is said to be in conduction. External circuit conditions can be changed to influence the product of the gains (β₁β₂). Some techniques of achieving this are briefly discussed next.

1.  Increasing applied voltage: On applying a voltage across the anode to cathode terminals of the thyristor (anode being more positive than the cathode), junctions J1 and J3 in Figure 24.26 are forward biased while junction J2 is reverse biased. The thyristor does not conduct any current and is said to be in a blocking state. On increasing the applied voltage, minority carriers in junction J2 (i.e., holes in n1, n2 and electrons in p1, p2) start acquiring more energy and hence start to migrate. In the process, these holes could dislodge more holes. Recombination of the electrons and holes also occur which creates more motion. If the voltage is increased beyond a particular level, the movement of holes and electrons becomes great and junction J2 ceases to exist. The product of the gains of the two transistors in the two-transistor model is said to achieve values close to unity. This method of forcing current to flow through the thyristor is not recommended since junction J2 gets permanently damaged and the thyristor ceases to block forward voltage. Hence this method is a destructive method.

2.  High dv/dt: As explained earlier, junction J2 is the forward blocking junction when a forward voltage is applied across anode to cathode of a thyristor. Any p-n junction behaves like a depletion region when it is reverse biased. Since J2 is reverse biased, this junction behaves like a depletion region. Another way of looking at a depletion region is that the boundary of the depletion region has abundant holes and electrons while the region itself is depleted of charged carriers. This characteristic is similar to that of a capacitor. If the voltage across the junction (J2) changes very abruptly, then there will be rapid movement of charged carriers through the depleted region. If the rate of change of voltage across this junction (J2) exceeds a predetermined value, then the movement of charged carriers through the depleted region is so high that junction J2 is again annihilated. After this event, the thyristor is said to have lost its capability to block forward voltage and even a small amount of forward voltage will result in significant current flow, limited only by the load impedance. This method is destructive too and is hence not recommended.

3.  Temperature: Temperature affects the movement of holes and electrons in any semiconductor device. Increasing the temperature of junction J2 will have a very similar effect. More holes and electrons will begin to move causing more dislodging of electrons and holes from neighboring lattice. If a high temperature is maintained, this could lead to an avalanche breakdown of junction J2 and again render the thyristor useless since it would no longer be able to block forward voltage. Increasing temperature is yet another destructive method of forcing the thyristor to conduct.

4.  Gate current injection: If a positive voltage is applied across the gate to cathode of a thyristor, then junction J3 would be forward biased. Charged carriers will start moving. The movement of charged carriers in junction J3 will attract electrons from n2 region of the thyristor (Figure 24.26). Some of these electrons will flow out of the gate terminal but there would be ample electrons that could start crossing junction J2. Since electrons in p2 region of junction J2 are minority carriers, these can cause rapid recombination and help increase movement of minority carriers in junction J2. By steadily increasing the forward biasing potential of junction J3, the depletion width of junction J2 can be controlled. If a forward biasing voltage is applied across anode to cathode of the thyristor with its gate to cathode favorably biased at the same time, then the thyristor can be made to conduct current. This method achieves conduction by increasing the leakage current in a controlled manner. The gain product in the two-transistor equivalent is made to achieve a value of unity in a controlled manner and the thyristor is said to turn ON. This is the only recommended way of turning ON a thyristor. When the gate-cathode junction is sufficiently forward biased, the current through the thyristor depends on the applied voltage across the anode-cathode and the load impedance. The load impedance and the externally applied anode-cathode voltage should be such that the current through the thyristor is greater than a minimum current known as latching current, I_l. Under such a condition, the thyristor is said to have latched ON. Once it has latched ON, the thyristor remains ON. In other words, even if the forward biasing voltage across the gate-cathode terminals is removed, the thyristor continues to conduct. Junction J2 does not exist during ON condition. The thyristor reverts to its blocking state only when the current through it falls below a minimum threshold value known as holding current, I_h. Typically, holding current is lower than latching current (I_h < I_l). There are two ways of achieving this. They are either (1) increase the load impedance to such a value that the thyristor current falls below I_h or (2) apply reverse biasing voltage across the anode-cathode of the thyristor. An approximate v-i characteristic of a typical thyristor and its symbol are shown in Figure 24.32.

Since the thyristor allows flow of current only in one direction like a diode and the instant at which it is turned ON can be controlled, the device is a key component in building a controlled rectifier unit. The diode in all the circuits discussed so far can be replaced with the thyristor. Because of its controllability, the instant at which the thyristor conducts can be delayed to alter the average and rms output voltages. By doing so, the output voltage and output power from the rectifier can be controlled. Rectifiers that employ thyristors are thus also known as silicon controlled rectifiers or SCR.

A typical single-phase R-L rectifier circuit with one thyristor as the rectifier is shown in Figure 24.33. The figure also shows the relevant circuit waveforms. The greatest difference between this circuit and its diode counterpart is also shown for comparison. Both circuits conduct beyond π radians due to the presence of the inductor L since the average voltage across an inductor is zero. If the value of the circuit components and the input supply voltage are the same in both cases, the duration for which the current flows into the output R-L load depends on the values of R and L. In the case of the diode circuit it does not depend on anything else while in the case of the thyristor circuit, it also depends on the instant the thyristor is given a gate trigger.

From Figure 24.33, it is important to note that the energy stored in the inductor during conduction interval can be controlled in the case of thyristor in such a manner that it reduces the conduction interval and thereby alters (reduces) the output power. Both the diode and the thyristor show reverse recovery phenomenon. The thyristor similar to the diode can block reverse voltage applied across it repeatedly, provided the voltage is less than its breakdown voltage.

FIGURE 24.32  v-i characteristic of a thyristor along with its symbol.

FIGURE 24.33  Comparing a single thyristor rectifier circuit with a single diode rectifier circuit. Note that the thyristor conduction is delayed deliberately to bring out the differences.

24.3.1  Gate Circuit Requirements

The trigger signal should have voltage amplitude greater than the minimum gate trigger voltage of the thyristor being turned ON. It should not be greater than the maximum gate trigger voltage, either. The gate current should likewise be in between the minimum and maximum values specified by the thyristor manufacturer. Low gate current driver circuits can fail to turn ON the thyristor. The thyristor is current controlled switch and so the gate circuit should be able to provide the needed turn ON gate current into the thyristor. Unlike the bipolar transistor, the thyristor is not an amplifier and so the gate current requirement does not absolutely depend on the voltage and current rating of the thyristor. Sufficient gate trigger current will turn ON the thyristor and current will flow from the anode to the cathode, provided the thyristor is favorably biased and the load is such that the current flowing is higher than the latching current of the thyristor. In other words, in single-phase ac to dc rectifier circuits, the gate trigger will turn ON the thyristor only if it occurs during the positive part of the ac cycle (Figure 24.33). Any trigger signal during the negative part of the ac cycle will not turn ON the thyristor and thyristor will remain in blocking state. Keeping the gate signal ON during the negative part of the ac cycle does not typically damage a thyristor.

24.3.2  Single-Phase H-Bridge Rectifier Circuits with Thyristors [1, 2 and 3]

Similar to the diode H-bridge rectifier topology, there exists SCR–based rectifier topologies. Because of their unique ability to be controlled, the output voltage and hence the power can be controlled to desired levels. Since the triggering of the thyristor has to be synchronized with the input sinusoidal voltage in an ac to dc rectifier circuit, soft charging of the filter capacitor can be achieved. In other words, there is no need for employing soft-charge resistor and contactor combination as is required in single-phase and three-phase ac to dc rectifier circuits with dc bus capacitors.

In controlled ac to dc rectifier circuits, it is important to discuss control of resistive, inductive, and resistive–inductive load circuits. DC motor control falls into the resistive–inductive load circuit. DC motors are still an important part of the industry. However, the use of dc motor in industrial application is declining rapidly. Control of dc motors is typically achieved by controlled rectifier circuits employing thyristors. Small motors of less than 3-kW (approximately 5 hp) rating can be controlled by single-phase SCR circuits while larger ratings require three-phase versions. A typical single-phase H-bridge SCR–based circuit for the control of a dc motor is shown in Figure 24.29. Typical output waveforms are shown in Figure 24.34. The current in the load side can be assumed continuous due to the large inductance of the armature of the dc motor.

FIGURE 24.34  Single-phase dc motor control circuit for controlling a separately excited dc motor. R_a indicates equivalent armature resistance and E is the back emf. Typical waveforms are shown in (a) topological representation, (b) discontinuous mode of operation, and (c) continuous mode of operation.

In Figure 24.34a, V_f is the field voltage, which is applied externally and generally is independent of the applied armature voltage. Such a dc motor is known as a separately excited motor. I_a is the armature current while I_f is the field current. By altering the instant of turn ON of the thyristors, the average output voltage can be altered. A dc motor typically generates a back emf that is dependent on speed. In Figure 24.34b, discontinuous mode of operation is depicted. When the trigger instant is delayed appreciably from the start of the sinusoidal supply voltage waveform, the average output voltage reduces, resulting in discontinuous current flow, which is characterized by zero output current durations as seen in Figure 24.34b. During the instant the current goes to zero, the output voltage is simply the back emf, E. When current starts flowing again, the input voltage is fed into the output and so the output has portions of the input voltage.

On advancing the instant of triggering the thyristors, the output current can be made continuous as seen in Figure 24.34c. The output voltage increases and since the thyristors conduct for the entire duration, the input wave shape appears at the output. Since the output voltage can be controlled, the armature current can be effectively controlled. Since the torque produced by a dc motor is directly proportional to the armature current, the torque developed can thus be controlled:

$T=K\phi I_a$

(24.18)

K is the motor constant and depends on the number of armature conductors, number of poles, and type of winding employed in the dc machine. ϕ is flux produced by the field and is proportional to the field current, I_f. Hence, the torque produced by a dc machine can be rewritten as

$T=K\left(K_1{I}_f\right)I_a$

(24.19)

By keeping the field current constant, the torque then becomes directly proportional to the armature current, which is controlled by controlling the output voltage of the ac to dc controlled rectifier. In the circuit shown in Figure 24.34, it is important to note that the current I_a, cannot flow in the opposite direction. Hence, the motor cannot generate negative torque. In order to make the motor run in the opposite direction, the direction of the field has to be changed. Speed control within the base speed can also be accomplished by controlling the armature voltage as follows:

$E=K\phi \omega =K\left(K_1{I}_f\right)\omega$

(24.20)

ω is the speed of the armature in radians/s. The back emf, E is the difference between the output dc voltage of the ac to dc controlled rectifier and the drop across the equivalent armature resistance. Hence, E can be rewritten as

$E=V_a-\left(I_a{R}_a\right);\omega =\frac{V_a-\left(I_a{R}_a\right)}{K{K}_1{I}_f}$

(24.21)

For control of speed above base speed, the field current has to be reduced. Hence, it can be shown that controlling the armature current controls torque and speed below base speed while controlling the field current achieves speed control above base speed. Because of the large inductance of the armature circuit, the current through it can be assumed continuous for practical operating region. The average output voltage of a single-phase ac to dc rectifier circuit for continuous current operation is given by (referring to Figure 24.34c:

$V_O=\frac{1}{\pi }{\displaystyle \underset{\alpha }{\overset{\pi +\alpha }{\int }}\left(\sqrt{2}\star V_{rms}\right)d\left(\omega t\right)=\frac{2\star \sqrt{2}\star V_{rms}\star \cos (\alpha )}{\pi }}$

(24.22)

Equation 24.22 is derived for continuous current condition. By controlling the triggering angle, α, the average value of the output voltage, V_O can be controlled. If armature current control is the main objective (to control output torque), then the controller of Figure 24.34 can be configured with a feedback loop. The measured current can be compared with a set reference and the error can be used to control the triggering angle, α. Since the output voltage and hence the armature current is not directly proportional to α but to cos(α), the previous method will yield a nonlinear (cosinusoidal) relationship between the output voltage and control angle, α. However, the error signal cos(α) instead of α can be chosen to be the control parameter. This would then yield a linear relationship between the output voltage and cos of control angle, α.

It is important to note from the equation for the output average voltage that the output average voltage can become negative if the triggering angle is greater than 90 electrical degrees. This leads us to the topic of regeneration. AC to DC controlled rectifiers employing thyristors and having large inductance on the dc side can be made to operate in the regeneration mode by simply delaying the trigger angle. This is quite beneficial in hoist applications as explained hereafter.

When a load on a hoist needs to be raised, electrical energy is supplied to the motor. The voltage across the motor is positive and the current through the armature is positive. Positive torque is generated and the load is raised. When the load is being brought down, the motor rotates in the opposite direction that results in a negative value of back emf. The current through the thyristors cannot go negative so the motor is still developing positive torque tending to raise the load and prevent it from running away due to the gravitational pull. The negative back emf is supported by advancing the gating angle to be greater than 90 electrical degrees so that the voltage across the armature of the motor is negative but remains slightly more positive than the back emf, the difference causing positive current flow into the motor. The large inductance of the motor helps to maintain the positive direction of current through the armature. From electrical energy flow point of view, the product of current through the motor and the voltage across it is negative meaning that the motor is in regeneration mode.

The kinetic energy due to the motors motion is converted to electrical energy and this produces considerable braking torque. The electrical energy is fed back to the source via the input thyristors. Converting kinetic energy to electrical energy has the desired braking effect and such conversion is known as regenerative braking.

The preceding application describes two-quadrant operation. Cranes and elevators employed in hoist operation are required to operate in all four quadrants (Figure 24.30). Using only one H-bridge rectifier allows two-quadrant operation—quadrants, one and four or quadrants two and three. For achieving four-quadrant operation, two H-bridge rectifiers are needed, as shown in Figure 24.31. The four different quadrants of operation are described next for a crane/hoist operation.

In the first quadrant, the motor develops positive torque and motor runs in the positive direction meaning, speed is positive—product of torque and speed is power and so positive electric power is supplied to the motor from the ac to dc rectifier.

When the crane with a load is racing upward, close to the end of its travel, the ac to dc controlled rectifier is made to stop powering the motor. The rectifier practically is switched off. The inertia of the load moving upward generates a voltage in the form of a back emf. This voltage is fed into a second rectifier bridge arranged in the opposite direction (Figure 24.35). The second bridge is turned ON to let the generated voltage across the upwardly mobile motor to flow into the utility thereby converting the inertial motion to electric power. In the second quadrant, speed remains positive but torque becomes negative, since the current through the motor flows in the opposite direction into the second rectifier bridge arrangement (Figure 24.35). The product of speed and torque is negative meaning that the motor behaves like a generator during this part of the travel.

Third quadrant operation occurs at the beginning of the lowering action. Both torque and speed are negative and so the product of torque and speed is positive. Power is applied to the motor to overcome static friction and allow the rotating parts of the mechanism to move the load downward. In this case, the direction of armature current through the motor is opposite to that in quadrant one and the electrical power needed by the motor is supplied by the second rectifier bridge arrangement (Figure 24.36).

FIGURE 24.35  Four-quadrant operation of a crane or hoist.

FIGURE 24.36  Two rectifier bridge arrangements for four-quadrant operation of dc motor.

The mechanical load and motor arrangement goes into the fourth quadrant of operation for the larger part of the downward motion. This is the duration during which, the motor resists the tendency of the load to accelerate downward by developing positive torque. Since motion is downward, speed is negative and the product of torque and speed is negative. This means the motor behaves like a generator. Due to the downward motion of the motor, the back emf is negative but the current is positive and so from electrical energy flow point of view, the power is negative, meaning that the motor is in regeneration mode.

Since the thyristors cannot conduct in the opposite direction, a new rectifier section arranged in an opposite manner had to be provided to enable the four-quadrant operation needed in cranes and hoists. The method by which unidirectional electrical power was routed to the bidirectional ac utility lines is known as inversion (opposite to rectification). Since no external means of switching OFF the thyristors was employed, the process of inversion is achieved by natural commutation provided by the ac source. Such an inverter is known as line commutated inverter.

24.3.3  Three-Phase Controlled AC to DC Rectifier Systems

The observations made so far for the single-phase controlled ac to dc rectifiers can be easily extended to three-phase versions. An important controlled rectification scheme that was not mentioned in the single-phase case is the semiconverter circuit. In Figure 24.37, if the thyristors Q2 and Q4 are replaced by diodes (D2 and D4), then the circuit of Figure 24.37 is converted into a semiconverter circuit. Such a circuit does not have the potential to provide regeneration capability and hence is of limited use. However, in dual converter applications, especially in three-phase versions, there are a few instances where a semiconverter can be employed to reduce cost. A typical three-phase semiconverter circuit will consist of three thyristors and three diodes arranged in an H-bridge configuration as shown in Figure 24.37.

FIGURE 24.37  A typical three-phase semiconverter.

Three-phase dual converter schemes similar to the single-phase version shown in Figure 24.36 are still employed to operate large steel mills, hoists, and cranes. However, the advent of vector controlled ac drives has drastically changed the electrical landscape of the modern industry. Most dc motor applications are being rapidly replaced by ac motors with field oriented control schemes. DC motor application in railway traction has also seen significant reduction due to the less expensive and more robust ac motors.

However, there are still a few important applications where three-phase controlled rectification (inversion) is the most cost-effective solution. One such application is the regenerative converter module that many inverter-drive manufacturers provide as an optional equipment to customers with overhauling loads. Under normal circumstance, during motoring mode of operation of an ac drive, the regenerative unit does not come into the circuit. However, when the dc bus voltage tends to go higher than a predetermined level due to overhauling of the load, the kinetic energy of the load is converted into electrical energy and is fed back into the ac system via a six-pulse thyristor-based inverter bridge. One such scheme is shown in Figure 24.38.

FIGURE 24.38  Use of six-pulse thyristor bridge in the inverter mode to provide regeneration capability to an existing ac drive system.

24.3.4  Average Output Voltage

In order to evaluate the average value of the output voltage for a three-phase full bridge converter, the process of integrating the output voltage similar to the one in Figure 24.39b has to be undertaken. For the circuit shown in Figure 24.39b, where the diodes are replaced by thyristors, the integration yields the following:

$\begin{array}{l}{V}_O=\frac{3}{\pi }{\displaystyle \underset{\alpha +\left(\pi /3\right)}{\overset{\alpha +\left(2\pi /3\right)}{\int }}\sqrt{2}}{V}_{L-L}\sin \left(\omega t\right)d\left(\omega t\right)\hfill \\ V_O=\frac{3\star \sqrt{2}\star V_{L-L}\star \cos (\alpha )}{\pi }=\frac{3\star \sqrt{2}\star \sqrt{3}\star V_{L-N}\star \cos (\alpha )}{\pi }\hfill \end{array}$

(24.23)

The average output voltage for the circuit in Figure 24.39b with the diodes being replaced by thyristors is only different in the cosine of the triggering angle, α. If the triggering angle is zero, the circuit performs similar to a three-phase diode rectifier and the average output voltages become the same.

24.3.5  Use of Thyristors for Soft Charging DC Bus of Voltage Source Inverters

Though thyristor-based inverters may have been replaced by better controlled and higher speed semiconductor switches, the thyristors are still the work horse in many rectifier applications.

As discussed earlier, variable frequency drives (VFDs) with diode rectifier front end are typically equipped with a resistor-contactor arrangement to limit the inrush current into the dc bus capacitors, thereby providing a means for soft charging the dc bus capacitors. Because of the mechanical nature of the magnetic contactor typically used in VFDs, there exists a concern for reliability. In addition, during a brownout condition, typically the contactor remains closed and when the voltage recovers, the ensuing transient is often large enough to possibly cause unfavorable influence to surrounding components in the VFD. Many researchers and application engineers have thought about this problem and have worked in resolving this dilemma in a cost-effective manner.

There have been suggestions of replacing the magnetic contactor (MC in Figure 24.39a) with a semiconductor switch, as shown in Figure 24.39b. The semiconductor switch shown in Figure 24.39b is typically a thyristor and requires intelligent control. Unfortunately, during steady state operation, it is associated with power loss and reduces the overall efficiency of the VFD. Thyristor controlled semiconverters, similar to the one shown in Figure 24.37 are also effective in soft charging the dc bus of VFDs. The logic used for controlling the three thyristors in Figure 24.37 are also effectively used to eliminate problems during brownout conditions and is perhaps a very effective way for soft charging the dc bus of VFDs. However, the only drawback of the topology shown in Figure 24.37 is the need for a logic controller and additional gate driver circuits that can add cost to the VFD. Yet another technique to soft charge the dc bus capacitor that employs thyristors is discussed in this section. The features of the circuit discussed are as follows:

FIGURE 24.39  Soft-charge circuit configuration, (a) with magnetic contactor (MC) and (b) with thyristor.

•  No mechanical contactors.

•  Should be able to handle brownout conditions in an efficient manner.

•  Autonomous operation (without any control logic) to handle various power supply conditions.

•  Unit should be compact and economical.

24.3.5.1  Thyristor Assist Clamp Circuit [9]

The proposed topology, shown in Figure 24.40, meets most of the desired features. A dc link inductor with a resistor assist circuit is employed to soft charge the dc bus capacitor. The assist resistor also has a series thyristor [9].

24.3.5.2  Principle of Operation

When ac power is applied to the circuit shown in Figure 24.40, an inrush current begins to flow, assuming that the dc bus capacitor has no initial stored voltage. The inrush current is divided into two distinct paths. The first path is through the resistor-thyristor (TH2) combination and the second path is through the dc link inductor, L_dc. The current through the resistor-thyristor path is initially higher and quicker than that through L_dc since the inductor delays the build up of current through it. The dc bus capacitor starts to charge, with the resistor-thyristor combination providing as much charging as possible. The second charging path, through L_dc, creates a resonant circuit. Due to the nature of LC circuit, the voltage across the dc bus capacitor C tends to increase over and above the peak value of the applied input ac voltage. At this time, the thyristor across L_dc, TH1, experiences a forward bias and turns ON. The turning ON of TH1, causes the voltage across the inductor to start falling and eventually turns OFF thyristor TH2 in series with the assist resistor, by reverse biasing it. The inductor voltage linearly ramps to zero and gets clamped by TH1. The voltage across the dc bus capacitor stops increasing and eventually discharges into its discharge resistor to a level dictated by the input voltage condition.

The important aspect of the resistor-assist circuit cannot be overlooked since the charging current flowing through L_dc is reduced due to the parallel resistor assist circuit. This reduces the stored energy in L_dc. It also lowers the saturation current requirement and makes the inductor physically smaller. Due to the LC nature of the circuit, the voltage across the capacitor is still higher than the peak value of the input voltage. The clamping circuit consisting of TH1 assures that the dc bus voltage is clamped to an acceptable value.

FIGURE 24.40  Proposed circuit for soft charging the dc bus capacitor, employing two thyristors.

FIGURE 24.41  (a) Equivalent circuit for interval I; (b) equivalent circuit for interval II.

The operation of Figure 24.40 can be seen to have two distinct intervals of operation. Referring to Figure 24.41a, interval 1 of operation begins when the power is turned ON and the peak line-line voltage is applied to the inductor-resistor-capacitor combination and lasts till the voltage across the dc capacitor, v_C1 goes above the peak input voltage. During interval 1, two current paths exist—one through the bypass resistor and the other through the dc link inductor. At the end of interval 1, current through R_byp is zero since TH2 is reverse biased.

The expression for capacitor current (i_Ldc + i_Rbyp) for zero initial capacitor voltage is

$i_{C1}=\frac{V_{dc\left(pk\right)}}{\sqrt{L_{dc}/C_1}}\sin \left({\omega }_{1}t\right)+\frac{V_{dc\left(pk\right)}}{R_{byp}}{e}^{-t/R_{byp}{C}_1};{\omega }_1=\frac{1}{\sqrt{L_{dc}\star C_1}}$

(24.24)

$v_{C1}=V_{dc\left(pk\right)}\left(1-\cos \left({\omega }_{1}t\right)\right)+V_{dc\left(pk\right)}\left(1-e^{-t/R_{byp}{C}_1}\right)$

(24.25)

$v_{Ldc}=V_{dc\left(pk\right)}-v_{C1}=V_{dc\left(pk\right)}\left(\cos \left({\omega }_{1}t\right)+e^{-t/R_{byp}{C}_1}-1\right)$

(24.26)

FIGURE 24.42  Theoretical waveforms.

Referring to Figure 24.41b, interval II begins when thyristor TH1 starts conducting and clamps the voltage at the capacitor to the rectifier output voltage. Interval II ends when i_Ldc decays to zero (Figure 24.42).

$0=L_{dc}\star \frac{d{i}_{Ldc}}{dt}+i_{Ldc}\star R_{par}$

(24.27)

$i_{Ldc}=\frac{V_{dc\left(pk\right)}}{\sqrt{L_{dc}/C_1}}\star \left(e^{-R_{par}t/L_{dc}}\right)$

(24.28)

$v_{Ldc}=-V_{TH};v_{C1}=V_{dc\left(pk\right)}+\left(V_{TH}\right)$

(24.29)

24.3.6  HVDC Transmission Systems

One area where it is difficult to replace the use of high voltage, high current carrying thyristors is high voltage dc (HVDC) transmission systems. When large amount of power is to be transported over long distances, or under water, it has been found that high-voltage dc transmission is more economical. HVDC systems are in reality back to back rectifier systems. The sending end rectifier system consists typically of 12- or 24-pulse thyristor bridges while the receiving end consists of a similar configuration but in the opposite direction. The receiving end 12- or 24-pulse bridge operates in the inverter mode while the sending end operates in the rectifier mode. 12-pulse configuration is achieved by cascading two 6-pulse bridges in series while 24-pulse configuration needs four 6-pulse bridges cascaded in series. Typical advantages of high-voltage dc transmission over high-voltage ac transmission are listed as follows:

1.  No stability problems due to transmission line length since no reactive power needs to be transmitted.

2.  No limitation of cable lengths for underground cable or submarine cable transmission due to the fact that no charging power compensation need be done.

3.  Ac power systems can be interconnected employing a dc tie without reference to system frequencies, short circuit power, etc.

4.  High-speed control of dc power transmission is possible because the control angle, α, has a relatively short time constant.

5.  Fault isolation between receiving end and sending end can be dynamically achieved due to fast efficient control of the high-voltage dc link.

6.  Employing simple-control logic can change energy flow direction very fast. This can help in meeting peak demands at either the sending or the receiving station.

7.  High reliability of thyristor converter and inverter stations makes this mode of transmission a viable solution for transmission lengths typically over 500 km.

8.  The right-of-way needed for high-voltage dc transmission is much lower than that of ac transmission of the same power capacity.

The advantages of dc transmission over ac transmission should not be misunderstood. DC transmission should not be substituted for ac power transmission. In a power system, it is generally accepted that both ac and dc should be employed to compliment to each other. Integration of the two types of transmission enhances the salient features of each other and helps in realizing a power network that ensures high quality and reliability of power supply. A typical rectifier-inverter system employing a 12-pulse scheme is shown in Figure 24.43.

Typical dc link voltage can be as high as 400–600 kV. Higher voltage systems are also in use. Typical operating power levels are over 1000 MW. There are a few systems transmitting close to 3500 MW of power through two bipolar systems. Most thyristors employed in large HVDC transmission system are liquid cooled to improve their performance.

FIGURE 24.43  Schematic representation of a bipolar HVDC system employing 12-pulse rectification/inversion scheme.

24.3.7  Power System Interaction with three-Phase thyristor AC to DC Rectifier Systems

Similar to the diode rectifiers, the thyristor-based ac to dc rectifier is associated with low order current harmonics. In addition to current harmonics, there is voltage notching phenomenon occurring at the input terminals of an ac to dc thyristor-based rectifier system. The voltage notching is a very serious problem. Since thyristors are generally slower to turn ON and turn OFF compared to power semiconductor diodes, there are nontrivial durations during which an outgoing thyristor and an incoming thyristor remain in conduction thereby creating a short circuit across the power supply phases feeding the corresponding thyristors. Thyristors used in rectifiers are generally known as phase control type thyristors and have typical turn OFF times of 50–100 μs. Thyristors employed in inverter circuits typically are faster and have turn OFF times in the 10–50 μs ranges.

Notching can create major disturbances in sensitive electronic equipment that rely on the zero crossing of the voltage for satisfactory operation. Multiple, pseudo zero crossings of the voltage waveform can occur due to the notching effect of thyristor-based rectifier systems. Notching phenomenon can create large magnitudes of currents to flow into power-factor correcting capacitors, thereby potentially causing permanent damage to them. IEEE 519-1992 in the United States has strict regulations regarding the depth of the notch as well as the duration of the notch. AC line inductors in series with the supply feeding power to the three-phase bridge help to minimize the notching effect on the power system. The theory behind this phenomenon is discussed next.

When an external inductance is added in front of a three-phase ac to dc rectifier employing thyristors, the duration of commutation increases. In other words, the time duration for which the outgoing thyristor remains in conduction along with the incoming thyristor increases. This overlap duration causes the average output voltage to reduce because during this period, the output voltage is composed of two shorted phases and a healthy phase. The extent of reduction in the output voltage depends on the duration of overlap in electrical degrees. The duration of overlap in electrical degrees is commonly represented by μ. The overlap duration is directly proportional to the value of the external inductance used. If no external line inductor is used, then this duration will depend on the existing inductance of the system including the wiring inductance. In order to compute the factors influencing the overlap duration, a simple model can be assumed. Assume that the line comprises inductance L in each phase. Let the dc load current be I_dc and let it be assumed that this current does not change during the overlap interval. The current in the incoming thyristor is zero at start and by the end of the overlap interval it increases to I_dc. Based on this assumption, the relationship between current and voltage can be expressed as

$\begin{array}{l}{v}_{ab}=\sqrt{2}\star V_{L-L}\star \sin \left(\omega t\right)=2\star L\star \left(\frac{di}{dt}\right)\hfill \\ \sqrt{2}\star V_{L-L}\star {\displaystyle \underset{\alpha +\left(\pi /3\right)}{\overset{\alpha +\left(\pi /3\right)+\mu }{\int }}\sin \left(\omega t\right)d\left(t\right)=2\star L\star {\displaystyle \underset{0}{\overset{I_{dc}}{\int }}{d}_i}}\hfill \\ I_{dc}=\frac{\sqrt{2}\star V_{L-L}\star \left(\cos \left(\alpha +\pi /3\right)-\cos \left(\alpha +\pi /3+\mu \right)\right)}{2\omega L}=\frac{\sqrt{2}\star V_{L-L}\star \sin \left(\alpha +\pi /3+\mu /2\right)\star \sin \left(\mu /2\right)}{\omega L}\hfill \end{array}$

(24.30)

For small values of overlap angle μ, sin(μ/2) = μ/2 and sin(α + π/3 + (μ/2)) = sin(α + π/3). Rearranging the previous equation yields

$\mu =\frac{2\omega L\star I_{dc}}{\sqrt{2}\star V_{L-L}\star \sin \left(\alpha +\pi /3\right)}$

(24.31)

From the preceding expression, it is interesting to note the following:

1.  If the inductance L in the form of either external inductance or leakage inductance of transformer or lead length is large, the overlap duration will be large.

2.  If the load current, I_dc is large, the overlap duration will be large.

3.  If the delay angle is small, then the inductance will store more energy and so the duration of overlap will be large. The minimum value of delay angle α is 0° and the maximum value typically is 60°.

The average output voltage will reduce due to the overlap angle as mentioned before. In order to compute the average output voltage with a certain overlap angle, the limits of integration have to be changed. This exercise yields the following:

$\begin{array}{l}{V}_O=\frac{3}{\pi }{\displaystyle \underset{\alpha +\mu +\left(\pi /3\right)}{\overset{\alpha +\mu +\left(2\pi /3\right)}{\int }}\sqrt{2}{V}_{L-L}\sin \left(\omega t\right)d\left(\omega t\right)}\hfill \\ V_O=\frac{3\star \sqrt{2}\star V_{L-L}\star \cos \left(\alpha +\mu \right)}{\pi }=\frac{3\star \sqrt{2}\star \sqrt{3}\star V_{L-N}\star \cos \left(\alpha +\mu \right)}{\pi }\hfill \end{array}$

(24.32)

Thus, it can be seen that the overlap angle has an equivalent effect of advancing the delay angle thereby reducing the average output voltage. From the discussions in the previous paragraphs on notching, it is interesting to note that adding external inductance increases the duration of the overlap and reduces the average value of the output dc voltage. However, when viewed from the ac source side, the notching effect is conspicuously reduced and in some cases not observable. Since all other electrical equipment in the system will be connected to the line side of the ac inductor (in front of a thyristor-based ac to dc rectifier), these equipments will not be affected by the notching phenomenon of thyristors. The external inductance also helps limit the circulating current between the two thyristors during the overlap duration.

24.4  Conclusion

Uncontrolled and controlled rectifier circuits have been discussed in this chapter. An introduction to the theory of diode and thyristor conduction has been presented to explain the important operating characteristics of these devices. Rectifier topologies employing both diodes and thyristors, their relative advantages and disadvantages have been discussed. The use of dual thyristor bridge converter to achieve four-quadrant operation of a dc motor has been discussed. The topic of HVDC transmission has been briefly introduced. Power quality issues relating to diode and thyristor-based rectifier topologies have also been addressed. To probe further into the various topics briefly discussed in this chapter, the reader is encouraged to refer to the references listed hereafter.

References

1.  S. B. Dewan and A. Straughen, Power Semiconductor Circuits, John Wiley & Sons, New York, 1975. ISBN 0-471-21180-X.

2.  R. G. Hoft, Semiconductor Power Electronics, Van Nostrand Reinhold Electrical/Computer Science and Engineering Series, Van Nostrand Reinhold Company, New York, 1986. ISBN 0-442-22543-1.

3.  P. C. Sen, Principles of Electric Machines and Power Electronics, John Wiley & Sons, New York, 1997. ISBN 0-471-02295-0.

4.  M. A. Laughton and M. G. Say (eds.), Electrical Engineer’s Reference Book–14th Edition, Butterworths, London, U.K., 1985. ISBN 0-408-00432-0.

5.  IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, IEEE Std. 519-1992.

6.  M. M. Swamy, Passive harmonic filter systems for variable frequency drives, U.S. Patent 5,444,609. August 1995.

7.  H. Akagi, State of the art of active filters for power conditioning, Key note Speech KB 1, EPE Conference 2005, Dresden, Germany.

8.  M. Swamy, T. J. Kume, and N. Takada, A hybrid 18 pulse rectification scheme for diode front END RECTIFIERS with large DC bus capacitor, IEEE Transactions on Industry Applications, 46(6), 2484–2494, November/December 2011.

9.  M. M. Swamy, T. Kume, and N. Takada, Evaluation of an alternate soft charge circuit for diode front-end variable frequency drives, IEEE Transactions on Industry Applications, 46(5), 1999–2007, September/October 2010.