3. POWER ELECTRONIC CONVERTERS

3.1. Power semiconductor switches Power semiconductor devices are used to control the voltage or current of electrical equipment. The advantage of a switch over continuous controller, like a resistor or a continuous amplifier transistor, is its lower energy losses (Figure 3.1).

Ud

i1

RL

R

ir

i2

Ud

i1

RL

i2 a) b)

current feedback

Figure 3.1. Control of load voltage and current using a) a resistor, b) a switch

By controlling the current of an electrical device (load resistance) RL, the input current from the power source is divided between the controller and the output current i1 = ir + i2. When we reduce the voltage of an electrical device to a half (q = 0.5) from the supply voltage, the power consumed by the controller is equal to the power consumed by the electrical device. Half of the input power detaches in the controller as losses (as heat).

( ) ( ) ( ) 22

222

221 11 iRiRqiiRqiRqiRqP Lrrrreg =−++=−+= . (3.1)

If a controller uses a transistor to control a continuous operation, the power balance is the same. Therefore, continuous controls of power (i.e. control of voltage or current) suit only if the power consumed is low, thus the losses are unimportant. High losses will occur in power appliances if continuous control is used. Therefore, continuous control of power devices must be avoided. Those methods of control is still used in some old types of direct current drives, with the resistors that are connected into the armature circuit of the motor. Nowadays, to achieve high efficiency of the control, the pulsed control of electrical devices with semiconductor switches is used.

The most widely used type of control is the pulse-width modulation (PWM). If the input voltage is constant, then the pulse-width is proportional to the output voltage (Fig 3.2). To achieve a smooth control, switching frequency (commutation frequency) should be relatively high. Fast semiconductor devices are most suitable for use in such switches. According to its operation principle, the direct current converter is called “voltage chopper”.

The switching of an active load off is not a problem, because the current is proportional to the supply voltage and the current through the switch stops immediately after switching off. The switching of circuits that contain reactive components, that store energy, like capacitors or inductances, is more complicated. In that case, the switch should stand high current peaks on switching on the capacitive load or high voltage spike on switch off the inductive load.

31

It should be recognized that ideal active loads do not exist and every real electrical circuit has its capacitances (like isolation capacitance) and inductances (like fringing inductance). The commutation process can be considered as an energy conversion process on which the energy transfers from one component of the electric circuit to another. The current curve in Fig. 3.2 differs on the inductive load iL from the voltage curve.

tp t i U a v e r = t i / ( t i + tp )U

t

iL

Figure 3.2. Pulse-width modulation principle

For example, the energy WL = Li2/2 is stored into inductance when switching on the inductive circuit and the energy WC = Cu2/2 is stored into capacitance when switching on the capacitive circuit. When we break a circuit, these energies divide and disperse as heat on active components. These processes are known as commutation transients (Fig. 3.3). These processes may be oscillating (1) or non-periodical (2) properties, depending on the RLC circuit parameters. On such transients, the rectangular shape is distorted and switching (commutation) losses occur on the converters. The dangers of overvoltages exist because oscillating processes can double voltage during switching processes. Therefore, semiconductor switches are equipped with several protection circuits and damping chains (snubber circuit), the function of which is damping or dividing the switching energy into other components of the circuit.

1

t

2

Figure 3.3. Switching transients and ringing effects

The properties of switching processes and construction of semiconductor switches depend significantly on the supply voltage (direct current voltage or alternating current voltage), load (active, reactive like inductive, capacitive or electromotive force of a generator), phase number of supply and load, type of semiconductor devices as well as on their protection and control circuits. Because of multifarious possibilities, different power and control circuits of semiconductor switches are widespread. The use of common thyristors requires the forced commutation principle. In that case, to close the current through a thyristor can be reduced below the holding current, using special closing circuitry between the anode and the cathode.

32

The closing circuitry contains an energy source (e.g. capacitor), in which the current is directed against the current through the thyristor. This allows a decrease in the sum of currents through the thyristor to zero. An additional energy source is switched to the circuit by help of an additional thyristor. Because of its function this thyristor is called a commutation thyristor (Fig. 3.4).

RL

VDUdUd

UC

i

LLL

VT1

VT2UC

VT1 VT2

RL R

i

+

a) b)

Figure 3.4. Commutation circuits of a thyristor in a direct current circuit

The closing circuit shown in Fig. 3.4,a works as follows: when the main thyristor VT1 is in the opened (conductive) state, then the current flows through the load RL. The capacitor charges through the resistor R and the voltage of the capacitor UC increases up to the supply voltage. To close the main thyristor VT1, the auxiliary thyristor VT2 will be opened, which connects the capacitor C to the negative potential. Voltage on the main thyristor VT1 anode relative to its cathode becomes negative, because the voltage UC cannot decrease immediately to zero. As voltage on the thyristor VT1 turns negative, the thyristor cannot conduct current and it closes (turns off). Load current commutates to the capacitor and it charges again through the load and the thyristor VT2. Voltage on the anode of the thyristor VT1 turns positive again. By that time, properties of the thyristor should be recovered (reverse recovery time). The resistor R should be chosen such that the current through the auxiliary thyristor VT2 remains below the holding current at the end. This allows closing the auxiliary thyristor as well. The disadvantage of such a closing circuit is that the open state time of the thyristor cannot be widely changed because the capacitor must charge during the open state time of the thyristor through high resistance.

Figure 3.4,b shows the closing circuit that is considerably faster and allows a change of switch on time on a large scale. The circuit works as follows: when the auxiliary thyristor VT2 is open, the capacitor C charges up to the voltage UC = Ud. When the capacitor is charged, the auxiliary thyristor VT2 closes (turns off). On the opening of the main thyristor, the capacitor C discharges through the branch VT1-VD-L. Because of the inductance, the current continues in this branch and the capacitor C charges to the inverse polarity voltage relative to the earlier UC = -Ud. To close the main thyristor, the auxiliary thyristor VT2 is opened and the load current commutates to the capacitor C. Voltage on the main thyristor VT1 turns negative and it closes (turns off). Capacitor charges through the load and thyristor VT2 again to the voltage UC = Ud. This process will repeat further.

The required capacitance of the capacitor C

d

dq U

ItC ≥ (3.2)

33

By help of completely controlled semiconductor switches (GTO thyristors or IGBT transistors), control is simplified, but irrespective of the type of a semiconductor device, redirection of the stored energy of reactive components should be solved. Damping circuits of commutation overvoltage On the closing of the thyristor (or diode) a huge current change di/dt occurs that causes the voltage u = −L di/dt. Because such voltage can be quite high, these overvoltages caused by the commutation process are called commutation overvoltages. Overvoltages can be reduced or dampen by RC-circuits (Fig. 3.5).

RVD

C

R VD

C

RV

R

VD

C

V

Figure 3.5. Overvoltage damping circuits of semiconductor switches:

a) RC-circuit, b) RC-circuit with a varistor, c) RCD-circuit Serial or parallel connection Serial connection of semiconductor switches is used if, according to their producer’s technical specifications, single switches do not afford the required voltage. Parallel connection is used if the current required from the converter is higher than the current allowed by the producer’s technical specifications of the semiconductor switch. If single switches do not allow one to design the required converter, these possibilities are used.

An equal distribution of switch voltages is the biggest problem in serial connection in the closed (turned off) state and during the commutation processes. For that reason, voltages should be equalized in the static and dynamic operation modes. By help of resistors in parallel to switches can equalize voltages of the closed or turned off switches. During commutation, RC circuits that limit the voltage fronts on the power semiconductors can equalize voltages. On the parallel connection of power semiconductors, the power semiconductors with equal forward parameters should be chosen.

R

Rr

C Figure 3.6. Equalization of power semiconductor voltages on serial connection

34

Serial and parallel connection problems of power thyristors are generally the same as those with serial or parallel connection of power diodes. In addition, it is necessary to achieve simultaneous switching (opening or closing) of several thyristors. A single thyristor cannot stand the voltage or current of the whole circuit. On serial connection, the calculated reverse voltage on a single thyristor should be reduced approximately by 10 % (additionally). On the parallel connection, the calculated current through a single thyristor should be reduced by 20 to 30 %.

3.2. Network synchronized controllable rectifiers and inverters The sinusoidal alternating current is converted to the pulsed direct current, using a rectifier. Rectifiers can be controlled or uncontrolled. An uncontrolled rectifier consists of diodes; a controlled rectifier consists of controlled semiconductor devices, like thyristors or transistors. Partially controlled rectifiers are used, in which some of the switches are controllable (thyristors) and others are uncontrollable (diodes). Many basic converters, incl. rectifiers and inverters, are standardized and they have standardized symbols, e.g., M1 for a half-period rectifier.

Changing the turn-on moment, i.e. the switching angle, controls the output voltage of the phase-controlled rectifiers. These converters are called network synchronized (online) phase controlled inverters and rectifiers. In the alternating current supply, the thyristor can open (switch on) only on the existing positive anode voltage that occurs on the positive half wave of the alternating voltage. A thyristor closes (turns off) when the current is decreased below the holding current. In the alternating current network, this occurs on the negative voltage half wave when the current through the thyristor decreases to zero. It should be mentioned that the control angle is measured in the sinusoidal waveform form, the point when the positive forward voltage (anode voltage) appears on this thyristor. In single-phase rectifiers, this point is the zero voltage point of the sinusoidal voltage. In three phase rectifiers, the phase control angle base point and range depend on the rectifier circuit. The current waveform and therefore the closing point of the thyristor depend on the properties of the load. With an ideal active load, the voltage waveform matches the current waveform. Reactive components, like inductance, causes a phase shift. In the circuit with a thyristor switch, the current waveform is distorted and the zero current point appears later than the zero voltage point.

A single-phase half period rectifier consists only of one semiconductor diode or transistor (Fig. 3.7). This is rarely used in practice, because its output voltage ripple (pulsation) is very high (Fig. 3.8). The mean value of the rectified voltage ud on the active load depends on the

control angle α, expressed by the equation ( α )π

cos122

+= sd

UU . (3.3)

α

Rd

Ld

udup

isip

us

Figure 3.7. Circuit diagram of a single-phase half-period rectifier

35

Figure 3.8. Current and voltage diagrams of the controlled half-period rectifier M1 on the active load (Ld = 0) with the control angle α = 45°

With the inductive load, the thyristor remains open on the negative anode voltage until the current through the thyristor decreases to zero. Thus, the output voltage can contain pulses from negative half waves of the voltage. According to its construction, a single-phase mid-point rectifier (M2) is a parallel connection of two half-period rectifiers M1 (Fig. 3.9), the input voltages of which are in the inverse phase. The output voltage pulses at double frequency of its input voltage. A controlled M2-type circuit can operate as a controlled rectifier or as a network-synchronized inverter.

α

α

Rd

Ld

up

is1

ip

ud

us1

is2

us2

E

Figure 3.9. Single-phase mid-point rectifier (M2)

The mean value of the rectified output voltage ud on the active load depends of the control angle α, expressed by the equation

( α )π

cos12

+= sd

UU . (3.4)

On the inductive load, the mean value of the rectified output voltage depends on the properties of the load current. The converter and load can work in the discontinuous current operation or continuous current operation. On the discontinuous current operation, the voltage and current waveform consist of separate pulses the length of which depends on the

36

inductance of the load circuit. On the continuous current operation, the output current is smoothed by load circuit inductance such that the output current becomes continuous (direct). The mean value of the output voltage on the active and inductive load is given by the previous equation (3.4). The properties of the output voltage and current depend on the back electromotive source located in the load circuit, like the back electromotive force of the rotating motor. A three-phase mid-point rectifier (M3) is a parallel connection of three single-phase mid-point rectifiers (Fig. 3.10) supplied from separate phases of the three-phase supply network. The phases of the three-phase system are shifted by 120° degrees to each other.

α

up

ip1 is1

Rd

Ld

ud

us1

ip3

ip2α

αus3

us2is2

is3

E

VT1

VT2

VT3

Figure 3.10 Three-phase mid-point rectifier (M3)

Figure 3.11. Voltage and current waveforms of the three-phase mid-point rectifier M3 on the inductive

load when the control angle α = 45º and commutation angle μ = 15º On the inductive load, the current continues through the thyristor after the voltage on the thyristor has changed its sign. For that reason the thyristor does not close (turn off) at the zero-voltage instant (time point), but remains open after that. Thyristor T1 (Fig. 3.10, 3.11) remains open after the next thyristor T2 is opened. Current transitions from one thyristor to another are called commutation processes. Because the thyristors in two phases are simultaneously open, in principle, it is the short circuit of the two phases and the output is the arithmetic mean of two-phase voltages. The lengths of the commutation process depend on the circuit inductance and the amount of current. This process causes the reduction the mean value of rectifier’s output voltage. Some important calculation formulas of technical

37

specifications of the three phase mid-point rectifier follow. Mean and root mean square (RMS) value of the current

3d

VkeskI

I = ; 3d

sVefI

II == . (3.5)

The maximum value of the reverse voltage on the switch in the closed (turned off) state is equal to the line voltage amplitude. The reverse voltage on the diode can be calculated from the rectifier output voltage

diVvp UU3

2 π= , (3.6)

where Udi is the mean value of the output voltage of the diode rectifier or thyristor rectifier if the control angle is zero (α = 0). The secondary voltage of the supply transformer

dis UU63

2π= . (3.7)

The primary voltage and primary current of the ideal supply transformer

disp UwwUU63

2π== ;

wI

I dp 3

2= . (3.8)

The secondary power of the supply transformer

ddid

dis IUI

US 48,1363

23 ≈=π . (3.9)

Apparent power of the primary winding of the supply transformer

ddid

dip IUwI

UwS 21.12

6323 ≈=π . (3.10)

The nominal power of the transformer is the arithmetic mean of the secondary and primary power. The power factor of M3 rectifier is

38

83,021.11cos ===

p

ddi

SIU

ϕ . (3.11)

A single-phase bridge rectifier (B2) can be considered as a series connection of two single-phase mid-point rectifiers (Fig. 3.12), where two semiconductor switches are in a common cathode connection and two in a common anode connection.

Rd

Ld

ud

α

E

α

α α

up

is ip

us

Figure 3.12. Single-phase bridge rectifier (B2)

Figure 3.13. Voltage and current waveforms of the single-phase bridge rectifier B2 on ideal current

smoothing, control angle α = 30° and commutation angle μ = 15°

The reverse voltage on the switch of the single-phase bridge rectifier is twice lower than with M2 rectifier, because the switches work in pair wise series. The mean and root mean square (RMS) of the switch current

2d

VkeskI

I = ; 2d

VefI

I = . (3.12)

The power of the transformer

39

( απ

cos12

11.1 +⋅⋅== sddisp

UIUSS ) . (3.13)

The power factor of the B2 rectifier

9.011.11cos ===

p

ddi

SIU

ϕ . (3.14)

A three-phase bridge rectifier (B6) can be considered a series connection of two M3 mid-point rectifiers, where three semiconductor switches are in a common cathode connection and three in a common anode connection. Thus, the output voltage of the B6 rectifier is twice greater than the output voltage of the mid-point rectifier M3. The output voltage ripple is less than on the M3 rectifier, because the output voltage of a B6 rectifier consists of 6 pulses per the input voltage period (p = 6). The switching order of semiconductor switches in Fig. 3.14 is V1, V6, V3, V2, V5, V4. At least two switches are simultaneously in the open state. On high load inductance, the forward current continues on the negative anode voltage and the closing of the switch is delayed. Because the previously open switches are not closed (turned off) when the next switches open, it is possible that 3 or even 4 switches are open during the commutation process. This means that there is more that one open switch in the cathode or anode group and the current is re-switched from one phase to another.

up

ip1 is1

us1

ip3

ip2

us3

us2is2

is3

α

Rd

Ld

ud

αα

E

α

αα

V2

V1

V6V4

V5V3

Figure 3.14 Three-phase bridge rectifier (B6)

The reverse voltage of the switch in the three-phase bridge rectifier B6 is two times lower than on the mid-point rectifier M3, because the switches work in pair-wise series. The mean and root mean square value of the switch current

3d

VkeskI

I = ; 3d

sVefI

II == . (3.15)

The nominal power of the transformer

40

ddisp IUSS 05.1== (3.16) The power factor of the B6 rectifier

95.005.11cos ===

p

ddi

SIU

ϕ (3.17)

Three-phase bridge rectifiers are predominant because of their good technical properties (low ripple, high power factor). Nowadays thyristor rectifiers are used on very powerful direct current drives. The uncontrolled diode rectifiers are used in smaller drives where voltage is controlled by separate pulse-width modulation controlled converters. Uncontrolled diode rectifiers are used too in frequency converters with direct current intermediate circuit. The advantages of the diode rectifiers are their simple construction and low price, but disadvantages are that they do not allow regenerating energy back to the alternating current network (e.g., on the generator operation of the electric drive) and their input current is distorted because of the diode commutation processes. The controlled rectifiers allow regenerating energy back to the network on the suitable control angle. It should be mentioned that the three-phase bridge circuit is used as the main circuit of the inverter with different commutation elements and switches (thyristors, transistors). The bridge circuit is very widely used in power electronics as a multi-functional converter circuit that can be used for rectification of the alternating current or for inverting (alternating) of the direct current.

3.3. Alternating voltage controllers Alternating voltage controller allows changing of the root mean square of the alternating current voltage using semiconductor switches. To control the alternating current, the bi-directional semiconductors switches (TRIAC) or anti-parallel connection of unidirectional semiconductor switches (SCR) can be used. Single-phase alternating voltage controllers are widely used to control the drive speed in household appliances like an electric drill (bit brace), a washing machine, a vacuum cleaner etc. Alternating voltage controllers are also used in lighting control. A single-phase alternating voltage controller (Fig. 3.15,a) consists of two thyristors in anti-parallel connection. The voltage of the load is changeable by controlling the opening (turn-on) time of the thyristors using the phase control principle. The pulse-width modulation principle can be used in the alternating current controller if its switches have turn-off (closing) capability. A three-phase alternating voltage controller (Fig. 3.15,b) consists of three single-phase alternating voltage controllers. Of all of the alternating voltage controller circuits, the most widely used is W3C controller. When the neutral of the star-connected load is connected to the neutral connector of source N, then the control characteristics of the three-phase alternating current controller are identical to the control characteristics of the single-phase controller. When there is no connection to the neutral connector N, thyristors can only switch pair-wise and this will deteriorate the control properties.

41

The main applications of three-phase voltage controllers are contactless switches (like semiconductor contactors) and soft starters of asynchronous motors. The main advantage of the contactless semiconductor switch over a common contactor is the capability of high switching frequency and the spark free (arc free) commutation process. The latter is extremely important in the electrical equipment installed into a flammable environment.

R

L

~U N

α

α

L

i2

N

α

R

L

~3 U1

α

L1

i21

R

L

α

L2

i22

R

L

α

L3

i23

α α

a b

Figure 3.15. Alternating current controllers: a) single-phase controller, b) three-phase controller

42

3.4. Direct current converters and controllers Direct current controllers are classified according to the polarity (sign) and properties of the output current or voltage. According to the figure of their volt-ampere-characteristic, these converters are one-, two- or four-quadrant converters. This means that their volt-ampere characteristics cover one, two or four quadrants on the U-I plane.

A converter with a unidirectional current and one voltage polarity called a single quadrant pulse-width converter allows controlling the output voltage below the input supply voltage. Therefore the converter is called a step-down converter or a buck converter. The buck converter (Fig. 3.16) is used to control and supply a unidirectional rotating direct current machine. On the equivalent circuit, the direct current motor can be mapped as a series connection of active resistance and inductance RL-LL and source back electromotive force EL.

RL

EL

PL

C

LL

Ud1 VD

id2id1

Ud2

Circuit 1

Circuit 2

Figure 3.16. One-quadrant step-down (buck) DC pulse-width converter together with supply and load circuits (e.g. motor)

One-quadrant pulse-width converter consists of a semiconductor switch PL and freewheeling diode VD. The semiconductor switch PL must be a completely controllable switch – a transistor, a GTO thyristor or a SCR thyristor with closing circuits. For simplification, the resistance of the switch in the open (turned on) state can be considered as zero and the resistance in closed (turned off) state as infinite. For simplification, the diode resistance on the forward current is considered as zero and infinite on the reverse current. For simplification, the state change on the switching process can be considered as immediate. Both the supply and load circuit consist of active-inductive resistance and the sources of electromotive forces. Usually, the LC-filter is connected into the switch circuit between the supply and the load, which decreases the influences of the high frequency ripple to the supply circuit (supply network). The semiconductor switch is controlled using the pulse-width modulation principle (p. 3.1).

If the switch PL is switched on and the electromotive force of supply source exceeds the back electromotive force of the load, then there will be positive current through the load (branch, path 1) id2 = id1, because the diode VD has reverse voltage and it will not conduct current. The voltage and the active-inductive resistance of the load determine the rise of the current. The current through the switch PL breaks when the circuit is switched off. The current through the load that contains inductance cannot decrease to zero immediately, because the energy stored into the inductance does not disappear and it must be converted (transferred). Load current

43

switches over to the freewheeling diode circuit (branch, path 2) and the energy stored in the inductance is converted to heat in the load active resistance. If the current through path (branch) 2 attenuates to zero before the switch is turned on again, then discontinuous current operation will occur in the circuit. The boundary (edge, border) between the continuous and discontinuous operation depends on the parameters of supply and load circuits and relative duty cycle of the switch. The output characteristic of the step-down converter (buck-converter) depends on the relative pulse length q (Fig. 3.17.). When the load current decreases, the converter goes from continuous into discontinuous operation and the voltage starts to increase abruptly, because when the current stops and the diode closes (turns off), then the voltage of the secondary circuit depends on the back electromotive force caused by the rotation of the motor.

Id

Ud

0

Discontinuous current limit

q = 0,1

q = 0,3

q = 0,5

q = 0,7

Figure 3.17. Output characteristics of a step-down DC converter

A step-up pulse-width converter (boost converter) allows gaining a higher voltage on the output than the supply voltage. Such a converter is used in active filters and in compensators of reactive power. The circuit diagram of a step-up converter is shown in Fig. 3.18.

RL

EL

PL C

LL

Ud1

VDid2id1

Ud2

C

L

Circuit 1

Circuit 2

Figure 3.18. Step-up (boost) DC converter

If the semiconductor switch PL conducts current (path, branch 1), then part of the supply energy is stored into the magnetic field of the inductance L. When the semiconductor switch turns off and breaks the circuit, then the current through the inductance commutates through the diode VD, load and capacitor C (branch, path 2) and the stored magnetic field energy of the inductance WL= Li2/2 is transferred and converted to the electric field energy of the capacitor WC = Cu2/2. The output voltage of the converter depends on the relative duty cycle of the semiconductor switch. The output voltage is equal to the input voltage if the switch PL

44

is continuously switched off (does not conduct current). Switching of the PL allows an increase in the voltage of the output capacitor by help of additional energy from the inductance. When the switch PL is turned on, the current through the inductance increases. When the switch is turned off, the capacitor charging current is higher and the voltage will increase.

The required inductance and capacitance is

( )min2

22

21

12 2 dad

ddad I

TUU

UUL −= ; 2

2

max2

ad

d

UIT

CΔ

≥ (3.18)

Current Id2 should not be lower than the minimal current

( )L

TUU

UUIad

ddadd 22

2

21

12min2 −= (3.19)

If the step-down (buck) converter is connected series to the step-up (boost) converter, then it allows an increase and a decrease in the input voltage. Such a direct current converter is called a buck-boost converter. One of such multifunctional direct current converters is the voltage-inverting converter called a Cuk converter, by its inventor.

3.5. Direct current converters used in electric drives Converters mentioned above can be used only in a drive with single directional rotating motor operation. To regenerate energy on the drive braking, it is necessary to change the current direction in a semiconductor switch. The two-quadrant pulse-width converter with a variable current direction (Fig. 3.19) can be used for that purpose.

RL

EL

PL2

LL

Ud1

id2id1

Ud2

PL1

D1

D2

Figure 3.19. Two-quadrant variable current direction DC converter

A two-quadrant converter consists of two separate converters: step-down converter PL2 and D2 and step-up converter PL1 and D1. The step-down converter works in the motor operation. Switch PL1 is continuously switched off (does not conduct current). Diode D1 has reverse voltage and it is closed (turned off) too. The step-up (boost) converter (PL1 and D1) functions in the generator operation and allows redirecting energy back to the supply source.

A two-quadrant converter with variable voltage polarity is shown in the circuit diagram 3.20. Semiconductor switches PL1 and PL2 are switched simultaneously on and off. The current through the motor is unidirectional in this example. When the direction of the machine changes, the sign of the electromotive force and the voltage polarity on the machine terminals is inverted too, but the direction of the current remains unchanged.

45

RL EL

PL2

LL

Ud1

id2

id1

Ud2

PL1

D1

D2

Figure 3.20. Two-quadrant variable output voltage polarity DC converter

A four-quadrant pulse-width converter is the converter that allows variable current direction and controlled output voltage with variable polarity. In principle, it combines two two-quadrant direct current converters (Fig. 3.21). The four-quadrant converter is called also a reversible direct current converter. It is used in electric drives with variable rotation direction (reversible electric drives). In the motor operation, the electromotive force is lower than the voltage of the supply source EL < Ud. The converter voltage and motor speed are controlled with semiconductor switches PL1 and PL2. Switches PL3 and PL4 are continuously switched off. When the switches PL1 and PL2 are turned on, the current through the motor is positive and increases. When one of them is switched off, the current continues through diode D1 or D2 and decreases. To change the rotation direction, it is necessary to change the voltage polarity and current direction. This is done by switching (turning) off switches PL1 and PL2, and by switching (turning) on switches PL3 and PL4.

RL EL

PL4

LL

Ud1

id2

id1

Ud2

PL3

D3

D4

PL1

PL2D1

D2

Figure 3.21. Four-quadrant DC converter

In generator operation (operating as a brake), voltage polarity remains the same, but current direction is changed as compared to the motor operation. According to the load voltage polarity shown in Fig. 3.21, diodes D3 and D4 will open and the direction of currents id1 and id2 is reversed as compared to the arrows shown in Fig. 3.21. The operation of the four-quadrant converter with only two semiconductor switches working (other two are switched off) is called a uni-polarity operation. The four-quadrant converter can be used in operations where semiconductor switches are switched pair-wise (PL1, PL2) and (PL3, PL4). In that case, the alternating square-wave voltage (bipolar voltage) will be formed at the output the mean value of which can be controlled by the relative duty cycle of the semiconductor switches. On equal relation between the positive and negative half wave, the mean value of the voltage is zero. This control method is widely used in direct current positioning servo drives.

46

3.6. Inverters An inverter converts direct current voltage to alternating voltage and direct current to alternating current. Inverters are classified as voltage or current inverters. The supply source of the voltage source inverter is the voltage source with low internal resistance. Its feature is commonly a capacitor with a high capacity connected parallel to the supply source that keeps the voltage constant. The output current of the voltage inverter is shaped according to (depending on) the voltage value and the load resistance. The supply source of the current source inverter is the direct current source with constant current. Its feature is the high inductance connected series to the supply source, which keeps the current constant. Current is fed to the output via semiconductor switches. The output voltage of the current source inverter is shaped according to (depending on) the voltage drop on the load caused by the output current.

The circuit diagram of the inverter with two symmetrical supply sources and two semiconductor switches (half-bridge) is shown in Fig. 3.22. Note that it is possible to use an artificial middle point instead of a symmetrical double voltage source (Fig. 3.22, b). Such a circuit is a voltage divider which consists of two series-connected capacitors and resistors. The offline inverter with a semiconductor switch is shown in Fig. 3.23.

RL

PL1

LL

Ud /2 +

Ud2

PL2

0

Ud /2 +

Controlsignal

a)

RL

PL1

LLUd +

Ud2

PL2

0

Control signal

b)

Figure 3.22. Inverter circuit diagrams: a) with two symmetrical supply sources,

b) with a voltage divider (artificial middle point)

RL

PL1

LL

Ud /2 +

Ud2

D2PL2

0

D1

Ud /2 +

Figure 3.23. Circuit diagram of an offline half-bridge inverter with

power thyristors and freewheeling diodes The inverters are controlled using the block or pulse control principle. On the block-control principle, one opening (turn-on) and closing (turn-off) of the semiconductor switch forms the positive or negative half period of the voltage. Thus, the rectangular voltage blocks are formed at the output of the inverter. The sinusoidal output voltage cannot be achieved using the block control principle. The output voltage diagram of the voltage inverter that is using

47

the block control principle is a piecewise exponential curve, which significantly differs from the sinusoidal curve. The circuit diagram of a simple block-controlled inverter is shown in Figure 3.23. Semiconductor switches PL1 and PL2 are switched after each other. Both switches should not be simultaneously on, because this is a short circuit condition. Special dead-time interlocking controls are used to avoid this condition (similar switching blockages are used on contacts of mechanical switches as well). When the pulse control is used, the switches are turned on several times during a half period of the output voltage. The duty cycle is then changed according to the required shape of the output voltage, and this means that the output voltage is formed using the pulse-width modulation principle. If the pulse-width modulation is done according to the sinusoidal wave, the output of the converter has pulsed voltage whose mean value varies according to the sinusoidal wave. The switching frequency used on the pulse control is significantly (ten times or more) higher than on the block control. A single-phase bridge inverter circuit shown in Fig. 3.24 is often used in practice for the single-phase alternating voltage supply. The magnitude of the output voltage is double (two times higher) of the half-bridge inverter shown in Fig. 3.23. This circuit does not require a double supply source with a middle point.

UL

RLLL

PL1

D2PL2

D1 PL3

D4PL4

D3 Ud /2 +

0

Ud /2 +

Figure 3.24. Offline inverter based on the single-phase bridge circuit

The single-phase bridge inverter can be controlled by help of the block or pulse control principle. With the block control, the bridge branches are switched such that their output voltages are shifted to each other by the angle β. If there is no shift angle β = 0, then the voltage is in the same phase and the output voltage of the converter is zero. If the phase angle between these two branches is β = π, then the voltages are in the opposite phase and the output voltage is maximal UL = Ud. Thus, the output voltage depends on the phase angle β. The voltage and current waveforms of the single-phase bridge inverter on the block control, inductive load and maximum output voltage (β =180°) are shown in Fig. 3.25. The root-mean square (RMS) of the load voltage is

πβω

π

β

ddL UtdUU == ∫0

2221 (3.20)

Because the shape of the output voltage differs significantly from the sinusoidal, besides the main harmonic, the voltage contains higher harmonic components. The amount of the main harmonic is relatively high (80...90 %) in the range of angle β values π/2 < β < π. The block

48

control is well applicable in this control range and allows controlling the frequency and RMS of the output voltage main harmonic.

If the pulse control is used, then the voltages of both branches are controlled using the pulse-width modulation principle. When the modulation is done according to the sinusoidal curve, the output of the converter is the pulsed voltage whose mean value varies according to the sinusoidal curve. The pulse control allows a very flexible control of the output voltage, frequency and the angle β between the branch (phase) voltages. The circuit shown in Fig. 3.24 can be used for control of the two-phase asynchronous motor. In that case, the phase voltages should be shifted by β = 90° and the middle point of the motor windings has to be connected to the middle point of the symmetrical supply source (or to its artificial middle point).

0

u1

tπ

2π

3π

4πi1

Figure 3.25. Waveforms of the output voltage and current on the block controlled inverter

A three-phase voltage inverter is shown in Fig. 3.26. This bridge-type offline voltage-inverter can be used for supplying a three-phase electrical device with the controlled frequency and voltage amplitude. Such a circuit is mainly used for the frequency control of alternating current drives and it is part of a power circuit in a frequency converter. On symmetrical phase voltages, the phases are shifted by 120 degrees to each other and shapes and amplitude of voltage and current curves in different phases are similar.

Like above with converter circuits described, the three-phase inverter allows us to apply the block and pulse control principle. Because of a wide use of the frequency control of electric drives and the operation principle of three-phase electrical machines (the symmetrical three-phase supply voltage causes the rotating magnetic field in the space-symmetrical stator winding system), the vector control principle is widely used. In principle, this means that the aim of the inverter control is not the symmetrical phase voltage generation, but the generation of such a voltage system the voltage complex-vector of which rotates in a complex plane. That inverter control principle is called the voltage vector control. The three-phase symmetrical system of sinusoidal voltages the phases of which are shifted to each other by 120° (Fig. 3.27) ensures a smooth rotating of the voltage vector. The same result can be achieved in two ways.

a) The symmetrically shifted voltages with the same shape and equal amplitude are generated in three phases. These voltages are used to supply the electrical machine.

b) Such switching order of semiconductor switches is chosen that causes the rotating magnetic field in the electrical machine.

The latter (b) method is called the voltage vector control (Figure 3.28). Choosing suitable semiconductor switches and their control on the pulse-width modulation (PWM) principle allows us to create a suitable voltage vector. By changing the semiconductor switches and pulse-width, the voltage vector can be rotated in the required way in a complex plane.

Compared to the pulse control, the voltage vector control allows a higher phase voltage and thus a higher output power of the converter. The output voltage amplitude in the pulse control

49

is Ud /2. With the voltage vector control, the amplitude is equal to the inner-circle radius of the hexagon 3/dU . Thus the maximal voltage on the voltage vector control is 15.5 % higher than with the pulse control. Note that with the three-phase bridge rectifier, the result of 220V phase voltage rectification is 540 V direct current voltage Ud = 540 V. If the inverter works in the six-pulse (tact) block control and its output voltage is stepped, then the amplitude of its maximal output voltage is U Um d= ⋅2 / 3 = 360 V. The mean value of the output voltage then is 240 V, which is 18 % higher than the mean value of the network voltage (198 V). Thus, the voltage converter will have some kind of voltage reserve in that case and the motor allows higher output torque at a higher frequency. However, this is achieved through abandoning the sinusoidal output. Note that this will cause higher losses caused by higher harmonic components.

ZL

UW

ud

is

us

ZLZL

UU

UV

VT1 VT2 VT3

VT4 VT5 VT6

Figure 3.26. Three-phase offline voltage inverter

0

UU

t

π

2π

a)

tπ 2π

b)

UU

tπ 2π

UV

tπ 2π

UW

0

UV

t

π

2π

0

UW

t

π

2π

Figure 3.27. Output voltages of a six-pulse three-phase inverter with block-control: a) by two simultaneously open switches, b) by three simultaneously open switches

50

1

23

4

56 1.15 U

a) b)

5 6

5 6

56

5

Figure 3.28. Operation of the inverter with the voltage vector control:

a) state polygon of the vector, b) control of the vector

Current source inverters can be used for such electrical equipment (electric-arc furnace, induction heating etc.) that needs the control of the current value (not voltage value). As compared to voltage inverters, they are not so widely used, because the voltage inverter can be used too as a current source with appropriate current feedback. When using common thyristors (SCR), current source inverters have some advantages over voltage source inverters because of simpler commutation (switching) of the thyristors. Today these advantages are not so important because well controllable switches (IGBT, etc.) are available. Resonant inverters consist of a switching (commutation) circuit and LC resonant circuit that forms the alternating voltage for the load. The parallel and series resonant circuits or their combinations as mixed resonant circuits are used in resonant inverters. Semiconductor switches are commutated in the way that the LC-resonant circuit can work close to its resonant frequency. Thus, the natural frequency of the resonant circuit is close to the commutation frequency of the switches. On thyristor switches, thyristors can be closed by natural commutation of the output voltage as in network-synchronized (online) inverters. As different from online inverters, the frequency of the output voltage is fixed by the natural frequency of the resonant circuit. The frequency of the resonant converters cannot be changed by the reference signal of the control system. The main application of resonant converters is electro-thermal processing, where these converters are used for the supply of heating equipment. These converters suit for microwave furnaces and ultrasound equipment where high frequency supply sources are needed without control. When the rectifier is switched to the output of the resonant converter, it is a resonant converter of the direct current voltage.

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3.7. Frequency converters Frequency converters can be divided to frequency converters with intermediate direct current link and direct frequency converters. A frequency converter with intermediate direct current link consists of a rectifier, a smoothing filter and an offline (autonomous) inverter. Alternating current voltage is rectified and inverted (alternated) to alternating voltage with variable magnitude and frequency. Changing the voltage and frequency allows us to control the rotating speed of three-phase asynchronous motors in a wide range, starting from zero up to a several nominal speeds of the motor (if mechanical properties of the motor allow it). A simplified block diagram (structure, circuit diagram) is given in Fig. 3.29.

Rectifier Filter Inverter

3~ U1

f1 3~ U2

f2

Figure 3.29. Power circuit diagram of a frequency converter containing

an uncontrolled diode rectifier and a transistor inverter

Its rectifier is commonly a three-phase uncontrolled (diode) bridge. Fully or partially controlled network synchronized rectifiers (with thyristors or transistors) are sometimes used. These allow regenerating energy back to the supply network. Several types of DC intermediate circuits are used. DC intermediate circuits consist of a smoothing low-pass filter or only a big inductor, which together with a rectifier form a constant current source. Intermediate circuits with low-pass filters are used together with voltage source inverters. Large inductor based intermediate circuits are used together with current source inverters. The intermediate circuit can contain a converter that varies its voltage (commonly reduces) and improves the power factor of the converter.

The intermediate circuit of an electric drive usually contains a braking resistor, which is switched on if fast stopping of a motor is needed. The braking resistance is needed for dispersal of the braking energy of the motor to avoid an increase in the DC intermediate circuit voltage. Note that if the rectifier is not capable of feeding the energy back to the network, the voltage on the intermediate circuit capacitor will exceed the allowed limit.

An inverter (alternator) converts the input direct current voltage to the alternating voltage at a required frequency. The inverter allows controlling the root mean square of an output voltage too. Inverters use the pulse-width modulation, pulse-magnitude modulation, voltage vector modulation or current vector modulation for output voltage modulation. When the pulse-magnitude modulation principle is used, the output voltage of the inverter is controlled by a controlled rectifier, which varies the DC intermediate circuit voltage. In that case, the duty cycle of the inverter is not controlled and kept on the value that conforms to the maximal output voltage: q = sinω t.

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Direct frequency converters do not contain energy storage in the intermediate circuit and their frequency of the input alternating voltage is directly converted to the output voltage. Their efficiency is higher, which is very important in high power applications. The main direct frequency converters are double pulse-width modulation frequency-converters, cycloconverters and matrix frequency converters. A double PWM converter consists a pulse-width modulation controlled rectifier and inverter (Fig. 3.30). Such a frequency converter allows flexible bi-directional transmission of energy from the network to the electric motor and from the motor (in the generator mode) back to the electrical power network. The circuit diagram of the pulse-width modulation rectifier is similar to an offline (autonomous) inverter, but it operates as a network synchronized converter. The low-frequency ripple of the output voltage of such rectifiers is low, because minimal filtering is needed and there is no need for energy storage although the DC intermediate circuit exists. These converters could become prospective and beneficial in high power applications and they will compete with cycloconverters. Compared to the cycloconverters, the output frequency of double PWM frequency converters is controllable in a wide range below and above the supply frequency. Its advantage is a simple energy redirection by using the symmetrical circuit.

Rectifier Filter Inverter 3~ U

f1

3~ U f2

21

Figure 3.30. Power circuit diagram of the pulse-width frequency converter with

a transistor rectifier and inverter

Cycloconverters are direct frequency converters that are directly synchronized to supply networks and use power thyristors as semiconductor switches. Note that other direct frequency converters use fully controllable semiconductor switches (turn-off capable thyristors and power transistors). Cycloconverters are used in high power applications (up to tens of megawatts) and lower frequencies of the supply voltage. The feature of this converter is that the thyristors are closing on natural commutation (turn-off on zero current). 6-, 12- and 24-pulse cycloconverters are used in practice. The circuit diagram of a simple six-pulse cycloconverter is shown in Fig. 3.31.

The frequency converter consists of two anti-parallel connected three-phase bridge rectifiers. The converter operates in the following way. The switches of the first bridge conduct on the positive half-wave of the output voltage U2 and the switches of the second bridge conduct on

53

the negative half-wave of the output voltage U2. The control angles are controlled such that the output voltage is kept close to sinusoidal form.

There are several ways to control the cycloconverter. The simplest way is the triangle control on which the control angles of the active bridge can be changed linear. Output voltage U2 alters nearly to sinusoidal in this case. The output voltage waveform on the triangular control is shown in Fig. 3.32. If single-operation thyristors (SCR) are used, then their closing is network voltage commutated. Thus, the frequency of the output voltage cannot precede the frequency of the supply voltage and is always at least twice lower. For smooth commutation of the current from one bridge to another, the control angle is shortly (momentarily) changed above 90° and the network synchronized rectifier bridge goes into the inverter operation mode.

Bridge 1 Bridge 2 Figure 3.31. Circuit diagram of the single-phase cycloconverter

Figure 3.32. Output voltage waveform of the single-phase cycloconverter

Matrix frequency converter (matrix converter) or forced commutation cycloconverter (Fig. 3.33) forms its output voltages directly from the multi-phase network voltage. The pieces of the output voltage are conducted (fed) to the outputs at appropriate moments and at the output are modulated voltages with the required frequency, number of phases, phase and amplitude. The frequency can be freely varied in a wide range, the upper limit only constrained by capabilities of semiconductors. For example, the three-phase matrix converter consists of nine pairs of power transistors, which allow commutating the current in both directions.

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On the control of the matrix converter, the pulse-width modulation, pulse-amplitude modulation and vector modulation principles are used. Matrix converters are not considered as prospective because of numerous semiconductor switches and complexity. Frequency converters of multi-motor drives are produced as sets (units) for the machines that contain several drives, e.g. for cranes. For high-power applications, it is reasonable to use one network-synchronized rectifier with a bi-directional energy flow and separate inverters for each motor. In this case, several parallel inverters are supplied from the local direct current network (DC bus). Energy flows are possible between different inverters and between the network and local direct current bus. The converters with flexible energy exchange capabilities (flows) become more beneficial (prosperous) because of the economy of the electrical energy.

3~ U ; f2 2

3~U ;

f1

1

Figure 3.33. Power circuit diagram of the matrix converter

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