………… o0o………… Topologies of Power Electronic Converters ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 18 3. TOPOLOGIES OF POWER ELECTRONIC CONVERTERS 3.1 Introduction Power electronic converters (PECs) are static devices, without any movable parts, that convert electric energy of one set of properties into electric energy of another, different set of properties. The properties that are changed by the action of the converter are one or more of the following: number of phases, frequency, and voltage rms (or average, in the DC case) value. Thus any power electronic converter is essentially a transformer in a broad sense. Action of a power electronic converter is illustrated in Fig. 3.1, in terms of the defined electric energy properties. m i ,f i ,V i m o ,f o ,V o PEC Fig. 3.1: Conversion of electric energy by means of a power electronic converter. Electric circuits that constitute power electronic converters vary to the great extent and depend on the function that PEC is supposed to perform in terms of electric energy properties. However, the unique feature of any power electronic converter is that it comprises at least one (and in reality always more than one) power semiconductor, that is operated in the switched mode. Operation in the switch mode means that the semiconductor is either fully on in the circuit (conducting required current with almost zero voltage drop) or it is fully off (blocking the required voltage with zero current). Power semiconductors are for this reason usually called switches when PECs are discussed. In order to arrive to a frequently used classification of PECs, consider the following couple of examples: 1. A DC motor for its normal operation has to be supplied with a DC voltage. Suppose that only mains AC voltage is available. In order to connect the DC motor to the mains, an interface has to be used, that will convert AC into DC. Thus AC→DC conversion is required, and it is called rectification. PECs that perform rectification are termed rectifiers. 2. Nowadays one frequently meets in homes light sources whose intensity of light can be varied. Light bulbs are supplied from single-phase AC source of 240 V, 50 Hz and, in order to have controllable light intensity, a PEC is required. As bulbs require AC supply, then the PEC has to convert fixed voltage, fixed frequency AC supply into fixed frequency, variable voltage AC supply (intensity of light will reduce when voltage applied to the bulb is decreased). Hence the PEC is required to perform AC→AC conversion, in which only rms value of the voltage at the output can be varied. This type of PEC is usually called AC voltage controller. 3. Milk delivery in early morning hours is done by electric vehicles with on-board source of electric energy (a battery). The vehicle is powered by a DC motor which has to operate at variable speed and therefore, as discussed later, requires variable DC voltage for its operation. ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 19 In order to obtain variable DC voltage from the available constant battery DC voltage, a PEC has to be used, which will perform DC→DC conversion. 4. An induction machine that is to be used as part of a variable speed drive has to be supplied with voltage of variable rms value and variable frequency. The utility supply is fixed frequency, fixed voltage (three phase, 50 Hz, 415 V). Therefore a PEC converter is needed that will converter input AC into variable voltage, variable frequency output AC. This conversion is usually done in two stages. Input AC is at first rectified, using a rectifier. Next, another PEC is used to perform DC→AC conversion. This process is called inversion and PECs that do inversion are known as inverters. The most frequently utilised classification of PECs is based on properties of electric energy at the input and at the output of the converter. Electric energy at both input and output may be either DC or AC, as shown in the four examples above. This leads to the subdivision of power electronic converters into four categories: AC to DC converters (rectifiers), DC to AC converters (inverters), DC to DC converters and AC to AC converters. This classification, that will be used further on, does suffer from one serious disadvantage: certain power electronic converters may operate as both rectifiers and inverters, making the classification invalid. However, there is not at present a better way of classifying the converters. The other possibility, mentioned in the literature, is to classify the converters on the basis of the way in which the semiconductor devices are switched. In this case there are only two groups, namely line frequency converters and switching converters. Line frequency converters are those where utility line voltages are present at one side of the converter (input or output) and these voltages facilitate the turn-off of the power semiconductor devices. Similarly, the semiconductors are turned on phase-locked to the line voltage wave-form. Consequently, the semiconductors are switched on and off at switching frequency equal to the utility (mains) frequency (50 or 60 Hz). The other group, switching converters, then encompasses all the converters in which semiconductors are turned on and off at a frequency that is different from, and usually high when compared to the utility frequency. This means that switching is independent of the utility frequency, although output of the converter may be DC or AC at a fundamental frequency that is comparable to the line frequency. Although this classification of PECs is probably the only fully consistent one, it is usually found impractical because the vast majority of converters that are nowadays in use would fall into the switching converter group. This is a consequence of the development of improved semiconductor devices that allow for higher switching frequencies. As will be shown later, higher internal switching frequency of a converter is highly desirable, because it leads to an improvement in the quality of the output and input voltage and current wave-forms. In other words, the output wave-form will be closer to the ideal one if the switching frequency is higher. It is worth noting that, depending on the output of the PEC, ideal voltage wave-form is either a constant voltage (if output is DC) or an ideal sine wave (if the output is AC). This is illustrated in Fig. 3.2. Unfortunately, PECs are not capable of realising these ideal wave-forms, as shown shortly. This means that the output voltage is never ideally constant (if output is DC) nor it is an ideal sine wave (if the output is AC). The consequence of this is that output of any PEC contains always not only the desired output voltage but higher harmonics of the output voltage as well. As already pointed out, increase in switching frequency enables reduction in undesired voltage components (higher harmonics) in the output voltage wave-form. In what follows basic circuits of the four above mentioned types of PECs, namely AC to DC, DC to AC, DC to DC and AC to AC converters, will be reviewed and their principles of operation explained. It should be noted that many applications will require series connection of more than one converter, as already mentioned in the fourth example. This is typically the ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 20 case in AC motor drives where two (and sometimes even three) converters are connected in series in order to obtain electric energy of required properties at the output. v o v o v o =V o v o = √2V o sin ωt tt Fig. 3.2: Desired, ideal voltage wave-forms at the output of AC→DC and DC→DC converters (left) and AC→AC and DC→AC converters (right). 3.2 AC to DC Converters (Rectifiers) Rectification is undoubtedly the most frequently met application of PECs. The input to the converter is in this case AC utility voltage of fixed frequency (50 or 60 Hz) and of fixed rms value. The output voltage is DC and, depending on the application, it may be required to be constant or variable. Vast majority of rectifiers is based upon utilisation of thyristors (or diodes if DC voltage is required to be constant) and rectifiers are operated as line frequency converters. In other words, thyristors are naturally commutated, by means of line voltage present at the AC side. Thus thyristor ceases conduction and returns to the off state when either current through the thyristor naturally falls to zero or when the next thyristor is turned on and it takes over the current from the thyristor which was in on state in the previous interval. The switching frequency of thyristors equals line frequency, meaning that each thyristor can be fired and brought into on state only once in a period of the input voltage. 3.2.1 Single-phase, single-semiconductor (half-way) rectifier Output voltage and current of any rectifier depend greatly on the type of the load at the DC side. The simplest possible rectifier, that comprises only one thyristor, is illustrated in Fig. 3.3. Characteristic wave-forms in the circuit are shown as well, for two types of loads: purely resistive load and resistive-inductive load. Operation is illustrated for two values of the thyristor firing angle α which is measured with respect to the zero crossing of the utility AC voltage: α = 0 degrees and α = 90 degrees. Note that α = 0 degrees represents at the same time operation of the same circuit in which a diode is placed instead of the thyristor. For purely resistive load current is in phase with the AC voltage and therefore thyristor ceases conduction when current and voltage fall to zero at 180 degrees. However, for resistive-inductive load current continues to flow for some time after the mains voltage has reversed, so that the output DC voltage contains negative sections. This indicates that for the same firing angle average DC voltage is lower when the load is resistive-inductive. Average DC voltage is denoted with constant value bold straight lines in Fig. 3.3 and with symbol ‘V’ (index o for output is omitted). With respect to the basic description of a PEC, equation (1.1), circuit of Fig. 3.3 performs the conversion of the type (assuming 240 V, 50 Hz input): 240 V, 50 Hz, single- ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 21 phase → 0 Hz, V. Average value of the output voltage V can be varied between zero and maximum value obtainable with zero firing angle. Consider at first operation with purely resistive load and zero firing angle. Output voltage and current in the circuit are then determined with (T is period of input voltage) vx t ivR v i == == 2 240 2 50 00 sin π kt < t < (2k +1)T / 2 k = 0,1,2, . otherw ise (3.1) Input voltage wave-form +v Th 50 Hz R, ωt AC v L i 0 180 360 (°) vv VV 180 360 (°) ii 180 360 (°) 180 360 (°) Zero firing angle vV v V 90 180 360 450 (°) 90 450 (°) ii 90 180 360 450 (°) 90 450 (°) Firing angle of 90 degrees Purely resistive load Resistive-inductive load Fig. 3.3: Single-thyristor rectifier and wave-forms for resistive and resistive-inductive load for two values of the thyristor firing angle. Note that input and output current are equal as there is only one current path in the circuit. Note as well that at all times applied input AC voltage equals sum of the output voltage and the voltage across thyristor. Thyristor voltage, when thyristor is on, is zero in positive half- periods of the input voltage, when output voltage equals input voltage. If thyristor is off during ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 22 positive half-cycle, then thyristor voltage equals input voltage, while output voltage is zero. In negative half-cycles of the input voltage output voltage is zero, while thyristor voltage becomes equal to the input voltage. Thus thyristor voltage is negative during negative input voltage half-periods. Operation of the circuit can be described in terms of angle rather than time, for any value of the firing angle, with the following set of equations (one period of input voltage is considered; θ = ω t): vx ivR v vivx Th Th == << === <<<< 2 240 00224020 sin / sin θαθπ θπθπ θα =0 and (3.2) Wave-form of the instantaneous output voltage in Fig. 3.3 considerably differs from the ideal one shown in Fig. 3.2. Although it can be improved, as shown shortly, the ideal one can never be obtained. Average value of the output voltage V is given with (T stands for period of the input voltage - for 50 Hz, T =20ms): [] [] () V T vdt vd V d VV V T vdt vd V d VV T i ii T i ii == = =−= == = =−= òòò òòò 11 2 1 2 2 2 2 2 11 2 1 2 2 2 2 2 2 00 2 0 0 00 2 π θ π θθ π θ π π θ π θθ π θ π α ππ π π α π α π sin cos sin cos for diode case 1+ cos for thyristor case (3.3) Variation of average output voltage with thyristor firing angle is illustrated in Fig. 3.4. V √2V i /π √2V i /2π 0 0 90 180 α(°) Fig. 3.4: Variation of average voltage with firing angle for single-phase, single thyristor rectifier with resistive load. If the load in the circuit of Fig. 3.3 is resistive-inductive, then the current in the circuit lags voltage and the instant in time when current falls to zero (i.e., when thyristor turns off) is not known in advance. In order to find this time-instant, it is necessary to at first solve differential equation of the circuit for current. Once when expression for current is obtained, instant when current reaches zero value can be calculated. When this instant is known, average value of the output voltage can be calculated using the procedure given in (3.3): it is only necessary to change upper border of integration from π to β,whereβ corresponds to time instant when current falls to zero and β>π. The rectifier of Fig. 3.3 is very rarely utilised in practice due to pure quality of the output DC voltage. The rectifier topology that is most frequently met in practice is the bridge topology, with either single-phase or three-phase input. 3.2.2 Single-phase, bridge (full-wave) rectifier Both single-phase and three-phase bridge rectifiers, that again utilise thyristors and are hence once more line commutated rectifiers, are shown in Fig. 3.5. These versions of the bridge topology are usually called fully controllable bridge rectifiers as all the semiconductors ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 23 are of the thyristor type. Alternatively, in certain applications so-called semi-controllable bridges are used: in this case upper half of the rectifier is based on thyristors while the lower half comprises diodes. In semi-controllable rectifiers diodes prevent instantaneous DC voltage from going negative. In what follows only the fully controllable bridge topology is discussed. Note that again all the thyristors can be substituted with diodes: in this case output voltage average value is fixed for given input voltage. Operation of the diode bridge rectifier coincides with operation of the thyristor bridge rectifier whose firing angle is zero. All the wave-forms that are to be shown apply to the single-phase fully controllable bridge rectifier. Operation of the three-phase bridge rectifier, that will be dealt with in the section on rectifier control of DC motor drives, is in principle the same but the wave-forms are more complicated due to three-phase input. However, quality of the DC voltage is better in three-phase rectifier, where so-called six-pulse wave-form is obtained as DC voltage. In the single-phase rectifier wave-form of the DC voltage is two-pulse. ii 12 LL OO vA v A DD 34 Single-phase bridge rectifier Three-phase bridge rectifier Fig. 3.5: Configurations of single-phase and three-phase fully-controllable bridge rectifiers. Wave-forms in the circuits of Fig. 3.5 greatly depend on the type of the load at the DC side. Four cases may be distinguished: resistive load, resistive-inductive load, resistive- inductive load with a DC source, and capacitive filter connected in parallel to the rectifier output and providing almost constant DC voltage to the subsequent load. The third and the fourth case will be dealt with later on. The remaining two cases are examined here for the single-phase bridge fully controllable rectifier. Figure 3.6 illustrates wave-forms in the circuit for two values of the firing angle, zero degrees and 90 degrees, for purely resistive load and for resistive-inductive load. In the case of resistive-inductive load it is assumed that the inductance is sufficiently high to maintain DC current at almost constant level. Such a situation is met when the rectifier supplies current source inverter (i.e., load at rectifier output is an inductance connected in series with the positive DC terminal; DC voltage after the inductance then serves as input into the current source inverter which performs DC to AC conversion). The single-phase bridge rectifier is called two-pulse rectifier because the output DC voltage contains two identical portions of the input sine-wave for one period of the input (Fig. 3.6). During positive half-cycle of the input voltage thyristors 1 and 4 are positively biased, they are connected in series, and can be fired to start the conduction at any time between 0 and 180 degrees. Thyristors 2 and 3 are negatively biased and cannot conduct in positive half-cycle. During negative half-cycle of the input voltage situation is reversed: thyristors 1 and 4 are now ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 24 negatively biased and they cannot conduct; however, thyristors 2 and 3 are positively biased and therefore they can be fired to start conduction at any time instant between 180 and Input AC voltage v 1,4 2,3 1,4 v 1,4 2,3 VV 180 360 (°) ii 180 360 (°) 180 360 (°) Input AC current Input AC current Zero firing angle vV v V 90 180 360 450 (°) ii 90 180 360 450 (°) 90 450 (°) Input AC current Input AC current Firing angle of 90 degrees Purely resistive load Highly inductive load Fig. 3.6: Wave-forms in single-phase bridge rectifier: purely resistive and highly inductive load. ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 25 360 degrees. Both half-cycles of the input voltage are now utilised and the output voltage contains, for zero firing angle, rectified input AC voltage (i.e., absolute value of the input). From Fig. 3.6 it is evident that neither output DC voltage nor current are pure DC nor is the current drawn from the utility pure sine wave (except for purely resistive load with zero firing angle). All these quantities contain considerable amount of undesirable higher harmonics. For highly inductive load input AC current is a square wave, displaced by the firing angle with respect to the input AC voltage. Thus the firing angle determines phase displacement between AC current and voltage at rectifier input terminals and the rectifier always appears to the mains as consumer of reactive energy (current is lagging voltage by the firing angle). Note that input AC current in bridge rectifier is no longer of the same wave-form as it was in the case of a single thyristor rectifier. It is AC, while output current is DC. It follows from Fig. 3.6 that output current can be either discontinuous (pure resistive load) or continuous (highly inductive load). Thus average voltage across the load has to be determined separately for these two cases. Average voltage is: [] [] () single- phase diode bridge rectifier single- phase thyristor bridge rectifier, purely resisitve load 1+cos single- phase thyristor bridge rectifier, highly inductive load V T vdt vd V d VV V T vdt vd V d VV V T vdt vd V d V T i ii T i ii T i i == = =−= == = =−= == = = òò ò òò ò òò ò + 11 2 2 1 2 2 222 11 2 2 1 2 2 22 11 2 2 1 2 2 2 00 2 0 0 00 2 00 2 π θ π θθ π θ π π θ π θθ π θ π α π θ π θθ π ππ π π α π α π π α πα sin cos sin cos sin [] −= + cos cos θ π α α πα 22V i (3.4) One notes from (3.4) that average output voltage as function of the firing angle considerably differs depending on whether the load is purely resistive or purely inductive. One notes as well that average output voltage of the bridge rectifier is doubled with respect to the values obtainable with single thyristor rectifier. Average output voltage is illustrated for these two cases in Fig. 3.7. V purely resistive load 2√2V i /π 0 90 180 α (°) highly inductive load -2√2V i /π Fig. 3.7: Average output voltage of a single-phase fully controllable rectifier for purely resisti- ve and highly inductive loads. The average output voltage for highly inductive load is thus directly proportional to the cosine of the firing angle for continuous DC current (i.e., V = k cos α). The average DC voltage is positive for firing angles between zero and 90 degrees and negative for firing angles between 90 and 180 degrees. As current flow is unidirectional then the power supplied to the ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 26 load is positive for firing angles between zero and 90 degrees and the circuit operates in rectifying mode. However, for firing angles greater than 90 degrees power supplied to the load attains negative sign. The circuit now operates in inverting mode and the meaning of the negative sign of power is that the power is transferred actually from DC to AC side. The operation of the circuit in inverting mode requires that a DC voltage source is present at the DC side and that its polarity is such that it supports current flow in the direction indicated in Fig. 3.6. Operation of the circuit in inverting mode is widely utilised in DC motor drives, where the circuit operates as rectifier during motoring and as a line-commutated inverter during regenerative braking. Inversion is illustrated in Fig. 3.8, assuming continuous DC current flow. Extreme case, with firing angle equal to 180 degrees, is shown. Average output voltage has now maximum, but negative value; output voltage direction arrow in the circuit shows the direction in which acts absolute value of the average output voltage. As current can flow only in the direction shown, then value of the DC source voltage E must be greater than the absolute value of the converter output voltage. Instantaneous voltage at converter DC side is at all times negative. Power is transferred from DC side to AC side, so that the converter now operates as a line commutated inverter (DC to AC conversion). iR v L 0 180 360 degs V EV + Fig. 3.8: Operation of the single-phase bridge converter in inverting mode. Note that the situation shown for highly inductive load with 90 degrees firing angle in Fig. 3.6 is the one for which average DC voltage is zero. Thus it denotes transition from rectifying to inverting mode, providing that there is a DC voltage source of adequate polarity at DC side. It should be noted that average voltage across any inductor at DC side equals zero. This means that the whole of the average voltage, assuming resistive-inductive load, is developed across the resistor. Hence the average value of the DC current delivered to the DC load equals I=V/R (3.5) regardless of the rectifier type. In other words, it is always necessary to find average value of the voltage only, using expressions of the type (3.4). Once when average voltage is known, average current follows from (3.5). Example: Aresistive5Ω load is to be supplied from a single-phase AC supply of 240 V, 50 Hz, through a rectifier. The required power which has to be delivered to the load is 500 W. There are two rectifiers available: the single thyristor rectifier and the single-phase bridge thyristor [...]... Principles of power electronics, Addison-Wesley Publishing Company, 1991 T.H.Barton; Rectifiers, cycloconverters and AC controllers, Clarendon Press, 1994 E.Ohno; Introduction to power electronics, Clarendon Press, 1988 S.K.Datta; Power electronics and control, Reston Pub Co., a Pretice-Hall Company, 1985 K.K.Sum; Switch mode power conversion, Marcel Dekker Inc., 1984 M.Kazimierczuk; Resonant power converters, ... way of dealing with the harmonic effects brought in by non-ideal nature of the power electronic converters As is well-known, Fourier series represents a non-sinusoidal periodic wave-form with a sum of the constant DC term (average value of the function) and a series of sinusoidal functions of different frequencies The second problem encountered in many circuits supplied from thyristor based power electronic. .. power converters, Wiley, 1995 P.C.Sen; Power electronics, McGraw-Hill, 1992 J.Vithayathil; Power Electronics: Principles and Applications, McGraw-Hill, 1995 B.K.Bose, ed.; Modern Power Electronics: Evolution, Technology, and Applications, IEEE Press, 1991 P.A.Thollot, ed.; Power Electronics Technology and Applications, IEEE Press, 1993 S.S.Ang; Power- Switching Converters, Marcel Dekker Inc., 1995 E... Regardless of whether the output is DC or AC, the voltage waveform will always depart from the ideal one to a smaller or greater extent The direct consequence of such a situation is that analysis of circuits supplied from power electronic converters is more tedious than the analysis of circuits supplied from ideal DC or AC sources Such a situation leads to utilisation of Fourier analysis of periodic... basic idea of the cycloconverter operation is given at the end of this section Topologies of a single-phase and of a three-phase AC to AC voltage controllers are shown in Fig 3.14 A back-to-back (anti-parallel) connection of two thyristors of the type shown in Fig 2.13 constitutes the voltage controller in each phase of the input AC supply Thyristor firing is symmetrical in the two half-periods of the... ENGNG3070 Power Electronics Devices, Circuits and Applications 4 FOURIER ANALYSIS AND TIME-DOMAIN ANALYSIS 4.1 Introduction As already pointed out in the previous chapter, desired ideal waveforms at the converter output are the pure DC and pure sinusoidal AC voltages, for converters whose output is DC and AC, respectively Unfortunately, as the discussion of the basic types of power electronic converters. .. connection of a rectifier and an inverter Matrix converters are still at development stage and there is not at present evidence of their wider application AC to AC voltage controllers and cycloconverters are based on thyristors and thyristor commutation is achieved in a natural manner, by means of mains voltages present at the input side of the converter Thus they belong to the class of line commutated converters. .. equal to 1/3 of the input frequency 3.6 Suggested Further Reading Books: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] N.Mohan, T.M.Undeland, W.P.Robbins; Power Electronics: Converters, Applications and Design, John Wiley and Sons, 1995 M.H.Rashid, Power Electronics: Circuits, Devices and Applications, Prentice-Hall International, 1994 C.W.Lander, Power Electronics,... synchronous machines with trapezoidal and with sinusoidal distribution of the flux in the air-gap, synchronous reluctance machines, switched reluctance machines, etc The topologies of power electronic converters that are used in conjunction with different types of machines vary to the great extent and it is therefore impossible to cover all the converters and all the control schemes here The emphasis is therefore... E Levi, Liverpool John Moores University, 2002 46 ENGNG3070 Power Electronics Devices, Circuits and Applications next Chapter, on three-phase induction motors Furthermore, only the most commonly used converter topologies for each of these three types will be dealt with Regardless of the type of the machine and regardless of the topology of the converter, open-loop low performance drive and closed-loop . Liverpool John Moores University, 2002 18 3. TOPOLOGIES OF POWER ELECTRONIC CONVERTERS 3.1 Introduction Power electronic converters (PECs) are static devices,. ………… o0o………… Topologies of Power Electronic Converters ENGNG3070 Power Electronics Devices, Circuits and Applications