Introduction. Chapter HISTORICAL REVIEW Work, Energy and Heat

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1 hapter 1 Introduction Power electronics and conversion technology are exciting and challenging professions for anyone who has a genuine interest in, and aptitude for, applied science and mathematics. Actually, the existing knowledge in power electronics is not completed. All switching power circuits including the power / converters and switched /A pulse-width-modulation (PWM) inverters (: direct current; A: alternative current) perform in high-frequency switching state. Traditional knowledge did not fully consider the pumping filtering process, resonant process and voltage-lift operation. Therefore, the existing knowledge cannot well describe the characteristics of switching power circuits including the power / converters. To reveal the disadvantages of the existing knowledge, we have to review the traditional analog Power Electronics in this hapter. 1.1 HITOIA EVIEW Power Electronics and conversion technology are concerned to systems that produce, transmit, control and measure electric power and energy. To describe the characteristics of power systems, various measuring parameters so-called the factors are applied. These important concepts are the power factor (PF), power-transfer efficiency (η), ripple factor (F) and total harmonic distortion (TH). For long-time education and engineering practice, we know that the traditional power systems have been successfully described by these parameters. These important concepts will be introduced in the following sections Work, Energy and Heat Work, W, and energy, E, are measured by the unit joule. We usually call the kinetic energy work, and the stored or static energy potential energy. Work and energy

2 2 igital power electronics and applications can be transferred to heat, which is measured by calorie. Here is the relationship (Joule enz law): 1 joule = 0.24 calorie or 1 calorie = 4.18 joules In this mechanism, there is a relationship between power, P, and work, W, and/or energy, E: W = P dt E = P dt and P = d dt W P = d dt E Power P is measured by the unit watt, and 1 joule = 1 watt 1 second or 1 watt = 1 joule/1 second and A Equipment Power supplies are sorted into two main groups: and A. orresponding equipment are sorted into anda kinds as well, e.g. generators, A generators, motors, A motors, etc. Power upply A power supply has parameters: voltage (amplitude) V dc and ripple factor (F). A power supply can be a battery, generator or / converter. A Power upply An A power supply has parameters: voltage (amplitude, root-mean-square (rms or M) value and average value), frequency ( f or ω), phase angle (φ or θ) and total harmonic distortion (TH). An A power supply can be an A generator, transformer or /A inverter. An A voltage can be presented as follows: v(t) = V p sin (ωt θ) = 2 V rms sin (ωt θ) (1.1) where v(t) is the measured A instantaneous voltage; V p, the peak value of the voltage; V rms, the rms value of the voltage; ω, the angular frequency, ω = 2πf ; f, the supply frequency, e.g. f = 50 Hz and θ, the delayed phase angle.

3 Introduction oads Power supply source transfers energy to load. If the characteristics of a load can be described by a linear differential equation, we call the load a linear load. Otherwise, we call the load a non-linear load (i.e. the diodes, relays and hysteresis-elements that cannot be described by a linear differential equation). Typical linear loads are sorted into two categories: passive and dynamic loads. inear Passive oads inear passive loads are resistance (), inductance () and capacitance (). All these components satisfy linear differential equations. If the circuit current is I as shown in Figure 1.1, from Ohm s law we have: V = I (1.2) V = di (1.3) dt V = 1 I dt (1.4) V = V + V + V = I + di dt + 1 I dt (1.5) Equations (1.2) (1.5) are all linear differential equations. inear ynamic oads inear dynamic loads are and A back electromagnetic force (EMF). All these components satisfy differential equation operation. The back EMF of a motor is back EMF with voltage that is proportional to the field flux and armature running speed: EMF = kω (1.6) where k is the machine constant;, the field flux and ω, the machine running speed in rad/s. V V I V V Figure 1.1 An circuit.

4 4 igital power electronics and applications The back EMF of an A motor is A back EMF with A voltage that is proportional to the field flux and rotor running speed Impedance If an circuit supplied by a voltage source with mono-frequency (ω = 2πf ) sinusoidal waveform as shown in Figure 1.1, we can simplify the differential equation (1.5) into an algebraic equation using the concept impedance, Z: V = ZI (1.7) We define impedance Z as follows: 1 Z = + jω j ω = + jx = Z θ (1.8) where Z = X = ω 1 ω 2 + ( ω 1 ) 2 (1.9) ω ( ) ω 1 θ = tan 1 ω (1.10) in which θ is the conjugation phase angle. The real part of an impedance Z is defined as resistance, and the imaginary part of an impedance Z is defined as reactance X. The reactance has two components: the positive part is called inductive reactance jω and the negative part is called capacitive reactance j/ω. The power delivery has been completed only across resistance. The reactance can only store energy and shift phase angle. No power is consumed on reactance, which produces reactive power and spoils power delivery. From Ohm s law, we can get the vector current (I) from vector voltage (V) and impedance (Z): I = V Z = V + jω j 1 = I θ (1.11) ω Most industrial application equipment are of inductive load. For example, an circuit is supplied by a sinusoidal voltage V, and it is shown in Figure 1.2. The impedance Z obtained is: Z = + jω = + jx = Z θ (1.12)

5 Introduction 5 I V V V Figure 1.2 An circuit. Z jω ω Figure 1.3 θ θ I V/Z The vector diagram of an circuit. V IZ with Z = ( ) ω 2 + (ω) 2 and θ = tan 1 The conjugation angle (θ) is a positive value. The corresponding vector diagram is shown in Figure 1.3. We also get the current as follows: I = V Z = V = I θ (1.13) + jω elect the supply voltage V as reference vector with phase angle zero. The current vector is delayed than the voltage by the conjugation angle θ. The corresponding vector diagram is also shown in Figure 1.3. The voltage and current waveforms are shown in Figure Powers There are various powers such as apparent power (or complex power),, power (or real power), P, and reactive power, Q.

6 6 igital power electronics and applications I O Figure Time (ms) The corresponding voltage and current waveforms. P jq jq Figure 1.5 θ The power vector diagram of an circuit. P Apparent Power We define the apparent power as follows: = VI = P + jq (1.14) Power P Power or real power P is the real part of the apparent power : P = cos θ = I 2 (1.15) eactive Power Q eactive power Q is the imaginary part of the apparent power : Q = sin θ = I 2 X (1.16) eferring to the circuit in Figure 1.2, we can show the corresponding power vectors in Figure 1.5.

7 Introduction TAITIONA PAAMETE Traditional parameters used in power electronics are the power factor (PF), powertransfer efficiency (η), total harmonic distortion (TH) and ripple factor (F). Using these parameters has successfully described the characteristics of power (generation, transmission, distribution, protection and harmonic analysis) systems and most drive (A and motor drives) systems Power Factor (PF) Power factor is defined by the ratio of real power P over the apparent power : PF = P = cos θ = I 2 VI = I V (1.17) Figure 1.5 is used to illustrate the power factor (PF) Power-Transfer Efficiency (η) Power-transfer efficiency (η) is defined by the ratio of output power P O over the input power P in : η = P O (1.18) P in The output power P O is received by the load, end user. The input power P in is usually generated by the power supply source. Both the input power P in and output power P O are real power Total Harmonic istortion (TH) A periodical A waveform usually possesses various order harmonics. ince the instantaneous value is periodically repeating in fundamental frequency f (or ω = 2πf ), the corresponding spectrum in the frequency domain consists of discrete peaks at the frequencies nf (or nω = 2nπf ), where n = 1, 2, 3,. The first-order component (n = 1) corresponds to the fundamental component V 1. The total harmonic distortion (TH) is defined by the ratio of the sum of all higher-order harmonics over the fundamental harmonic V 1 : Vn 2 n=2 TH = (1.19) V 1 where all V n (n = 1, 2, 3, ) are the corresponding rms values.

8 8 igital power electronics and applications ipple Factor (F) A waveform usually possesses component V dc and various high-order harmonics. These harmonics make the variation (ripple) of the waveform. ince the instantaneous value is periodically repeating in fundamental frequency f (or ω = 2πf ), the corresponding spectrum in the frequency domain consists of discrete peaks at the frequencies nf (or nω = 2nπf ), where n = 0, 1, 2, 3,. The zeroth-order component (n = 0) corresponds to the component V dc. The ripple factor (F) is defined by the ratio of the sum of all higher-order harmonics over the component V dc : F = Vn 2 n=1 (1.20) V dc where all V n (n = 1, 2, 3, ) are the corresponding rms values Application Examples In order to describe the fundamental parameters better, we provide some examples as the application of these parameters in this section. Power and Efficiency (η) A pure resistive load supplied by a voltage source V with internal resistance O is shown in Figure 1.6. The current I is obtained by the calculation expression: I = V + O (1.21) The output voltage is: = + O V (1.22) O I V Figure 1.6 A pure resistive load supplied by a source with internal resistance.

9 Introduction 9 The output power P O is: P O = I 2 = The power-transfer efficiency (η) is: ( + O ) 2 V 2 (1.23) η = P O = I 2 P in IV = (1.24) + O In order to obtain maximum output power, we can determine the condition by differentiating Equation (1.23): d d P O = d d ] ( + O ) 2 V 2 [ = 0 (1.25) 1 ( + O ) 2 2 ( + O ) 3 = 0 Hence, = O (1.26) When = O, we obtain the maximum output power: P O-max = V 2 (1.27) 4 O and the corresponding efficiency: η = =O = 0.5 (1.28) + O This example shows that the power and efficiency are different concepts. When load is equal to the internal resistance O, maximum output power is obtained with the efficiency η = 50%. Vice versa, if we would like to obtain maximum efficiency η = 1 or 100%, it requires load is equal to infinite (if the internal resistance O cannot be equal to zero). It causes the output power, which is equal to zero. The interesting relation is listed below: Maximum output power η = 50% Output power = 0 η = 100% The second case corresponds to the open circuit. Although the theoretical calculation illustrates the efficiency η = 1 or 100%, no power is delivered from source to load. Another situation is = 0 that causes the output current is its maximum value I max = V / O as (1.21) and: Output power = 0 η = 0%

10 10 igital power electronics and applications An ircuit alculation Figure 1.7 shows a single-phase sinusoidal power supply source with the internal resistance O = 0.2, supplying an circuit with = 1 and = 3 mh. The source voltage is a sinusoidal waveform with the voltage 16 V (rms voltage) and frequency f = 50 Hz: The internal impedance is: The impedance of load is: V = 16 2 sin 100πt V (1.29) Z O = O = 0.2 (1.30) Z = 1 + j100π 3m = 1 + j0.94 = (1.31) The current is: I = Z + Z O = j0.94 = (1.32) The output voltage across the circuit is: The apparent power across the load is: V Z + Z O = sin(100πt ) A (1.33) = ZI = sin(100πt 5.16 ) A (1.34) The real output power P O across the load is: = I = = VA (1.35) P O = P = I 2 = = W (1.36) O I V V V Figure 1.7 An circuit supplied by an A source with internal resistance.

11 Introduction 11 The real input power P in is: P in = I 2 ( + O ) = = W (1.37) Therefore, the power factor PF of the load is: PF = P O = cos θ = cos = 0.73 (lagging) (1.38) The corresponding reactive power Q is: Q = sin θ = sin = VA (1.39) Thus, the power-transfer efficiency (η) is: Other way to calculate the efficiency (η) is: η = P = = (1.40) P in η = + O = = To obtain the maximum output power we have to choose same condition as in Equation (1.26), The maximum output power P O is: with the efficiency (η) is: P O-max = V 2 = O = 0.2 (1.41) 4 O = = 320 W (1.42) η = 0.5 (1.43) A Three-Phase ircuit alculation Figure 1.8 shows a balanced three-phase sinusoidal power supply source supplying a full-wave diode-bridge rectifier to an load. Each single-phase source is a sinusoidal voltage source with the internal impedance 10 k plus 10 mh.the load is an circuit with = 240 and = 50 mh. The source phase voltage has the amplitude 16V (its rms value is 16/ 2 = 11.3V) and frequency f = 50 Hz. It is presented as: V = 16 sin 100πt V (1.44)

12 12 igital power electronics and applications V m a a 10 m 10 k b b c 10 m 10 k 10 m c 10 k V A V V a V b V c Figure 1.8 A three-phase source supplies a diode full-wave rectifier to an load. The internal impedance is: 10,000 10,000 j Z O = = j (1.45) j100π 10 m 10,000 + j The impedance of the load is: Z = j100π 50 m = j = (1.46) The bridge input A line-to-line voltage is measured and shown in Figure 1.9. It can be seen that the input A line voltage is distorted. After the fast Fourier transform (FFT) analysis, the corresponding spectrums can be obtained as shown in Figure 1.10 for the bridge input A line voltage waveforms. The input line line voltage fundamental value and the harmonic peak voltages for TH calculation are listed in Table 1.1. Using formula (1.19) to calculate the TH, wehave, v 2 AB-n n= TH = = % = 4.86% v AB (1.47) We measured the output voltage in Figure It can be seen that the voltage has ripple. After FFT analysis, we obtain the corresponding spectrums as shown in Figure 1.12 for the output voltage waveforms.

13 Introduction V AB Time (ms) Figure 1.9 The input line A voltage waveform V AB Figure Frequency (khz) The FFT spectrum of the input line A voltage waveform. Table 1.1 The harmonic peak voltages of the distorted the input line line voltage Order no. Fundamental Volts Order no TH Volts %

14 14 igital power electronics and applications Figure Time (ms) The output voltage waveform Figure Frequency (khz) The FFT spectrum of the output voltage waveform The output load voltage and the harmonic peak voltages for F calculation are listed in Table 1.2. Using formula (1.20) to calculate the F, wehave, v 2 O-n n= F = = v O-dc % = 5.24% 2 (1.48) From input phase voltage and current, the partial power factor (PF p ) is obtained, PF p = cos θ = (1.49)

15 Introduction 15 Table 1.2 The harmonic peak voltages of the output voltage with ripple Order no F Volts % Table 1.3 The harmonic peak voltages of the input phase current Order no. Fundamental Amperes e e e e e e 3 Order no Total PF Amperes e e e e e e Table 1.4 The harmonic peak voltages of the output current Order no. (0) η Amperes e e e e e e The input phase current peak value and the higher-order harmonic current peak values are listed in Table 1.3. I a-1 = = A I a-rms = in 2 = A 2 Total power factor n=0 PF total = I a-1 cos θ = = I a-rms The average output load current and the higher-order harmonic current peak values are listed in Table 1.4. The efficiency (η) is: -rms = vn 2 = V I O-rms = in 2 = A n=0 η = P dc = -dci O-dc % = 100% = 99.28% (1.50) P ac -rms I O-rms n=0

16 16 igital power electronics and applications From this example, we fully demonstrated the four important parameters: power factor (PF), power-transfer efficiency (η), total harmonic distortion (TH) and ripple factor (F). Usually, these four parameters are enough to describe the characteristics of a power supply system. 1.3 MUTIPE-QUAANT OPEATION AN HOPPE Multiple-quadrant operation is required in industrial applications. For example, a motor can perform forward running or reverse running. The motor armature voltage and armature current are both positive during forward starting process. We usually call it the forward motoring operation or Quadrant I operation. The motor armature voltage is still positive and its armature current is negative during forward braking process. This state is called the forward regenerative braking operation or Quadrant II operation. Analogously, the motor armature voltage and current are both negative during reverse starting process. We usually call it the reverse motoring operation or Quadrant III operation. The motor armature voltage is still negative and its armature current is positive during reverse braking process. This state is called the reverse regenerative braking operation or Quadrant IV operation. eferring to the motor operation states, we can define the multiple-quadrant operation as below: Quadrant I operation: Forward motoring; voltage and current are positive; Quadrant II operation: Forward regenerative braking; voltage is positive and current is negative; Quadrant III operation: everse motoring; voltage and current are negative; Quadrant IV operation: everse regenerative braking; voltage is negative and current is positive. The operation status is shown in the Figure hoppers can convert a fixed voltage into various other voltages. The corresponding chopper is usually called which quadrant operation chopper, e.g. the first-quadrant chopper or A -type chopper. In the V Quadrant II Forward regenerating Quadrant I Forward motoring Quadrant III everse motoring Quadrant IV everse regenerating I Figure 1.13 The four-quadrant operation.

17 Introduction 17 following description we use the symbols V in for fixed voltage, V p for chopped voltage and for output voltage The First-Quadrant hopper The first-quadrant chopper is also called A -type chopper and its circuit diagram is shown in Figure 1.14(a) and the corresponding waveforms are shown in Figure 1.14(b). The switch can be some semiconductor devices such as BJT, integrated gate bipolar transistors (IGBT) and power MO field effected transistors (MOFET). Assuming all parts are ideal components, the output voltage is calculated by the formula: = t on T V in = kv in (1.51) V in V P (a) V in t V P t on T t Figure 1.14 (b) kt T t The first-quadrant chopper. (a) ircuit diagram and (b) voltage waveforms.

18 18 igital power electronics and applications where T is the repeating period (T = 1/f ), in which f is the chopping frequency; t on is the switch-on time and k is the conduction duty cycle (k = t on /T) The econd-quadrant hopper The second-quadrant chopper is also called B -type chopper and its circuit diagram is shown in Figure 1.15(a) and the corresponding waveforms are shown in Figure 1.15(b). The output voltage can be calculated by the formula: = t off T V in = (1 k)v in (1.52) where T is the repeating period (T = 1/f ), in which f is the chopping frequency; t off is the switch-off time (t off = T t on ) and k is the conduction duty cycle (k = t on /T). V in I (a) V P V in t V P t on T t Figure 1.15 (b) kt T t The second-quadrant chopper. (a) ircuit diagram and (b) voltage waveforms.

19 Introduction The Third-Quadrant hopper The third-quadrant chopper is shown in Figure 1.16(a) and the corresponding waveforms are shown in Figure 1.16(b). All voltage polarities are defined in the figure. The output voltage (absolute value) can be calculated by the formula: = t on T V in = kv in (1.53) where t on is the switch-on time and k is the conduction duty cycle (k = t on /T) The Fourth-Quadrant hopper The fourth-quadrant chopper is shown in Figure 1.17(a) and the corresponding waveforms are shown in Figure 1.17(b). All voltage polarities are defined in the figure. V in (a) V P I O V in t V P t on T t Figure 1.16 (b) kt T t The third-quadrant chopper. (a) ircuit diagram and (b) voltage waveforms.

20 20 igital power electronics and applications V in I V P (a) V in t V P t on T t (b) kt T t Figure 1.17 The fourth-quadrant chopper. (a) ircuit diagram and (b) voltage waveforms. The output voltage (absolute value) can be calculated by the formula: = t off T V in = (1 k)v in (1.54) where t off is the switch-off time (t off = T t on ) and k is the conduction duty cycle (k = t on /T) The First econd-quadrant hopper The first second-quadrant chopper is shown in Figure ual-quadrant operation is usually requested in the system with two voltage sources V 1 and V 2. Assume the condition V 1 > V 2, the inductor is the ideal component. uring Quadrant I operation, 1 and 2 work, and 2 and 1 are idle. Vice versa, during Quadrant II operation, 2 and 1 work, and 1 and 2 are idle. The relation between the two voltage sources can

21 Introduction 21 V V V 2 P Figure 1.18 The first second quadrant chopper. 2 1 V V P V 2 Figure 1.19 The third fourth quadrant chopper. be calculated by the formula: V 2 = { kv1 Quadrant I operation (1 k)v 1 Quadrant II operation (1.55) where k is the conduction duty cycle (k = t on /T) The Third Fourth-Quadrant hopper The third fourth-quadrant chopper is shown in Figure ual-quadrant operation is usually requested in the system with two voltage sources V 1 and V 2. Both the voltage polarities are defined in the figure, we just concentrate on their absolute values in analysis and calculation. Assume the condition V 1 > V 2, the inductor is the ideal component. uring Quadrant III operation, 1 and 2 work, and 2 and 1 are idle. Vice versa, during Quadrant IV operation, 2 and 1 work, and 1 and 2 are idle. The relation between the two voltage sources can be calculated by the formula: V 2 = { kv1 Quadrant III operation (1 k)v 1 Quadrant IV operation (1.56) where k is the conduction duty cycle (k = t on /T).

22 22 igital power electronics and applications V V Figure 1.20 The four-quadrant chopper. Table 1.5 The switches and diodes status for four-quadrant operation witch or diode Quadrant I Quadrant II Quadrant III Quadrant IV 1 Works Idle Idle Works 1 Idle Works Works Idle 2 Idle Works Works Idle 2 Works Idle Idle Works 3 Idle Idle On Idle 3 Idle Idle Idle On 4 On Idle Idle Idle 4 Idle On Idle Idle Output V 2 +, I 2 + V 2 +, I 2 V 2, I 2 V 2, I The Four-Quadrant hopper The four-quadrant chopper is shown in Figure The input voltage is positive, output voltage can be either positive or negative. The status of switches and diodes for the operation are given in Table 1.5. The output voltage can be calculated by the formula: kv 1 Quadrant I operation (1 k)v V 2 = 1 Quadrant II operation kv 1 Quadrant III operation (1 k)v 1 Quadrant IV operation (1.57) 1.4 IGITA POWE EETONI: PUMP IUIT AN ONVEION TEHNOOGY Besides choppers there are more and more switching circuits applied in industrial applications. These switching circuits work in discrete-time state. ince high-frequency switching circuits can transfer the energy in high power density and high efficiency, they have been applied on more and more branches of power electronics. The energy

23 Introduction 23 (a) I 1 I 2 V 1 V 2 I 1 I 2 V 1 (b) V 2 I 1 I 2 V 1 V 2 (c) I I 2 1 I 1 V 1 V 2 V 1 I 2 V 2 (d) (e) I in 1 2 I in I 1 I 1 V in 1 1 V 1 2 V 2 V in 1 1 V V 2 (f) Figure 1.21 Pumping circuits: (a) buck pump, (b) boost pump, (c) buck boost pump, (d) positive uo-pump, (e) negative uo-pump, (f) positive super uo-pump and (g) negative super uo-pump. and power delivery from source to the users are not in continuous mode. Therefore, digital control theory has to be applied in this area. All conversion technologies (such as pumping circuits, A/ rectifiers, /A inverters, / converters and A/A (and/or A//A) converters) are theoretically based on the switching circuit. It is urgent to investigate the digital power electronics rather than the traditional analog control applied in analog power electronics. The following typical circuits are examples of switching circuits working in the discrete-time mode Fundamental Pump ircuits All power / converters have pumping circuit. Pumping circuits are typical switching circuits to convert the energy from an energy source to energy-storage components in discrete state. Each pump has a switch and an energy-storage component that can be an inductor. The switch turns on once in a period T = 1/f, where f is the switching frequency. Therefore, the energy transferred in a period is a certain value that can be called energy quantum. Figure 1.21 shows seven (buck, boost, buck boost, positive uo, negative uo, positive super uo and negative super uo) pumping circuits, which are used in the corresponding / converters. (g)

24 24 igital power electronics and applications All pumping circuits are switching circuits that convert the energy from source to load or certain energy-storage component in discrete state. Each pumping circuit has at least one switch and one energy-store element, for example an inductor. The switch is controlled by a PWM signal with the period T (T = 1/f, where f is the switching frequency) and the conduction duty cycle k. The energy was absorbed from the energy source to the inductor during switching-on period kt. The energy stored in the inductor will be delivered to next stage during switching-off period (1 k)t. Therefore, the energy from the source to users is transferred in discrete-time mode A/ ectifiers All A/ controlled rectifiers are switching circuits. Figure 1.22 shows few rectifier circuits (namely single-phase half-wave, single-phase full-wave, three-phase half-wave, and three-phase half-wave controlled rectifier), which are used in the corresponding A/ converters. All A/ rectifier circuits are switching circuits that convert the energy from an A source to load in discrete state. Each A/ controlled rectifier has at least one switch. For example, a half-wave controlled thyristor (silicon controlled rectifier, ) rectifier has one switch. The switch is controlled by a firing pulse signal with the repeating period T (T = 1/f, where f is the switching frequency for the single-phase rectifiers) and the conduction period. The energy was delivered from the energy source to the load during switching-on period. The energy is blocked during switching-off period. Therefore, the energy from the source to loads is transferred in discrete-time mode /A PWM Inverters All /A inverters are switching circuits. Figure 1.23 shows three (single-phase, three-phase, three-level three-phase) /A PWM inverter circuits, which are used in the corresponding /A inverters. All /A PWM inverter circuits are switching circuits that convert the energy from a source to load in discrete state. Each /A inverter has multiple switches. The switches are controlled by PWM signals with the repeating period T (T = 1/f, where f is the switching frequency for the single-phase rectifiers) and the modulation ratio m. The energy was delivered from the energy source to the load during switchingon period. The energy is blocked during switching-off period. Therefore, the energy from the source to loads is transferred in discrete-time mode / onverters All / converters are switching circuits. Figure 1.24 shows seven (buck, boost, buck boost, positive output uo, negative output uo, positive output super-lift uo and negative output super-lift uo converters) / converter circuits.

25 Introduction 25 I Q I G V AK V V V 2V sin ωt (a) On V m T 3, T 4 v T 1, T 2 T 3, T 4 v V m sin ωt 0 a π π α 2p ωt I T 1 T 3 V T 4 T 2 0 a π π α 2p ωt I O I ircuit I 0 I a V 0 ωt dc p 2p I I a I O 0 I π α 2p dc 0 ωt a p V dc I a (b) Quadrant Waveforms Figure 1.22 A/ controlled rectifiers: (a) ingle-phase half-wave controlled rectifier and (b) single-phase full-wave controlled rectifier.

26 26 igital power electronics and applications a I a I T1 T 1 b n I b T 2 I O I a V dc I c c T 3 oad 0 I dc I O ircuit Quadrant a = 0 V ah V bh V ch 0 π π π 2π 6 3 ωt α 0 α π 6 T 3 T 1 T 2 T 3 π 6 T 3 T 1 T 2 T 3 α π 3 T 3 T 1 T 2 T 3 α 2π 3 (c) T 3 T 1 T 2 T 3 Waveforms a I a l 1 I T 1 T 1 T 3 T 5 I O l a n c b I b oad Highly inductive load I c T 4 T 6 T 2 I (d) T 4 Figure 1.22 (contd.) (c) Three-phase half-wave controlled rectifier and (d) three-phase half-wave controlled rectifier.

27 Introduction V d (a) V d (b) A B V 0 A V d B (c) Figure 1.23 three-phase. /A PWM inverters: (a) single-phase, (b) three-phase and (c) three-level

28 28 igital power electronics and applications I 1 I 2 I 1 I 2 I 1 I 2 I I V V 1 V V V 2 V 1 V V I 2 I V 1 V I I V 2 (a) (b) (c) V I O I O I s I V I O O I V I O V I s I O I O I O V in V V O (d) (e) I in 1 2 I O 1 1 V 1 V in 2 V 2 I in 2 I O V in 1 V 1 1 VO _ 1 2 V 2 (f) (g) Figure 1.24 / converters: (a) buck converter, (b) boost converter, (c) buck boost converter, (d) positive output uo-converter, (e) negative output uo-converter, (f) positive output super-lift uo-converter and (g) negative output super-lift uo-converter.

29 Introduction 29 All / converters circuits are switching circuits that convert the energy from a source to load in discrete state. Each power / converter has at least one pumping circuit and filter. The switch is controlled by a PWM signal with the repeating period T (T =1/f, f is the switching frequency) and the conduction duty cycle k. The energy was delivered from the energy source to the load via the pumping circuit during switching-on period kt. The energy is blocked during switching-off period (1 k)t. Therefore, the energy from the source to loads is transferred in discrete-time mode A/A onverters All A/A converters are switching circuits. Figure 1.25 shows three (single-phase amplitude regulation, single-phase and three-phase) A/A converter circuits. All A/A converter circuits are switching circuits that convert the energy from an A source to load in discrete state. Each A/A converter has multiple switches. The V T1 I s T 1 I g1 I O I s Triac I O I g2 T 2 v s 2V s sin ωt O v s 2V s sin ωt O V A O A 1 2 I s I O I s T 1 I O 3 4 v s 2V s sin ωt O v s 2V s sin ωt A O A T 1 I s I O v s 1 2V s sin ωt O A (a) Figure 1.25 A/A converters. (a) ingle-phase amplitude regulation.

30 30 igital power electronics and applications P-onverter N-onverter I V I O P 1 P 2 N 1 N A 2 I l v V o a P 3 P 4 d N 3 N 4 (b) V AO I A A Matrix converter Bidirectional switches Aa Ab Ac 0 V BO I B B Ba Bb Bc I Three-phase input Input filter a b c I a I b I c a b c Three-phase inductive load V an V bn V cn M V AO Aa V an Ab Ba Ac a V BO Bb V bn b Bc (c) c V cn Figure 1.25 (contd.) (b) ingle phase A/A cyclo converter and (c) three-phase A/A matrix converter.

31 Introduction 31 switches are controlled by PWM signals with the repeating period T (T = 1/f, where f is the switching frequency for the single-phase rectifiers) and the modulation factor. The energy was delivered from the energy A source to the load during switching-on period. The energy is blocked during switching-off period. Therefore, the energy from the source to loads is transferred in discrete-time mode. 1.5 HOTAGE OF ANAOG POWE EETONI AN ONVEION TEHNOOGY Analog power electronics use the traditional parameters: power factor (PF), efficiency (η), total harmonic distortion (TH) and ripple factor (F) to describe the characteristics of a power system or drive system. It is successfully applied for more than a century. Unfortunately, all these factors are not available to be used to describe the characteristics of switching circuits: power / converters and other high-frequency switching circuits. Power / converters have been usually equipped by a power supply source, pump circuit, filter and load. The load can be of any type, but most investigations are concerned to resistive load and back EMF or battery. It means that the input and output voltages are nearly pure voltages with very small ripple, e.g. output voltage variation ratio is usually less than 1%. In this case, the corresponding F is less than 0.001, which is always ignored. ince all powers are real power without reactive power jq, we cannot use power factor (PF) to describe the energy-transferring process. As only components exists without harmonics in input and output voltage, TH is not available to be used to describe the energy-transferring process and waveform distortion. To simplify the research and analysis, we usually assume the condition without power losses during power-transferring process to investigate power / converters. onsequently, the efficiency η = 1 or 100% for most of description of power / investigation. Otherwise, efficiency (η) must be considered for special investigations regarding the power losses. In general conditions, all four factors are not available to apply in the analysis of power / converters. This situation lets the designers of power / converters confusing for very long time. People would like to find other new parameters to describe the characteristics of power / converters. There is no correct theory and the corresponding parameters to be used for all switching circuits till r. Fang in uo and r. Hong Ye firstly created new theory and parameters to describe the characteristics of all switching circuits in Energy storage in power / converters has been paid attention long time ago. Unfortunately, there is no clear concept to describe the phenomena and reveal the relationship between the stored energy and the characteristics of power / converters. We have theoretically defined a new concept, energy factor (EF), and researched the relations between EF and the mathematical modeling of power / converters.

32 32 igital power electronics and applications EF is a new concept in power electronics and conversion technology, which thoroughly differs from the traditional concepts such as power factor (PF), power-transfer efficiency (η), total harmonic distortion (TH) and ripple factor (F). EF and the subsequential other parameters can illustrate the system stability, reference response and interference recovery. This investigation is very helpful for system design and / converters characteristics foreseeing. 1.6 POWE EMIONUTO EVIE APPIE IN IGITA POWE EETONI High-frequency switching equipment can convert high power, and its power density is proportional to the applying frequency. For example, the volume of a 1-kW transformer working in 50 Hz has the size 4 in. 3 in. 2.5 in. = 30 in. 3 The volume of a 2.2-kW flat-transformer working in 50 khz has the size 1.5 in. 0.3 in. 0.2 in. = 0.09 in. 3 The difference between them is about 1000 times. To be required by the industrial applications, power semiconductor devices applied in digital power electronics have been improved in recent decades. Their power, voltage and current rates increase in many times, the applying frequency is greatly enlarged. For example, the working frequency of an IGBT increases from 50 to 200 khz, and the working frequency of a MOFET increases from 5 to 20 MHz. The power semiconductor devices usually applied in industrial applications are as follows: diodes; s (thyristors); GTOs (gate turn-off thyristors); BTs (power bipolar transistors); IGBTs (insulated gate bipolar transistors); MOFETs (power MO field effected transistors); Ms (MO controlled thyristors). All devices except diode are working in switching state. Therefore, the circuits consists them to be called switching circuits and work in discrete state. FUTHE EAING 1. uo F.. and Ye H., Advanced / onverters, Press, Boca aton, Florida, UA, IBN: uo F.., Ye H. and ashid M. H., / conversion techniques and nine series luoconverters. In Power Electronics Handbook, ashid M. H. and uo F.. et al. (Eds), Academic Press, an iego, UA, 2001, pp Mohan N., Undeland T. M. and obbins W. P., Power Electronics: onverters, Applications and esign, 3rd edn., John Wiley & ons, New York, UA, 2003.

33 Introduction ashid, M. H., Power Electronics: ircuits, evices and Applications, 2nd edn., Prentice- Hall, UA, Nilsson J. W. and iedel. A., Electric ircuits, 5th edn. Addison-Wesley Publishing ompany, Inc., New York, UA, Irwin J.. and Wu. H., Basic Engineering ircuit Analysis, 6th edn., John Willey & ons, Inc., New York, UA, arlson A. B., ircuits, Brooks/ole Thomson earning, New York, UA, Johnson. E., Hilburn J.., Johnson J.. and cott P.., Basic Electric ircuit Analysis, 5th edn., John Willey & ons, Inc. New York, UA, Grainger J. J. and tevenson Jr. W.., Power ystem Analysis, McGraw-Hill International Editions, New York, UA, Machowski J., Bialek J. W. and Bumby J.., Power ystem ynamics and tability, John Wiley & ons, New York, UA, uo F.. and Ye H., Energy Factor and Mathematical Modelling for Power / onverters, IEE-Proceedings on EPA, vol. 152, No. 2, 2005, pp uo F.. and Ye H., Mathematical Modeling for Power / onverters, Proceedings of the IEEE International onference POWEON 2004, ingapore, 21 24/11/2004, pp Padiyar K.., Power ystem ynamics, tability and ontrol, John Wiley & ons, New York, UA, 1996.