Power Electronics Notes

Université de Tunis - ESSTT - Département de Génie Electrique

Electronique de Puissance - Introduction

• This document covers the official power electronics program for the third year of master's degree in electrical engineering.

• It's structured into six chapters, some with associated tutorials.

• Chapter Breakdown:

  • Chapter 1: Static and dynamic characteristics of power electronic components (diodes, thyristors, transistors, and derivatives).

  • Chapter 2: Single-phase uncontrolled rectifiers.

  • Chapter 3: Polyphase AC/DC converters (controlled and uncontrolled).

  • Chapter 4: AC/AC converters.

  • Chapter 5: DC/DC converters, focusing on different chopper configurations.

  • Chapter 6: DC/AC converters, specifically single-phase and three-phase inverters with R-L loads.

• An appendix provides necessary mathematical tools.

Programme Enseigne (Course Program)

• I - Introduction to Power Electronic Systems

• II - Static Switches in Power Electronics

  • Static and dynamic characteristics, along with their control.

  • Components: Diodes, Thyristors, GTO, Triac, Bipolar Transistors, MOS Transistors, and IGBTs.

• III - Power Electronic Converters

  • III-1. Rectifier Circuits: Diodes, thyristors, and mixed configurations.

  • III-2. DC/DC Converters:

    • Buck (step-down) chopper

    • Boost (step-up) chopper

    • Reversible chopper

    • Switching power supply

  • III-3. DC/AC Converters:

    • Single-phase and three-phase voltage inverters

    • Single-phase and three-phase current inverters

    • Single-phase and three-phase PWM (Pulse Width Modulation) inverters

    • Resonant inverters

  • III-4. AC/AC Converters:

    • Single-phase and three-phase AC voltage controllers (variacs)

Etude des Caractéristiques Statiques et Dynamiques des Composants Utilisés en Electronique de Puissance (Study of Static and Dynamic Characteristics of Components Used in Power Electronics)

1-Les Diodes (Diodes)

1-1. Caractéristiques statiques (Static Characteristics)

• A diode acts as an electronic switch:

  • Closed (conducting) in one direction (forward).

  • Open (non-conducting) in the opposite direction (reverse).

• Ideal static characteristics:

  • V_k < 0: inverse

  • $i = 0$: inverse

  • V_k > 0: direct

  • $V_k = 0$: direct

• Real component characteristics deviate from the ideal.

1-1.a. En direct (Forward Bias)

• In the conducting state, a diode exhibits a non-zero voltage drop $\v<em>F$, which increases with the crystal's temperature and the forward current \iF.

• $v<em>F = f(i</em>F, T)$ where $T$ is temperature.

• Away from the "knee" (very small $i_F$ values), the forward characteristic approaches a linear asymptote expressed as:

• $v<em>F = v</em>{T0} + r<em>f i</em>F$

  • $v_{T0}$: Threshold voltage (0.8V to 1.4V).

  • $r_f$: Apparent dynamic resistance (0.1 to 100mΩ).

• Maximum acceptable values are specified by the manufacturer:

  • Average forward current: $I_{FAV}$

  • RMS forward current: $I_{FRMS}$

  • Non-repetitive peak current: $I_{FSM}$

  • Junction temperature in permanent regime: $T_{VJ}$

• Power dissipation in the diode due to conduction losses is given by:

  • $P<em>c = \frac{1}{T} \int</em>0^T v<em>F(t) i(t) dt = v</em>{T0} I<em>{FAV} + r</em>f I_{FRMS}^2$

  • Derivation:

    • $P<em>c = \frac{1}{T} \int</em>0^T (v<em>{T0} + r</em>f i(t)) i(t) dt$

    • $P<em>c = v</em>{T0} \frac{1}{T} \int<em>0^T i(t) dt + r</em>f \frac{1}{T} \int_0^T i^2(t) dt$

    • $P<em>c = v</em>{T0} I<em>{FAV} + r</em>f I_{FRMS}^2$

1-1.b. En inverse (Reverse Bias)

• In the blocked state, the diode conducts a small reverse leakage current, much smaller than the nominal forward current (µA to mA depending on $I_{FAV}$).

• $Ri$ value negligible.

• Average power loss in the diode during blocking is practically zero:

• $P<em>b = \frac{1}{T} \int</em>0^T v<em>R(t) i</em>R(t) dt \approx 0$

1-2. Comportement des diodes en régime de commutation (Diode Behavior in Switching Mode)

• Diodes are commonly used in rectification or switching applications.

• Crucial to understand diode behavior during current establishment and blocking.

1-2-1. Commutation à l’établissement (Turn-On Switching)

• a- Description: When a current is established through a diode that was initially blocked, the voltage drop doesn't immediately reach its static value $v_F$. It goes through a transient value that is notably higher.

• The direct current $i_F$ doesn't necessarily establish faster than other elements in the circuit allow.

• The dynamic characteristics of a diode during turn-on include:

  • Forward voltage overshoot \V{FP}: Its value can reach several tens of volts for current rise rates $\frac{di</em>F}{dt}$ up to 500 A/µs.

  • Forward recovery time \t{fr}: The duration between applying the forward voltage and $v</em>F(t)$ reaching a reference value $v<em>R$ relative to its final value $v</em>F$.

• These parameters strongly depend on external conditions. The amplitude \V{FP} depends mainly on the rate of change of current $\frac{di</em>F}{dt}$ and the amplitude of the voltage source generating the current.

• Turn-on switching is less sensitive to current amplitude but evolves relatively quickly with temperature (approximately a 50% increase in \t{fr} and \V{FP} for a 100°C increase in junction temperature).

• The overvoltage \V{FP} is primarily related to the thickness of the diode's central region. High voltage diodes (thick central zone) exhibit a higher \V{FP} than low voltage diodes.

• Order of magnitude for \V{FP} and \t{fr} for different diodes:

  • Conditions $E = 50 V, \frac{d<em>i}{dt} = 50 \frac{A}{\mu s}, i</em>F = 0.5 A$

    • BAX12 (120V): $V<em>{FP} = 1.4V, t</em>{fr} = 8ns$

    • PLQ1 (150V): $V<em>{FP} = 1.5V, t</em>{fr} = 12ns$

    • PLR816 (1100V): $V<em>{FP} = 18V, t</em>{fr} = 170ns$

    • PYV88 (1250V): $V<em>{FP} = 26V, t</em>{fr} = 200ns$

    • BA159 (1500V): $V<em>{FP} = 38V, t</em>{fr} = 400ns$

    • 1N4007 (~1600V): $V<em>{FP} = 42V, t</em>{fr} = 640ns$

• - Pertes d’énergie en commutation à la fermeture (Switching Energy Losses at Turn-On)

  • During the transition from 0 to \t_{fr} figure(1-5)

    • It is assumed Fi(t)= FI and $v(t)=V<em>{FP}-(V</em>{FP}-V) \frac{t}{t_{fr}}$

  • The energy dissipated in the diode during the transition is:

    • $W<em>c = \int</em>0^{t<em>{fr}} v(t) i(t) dt = \frac{1}{2} (V</em>{FP} + V<em>F) I</em>F t_{fr}$

  • If the switch is ideal: $W<em>{c</em>{ideal}} = \int<em>0^{t</em>{fr}} v(t) i(t) dt = V<em>F I</em>F t_{fr}$

  • The additional loss of energy is expressed as:
    * $\Delta W<em>c = W</em>c - W<em>{c</em>{ideal}}=\frac{1}{2} (V<em>{FP} - V</em>F) I<em>F t</em>{fr}$

  • Therefore, the additional power developed in the component is calculated by:
    * $P<em>c = \frac{1}{2} f (V</em>{FP} - V<em>F) I</em>F t_{fr}$

• b- Conséquences (Consequences)

  • The diode's turn-on behavior doesn't damage the component itself but can harm other circuit elements.

    • - The slow rise of the direct current: it can increase the turn-off time of a component driven by the diode.

    • - The turn-on overvoltage: which is significant at high direct current establishment rates, can increase the voltage supported by another component in the circuit.

1-2-2. Commutation au blocage (Turn-Off Switching)

• When a reverse voltage is suddenly applied to a switching diode, it does not block instantly. There's a delay before it regains its blocking capability. This duration is the reverse recovery time \t_{rr}.

• During this time, the diode acts like a short circuit in reverse due to stored charges from conduction.

• Stored Charge:

  • $Qs = \tau * i_F$

    • $\tau$: minority carrier lifetime.

    • $i_F$: forward current.

• Evacuation by recombination and by reverse current.

• When the rate of change of forward current $\frac{di<em>F}{dt}$ is very high, internal recombination is negligible, and recovered charge \QR is close to stored charge \Q_s.

• The reverse recovery is divided into two phases:

  • $0t$ to $1t$: forward current goes to 0 and reverse current \i_{rr} establishes. The charge Qs is removed.

  • $1t$ to $2t$: the reverse current passes the maximum value $I<em>{RM}$. The charge $Q</em>R$ is removed and the diode begins to regain blocking capability.

• Two types of diodes based on reverse recovery current waveform:

  • Rapid recovery (Snap-off): Abrupt current decrease.

  • Soft recovery:Gradual current decrease.

2- Les thyristors (Thyristors)

2-1. Caractéristique statique des thyristors (Static Characteristics of Thyristors)

• A thyristor has two stable states:

  • Blocked state:This occurs in two situations:

    • When it is polarized under negative voltage \V_{AK} < 0; it can withstand a reverse voltage VRRM or VRROM in repetitive mode or VRSM in non-repetitive mode.

    • When it is forward-biased \V_{AK} > 0 but the gate current intensity is maintained at zero.

  • Conducting state: This is achieved if the thyristor, initially forward-biased (point B), receives a sufficient current pulse in the − junction GK . Point comes to C, and the intensity Ai is fixed by the other elements of the assembly.

• After trigger current ceases, the thyristor remains on (like a diode) if anode current exceeds the holding current \I_H.

• The forward voltage drop across the conducting thyristor:

  • $v<em>{AK} = v</em>{T0} + r<em>i i</em>A$

    • $v_{T0}$: Threshold voltage

    • $r_i$: Dynamic resistance

• Instantaneous power dissipation:
  * \p = v{T0} iA + ri iA^2

• Average power dissipation:
  * $P= v<em>{T0} I</em>{Amoy} + r<em>i I</em>A^2$

2-2. Commutation (Switching)

• -Pendant la fermeture: It is the passage from a direct state to a passing state; It requires a gate current \iG(t) having a certain intensity for a certain duration. The closure is characterized by the duration \tG= tr+td
  s’écoulant between the instant, where iG vaut 10% of its maximum value and the one where vAK is brought back to 10% of its initial value. The start-up delay td decreases when
  we increase iG and its speed $\frac{diG}{dt}$ where if we increase vAK . The rise time rt depends on $\frac{diA}{dt}$.

• -Pendant l’ouverture:
  We can open a thyristor by putting it under reverse voltage. The manufacturer indicates the minimum value of the duration of the opening under zero or reverse voltage beyond which the blocking of a direct voltage is possible.

• - Sécurité d’un thyristor (Thyristor Security)
  * The safety of the thyristor assumes compliance with the following contraints. :
  * \frac{di}{dt}<(\frac{di}{dt}){cr} * \frac{dv}{dt} <(\frac{dv}{dt}){cr}
  * a- Protection contre les (dv/dt) à l’état bloqué
  * La fonction est assurée par circuit RC série entre anode et cathode et par une bobine d’inductance L en série
  * b- Protection contre les (di/dt) à la fermeture
  * D R Ai RL L AK vc i i C U R'

• 2-2-1. Commande de la fermeture
  * Le command circuit must mainly deliver, to start a thyristor, a gate current that is greater than iGT (supplied by the manufacturer) for a duration such as Ai becomes higher than the holding current IH . It must also:
  * - provide galvanic isolation between power and control circuits,
  * - produce a delayed start-up with respect to certain supply voltages and allow the adjustment of the delay on start-up,
  * - put the thyristor in conditions allowing it to start up as soon as the state of load will allow him.

• 2-2-2. Blocage d’un thyristor
  * For a blockade can be obtained by different families:
  * - Blocage en tension
  * - Blocage en courant sous fable tension
  * - Blocage mixte at réciproque ….

3- Les transistors bipolaires (Bipolar Transistors)

• A transistor working in switching can only occupy two stable states in a stable way state:

  • blocked state, it theoretically suffices not to supply its base,

  • saturated state, it is necessary to send to its base a current greater than i / β C ; where β is static gain.

• Practically the start-up and blocking processes are complex and generally lead to a reverse polarization of the base VBE during the blocking phases of the transistor.

3-1. Commutations (Commutations)

• - Amorçage (Start-up)

  • The start-up is characterized:
    * un temps de retard dt «delay time» between the moment d’application de Bi et the passage of ci at 10% of its final value,
    * un temps de montée rt «rise time» between the moment of passage de Bi entre 10% et 90% of its final value.

  • The builder indicates the closing time on d r t t t = + .

• - Fermeture (Closure)

  • The closure is characterized: * Un temps d’évacuation de la charge stockéest «storage time» between the suppression of Bi et the passage of ci at 90% of its initial value, * Un temps de descente ft «fall time» between the instant of passage de Bi entre 90% et 10% of its initial value. -L’overture peut être réalisé par deux types de condition pour la jonction : * Polarisation directe

    • Polarisation inverse

3-2. Problèmes posés par la commutation (Problems Posed by Commutation){

En admettant que le courant collecteur Ci évolue linéairement en fonction du temps lors des transitions (mise en conduction et blocage). Les chronogrammes de ci, cev et PT one les allures indiquées par la figure (1-).
Durant la commutation, les pertes sont élevées. On se propose de les réduire en ajoutant un circuit auxiliaire dit ‘circuit d’aide à la commutation’. Ce circuit permet:
à l’ouverture, un condensateur C, mis en parallèle sur Tr limite la croissance de cev,
à la fermeture, une inductance L, mise en série avec le transistor, limite
the montée du courant ci. Une diode DL allows l’extinction du courant ci before la fermeture suivante. Une résistance Rc limite le courant de décharge de C à la fermeture.

4- Les transistors à effet de champ (Field Effect Transistors)

The builders realize field-effect transistors (or switching). These are generally insulated grid components, figure (1-). These components allow performances comparable to those of the bipolar transistor while taking advantage of the advantages of the field effect transistor:
*Very high input impedance; which means that the operating state of transistor is determined by the input voltage,

• Very short switching time and in principle no delay time or dwell time of stored charge.

4- Les transistors IGBT (Insulated-Gate Bipolar Transistor)

A transistor IGBT is the marriage of a bipolar transistor and a field effect transistor as shown in the following figures:
Principle
The diagram of an IGBT is then