English

not defined

no text concepts found

ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain Resonant converters are used to reduce/eliminate the switching losses. There are three basic types of the resonant DC/DC converters: 1. Series resonant converter 2. Parallel resonant converter 3. Series-Parallel resonant converter I. Series Resonant Converter: S1 S2 D1 + D2 Vi _ S4 S3 D4 is L C Dr1 N1: N2 + + vs _ vp _ + vsec _ ior Io Co RL + Vo _ Dr2 D3 Figure 1 One method of controlling the output voltage in resonant converters is to control the switching frequency of the full-bridge inverter. This method is called ‘variable frequency control’. In this type of control, the switching frequency (fs) controls the impedance of the resonant components connected between the inverter and the load. This in-turn controls the power flow from the input to the output and, therefore, the output voltage. The resonant components L and C have a fixed value of the resonant frequency ( f r 1 2 LC ). Depending upon the value of the frequency, the converter operates in the following three modes: 1. 2. 3. Below resonance mode (fs < fr) Above resonance mode (fs > fr) At resonance mode (fs = fr) In the below resonance mode, the switching frequency of the converter is lower than the resonant frequency. While in the above resonance mode, the switching frequency of the converter is higher than the resonant frequency. Obviously, at the resonance mode, both the frequencies are equal. The operating waveforms of the converter in these modes are given in Figure 2. In Figure 2, Vg,S1, Vg,S2, Vg,S3 and Vg,S4 represent the gate signal applied to switch S1, S2, S3 and S4 respectively. 1 ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain Vg,S1 Vg,S3 t Vg,S2 Vg,S4 vs t Vi t is t vp t ior Io t Vo t Ts /2 Ts (a) Below resonance 2 current is leads voltage vs ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain Vg,S1 Vg,S3 t Vg,S2 Vg,S4 vs t Vi t is t vp t ior Io t Vo t Ts /2 Ts (b) Above resonance 3 current is lags voltage vs ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain Vg,S1 Vg,S3 t Vg,S2 Vg,S4 vs t Vi t is t current is in phase with voltage vs vp t ior Io t Vo t Ts /2 Ts (c) At resonance Figure 2 Analysis of the Series Converter Since a resonant circuit is connected between the inverter and the load, it can be assumed that the current harmonics in the series resonant circuit are very small. Therefore, we are going to consider the fundamental equivalent circuit only. Also, for the fundamental circuit, the rectifier load at the primary 4 ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain of the transformer can be represented by an equivalent AC resistance Rac 8 RL . The equivalent 2 circuit of the converter of Figure 1 is given in Figure 3. jωsL is -j/ωsC + + vs1 _ vop _ Rac Zs Figure 3 Mathematical Analysis According to the Equivalent Circuit shown in Figure 3: Since vs is a square voltage waveform, the RMS value of the inverter voltage (vs) is represented by Vs1 as shown in (1): Vs1 2 2 Vi 0.9Vi ------------------------------------------------------ 1 Z s Rac j s L s C ------------------------------------------- (2) ------------------------------------------------------ (3) v s1 v s1 -----------------------------------------------------Zs Zs (4) Z s is (1) s L 1 s C 1 tan Rac Defining the following quantities: s 2f s operating angular switching frequency 5 [rad/s] ELEC 431 Class notes Resonant DC/DC Converters fs = operating switching frequency Q fr P.K. Jain [Hz] 2f r L 1 Quality factor Rac 2f r CRac 1 2 LC Resonant frequency [Hz] r 2f r Angular resonant frequency [rad/s] From equation (2): L 1 Z s Rac 1 j s R CR s ac ac L 1 Rac 1 j s r r r Rac s r CRac 1 Rac 1 j Q Q 1 Rac 1 jQ --------------------- (6) In equation (6), s Relative angular operating frequency r Since, Z s Z s 1/ 2 Hence → 2 1 Z s Rac 1 Q 2 ----------------------------------- (7) → 1 tan 1 Q ----------------------------------- (8) The inverter’s output current: 6 ELEC 431 Class notes Resonant DC/DC Converters is is P.K. Jain Vs1 Z s 0.9Vi 2 1 2 Rac 1 Q 1/ 2 ----------------------------------- (9) 1/ 2 ---------------------------------- (10) The magnitude of the output voltage vop is then vop is Rac vop 0.9Vi 2 1 Q 2 1 The output voltage of the converter can, therefore, be controlled by controlling the relative operating frequency ω or f. Figure 4 shows the output voltage control as a function of f. 7 ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain vop 0.9vi Small Q (a) output voltage High Q f= fr / fs Capacitive impedance Inductive impedance |Zs| ɸ (b) Impedance magnitude f= fr / fs 90° (c) Impedance angle 0 f= fr / fs -90° 1.0 Figure 4 The converter can operate in the following three modes: 1. f < 1: In this mode fs/fr < 1, and it is called “below resonance mode”. In this mode, the impedance seen by the inverter is capacitive. This causes a “leading” current with respect to the inverter output voltage vs. With the leading current, the inverter operates with the zero current switching (ZCS). 2. f = 1: In this mode fs/fr = 1, and it is called “At resonance mode”. In this mode, the impedance seen by the inverter is resistive. Both the inductive and capacitive impedances cancel each other. The output current ‘or’ voltage of the converter is maximum. The inverter output current is in phase with the voltage. With this the inverter operates with ZCS. 3. f > 1: In this mode fs/fr > 1, and it is called “above resonance mode”. 8 ELEC 431 Class notes Resonant DC/DC Converters P.K. Jain In this mode, the impedance seen by the inverter is inductive. This causes a “lagging” current with respect to the inverter output voltage vs. With the lagging current, the inverter operates with the zero voltage switching (ZVS). From Figure 4(a), it is clear that the maximum output voltage, therefore, the maximum power is obtained at the resonance point. The output voltage can be controlled either by reducing the operating frequency or by increasing the operating frequency. The operation of the converter is, however, preferred by increasing the frequency because the converter operates with ZVS. ZVS is a better technique than ZCS because with ZVS, both the turn-on and turn-off losses can be effectively reduced. In ZCS, only the turn-off loss can be reduced. However, the ZCS technique is preferred with the switches that rely on the external circuits to commutate. One example of such a switch is the “thyristor or SCR”. Advantages of the Series Resonant Circuit: The main advantage of the series resonant converter is its simplicity and its high efficiency from full-load to reduced-load. Disadvantages of the Series Resonant Circuit: The main drawback of the series resonant circuit is that it loses the output voltage control at very reduced loads and no loads. 9 ELEC 431 Class notes II. Resonant DC/DC Converters P.K. Jain Parallel Resonant Converter: S1 S2 D2 D1 + Vi _ L is C vs _ S3 D4 ior Lo io + vsec _ + + S4 Dr1 N1: N2 vp _ Co RL + Vo _ Dr2 D3 Figure 5 Advantage: No-load to full-load possible Disadvantage: Low efficiency at reduced loads III. Series-Parallel Resonant Converter: S1 S2 D1 + D2 Vi _ is L Cs + + S4 vs _ S3 D4 Cp Dr1 N1: N2 vp _ Figure 6 Advantage: No-load to full-load possible Disadvantage: Good efficiency from full-load to reduced-load 10 Lo Co + vsec _ Dr2 D3 ior io RL + Vo _