LCL-T Resonant Converter Based on Dual Active Bridge Topology in Solar Energy Applications

AbstrAct: Resonant LCL-T converter can operate as stable voltage source, being fed from current, for instance, the photovoltaic battery. It is shown that LCL-T resonant tank has intrinsic ability to convert stable AC current into stable AC voltage thus parametrically regulating output voltage at a fixed value. This mode of operation is made possible by the use of active (synchronous) rectifier to recoup energy from the output back to the LCL-T resonant tank. Basic characteristics of resonant LCL-T converter regulated by phase shift between inverter and rectifier regardless of a solar battery current drift have been defined. It is shown that phase control guarantees 0 voltage and 0 current on switching; however, turn-off current could be substantial. Calculations and assumptions made in this study have been confirmed by simulation and hardware prototype.


IntroductIon
Advancements in spacecraft (SC) power supply unit (PSU) are mostly related to enhancements in specific energy parameters, notably size, weight, and efficacy.Contemporary power converters in PSU are presented by non-isolated boost types controlled by pulse width modulation (PWM).The most prohibitive feature of such converters is hard commutation of switching devices, being a source of high losses as well as electromagnetic interference (EMI).The mitigation of hard switching shortcomings by introduction of various snubbing circuits to provide resonant switching transitions is not helpful due to added complexity and need for additional active elements to be commutated in the very same way (Pavlovic et al. 2012;Shiva Kumar et al. 2015;Bodur et al. 2003;Akın 2014;Goryashin and Khoroshko 2011).The commutation itself becomes too long and quite often creates unwanted oscillations thus increasing safety margin required and limiting conversion frequency as well as regulation range.All of this have led to the use of dual active bridge (DAB) resonant converters (Hillers et al. 2012;Selvaperumal et al. 2009;Sowjanya and Raghavendran 2013;Krismer and Kolar 2009;Osipov et al. 2015;Shivaraja 2015), including series LC tank, which is a resonant circuit.Sinusoidal waveform of inverter current automatically provides soft switching without axillary components.However, the energy source of SC PSU is usually a photovoltaic (PV) battery.It operates as current source while voltage is usually limited by isolation breakdown level in vacuum.At the same time load can vary a lot.Typical resonant LC converter cannot be used as a voltage regulator Osipov AV, Shinyakov YA, Shkolniy VN, Sakharov MS just because no-load condition will force the PV battery to operate in voltage source mode, creating high voltage across its terminals and increasing the possibility of breakdown.
The solution for this problem is the use of LCL-T converters (usually referred as "inductive-capacitive converter" in the Russian literature), typically applied as alternating current (AC) source and fed by stable AC voltage.The performance of such converters was analyzed in Russia (Milach et al. 1964;Dozorov 2013) and elsewhere (Borage et al. 2005;Borage and Tiwari 2012;Zouggar et al. 2000).However LCL converters can operate just in opposite way converting current source into voltage source, which is exactly the task the converter should perform in PV battery fed by PSU.In that case input current defines resonant tank 1, which, in turn, makes the value of AC voltage at resonant capacitor near constant regardless the load.Interestingly enough no investigations of such mode of operation could be referredto.
To date published research papers describe the operation of LCL-T converter with diode-based (passive or uncontrollable) rectifier in output current stabilization mode, for instance, Borage et al. (2005).Therefore, the purpose of this study was to analyze resonant LCL-T converter in DAB configuration as voltage source mode being fed by PV battery operating in current source mode.

MEtHodoLoGY
LcL-t resonAnt converter operAtion in current-to-voLtAge conversion mode Transistors in resonant converters are commutated at the frequency near LC tank resonant 1, which provides sinusoidal current with near 0-value at switching instances, minimizing losses.Resonant tank can be loaded in different ways depending on the input source impedance.If the PV battery operates in voltage mode then the load is connected in series with the resonant tank (typical resonant DCDC converter) (Fig. 1а).If PV battery operates as current source the load is connected in parallel to the capacitor in resonant tank creating the so-called Boucherot circuit, in which circuit inverter's output voltage is square by waveform.If the frequency equals to resonance 1 the current has sinusoidal waveform allowing switching transistors with minimal losses.
Regarding Boucherot circuit being fed by current source, capacitor's current I Сn amplitude is stable and actually does not depend on the load; correspondingly output voltage is stable, picked up at terminals of the capacitor С n , and the value is defined by the equation where: ρ = √L n /C n is the tank's characteristic impedance; L n is the inductance value of resonant inductor L n ; C n is the capacitance value of resonant capacitor C n .
Accordingly, varying parameters of the resonant tank 1 may match the current level of PV battery to the output voltage required without the use of transformer allowing to have output voltage lower than the input one, i.e.R L < ρ, where R L means load resistance.
In Busherot circuit (Fig. 1а) load current is the difference between capacitor and inverter ones, while capacitor's current is stable by amplitude and is in phase with inverter's voltage; inverter current is lagging voltage U 1м by angle α, depending on the load (Fig. 1b): (1) Voltage across the load U Cn is shifted in respect to inverters one by π/2.In that case the phase of capacitor current is shifted in regard to the inverter's one by the angle α defined by the load If the frequency is fixed as ω 0 = √1/L n C n the load increase yields the phase shift defined in Eq. 2; in that case output voltage of an angular frequency ω 0 becomes stable due to compensation by the inductor current.Bode plot shows that load increase leads to the loss of converter resonance properties.To reduce phase shift due to the load change LCL-T topology may be used (Fig. 2).The vector diagram of LCL-T converter (Fig. 2b) shows that in case of L n = L f an additional voltage drop across L f allows forming an angle equal to π/2 between the vectors of load current and inverter one regardless of the load.This condition can be met by the equality of right triangles formed where: U PV represents photovoltaic voltage.
Frequency-related parameters of LCL-Т converter are shown in Fig. 2c.It can be observed that LCL-T tank allows stabilizing output voltage parametrically operating at the resonant frequency for the full load range.

LcL-t converter operAtion AnALysis in current-to-voLtAge conversion mode with output rectifier
In order to supply constant output voltage one may need to use rectifier, bridge type, for instance (Fig. 3а), which substantially changes the converter behavior.Before anything else, the first harmonic experiences least resistance as a result, the output voltage can be defined as So the resonant tank values could be defined as The simulation for fixed output voltage U out = 100 V, input current I PV = 8 A, f = 50 kHz, and resonant tank parameters taken in accordance with Eq. 7 shows that output current is discontinuous, distorting rectifier input voltage U rect , having I Lf = 0 and U rect = U Cn (Fig. 3b).The converter operates in non-resonant mode, and output voltage value does not comply with calculated value U out = 100 V, increasing along with the load resistance.Idle operation is not possible.These problems can be partially solved by operating frequency adjustment (Borage et al. 2005;Zouggar et al. 2000).
If one uses fully-controlled switches for rectifier, operation in continuous conduction mode could be forced and the aforementioned problems fixed by recouping energy from the output capacitor back to the resonant tank (Fig. 4а) thus making topology commonly referred as DAB.For proper operation output bridge control should be shifted by π/2 in respect to inverter.This is exactly the phase between inverter and load currents (Fig. 2b).
From the simulation it is clearly verified that, in order to stabilize output voltage at calculated value of U out = 100 V, regardless of the load, one needs to operate at resonant point in continuous conduction mode for active rectifier I rect (Fig. 4b).Rectifier current I rect is not sinusoidal, being result of the application of 2 voltages to output inductor, rectangular U rect , and sinusoidal U Cn , which is specific to that topology.As a result rectifier current contains sinusoidal as well as saw tooth components: as well as sinusoidal components in current do have equal fundamental harmonic and, correspondingly, there is no fundamental harmonic in the output current.Besides, averaged rectified current is equal to 0 (Fig. 5а).
As we increase the load phase shift between capacitor and rectifier voltages, α starts to appear, and capacitor's voltage starts (Fig. 5b).In the case when R H = π 2 /8ρ, i.e., at the valueR H *= 1, phase shift α = π/4 and rectifier's current contains fundamental harmonic For a given case there are diagrams shown in Fig. 6b.If PV battery current is decreased to I PV = 5.6 А, σI PV = √2 and R L * = 2, in accordance with Eq. 10; to produce previous output voltage level, control angle β = π/4 is necessary, meaning α = β.Thus using Eq. 12 we can derive U Cn = (2√2/π)U out , which is shown in the diagram of Fig. 6b.
Commutation mode of switches in LCL-T converter using phase regulation: the condition necessary for ZVS is the lag of rectifier voltage in respect to inverter's voltage by π/2 + β.Such control mode provides conditions for turning transistors ON.Commutation transitions depend on a bridge place.In the inverter, one has to make commutation before the current changes the sign (Fig. 8b), which provides turning in the complementary switch at reverse bias or 0 voltage across.In rectifier, one has to make commutation after the change of the current sign (Fig. 8).This way, in order to provide ZVS, one has to supply a leading current phase of the inverter and a lagging one for the rectifier.Turn off transition occurs at rather high current; however, proper snubbing capacitor across the switch or even transistor's output capacitance together with dead time adjustment does provide proper commutation.

rEsuLts
The components used in hardware prototype are shown in Table 1.To verify simulation data hardware prototype has been built (Fig. 4a) Actual diagrams are presented in Fig. 9.The parametric stabilization obtained 2%, and soft commutation could be observed in all cases.
It is shown that, if input current amplitude is held constant at 0.86 A (using hardware PV battery simulator IPV-200/7-4),   et al. 2012;Hillers et al. 2012;Selvaperumal et al. 2009), there is no need for frequency adjustment, which in turn eases control effort.

PV
Fig. 1c.It is clear that the shunting influence of the load shifts resonant frequency of the tank in accordance with
Regulation curves are shown in Fig. 7.It is clear that the angle of control α depends on the control angle β, while minimum capacitor voltage occurs if α = β, and it corresponds to U Cn * = (π/2)(1/cosβ); in case of β = π/4 and R L * → ∞ , the voltage across C n would be U Cn * = (π/√2).
It is very important to hold phase shift of π/2 between inverter voltage U inv and rectifier current I rect to provide conditions for parametric stabilization of the output voltage, because it will preserve the equality of triangles formed by the vectors U inv , U Ln , U Cn and U rect , U Lf , U Cn , respectively.Angle α is determined by the load value similarly to the previous case and could be calculated as follows:where: R L * = (8/π 2 )(RL/ρ) is the normalized load value.Angle α, in turn, defines voltage across С n :

Figure 8 .
Figure 8.Current and voltage waveforms of rectifier and inverter in resonant LCL-T converter using phase control.Figure 7. (a) Control angle α; (b) Resonant capacitor voltage, U Cn , versus normalized load in the LCL converter.

Figure 7 .
Figure 8.Current and voltage waveforms of rectifier and inverter in resonant LCL-T converter using phase control.Figure 7. (a) Control angle α; (b) Resonant capacitor voltage, U Cn , versus normalized load in the LCL converter.
then output voltage stays at 60 V. Variation of the load resistance does change input current consumed.full load.Moreover, for operation at the idle unlike the state-of-the-art prototypes (Pavlovic