The LLCLC resonant converter based pseudo-DC link inverter

Technological advancements in solar power systems necessitate highly reliable power inverters with high efficiency and small size. An LLC resonant converter-based pseudo-Direct Current (DC) link inverters offer these qualities to some extent. The resonant circuits of conventional pseudo-DC link inverters cannot attain a zero gain and cannot handle variable frequency control which in turn requires very large filters to produce pure sinusoidal output voltages for the grid. The usage of these filters consequences in the enhanced price and size of inverters; moreover, the reliability of inverters is also reduced. We propose a novel topology for a pseudo-DC link inverter based on an LLCLC resonant converter. The proposed inverter does not require large filters, because it generates rectified sinusoidal output voltages. An additional parallel LC component is added in series to the resonant circuit, which makes it able to attain a zero gain through an infinite circuit impedance. The 400 W pseudo-DC link inverter with a 40 V input and a 400 V output is designed and simulated on OrCAD PSpice software. The results showed that there is a significant improvement in achieving a zero gain. The possible lowest gain achieved is approximately 0.125. The proposed technique claimed to be more efficient than those formerly used, subsequently contributing to satisfying outcomes.


INTRODUCTION
The depletion of fossil fuels triggered solar panels to become popular in producing electrical energy for years (N. Abas et al., 2015). These power plants have several advantages being easy to use, less overall cost, and environment-friendly operation (F. M. Guangul et al., 2019). Micro-inverters are an excellent choice for these systems as there is only one solar panel connected to each inverter which can provide benefits such as less installment space, no mismatch losses, and failure of one panel or inverter does not affect whole plant performance (S. Narendiran, 2013). Solar power plants provide a very low voltage (40V approximately) which needs to be increased 5 to 10 times for home appliances. The key design considerations for solar microinverters are small size, high efficiency, and reliability. The three main types of microinverters include those without any DC link, with a DC link, and with a pseudo-DC link (Y. Xue et al., 2004). The basic block diagram of the Pseudo-DC link inverter is given in Figure   1. The inverter consists of two stages i.e. DC-DC stage and the DC-AC stage. The DC-DC stage provides buck-boost operation and converters convert input DC voltage to rectified AC voltage which is then unfolded in the DC-AC stage. Pseudo-DC link inverters are promising because their secondary side only unfolds the rectified sinusoidal voltage (Q. Li et al., 2008).
So, a suitable DC-DC stage can provide all the required qualities. In the literature, a large number of DC-DC converters for the DC-DC stage are presented.
The reliability and high efficiency of an inverter can be achieved through soft switching techniques. Pulse width modulation-based flyback inverters have very small sizes because of fewer switching components but their hard switching operations decrease the overall efficiency. The hard switching can be reduced by using auxiliary switches, but it complicates the control process and decreases the low switching component advantages (L. mol K Johny et al., 2013). The inverters comprise of resonant converters provide excellent efficiency because of soft switching operations (S. Pervaiz et al., 2013). Their high-frequency operations also reduce the size of energy-storing components which is a key factor for having a smaller size.
The LLC resonant converter-based inverters working on pulse density modulation produce pure sinusoidal output, but large output filters further reduce the reliability and create size issues (Y. Zhao et al., 2015). Inverters with a hybrid control method can provide pure sinusoidal output without any extra-large filter but their control technique itself is very complicated (C. Yeh et al., 2020). The main reason for adopting hybrid control is that LLC resonant converters require a very high switching frequency to achieve zero tank gain which is practically not possible (M. Xingkui et al., 2016). Because of this drawback, inverters based on resonant DC-DC converters do not work completely on variable frequency control.
The LCLC or other four-element resonant converters provide two peak gain values in voltage gain characteristics but achieving zero gain is still not possible (R. Lin et al., 2018). On the other hand, LLCLC resonant converters can achieve approximately zero gain at an achievable switching frequency (R. Mazgut et al., 2016& J. Koscelnik et al., 2020. These converters consist of LLC resonant components with additional parallel LC components in series on the primary side. The additional components can also be added in series on the secondary side of the converter (H. Wu et al., 2016). The addition of the LC component provides a zero-gain property that can be used in the DC-DC stage of the converters to deliver complete variable frequency control without using a large filter on the output side.
In this paper, a novel LLCLC resonant converter based Pseudo-DC link inverter is proposed.
The paper is organized in such a way that after the introduction, the proposed topology of an inverter is presented followed by its analysis and operation. The design consideration is described next. In the end, the simulation results are discussed, and the conclusion is drawn.

PROPOSED TOPOLOGY
The circuit topology of the proposed inverter is given in Figure 2. The inverter consists of two stages i.e., DC-DC stage and the DC-AC stage. The DC-DC stage consists of a full bridge inverter having four semiconductor switches (S1 to S4). The full bridge converts input DC voltage to square wave voltage which is fed to LLCLC resonant tank whose gain changes by input square wave frequency variation. The tank is connected to a highfrequency transformer which can be used for buck-boost operation and isolation purposes.
The transformer is further connected to a full wave rectifier for rectification of transformer output. Another full bridge inverter consisting of four switches (S5 to S8) is used in the DC-AC stage. This stage unfolds the input rectified voltage to the sinusoidal output voltage. The DC-DC stage of the inverter is operated at a variable frequency to produce rectified sinusoidal voltage at the DC link stage while the DC-AC stage is operated at a constant frequency to unfold rectified sinusoidal voltage.

LLCLC Resonant Tank Analysis
The resonant tank circuit of the proposed inverter consists of five elements i.e., CS, CP, LS, LP, and Lm. CS and LS are series resonant components while CP and LP are parallel resonant components. Lm provides magnetizing inductance for the transformer. The addition of CP and LP changes the gain characteristics of the resonant tank helping to achieve zero gain. The gain values for the tank at different Q points are shown in Figure 3. The resonant tank has three main resonant frequencies i.e., fR1, fR2, and fR3. At resonant frequency fR1, the resonant circuit has a gain value equal to one. Below fR1, the operation of the LLCLC resonant tank is the same as the conventional LLC resonant tank. The gain is always more than one for the converter to have a boost operation. The converter has a buck operation between resonant frequency fR1 and fR2 because the gain is always less than one in this region. At resonant frequency fR2, the impedance of the resonant tank increases to infinity providing zero gain.
At resonant frequency fR3, the gain of the converter is again one and this resonant frequency has a very low impedance for the third harmonic which can reduce the reactive power of the resonant tank circuit. So overall, the buck-boost operation is performed by just changing the input frequency of the converter. The gain of a resonant tank with L as the inductance ratio, Q as the quality factor, and fN as the normalized switching frequency is given by (R. Mazgut et al., 2016): The resonant frequencies of the LLCLC resonant tank are given as f R1 = 1 2π where, A=L s C s +L p C p +L p C s and B=L s L p C s C p .

Modes of Operation
One complete switching cycle consists of 8 modes of operation. Firstly, it is assumed that all the switching components are ideal. Secondly, the circuit is already working and is in stable condition. The modes of operation of the LLCLC resonant converter (DC-DC stage) for the fR1≤fS≤fR2 frequency region are as follows: Mode 1 [t0-t1]: At time t0, the switches S1 and S4 are turned ON with ZVS, and diodes D1 and D4 conduct as shown in Figure 4a. Physically, when the secondary side is separated from the primary side, the components CS, CP, LS, LP, and Lm resonate together. When the primary side transmits power to the load, only CS, CP, LS, and LP resonate together. The successive modes of converter repeat the same way as described above. During the fR1≤fS≤fR2 region, the converter injects a third harmonic to the load, so the resulting shape of the series resonant current is like a square wave. The graphical representation of modes of operation in the regions fR1≤fS≤fR2 and fS<fR1 are given in Figure 5a and Figure 5b respectively. The converter works on discontinuous conduction mode and has two more modes in one complete switching cycle.

Working Operation of Inverter
The working principle of the proposed inverter with different stages is shown in Figure 6   The maximum switching frequency of the resonant tank is fR2. The lower switching frequency can be of any value in the ZVS region. It is preferred to use a switching frequency range between fR1 and fR2 because in this region the gain is evenly divided and below fR1 the gain changes exponentially. The design of CP and LP provides zero gain resonant frequency fR2. So, there should be a proper distance between resonant frequencies so that fR2 is too close to fR1 or fR3. For that purpose, if CS=CP=C and LS=LP=L, fR1 is 61.8% of fR2 while fR3 is 161.8% of fR2. The corresponding frequencies become f R1 =0.618f R2 and f R3 =1.61f R2 .

Reactive Components Design
A 400W pseudo-DC link inverter is designed on our proposed topology. The input voltage is 40V while the maximum output voltage is 400V. The load resistance RL is =0.1 and R eq = 8 π n 2 V 0 2 P o =10.19. The Q point is 0.25 and the inductance ratio (L) is 3.
The switching frequencies for the primary and secondary sides are selected as 200 kHz and 50 Hz respectively. The switching frequency range is fR1<fS<fR2 as the gain is evenly divided in this region. We consider CS=CP= 1 2πf R2 QR eq = 310nF and LS=LP= QR eq 2πf R2 = 2uH, so that fR1 is 61.8% of fR2 while fR3 is 161.8% of fR2. The f R1 =0.618*f R2 =123 kHz and f R3 =1.618*f R2 =323 kHz. The magnetizing inductance Lm is L*L s =3*2=6uH. The remaining components used in the inverter are given in Table 1.

SIMULATION RESULTS
The working of our proposed inverter is verified by simulating our designed inverter on OrCAD PSpice software. The simulated graphs of inverter voltage analysis at different The variable input voltage frequency of the resonant tank is between fR1 and fR2. At fR1 the output is approximately equal to the input, so the gain is one. But at fR2, the tank output is approximately 5V, therefore the minimum possible gain is 0.125 which is still much less than conventional LLC resonant tanks. The peak output voltage is approximately 400V for the rectifier and the DC link stage. The inverter voltage output has a peak value of 400V and an inverted peak value of -400V in a full AC sinusoidal voltage cycle.

DC-DC Stage Analysis
The simulated graphs of DC-DC stage analysis for current and voltage at different frequency regions are illustrated in this part and shown in Figure 10 to Figure  The voltage is reduced to zero before the resonant current achieves ZVS through inverter operation. The third harmonic is added to the resonance current when operating below fR1.
The resonant current is approximately zero at the fR2 switching frequency. The relation of series resonant capacitor voltage VCs versus ILs and ILs versus ILm at different regions of fS are depicted in Figure 11. The current ILs lag the voltage VCs confirming ZVS in these regions. Also, the magnetizing current ILm increases and decreases linearly with the resonant current ILs in every cycle. The amplitude values became less for fS>fR1 but the behavior remains the same. The secondary side diodes (D3 & D1) current according to the primary side voltage at fR1 ≤ fS ≤ fR2 are given in Figure 12. Here, the voltage across diodes is proportional to the primary side switch's voltage. The currents through diodes (D1 & D3) at fS=fR1 are following the voltage waveform of primary side switches (S1 & S2). The diodes turn off at zero current achieving ZCS across them. For fR1<fS<fR2 region, the behavior of output is the same as discussed above but with low amplitude values because the gain is higher near fR1. At fS=fR2, the current through the diodes is very small because the gain is approaching zero.

CONCLUSION
An LLCLC resonant converter based pseudo-DC link inverter topology is proposed. The inverter uses LLC resonant DC converter with an additional LC component providing 0.125 gain at resonant frequency fR2 by increasing the impedance of the tank to infinity. The inverter regulates the output voltage by changing the switching frequency of the primary switches. The inverter provides rectified DC voltage at the DC link stage which is unfolded to a sinusoidal voltage by the full bridge inverter. The performance of a 400W, 40V input, and 400V output pseudo-DC link inverter is evaluated by simulation on OrCAD PSpice.