**1. Introduction**

Since the past two decades, Distributed Energy Sources based on Renewable Energy have grabbed much attention in power transformation and distribution sectors. In particular, solar-photovoltaic (PV) systems have the highest growing rate (along with wind energy) with the addition of 109 GW in 2018–2019 [1]. In terms of installed capacity, PV energy increased from 22 to 489 GW in this decade [2]. The integration of solar energy to the utility grid requires power processing stages in order to successfully inject the gathered energy. The implementation of utility-scale solar systems requires galvanic isolation according to standards in many countries, and it is conventionally implemented by a grid frequency transformer. Even though traditional transformers are reliable and efficient, they are also heavy and bulky [3].

Some approaches for PV systems propose the implementation of Medium-Frequency (MF) isolation in order to reduce volume and weight [3–5]. The topologies with MF links usually features: a DC-AC stage consisting on a DC-DC converter and a DC-AC stage in order to drive the transformer, a Magnetic link operating in medium-high frequency, and an AC-AC stage consisting on a rectifier and a DC-AC stage. The key features of these systems are: individual maximum power point tracking (MPPT), galvanic isolation, enhanced voltage elevation ratio, reduced total harmonic distortion (THD), voltage stress reduction in medium-voltage (MV) stage, and reduced overall system volume and weight. Some drawbacks are: voltage imbalance in multilevel cells due to different power levels in each string, more power stages due to the presence of an additional low voltage inverter and MV rectifier, and increased stress in low voltage stage switches since the all the input power must be handled by a single switch. A solution for multilevel cell imbalance is presented in [3] featuring a MF link that consists on a transformer with several secondary windings which being magnetically coupled *naturally* balances the cascaded cells of the multilevel converter. Some downsides are that the system has four power stages, and reports low global efficiency levels. However, some adjustments in the topology can help improving reliability and efficiency. The PV system low voltage side in [5] consists on a PV string and a DC-AC power stage. The DC-AC power stage requires buck-boost and MPPT capability. DC-AC stage is commonly integrated by a boost converter and an inverter in order to drive the MF transformer [5]. Another approach is stated in [6], proposing a flyback converter plus a H-bridge topology for DC-AC stage features, and enhanced efficiency with high frequency isolation; however, the number of semiconductors and current stress limits the topology to low power applications (<300 W). In [7] a Cuk-SEPIC combination featuring a single switch and coupled inductors is presented in order to obtain a bipolar output enhancing efficiency, however current stressed switch can present reliability problems.

Since PV system behave as current sources, current-fed converters are considered for the DC-AC stage. The isolated current-fed push-pull converter features a low component count and simply circuitry which makes it rather reliable and simple to implement; it also benefits from a high-voltage conversion ratio [8–10]. Some identified drawbacks of the topology are: high switching losses, high-voltage spikes in switches, high start-up current, and central tapped transformer coils requires a bigger core and can be a serious limitation for a magnetically coupled multiport configuration [9,11–13].

The L-type converter is an interesting topology that features reduced current stress in switches and reduced voltage stress on output capacitor and diodes [8,11]. There are a better use of the magnetic core of the MF link and thus making the topology a good option for the multiport implementation. Some limitations of the topology are: higher voltage efforts in switches, voltage spikes in switches due to a resonance with the leakage inductance of the transformer. Current-fed topologies with boost operation also require additional start-up circuitry due to the current in inductors during starting process. The L-type converter is suitable to low voltage, high current applications [8,11].

The Z-source inverter (ZSI) has been considered for DC-AC converters [14,15]; this topology has a buck-boost DC-AC capability in a single-stage which suggests an efficiency and reliability enhancement. The operation principle of the ZSI and current-fed topologies mentioned consist in apply a shoot-through state to overlap the H-bridge branches (0V) which provides natural protection against short-circuits, making it suitable for large-scale applications. After its presentation, variations on the topology were proposed for many applications such a grid-tied converters without galvanic isolation [16–18], with galvanic isolation [19–21], and finally for grid-tied PV systems [22–24].

Z-sources topologies are interesting for PV applications because they can operate as voltage and current source. Additionally, Z-source converters operating as current source can be better applied in medium-high power applications due to the restriction of <1 kV in PV arrays terminals. A current fed Z-source Inverter (CZSI) version is proposed in [25] which features a constant source current, protecting the PV array from returning current.

The CZSI shares many features of the above mentioned topologies such as DC-AC power processing in a single stage and voltage spikes in switches due to resonance with the leakage inductance [12]. Some particular feature of the CZSI in deference to the mentioned topologies is a very low current stress in diode a capacitors, which are the most vulnerable elements on the Z network and thus enhancing the reliability of the circuit. Some drawbacks of the CZSI against the other topologies are the number of passive components and limited voltage boost. Since the PV system voltage does not presents a wide variation, voltage boost drawback is not considered of high relevance. The CZSI has similar to L-type topology power requirements for the magnetic core of the MF link, which is an important feature for multiport applications.

The system considered in this work is shown in Figure 1 and consists in three power stages: Low voltage DC-AC stage consists in a PV array, followed by an elevation stage based on a current-fed Z-source inverter (CZSI) that performs MPPT and sets the voltage for the inverter who will drive the MF link; MF Link is an elevation AC-AC stage which provides multiport configuration integrated by multiple isolated and magnetically coupled inputs and outputs. The MF Link can manage *x* primary ports and *y* secondary ports, only restricted by the physical space and power the magnetic core of the transformer can handle. In this study, three input ports where selected since is the minimum number of modules in order to validate that different power levels can be processed in *x* modules and not only flowing between two modules, and in order to show that output ports are balanced, two ports where selected.

**Figure 1.** Multiport isolated link system with CZSI input cells to manage asymmetrical power supplies.

The focus of this paper is derived from [26] and presents the analysis of a multiport isolated link in asymmetrical input power transference conditions using CZSI modules to manage the energy. This work shows CZSI analysis, simulation and experimental results to validate the analysis performed. This proposal offers reduction of power stage by using CZSI modules energized by unbalanced PV systems, reliable magnetic isolation with a multiport link to meet standard requirements and, naturally balanced output ports and isolated sources for grid-connected oriented applications.

#### **2. Current-Fed Z-Source Inverter Operation and Design**

In Figure 2, the CZSI circuit is presented and Figure 3 shows the equivalent circuits for operation states. In steady state, average voltage in *L*1, *L*2 and *L*3 remains zero as well as current in *C*1 and *C*2 over a switching period *T*. The CZSI presents two main operation states: conduction and shoot-through; in conduction state mode (*Sw*1 and *Sw*4 ON and *Sw*2 and *Sw*3 OFF, Figure 3a), current across inductors *L*1, *L*2 and *L*3 is given by PV array *iPV*, and the voltage across the capacitors is set by the PV source *VPV*. During conduction state, *L*3 is charging with *VPV*, to supply current for the impedance network later.

**Figure 2.** Current-fed Z-source inverter.

In shoot-through state (All switches are ON, Figure 3b), *iL*1 and *iL*2 rises as *iL*3 falls since *L*3 supplies the current, *iPV* remains constant in <sup>Δ</sup>*iL* , limited by inductance *L*. In this time, voltages in inductors are imposed by *vC*. The capacitor voltage decrease in <sup>Δ</sup>*vC* and is limited by a capacitance *C*. As it can be seen, that the Z LC circuit is always in conduction and the switches are the ones that control operation modes, an hence, the output voltage. The required shoot-through duty cycle *Dz* for a desired *Vozp* can be found by the following expression:

$$D\_z = 1 - \frac{V\_{PV}}{V\_{ozp}} \tag{1}$$

where *Vozp* is the peak value of *voczsi*. The voltage boost for the CZSI is directly modified by *Dz*; therefore, by manipulating this duty cycle the MPPT can be performed and the DC-AC conversion remains in a single stage.

**Figure 3.** CZSI equivalent circuits: (**a**) CZSI conduction state, (**b**) CZSI shoot-through state.

Output voltage can be obtained through Equation (1), as it is a function of *Dz*; higher values of *Dz* produces higher gain limited to 2 *VPV*. *voczsi* RMS voltage is obtained by:

$$V\_{oRMS} = V\_{ozp} \sqrt{1 - D\_z} \,\tag{2}$$

The shoot through time *TDz* is shared by all of the modules due to the parallel connection, thus if one of the windings is in OV, the rest will be in OV as well. The last results in all of the windings sharing the duty cycle *Dz* at the higher value.

The effect of *Dz* in switches is that during *t* = [0 *T* − *DzT*], half of the current *i*2 given by:

$$\dot{\mathbf{u}}\_2 = 2\dot{\mathbf{u}}\_{L\_2} - \dot{\mathbf{u}}\_{L\_1\prime} \tag{3}$$

is conducted by all switches. During *t* = [*T* − *DzT <sup>T</sup>*], current in switches is *i*2. In conduction mode, *ioczsi* has a ripple Δ*io* with a slope given by:

$$m = \frac{\Delta i\_o}{\Delta\_t} = \frac{I\_A - I\_B}{\Delta\_t},\tag{4}$$

where *IA* and *IB* are peak values of *i*2 (Figure 4). However, *ioczsi* is affected by winding impedance *Z* composed by the leakage inductance *Lp* and the winding resistance, producing a non-zero current *ioczsi* = *iLp* (Figure 4). The RMS current for *ioczsi* is given by:

$$I\_{oRMS} = \sqrt{\frac{1}{T} \int\_0^{T-D\_zT} (mT + I\_A)^2 dt + \int\_{T-D\_zT}^T \mathbf{f}\_{L,p}^2 dt}. \tag{5}$$

By solving Equation (5), *IoRMS* is given by:

$$I\_{oRMS} = \sqrt{(\dot{i}\_{PV}^2 + \frac{3}{4}\Delta \dot{i}\_L^2)(1 - D\_z) + \dot{i}\_{Lp}^2 D\_{z\prime}}\tag{6}$$

where *IA* is the upper *i*2 value, *IB* the lower value, and *Lp* the leakage inductance.

**Figure 4.** CZSI Output: *Voczsi*, *ioczsi*, and power *poczsi*.

In Figure 5a, a simplified representation of a multiport configuration consisting on *x* primary windings transformer and a single output is shown. Voltages *V*1, *V*2 through *Vx* are the RMS value of CZSI modules output voltage *Voczsi*, and *Vm* is the secondary voltage *vsec*. In the MF link, the sum of average power supplied to each primary port must match the average power on the secondary ports, thus for a single output:

$$P\_1 + P\_2 + \dots + P\_x = P\_{\text{sec}\prime} \tag{7}$$

expanding the concept to *y* secondary ports, the sum of the average power on each secondary output must also match the sum of the average input power:

$$P\_1 + P\_2 + \dots + P\_x = P\_{\text{sec}\_1} + P\_{\text{sec}\_2} + \dots + P\_{\text{sec}\_y} \tag{8}$$

For multilevel converters applications, it can be considered that power in each secondary port is balanced since they all have the same number of turns and the same output voltage. Secondary ports also share the same current since the all supply the same load, thereby Equation (8) can be expressed as:

$$P\_1 + P\_2 + \dots + P\_x = yP\_{s\alpha\varepsilon} \,\tag{9}$$

The parallel configuration shows that when a module is in shoot-through state, the remaining modules will share this state, thus voltage *voczsi* will be zero for all of the windings, resulting in an identical equivalent *Dz* value for all input CZSI modules. The last implies that all the cells will have very similar values of *voczsi*.

The imposed duty cycle *Dz* will be the higher value of all CZSI modules for the MPP, thus having different *Dz* references is not necessary. Current levels will be in function of the power supplied by the PV array, thus different in all primary ports.

Despite the different power levels on the modules, the non-zero current associated to *Lp*, remains similar for all windings since it is product of parasitic elements, and it is assumed that all windings are homogeneous.

**Figure 5.** (**a**) Multiport transformer, (**b**) Equivalent circuit.

#### *Semiconductor Sizing for CZSI Modules*

The voltage and current stress on semiconductors are defined by the operation mode of the CZSI module. The voltage stress for the semiconductors on CZSI conduction mode, is the voltage *vozp* and can be found with Equation (1) and zero for shoot-through mode:

$$v\_{Sw} = \begin{cases} v\_{ozp} & 0 \le t < T(1 - D\_z) \\ 0 & T(1 - D\_z) \le t \le T. \end{cases} \tag{10}$$

For selection purposes, a security factor of 50% can be added to *vozp* and is given by:

$$V\_{\rm Sw\_{slec}} = V\_{ozp} \mathbf{1}.5 = \left( V\_{PV} \frac{1}{1 - D\_z} \right) \mathbf{1}.5. \tag{11}$$

The current across the semiconductors, also depends on operation mode and can be expressed by:

$$i\_{Sw} = \begin{cases} i\_2 & 0 \le t < T(1 - D\_z) \\ i\_2/2 & T(1 - D\_z) \le t \le T. \end{cases} \tag{12}$$

The maximum current that semiconductors must conduct is the peak value of *i*2 plus a security factor of 25%. The current to be considered when choosing a device is given by:

$$I\_{Sw\_{slec}} = i\_{2\_{max}} = \left(I\_{PV} + \frac{3\Delta i\_L}{2}\right) 1.25.\tag{13}$$

#### **3. Power Transfer under Unbalanced Conditions**

An issue of having the whole installed capacity divided in strings is that the power in each array of PV panels can be unbalanced. Let's consider a two input modules scenario, where *P*1 and *P*2 are CZSI modules output power and are different from each other.

A simple scheme is given in Figure 5b for analysis purposes. Resistance *R* is considered equal for all windings and thus *R*1 = *R*2 = *R*. From Figure 5b, the voltage on the secondary side can be computed by:

$$V\_1 n - I\_1 R = V\_m = V\_2 n - I\_2 R\_\prime \tag{14}$$

where *n* is the turn ratio and, *V*1 and *V*2 are the RMS values of *voczsi* in modules 1 and 2 respectively. Such voltages cannot be arbitrary set to extract two different power levels on each loop, since (14) has to be fulfilled. If the voltage *V*1 is imposed, then *V*2 will be in function of the desired power, thus *V*2 is a variable voltage source. To find a combination of *V*1 and *V*2, that will allow different power transfer on modules, first *Vm* must be found in terms of *V*1 with (14). Then *P*2 can be computed from:

$$P\_2 = \frac{R}{n}I\_2^2 + \frac{V\_m}{n}I\_2.\tag{15}$$

By solving (15) for *I*2, a voltage value for *V*2 to transfer *P*2 can be found. For more than two modules or windings, a similar analysis can be performed. One module has a fixed voltage, and all the subsequent modules adapt their voltage to meet the power transference needed.

$$V\_1 \mathbf{n} - I\_1 \mathbf{R} = V\_\mathbf{m} = V\_2 \mathbf{n} I\_2 \mathbf{R} = \dots = V\_\mathbf{x} \mathbf{n} I\_\mathbf{x} \mathbf{R}.\tag{16}$$

Therefore the current for *x* given modules, (17) can be solved for *Ix*:

$$P\_x = \frac{R}{n}I\_x^2 + \frac{V\_m}{n}I\_x.\tag{17}$$

Once expressions for output voltage and current are given, power on each winding can be calculated. Based on Figure 4, the average power is given by:

$$P = \frac{1}{T} \int\_{0}^{T - TD\_x} Vol\_B + \frac{V\_o(I\_A - I\_B)}{2} t(dt),\tag{18}$$

$$P = \frac{V\_o(I\_A + I\_B)}{2}(1 - D)\_\prime \tag{19}$$

where *IA* and *IB* are the upper and lower *I*2 values respectively. Apparent power S is expressed by:

$$S = V\_{oRMS} \sqrt{(\dot{l}\_{PV}^2 + \frac{3}{4} \Delta \dot{l}\_L^2)(1 - D\_z) + \dot{l}\_{Lp}^2 D\_z} \tag{20}$$

From (20) it can be observed that the *i* 2 *Lp Dz* component is associated to reactive power, and since all cells have similar values of *Lp* (because all windings are identical) the component in *i* 2 *Lp Dz* will be the same for all modules, an thus, have similar reactive power levels on all cells despite power level.
