**3. Power Electronic Converters used to Control the Proposed Micro Grid System. Description and Mathematical Modelling**

The power converters have been developed to manage the maximum energy harvesting and power processing for the hybrid solution with Photovoltaic (PV) and wind power generators. The topologies involved in this study contains two topologies of power electronic converters: a SEPIC converter and a Quasi Z-Source Inverter (QZsi). The MPPT method for QZsi is introduced based on the P&O method to minimize the voltage stress on the inverter. Moreover, it prevents overlapping between Shoot-Through (ST) duty ratio and modulation index using DC-Link voltage controller. The output current is regulated using the stationary frame current controller, achieving lower Total Harmonic Distortion (THD) as much as possible. The SEPIC based soft switching for MPPT action is controlled through an advanced MPRVS based P&O MPPT. A quasi Z-source inverter with the common grounding characteristics is employed to get high voltage gain. Employed inverter operates in two modes of operation as the shoot through and the non-shoot through the states.

#### *3.1. SEPIC Converter Model*

Single ended primary inductor converter (SEPIC) is considered as an impedance adapter between the PV module and the Z-source inverter as it provides high gain throughout the operation, better voltage performance and high voltage rating for lower/higher power requirements. When boost converter combines with the additional inductor and the capacitor, a SEPIC converter is developed. In contrast with the buck boost converter, the polarity of SEPIC is kept positively as it is depicted in Figure 5. Table 1 portrays the employed SEPIC converter parameters during an implementation.

$$V\_{output} = V\_{supply} \times \frac{D\_{duty}}{1 - D\_{duty}} \tag{11}$$

$$L\_A = \frac{V\_{supply} \times D\_{duty}}{\Delta I\_{L\_A} \times f\_{switching}} \tag{12}$$

$$L\_B = \frac{V\_{supply} \times D\_{duty}}{\Delta I\_{L\_B} \times f\_{switching}} \tag{13}$$

$$\mathbb{C}\_A = \frac{V\_{\text{output}} \times D\_{\text{duty}}}{R\_{\text{Load}} \times \Delta V\_o \times f\_{\text{switching}}} \tag{14}$$

$$C\_B = \frac{V\_{output} \times D\_{duty}}{R\_{Load} \times \Delta V\_o \times f\_{switching}} \tag{15}$$

**Figure 5.** SEPIC converter equivalent circuit.

**Table 1.** SEPIC converter parameter.


#### *3.2. Modified Power Ratio Variable Step Based P&O MPPT*

Figure 6 demonstrates the working model of MPRVS based P&O technique for optimal PV power extraction from solar modules. The generation of gating pulses to the SEPIC converter is possible without the action of the PI controller, which makes the reduction of power oscillation nearer to MPP and forces operating point close to the MPP. It also prevents the battery charging system from over voltage. The instantaneous power obtained through PVG [*PPV*(*N*)] at SEPIC output terminal is calculated as:

$$P\_{PV}(N) = V\_0(N) \times I\_{PV}(N) \tag{16}$$

Also, the previous instantaneous power is mathematically described as:

$$P\_{PV}(N-1) = V\_{PV}(N-1) \times I\_{PV}(N-1) \tag{17}$$

And if

$$
\Delta P\_{PV}(N) = P\_{PV}(N) - P\_{PV}(N-1) > 0,\\
\text{S} = -1 \tag{18}
$$

$$\&PPV(N) - PPV(N-1) < 0, \ S = +1\tag{19}$$

Again,

$$D(N) = D(N-1) + S \times \Delta D \tag{20}$$

Δ*D* = Step perturbation of duty ratio = *K* × *dT*

dT = Fixed step size

K = Variable power ratio

$$K = \frac{P\_{PV}^{\text{max}} - P\_{PV}(N)}{P\_{PV}(N)} \tag{21}$$

**Figure 6.** Working model of MPRVS based P&O technique.

#### *3.3. Quasi Z-Source Inverter Mathematical Modeling*

Figure 7 presents the equivalent power circuit of Quasi Z-source inverter which comprises of LA, LB, CA, CB components with impedance circuit. The considered Z-Source Quasi inverter has no filter requirement, better buck/boost characteristics, able to regulate the phase angle output, less size, continuous conducting mode working, less harmonic content, high efficiency and with better power performance over the conventional inverter as major advantages. The Quasi Z-source inverter operates in two modes of operation. In the non-shoot mode, the equivalent circuit has 6 active states with 2 zero states. The *TS* is the total switched inverter with *TA* and *TB* as the shoot through the state and the non-shoot through state, respectively. The duty ratio *Dduty* of SEPIC converter is mathematically written as:

$$D\_{duty} = \frac{T\_A}{T\_S} \tag{22}$$

Mode I: The equivalent model of Quasi Z-source inverter is depicted in Figure 8 and mathematical equations governing non-shoot through the state is expressed as:

$$V\_{L\_A} = V\_{IN} - V\_{C\_A}$$

$$V\_{L\_B} = -V\_{C\_B} \\ \tag{23}$$

$$V\_{DIODE} = 0$$

Mode II: Figure 9 illustrates the equivalent model of Quasi Z-source inverter in shoot through the state mode with the mathematical expression as:

$$V\_{L\_A} = V\_{IN} + V\_{C\_A}$$

$$V\_{L\_B} = V\_{C\_B} \tag{24}$$

**Figure 7.** Equivalent power circuit of Quasi Z-source inverter.

**Figure 8.** The equivalent model of Quasi Z-source inverter governing non-shoot through the state.

**Figure 9.** Equivalent model of Quasi Z-source inverter in shoot through the state.

Under the steady condition, the average inductor voltage becomes zero.

$$V\_{LA} = \left[\frac{\left(V\_{IN} + V\_{C\_B}\right)T\_A + \left(V\_{IN} - V\_{C\_A}\right)T\_B}{T\_S}\right] = 0\tag{25}$$

$$V\_{L\_B} = \left[\frac{V\_{C\_A}T\_A + \left(-V\_{C\_B}\right)T\_B}{T\_S}\right] = 0\tag{26}$$

On solving the above equations, capacitor voltage (*VCA*&*VCB* ) is calculated mathematically as:

$$V\_{C\_A} = \left(\frac{T\_B}{T\_B - T\_A}\right) \times V\_{IN} \tag{27}$$

$$V\_{C\_B} = \left(\frac{T\_A}{T\_B - T\_A}\right) \times V\_{IN} \tag{28}$$

Maximum voltage across DC-link = *VCA* + *VCB* (29)

Putting Equations (26) and (27) in (28) we get

$$\text{Maximum DC-link voltage} = \left| \frac{1}{1 - 2\frac{T\_A}{T\_S}} \right| V\_{IN} = K \times V\_{IN} \tag{30}$$

#### **4. Experimental Setup Description and Results**

#### *4.1. Description of the Experimental Setup*

The considered hybrid PV-Wind micro grid is tested using MPRVS based P&O MPPT with employed Z-source inverter. Figure 10 depicts the developed practical structure of the proposed hybrid micro grid based on a real-time platform, dSPACE. The SEPIC converter is controlled through the MPRVS based P&O based MPPT, in which LV-25P and LA-25P, current and voltage sensors are employed for measuring the PV panel parameters, VPV and IPV respectively. The power factor coefficient and THD are evaluated using the power quality analyzer (FLUKE 43B), considering the main components of the converter: IGBT (IRG4PH50U), diode (Freewheel RHRG30120), driver circuit (HCPL 3120) etc. permanent magnet synchronous generator (PMSG) based wind emulator system is employed as the wind turbine generator and is mechanically coupled with the DC-motor. The switched mode power converter makes the wind turbine to have varying wind speed which produces the required mechanical torque by controlling wind turbine characteristics.

**Figure 10.** Developed experimental setup of the proposed hybrid micro grid system based on a real-time digital simulator-dSPACE platform.

#### *4.2. Experimental Results and Scenarious Development*

The accuracy of the proposed MPRVS based P&O MPPT has been tested with changing wind operating condition depicted in Figure 11a. The employed controller works in MPP area and provides optimal tracking of wind power under the sudden changes of wind velocity shown in Figure 11b.The corresponding duty ratio of SEPIC converter is shown in Figure 11c. Furthermore, the capability of proposed MPPT tracker is examined under the first scenarios with step varying solar irradiation. Figure 12 demonstrates that the PV array has obtained parameters under the step-changes in solar irradiation and the propped system has proved high accuracy and effective PV tracking in MPP region. The obtained experimental results in Figure 13a illustrate that the performance of the proposed hybrid micro grid under the second scenarios by varying wind velocity and constant solar irradiation. Also, Figure 13b demonstrates the behavior responses of the hybrid micro grid under varying solar irradiance and constant wind velocity with MPRVS based P&O MPPT employed. The performance of the hybrid micro grid is also tested under the third proposed scenarios in the absence of wind velocity and during this operation: the load is connected/disconnected to the utility grid, which is shown in Figure 14a under the load cutting condition, and in Figure 14b, under the load removing conditions. The performance of the wind generator is evaluated under disconnecting/reconnecting operating conditions to the micro grid, which are depicted in Figures 15 and 16 and reveal that the accurate performance of the proposed hybrid micro grid in varying operating situations (disconnecting operating conditions to the micro grid and reconnecting operating conditions to the micro grid), respectively.

**Figure 11.** Experimental results (**a**) during a step-changed in wind speed; (**b**) wind power; and (**c**) Duty cycle of Cuk converter.

**Figure 12.** PV system responses under step-changes in solar irradiation.

**Figure 13.** (**a**) Capability of the proposed hybrid micro grid under varying wind velocity and constant solar irradiation; (**b**) Behavior responses of the hybrid micro grid under varying solar irradiance and constant wind velocity.

**Figure 14.** The performance of the hybrid micro grid (**a**) load cutting condition; (**b**) Load removing condition.

**Figure 15.** The performance of the wind generator is evaluated under disconnecting operating conditions to the micro grid.

**Figure 16.** The performance of the wind generator is evaluated under reconnecting operating conditions to the micro grid.

#### **5. Conclusions**

The proposed hybrid PV-Wind micro-grid system using Quasi Z-source inverter is established practically and tested with the Real-time digital simulator dSPACE (DS 1104) platform.

The point wise findings that have been included in this section are as follows:


As a future work, the paper can be extended by using the multilevel inverter with the application of advanced intelligent MPPT algorithms viz. Jaya DE, hybrid ANFIS-ABC methods.

**Author Contributions:** All authors contributed equally and formulated the research work to present in current version as full research article.

**Funding:** No funding addressed to this research activities.

**Conflicts of Interest:** The authors declare no conflict of interest.
