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In this paper, a single phase doubly grounded semi-Z-source inverter with maximum power point tracking (MPPT) is proposed for photovoltaic (PV) systems. This proposed system utilizes a single-ended primary inductor (SEPIC) converter as DC-DC converter to implement the MPPT algorithm for tracking the maximum power from a PV array and a single phase semi-Z-source inverter for integrating the PV with AC power utilities. The MPPT controller utilizes a fast-converging algorithm to track the maximum power point (MPP) and the semi-Z-source inverter utilizes a nonlinear SPWM to produce sinusoidal voltage at the output. The proposed system is able to track the MPP of PV arrays and produce an AC voltage at its output by utilizing only three switches. Experimental results show that the fast-converging MPPT algorithm has fast tracking response with appreciable MPP efficiency. In addition, the inverter shows the minimization of common mode leakage current with its ground sharing feature and reduction of the THD as well as DC current components at the output during DC-AC conversion.

The development and application of renewable energy sources like fuel cells, wind, geothermal heat and solar,

As mentioned earlier, PV has limited energy conversion efficiency which has led researchers to design MPPT systems to utilize the maximum available power from the PV. The PV array has nonlinear current against voltage (I-V) characteristics and Earth has rotation and revolution around the Sun, which results in the variation of the maximum power point (MPP) of the PV array with the variation of the solar irradiance level and temperature. In the past literature many techniques and algorithms for tracking the maximum power from the PV array have been discussed. These techniques include perturb and observe (P&O) [

Another important challenge for researchers is how to design high conversion efficiency inverters for power conditioning to take full advantage of the available solar energy. Great interests have been shown in designing the inverter as the power conditioner of solar PV systems. Isolated inverters increase the system costs, size and decrease the overall system efficiency due to presence of small high frequency or bulky line frequency transformers in the system for electrical isolation [

Transformer-less inverters require the minimization of the connection effect between the input source and the grid. Another great problem is the common mode leakage current of transformer-less inverter, particularly for PV inverter topology. Presently, most PV arrays contain metallic frames and have large surface areas. These large surfaces and metallic frames create parasitic capacitances in the PV array [

In addition, another problem associated with transformer-less inverters is the injection of DC current into utility grid due to the absence of transformers and thus causes the degradation in the power quality. It can be found from [

Several transformer-less inverters with MPPT have been proposed in [

Considering the aforementioned discussion, a single phase transformer-less doubly grounded semi-Z-source inverter for PV system with MPPT is proposed in this paper, as shown in

Proposed single phase semi-Z-source inverter with MPPT.

A fast-converging algorithm for tracking the MPP of PV has been used which is fast in response and shows higher MPP efficiency. This cost-effective downsized inverter system aims to minimize the common mode leakage current with its ground sharing feature. It also ensures less THD and DC current at its output as the inverter utilizes a coupled inductor technique. Moreover, this power conditioner is acceptable for interfacing RESs as well as PVs to a utility AC grid, thus providing a stand-alone PV or RESs power conditioner. Besides, the Z source network on the AC side of the semi-Z-source network is different from the conventional Z source or quasi Z source inverter topology and thus in the size of the system is minimized. In addition, the coupled inductor contributes to minimizing the size of the inverter and diminishes the input current ripple as well. Furthermore, the use of the MPPT contributes to the utilization of the maximum power of the PV array. To generate sinusoidal voltage at the output, this inverter topology uses the nonlinear sinusoidal voltage gain curve as voltage reference. For this, a nonlinear SPWM technique is used to obtain necessary control signal.

A single ended primary inductor converter (SEPIC) has been used as a DC-DC converter for tracking the MPP of the PV array. The relationships between the voltage and current of the converter at the input and output sides are shown in Equations (1) and (2). The following equations are specifically required for SEPIC and may be different for other types of converter. Equation (3) shows that the duty cycle can be regulated, and thus, the input resistance (load line) of the converter can be varied until the load line cuts through the I-V curve at MPP:

Equation (1) is then divided by Equation (2) to obtain Equation (3) as follows:
_{in} is the input voltage of the converter or the voltage of the PV module _{pv}; _{in} is the input current of the converter or the current of the PV module _{pv}; _{in} is the input resistance of the converter or the resistance seen by the PV module; and _{out} is the output resistance of the converter or load resistance _{load}.

The proposed algorithm adopts the relationship between the load line and the I-V curve to introduce a fast-converging algorithm. In the proposed system, the voltage and current of the PV module are sensed by the MPPT controller. In the PV system, Equation (3) can be rewritten to obtain Equations (4) and (5) as follows:

The duty cycle, voltage, and current of the PV module are substituted into Equation (5) to obtain the load resistance. Then, the duty cycle can be calculated by substituting the desired voltage (_{mpp}) and current (_{mpp}) of the PV module into Equation (7) as follows:

In the proposed algorithm, the load of the PV system is calculated by using Equation (5). Then, Equation (7) is used to ensure that the system responds rapidly to operate near the new MPP after a increase or decrease in the solar irradiation. Meanwhile, for the variation in load, Equation (5) is used to calculate the new load resistance, and then _{mpp} and _{mpp} are substituted into Equation (7) to obtain the new duty cycle.

Initially, the PV system operates at load line 1 as in _{mpp} and _{mpp}. When the solar irradiation decreases, the operating point changes to load line 1, point A (_{1}, _{1}). The proposed algorithm is used to accelerate the convergence of the system. Therefore, the desired values of voltage and current are needed to substitute into Equation (7). Normally, the current of the PV module at the MPP is close to the short circuit current _{sc} (about 0.8I_{sc}). When the solar irradiation decreases, the operating current of the PV module (_{1}) is near to the short circuit current _{sc} at 0.4 kW/m^{2}, as shown in _{1} can be approximated as _{mpp0.4}. Generally, the MPP voltages for each level of solar irradiation are close to one another. Hence, the previous MPP voltage, _{mpp}, and the operating current _{1} are substituted into Equation (7) to obtain the new duty cycle. Then, the new duty cycle is applied to the converter, and the PV module operates at load line 3, point B (_{2}, _{2}), which is very close to the new MPP at 0.4 kW/m^{2} of solar irradiation. During only one sampling time, the operating point of the PV module is regulated from point A to B. Then, the conventional incremental conductance algorithm is applied to track the new MPP. With only a few more conventional steps, the proposed algorithm can track the new MPP at 0.4 kW/m^{2} which helps to reduce the convergence time from point A to point C.

Load lines on I-V curves for solar irradiation level of 0.4 kW/m^{2} and 1.0 kW/m^{2}.

Initially, the PV system operates at load line 1 as in _{mpp0.4} and _{mpp0.4}, respectively. When the solar irradiation increases, the operating point changes to load line 1, point D (_{1}, _{1}). During the decrease in solar irradiation, the new operating current _{1} is approximated as the new _{mpp}. However, during the increase in solar irradiation, _{1} cannot be approximated to _{mpp} because it is far away from the short circuit current _{sc} for the new level of solar irradiation, as shown in _{oc1.0}, and _{mpp0.4} form a right-angled triangle. Then, trigonometic rule is used in Equation (8) to obtain the operating current _{x}, which is near to the _{sc} for 1.0 kW/m^{2} of solar intensity. The open circuit voltage _{oc} of the PV module in Equation (9) is the estimated open circuit voltage obtained by _{mpp}/0.8. Then, _{mpp} is the voltage at the MPP before variation in solar irradiation. _{1} is the voltage of PV module after the variation of solar irradiation:

Equation (8) is rearranged to obtain Equation (9):

In the second step, _{x} and the voltage of the previous MPP _{mpp0.4} are substituted into Equation (7) to obtain the new duty cycle. With the new duty cycle, the PV module operates at point F (_{2}, _{2}), which is close to the new MPP at 1.0 kW/m^{2}. Then, the conventional incremental conductance algorithm is used to track the MPP.

When the load is varied, the operating point of the PV module diverges from the MPP (change in load line position). A new duty cycle is required to ensure that the PV module operates at the MPP again. The new resistance of the load is calculated by using Equation (5). As variation only exists in the load and the I-V curve is unchanged, the voltage and current at the MPP remain unchanged. The _{mpp} and _{mpp} are substituted into Equation (7) to obtain the new duty cycle can be calculated after variation in the load. With the new duty cycle, the PV module operates at the point close to the MPP. The conventional algorithm is then used to track the MPP.

Flow chart of the proposed MPPT algorithm.

When the MPP is tracked, the flag is set to 1. Then, Equation (10) is checked. If the equation is satisfied there is no variation in duty cycle. When there are variations in solar irradiation or load, Equation (10) no longer holds, and the flag is cleared. Then, Equation (5) is used to calculate the resistance of the load. If both the current and voltage of the PV module are decreased, Equation (7) is used to calculate the new duty cycle. If both the current and voltage of the PV module are increased, _{x} is calculated by using Equation (9), and then, the new duty cycle is calculated using Equation (7). In the case of a nonlinear load, the response of the system is slower (not able to operate near the new MPP in single perturbation), and thus, changes in the power of the PV module are observed. If the power of the PV module increases, the algorithm will be in a loop; Equation (7) is used to calculate the new duty cycle. Until the difference in power (dP) is smaller than 0.06, then the algorithm goes into conventional algorithm. Meanwhile, for load variation, the new duty cycle is calculated using Equation (7) after the resistance of the load is obtained by Equation (5).

Topology of the semi-Z-source inverter [_{1} varies from 0 to 1/2, the inverters can provide positive voltage at the output, whereas, from 1/2 to 2/3 the output voltage is negative. For the duty cycle of 1/2, the inverter produces zero voltage at output.

(

The single phase transformer-less semi-Z-source inverter topology shown in _{1} conducts while switch S_{2} does not conduct as shown in _{2} conducts while switch S_{1} does not conduct as shown in _{1} is represented by D. _{1} conducts to allow input voltage source and capacitor C_{1} charge the two inductors. In state II of _{2} conducts and the two inductors have turned into sources. For both states, the output voltage has positive polarity.

Modes of operation of semi-Z-source inverters when

In state I of _{1} conducts and the two inductors operate as two sources while in state II of _{2} conducts and input voltage source as well as capacitor C_{1} and C_{2} again charge the two inductors. For both states, output voltage has the negative polarity.

Modes of operation of semi-Z-source inverters when

For the following steady state equations the capacitors C_{1} and C_{2} voltages have been considered as _{C1} and _{C2} respectively. Also, the directions of current references of the inductor and the voltage references of the capacitor are shown in the _{1} over one switching period, it can be found that:

Applying net volt-seconds balance principle to inductor _{2} over one switching period, it can be found:

From Equations (11) and (12), it can be said that:
_{C1} = _{in}

By applying net capacitor charge balance principle to capacitor C_{1} and C_{2} over one switching period, the following equations can be derived:
_{L2} = − _{0}

If it can be assumed that, inverter output voltage is Equation (18) then the modulation index can be expressed as in Equation (19):
_{0} =

By substituting the values from Equations (18) and (19) into Equation (14), it can be found:

The duty cycle of the switch S_{2} is D′ = 1-D, which can be expressed as Equation (21):

Let the output current expressed in Equation (22) have the same phase as the output voltage. Voltage across the switch during the OFF state can be presented by Equation (23), which is depicted in _{in}. At the same time, the maximum ON state current through the switch can be determined from _{o} =

(

Voltage across capacitor C_{1} can be derived from Equations (15) and (20) which is shown in Equation (25). _{1} is 2_{in} when, the value of

(_{1} _{1}

In the same way, current through inductor _{1} is stated in Equation (26) which derived from Equations (17), (20) and (22). Current through inductor _{1} is shown in _{1} is 2

Voltage ripple of the capacitor C_{1} and the current ripple of the inductor can be dictated by Equations (27) and (28) respectively considering L_{1} = L_{2}. Voltage ripple of the capacitor C_{1} is presented in _{1} can be calculated by considering the peak ripple requirement of the current. Current ripple of the inductor L_{1} is depicted in _{1} can be selected by considering the peak ripple requirement of the current. More details can be found in [

(_{1}; (_{1}.

It is possible to control the voltage gain polarity by controlling the duty cycle of the switch, but the relation between duty cycle and voltage gain is a straight line for a traditional full bridge inverter and for this reason, to generate a sinusoidal voltage at the output, the SPWM technique is used [_{2}. To turn on switch S_{2}, it is necessary that the reference value should be greater than carrier value. Equation (20) shows the reference signal for controlling the duty cycle of switch S_{1} which is complementary from the duty cycle of switch S_{2} and the range of modulation index is between 0 and 1. _{1} and S_{2} at the time when the modulation index is 2/3.

Modulation principle of semi-Z-source inverter.

For the purpose of experimental validation, a prototype rated 48-W, 50 Hz transformer-less semi-Z-source inverter is constructed according to the diagram shown in _{1} is 100 V. The values of both the capacitor C_{1} and C_{2} are 4.7 µF considering voltage ripple is limited to 5.75% of the peak voltage across the capacitors. For the prototype, polyester film capacitors (MPE475K) are chosen. A performance real time target machine (SPEEDGOAT) has been used to produce the switching signals for the inverter.

Two inductors (L_{1} and L_{2}) used in semi-Z-source inverters can be placed in a single core or in two different cores. To minimize the input current ripple and to reduce the size, the coupled inductor method is chosen for the prototype thus ensuring identical current flow. For high frequency operation, ferrite materials have low loss features and for this, a magnetic core of ferrite material (45528EE) is chosen for this prototype. To prevent the inductor core from saturation under load, an air gap is used within the core structure because the energy being stored in air gap will prevent the core from saturation under load. For the prototype, the maximum load current peak value is around 2A. According to the design procedure mentioned earlier, the peak current of inductor L_{1} is 4A. The value of the inductor L_{1} is 400 µH considering the current ripple is limited to 1/3 of the peak current of the inductor. The values of the inductor L_{2} is also 400 µH that can be calculated by the same procedure. Finally, the total harmonic distortion (THD) of the output voltage and current has been analyzed using a YOKOGAWA WT 1800 precision power analyzer.

Experimental results of the laboratory prototype model of 48-W transformer-less semi-Z-source inverter are shown in

(

_{GS1} of switch S_{1}, drain to source voltage _{DS1} of switch S_{1}, output voltage _{0}, output current _{0} and their zoomed version respectively during R load condition. _{GS1} and V_{DS1} of switch S_{1} are operating in completely reverse according to the given figures. In addition, output voltage polarity changes with the change of duty cycle of the switch which satisfies the theoretical background. Drain to source voltage _{DS1} of switch S_{1}, drain to source voltage _{DS2} of switch S_{2}, output voltage _{0}, output current I_{0} and certain magnified versions of the are represented in _{GS1} of switch S_{1}, drain to source voltage V_{DS1} of switch S_{1}, output voltage V_{0}, output current I_{0} and their zoomed version respectively during R-L load condition.

(_{1} voltage, output voltage, output current for R load; (_{1} voltage, output voltage, output current for R-L load.

When _{in}, voltage across capacitor C_{1}, output voltage _{0} and output current _{0} for _{in} is almost constant and contains no high frequency variation. As a consequence, the generation of common mode voltage is minimized which in turns results in reduction of common mode leakage current.

(_{1} voltage, output voltage, output current for _{1} voltage, output voltage, output current for

The voltage across capacitor C_{1}, current through inductor L_{1}, output voltage and output current of the inverter for both _{1} followed by the inductor current _{L1} and inductor current is approximately twice the output current for both the load conditions.

THD and harmonic spectrum of the output voltage and current for

For the purposes of experimental validation of the complete single phase semi-Z-source inverter with MPPT system, a practical experimental MPPT setup connected with a semi-Z-source inverter has been applied to the PV module according to

_{max} is the maximum power point of the PV module. When the simulator is connected to the load, the power supplied or the power of the PV module, _{pv} has been measured and compare to the maximum power available from the PV module. Thus, the MPP efficiency is calculated by the simulator by using the Equation (29):

^{2} to 1.0 kW/m^{2} and at ^{2}. The response of the conventional algorithm is slow due to the constant step change in the duty cycle.

(

A comparison of the proposed algorithm with the conventional incremental conductance and modified incremental conductance is shown in

Comparison of the proposed algorithm with the conventional incremental conductance and modified incremental conductance algorithm.

Parameters | Conventional Incremental Conductance algorithm [ |
Modified incremental conductance algorithm [ |
Proposed fast convergence algorithm |
---|---|---|---|

Steady state oscillation | Yes | No | No |

Response under fast varying solar irradiation | Slow | Fast | Fast |

MPP efficiency (%) | 98.49 | 99.89 | 99.94 |

_{in} is almost constant and contains no high frequency variation. As a consequence, the generation of common mode voltage is minimized which in turns reduces the common mode leakage current. The experimental waveforms of R-L load when the output voltage of DC/DC converter of MPPT has been fixed to the DC voltage of around 100 V which acts as the input voltage of inverter is shown in _{in} is almost constant and contains no high frequency variation. As a consequence, the generation of common mode voltage is minimized for R-L load conditions, which in turns reduces of common mode leakage current, so it can be said that the proposed MPPT based semi-Z-source inverter is acceptable for PV systems for tracking the maximum power of the PV array and to generate adjustable sinusoidal output voltage with the minimization of common mode leakage current by doubly grounded features.

This paper presents a doubly grounded semi-Z-source inverter with a MPPT controller for PV systems. This low cost, downsized micro-modular system is applicable for connecting utility grids with standalone PV power conditioners and interfacing PV systems because this system is able to track the MPP of PV arrays and produce an AC voltage at their output by utilizing only three switches. The experimental results demonstrate that by utilizing fast-converging algorithm this inverter system is capable to track the maximum power from the PV array which is fast in response. Also, this system is able to minimize common mode leakage currents for PV arrays by its doubly grounded features. Other than that, it can convert the DC power of a PV array to AC power with reduced THD and DC current at the output by utilizing the coupled inductor technique. Moreover, the tracking efficiency of the MPP is 99.94%, which is higher than that of conventional and modified incremental conductance algorithms.

The authors would like to thank the Ministry of Higher Education of Malaysia and University of Malaya for providing financial support under the UMRG project RP015A-13AET.

In this paper, Tofael Ahmed contributes to the design and implementation of semi-Z-source inverter and writing the manuscript. Tey Kok Soon contributes to the design, implementation and writting of the section MPPT. Saad Mekhilef provides overall supervision and guidance to finalyze the work. All the authors read and approve the manuscript.

The authors declare no conflict of interest.