Nature's remarkable and merciful gift to the planet Earth is sunlight which may be highly lucrative if harvested and harnessed properly. Photovoltaic (PV) panels are used to convert the solar energy to electrical energy which are currently used to feed AC loads/grid. In this paper, modelling, performance and power flow studies of grid connected single phase inverter fed from PV array under steady state as well as transient conditions are considered. This paper focuses on the study and development of analytical model of micro-grid integrated single phase five level cascaded H-bridge inverter (MGISPFLCHBPVI) powered by a PV panel. A simple power control strategy for MGISPFLCHBPVI is also considered. The simulations are completely carried out using MATLAB software for power-flow studies. The performance characteristics of the inverter are studied from the analytical model developed. The validation of the analytical model is carried out by comparing the results of simulation in Simulink/Matlab. In order to reduce the time to reach steady state taken by the system, a simple PQ control strategy for insolation is introduced in this paper. The proposed method is evaluated based on performance parameters such as settling time and rising time of the system compared with the results available in the literature.

Sunlight is readily available in abundance all over the world and its proper deployment eliminates approximately 45% power deficiency existing globally. Extracting maximum power from PV array increases the overall efficiency of the PV system [

The energy yield study of 1kWp residential PV plant at Chennai is considered for brief discussion. The diurnal, monthly and seasonal variation of solar radiation at Chennai during the years 2013, 2014 and 2015 are recorded. Similarly, the output energy yield of the PV plant during the year 2013, 2014 and 2015 are also estimated and recorded [

Based on the review, a modified five parameter analytical model of PV array is developed and its performance is obtained for different operating conditions. This paper focuses on the study and development of analytical model of micro-grid integrated single phase five level cascaded H-bridge inverter (MGISPFLCHBPVI) powered by a PV panel as shown in

The equivalent electrical circuit model of a silicon photovoltaic cell consists of a controlled dc current source (_{L}_{sh}_{se}

The mathematical expression used to calculate the output current of solar cell is given by _{L} is the measured photocurrent for the irradiance S(W/m^{2}), I_{0} is the diode reverse saturation current, V_{T} is diode thermal voltage and V_{T} = k_{b}*T_{cell}/q, k_{b} is Boltzmann constant and k_{b }=_{ }1.3807 × 10 ^{−}^{23} J ^{−}^{1}, q is charge of a proton where q = 1.602 × 10^{−19} C, T_{cell} is working temperature of PV cell, V_{PV} is the output voltage across the solar cell, I_{PV} is the output current of the cell, R_{se} and R_{sh} are series and shunt resistances, N is diode ideality factor. The ideality factor varies for amorphous cells, and is typically 1–2 for polycrystalline cells and less than 1 for mono-crystalline silicon cells (c-Si). The expression used to calculate the reference and generated photo current are given by _{L} is the photo-current generated, S_{ref} is standard insolation (1000 W/m^{2}), I_{scref} is short circuit of PV array at STC, α_{isc} is temperature coefficient of current (0.102%^{°}C^{−1}), T_{cell} and T_{ref} (298 K or 25^{°}C) are cell and reference temperatures in kelvin.

The expression used to calculate the energy band gap can be written as_{g}dT is energy band gap coefficient and dE_{g}dT = −0.02677% (eV^{°}C^{−1}), E_{gref} is reference energy band gap of Si diode and it is equal to 1.12 eV.

The diode quality factor and PV array shunt resistance can be mathematically estimated using _{MPP} and I_{MPP} are peak voltage and peak current of PV array, R_{sh}^{(0)} is shunt resistance at short circuit condition which can be estimated using

The mathematical expression used to calculate the reference thermal voltage, array thermal voltage, reference diode reverse saturation current and diode reverse saturation current are given in _{scref} and V_{ocref} are short circuit current and open circuit voltage of PV array at standard test conditions(1 kW/m^{2} at 25^{°}C). Based on

The design and analysis of a 1 kWp, 250 V domestic roof-top PV panel situated at Chennai is considered for performance study. The specification of stand-alone PV panel is shown in

Parameters | Values |
---|---|

PV cell area | 8.2 cm × 8.2 cm |

No. of series connected cells in a PV string | 500 |

No. of parallel connected strings in PV array | 2 |

Open circuit voltage at STC | 300 V |

Short circuit current at STC | 4.34 A |

Maximum power(MP) at STC | 1 kW |

Voltage at maximum power point(STC) | 250 V |

Current at maximum power point(STC) | 4 A |

Coupling capacitor | 3.5 μF |

Load Resistance at MPP(STC) | 62.5 Ω |

The Simulink model of stand-alone 1 kW, 250 V PV panel is developed as shown in

In a typical scenario both temperature and insolation may vary during an operation. The typical variations of insolation and temperature are depicted in the

The simulation is run for 6 ms with above data as inputs. The performance of the output voltage for R and RL load are recorded as shown in the

For step increase in insolation from 850 to 1000 W/m^{2}, the output voltage rises exponentially from 222.8 V and settles at 250 V in 0.5 ms. For step increase in temperature from 25 to 40^{°}C, the load voltage exponentially decays from 250 V and settles to 241.3 V in 0.3 ms with an undershoot of about 1 V. The response is in line with the reports published already.

The power circuit of a 1 kW, 230 V, 5.4 A single phase five level cascaded H-bridge inverter (SPFLCHBI) consists of a pair of DC voltage source (_{DC}

A pair of 208 V DC is considered as input voltage for SPFLCHBI. The frequency operation of inverter ranges from 49.5 to 50.5 Hz with nominal frequency of 50 Hz. The modulation index ranges from 0.7 to 0.9 with nominal value of 0.8. A 300 V NPN MOSFET is considered for power switch. An LC filter with a cut off frequency of 1.5 kHz is considered for filter operation so that voltage is sinusoidal at the point of coupling to the grid. The filter inductance and filter capacitance are specified as 4 mH and 3 μF respectively. The 1 kW, 230 V resistive loads is realized using a 53 Ω wire wound resistor. In order to realize 1 kW, 230 V inductive load of 0.8 pf, a resistance of 42.32 ohm is connected in series with a 0.1013 H inductor, rated 8 amperes. A 100 μF, 400 V AC capacitor is connected with 42.32 ohm in order to realize a 1 kW, 230 V 0.8 pf capacitive load. The positive and negative half-cycle switching pattern for SPFLCHBI is shown in

Switch number/voltage | S_{1} |
S_{2} |
S_{3} |
S_{4} |
S_{5} |
S_{6} |
S_{7} |
S_{8} |
---|---|---|---|---|---|---|---|---|

+V_{DC}/2 |
1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |

-V_{DC}/2 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

+V_{DC} |
1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |

-V_{DC} |
0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |

The carrier signal and modulating signal frequencies are set as 10 kHz and 50 Hz respectively. The modulating and carrier signals waveforms for SPWM is shown in

The Modulation Index (MI) can be calculated using the expression given in _{m}_{c}

The RMS voltage for different values of modulation index (MI) under various power factor conditions are calculated and plotted as shown in _{RC} > V_{R} > V_{RL}_{R} _{RL}_{RC}

The Simulink model of 1 kWp stand-alone single phase inverter fed from PV array is developed as shown in

For step decrease in insolation from 1000 to 800 W/m^{2} at 0.04 s, the peak voltage decreases from 565.6 V and settles at 553.5 V. The output current peak decreases from 3.535 to 3.46 A. For step increase in temperature from 25^{°}C to 45^{°}C at 0.06 s, the peak voltage decreases from 553.5 V and settles at 520 V. Similarly, the output current peak decreases from 3.46 to 3.21 A. It is seen from the results that there are no noticeable transients in the voltage and current wave forms.

The analytical model of MGISPFLCHBPVI is developed using MATLAB function as shown in

Based on I-V and P-V characteristics of 1 kWp, 250 V PV array, a 2-D lookup table model for extracting maximum power from PV array is constructed using MATLAB/Simulink platform. Two lookup tables are constructed for estimating V_{MPP} and P_{MPP} with each table having inputs as solar insolation (W/m^{2}) and cell temperature (°C).

The real power (P_{g}) and reactive power (Q_{g}) injected by inverter to the grid are given by

Z_{g} is grid impedance.

δ is angle between E and V (in radians). δ is positive if E leads V and δ is considered negative if E lags V.

In order to operate the inverter in generating region, P > 0 and δ must be positive, i.e., E should lead V by + δ(rad). With grid voltage as reference, the grid current, I_{g} can be written as_{g}.

The necessary real power to be injected into the grid is given by the power tracked from PV array (as discussed in previous sections) at a particular insolation and cell temperature. Thus a dependent PQ control strategy is implemented by estimating modulation index and phase angle of the inverter modulating signal. The mathematical relationship between modulation index and inverter voltage is given in the

The reference phase angle (δ_{ref}) and modulation index (m_{ref}) are determined using _{DC} is input voltage of the single phase PV inverter.

P_{g_ref} and Q_{g_ref} are reference real and reactive powers respectively.

Based on the above

This section focuses on the comparison of P&O method with proposed PQ control strategy developed to inject P_{max} from PV panel into the grid. The parameters such as settling time and rising time are used for comparison among various methodologies.

A P&O for MPPT from PV array mentioned in above sections considered for comparison. The PV voltage, current and power responses for variation in insolation and temperature are reproduced as given in this section and these are shown in

The proposed PQ control technique is implemented and the steady state inverter voltage, grid voltage and current waveforms for a period of 3 cycles are obtained at STC as shown in

To study the transient voltage response of the grid connected single phase PV inverter system, the typical variations of solar insolation and temperature are considered as already shown in

From the ^{2} at 40 ms similarly the peak power point voltage changes from 250 to 247.2 V. For step change in temperature from 25°C to 40°C at 80 ms, the peak power of each panel changes from 248 to 233 W. Similarly the peak power point voltage changes from 247.2 to 221.2 V.

From

The parameters such as settling time and rise time are compared for different technologies are shown in

P&O | GA-INC | Proposed | |
---|---|---|---|

Settling time | 0.598 s | 0.432 s | 10 ms |

Rising time | 0.103 s | 0.124 s | 1.2 ms |

It is clear from the table that the settling time taken by the conventional method is large when compared with that of the time taken by proposed control strategy. The rising time is at a minimal microseconds in comparision with other strategy. It is anticipated that the employed method can track the global arrays when evaluating the power yield from the arrays. The estimated power yield from each array is calculated by multiplying the total power retrieved from the two arrays by the stated or estimated respective methods.

A 1 kWp PV array fed single phase grid connected inverter system is designed, modeled and simulated for performance study. Analytical models for PV panel and 1-phase inverter were developed. The performance of this model is validated by comparing its results with those obtained from Simulink model. The transient response of the system has been studied by varying insolation and temperature. The proposed PQ control strategy is able to inject the maximum extracted power from PV panel effectively into the grid. Its performance is compared with the conventional methods during transient and steady state periods. It is finally concluded that the settling time was effectively reduced to 10 ms with minimum oscillations in the output voltage waveforms and the proposed methodology results 97.2% efficiency.

The authors with a deep sense of gratitude would thank the supervisor for his guidance and constant support rendered during this research.