# Analysis of Some Power Quality Parameters at the Points of Common Coupling of Photovoltaic Plants Based on Data Measured by Inverters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{AC}), the AC current injected into the grid (I

_{AC}), the AC voltage in the grid phases (V

_{AC}) and the grid frequency (f

_{grid}) measured by the inverters were used in this work. The maximum measurement error in the inverters, at a temperature of 25 °C, was ±1% for the grid voltage V

_{AC}, that of the injected power P

_{AC}was ±3%, that of the injected current I

_{AC}was ±2%, and that of the grid frequency f

_{grid}was ±0.1% [40].

## 3. Results and Discussion

#### 3.1. Grid Voltage Values Recorded at Each PV Installation during the Monitoring Period

_{AC}measured by the inverters during the entire monitoring period at the PCC of each PV installation were evaluated to assess their possible relationship with the injection of the electricity generated at each plant. Authors such as Chaudhary et al. [43] consider that the voltage rise issue is one of the most likely negative effect of the high PV penetration, or Ganghi et al. [9] have indicated that voltage violations to be the most important factor limiting PV penetration.

_{AC}and the current injected I

_{AC}by each installation have been represented in the form of colour maps. Figure 2 corresponds to one of the inverters of PV plant 1. With these graphs, it is possible to clearly visualise the values of these parameters over the period monitored in each of the installations.

_{AC}voltage, measured in V. As can be seen in the colour scale of these figures, the higher values of these parameters are represented in red; as they decrease, they turn yellow, then green, and finally, the lower values are shown in blue.

_{AC}grid voltage data recorded by the inverters are plotted in box plots, showing the mean voltage for each installation (red line inside the box), the 75th percentile (the upper side of the box) and the 25th percentile (lower side of the box). The distance between these last two values is the inter quartile range. Since each PV installation injects into different distribution lines, the average voltage values in each of them were different, as they will depend on the specific point of the grid where they are located, and the distance from the transformer. The distribution of V

_{AC}values at each PCC was around 240 V in all the installations, except in the case of installation 3, where the values were lower, at around 220 V. The outliners that appear in Figure 14 (any values outside of the whiskers), show on the one hand, voltage values higher than the upper horizontal black lines, which correspond to the higher values recorded in each installation; and on the other hand, voltage values below the lower horizontal black lines are shown, which are point data that basically correspond to instants of time in which, after a fault, the inverter returns to operation but is not yet injecting energy into the grid. Therefore, these are not real grid voltage data but a consequence of how the inverter measures during reconnection after a fault period. If the grid voltage is outside the allowed range, the inverters have mechanisms to disconnect from the grid.

#### 3.2. Analysis of the Relationship between the Grid Voltage and the Power Generated by the Inverters

_{AC}was represented on the Y-axis, and the value of the power injected into the grid at each time instant P

_{AC}was represented on the X-axis. Both parameters were measured by the inverters. Due to the large volume of data to be processed, these graphs were made for each of the months corresponding to the period monitored, and in each of the three different phases. Given the particularities of each installation, the following shows how this analysis was carried out in each one of them.

_{AC}voltage value of each phase was represented with respect to P

_{AC}value resulted from the sum of the power produced by the three inverters divided by three due to the distribution between the three phases.

_{AC}voltage value of each phase was represented with respect to the sum of the P

_{AC}power produced by the two inverters and in turn divided by three due to the distribution between the three phases.

_{AC}voltage of each phase recorded by one of the inverters connected to each phase was plotted against the sum of the P

_{AC}power generated by the two inverters connected to the same phase.

_{AC}voltage measured by each inverter on the phase into which it injects was therefore plotted against the P

_{AC}power generated by the same inverter.

_{AC}measured by one of the inverters injecting on each phase was plotted against the sum of the P

_{AC}power generated by the six inverters injecting together on the same phase.

_{AC}voltage measured by each inverter was therefore plotted against the P

_{AC}power generated by the same inverter.

_{AC}versus P

_{AC}, the voltage limits established in the current standard were also included. The standard EN-50160 “Voltage characteristics of electricity supplied by public electricity networks”, indicates that the supply voltage variations must be 95% of time within the range 230 ± 10% at all supply terminals of the LV network [44]. Therefore, the lower and upper permissible levels for this parameter of the grid signal, corresponding respectively to the values 207–253 V, were represented in the figures in red.

^{2}) values (shown below) obtained. However, the same type of adjustment was always used to be able to make a comparative analysis of the behaviour obtained during the whole monitoring period.

_{AC}power injected in the installations, the voltage values observed had a variation range of between 5 and 10 V. In some cases, there may even be a greater variation range. This variation interval was maintained for all the power values, and it shows that the voltage values in the grid presented a previous variation that does not depend on the production of the plant and that can be considered unrelated to the operation of the PV installations.

_{AC}versus P

_{AC}ratios, calculated from the weekly data at each of the six PV plants studied. The values of the determination coefficients obtained in these weekly linear fits are shown in Figure 22. The periods in which there is no monitored data in the inverters were shown in these graphs as null values.

#### 3.3. Imbalance of Network Voltage Values between Phases

_{grid_phase_i}versus the mean value of the voltages of the three phases V

_{grid_phase_i}, with i = 1, 2 and 3, was calculated by the Equation (1)

_{AC_grid_phase_i}versus the average value of the production of the three phases P

_{AC_grid_phase_i}, with I = 1, 2 and 3, was determined in the same way as the imbalance of the voltage in the phases, by means of the Equation (2)

#### 3.4. Analysis of the Grid Frequency Values Measured by the Inverters of PV Systems

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geographical distribution of the six PV plants analysed in the province of Córdoba, South Spain. The numbers correspond to the order of the installations shown in Table 1.

**Figure 2.**Values of the current generated in one of the inverters in PV plant 1 and values of the grid voltage measured by the inverter in one of the phases.

**Figure 3.**Values of the grid voltage measured by an inverter in one of the phases without and with electricity production in the PV plant 1.

**Figure 4.**Values of the current generated in one of the inverters in PV plant 2 and values of the grid voltage measured by the inverter in one of the phases.

**Figure 5.**Values of the grid voltage measured by an inverter in one of the phases without and with electricity production in the PV plant 2.

**Figure 6.**Values of the current generated in one of the inverters in PV plant 3 and values of the grid voltage measured by one of the inverters in one of the phases.

**Figure 7.**Values of the grid voltage measured by an inverter in one of the phases without and with electricity production in the PV plant 3.

**Figure 8.**Values of the current generated in one of the inverters in PV plant 4 and values of the grid voltage measured by one of the inverters in one of the phases.

**Figure 9.**Values of the grid voltage measured by an inverter in one of the phases without and with electricity production in the PV plant 4.

**Figure 10.**Values of the current generated in one of the inverters in PV plant 5 and values of the grid voltage measured by one of the inverters in one of the phases.

**Figure 11.**Values of the grid voltage measured by an inverter in one of the phases without and with electricity production in the PV system 5.

**Figure 12.**Values of the current generated in one of the inverters in PV plant 6 and values of the grid voltage measured by one of the inverters in one of the phases.

**Figure 13.**Values of the grid voltage measured by an inverter in one of the phases without and with electricity production in the PV plant 6.

**Figure 14.**Values of the grid voltage measured by the inverters in one of the phases in each of the PV installations analysed, when there is production from the installation being fed into the grid.

**Figure 15.**Ratio between the values of the grid voltage V

_{AC}on one of the phases versus the values of the P

_{AC}power produced in PV installations (

**a**) Installation 1 measured during month 5 (May), (

**b**) Installation 2 measured during month 11 (November), (

**c**) Installation 3 measured during month 9 (September), (

**d**) Installation 4 measured during month 3 (March), (

**e**) Installation 5 measured during month 4 (April) and (

**f**) Installation 6 measured during month 10 (October).

**Figure 16.**Weekly variation of the slope and the ordinate at the origin corresponding to the V

_{AC}versus P

_{AC}regressions in PV installation 1 during the three years monitored.

**Figure 17.**Weekly variation of the slope and ordinate at the origin corresponding to the V

_{AC}versus P

_{AC}regressions in PV installation 2 during the three years monitored.

**Figure 18.**Weekly variation of the slope and the ordinate at the origin corresponding to the V

_{AC}versus P

_{AC}regressions in PV installation 3 during the three years monitored.

**Figure 19.**Weekly variation of the slope and the ordinate at the origin corresponding to the V

_{AC}versus P

_{AC}regressions in PV installation 4 during the three years monitored.

**Figure 20.**Weekly variation of the slope and the ordinate at the origin corresponding to the V

_{AC}versus P

_{AC}regressions in PV installation 5 during the three years monitored.

**Figure 21.**Weekly variation of the slope and the ordinate at the origin corresponding to the V

_{AC}versus P

_{AC}regressions in PV installation 6 during the three years monitored.

**Figure 22.**Weekly variation of the determination coefficient corresponding to the V

_{AC}versus P

_{AC}regressions in the PV installations during the three years monitored. (

**a**) Results for Installation 1, (

**b**) Results for Installation 2, (

**c**) Results for Installation 3, (

**d**) Results for Installation 4, (

**e**) Results for Installation 5 and (

**f**) Results for Installation 6.

**Figure 23.**Maximum values of PV power that would be admitted in each phase in the network at the PCC of installation 3, depending on the maximum (green line), average (black line) and minimum (yellow line) slopes and Y-axis intercept.

**Figure 24.**Grid voltage imbalance on phase 2, measured by inverter 2 in PV installation 1 (

**a**) and the histogram of these grid voltage imbalance values (

**b**).

**Figure 25.**Grid voltage imbalance on phase 3, measured by inverter 1 in PV installation 2 (

**a**) and the histogram of these grid voltage imbalance values (

**b**).

**Figure 26.**Grid voltage imbalance on phase 2, measured by inverter 2 in PV installation 4 (

**a**) and these grid voltage imbalance values detailing smaller deviations (

**b**).

**Figure 27.**PV production imbalance on phase 2 with respect to the production on the three phases, measured by inverter 2 in PV installation 4.

**Figure 28.**Grid voltage imbalance on phase 1, measured by inverter 1 in PV installation 6 (

**a**) and these grid voltage imbalance values detailing smaller deviations (

**b**).

**Figure 29.**PV production imbalance on phase 1 respect the production on the three phases, measured by inverter 1 in PV installation 6.

**Figure 30.**Relationship between the values of the grid frequency in one of the phases versus the values of the power produced P

_{AC}in the PV 4 system measured during month 11 (November).

**Figure 31.**Relationship between the variations of the grid frequency in one of the phases versus the values of the variations of the P

_{AC}power produced in the PV 4 installation measured during month 11 (November).

**Figure 32.**Relationship between the values of the grid frequency in one of the phases versus the values of the P

_{AC}power produced in the PV 4 installation measured during month 11 (November).

Plant 1 | Plant 2 | Plant 3 | Plant 4 | Plant 5 | Plant 6 | |
---|---|---|---|---|---|---|

Total power (kW) | 672.0 | 217.6 | 36.7 | 22.2 | 100.2 | 17.8 |

Number of inverters | 3 | 2 | 6 | 3 | 18 | 3 |

Inverter model | SMA SC-200 | SMA SC-100 | SMA SMC-5000 | SMA SMC-7000HV | SMA SMC-5000A | SMA SMC-5000 |

Number of modules per inverter | 1280 | 640 | 36 | 38 | 26 | 36 |

Total number of modules | 3840 | 1280 | 216 | 114 | 468 | 108 |

Module model | Suntech, STP 175S-24/Ac | BP-3170 | Suntech, STP 170S-24/Ac | Bosch, c-Si M48195 | Atersa, A-214P | BP-3165 |

Module nominal power (W) | 175 | 170 | 170 | 195 | 214 | 165 |

Single-phase or Three-phase | Three-phase | Three-phase | Single-phase | Single-phase | Single-phase | Single-phase |

Rooftop or ground | Rooftop and ground | Rooftop | Rooftop | Rooftop | Rooftop | Rooftop |

Geographical location | Carcabuey | Pozoblanco | Carcabuey | Hinojosa del Duque | Córdoba | Córdoba |

Rural or city area | Rural, industrial area | Rural, industrial area | Rural, industrial area | Rural, industrial area | City, industrial area | City, residential area |

Latitude | 37.463889 | 38.35939 | 37.446389 | 38.481812 | 37.899167 | 37.896389 |

Longitude | −4.268611 | −4.84436 | −4.271944 | −5.123581 | −4.715278 | −4.795556 |

**Table 2.**Maximum, minimum, and average values of the slope obtained by correlating weekly over the three-year period the values of the grid voltage versus the power generated in the PV installations.

Max Slope | Min Slope | Average Slope | |
---|---|---|---|

PV Installation 1 | 0.055 | 0.021 | 0.039 |

PV Installation 2 | 0.13 | 0.050 | 0.078 |

PV Installation 3 | 0.00074 | 0.00031 | 0.00050 |

PV Installation 4 | 0.95 | 0.051 | 0.5 |

PV Installation 5 | 0.00027 | −0.0000031 | 0.00015 |

PV Installation 6 | 0.00074 | −0.00030 | 0.00027 |

**Table 3.**Maximum, minimum, and average values of the Y-axis-intercept obtained by correlating weekly over the three-year period the values of the grid voltage versus the power generated in the PV installations.

Max V_{AC} Intercept | Min V_{AC} Intercept | Average V_{AC} Intercept | Difference between Max and Min | |
---|---|---|---|---|

PV Installation 1 | 236.83 | 232.15 | 234.89 | 4.68 |

PV Installation 2 | 243.56 | 233.40 | 237.89 | 10.16 |

PV Installation 3 | 219.78 | 215.23 | 217.47 | 4.55 |

PV Installation 4 | 237.83 | 232.33 | 236.03 | 5.50 |

PV Installation 5 | 240.33 | 236.76 | 238.80 | 3.57 |

PV Installation 6 | 236.81 | 233.54 | 232.89 | 3.27 |

**Table 4.**Maximum, minimum, and average values of the determination coefficient R

^{2}obtained by correlating weekly over the three-year period the values of the grid voltage versus the power generated in the PV installations.

Max Determination Coefficient | Min Determination Coefficient | Average Determination Coefficient | |
---|---|---|---|

PV Installation 1 | 0.89 | 0.35 | 0.73 |

PV Installation 2 | 0.84 | 0.51 | 0.72 |

PV Installation 3 | 0.88 | 0.31 | 0.70 |

PV Installation 4 | 0.74 | 0.04 | 0.44 |

PV Installation 5 | 0.79 | −0.01 | 0.51 |

PV Installation 6 | 0.63 | −0.26 | 0.28 |

**Table 5.**PV power values allowed in each phase at the grid feed-in point of each PV installation, obtained from the maximum values of slope and Y-axis intercept obtained in the weekly regressions.

Current Nominal Power of the Plant (kW) | Current Nominal Power Per Phase (kW) | Maximum Nominal Power Per Phase with the Most Unfavourable Slope (kW) | Increase Allowed (kW) | Increase in Power Compared to the Current Installed Power Per Phase (%) | |
---|---|---|---|---|---|

PV Installation 1 | 672.0 | 224.0 | 364.7 | 140.7 | 62.8 |

PV Installation 2 | 217.6 | 72.5 | 142.0 | 69.5 | 95.8 |

PV Installation 3 | 36.7 | 12.2 | 50.7 | 38.5 | 314.2 |

PV Installation 4 | 22.2 | 7.4 | 18.2 | 10.8 | 145.7 |

PV Installation 5 | 100.2 | 33.4 | 60.0 | 26.6 | 79.7 |

PV Installation 6 | 17.8 | 5.9 | 25.5 | 19.6 | 329.3 |

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**MDPI and ACS Style**

Santiago, I.; García-Quintero, J.; Mengibar-Ariza, G.; Trillo-Montero, D.; Real-Calvo, R.J.; Gonzalez-Redondo, M.
Analysis of Some Power Quality Parameters at the Points of Common Coupling of Photovoltaic Plants Based on Data Measured by Inverters. *Appl. Sci.* **2022**, *12*, 1138.
https://doi.org/10.3390/app12031138

**AMA Style**

Santiago I, García-Quintero J, Mengibar-Ariza G, Trillo-Montero D, Real-Calvo RJ, Gonzalez-Redondo M.
Analysis of Some Power Quality Parameters at the Points of Common Coupling of Photovoltaic Plants Based on Data Measured by Inverters. *Applied Sciences*. 2022; 12(3):1138.
https://doi.org/10.3390/app12031138

**Chicago/Turabian Style**

Santiago, Isabel, Javier García-Quintero, Gonzalo Mengibar-Ariza, David Trillo-Montero, Rafael J. Real-Calvo, and Miguel Gonzalez-Redondo.
2022. "Analysis of Some Power Quality Parameters at the Points of Common Coupling of Photovoltaic Plants Based on Data Measured by Inverters" *Applied Sciences* 12, no. 3: 1138.
https://doi.org/10.3390/app12031138