# Evaluation of the Reactive Power Support Capability and Associated Technical Costs of Photovoltaic Farms’ Operation

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## Abstract

**:**

## 1. Introduction

## 2. PV Farm Models

#### 2.1. Single-Stage PV Farm Model

#### 2.2. Two-Stage PV Farm Model

## 3. Methodology

#### 3.1. Flowcharts

#### 3.2. PV System Losses

#### 3.3. Technical Costs

## 4. Operation without Reactive Power Support

#### 4.1. Single-Stage PV Farm Losses without Reactive Power Support

#### 4.2. Two-Stage PV Farm Losses without Reactive Power Support

## 5. Operation with Reactive Power Support

#### 5.1. Reactive Power Support Capability Area

#### 5.2. PV Farm Losses with Reactive Power Support

#### 5.3. Technical Cost for Reactive Power Support

#### 5.4. Reactive Power Support Economics

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Single-stage PV farm losses per component, without reactive power support. The losses without reactive power support are approximately linear as a function of the irradiance.

**Figure 9.**Two-stage PV farm losses per component for various ${v}_{dc}$, without reactive power support. (

**a**) At 720 V; (

**b**) at 750 V; (

**c**) at 800 V. The losses without reactive power support are approximately linear as a function of the irradiance.

**Figure 13.**Two-stage PV farm losses per component at 500 W/m${}^{2}$ for various ${v}_{dc}$, with reactive power support. (

**a**) At 720 V; (

**b**) at 750 V; (

**c**) at 800 V. The losses with reactive power support are approximately a quadratic function of the reactive power reference value.

**Figure 14.**Single-stage PV farm losses per component at 500 W/m${}^{2}$, with reactive power support. The losses with reactive power support are approximately a quadratic function of the reactive power reference value.

**Figure 15.**Technical costs of providing reactive power support at 500 W/m${}^{2}$ for both PV farms, as a percentage of the rated power. Despite losses from two-stage PV farms being higher, the technical costs are similar for both topologies.

**Figure 16.**Reactive support capability areas with associated technical costs: (

**a**) Single-stage; (

**b**) Two-stage at 720 V; (

**c**) Two-stage at 750 V; (

**d**) Two-stage at 800 V. At 1000 W/m${}^{2}$, there is no reactive power capability since full converter capacity is being used to inject active power.

**Figure 17.**Hourly average solar irradiance data and reactive power dispatch for estimation of the reactive power support revenue. The base value considered for the solar irradiance is 1000 W/m${}^{2}$ and for reactive power is 850 kVAr.

**Figure 18.**Technical costs for the test systems following the reactive power dispatch and daily irradiation cycle presented in Figure 17.

Parameter | Value | Unit | Parameter | Value | Unit | Parameter | Value | Unit |
---|---|---|---|---|---|---|---|---|

Rated power | 850 | kW | ${v}_{\Delta}$ | 380 | V | ${R}_{f}$ | 0.5 | $\mathsf{\Omega}$ |

${v}_{pv}$ @1000 W/m${}^{2}$ | 798 | V | f | 50 | Hz | ${L}_{f}$ | 397.8 | $\mathsf{\mu}$H |

C | 87.8 | mF | ${r}_{r}$ | 1 | m$\mathsf{\Omega}$ | ${C}_{f}$ | 0.64 | $\mathsf{\mu}$F |

${L}_{r}$ | 54.1 | $\mathsf{\mu}$H | ||||||

Component | Reference | Series modules | Parallel modules | Total | ||||

PV module | Kyocera Solar KD205GX-LP | 30 | 138 | 4.140 | ||||

DC/AC converter | ABB 5SNA1600N170100 IGBT | 1 | 2 | 12 |

Parameter | Value | Unit | Parameter | Value | Unit | Parameter | Value | Unit |
---|---|---|---|---|---|---|---|---|

Rated power | 850 | kW | ${v}_{\Delta}$ | 380 | V | f | 50 | Hz |

${v}_{pv}$ @ 1000 W/m${}^{2}$ | 691 | V | ${r}_{DC}$ | 1 | m$\mathsf{\Omega}$ | ${R}_{f}$ | 0.5 | $\mathsf{\Omega}$ |

C, ${C}_{pv}$ | 87.8 | mF | ${L}_{DC}$ | 5.0 | mH | ${L}_{f}$ | 397.8 | $\mathsf{\mu}$H |

${r}_{r}$ | 1 | m$\mathsf{\Omega}$ | ${L}_{r}$ | 54.1 | $\mathsf{\mu}$H | ${C}_{f}$ | 0.64 | $\mathsf{\mu}$F |

Component | Reference | Series modules | Parallel modules | Total | ||||

PV module | Kyocera Solar KD205GX-LP | 26 | 159 | 4.134 | ||||

DC/DC converter | ABB 5SNA1600N170100IGBT | 1 | 1 | 1 | ||||

DC/AC converter | ABB 5SNA1600N170100IGBT | 1 | 2 | 12 |

**Table 3.**Reactive power support economic feasibility evaluation. Revenue, expenses and profit are expressed in BRL.

Test System | Reactive Power (MVArh) | Technical Costs (MWh) | Revenue | Expenses | Profit |
---|---|---|---|---|---|

Single-stage | 8.59 | 0.046 | 59.06 | 46.53 | 12.16 |

Two-stage @720V | 8.59 | 0.045 | 59.06 | 45.57 | 13.12 |

Two-stage @750V | 8.59 | 0.047 | 59.06 | 47.18 | 11.51 |

Two-stage @800V | 8.59 | 0.049 | 59.06 | 48.93 | 9.75 |

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## Share and Cite

**MDPI and ACS Style**

Lourenço, L.F.N.; Monaro, R.M.; Salles, M.B.C.; Cardoso, J.R.; Quéval, L.
Evaluation of the Reactive Power Support Capability and Associated Technical Costs of Photovoltaic Farms’ Operation. *Energies* **2018**, *11*, 1567.
https://doi.org/10.3390/en11061567

**AMA Style**

Lourenço LFN, Monaro RM, Salles MBC, Cardoso JR, Quéval L.
Evaluation of the Reactive Power Support Capability and Associated Technical Costs of Photovoltaic Farms’ Operation. *Energies*. 2018; 11(6):1567.
https://doi.org/10.3390/en11061567

**Chicago/Turabian Style**

Lourenço, Luís F. N., Renato M. Monaro, Maurício B. C. Salles, José R. Cardoso, and Loïc Quéval.
2018. "Evaluation of the Reactive Power Support Capability and Associated Technical Costs of Photovoltaic Farms’ Operation" *Energies* 11, no. 6: 1567.
https://doi.org/10.3390/en11061567