# Review on Optimization Techniques of PV/Inverter Ratio for Grid-Tie PV Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

_{2}) emissions percentage, net present cost (NPC), the percentage of renewable electricity, excess electricity, and unmet load weretaken into account. It was reported that the DC/AC inverter ratio with a unity value and minimized CO

_{2}emissions produced the best results for providing energy (to Mecca, Saudi Arabia), with excess electricity of 0% and an unmet load. However, it was found that it is possible to downsize the inverter size to 68% with respect to the nominal PV power to decrease the total NPC of the system, as well as reduce inverter cost.

#### 2.1. Derating Factor of PV Technology

#### 2.2. PV Array to Inverter Sizing Strategies

- Manufacturers’ recommendations based on PV guidelines.
- DC/AC sizing ratio according to third-party publications.

_{norm}) relation can be derived by:

#### 2.2.1. Manufacturers’ Recommendations Based on PV Guidelines

#### 2.2.2. DC/AC Sizing Ratio According to Third-Party Publications

_{inv,dc,nom,}and P

_{PV,nom}. The authors point out that a number of variables, including weather, price, and inverter features, may impact an inverter scaling strategy. The threshold (occurrence percentage) of irradiance (GTH) at a specific site should not be exceeded by the distribution of irradiance, as this may result in excessive power that exceeds the inverter capacity. This could result in some energy losses under greater irradiance and a reduced coefficient of power with temperature. The relationship between P

_{inv,dc,nom}, and P

_{PV,nom}is called the inverter downsize coefficient (R) and is derived by [71]:

_{STC}= 1000 W/m

^{2}is the STC irradiance, G

_{TH}is the irradiance threshold at a chosen site (W/m

^{2}), P

_{PV,nom}is the rated PV installed power (kWp), and P

_{inv,dc,nom}is the DC input rated power of inverter (kW).

#### 2.2.3. A Climate Classification

#### 2.3. Analytical Methods Affect the Inverter in the PV Inverter

## 3. Recommended Deep Learning for Inverter Sizing

#### 3.1. System Cost Consideration

_{t}represents the net cash flow at time t. The net present value can be defined as the summation of a time series of cash flows brought into the present. The choice of the ideal PV-inverter ratio that maximizes NPV is a moving target, as represented in Figure 4, while the significant variables that affect NPV and how they interact is shown in Figure 5.

#### 3.2. Recommended Approach

#### 3.3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Explanation of the oversizing ratio of the DC solar PV-to-inverter AC power output over a whole day.

**Figure 2.**Normalized revenue vs. DC/AC ratio at 35° Tilt, 0° Az, North Victoria/South NSW (35°) with fixed tilt angle on the left, while tracking tilt angle to the right.

**Figure 6.**Diagram of a recommended approach to optimize PV array DC/AC inverter power, while maximizing yearly energy yield for on-grid photovoltaic systems that use Deep Learning networks.

**Figure 8.**The relationship between the system cost with respect to PV capacity and the DC/AC ratio for the studied system.

Ref. | Range of Discussion on DC/AC Sizing and Cost | Literature Focus | Related Analysis and Results | Inverter Undersizing | Proposing System | Date Publish |
---|---|---|---|---|---|---|

[32] | Extensive | sizing optimization issues, hybrid PV/wind/diesel generator systems, hybrid PV/wind systems, hybrid PV/diesel generator, and standalone PV systems | No | Limited | No | 2013 |

[33] | Limited | Power and Energy Losses in PV Plants in Future Ancillary Services Markets | Limited | No | No | 2020 |

[34] | Limited | Optimization goals, utilized optimization methods, grid type as well as the investigated technology | Yes, statistical results | No | No | 2018 |

[35] | Limited to PV system installed | Environmental, PV system, installation, cost factors as well as other miscellaneous factors | Limited | No | No | 2017 |

This work | Extensive | DC/AC ratio optimization techniques | Yes, main results | yes | Yes | 2023 |

Ref. | PV/Inverter Ratio | Company/Country | Recommendations |
---|---|---|---|

[56] | 0.88–1.1 | KACO New Energy | Power Ratio = PV_{GEN}/P_{AC,INV} |

[57] | 0.7–1.0 | Power-One Inc. | PV Power @ STC/AC Power Nom. Max. of Inverter |

[58] | 1.0 | Leonic Co., Ltd. | N/A |

[54] | 0.8–1.2 | Danfoss Solar Inverters | Si PV = 0.94; Thin-Film = 0.94–0.90 and Thin–Film = 1.0 if Free-standing |

[59] | 0.75–0.85 | AE PV-powered Inc | N/A |

[60] | 0.8–1.2 | SMA Solar AG | PV/inverter power ratio (Vp) = input power inverter/peak power PV (0.9–1.0); Accepted Vp = 0.8–1.2 = (under extreme climate) |

[61] | 0.8–1.1 | Energy, Staffelstein & Engineering | DF (Dimensioning factor) = P_{solar}/P_{WR,ACmax} < 0.8:for DF = 0.8–1.15 = inverter too high; recommended for 35° inclination and south orientation; DF = (1.2–1.3): recommended facades (90° inclination), west or facing east; DF over 1.3: inverter too small; DF = (1.15 to 1.2): recommended to orient well to a very flat module under 15° inclinations or/and south (SW, SE). |

[62] | 1.3–0.8 | Solar Photovoltaic Power: Designing Grid-Connected Systems, Malaysia | ${\mathrm{PR}}_{\mathrm{k}}=\frac{{\mathrm{P}}_{\mathrm{ac}\_\mathrm{inv}}}{{\mathrm{P}}_{\mathrm{PV}@\mathrm{STC}}}$ For Si PV = 0.80–0.75; for Thin–Film = 1.30–1.00 |

[63] | 0.7–1.5 | UD, Delaware, US, Syllabus Book | Cost-effective and limited choice of inverter sizes to choose SF, even if overloaded occasionally. |

[64] | 0.7–1.0 | Europe | Southern Europe (35–45° N) = 1.0–0.85; Central Europe (45–55° N) = 0.9–0.75; Northern Europe (55–70° N) = 0.8–0.7; |

[65] | 0.8–1.2 | India | N/A |

[66] | 0.7–0.65 | United States | N/A |

[45] | 1–0.8 | United Kingdom | PV array-to-inverter ratio must be sized between 1:0.8 to 1:1 |

[67] | 0.75 | Guideline/Standard Australia | The nominal AC output power of the inverter cannot be under 75% of the peak power of the PV array. |

Climate Classification | Country/Territory with the Weather |
---|---|

Dfb | Humid continental climate, warm summer; at least four months averaging above 10 °C, all months with average temperatures below 22 °C, and coldest month averaging below 0 °C (or −3 °C). |

Csb | Mediterranean climate, warm summer; the driest month of summer receives less than 40 mm, at least three times as much precipitation in the wettest month of winter as in the driest month of summer, all months with average temperatures below 22 °C, at least four months averaging above 10 °C, and coldest month averaging above 0 °C (or −3 °C). |

Csa | Mediterranean climate, hot summer; the driest month of summer receives less than 40 mm, at least three times as much precipitation in the wettest month of winter as in the driest month of summer, at least four months averaging above 10 °C, at least one month’s average temperature above 22 °C, and coldest month averaging above 0 °C (or −3 °C). |

Cfb | Subtropical highland climate or temperate oceanic climate; at least four months averaging above 10 °C, all months with average temperatures below 22 °C, and coldest month averaging above 0 °C (or −3 °C). |

Cfa | No dry months in the summer. No significant precipitation difference between seasons. Humid subtropical climate; at least four months averaging above 10 °C (50 °F), at least one month’s average temperature above 22 °C (71.6 °F),and coldest month averaging above 0 °C (32 °F) (or −3 °C (27 °F)). |

BSk | Cold semi-arid climate |

BWh | The hot desert climate, and no month with an average temperature greater than 10 °C. |

Cwa | Monsoon-influenced humid subtropical climate; at least ten times as much rain in the wettest month of summer as in the driest month of winter, at least four months averaging above 10 °C, at least one month’s average temperature above 22 °C, and coldest month averaging above 0 °C (or −3 °C). |

Af | The average precipitation of at least 60 mm every month (tropical rainforest climate) |

Aw | The driest month has a precipitation of less than 60 mm (tropical savanna or dry and wet climate). |

**Table 4.**Studies in relation to the sizing ratio theory and values considered in publications by third parties worldwide divided into climatic regions.

Optimal Power Ratio | Method/Relation | Recommendation | Climate Classification | Country/Group | Ref. |
---|---|---|---|---|---|

1.50–1.00 | $\frac{{\mathrm{P}}_{\mathrm{pv}}}{{\mathrm{P}}_{\mathrm{inv}}}$ | SI; r = 1.5 medium efficiency inverter, r = 1.2 high-efficiency inverter. HSI; r = 1.10 medium and low-efficiency inverter, r = 1.00 high and medium efficiency inverter. | Dfb | Finland | [73,74] |

0.71 | $\frac{{\mathrm{P}}_{\mathrm{inv},\mathrm{dc},\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{PV},\mathrm{nom}}}=\frac{{\mathrm{G}}_{\mathrm{TH}}}{{\mathrm{G}}_{\mathrm{STC}}}$ | 0.71 | Csb | Eugene, OR, USA | [14] |

0.71 | $\frac{{\mathrm{P}}_{\mathrm{inv},\mathrm{dc},\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{PV},\mathrm{nom}}}=\frac{{\mathrm{G}}_{\mathrm{TH}}}{{\mathrm{G}}_{\mathrm{STC}}}$ | 0.71 | Csa | Sacramento, CA, USA | [14] |

1.291–1.204 | $\frac{{\mathrm{P}}_{\mathrm{pv},\mathrm{rated}}}{{\mathrm{P}}_{\mathrm{inv},\mathrm{rated}}}$ | β = 60° (1.204), β = 45° (1.291) | Csa | Batna, Algeria | [75,76] |

1.220–1.153 | $\frac{{\mathrm{P}}_{\mathrm{pv},\mathrm{rated}}}{{\mathrm{P}}_{\mathrm{inv},\mathrm{rated}}}$ | β = 60° (1.153), β = 45° (1.220) | Csa | Algiers, Algeria | [77] |

0.67 | NA | 0.67 | Csa | Portugal | [78,79] |

1.00–0.80 | $\frac{{\mathrm{P}}_{\mathrm{max},\text{}\mathrm{inverter}}}{{\mathrm{P}}_{\mathrm{nom},\mathrm{generator}}}$ | 0.85 | Cfb | Bogota, Colombia | [80] |

0.65 | NA | 0.65 | Cfb | The Netherlands | [81] |

1.20–0.75 | $\frac{{\mathrm{P}}_{\mathrm{pv}-\mathrm{inv},\text{}\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{pv}\text{}\mathrm{peak}}}$ | v = 0.90 (Germany) | Cfb | Germany | [82] |

0.95–0.85 | $\frac{{\mathrm{P}}_{\mathrm{pv}}}{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{AC}\_\mathrm{nom}}}$ | NA | Cfb | Freiburg, Germany | [83] |

1.30–1.15 | $\frac{{\mathrm{P}}_{\mathrm{max},\text{}\mathrm{inverter}}}{{\mathrm{P}}_{\mathrm{peal}\_\mathrm{PV}\_\mathrm{array}}}$ | 1.15 | Cfb | Nottingham, UK | [15] |

0.90–0.70 | $\frac{{\mathrm{P}}_{\mathrm{pv},\mathrm{rated}}}{{\mathrm{P}}_{\mathrm{inv},\mathrm{rated}}}$ | TF = 1.3, Overcast sky = 0.9–0.7 | Cfb | Northern Ireland, UK | [84] |

1.10–1.50 | $\frac{{\mathrm{P}}_{\mathrm{DC}\_\mathrm{STC}}}{{\mathrm{P}}_{\mathrm{RATED}}}$ | Low Eff. Inv; LSI = 1.4–1.5; HIS = 1.2–1.3, High Eff. Inv; LSI = 1.3–1.4; HIS = 1.1–1.2, | Cfb | Loughborough, UK | [7] |

1.25 | $\frac{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{dc},\text{}\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{PV},\text{}\mathrm{nom}}}=\frac{{\mathrm{G}}_{\mathrm{TH}}}{{\mathrm{G}}_{\mathrm{STC}}}$ | 1.10–1.40 | Cfb | Oak ridge, TN, USA | [85] |

1.25 | $\frac{{\mathrm{P}}_{\mathrm{pv},\mathrm{rated}}}{{\mathrm{P}}_{\mathrm{inv},\mathrm{rated}}}$ | 1.10–1.40 | Cfb | Northern Ireland, UK | [7] |

1.25 | $\frac{{\mathrm{P}}_{\mathrm{DC}\_\mathrm{STC}}}{{\mathrm{P}}_{\mathrm{RATED}}}$ | TF = 1.10–1.15 | Cfb | Loughborough, UK | [86] |

NA | $\frac{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{dc},\text{}\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{PV},\text{}\mathrm{nom}}}=\frac{{\mathrm{G}}_{\mathrm{TH}}}{{\mathrm{G}}_{\mathrm{STC}}}$ | 0.69 | Cfa | Oak ridge, TN, USA | [14] |

1.30–1.20 | $\frac{{\mathrm{P}}_{\mathrm{pv}}}{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{AC}\_\mathrm{nom}}}$ | Si PV = 1.30–1.20; Thin-Film < 1.00 | Cfa | UFSC, Florianópolis, South Brazil | [15] |

0.83–0.78 | $\frac{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{AC}\_\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{array},\text{}\mathrm{STC}}}$ | Thin-Film Fall = 0.82; Thin-Film Summer = 0.83; Thin-Film Spring = 0.82; Thin-Film Winter = 0.78; | BSk | Golden, Colorado | [87] |

1.00–0.60 | $\frac{{\mathrm{P}}_{\mathrm{inverter},\text{}\mathrm{max},\text{}\mathrm{AC}\text{}\mathrm{output}}}{{\mathrm{P}}_{\mathrm{DC},\text{}\mathrm{rating}}}$ | 1.22 | BSk | San Diego, California | [18,27] |

NA | $\frac{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{dc},\text{}\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{PV},\text{}\mathrm{nom}}}=\frac{{\mathrm{G}}_{\mathrm{TH}}}{{\mathrm{G}}_{\mathrm{STC}}}$ | 0.74 | BSk | Prewitt, NM, USA | [14] |

0.85–0.65 | $\frac{{\mathrm{P}}_{\mathrm{inv}}}{{\mathrm{P}}_{\mathrm{array}\left(\mathrm{Act}\right)\text{}}}$ | Sfmin = 0.65; Sfmax = 0.85 for Gulf Council Countries | BWh | Kuwait | [88] |

NA | 0.67 | BWh | Phoenix, AZ, USA | [14] | |

NA | 1.00 | BWh | Las Vegas, NV, USA | [14] | |

1.02–0.55 | $\frac{{\mathrm{P}}_{\mathrm{inv}}}{{\mathrm{P}}_{\mathrm{PV}\text{}}}$ | NA | Cwa | Sao Paulo, Brazil | [89] |

1.321–1.210 | $\frac{{\mathrm{P}}_{\mathrm{pv},\mathrm{rated}}}{{\mathrm{P}}_{\mathrm{inv},\mathrm{rated}}}$ | β = 45° (1.321), β = 60° (1.210) | BWh | Adrar, Algeria | [3] |

0.85–1.07 | Valid on all PV technologies | Af | Malaysia | # | |

NA | $\frac{{\mathrm{P}}_{\mathrm{inv},\text{}\mathrm{AC}\_\mathrm{nom}}}{{\mathrm{P}}_{\mathrm{PV},\text{}\mathrm{dc},\text{}\mathrm{STC}}}$ | 0.761 (Lanai)/0.741 (Oahu) | Aw | Lanai/Oahu, Hawaii, USA | [14] |

1.43–1.21 | $\frac{{\mathrm{P}}_{\mathrm{pv},\mathrm{rated}}}{{\mathrm{P}}_{\mathrm{inv},\mathrm{rated}}}$ | Valid on all PV technologies | Af | Kuala Lumpur, Kuching and Alor Setar, Johor Bharu, Ipoh, Malaysia | [90] |

1.03–0.93 | $\frac{{\mathrm{P}}_{\mathrm{inv},\mathrm{max}}}{{\mathrm{P}}_{\mathrm{PVG},\mathrm{stc}}}$ | Integrated (0.93), Flat surface (1.03) | Csa | Cadiz, Spain | [80] |

Description | Dimensions |
---|---|

Minimum Batch Size | 128 |

Initial Learning Rate | 0.0003 |

Maximum Epochs | 15 |

layers convolution 2d Layer 3 | 3 |

batch Normalization Layer | 1 |

relu Layer | 1 |

Maximum Pooling 2d Layer 3, Stride = 2 | 3, 2 |

convolution 2d Layer 3, 2 × Number of filters | 3, 2 × 12 |

batch Normalization Layer | 1 |

relu Layer | 1 |

maximum Pooling 2d Layer 3, Stride = 2 | 3, 2 |

convolution 2d Layer 3, 4 × Number of filters | 3, 4 × 12 |

batch Normalization Layer | 1 |

relu Layer | 1 |

Maximum Pooling 2d Layer 3, Stride = 2 | 3, 2 |

convolution 2d Layer 3, 4 × Number of filters | 3, 4 × 12 |

batch Normalization Layer | 1 |

relu Layer | 1 |

convolution 2d Layer 3, 4 × Number of filters | 3, 4 × 12 |

batch Normalization Layer | 1 |

relu Layer | 1 |

Maximum Pooling 2d Layer (time Pool Size 1) | 1 |

dropout Layer | 1 |

fully Connected Layer (12 = numClasses) | 12 |

Soft-max Layer | 1 |

classification Layer | 1 |

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## Share and Cite

**MDPI and ACS Style**

Hazim, H.I.; Baharin, K.A.; Gan, C.K.; Sabry, A.H.; Humaidi, A.J.
Review on Optimization Techniques of PV/Inverter Ratio for Grid-Tie PV Systems. *Appl. Sci.* **2023**, *13*, 3155.
https://doi.org/10.3390/app13053155

**AMA Style**

Hazim HI, Baharin KA, Gan CK, Sabry AH, Humaidi AJ.
Review on Optimization Techniques of PV/Inverter Ratio for Grid-Tie PV Systems. *Applied Sciences*. 2023; 13(5):3155.
https://doi.org/10.3390/app13053155

**Chicago/Turabian Style**

Hazim, Hazim Imad, Kyairul Azmi Baharin, Chin Kim Gan, Ahmad H. Sabry, and Amjad J. Humaidi.
2023. "Review on Optimization Techniques of PV/Inverter Ratio for Grid-Tie PV Systems" *Applied Sciences* 13, no. 5: 3155.
https://doi.org/10.3390/app13053155