# Self-Consumption and Self-Sufficiency in Photovoltaic Systems: Effect of Grid Limitation and Storage Installation

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{2}emissions have resulted in increasing progress in the generation of energy from renewable sources, such as photovoltaic (PV) systems, both in terms of implementation and in reducing its costs. This goal raises new challenges for national and international policy systems by addressing not only industrial or large-scale users, and therefore businesses, but also small users, namely households, in order to meet all or part of the needs of their energy demand. In this way, passive consumers, thanks to the process of self-consumption, i.e., on-site energy production and consumption, are gradually becoming active prosumers [1]. The presence of active prosumers has impacts on the network operation: it introduces new challenges and opens new scenarios, by introducing also novel roles for the system operators in the future [2]. Moreover, also the role of the prosumer as actively involved in the network operation must be taken into consideration, thanks to the implementation of new control systems [3] and novel measurement approaches (such as the net metering [4]), enabling the complete integration of intermittent energy sources in the system.

## 2. Review of the Most Common Strategies to Maximize Self-Consumption and Self-Sufficiency

#### 2.1. Definition of Self-Consumption and Self-Sufficiency

_{lgc}) with respect to the total local generation (E

_{gen}) [5]:

_{lgc}the same numerator of the SC) with respect to the total consumption (E

_{load}). It quantifies user independence from the grid [8] and it is calculated according to:

#### 2.2. Main Strategies to Maximize the Self-Consumption and the Self-Sufficiency

#### 2.3. Description of Peak Shaving Techniques without Energy Storage

#### 2.4. Review of Methodologies Maximizing Self-Consumption or Self-Sufficiency

## 3. A Methodology for the Optimal Sizing of PV and Batteries

#### 3.1. STEP #1—Import of the Energy Inputs

^{2}) on a surface with a defined tilt and azimuth, air temperature (°C), and wind speed (m/s) at a defined measurement height. Regarding the time step, PVGIS provides hourly profiles. Nevertheless, the proposed procedure works also with smaller time steps, according to data availability and the accuracy required by the analysis.

#### 3.2. STEP #2—Selection of the Technologies and of the Parameters of the Energy Models

_{PV}. However, η

_{PV}has a nonlinear dependence on irradiance: in fact, a PV system requires a minimum irradiance (a threshold irradiance G

_{0}, which is around 17 W/m

^{2}) to generate power. Thus, PV efficiency can be calculated starting from the rated efficiency in standard test conditions (STC, corresponding to irradiance G

_{STC}= 1000 W/m

^{2}and module temperature T

_{STC}= 25 °C), as follows:

_{STC}is a function of rated power at STC P

_{STC}, of irradiance G

_{STC,}and of the PV surface A

_{PV}(η

_{STC}= P

_{STC}/(A

_{PV}∙G

_{STC})), and it is ≈21% in actual commercial modules. The quantity Π

_{η}is an equivalent efficiency calculated as the product of the thermal efficiency (η

_{th}), the efficiency in the DC/AC conversion (η

_{DC/AC}), and the other so urces of losses (1 − ξ

_{mix}) ≈ 92%. In particular, η

_{th}can be estimated as:

_{c}is the module temperature.

_{mix}≈ 8% is a miscellaneous factor that takes into account losses due to dirt, glass reflection, Joule effect in cables, and the MPP tracking.

_{STC}to be at least higher than 80% after 20 years, corresponding to a linear decrease of −1%/year. However, in recent years, several experimental campaigns have stated that the degradation of crystalline silicon modules may be lower, if there are no damages. In particular, in the present paper, the decrease has been assumed to be −0.5%/year [46,47].

_{PV}of the generator, e.g., the annual energy production per unit of power installed in kWh/kW/year.

_{i}can be evaluated as a function of the SOC at the previous instant t

_{i−1}(SOC

_{ti−1}) [49]:

_{bat}is the average power exchanged between the batteries and the system in the time step Δt (P

_{bat}is assumed negative in charging phase and positive during discharge), η

_{bat}is the charge/discharge efficiency of the storage in charging operation, and C

_{E,bat}is the energy capacity of the storage facility. The performance of batteries decreases over time due to degradation: their state of health (SOH), which is the ratio between actual energy capacity and rate value [50], decreases while cycling and the manufacturer provides two additional limits in order to avoid too low values of SOH. In particular, the manufacturer provides a maximum number of cycles and a maximum number of operating years: the replacement of batteries is recommended after exceeding the minimum between the two limits. For the sake of clarity, an example is provided. For commercial lithium batteries for stationary purposes, a typical maximum age before replacement is 10 years, and the maximum number of charge–discharge cycles is equal to 10,000 [51]. Supposing a single charge–discharge cycle per day (average value), during one whole year, the storage performs 365 cycles, and after 10 years, it is 3650. This value is lower than the 10,000, but the battery is substituted, because it worked for 10 years. On the contrary, in the case of five cycles per day, after 6 years, the battery has performed 10,950 cycles and has to be changed. In the proposed methodology, dynamics for frequent charging and discharging are not investigated. Actually, the safety parameters provided by manufacturers (maximum/minimum SOC, maximum power) are respected. Moreover, the replacement of batteries after their lifetime is performed to avoid a huge decrease in their SOH over time.

#### 3.3. STEP #3—Selection of the Parameters for the Financial Calculation

_{I}is the investment cost, C is the absolute value of the negative cash flow for the n

^{th}year, and R is the positive cash flow for the nth year. In the case of PV and battery systems, the negative cash flow C includes planned maintenance and extraordinary maintenance, e.g., replacement of batteries, inverters, or damaged PV modules. The positive cash flow (revenue) R takes into account the earnings from the sale of electricity injection into the grid. In the case of prosumers, the self-sufficiency reduces the absorption from the grid; thus, another positive cash flow is the saving due to a lower electricity bill. In the case of economic incentives (e.g., tax discounts) or feed-in tariffs, they can be taken into account.

_{2}emission, the energy payback time, and the life cycle conversion efficiency are the most important [56].

#### 3.4. STEP #4—Planning of Renewable Generation and Storage Systems

_{PV}and the electric load. Regarding storage, a reasonable starting size can be that to store the daily requirement from the load. It corresponds to the average daily consumption of the user during the year.

_{load}, generation E

_{gen}, and battery charge/discharge E

_{bat}are the injections and absorptions from the grid E

_{grid}(with the generation convention):

_{bat}> 0 during battery discharge;

_{grid}> 0 during absorption from the grid.

#### 3.5. Considerations Related to the Optimization Criterion

_{1}) and the economic return (Γ

_{2}), respectively. They are defined according to Section 2.1 and Section 3.3, respectively, and the optimization variables are the size of PV system (P

_{PV}) and the energy capacity of batteries (C

_{E,bat}):

_{inj}≤ P

_{inj,limit}

_{PV}≤ P

_{PV,max}

_{E,bat}≤ C

_{E,bat,max}

_{inj}

_{,limit}to the injection into the grid P

_{inj}, i.e., the maximum power that may be injected into the electricity grid for a specific site. As described in Section 2.4, the proposed methodology takes into account the adoption of peak shaving strategy on generation profiles in order to increase the energy and economic benefits for the users. The effect of different values of P

_{inj}

_{,limit}is investigated by a sensitivity analysis: different injection limits are imposed, and, for each case, the optimal sizes are calculated and compared.

_{PV,max}and C

_{E,bat,max}are always selected to be far from the optimal values.

_{2}) in the paper. Moreover, one constraint of the optimization is related to the IRR, which is evaluated according to the following implicit formulation:

_{PV}, and the energy capacity of batteries, C

_{E,bat}) is implicit. Actually, these variables impact on the NPV and the IRR by affecting the energy exchanges of the system and its cash flows. In this context, the optimization problem is solved using sequential quadratic programming (SQP). It is an iterative algorithm that, at each iteration, approximates the nonlinear problem as a quadratic one, linearizing the equality/inequality constraints. The SQP is one of the best choices for constrained optimization problems because it does not require high computational cost, providing comparable accuracy with other nonlinear programming algorithms [60]. In order to check the correct operation of the SQP, the results were also calculated by following an exhaustive but with slow calculation of the results of all the possible sizes of PV and storage. It consists of an iterative method. Actually, the initial ranges and the discrete steps for the variables are large, while they become lower when solutions approach the optimum one. The result of this analysis demonstrates the correct operation of the SQP algorithm.

#### 3.6. Application of the Procedure in a Software Program for Research and Remote Teaching

## 4. Case Study for the Calculation of Self-Consumption and Self-Sufficiency

#### 4.1. Calculation Inputs

^{2}and an annual productivity of ≈1200 kWh/kW per year.

#### 4.2. Financial Parameters

_{load}) is 7000 kWh and their PV system produces E

_{PV}= 7300 kWh/year. The self-consumption is 40%; the energy locally produced and consumed (E

_{lgc}) is 2920 kWh. At the end of the year, 4380 kWh is injected into the grid, while 4080 kWh is absorbed from the grid.

_{surplus}) in the grid is equal to 300 kWh. The economic values of injection and absorption flows are, respectively, EUR ≈ 482 and EUR ≈ 449 (0.11 EUR/kWh); thus, GSE pays EUR ≈ 449 to the user. In addition, EUR 12 are obtained from the sale of E

_{surplus}to the grid (0.04 EUR/kWh), resulting in a total annual gain of EUR ≈ 461. The saving on the electricity bill is given by the avoided purchase of E

_{lgc}from the grid at 0.20 EUR/kWh (EUR 584): the passive user pays EUR 1400 (7000 kWh with a unitary cost of 0.20 EUR/kWh) for electricity, while the prosumer pays EUR 816 (4080 kWh × 0.20 EUR/kWh). Thus, the total economic benefit for the prosumer is EUR ≈ 1045. Since investments must be cost-effective, two economic constraints were considered in the optimizations: the NPV over the plant lifetime of 25 years (assuming a discount rate of 3%) must be positive, and the IRR must be higher than 6%.

#### 4.3. Reference Case

#### 4.4. PV Plant Coupled to BESS

#### 4.5. Variation in BESS Investment Cost

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Acronym | Definition |

BESS | Battery energy storage system |

DHW | Domestic hot water |

MPP | Maximum power point |

O&M | Operation and maintenance |

OS | Operating system |

PV | Photovoltaic |

RES | Renewable energy sources |

STC | Standard test conditions |

WT | Wind turbine |

Symbol | Description |

A_{PV} | PV surface (m^{2}) |

C_{E,bat} | Storage energy capacity (kWh) |

C_{I} | Investment cost (EUR) |

C | Negative cash flow (EUR) |

E_{bat} | Energy from batteries (kWh) |

E_{gen} | Local energy generation (kWh) |

E_{grid} | Energy exchanged with the grid (kWh) |

E_{lgc} | Locally generated and consumed energy (kWh) |

E_{load} | Total energy consumption (kWh) |

E_{PV} | PV energy (kWh) |

E_{surplus} | PV energy injected into the grid (kWh) |

Γ_{1} | Objective function maximizing self-sufficiency |

Γ_{2} | Objective function maximizing economic return |

G | Solar irradiance (W/m^{2}) |

G_{0} | Threshold irradiance (W/m^{2}) |

G_{STC} | Solar irradiance at STC (W/m^{2}) |

i | Discount rate (%) |

I.L. | Injection limit (kW) |

IRR | Internal rate of return (%) |

n | Number of years (-) |

N | Expected lifetime of the system (years) |

NPV | Net present value (EUR) |

P_{bat} | Exchanged power of battery during charge/discharge (kW) |

P_{STC} | PV power at STC (kW) |

P_{PV} | Size of PV system (kW) |

R | Positive cash flow (EUR) |

SC | Self-consumption (%) |

SOC | State of charge (%) |

SOH | State of health (%) |

SS | Self-sufficiency (%) |

t | Time instant (s) |

T_{c} | PV module temperature (°C) |

T_{STC} | PV module temperature at STC (°C) |

γ | PV thermal coefficient for power (%/°C) |

Δt | Time step (s) |

η_{bat} | Battery efficiency (%) |

η_{DC/AC} | DC/AC conversion efficiency (%) |

η_{mix} | PV miscellaneous efficiency (%) |

η_{PV} | PV efficiency (%) |

η_{STC} | PV efficiency at STC (%) |

η_{th} | PV thermal efficiency (%) |

${\Pi}_{\mathsf{\eta}}$ | PV equivalent efficiency (%) |

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**Figure 3.**Comparison of power profiles with different time-steps: 5 min (

**top**), 15 min (in the

**middle**), and 1 h (

**bottom**).

**Figure 4.**PV efficiency as function of irradiance and temperature (

**a**) and DC/AC conversion efficiency (

**b**).

**Figure 11.**Self-sufficiency and NET Present Value (NPV) as functions of PV nominal power with different injection limits.

**Figure 13.**Hourly energy profiles of Figure 11 with a curtailment in the grid injection I.L. = 1 kWh/h.

**Table 1.**Energy quantities related to the example in Figure 3: daily balances.

Energy Quantities | Measurement Unit | Time Step | ||
---|---|---|---|---|

5 min | 15 min | 1 h | ||

Consumption | kWh | 9.6 | 9.6 | 9.6 |

PV generation | kWh | 29.6 | 29.6 | 29.6 |

Injection in the grid | kWh | 24.2 | 24.1 | 23.7 |

Absorption from the grid | kWh | −4.3 | −4.2 | −3.8 |

Self-sufficiency | - | 55.6% | 56.6% | 61.1% |

Self-consumption | - | 18.1% | 18.5% | 19.9% |

**Table 2.**Energy quantities related to the example in Figure 3: yearly balances.

Energy Quantities | Measurement Unit | Time Step | ||
---|---|---|---|---|

5 min | 15 min | 1 h | ||

Consumption | kWh | 6700 | 6700 | 6700 |

PV generation | kWh | 5715 | 5715 | 5715 |

Injection in the grid | kWh | 3318 | 3254 | 3102 |

Absorption from the grid | kWh | −4303 | −4238 | −4087 |

Self-sufficiency | - | 35.8% | 36.7% | 39.0% |

Self-consumption | - | 41.9% | 43.1% | 45.7% |

Energy and Economic Quantities | Maximization of Self-Sufficiency | Maximization of NPV | ||||
---|---|---|---|---|---|---|

No I.L. | I.L. = 2 kWh/h | I.L. = 0 kWh/h | No I.L. | I.L. = 2 kWh/h | I.L. = 0 kWh/h | |

PV nominal power | 13 kW | 10 kW | 5 kW | 6 kW | 6 kW | 4 kW |

SS | 49% | 48% | 41% | 43% | 43% | 38% |

SC | 21% | 40% | 100% | 40% | 45% | 100% |

IRR | 6.4% | 6.3% | 6.5% | 11.2% | 10.5% | 8.0% |

NPV | EUR 7423 | EUR 5657 | EUR 2996 | EUR 9594 | EUR 8663 | EUR 3571 |

Energy and Economic Quantities | Maximization of Self-Sufficiency | ||||
---|---|---|---|---|---|

No I.L. | I.L. = 3 kWh/h | I.L. = 2 kWh/h | I.L. = 1 kWh/h | I.L. = 0 kWh/h | |

PV nominal power | 7 kW | 7 kW | 7 kW | 6 kW | 4 kW |

BESS nominal energy | 6 kWh | 6 kWh | 5 kWh | 4 kWh | 4 kWh |

SS | 65% | 65% | 62% | 58% | 52% |

SC | 51% | 54% | 59% | 71% | 98% |

IRR | 6.4% | 6.1% | 6.4% | 6.4% | 6.2% |

NPV | EUR 4364 | EUR 4028 | EUR 4278 | EUR 3654 | EUR 2367 |

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## Share and Cite

**MDPI and ACS Style**

Ciocia, A.; Amato, A.; Di Leo, P.; Fichera, S.; Malgaroli, G.; Spertino, F.; Tzanova, S.
Self-Consumption and Self-Sufficiency in Photovoltaic Systems: Effect of Grid Limitation and Storage Installation. *Energies* **2021**, *14*, 1591.
https://doi.org/10.3390/en14061591

**AMA Style**

Ciocia A, Amato A, Di Leo P, Fichera S, Malgaroli G, Spertino F, Tzanova S.
Self-Consumption and Self-Sufficiency in Photovoltaic Systems: Effect of Grid Limitation and Storage Installation. *Energies*. 2021; 14(6):1591.
https://doi.org/10.3390/en14061591

**Chicago/Turabian Style**

Ciocia, Alessandro, Angela Amato, Paolo Di Leo, Stefania Fichera, Gabriele Malgaroli, Filippo Spertino, and Slavka Tzanova.
2021. "Self-Consumption and Self-Sufficiency in Photovoltaic Systems: Effect of Grid Limitation and Storage Installation" *Energies* 14, no. 6: 1591.
https://doi.org/10.3390/en14061591