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This paper proposes an economic performance optimization strategy for a PV plant coupled with a battery energy storage system. The case study of La Reunion Island, a non-interconnected zone (NIZ) with a high level of renewable energy sources (RES), is considered. This last decade, to reach the ambitious target of electricity autonomy by 2030 set by the local authorities, local and national plans have been launched to promote renewable energy sources integration that led to a noticeable development of photovoltaic (PV) systems. To avoid a decrease of the grid reliability due to a large integration of intermittent energy sources into a non-interconnected grid, the authorities have introduced new regulatory rules for RES producers. The proposed optimization strategy relies on these new regulatory rules and takes into account the energy market data, the amount of PV production subject to penalties for imbalance, the batteries and the PV technological characteristics together with a PV production forecast model. Due to its high convergence rate to the true global minimum and its perfect suitability to practical engineering optimization problems, the recently developed Modified Cuckoo Search algorithm is used as optimization algorithm. The effectiveness and relevance of the proposed strategy are assessed on experimental data collected on a real PV power plant. An economical analysis demonstrates that the proposed optimization strategy is able to fulfill the new regulatory rules requirements while increasing the economic performance of the system.

To date, reducing carbon emission has become a major concern. Among possible options, increasing shares of renewable energy sources (RES) such as solar, wind or biomass resources appear as a promising solution for a cleaner power generation. High shares of RES may then become a critical aspect of future energy systems. In this context, small islands that mainly rely on imported fossil fuels for energy production are likely to be pioneers in the development of decarbonized electricity production [

In this study, the case of La Reunion Island, a non-interconnected zone (NIZ), is considered. Even if the territory has a high level of RES, its electricity production remains strongly based on imported fuels. In this context, local authorities have set the ambitious objective of reaching electricity autonomy by 2030. This last decade, to reach this target, local and national plans have been launched to promote RES integration [

In the case of La Reunion, and according to our best knowledge, none work has been conducted to optimize the economical performance of existing hybrid photovoltaic-battery energy storage system (BESS) power generators, based on the latest regulatory rules. In this paper, an economical optimization of a hybrid PV-BESS power generator is developed. The proposed methodology relies on a metaheuristic optimization algorithm taking into account the energy market data, the amount of PV-generated energy subject to penalties for imbalance, the PV and the batteries technological characteristics together with a PV production forecast model. To assess the effectiveness and relevance of the proposed strategy, the economic analyses are performed on data measured on a real power plant. Indeed, a one-year experimental data, collected from August 2013 to August 2014 on a 57 kWp PV farm coupled with a 78.5 kWh BESS, are considered.

The rest of this paper is organized as follows. The regulatory rules applied in La Reunion are presented in Section 2. Section 3 is dedicated to model design. In this section the PV production forecast model and the energy storage model are detailed. The performance of the proposed optimization strategy in terms of economical efficiency improvement is demonstrated in Section 4.

In non-interconnected zones (NIZ) such as La Reunion, the large integration of intermittent sources raises critical technical issues issue related to the reliability of power supply. The reliability of an electrical grid can be defined by its ability to supply the aggregate electrical demand and energy requirements of the customers at all times, while withstanding sudden disturbances such as unanticipated loss of system elements (e.g. load or production fluctuations) [

In this context, and considering the rapid and important growth of PV systems in La Reunion the last decade, the authorities have recently decided to set up new regulatory rules to ensure the reliability of the power supply. Henceforth, producers have to declare a time generation profile that represents the day-ahead power injected by their plants, at a minute basis. If the mismatches between the actual injected power and the announced power exceed the admitted tolerance, financial penalties are applied. According to this regulatory framework, energy imbalance is calculated with minutely resolution, and the tolerance band is taken equal to ±5% of the installed PV power capacity

The electricity tariff system relies on peak and off-peak hours. During peak hours, 7 PM to 9 PM, the electricity feed-in tariff is more attractive. However, during this time period, producers have to guarantee a constant power injection to the grid comprised between 20% and 70% of

Peak hours (7 PM to 9 PM) [? ct/kWh] | Off-peak hours [? ct/kWh] | |
---|---|---|

Selling price | 60 | 40 |

Buying price | 40 | 40 |

Note that producers have the possibility to buy electricity from the grid. In some very specific cases, it could be interesting to buy electricity from the grid during off-peak, store the energy in an ESS, and sell it back during peak hours.

The producer’s revenue is calculated each minute using the follow expression:

where

where

Every time

In this work, the economic effectiveness of the system is assessed using two criteria, which are the revenue and the daily fault rate (DFR). This last criterion defines the ratio of time where the system is in faulty condition each day:

With

To fulfill the requirements of the new regulatory rule, PV power producers have to announce a day in advance the power profile to be injected to the grid, which requires a PV production forecast model. Besides, regardless of the accuracy of the PV production forecast model, financial penalties due to imbalance are unavoidable. Therefore, to reduce financial penalties and above all take advantage of peak hours feed-in tariff, the use of ESS appears to be a relevant option.

In the literature, a wide variety of parametric and non-parametric forecast models have been reported [

In this study, regarding practical purposes, the widely used persistence model is chosen to forecast the PV output power at a minute basis. This is a simple

Variable | Description [Unity] |
---|---|

Scheduled profile to be injected to the grid [kW] | |

Power injected to the grid [kW] | |

Measured PV power [kW] | |

Forecasted PV power [kW] | |

Installed PV power capacity [kW_{p}] | |

Storage power [kW] (>0 charge, <0 discharge) | |

Storage power exchanged with the AC bus | |

Maximal power in discharge [kW] | |

Maximal power in charge [kW] | |

Imbalance power [kW] | |

Amount of energy dedicated to evening peak [kWh] | |

Estimated total energy produced by PV plant [kWh] | |

Parameter to be estimated | |

Parameter to be estimated | |

Maximum usable storage capacity [kWh] | |

Min. energy storage level [% | |

Max. energy storage level [% | |

Efficiency of storage in charge | |

Efficiency of storage in discharge | |

Electricity selling price | |

Electricity buying price | |

DFR | Daily fault rate |

Cumulated time of faulty condition [minute] |

model based on the assumption that the PV production of today is the same as yesterday [

where

Even if this method does not take into account the intra-day variability of solar irradiance, it represents with a good accuracy the periodicity and seasonality of weather conditions (day/night and summer/winter cycles) [

Regarding optimization purposes and according to the considered time scale

Variable | Description [Unity] | Value |
---|---|---|

Maximum storage capacity [kWh] | 78.5 | |

Min. energy storage level [% | 20 | |

Max. energy storage level [% | 99 | |

Efficiency of storage in charge | 0.9 | |

Efficiency of storage in discharge | 0.9 | |

Maximal power in discharge [kW] | 36.1 | |

Maximal power in charge [kW] | 17.2 | |

DOD_{max} | Maximal depth of discharge [%] | 80 |

(minutes in this study), a simplified static model is proposed. This model relies on the static characteristics of the battery (Cf.

Subjected to constraints on power and capacity:

where

The PV, battery, grid, and loads are all connected to an AC bus. Since the battery is operated on DC, an AC-to-DC (respectively DC-to-AC) converter is necessary when charging (respectively discharging) the battery. Therefore, considering the storage charge and discharge efficiencies (

In this work, a minute dispatch strategy for a 57 kWp PV farm with 78.5 kWh BEES is implemented and an economical optimization of the dispatch strategy is proposed. BESS has two main applications: first, compensate PV production forecast errors during off-peak and thus reduce financial penalty due to imbalance. Second, inject power to the grid during peak hours and thus take advantage of the attractive feed-in tariff.

In this context, two parameters are introduced. The first one, denoted

Here

To assess the effectiveness and relevance of the proposed strategy, the economic analyses are performed on a one-year experimental data, collected from August 2013 to August 2014 at La Reunion on a real PV power plant. Due to its high convergence rate to the true global minimum and its perfect suitability to practical engineering optimization problems, the recently developed Modified Cuckoo Search algorithm proposed by [

Modified Cuckoo Search (MCS) algorithm can be regarded as a modification of the standard Cuckoo Search (CS) proposed by Yang and Deb [

CS algorithm relies on the observation of the reproduction strategy of cuckoos. Cuckoos lay their eggs in the nests of other host birds that may be of different species. If the host bird discovers that the eggs are not its own it could either destroy the egg or abandon the nest [

・ Each cuckoo lays one egg (a set of solution) at a time and dumps it in a random nest;

・ The best nests, those containing the highest quality of eggs (solutions), will carry over to the next generation;

・ The number of nests is fixed, and there is a probability

The main modification introduced by [

The power injected to the grid is defined as the sum of the PV output power and the storage power exchanged with the AC bus:

The BESS is used to adjust the PV power plant

Every time

Above the upper limit

When

where

Below the lower limit

When

if

else

end if

where

Within the tolerance band

When

The economical performance improvement relies on the estimation of two parameters

As expected, while

As illustrated on

In a first attempt, the economic performance improvement strategy consists on finding the optimal values of

with

and subjected to

The optimization procedure, performed on experimental data collected from August 31^{st} 2013 to September 1^{st} 2014, leads to the optimal set of parameter

It can be noticed that the DFR seems to contain a periodic component. The analysis of the DFR in the frequency domain reveals that the frequency component with the higher magnitude is located at 0.002732 day^{−1}, which corresponds to a periodicity of 366 days. Moreover, a thorough study of the DFR reveals a strong and significant correlation between DFR and the forecast error, with a Pearson’s correlation coefficient of 82% (p-value < 0.0001).

The analysis of the forecast error reveals the same periodicity of 366 days, which means that the forecast error is linked to the season. Indeed, as illustrated on

The analysis of the total energy produced by the PV plant each day

nent contained into

Regarding the seasonality of the solar irradiance, and since

In this work, a minute dispatch strategy for a 57 kWp PV farm with 78.5 kWh BEES has been simulated, and an economical optimization of the dispatch strategy has been developed. This strategy has been designed to fulfill the requirements of the new regulatory rules set in La Reunion while optimizing the economic performance of the system. The BESS is used during off-peak to compensate PV production forecast error and during peak hours to inject power to the grid. Therefore, two parameters have been introduced. The first one is related to amount of energy to store for the evening peak hours whereas the second one represents the fraction of the storage capacity that is dedicated to compensate power imbalance due to forecast errors. The optimization goal is to find the optimal value of these parameters that maximizing the revenue while taking into account the new regulatory rules constraints. The proposed optimization strategy takes into account the energy market data, the amount of PV production subject to penalties for imbalance, the batteries and the PV technological characteristics together with a PV production forecast model. The effectiveness and relevance of the proposed strategy have been assessed on experimental data collected on a real PV power plant. An economical analysis demonstrated that the proposed optimization strategy has been able to fulfill the new regulatory rules requirements while increasing the economic performance of the system.

Due to the seasonal behavior of solar radiation, it is likely that economical performance can be further increased using a seasonal-based optimization approach. Additional works are currently in progress to study if the revenue can be increased by taking into account the seasonal component contained in the forecast error and the total energy produced by the PV plant.

This work is a contribution to the FEDER project GYSOMATE funded by the European Social Fund and the Reunion Region. The authors would like to kindly acknowledge Pr. Jean-Daniel Lan-Sun-Luk for the fruitful scientific discussions and M. Patrick Jeanty for the solar experimental data.

Damour, C., Benne, M., Alicalapa, F., Grondin-Perez, B. and Chabriat, J.-P. (2017) Economic Performance Optimization of a PV-BESS Power Generator: A Case Study La Reunion Island. Smart Grid and Renewable Energy, 8, 114- 128. https://doi.org/10.4236/sgre.2017.84008