HAL Id: hal-02355288
https://hal.archives-ouvertes.fr/hal-02355288
Submitted on 8 Nov 2019
HAL
is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from
L’archive ouverte pluridisciplinaire
HAL, estdestinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de
Economic performance optimization of a hybrid PV-BESS power generator: a case study la Réunion
island
Cédric Damour, Michel Benne, Yassine Gangat, D Payet, Mickaël Hilairet
To cite this version:
Cédric Damour, Michel Benne, Yassine Gangat, D Payet, Mickaël Hilairet. Economic performance
optimization of a hybrid PV-BESS power generator: a case study la Réunion island. International
Conference on Renewable Energy: Generation and Applications, Feb 2016, Belfort, France. �hal-
02355288�
ECONOMIC PERFORMANCE OPTIMIZATION OF A HYBRID PV- BESS
1
POWER GENERATOR: A CASE STUDY LA REUNION ISLAND
2
C. Damour1, M. Benne1*, Y. Gangate2, D. Payet2, M. Hilairet3
3
1
LE2P, EA 4079, Univ. of La Reunion, 15, avenue R. Cassin, CS 92003, 97744 Saint Denis Cedex 9, France
4
2LIM, EA 2525, Univ. of La Reunion, PTU, Bât. 2, 2, rue J. Wetzell, 97490 Sainte-Clotilde, France
5
3F
CLAB, FR CNRS 3539, FEMTO-ST, UMR CNRS 6174, Univ. of Franche-Comté, rue T. Mieg, 90010 Belfort Cedex, France6
7
8 9
Abstract.
This paper proposes an economic performance optimization strategy for a PV plant coupled with a battery energy10
storage system (BESS). The case study of La Reunion Island, a non-interconnected zone (NIZ) with a high level of renewable
11
energy sources (RES), is considered. This last decade, to reach the ambitious target of electricity autonomy by 2030 set by the
12
local authorities, local and national plans have been launched to promote RES integration that led to a noticeable development of
13
photovoltaic (PV) systems. To avoid a decrease of the grid reliability due to a large integration of intermittent energy sources
14
into a non-interconnected grid, the authorities have introduced new regulatory rules for RES producers. The proposed
15
optimization strategy relies on a these new regulatory rules and takes into account the energy market data, the amount of PV
16
production subject to penalties for imbalance, the batteries and the PV technological characteristics together with a PV
17
production forecast model. The effectiveness and relevance of the proposed strategy are assessed on experimental data collected
18
on a real PV power plant. An economical analysis demonstrates that the proposed optimization strategy is able to fulfill the new
19
regulatory rules requirements while increasing the economic performance of the system.
20 21
1. Introduction 22
To date, reducing carbon emission has become a major
23
concerned. Among possible options, increasing shares of
24
renewable energy sources (RES) such as solar, wind or
25
biomass resources appears as a promising solution for a
26
cleaner power generation. High shares of RES may then
27
become a critical aspect of future energy systems. In this
28
context, small islands that mainly rely on imported fossil fuels
29
for energy production are likely to be pioneers in the
30
development of decarbonized electricity production [1-2].
31 32
In this study, the case of La Reunion Island, a non-
33
interconnected zone (NIZ), is considered. Even if the territory
34
has a high level of RES, its electricity production remains
35
strongly based on imported fuels. In this context, local
36
authorities have set the ambitious objective of reaching
37
electricity autonomy by 2030. This last decade, to reach this
38
target, local and national plans have been launched to
39
promote RES integration [3-4]. Thus, supported by incentive
40
mechanisms such as tax exemptions, direct subsidies or feed-
41
in tariffs, photovoltaic (PV) systems have experienced a rapid
42
and noticeable development [5]. However, a large integration
43
of intermittent sources into a non-interconnected grid raises
44
critical technical issues due to the uncertainties of the energy
45
production. The intermittency and unreliability of solar-
46
generated power may reduce the network stability and lead to
47
load shedding or to the interruption of electric service [6].
To
48
avoid such situations, the authorities have set a limit of 30%
49
of intermittent sources in the instantaneous electricity
50
production and have introduced new regulatory rules for RES
51
development. Henceforth, RES producers have to declare to
52
the grid operator, a day in advance, the power profile that will
53
be injected to the grid. Then, if the power plants do not meet
54
the submitted schedule for injected power, they face financial
55
penalties. In La Reunion Island, if mismatches between actual
56
and scheduled power injection exceed a given tolerance, RES
57
producers are charged with imbalance penalties. In order to
58
address the problem related to the intermittency of solar-
59
generated electricity while reducing the amount of PV
60
production subject to penalties for imbalance, energy storage
61
systems (ESSs) appears as one of the most relevant option.
62
Recently, several works related to the applicability,
63
advantages and disadvantages of various ESS technologies
64
for RES integration have been reported [7]. As regards PV
65
power plants coupling with ESS, several works dealing with
66
technical issues and economic feasibility have been
67
conducted [8-11]. However, from a regulatory point of view
68
(incentive schemes and economic feasibility), nearly all
69
works reported in the literature focus on the determination of
70
the optimal sizing of the ESS [12-15].
71 72
In the case of La Reunion, and according to our best
73
knowledge, none work has been conducted to optimize the
74
economical performance of existing hybrid photovoltaic-
75
battery energy storage system (BESS) power generators,
76
based on the latest regulatory rules. In this paper, an
77
economical optimization of a hybrid PV-BESS power
78
generator is developed. The proposed methodology relies on a
79
metaheuristic optimization algorithm taking into account the
80
energy market data, the amount of PV-generated energy
81
subject to penalties for imbalance, the PV and the batteries
82
technological characteristics together with a PV production
1
forecast model. To assess the effectiveness and relevance of
2
the proposed strategy, the economic analyses are performed
3
on data measured on a real power plant. Indeed, a one-year4
experimental data, collected from August 2013 to August5
2014 on a 57 kWp PV farm coupled with a 78.5kWh BESS,
6
are considered.
7 8
The rest of this paper is organized as follows. The regulatory
9
rules applied in La Reunion are presented in Section 2.
10
Section 3 is dedicated to model design. In this section the PV
11
production forecast model and the energy storage model are
12
detailed. The performance of the proposed optimization
13
strategy in terms of economical efficiency improvement is
14
demonstrated in Section 4.
15 16
Table 1: Nomenclature.
17
Variable Description [unity]
𝑃!"# Scheduled profile to be injected to the grid [kW]
𝑃!"# Power injected to the grid [kW]
𝑃!"_! Measured PV power [kW]
𝑃!"_! Forecasted PV power [kW]
𝑃!"_!"#$ Installed PV power capacity [kWp]
𝑃!"# Storage power [kW] (>0 charge, <0 discharge)
𝑃!"#_!" Storage power exchanged with the AC bus
− P! Maximal power in discharge [kW]
P! Maximal power in charge [kW]
𝑃! Imbalance power [kW]
E!"#_!"#$ Amount of energy dedicated to evening peak [kWh]
𝐸!"_!_!"!#$ Estimated total energy produced by PV plant [kWh]
α!"#$ Parameter to be estimated
β!"#$%&'( Parameter to be estimated
𝐶!"# Maximum usable storage capacity [kWh]
𝑆𝑂𝐶!"# Min. energy storage level [%𝐶!"#]
𝑆𝑂𝐶!"# Max. energy storage level [%𝐶!"#] η! Efficiency of storage in charge η! Efficiency of storage in discharge 𝐶! Electricity selling price
𝐶! Electricity buying price
DFR Daily fault rate
𝜏!"#$% Cumulated time of faulty condition [minute]
18
2. Regulatory rules 19
In NIZ such as La Reunion, the large integration of
20
intermittent sources raises critical technical issues related to
21
the reliability of power supply. The reliability of an electrical
22
grid can be defined by its ability to supply the aggregate
23
electrical demand and energy requirements of the customers
24
at all times, while withstanding sudden disturbances such as
25
unanticipated loss of system elements (e.g. load or production
26
fluctuations) [16-18]. Currently the sustainability of power
27
supply in La Reunion is already lower than in Metropolitan
28
France, with an average power outage duration estimated at
29
4 h/year/consumer vs 73 min [5]. In this context, and
30
considering the rapid and important growth of PV systems in
31
La Reunion the last decade, the authorities have recently
32
decided to set up new regulatory rules to ensure the reliability
33
of the power supply. Henceforth, producers have to declare a
34
one minute based profile that represents the day-ahead
35
forecasted power to be injected by their plants. If the
36
mismatches between the actual injected power and the
37
announced power exceed the admitted tolerance, financial
38
penalties are applied. According to this regulatory framework,
39
energy imbalance is calculated with minutely resolution, and
40
the tolerance band is taken equal to ± 5% of the installed PV
41
power capacity (𝑃!"_!"#$).
42 43
The electricity tariff system relies on peak and off-peak hours.
44
During peak hours, 7PM to 9PM, the electricity feed-in tariff
45
is more attractive. However, during this time period,
46
producers have to guarantee a constant power injection to the
47
grid comprise between 20 % and 70 % of 𝑃!"_!"#$. The
48
current electricity tariff system applied to PV power
49
producers in La Reunion, including peak and off-peak feed-in
50
tariffs, is summarized in Table 2.
51 52
Table 2: Summary of tariff system in La Reunion.
53
Peak hours (7PM to 9PM) [€ ct/kWh]
Off-peak hours [€ ct/kWh]
Selling price (𝐶!) 60 40
Buying price (𝐶!) 40 40
54
Note that producers have the possibility to buy electricity
55
from the grid. In some very specific cases, it could be
56
interesting to buy electricity from the grid during off-peak,
57
store the energy in an ESS, and sell it back during peak hours.
58 59
The producer’s revenue is calculated each minute using the
60
following expression:
61 62
revenue = Pinj CS/60 – Pout Cb/60 – penalties (1)
63
64
where Pinj denotesthe power injected to the grid and Pout the
65
power extracted from the grid. The financial penalties are
66
calculated as follows:
67 68
if Pbid – 0.05 PPV_peak < Pinj < Pbid + 0.05 PPV_peak then
69
70
penalties = 0
71 72
elseif Pinj > Pbid + 0.05 PPV_peak then
73 74
penalties = Pinj CS/60
75 76
else
77 78
𝑝𝑒𝑛𝑎𝑙𝑡𝑖𝑒𝑠=𝐶!
60 𝑃!"# 𝑃!"#
𝑃!!!"#$− 0.1+ 2𝑃!"#
𝑃!!!"#$ 𝑃!"#
+ 𝑃!"#−0.05𝑃!"_!"#$ 0.015− 𝑃!"#
𝑃!!!"#$
where Pbid denotes the day-ahead schedule power profile to be
79
injected to the grid.
80 81
Every time Pinj is outside the tolerance band, the system is
82
said to be in faulty condition and financial penalties are
83
applied.
84
In this work, the economic effectiveness of the system is
1
assessed using two criteria, which are the revenue and the
2
daily fault rate (DFR). This last criterion defines the ratio of
3
time where the system is in faulty condition each day:4 5
DFR = 𝜏!"#$% 1440
6 7
With 1440 minutes per day, 𝜏!"#$% represents the cumulated
8
time of fault condition in minute.
10 9
To fulfill the requirements of the new regulatory rule, PV
11
power producers have to announce a day in advance the
12
power profile to be injected to the grid, which requires a PV
13
production forecast model. Besides, regardless of the
14
accuracy of the PV production forecast model, financial
15
penalties due to imbalance are unavoidable. Therefore, to
16
reduce financial penalties and above all take advantage of
17
peak hours feed-in tariff, the use of ESS appears to be a
18
relevant option.
19 20
3. Model design 21
PV production forecast model
22
In the literature, a wide variety of parametric and non-
23
parametric forecast models have been reported [19].
24
Parametric models require a wide set of information about the
25
PV power plant technology and its installation configuration.
26
Non-parametric models are generally based on weather
27
forecast models [20]. These limitations make the reliability
28
and the suitability for “on field” uses of parametric and non-
29
parametric forecast models questionable.
30 31
In this study, regarding practical purposes, the widely used
32
persistence model is chosen to forecast the PV output power
33
at a minute basis. This is a simple model based on the
34
assumption that the PV production of today is the same as
35
yesterday [21]:
36 37
𝑃!"_! 𝑡 = 𝑃!"_! 𝑡−1440 (2)
38 39
where 𝑃!"_! and 𝑃!"_! denotes respectively the measured and
40
forecast PV output power at time 𝑡.
41
42
Even if this method does not take into account the intra-day
43
variability of solar irradiance, it represents with a good
44
accuracy the periodicity and seasonality of weather conditions
45
(day/night and summer/winter cycles) [13]. Besides, as a low-
46
tech approach compared with irradiance forecast based
47
strategies, it has the merit of avoiding additional costs, which
48
cannot be underestimated for small cases applications.
49
Obviously, the accuracy of the PV production forecast could
50
be improved using more sophisticated models but at the price
51
of increasing complexity and computational cost.
52 53
Energy storage model
54
Regarding optimization purposes and according to the
55
considered time scale (minutes in this study), a simplified
56
static model is proposed. This model relies on the static
57
characteristics of the battery (Cf. table 3) and neglects the
58
transient dynamics of the process. In the sequel, powers are
59
considered negative (respectively positive) during the
60
discharge (respectively charge) phase. In this context, the
61
battery state of charge (SOC) at time t is computed by:
62 63
𝑆𝑂𝐶 𝑡 =𝑆𝑂𝐶 𝑡−∆𝑡 +𝑃!"# 𝑡 ∆𝑡 𝐶!"# (3)
64 65
Subjected to constraints on power and capacity:
66 67
𝑃!≤𝑃!"# 𝑡 ≤𝑃!
𝑆𝑂𝐶!"#≤𝑆𝑂𝐶 𝑡 ≤𝑆𝑂𝐶!"# (4)
68 69
where 𝑃!"# 𝑡 is the storage power at time t. 𝑃!<0, − 𝑃!
70
represents the maximum battery discharging power, and
71
𝑃!>0 the maximum battery charging power. 𝑆𝑂𝐶!"# and
72
𝑆𝑂𝐶!"# are the minimum and maximum battery state of
73
charge, respectively. 𝐶!"# denotes the maximum usable
74
storage capacity of the ESS. Note that the battery aging and
75
self-discharge rate, which obviously affect 𝐶!"#, has not been
76
considered. Besides, powers are considered constant during
77
the time interval t; t+∆t . In this work, ∆t is equal to one
78
minute.
79 80
The PV, battery, grid, and loads are all connected to an AC
81
bus. Since the battery is operated on DC, an AC-to-DC
82
(respectively DC-to-AC) converter is necessary when
83
charging (respectively discharging) the battery. Therefore,
84
considering the storage charge and discharge efficiencies (η!
85
and η! respectively), the storage power exchanged with the
86
AC bus 𝑃!"#_!" 𝑡 isexpressed as follows:
87 88
P!"#_!" t = P!"# t η! if P!"# t <0 discharge
P!"!!" t = P!"# t/η! if P!"# t ≥0 charge (5)
89 90
Table 3: Storage system parameter values.
91
Variable Description [unity] Value
𝐶!"# Maximum storage capacity [kWh] 78.5
𝑆𝑂𝐶!"# Min. energy storage level [%𝐶!"#] 20
𝑆𝑂𝐶!"# Max. energy storage level [%𝐶!"#] 99
η! Efficiency of storage in charge 0.9 η! Efficiency of storage in discharge 0.9
− 𝑃! Maximal power in discharge [kW] 36.1
𝑃! Maximal power in charge [kW] 17.2
DODmax Maximal depth of discharge [%] 80
92
4. Economic performance optimization 93
In this work, a minute dispatch strategy for a 57 kWp PV
94
farm with 78.5 kWh BESS is implemented and an economical
95
optimization of the dispatch strategy is proposed. BESS has
96
two main applications: first, compensate PV production
97
forecast errors during off-peak and thus reduce financial
98
penalty due to imbalance. Second, inject power to the grid
99
during peak hours and thus take advantage of the attractive
100
feed-in tariff. In this context, two parameters are introduced.
101
The first one, denoted α!"#$, is related to the amount of
102
energy dedicated to the evening peak hours (E!"#_!"#$), which
1
have to be stored in the BESS meanwhile, and is written as a
2
fraction of the estimated total energy produced by the PV3
plant (𝐸!"_!_!"!#$):4 5
𝐸!"#_!"#$=𝛼!"#$ 𝐸!"_!_!"!#$ (6)
6 7
Here E!"_!_!"!#$= !""#P!"_!𝑑𝑡
! . The second one, denoted
8
𝛽!"#$%&'(, represents the fraction of the storage capacity that is
9
dedicated to compensate power imbalance (𝐶!"#$%&%'() due to
10
forecast errors:
11 12
𝐶!"#$%&%'(=𝛽!"#$%&'( 𝐶!"# (7)
13 14
To assess the effectiveness and relevance of the proposed
15
strategy, the economic analyses are performed on a one-year
16
experimental data, collected from August 2013 to August
17
2014 at La Reunion on a real PV power plant. Due to its high
18
convergence rate to the true global minimum and its perfect
19
suitability to practical engineering optimization problems, the
20
recently developed Modified Cuckoo Search algorithm
21
proposed by [22] is used as optimization algorithm.
22 23
PV/BESS control rules
24
The power injected to the grid is defined as the sum of the
25
PV output power and the storage power exchanged with the
26
AC bus:
27 28
𝑃!"#=𝑃!"_!+P!"#_!" (8)
29 30
The BESS is used to adjust the PV power plant 𝑃!"_! to
31
maintain, as much as possible, the difference between the
32
day-ahead announcement 𝑃!"# and the actual power injected
33
𝑃!"# to the grid within the tolerance band. If 𝑃!"_! is above
34
(respectively below) the tolerance limit, the BESS can be
35
used, when it is possible, to store (respectively deliver) the
36
imbalance power 𝑃!. Depending on whether the measured
37
output PV is within, below or above the tolerance band, 𝑃! is
38
defined as follows:
39 40
P!=0 within
P! = 𝑃!!_!− 𝑃!"#+0.05 𝑃!!!"#$ above charge
P! =𝑃!!_!− 𝑃!"#−0.05 𝑃!!!"#$ below discharge
(9)
41
42
Every time P!≠0 financial penalties for imbalance are
43
applied. Therefore, the storage charge/discharge process must
44
be suitably controlled in order to reduce the DFR and thereby
45
the amount of financial penalties, while ensuring that there is
46
enough energy stored in the BESS for the evening peak. In
47
this aim, a tolerance band control strategy is proposed and a
48
specific control rules is designed for each zone: above, within
49
and below the band.
50 51
Above the upper limit
52
When 𝑃!"_! is above the tolerance band, the BESS is used to
53
compensate the imbalance power and store the excess of
54
energy whenever possible. Indeed, the imbalance power
55
cannot always be compensated. Several conditions related to
56
operational and technical limits of the BESS have to be
57
verified (i.e state of charge, charge/discharge rate limits). In
58
this case, the storage power is computed as follows:
59 60
P!"#_!"=𝑚𝑖𝑛 𝑃! 𝜂!,𝑃!,𝑃!"#_!"# 𝜂! (10)
61 62
where P!"#_!"#= SOC!"#−SOC t C!"# ∆t
63
64
Below the lower limit
65
When 𝑃!"_! is below the tolerance band, the imbalance
66
power due to forecast error can be compensated using the
67
energy stored in the BESS. However, this energy has to be
68
manipulated very wisely in order to ensure that enough
69
energy remains to guarantee peak hours. The storage power is
70
calculated according to operational and technical limits of the
71
BESS and subjected to constraints on 𝐸!"#_!"#$ and
72
𝐶!"#$%&%'(:
73
74
P!"#_!"=𝑚𝑎𝑥 𝑃!𝜂!,𝑃!,−𝑃!"#_!"#𝜂! 𝑖𝑓 𝑆𝑂𝐶𝑡 >𝐸!"!!"#$ C!"#
75
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 P!"#_!"=0 (11)
76 77
where
78
𝑃!"#_!"#=𝑚𝑖𝑛 SOCt −𝐸!"#_!"#$ C!"# C!"# ∆t, 𝐶!"#$%&%'( ∆t
79 80
Within the tolerance band
81
When 𝑃!"_! is within the tolerance band, the power
82
imbalance is equal to zero and there is not need to
83
absorb/inject power from/to the grid through the BESS:
84 85
P!"#_!"=0 (12)
86 87
Economic performance improvement
88
The economical performance improvement relies on the
89
estimation of two parameters α!"#$ and 𝛽!"#$%&'(. The effects
90
of these parameters on the annual revenue and the average
91
annual DRF are illustrated on Fig. 1 and 2.
92 93
As expected, while 𝛽!"#$%&'( is increasing the DRF is
94
decreasing. Indeed, 𝛽!"#$%&'( is straightforwardly linked to the
95
fraction of the storage capacity dedicated to compensate
96
power imbalance due to forecast errors. However, it is
97
important to highlight that decreasing the DRF and so the
98
financial penalties do not necessary means increasing the
99
revenue. In fact, while 𝐶!"#$%&%'( becomes closer to 𝐶!"#, the
100
amount of energy that can be stored in the BESS for the
101
evening peak hours decreases. Since peak hours feed-in tariff
102
is more attractive than off-peak one, it could be more
103
interesting to sell more energy during peak hours even if that
104
means paying more penalties during off-peak due to forecast
105
error.
106
As illustrated on Fig. 2, while α!"#$ is increasing the DRF is
107
increasing, whereas the revenue increasing to a maximum
108
before decreasing. Which seems indicate that, for a fixed
109
value of 𝛽!"#$%&'(, there is an optimal amount of energy to
110
store in the BESS for the evening peak hours.
111
1
Fig. 1: Effects of 𝛽!"#$%&'( on the revenue and the DRF (with2
α!"#$=0.3 and calculated over one year)
3 4
5
Fig. 2: Effects of α!"#$ on the revenue and the DRF (with6
𝛽!"#$%&'(=0.2and calculated over one year)
7 8
9
Annual optimization10
In a first attempt, the economic performance improvement
11
strategy consists on finding the optimal values of α!"#$ and
12
𝛽!"#$%&'( that maximizes the annual revenue. The
13
optimization goal is to find the optimal set of parameter
14
p= α!"#$ 𝛽!"#$%&!" ! that maximizes the cost function J:
15 16
p=𝑎𝑟𝑔max
! 𝐽 (13)
17 18
with 𝐽= !""#𝑃!"!,!𝐶! 60−𝑃!"#!,!𝐶! 60− 𝑃𝑒𝑛𝑎𝑙𝑡𝑖𝑒𝑠!,!
!"# !!!
!!! and
19
subjected to p∈ 𝑝!"#,𝑝!"#; 𝑝!"#= 0 0!; 𝑝!"#= 1 0.8!.
20
21
The optimization procedure, performed on experimental data
22
collected from August 31st 2013 to September 1st 2014, leads
23
to the optimal set of parameter p= 0.2978 0.1387 !, which
24
results to an annual revenue of 25 449.20 euros and an
25
average DRF of 13.12%. The revenue and the DRF for each
26
day are presented in Fig. 3.
27
28
29
30
Fig. 3: Daily revenue and DRF obtain over one year
31
32
It can be noticed that the DFR seems to contain a periodic
33
component. The analysis of the DFR in the frequency domain
34
reveals that the frequency component with the higher
35
magnitude is located at 0.002732 day-1, which corresponds to
36
a periodicity of 366 days. Moreover, a thorough study of the
37
DRF reveals a strong and significant correlation between
38
DRF and the forecast error, with a Pearson’s correlation
39
coefficient of 82% (p-value < 0.0001).
40 41
The analysis of the forecast error reveals the same periodicity
42
of 366 days, which means that the forecast error is linked to
43
the season. Indeed, as illustrated on Fig. 4, the forecast error
44
is higher in summer than in winter.
45
46
Fig. 4: Forecast error
47
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2.42 2.44 2.46 2.48 2.5 2.52 2.54 2.56x 104
ßforecast
Revenue [euros]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.89
10 11 12 13 14 15 16
Average DFR [%]
0.2 0.3 0.4 0.5 0.6 0.7 0.8
2.49 2.495 2.5 2.505 2.51 2.515 2.52 2.525 2.53 2.535
2.54x 104
Revenue [euros]
0.2 0.3 0.4 0.5 0.6 0.7 0.813.15
13.2 13.25 13.3 13.35 13.4 13.45 13.5 13.55 13.6 13.65
Apeak
Average DFR [%]
0 50 100 150 200 250 300 350
−20 0 20 40 60 80 100 120 140
Time [day]
Revenue [euro]
50 100 150 200 250 300 350
0 10 20 30 40 50
Time [day]
DFR [%]
Raw data Filtered data
50 100 150 200 250 300 350
20 30 40 50 60 70 80
Time [day]
Forecast error [kWh]
Filtered data
Summer (october to april)
Winter (april to october)
This can be mainly explained by the fact that the forecast
1
model does not take into account the intra-day variability of
2
solar irradiance and that in La Reunion Island the intra-day
3
variability is higher in summer. In this context, when the4
intra-day variability increases the error modeling increases5
too, which leads to an increase of the DFR. In other worlds,
6
the seasonality of the solar irradiance variability introduces a
7
seasonal component into the forecast error that is transmitted8
to the DFR.
10 9
The analysis of the total energy produced by the PV plant
11
each day (𝐸!"_!_!"!#$) reveals a seasonal component that is
12
due to the yearly solar irradiance variability (Cf. Fig. 5). The
13
amount of energy dedicated to the peak hours (𝐸!"#_!"#$),
14
which could have a strong influence on the revenue, is taken
15
as a fraction of 𝐸!"_!_!"!#$ using α!"#$. In this context, the
16
seasonal component contained into 𝐸!"_!_!"!#$ is transmitted
17
to 𝐸!"#_!"#$. A thorough study of intra-day and yearly
18
irradiance variability in La Reunion can be consulted in [23].
19 20
21
Fig. 5: Energy produced by the PV plant
22
23
Regarding the seasonality of the solar irradiance, and since
24
𝛽!"#$%&'( and α!"#$ respectively influence the DRF and the
25
amount of energy dedicated to the peak hours, it is likely that
26
a seasonal-based or even a daily-based optimization of these
27
parameters could increase the revenue.
28 29
6. Conclusions and prospects 30
In this work, a minute dispatch strategy for a 57 kWp PV
31
farm with 78.5 kWh BESS has been simulated, and an
32
economical optimization of the dispatch strategy has been
33
developed. This strategy has been designed to fulfill the
34
requirements of the new regulatory rules set in La Reunion
35
while optimizing the economic performance of the system.
36
The BESS is used during off-peak to compensate PV
37
production forecast error and during peak hours to inject
38
power to the grid. Therefore, two parameters have been
39
introduced. The first one is related to amount of energy to
40
store for the evening peak hours whereas the second one
41
represents the fraction of the storage capacity that is dedicated
42
to compensate power imbalance due to forecast errors. The
43
optimization goal is to find the optimal value of these
44
parameters that maximizing the revenue while taking into
45
account the new regulatory rules constraints. The proposed
46
optimization strategy takes into account the energy market
47
data, the amount of PV production subject to penalties for
48
imbalance, the batteries and the PV technological
49
characteristics together with a PV production forecast model.
50
The effectiveness and relevance of the proposed strategy have
51
been assessed on experimental data collected on a real PV
52
power plant. An economical analysis demonstrated that the
53
proposed optimization strategy has been able to fulfill the
54
new regulatory rules requirements while increasing the
55
economic performance of the system.
56
Due to the seasonal behavior of solar radiation, it is likely that
57
economical performance can be further increased using a
58
seasonal-based optimization approach. Additional works are
59
currently in progress to study if the revenue can be increased
60
by taking into account the seasonal component contained in
61
the forecast error and the total energy produced by the PV
62
plant.
63 64
Acknowledgement 65
This work is a contribution to the FEDER project
66
GYSOMATE funded by the European Social Fund and the
67
Reunion Region. The authors would like to kindly
68
acknowledge Pr. Jean-Daniel Lan-Sun-Luk for the fruitful
69
scientific discussions, and M. Patrick Jeanty for the solar
70
experimental data.
71 72
References 73
[1] Weisser D. On the economics of electricity consumption in
74
small island developing states: a role for renewable energy
75
technologies? Energy Policy 2004;32(1):127–40.
76
http://dx.doi.org/10.1016/S0301-4215(03)00047-8.
77
[2] Guerassimoff G, Maïzi N, Mastère. OSE. Îles et Énergie: un
78
paysage de contrastes. Les Presses-MINES ParisTech; 2008 [in
79
french].
80
[3] ARER. PETREL - île de la Réunion. Plan économique de
81
Transition et de Relance via des énergies 100 % Locales île de
82
la Réunion. Technical Report, ARER; 2009 [in french].
83
[4] Praene JP, David M, Sinama F, Morau D, Marc O. Renewable
84
energy: progressing towards a net zero energy island, the case
85
of Reunion Island. Renew Sustain Energy Rev 2012;16(1):426–
86
42. http://dx.doi.org/10.1016/j.rser.2011.08.007.
87
[5] Drouineau, M., Assoumou, E., Mazauric, V., Maïzi, N.
88
Increasing shares of intermittent sources in Reunion Island:
89
Impacts on the future reliability of power supply. Renewable
90
and Sustainable Energy Reviews 46, 120–128, 2015.
91
[6] Fesquet F, Juston P, Garzulino I. Impact and limitation of wind
92
power generation in an island power system. In: IEEE Bologna
93
power technical conference; 2003.
94
[7] Beaudin M, Zareipour H, Schellenberglabe A, Rosehart W.
95
Energy storage for mitigating the variability of renewable
96
50 100 150 200 250 300 350
0 50 100 150 200 250 300 350
Time [day]
Energy produced by PV plant [kWh]
electricity sources: an updated review. Energy Sustain Dev. 14,
1
302-14, 2010.2
[8] Delfanti M, Falabretti D, Merlo M, Monfredini G. Distributed
3
generation integration in the electric grid: energy storage4
system for frequency control. J Appl Math. 13, 2014.5
[9] Weiss T, Schulz D. Development of fluctuating renewable
6
energy sources and its influence on the future energy storage7
needs of selected European Countries. In: 4th International8
Youth Conference on Energy (IYCE), Hungary, 6-8; June 2013.9
[10] Alam MJE, Muttaqi KM, Sutanto D. Mitigation of rooftop solar
10
PV impacts and evening peak support by managing available
11
capacity of distributed energy storage systems. IEEE Trans
12
Power Syst 28(4), 3874-3884. 2013.
13
[11] Hill CA, Such MC, Chen D, Gonzalez J, Grady WM. Battery
14
energy storage for enabling integration of distributed solar
15
power generation. IEEE Trans Smart Grid 3(2), 850-857, 2012.
16
[12] Ru, Y., Kleissl, J., Martinez, S. Storage Size Determination for
17
Grid-Connected Photovoltaic Systems. IEEE Transactions on
18
Sustainable Energy. 4(1), 68-81, 2011.
19
[13] Delfanti, M., Falabretti, D., Merlo, M. Energy storage for PV
20
power plant dispatching. Renewable Energy 80, 61-72, 2015.
21
[14] Cervone, A., Santini, E., Teodori, S., Romito, D.Z. Impact of
22
regulatory rules on economic performance of PV power plants.
23
Renewable Energy 74, 78-86, 2015.
24
[15] Bridier, L., David, M., Lauret, P. Optimal design of a storage
25
system coupled with intermittent renewables. Renewable
26
Energy 67, 2-9, 2014.
27 28
[16] European Network of Transmission System Operators for
29
Electricity. Operation Handbook. Technical Report, European
30
Network of Transmission System Operators for Electricity;
31
2004.
32
[17] Bergen AR, Vittal V. Power system analysis, 2nd ed.,
33
Englewood Cliffs, NJ: Prentice-Hall Series; 2000.
34
[18] Bornard P, Pavard M, Testud G. Réseaux d'interconnexion et de
35
transport: fonctionnement (in French). Techniques de
36
l'ingénieur 2005;(D4091):1–12.
37
[19] Perez R, Lorenz E, Pelland S, Beauharnois M, Knowe GV,
38
Hemker K, et al. Comparison of numerical weather prediction
39
solar irradiance forecasts in the US, Canada and Europe. Sol
40
Energy 2013;94:305e26.
41
[20] Almeida, M.P., Perpinan, O., Narvarte, L. PV power forecast
42
using a nonparametric PV model. Solar Energy 115, 354–368,
43
2015.
44
[21] Lorenz E, Scheidsteger T, Hurka J, Heinemann D, Kurz C.
45
Regional PV power prediction for improved grid integration.
46
In: Special Issue: 25th EU PVSEC WCPEC-5, Valencia, Spain,
47
vol. 19(17); 2011. p. 757e71.
48
[22] Walton, S., Hassan, O., Morgan, K., Brown, M.R. Modified
49
cuckoo search: A new gradient free optimisation algorithm.
50
Chaos, Solitons & Fractals 44 , 710–718, 2011.
51
[23] Jeanty P., M. Delsaut, L. Trovalet, H. Ralambondrainy, J.D.
52
Lan-Sun-Luk, M. Bessafi, P. Charton, J.P. Chabriat. Clustering
53
daily solar radiation from Reunion Island using data analysis
54
methods. Renewable Energy and Power Quality Journal
55
(RE&PQJ) ISSN 2172-038 X, No.11, March 2013.
