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ScienceDirect
Available online at www.sciencedirect.com
Available online at www.sciencedirect.com
ScienceDirect
Energy Procedia 00 (2017) 000–000
www.elsevier.com/locate/procedia
18766102 © 2017The Authors. Published by Elsevier Ltd.
Peerreview under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
The 15th International Symposium on District Heating and Cooling
Assessing the feasibility of using the heat demandoutdoor
temperature function for a longterm district heat demand forecast
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
aIN+ Center for Innovation, Technology and Policy Research Instituto Superior Técnico,Av. Rovisco Pais 1, 1049001 Lisbon, Portugal
bVeolia Recherche & Innovation,291 Avenue Dreyfous Daniel, 78520 Limay, France
cDépartement Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
Abstract
District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the
greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat
sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease,
prolonging the investment return period.
The main scope of this paper is to assess the feasibility of using the heat demand –outdoor temperature function for heat demand
forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665
buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district
renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were
compared with results from a dynamic heat demand model, previously developed and validated by the authors.
The results showed that when only weather change is considered, the margin of error could be acceptable for some applications
(the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation
scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered).
The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the
decrease in the number of heating hours of 22139h during the heating season (depending on the combination of weather and
renovation scenarios considered). On the other hand, function intercept increased for 7.812.7% per decade (depending on the
coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and
improve the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd.
Peerreview under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and
Cooling.
Keywords: Heat demand; Forecast; Climate change
Energy Procedia 153 (2018) 95–100
18766102 © 2018 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BYNCND license (https://creativecommons.org/licenses/byncnd/4.0/)
Selection and peerreview under responsibility of the scientiﬁc committee of the 5th International Conference on Energy and
Environment Research, ICEER 2018.
10.1016/j.egypro.2018.10.037
10.1016/j.egypro.2018.10.037
© 2018 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BYNCND license (https://creativecommons.org/licenses/byncnd/4.0/)
Selection and peerreview under responsibility of the scientic committee of the 5th International Conference on Energy and
Environment Research, ICEER 2018.
18766102
Available online at www.sciencedirect.com
ScienceDirect
Energy Procedia 00 (2018) 000–000
www.elsevier.com/locate/procedia
18766102 © 2018 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BYNCND license (https://creativecommons.org/licenses/byncnd/4.0/)
Selection and peerreview under responsibility of the scientific committee of the 5th International Conference on Energy and Environment
Research, ICEER 2018.
5th International Conference on Energy and Environment Research, ICEER 2018
Influences and uncertainty of batteryswapping electric scooters on
energy system in Taiwan
PeiYing Hsieha*, TaiYi Yub, KuangChong Wuc, and LenFu W. Changa
aGraduate Institute of Environmental Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.)
bDepartment of Risk Management and Insurance, Ming Chuan University, NO. 250, Sec. 5, Zhong Shan N. Rd., Taipei 11103, Taiwan (R.O.C.)
cInstitute of Applied Mechanics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.)
Abstract
This paper proposes a new formula to estimate the electricity demand from batteryswapping stations (BSSs) at peak hours,
combining parameters of the number of batteryswapping electric scooters (NBSES) and the number of scooters served per BSS.
It also presents a novel decisionsupport analysis for assessing future impact on energy system with an increasing NBSES in Taiwan.
The VaR (Value at Risk) values and Monte Carlo method are combined to assess key variables of NBSES and potential benefits.
This study finds that the probability for the percentage of operating reserve (OR), R, beyond 6.0 percent is only 86.3% in the past
four years. When NBSES reaches 1.28 million, the probability for R beyond 6.0 percent is down to 69.0% and R is 2.9% (95%CI)
without considering the storage ability of BSSs. However, R could be higher than 6.0% (95%CI) if considering the storage ability
of BSSs.
© 2018 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BYNCND license (https://creativecommons.org/licenses/byncnd/4.0/)
Selection and peerreview under responsibility of the scientific committee of the 5th International Conference on Energy and
Environment Research, ICEER 2018.
Keywords: batteryswapping electric scooters; value at risk; Monte Carlo simulation
* Corresponding author. Tel.:+886233665680
Email address: d00541007@ntu.edu.tw
Available online at www.sciencedirect.com
ScienceDirect
Energy Procedia 00 (2018) 000–000
www.elsevier.com/locate/procedia
18766102 © 2018 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BYNCND license (https://creativecommons.org/licenses/byncnd/4.0/)
Selection and peerreview under responsibility of the scientific committee of the 5th International Conference on Energy and Environment
Research, ICEER 2018.
5th International Conference on Energy and Environment Research, ICEER 2018
Influences and uncertainty of batteryswapping electric scooters on
energy system in Taiwan
PeiYing Hsieha*, TaiYi Yub, KuangChong Wuc, and LenFu W. Changa
aGraduate Institute of Environmental Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.)
bDepartment of Risk Management and Insurance, Ming Chuan University, NO. 250, Sec. 5, Zhong Shan N. Rd., Taipei 11103, Taiwan (R.O.C.)
cInstitute of Applied Mechanics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.)
Abstract
This paper proposes a new formula to estimate the electricity demand from batteryswapping stations (BSSs) at peak hours,
combining parameters of the number of batteryswapping electric scooters (NBSES) and the number of scooters served per BSS.
It also presents a novel decisionsupport analysis for assessing future impact on energy system with an increasing NBSES in Taiwan.
The VaR (Value at Risk) values and Monte Carlo method are combined to assess key variables of NBSES and potential benefits.
This study finds that the probability for the percentage of operating reserve (OR), R, beyond 6.0 percent is only 86.3% in the past
four years. When NBSES reaches 1.28 million, the probability for R beyond 6.0 percent is down to 69.0% and R is 2.9% (95%CI)
without considering the storage ability of BSSs. However, R could be higher than 6.0% (95%CI) if considering the storage ability
of BSSs.
© 2018 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BYNCND license (https://creativecommons.org/licenses/byncnd/4.0/)
Selection and peerreview under responsibility of the scientific committee of the 5th International Conference on Energy and
Environment Research, ICEER 2018.
Keywords: batteryswapping electric scooters; value at risk; Monte Carlo simulation
* Corresponding author. Tel.:+886233665680
Email address: d00541007@ntu.edu.tw
96 PeiYing Hsieh et al. / Energy Procedia 153 (2018) 95–100
2 PeiYing Hsieh et al. / Energy Procedia 00 (2018) 000–000
Nomenclature
A Battery nominal capacity (Ah)
BSES Batteryswapping electric scooter
BSS Batteryswapping station
C Installed Capacity at peak time (MW)
C0 Installed Capacity for not including N at peak time (MW)
CI Confidence interval
D Peak load at peak time (MW)
D0 Peak load for not including N at peak time (MW)
E The electricity each cell (kWh)
eff Charge efficiency, 01 constant
eff _B Cell’s Efficiency of charging
freq The frequency of riders swapping batteries (days1)
G The installed capacity minus 1.06 times peak load (MW)
G0 The installed capacity minus 1.06 times peak load for not including N at peak time (MW)
G* The gap between G and N with the acceptable risk level (1.06 times) (MW)
G*i The gap between G and N with the acceptable risk level (1.06 times) in scenario i, i=1,2
N The electricity of new demand from BSSs at peak time (MW)
NBSES The number of batteryswapping electric scooters (vehicle unit)
OR Operating reserve (MW)
PDF The probability density function
pf The policy factor which is zero or one of the integers
prob Probability of G*i is positive
R The percentage of OR
R* The percentage of OR with N
R*i The percentage of OR with N in scenario i, i=1~2
SoC The average stateofcharge of swapped batteries
T Charging time (hrs)
V Battery nominal voltage (V)
VaR Value at Risk
β The ratio of NBSES to the number of BSSs
ρ The average percentage of the electricity that is needed to charge in BSSs at peak time, 01 constant
ε The number of cells each batteryswapping station
1. Introduction
In Taiwan, BSES has an enormous potential to increase for three main reasons. First, the marketshare record of
BSES, which keeps growing from 2015 July and is more than 90% in 2018 [1], reveals that BSES is more attractive
than traditional electric scooters for the high performance and the convenience of batteryswapping. Second, in Taiwan
there are 13.76 million registered scooters and almost 92 scooters per 100 persons [2]. Third, the government has
announced that new petrol scooters will be banned from 2035 for air quality improvement [3].
This paper utilizes VaR and Monte Carlo method to study the energy consumption of BSESs associated with the
BSS to evaluate the impact of the growth of BSESs on the energy system. VaR is a useful tool for measuring and
managing risk for energy system policy and is able to yield extreme values with uncertainty issues [4]. Monte Carlo
analysis allows consideration for uncertain parameters and produces probabilistic models which incorporate risk
assessment in energy system [5]. In this paper a novel decisionsupport analysis is made for assessing future impact
on energy system with an increasing NBSES. An uncertainty assessment (Fig. 1) composed of selecting essential
parameters, determining probability distributions, calculating VaR values with Monte Carlo simulation, and assessing
the potential benefits to the future smart grid, is applied.
PeiYing Hsieh et al. / Energy Procedia 153 (2018) 95–100 97
2 PeiYing Hsieh et al. / Energy Procedia 00 (2018) 000–000
Nomenclature
A Battery nominal capacity (Ah)
BSES Batteryswapping electric scooter
BSS Batteryswapping station
C Installed Capacity at peak time (MW)
C0 Installed Capacity for not including N at peak time (MW)
CI Confidence interval
D Peak load at peak time (MW)
D0 Peak load for not including N at peak time (MW)
E The electricity each cell (kWh)
eff Charge efficiency, 01 constant
eff _B Cell’s Efficiency of charging
freq The frequency of riders swapping batteries (days1)
G The installed capacity minus 1.06 times peak load (MW)
G0 The installed capacity minus 1.06 times peak load for not including N at peak time (MW)
G* The gap between G and N with the acceptable risk level (1.06 times) (MW)
G*i The gap between G and N with the acceptable risk level (1.06 times) in scenario i, i=1,2
N The electricity of new demand from BSSs at peak time (MW)
NBSES The number of batteryswapping electric scooters (vehicle unit)
OR Operating reserve (MW)
PDF The probability density function
pf The policy factor which is zero or one of the integers
prob Probability of G*i is positive
R The percentage of OR
R* The percentage of OR with N
R*i The percentage of OR with N in scenario i, i=1~2
SoC The average stateofcharge of swapped batteries
T Charging time (hrs)
V Battery nominal voltage (V)
VaR Value at Risk
β The ratio of NBSES to the number of BSSs
ρ The average percentage of the electricity that is needed to charge in BSSs at peak time, 01 constant
ε The number of cells each batteryswapping station
1. Introduction
In Taiwan, BSES has an enormous potential to increase for three main reasons. First, the marketshare record of
BSES, which keeps growing from 2015 July and is more than 90% in 2018 [1], reveals that BSES is more attractive
than traditional electric scooters for the high performance and the convenience of batteryswapping. Second, in Taiwan
there are 13.76 million registered scooters and almost 92 scooters per 100 persons [2]. Third, the government has
announced that new petrol scooters will be banned from 2035 for air quality improvement [3].
This paper utilizes VaR and Monte Carlo method to study the energy consumption of BSESs associated with the
BSS to evaluate the impact of the growth of BSESs on the energy system. VaR is a useful tool for measuring and
managing risk for energy system policy and is able to yield extreme values with uncertainty issues [4]. Monte Carlo
analysis allows consideration for uncertain parameters and produces probabilistic models which incorporate risk
assessment in energy system [5]. In this paper a novel decisionsupport analysis is made for assessing future impact
on energy system with an increasing NBSES. An uncertainty assessment (Fig. 1) composed of selecting essential
parameters, determining probability distributions, calculating VaR values with Monte Carlo simulation, and assessing
the potential benefits to the future smart grid, is applied.
PeiYing Hsieh et al. / Energy Procedia 00 (2018) 000–000 3
Fig. 1. Procedure for uncertainty assessment.
2. Methodology
2.1. Key variables and VaR
The OR is the generating capacity that is available to the system operator within a short interval of time to meet
demand in case where there is a disruption to the supply or where a generator goes down in electricity networks. In
Taiwan, six percent OR is a security threshold. The power supply is considered ample if R is higher than 10% and
tight within 10% to 6%. R less than 6% triggers a power alarm [6]. R is defined as
(1)
Let the acceptable risk level be 0.06. From equation (1), R is higher than 6% if and only if C is higher than 1.06D.
G is the gap between installed capacity and 1.06 times peak load as tolerable OR with the acceptable risk level. i.e.:
(2)
In the BSS system, batteries are not charged directly from the grid, but are swapped at BSSs. According to the
historic record, the number of BSSs is dependent on the parameter, , the service availability for each station, which
is the number of scooters served by one station. In this way, the new peak load from BSSs per day, N, is
(3)
where E is the electricity of each cell (
). The values of parameters in the system are V=43.2 (V), A=30.3
(Ah), eff_B=95.5%, T=3 (hours), eff = 93.7%, E = 1.37 (kWh).
To understand the benefits of regulation and regulatory policy, this research defines pf as the policy factor which is
zero or one. When pf is zero, all batteries at BSSs are charged at peak time such that
for pf = 0 (4)
When pf is one, all batteries are not allowed to be charged at peak time but allowed to be a part of OR such that
for pf = 1 (5)
To understand the probability that G with N is positive at peak time, this research defines G* as the gap between
G0 and N with the acceptable risk level. From equations (2), (4) and (5)
(6)
To understand R with N, this research defines R* as the percentage of OR with N. From equations (1), (4) and (5)
(7)
Sensitivity Analysis
Compilation of
BESE and Energy
system data
Selection
of essential
factors
Fitted
probability
density function
Determination of
distribution for
extensively available data
Determine
Va R
values
Monte
Carlo
simulation
Distribution of data base on historical data and
information from news, literatures and experts.
Analysis and
discussion of
results
98 PeiYing Hsieh et al. / Energy Procedia 153 (2018) 95–100
4 PeiYing Hsieh et al. / Energy Procedia 00 (2018) 000–000
2.2. Scenarios design
In this paper, OR and R are the instantaneous spike load data every day from 2014 to 2017 [7]. C and D are
calculated from OR and R by equation (1). This research analyzes the PDFs of G*, R* and finds out the VaR values
of G*, R* (95%, 99% CI). To understand extreme influences the batteryswapping scooters system would have, the
following two scenarios are considered.
• Scenario 1: Assume that riders swap the batteries, which are charged during peak time, every day. The SoC of all
swapped batteries is 0%. In this case, ρ = 1, freq = 1, and SoC = 0 in equation (3); =0 in equations (6) and (7).
The gap between G0 and N with the acceptable risk level is G*1, and R with N is R*1.
• Scenario 2: Assume that all BSSs are fully charged, no batteries are charged at peak time, and all BSSs are allowed
to be a part of operation reserve. In this case, ρ = 1, freq =1, and SoC = 0 in equation (3); = 1 in equations
(6) and (7). The gap between G0 and N with the acceptable risk level is G*2, and the R with N is R*2.
3. Discussions and results
3.1. The key variables
It is found that the optimal PDFs of G, D and OR are lognormal using the AndersonDarling test. The optimal PDF
of β also appears to be lognormal according to the relationship between the number of BSSs and NBSES in the past
1.5 years. The optimal PDF of ε is minimum extreme according to the consultation with experts. On an average, every
BSS could serve 50 BSESs and there are 30 cells in every BSS. The PDFs of those variables are shown in Table 1.
Table 1. Optimal PDFs of variables.
Variable
Optimal PDF
Parameters
p value
G(2014~2017)
Lognormal
Location= 6,742, Mean= 1,070, S.D.= 1,098
0.000
D
Lognormal
Location= 0.00, Mean=28,747, S.D.= 3,571
0.000
OR
Lognormal
Location=1,781, Mean= 2,796, S.D.= 1,004
0.000
β
Lognormal
Location= 23.88, Mean= 53.12, S.D.= 20.19
0.020
ε
Minimum extreme
Likeliest=31.68, scale= 3.93

3.2. The impact of energy system
This study puts the results of VaRs for G*1 and R*1 in Fig. 2 for comparison. In scenario 1, all batteries in BSSs
are swapped every day and charged at peak times. According to the equations (3), (4), (6) and (7), the probabilities of
G*1, R*1, and VaR values are functions of NBSES. When NBSES reaches 2 million, the prob of G*1 (the probability
of the tolerable OR) is 59.9 %, and that of R*1 higher than 6% is 59.8% (Fig. 2 (a)); the VaR of R*1 is 1.8% (95%
CI); the median of R*1 is 6.9% (Fig. 2 (b)). When NBSES reaches 2.8 million, the prob of G*1 being positive is 50%
(Fig. 2 (c)), and the median of R*1 is 5.9% (Fig. 2 (b)). Until NBSES reaches 8 million, the median of R*1 is down
to 0.5% and the R*1 is 14.5% (99% CI) (Fig. 2 (b)). Besides, all VaRs of G*1 are below zero (95% CI), and the
median will be less than zero when NBSES reaches 2.8 million (Fig. 2 (c)).
Scenario 2 is the most optimistic case. According to the equations (5), (6) and (7), this study describes the possibility
that the BSS could be a useful storage system for the grid. When NBSES reaches 1.28 million, the prob of G*2 being
positive is 92.4 %, and that of R*2 higher than 6% is 69.8 % (Fig. 2 (a)); R*2 will go beyond 6 % (95% CI) (Fig. 2
(b)). However, the prob of G*1 being positive is only 72.4 %, and that of R*1 higher than 6% is only 73.7 % (Fig. 2
(a)); R*1 will go below 2.9% (95% CI) (Fig. 2 (b)). With 95% confidence, when NBSES reaches 1.9 million, G*2
will change from negative to positive, but G*1 will go below 1392 MW (Fig. 2 (c)). When NBSES reaches 2 million,
the prob of G*2 being positive is 95.2 %, while that of G*1 higher than zero is 59.9 % (Fig. 2 (a)). When NBSES
reaches 3.06 million, R*2 will go beyond 6% (99% CI) but R*1 will go below 2.5% (Fig. 2 (b)).
PeiYing Hsieh et al. / Energy Procedia 153 (2018) 95–100 99
PeiYing Hsieh et al. / Energy Procedia 00 (2018) 000–000 5
Fig. 2. (a) The probability of G1*≥0%, R*1≥6%, G*2 ≥0%, R*2≥6%; (b) Influences on R*1, R*2; (c) Influences on G*1 when all batteries at
BSSs are charged at peak time (for pf = 0), and G*2 for pf = 1.
3.3. Sensitivity analysis
Sensitivity analysis results (Table 2) indicate that the most important variable is G, so this study analyzes optimal
PDF and the VaR of G* of different years below (Table 3, Fig. 3), denoted as G*(2017), G*(2016), G*(2015), and
G*(2014). According to the results, the prob of G* is getting smaller over the years. In the past four years, the prob of
G* is only 86.3 %; the prob of G*(2017) and G*(2014) are 72.2 %, and 97.9 %, respectively. When NBSES reaches
2 million, the prob of G*1(2017), and G*2(2014) are 32.9 % and 91.2 %, respectively; the prob of G*2(2017) and
G*2(2014) are 92.4 % and 99.8 %, respectively. When NBSES reaches 6 million, the prob of G*1(2017) and
G*2(2014) are 3.9 % and 50.2 %, respectively; the prob of G*2(2017) and G*2(2014) are 99.5 %, and 99.9 %.
Table 2. The results of sensitivity analysis (NSBS=50,000).
Variables
Elasticity
G*(10%)
G*(20%)
G*(30%)
G*(40%)
G*(50%)
G*(60%)
G*(70%)
G*(80%)
G*(90%)
G(2014~2017)
1.02
291
119
431
709
978
1,257
1,567
1,945
2,497
β
0.02
967
972
975
977
978
980
981
982
984
ε
0.02
980
980
979
979
978
978
977
977
976
D
0.00
978
978
978
978
978
978
978
978
978
Table 3. Optimal PDF o f G (lognormal)
Variables
Parameters
p value
Variables
Parameters
p value
G(2017)
Location= 61,638, Mean= 378, S.D.= 693
0.2577
G(2015)
Location= 9,047, Mean= 1,081, S.D.= 918
0.000
G(2016)
Location= 6,404, Mean= 726, S.D.= 965
0.4853
G(2014)
Location=7,813,106, Mean= 2,073, S.D.= 957
0.000
Fig. 3. Probability of G* ≥0 from 2014 to 2017 for scenario 1 and 2.
In scenario 1, the riders swap the batteries, which are charged during peak time, every day. However, this is the
worst scenario. Another sensitivity analysis is shown below to figure out how the change of ρ influences on the prob.
Assuming that riders swap the batteries every day and the batteries in BSSs could be charged any time, such that, ρ =
1.28
92.4 %
2
95.3 %
3, 97.7 %
1.28
69.0 %
2, 59.9 %
2.8
50.0 %
3, 47.5 %
4
37.2 %
11
4.9 %
0
20
40
60
80
100
02.5 57.5 10 12.5
Probabil ity of value ≥0 (% )
NB S ES ( E+ 6 )
R*2 ≥ 6%
G*2 ≥ 0
R*1 ≥ 6%
G*1≥ 0
a
8, 0.5 %
1.9, 11.7 %
1.28
6.0 %
1.9, 6.6 %
3, 7.6 %
8, 14.5 %
1.9
5.0 %
3.06
6.0 %
15
10
5
0
5
10
15
20
02.5 57.5 10 12. 5
R ( %)
NB S ES ( E+ 6 )
R*1 M edian VaR R*2 Median VaR
R*1 ( 95% Cl ) VaR R*2 (95% CI) VaR
R*1 ( 99% Cl ) VaR R*2 (99% CI) VaR
b
4, 0.40
1.28
1.43
4
2.33 6
2.97
9, 3.89
1.9
1.39
4, 2.44
1.28
0.19
1.9
0
2.80
0.24
4, 0.54
8
4
0
4
8
02.5 57.5 10 12.5
G (GW )
NB S ES ( E+ 6 )
G*1 M edi an V aR G*2 M edi an V aR
G*1 (95% Cl) VaR G*2 (95%CI) VaR
G*1 (99% Cl) VaR G*2 (99%CI) VaR
c
0
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Probability of
target value ≥0
(%)
NBS ES (E+6 )
G*1 (201 4) G*2 (201 4)
G*1 (201 5) G*2 (201 5)
G*1 (201 6) G*2 (201 6)
G*1 (201 7) G*2 (201 7)
100 PeiYing Hsieh et al. / Energy Procedia 153 (2018) 95–100
6 PeiYing Hsieh et al. / Energy Procedia 00 (2018) 000–000
{0,0.1,0.2,0.3, 0.4, 0.5….1}
, freq =1, and SoC = 0 in equation (3);
= 0 in equations (6) and (7).
The gap between G0 and N with the acceptable risk level is G*3. The relationship between G*3, ρ, and NBSES is
shown in Fig. 4. When ρ is 0.1 and prob of G*3 is 80.1%, the maximum limited NBSES is 3 million. When ρ is 0.3
and the prob is 80.1%, the maximum limited NBSES is 1 million. To sum up, the government could persuade riders
to switch the batteries at nonpeak hours so that the associate maximum limited NBSES would be higher.
Fig. 4. The relationship between NBSES and ρ for prob = 0.2, 0.4, 0.6, 0.8, 1 of G*3 ≥0%.
4. The conclusions and recommendations
This paper proposed a new formula, considering electricity demand and capacity of storage potential from BSSs at
peak hours, and applied Monte Carlo method and VaR values to assess dominant factors for the interactions among
NBSES, demand of electricity, and energy system. The results highlight some significant challenges and opportunities
in the power sector, including the limited NBSES under the existing Electricity Act and the power structure in Taiwan.
When NBSES reaches 3 million, the probability for R beyond 6.0 percent is down to 47.5% and R is only 0.2%
(95%CI) without considering the storage ability of BSSs. However, considering the storage ability of BSSs by
formulating proper complementary policies, the probability for R beyond 6.0 percent could be 97.7% and R could be
higher than 7.6% (95%CI).
The VaR values of dominant indicators for two scenarios were applied to discuss extreme influences BSES could
have. The analytical results revealed the relationships between the number of BSSs and BSESs for risk assessment
and could be applied to formulate the price adjustment strategies for the power system. The NBSES, the charge time
of BSSs, and OR can play key roles in reducing the impact of peak load on the energy system. The VaR values could
offer valuable decision information for early warning and relevant complementary measures to policy makers.
Acknowledgements
The authors would like to thank the reviewers for their helpful comments on the paper and the consultant, Hong
Shi Chang for valuable advice to the research.
References
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.05
1
2
3
4
5
6
7
8
9
10
11
12
13
ρ
NBSES( E+6)
prob.=0.2
prob.=0.4
prob.=0.6
prob.=0.8
‧
‧