Sizing battery energy storage systems for industrial customers with photovoltaic power

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Energy Procedia 158 Energy Procedia 00(2019) (2017)4953–4958 000–000 www.elsevier.com/locate/procedia

10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China

Sizing battery energy storage systems for industrial customers with Sizing battery energy storage systems for industrial with The 15th International Symposium on District Heating andcustomers Cooling photovoltaic power photovoltaic power Assessing of using the heat demand-outdoor 1 the feasibility Guodong Xu1*, Ce Shang11, Songli Fan11, Xiaohu Zhang22, Haozhong Cheng11 Guodong Xufunction *, Ce Shang Fan , Xiaohu Zhangheat , Haozhong Cheng temperature for, Songli a long-term district demand forecast 1-Key Laboratory of Control of Power Transmission and Conversion, Shanghai Jiao Tong University, Minhang District, Shanghai 200240,

1-Key Laboratory of Control of Power Transmission and Conversion, Shanghai Jiao Tong University, Minhang District, Shanghai 200240, China a,b,c a a b c c China New District, Shanghai 200120, China 2-East China Grid Company Limited, Pudong 2-East China Grid Company *Limited, Pudong New District, Shanghai 200120, China [email protected] a * [email protected] IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract

I. Andrić

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

Abstract The battery energy storage system (BESS) helps reduce the electricity bill of industrial customers (IC) with photovoltaic power TheGiven batterythe energy storage (BESS) reduce electricity bill of industrial (IC) with photovoltaic power (PV). current high system investment costhelps of BESS, thethe detailed cost-benefit analysis customers of BESS considering PV uncertainty is Abstract (PV). Given the currentowners high investment cost of BESS, the detailed cost-benefit of BESS considering PV uncertainty is needed for enterprise to judge whether the profits can be obtained by analysis incorporating BESS. In this context, a bi-level needed forprogramming enterprise owners whether the profitsthe canoptimal be obtained In this context, stochastic modeltoisjudge proposed to determine powerby andincorporating capacity of BESS. The upper modela bi-level aims at District the heating networks areBESS, commonly addressed in the literature asoptimizing one and of the mostoperation. effective formodel decreasing the stochastic programming model is proposed tolower determine thefocuses optimal capacity of BESS.solutions Thebenefit upper aims at deciding optimum size of and the model onpower BESS The from reducing greenhouse gas emissions from the building These systems require high as investments which returned the heat deciding the optimum size from of BESS, and subsidies, the sector. lower the model focuses cost, on optimizing BESS operation. The benefit through from reducing electricity bills, the benefit financial investment as well the operation andare maintenance cost of BESS sales. Due to the the benefit changed climate conditions andthebuilding renovation heat demand in maintenance the future could decrease, electricity bills, from financial subsidies, investment cost, as well as are the operation cost of BESS are assessed carefully, the impacts of the lifetime characteristics of BESS onpolicies, which fully takenand account of. Simulation results prolonging the investment return period. are assessed carefully, impacts the lifetime characteristics BESS on which are fully taken account of. Simulation results on an actual IC with PVthe validate theofeffectiveness of the proposedofmethodology. of this paper is the to assess the feasibility of using the heat demand – outdoor temperature function for heat demand onThe an main actualscope IC with PV validate effectiveness of the proposed methodology. forecast. © The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Copyright 2018 Elsevier Ltd. All rights reserved. ©buildings 2019 The Authors. Published by Elsevier Ltd. and typology. Three weather scenarios vary in both construction period medium,Conference high) and on three district Copyright ©that 2018 Elsevier Ltd. Allresponsibility rights reserved. International Applied Selection and peer-review under of the scientific committee of the 10th (low, This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) th renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Peer-review under responsibility of the scientific committee ICAE2018developed – The 10th International on Applied Energy. compared with results from a dynamic heat demand model,ofpreviously and validated byConference the authors. Energy (ICAE2018). The results showed thatstorage when system; only weather is considered, the margin error could be acceptable for someprogramming applications Keywords: Battery energy Lifetimechange characteristics; Photovoltaic power;ofIndustrial customer; Bi-level stochastic (the errorBattery in annual demand lower than 20% for all weather scenarios considered). However, after introducing renovation Keywords: energy storagewas system; Lifetime characteristics; Photovoltaic power; Industrial customer; Bi-level stochastic programming model scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). model The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1.decrease Introduction scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the 1.renovation Introduction coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and Both energy crisis and environmental degradation promote the blistering advancement of renewable energy improve the accuracy heat demand estimations. Both energy crisisof and environmental degradation promote the blistering advancement of renewable energy

sources (RES) such as photovoltaic power (PV) [1]. In this context, the number of the industrial customer (IC) with sources (RES) such as photovoltaic power (PV) [1]. In this context, the number of the industrial customer (IC) with PV is increasing rapidly for thebyhigher power © 2017 The Authors. Published Elsevier Ltd. supply reliability and lower electricity bill. The battery energy storage PV is increasing rapidly for the higher power supply and lower bill. The load-shifting. battery energy storage system (BESS) helps further reduce the electricity billreliability ofofthe IC15th withInternational PV byelectricity peak-shaving Peer-review under responsibility of the Scientific Committee The Symposiumand on District Heating In andterms system (BESS) helps further reduce the electricity bill of the IC with PV by peak-shaving and load-shifting. In terms of the current high investment cost of BESS, the challenge in applying BESS in the IC with PV is deciding the Cooling. of the current investment cost of BESS, the challenge optimum size ofhigh BESS through detailed cost-benefit analyses. in applying BESS in the IC with PV is deciding the optimum BESSForecast; through detailed cost-benefit analyses. Keywords:size Heatof demand; Climate change

1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102and Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.693

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Guodong Xu et al. / Energy Procedia 158 (2019) 4953–4958 Author name / Energy Procedia 00 (2018) 000–000

Nomenclature m Index of months d Index of typical daily load profiles s Index of the output power scenarios of PV t Index of time slots Number of the typical daily load profiles of the m-th month Nmload N msce,d Number of the scenarios for the d-th typical daily load profile of the m-th month Tm , d Lasting days of the d-th typical daily load profile of the m-th month m,d ,s Probability of the s-th scenario for the d-th typical daily load profile of the m-th month cpower Power electricity price of IC Time-of-use price of IC at time slot t ctou (t ) T Number of time slots in a day Fixed retail electricity price of IC csell Unit financial subsidy of BESS Discount rate r cfs ce Unit power cost of BESS Unit energy cost of BESS cp com Unit operation and maintenance cost (OMC) of BESS Pld, m , d (t ) Load of IC Ppv, m , d , s (t ) Output power of PV Pg,pum , d , s (t ) Power of IC purchased from the grid Pg,sem , d , s (t ) Power of IC sold to the grid pu U g, m , d , s (t ) Purchasing state indicator of IC U g,sem , d , s (t ) Selling state indicator of IC dis Pba,cham , d , s (t ) Charging power of BESS Pba, m , d , s (t ) Discharging power of BESS The problem of sizing BESS has been extensively studied, especially for smoothing out the output power of RES, reducing the curtailed energy of RES, as well as improving the operation economy of power systems. In contrast, few researches have been conducted on deciding the optimum size of BESS for reducing the electricity bill of electricity customers. Oudalov et al. [2] proposed a sizing methodology for BESS to provide a peak load shaving. In [3], a total annual cost evaluation model was presented to determine the possible profit of BESS used for peakshaving. In [4], the optimum size of BESS was decided through maximizing the annual net benefit, which was employed to perform both peak-shaving and load-shifting. However, the RES such as PV was not considered in such sizing methods, which attenuated their applicabilities. In [5], the simulated annealing algorithm was utilized to produce the PV size, wind turbine rotor swept area, and BESS capacity. Erdinc et al. [6] determined the optimal capacity of PV and BESS for a smart household with consideration of the notably changing load pattern. In [7], an efficient algorithm was introduced to calculate a unique critical value of the BESS size for gird-connected PV systems. Nevertheless, the uncertainty of RES was not taken account of in [5-7], which reduced the rationality of BESS planning schemes. Furthermore, the effects of the cycling behavior such as charge-discharge cycles with different depth of discharge (DOD) on the lifetime of BESS, were not taken into account in [2-7], which might lead to optimistic evaluation. Kahrobaee et al. [8] proposed a hybrid stochastic method to determine the optimum size of the wind generation and BESS in view of stochastic variables such as wind speed and electricity rates. However, the lifetime of BESS was only set as a fixed value, the impacts of the cycling behavior on which were neglected either. In summary, the literature on sizing BESS for the IC with PV taking account of the PV uncertainty and lifetime characteristics of BESS, is scarce to the authors’ best knowledge. The major contributions of this paper include the following. (1) A bi-level stochastic programming model is proposed for the IC with PV to decide the optimum size of BESS. (2) The impacts of the cycling behavior of BESS on the lifetime of BESS are considered comprehensively. The rest of this paper is organized as follows. Section 2 describes the model formulation, and section 3 provides the simulation results. The conclusions are drawn in section 4. 2. Model formulation 2.1. Lifetime of BESS The lifetime of BESS is closely associated with the cycling behavior. Frequent and deep charge-discharge cycles would accelerate the cyclic aging and reduce the cycle life [9]. The cycle life of BESS can be estimated as.



Guodong Xu et al. / Energy Procedia 158 (2019) 4953–4958 Author name / Energy Procedia 00 (2018) 000–000

Yc 

1

4955 3

(1)

Ncyc

(Tyr / Ts ) 1/ f (di ) i 1

where Yc indicates the cycle life of BESS; Tyr is one year; Ts is the time duration of a simulation (e.g., one day); Ncyc is the number of charge-discharge cycles in the simulation; di is the DOD of the i-th charge-discharge cycle; f ( d i ) is the maximum number of charge-discharge cycles at a specific DOD before the BESS’s failure. The float life of BESS corresponds to the normal corrosion processes. It is independent of the cycling behavior, and thus considered as a constant. As temperature’s impacts on BESS life are beyond the scope of this paper, such impacts are no longer considered. Based on these, the lifetime of BESS can be decided as. Yba =min{Yc , Yf } (2) where Yba is the lifetime of BESS; Yf is the float life of BESS. 2.2. Bi-level stochastic programming model A bi-level stochastic programming model is proposed to decide the optimum size of BESS. The upper model aims at deciding the optimum size of BESS, and the lower model focuses on optimizing BESS operation. For the IC with PV but without BESS, the priority is given to PV to offer electricity to the IC. Once the output power of PV is insufficient to supply the IC, the IC will purchase power from the grid to realize the power balance. If the output power of PV is larger than the load of IC, the excess power will be sold to the grid. 2.2.1 Upper model The goal is to maximize the annual expected net benefit (AENB) of BESS, which comprises the benefit from reducing electricity bills (BRB), the benefit from financial subsidies (BFS), the investment cost (INC), as well as the OMC of BESS. Note that, the BRB can be divided into two parts. One is the benefit from reducing the power electricity bills (BRPB), and the other is the benefit from reducing the energy electricity bills (BREB). N msce,d N mload 12   (3) max   Bmrp   Tm, d  m, d , s ( Bmre, d , s +Bmfs, d , s  Cmin, d , s  Cmom, d , s )  m 1  d 1 s 1    where Bmrp indicates the BRPB in the m-th month; Bmre, d , s ,Bmfs, d , s , Cmin, d , s , Cmom, d , s are the BREB, BFS, INC, and OMC in the s-th scenario for the d-th typical daily load profile of the m-th month, respectively. The BRPB is the difference between the power electricity bills of the IC with PV but without BESS and those of the IC with PV and BESS. Notice that, the power electricity bills of the IC are charged based on the maximum load of the IC in such month and the power electricity price of IC.





Bmrp =cpower max [ Pld, m, d (t )  Ppv, m, d , s (t )]   max Pg,pum, d , s (t )

d  [1, Nmload ], s  [1, Nmsce, d ], t  [1, T ]

(4)

where [ ] is a function, whose value is  when  is non-negative and is 0 otherwise. The BREB is the difference between the energy electricity bills of the IC with PV but without BESS and those of the IC with PV and BESS. Notice that, the IC would purchase power from the grid at time-of-use prices, and sell power to the grid at a fixed retail electricity price. T

Bmre, d , s =  ctou (t )[ Pld, m, d (t )  Ppv, m, d , s (t )]  csell [ Pld, m, d (t )  Ppv, m, d , s (t )]  [ctou (t ) Pg,pum, d , s (t )  csell Pg,sem ,d , s (t )]

(5)

t 1

where [  ] is a function, whose value is minus  when  is negative and is 0 otherwise. The BFS is related to both the rated power of BESS and the estimated lifetime of BESS. Y r (1  r ) ba,m ,d ,s Bmfs, d , s =cfs Pbara Y 365[(1  r ) ba,m ,d ,s  1]

(6)

where Pbara is the rated power of BESS; Yba, m, d , s is the estimated lifetime of BESS according to the

Guodong Xu et al. / Energy Procedia 158 (2019) 4953–4958 Author name / Energy Procedia 00 (2018) 000–000

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charging/discharging power of BESS in the s-th scenario for the d-th typical daily load profile of the m-th month. The costs of BESS include the INC and OMC, which are described as (7) and (8), respectively. Y  in r (1  r ) ba,m ,d ,s ra ra  C ( c P + c E )  m,d , s p ba e ba Y 365[(1  r ) ba,m ,d ,s  1]  (7)  N N md  ra md ra ra ra  Pba =  xba,i Pba,i , Eba =  xba,i Eba,i i 1 i 1   T

Cmom, d , s =  {com [ Pba,dism , d , s (t )  Pba,cham , d , s (t )]}

(8)

t 1

ra where Ebara is the rated capacity of BESS; xba,i is the number of the i-th type of BESS modules; Pba,rai , Eba, i are the

rated power and rated capacity of the i-th type of BESS modules; N md is the number of BESS module types. The constraint includes the BESS budget constraint, which is defined as (9). cp Pbara +ce Ebara  Cinlim

(9)

lim in

where C is the investment budget of BESS. As the BESS is composed of basic modules, the decision variables are the number of each type of BESS modules. It should be noted that Bmrp , Bmre, d , s ,Bmfs, d , s , Cmin, d , s , Cmom, d , s are the key variables connecting the upper and lower models. They are correlated not only with the size of BESS in the upper model, but also with the optimal solutions of BESS in the lower model. 2.2.2 Lower model The objective is to minimize the daily comprehensive costs of the IC with PV and BESS. The costs include the daily virtual power electricity bill, the daily energy electricity bill, as well as the daily OMC of BESS. For the environment-friendly characteristic, the output power of PV will be regarded as the negative load, rather than the decision variable. T

min  ctou (t ) Pg,pum, d , s (t )  csell Pg,sem, d , s (t )+com [ Pba,dism , d , s (t )  Pba,cham , d , s (t )]+cpower Pg,pu,max m , d , s / Dm

(10)

t 1

where Pg,pu,max m , d , s is the maximum power of IC purchased from the grid in the s-th scenario for the d-th typical daily load profile of the m-th month; Dm is the number of days in the m-th month. Since the arising time of the daily peak load of the IC is not always within the high-price periods, the daily virtual power electricity bill (i.e., cpower Pg,pu,max m , d , s / Dm ) is introduced to take into account the effects of BESS on reducing the daily peak load. The constraints include the power balance constraints, the IC exchanged power constraints, the BESS constraints, and the auxiliary variable constraints. For any time slot, the produced power is equal to the load in (11). Pg,pum , d , s (t )  Pg,sem , d , s (t )+Pba,dism , d , s (t )  Pba,cham , d , s (t )+Ppv, m , d , s (t )=Pld, m , d (t ) (11) The IC is prohibited from purchasing power and selling power simultaneously by (12). 0  Pg,pum, d , s (t )  U g,pum, d , s (t ) Pgmax  se se max (12) 0  Pg, m, d , s (t )  U g, m, d , s (t ) Pg  pu se U g, m, d , s (t )+U g, m, d , s (t )  1 The BESS constraints include the charging/discharging power constraints, the state of charge (SOC) constraints, and the daily SOC variation constraint. They can be referred to [10], which are not described for space saving. The auxiliary variable constraints enforce that Pg,pu,max m , d , s should be not less that the power of IC purchased from the grid at any time slot in the scenario. pu Pg,pu,max m , d , s  Pg, m , d , s (t )

t  [1, T ]

(13)



Guodong Xu et al. / Energy Procedia 158 (2019) 4953–4958 Author name / Energy Procedia 00 (2018) 000–000

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3. Case study The one-year historical data of an actual IC with PV in Shanghai, China is employed to test the effectiveness of the proposed methodology. The peak load of IC is 5.93MW, and the rated power of PV is 2MW. The k-means clustering algorithm is adopted to generate the output power scenarios of PV and the typical daily load profiles of IC. Taking the output power scenarios of PV as an example, the one-year power data of PV can be considered as 365 output power scenarios of PV. As the power characteristics of PV in different months are distinct, 5 scenarios are generated independently in each month. Similarly, 1 typical daily load profile would be generated in each month. The time-of-use price of IC in Shanghai, China is adopted, and the power electricity price of IC is set as 42 Yuan/ (kW*month). The fixed retail electricity price of IC is assumed to be zero. The unit OMC of PV is 0.06 Yuan/kWh. In view of the relatively high energy density, the all-vanadium redox flow battery is chosen as the BESS. Three types of BESS modules are chosen, whose technical and economic parameters are shown in Table 1. The curve of the cycle life of BESS versus DOD can be referred to [8]. The unit power cost of BESS is 1 million Yuan/MW, and the unit capacity cost of BESS is 4 million Yuan/MWh. Meanwhile, the unit financial subsidy of BESS is 0.44 million Yuan/MW, and the investment budget of BESS is 10 million Yuan. Besides, the initial SOC, maximum allowable SOC, minimum allowable SOC of BESS are set as 0.5, 1, and 0.2, respectively. Module number

Rated power (MW)

1 2 3

0.25 0.25 0.25

Table 1 Technical and economic parameters of BESS modules Rated capacity Charging Discharging Unit OMC (MWh) efficiency efficiency (Yuan/kWh) 0.5 0.75 1

0.85 0.85 0.85

0.85 0.85 0.85

0.05 0.05 0.05

Float life (Year) 20 20 20

1

(Million Yuan)

Annual expected net benefit of BESS

In terms of the model characteristics, a hybrid intelligent algorithm is utilized to solve the proposed model. The upper model is solved by the particle swarm optimization algorithm, and the lower model is calculated by CPLEX. The simulation platform is Matlab 2013(a) on a PC with Intel Core dual i5-4220M and 8 GB RAM. Given the relatively high unit power cost and unit capacity cost of BESS, the BESS is unable to be profitable currently. Therefore, a sensitivity analysis of the AENB of BESS to the cost reduction and unit financial subsidy of BESS is conducted, whose results are shown in Fig. 1. It should be noted that, the unit power cost and unit capacity cost are considered to decrease with the same ratio, whereas the unit OMC remains unchanged.

0.8 0.6

0.4 0.2

0 20%

0.74

40%

0.64

60% BESS cost ratio 80%

100% 0.44

0.54 Unit financial subsidy of BESS (Million Yuan/MW)

Fig. 1 Sensitivity analysis of the annual expected net benefit of BESS to the cost reduction and unit financial subsidy of BESS

As can be seen from Fig. 1, both the decrease of BESS costs and the increase of the unit financial subsidy of BESS will help increase the AENB of BESS. When the costs decrease to 40% of the current costs, the AENB would be positive (i.e., installing BESS is profitable for the IC), for the unit financial subsidy of BESS in the range of 0.44 to 0.74 million Yuan/MW. To illustrate the advantage of the proposed model, four cases are established in Table 2. The corresponding results are presented in the same table. In this comparison analysis, the unit power cost and unit capacity cost of BESS are assumed to be 40% of the current costs. Meanwhile, the unit OMC is still 0.05 Yuan/kWh.

Guodong Xu et al. / Energy Procedia 158 (2019) 4953–4958 Author name / Energy Procedia 00 (2018) 000–000

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The four cases in Table 2 correspond to four programming models of BESS. As both the PV uncertainty and lifetime characteristics of BESS are considered in case 1, the model for case 1 corresponds to the proposed model in this paper. In case 2, the lifetime characteristics of BESS are neglected. In other words, the lifetime of BESS is set as the float life, which is not affected by the cycling behavior. In case 3, the PV uncertainty is not considered. That is to say, there is only one output power scenario of PV for each typical daily load profile. The model for case 4 can be perceived as a combination of the models for case 2 and case 3. Case number

PV uncertainty

1 2 3 4

√ √ × ×

Table 2 Result comparison of different cases Lifetime characteristics Rated power of Rated capacity of of BESS BESS (MW) BESS (MWh) √ × √ ×

0.5 0.75 0.25 0.75

1.5 1.5 1 1.5

AENB of BESS (Million Yuan) 0.058 0.118 0.024 0.078

Comparing the results of case 1 with those of case 2, we can observe that both the rated power and AENB of BESS for case 2 are larger than those for case 1. This is mainly because the lifetime of BESS for case 2 is set as the float life, which is not less than that for case 1. On the premise of the same rated power and capacity of BESS, the annual INC of BESS for case 2 would be not larger than that for case 1. Based on this, both the rated power and AENB of BESS for case 2 will show a raising tendency. Comparing the results of case 1 with those of case 3, the rated power, rated capacity, and AENB of BESS for case 3 are all less than those for case 1. This can be explained by the fact that the neglect of PV uncertainty can magnify the effects of PV on reducing the peak load of IC. In this regard, the BRPB of BESS will drop. As a result, the rated power, rated capacity, and AENB of BESS for case 3 will show a downward trend. 4. Conclusions A bi-level stochastic programming model has been proposed for the IC with PV to size BESS. The upper model is to decide the optimum size of BESS, and the lower model concentrates on optimizing BESS operation. Simulation results demonstrate the effectiveness of the proposed methodology. Also, the neglect of PV uncertainty or lifetime characteristics of BESS can lead to the variation of BESS planning schemes and unreasonable evaluation results. Acknowledgements This work is supported by the National Basic Research Program of China (973 Program) (2014CB239703). References [1] Zhang S, Cheng H, Li K, Tai N, Wang D, Li F. Multi-objective distributed generation planning in distribution network considering correlations among uncertainties[J]. Applied Energy 2018; 226: 743-55. [2] Oudalov A, Cherkaoui R, Beguin A. Size and optimal operation of battery energy storage system for peak-shaving application. 2007 IEEE Lausanne Powertech, 1-5 July 2007, Lausanne, Switzerland. [3] Zheng M, Meinrenken C, Lackner K. Smart households: dispatch strategies and economic analysis of distributed energy storage for residential peak shaving. Applied Energy 2015; 147: 246–57. [4] Yan Z, Wang C, Lian H, Yi T, Shi Z, Zhang Y. Capacity plan of battery energy storage system in user side considering power outage cost. Automation of Electric Power Systems 2012; 36: 50-4. [5] Ekren O, Ekren B. Size optimization of a PV/wind hybrid energy conversion system with battery storage using simulated annealing. Applied Energy 2010; 87: 592–98. [6] Erdinc O, Paterakis N, Pappi I, Bakirtzis A, Catalao J. A new perspective for sizing of distributed generation and energy storage for smart households under demand response. Applied Energy 2015; 143: 26–37. [7] Ru Y, Kleissl J, Martinez S. Storage size determination for grid-connected photovoltaic systems. IEEE Transactions on Sustainable Energy 2013; 4: 68-81. [8] Kahrobaee S, Asgarpoor S, Qiao W. Optimum sizing of distributed generation and storage capacity in smart households. IEEE Transactions on Smart Grid 2013; 4: 1791-801. [9] Xu G, Shang C, Fan S, Hu X, Cheng H. A hierarchical energy scheduling framework of microgrids with hybrid energy storage systems. IEEE Access 2018; 6: 2472-83. [10] Xu G, Cheng H, Fang S, Ma Z, Zeng P, Yao L. Optimal size and location of battery energy storage systems for reducing the wind power curtailments. Electric Power Components & Systems 2018; 22: 1-11.