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Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment
Energy xxx (2013) 1e14
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Energy journal homepage: www.elsevier.com/locate/energy
Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment Nian Liu*, Zheng Chen, Jie Liu, Xiao Tang, Xiangning Xiao, Jianhua Zhang School of Electrical and Electronic Engineering, North China Electric Power University, Beinong Road 2#, Changping District, 102206 Beijing, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 June 2013 Received in revised form 28 October 2013 Accepted 30 October 2013 Available online xxx
With the rapid development of EVs (electric vehicles), the integration of PV (photovoltaic) generation with EV charging infrastructure can effectively improve the efficiency of clean energy utilization and carbon emission reduction. How to optimize the capacities of components in the PV-based BSS (battery switch stations) is still unsettled. This paper focuses on the mathematical model of the problem. With consideration of battery swapping requirement and maximally utilizing PV energy, an energy exchange strategy is introduced for the PV-based BSS, including battery swapping service model and power distribution model. Towards benefits of economy and environment, objective functions of capacity optimization are modeled with the purpose of minimizing annual cost and maximizing the percentage of utilized PV energy in total energy. The constraints include the construction scale, power balance and battery swapping service etc. Based on the energy exchange strategy, the optimization model is solved by NSGA-II algorithm. Finally, taking the planning of a PV-based BSS in a certain district as example, optimized capacities of PV panels, EV batteries, EV chargers and grid-connected modules can be obtained. From the analysis of the results, the method can provide a foundation for the plan and design of the PV-based BSSs. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Battery switch station Capacity optimization Energy exchange strategy Photovoltaic generation
1. Introduction In the transport sector, EV (electric vehicles) have been regarded as a type of environmentally friendly vehicles. It has been established as an effective way to promote the development of EVs to realize low-carbon economic transition and ensure energy security by many countries. However, EVs need to be connected to the electric power grid for charging and there are still many barriers remaining to be considered. Firstly, according to the prior studies, the indirect emissions of EVs are sensitive to the generation mix of a particular region’s electric power system [1e4]. If the power generation of the grid is dominated by coal-fired power plants, the emission advantage for EVs is not obvious. Secondly, with large scale use of EVs, it will need more investment on the capacities of generation, transmission and distribution due to the boosting charging requirements of EVs. As a renewable and clean energy, solar PV (photovoltaic) can be produced anywhere, including the urban areas for EV applications. The direct integration of PV with EV charging infrastructure can be a suitable way to effectively improve * Corresponding author. Tel.: þ86 10 80790940; fax: þ86 10 51971652. E-mail address: [email protected] (N. Liu).
the emission reduction of EVs and reduce the dependence on the power grid [5e9]. There have been many studies on the integration of PV with EV charging facilities. The technical feasibility of directly charging vehicle batteries with solar PV panels is provided in Refs. [7,8]. These two studies provide a proof of concept for this approach, demonstrating the safety and viability of this charging scheme. The idea that solar PV arrays built over parking lots to provide daytime charging for commuter vehicles is proposed in Ref. [6], which broadly sketches out what such a system would look like and assesses the potential energy production from a single parking space. A system with bidirectional, highly efficient, DC/DC EV charger placed between the high-voltage DC bus of a PV inverter and EV battery is presented in Ref. [5]. The system partially alleviates the overload of distribution system feeder by providing EV batteries with fast charging. In addition, the charger is capable of diverting fast changes in the PV output to the battery. Similarly, a concept of bi-directional battery charger for PHEV/EV with PV system and related algorithms are proposed in Ref. [10]. In order to integrate PHEV (plug-in hybrid vehicles) with an existing residential PV system, an approach for the control and optimization of power flow is proposed in Ref. [11]. With PHEVs serving as an energy storage
0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.10.090
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
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N. Liu et al. / Energy xxx (2013) 1e14
Nomenclature EV PV EVB BSS PUPT Nevba(t) Pr Ps(t) Pdc Pdc2(t) Pdc2a Pac Pevb(t) Pevbm(t) Pevbn(t) Pevbe(t)
electric vehicle photovoltaic electric vehicle battery battery switch station percentage of utilized PV energy in total energy number of swapping available EV batteries at time t rated power of a PV cell (KW) output power of PV arrays at time t (KW) rated power of a single DC/DC module charging power of MOD2 at time t average charging power of MOD2 for a whole cycle T rated power of a single AC/DC module charging power of EVB system at time t maximum charging power of EVB system at time t newly-added charging power at time t existing charging power at time t
unit, the integrated system provides flexible and efficient control of power flow with the coordination of PCU (power conditioning unit) and controller. Similarly, a residential PV system for PHEV load is designed in Ref. [12]. A power management algorithm is introduced to control the power flow between the grid and EV battery according to load profile. In order to maximize the use of solar and wind energy in transportation, a stochastic optimization algorithm, which may eventually be used by electric energy suppliers to coordinate charging of EDVs (electric-drive vehicles), is presented in Ref. [13]. Summarizing the aforementioned studies, most of them focus on the systems that integrate PV with EV battery chargers. Related control strategies and evaluations are proposed to prove the feasibility of the system. To promote the development of EVs, it is necessary to build infrastructures that can charge EVs in a short time. BSS (battery switch station) is one of the solutions to this problem [14e16], in which the automated switch platform will replace the depleted batteries with fully-charged batteries. The depleted batteries will be placed in a storage room and recharged to be available for other drivers [17]. Consequently, this paper mainly concentrates on the plan and design of the integrated system of PV and BSS. Before the construction of a PV-based BSS, it needs to design the electrical structure of the system and determine the capacities of primary components including PV panels, EV batteries, DC/DC EV chargers and grid-connected AC/DC modules. Generally, considering the solar irradiation, temperature and EV battery swapping requirements in a specific area, the capacities of the components should be suitable to provide enough fully-charged batteries for swapping service. On the basis of service availability, the construction cost of the system is the primary problem to be considered by investors. Besides, in order to reduce the emission, the PUPT (percentage of utilized PV energy in total energy) should be advanced as far as possible. However, the benefits between economy and environment are always contradictory. An economic and environmental analysis model for EVs operated under different conditions is proposed in Ref. [18], and the feasibility of the model is also tested using case studies. If we want to reduce the emission, more PV panels need to be purchased, and more EV batteries should be reserved due to the solar irradiance intermittency. Although the electricity purchased from the power grid is reduced, the total investment will inevitably increase in the additional cost of PV panels and EV batteries.
Pevbr(t) Pg(t) Wevb Wevba(t)
required power of EVB system power supplied by power grid at time t rated energy capacity of a single EV battery (kWh) electric energy of the swap available EV batteries at time t Wevbn(t) electric energy of newly fully charged EV batteries at time t Wevbt(i) capacity of EVB system to be complemented at year i(kWh) Wev ðtÞ energy exchange demand during period [t, t þ 1] Wevbr ðt; tr Þ energy reserve demand of EVB system within a certain period tr in the future at time t h1 energy conversion efficiency of MOD1 h2 energy conversion efficiency of MOD2 hac(t) energy conversion efficiency of MOD3 ht(t) energy conversion efficiency of transformers tr energy reserve time for EVB system
For the above reasons, this paper proposes a multi-objective capacity optimization approach for the components of the PVbased BSS, which includes the benefits of economy and environment as two objectives to be optimized. The content of this paper is organized as follows. Section 2 describes the system structure and function of the components of the PV-based BSS. In Section 3, an energy exchange strategy is introduced. Section 4 establishes a mathematical model for capacity optimization, aiming at minimizing system annual cost and maximizing PUPT. In Section 5, problem solving process of the multi-objective capacity optimization model is introduced. Case study and related analysis of results are presented in Section 6. Finally, conclusions are given in Section 7. 2. System structure and function of the PV-based BSS 2.1. System structure The PV-based BSS system established in this paper is mainly composed of PV system, EVB system, grid-connected system and central control system (see Fig. 1). 2.2. Function of system components 1) PV system is composed of PV arrays and related DC/DC modules (abbreviation as MOD1). PV arrays, composed of PV cells in series and parallel, convert solar energy directly into electric energy, connecting to the DC bus through MOD1. And the maximum power generated by PV arrays has a fixed relationship with the rated power of MOD1. Define h1 as the energy conversion efficiency of MOD1; Vmpp as the PV cell voltage at the maximum power point; Impp as the PV cell current at the maximum power point; Tc as the operating temperature of PV cells ( C); GT as the hourly irradiance on a tilted surface (W/m2); Pr as the rated power of a PV cell; Npvs as the number of PV cells in series, which is determined by both the range of operating voltage of MOD1 and Vpmp; Npvp as the number of PV cells in parallel, and its value determines the total rated capacity of PV arrays; Ps(t) as the output power of PV arrays at time t, details of the calculation can be acquired from Ref. [19]. So there is:
Tc ¼ f1 ðNOCT; Ta ; GT Þ
(1)
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
N. Liu et al. / Energy xxx (2013) 1e14
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Fig. 1. System structure.
Vmpp ; Impp ¼ f2 ðVoc ; Isc ; Vmax ; Imax ; Tc Þ
(2)
Wevb ¼ h2 $
ZtþT Pdc2 ðtÞdt
(6)
t
Ps ðtÞ ¼ f3 h1 ; Vmpp ; Impp ; Npvs ; Npvp ; 0 Ps ðtÞ < Pr Npvs Npvp (3) where NOCT (normal operating cell temperature) is usually between 42 C and 46 C; Ta is the ambient temperature of the location area; Voc means the open circuit voltage of PV cell; Vmax means the maximum voltage of PV cell at the reference operating conditions; Isc means the short circuit current of PV cell; Imax means the maximum current of PV cell at the reference operating conditions. 2) EVB system is composed of EV batteries and related DC/DC modules (abbreviation as MOD2). The PV-based BSS provides fullycharged EV batteries for EVs. The replaced EV batteries will be placed in a storage room and recharged to be available for other drivers. Therefore, for EV batteries of the BSS, some are on the EVs while the others are at the station. Define h2 as the energy conversion efficiency of MOD2; Nevb as the total number of EV batteries; Nevbs as the number of EV batteries at the station; Nevbc as the number of EV batteries being charged; Nevbv as the number of EV batteries on the EVs.
Nevb ¼ Nevbs þ Nevbv
(4)
Nevbs Nevbc
(5)
During the whole charging cycle T, each EV battery should be charged by only one MOD2. Define Pdc as the rated power of a single MOD2; Pdc2(t) as the charging power of MOD2 at time t; Wevb as the rated energy capacity of an EV battery (kWh).
The charging power may be not constant during the charging cycle. From the battery side, a conventional lithium-ion battery charging is characterized by two main phases: constant current and constant voltage. Recently, constant power charging became popular in large vehicle battery packs [20]. Hence, if the constant power charging is used, the charging power will be unchanged. If the conventional charging method is utilized, the charging power of an EV battery is time-vary according to the SOC (state of charge) [21,22]. The SOC mainly increases in the period of constant-current, which takes up most of the time of charging process. Besides, the charging power changes with a small increase in this period. Therefore, to simplify the calculation, this paper uses the average charging power Pdc2a to describe the demand for charging of an EV battery.
Pdc2a ¼ ðWevb =TÞ=h2
(7)
Therefore, the charging power of the EVB system at time t can be described as:
Pevb ðtÞ ¼ Nevbc $Pdc2a
(8)
3) The grid-connected system is mainly composed of transformers and related AC/DC modules (abbreviation as MOD3). Transformers are used to transform the electric energy from the grid into the energy that matches the operating voltage of MOD3. MOD3 are used as the components that transmit the power from the grid to the system by converting AC to DC. Define ht(t) and hac(t) as the energy conversion efficiency of transformers and MOD3; Pg(t) as the power supplied by the power grid at time t; Pac as the rated power of a single MOD3. As the efficiency of transformers ht(t)
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
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and efficiency of AC/DC inverters hac(t) are not constant and vary by the load rate, their variations are provided in Figs. 2 and 3 respectively. 3. Energy exchange strategy of the PV-based BSS 3.1. Basic principles The main load of the BSS is the EV batteries waiting to be recharged, which are removed from EVs and placed in a storage room. During the operation, there are two basic principles that need to be followed. One is the PV-based BSS should provide the battery swapping service for EVs all the time. The other is, in order to reduce the carbon emissions of EVs, EVB system should be charged by the PV system as much as possible. Only when the PV system cannot meet the charging demand of EVB system, would the charging power of EV batteries be conditionally supplied by the power grid. Consequently, the system energy exchange strategy can be divided into battery swapping service model and power distribution model. Fig. 3. Efficiency curve of AC/DC converters.
3.2. Battery swapping service model This model mainly describes the variation of the electric energy of swapping available EV batteries Wevba(t), while taking a series of factors into consideration, including the effect of newly fullycharged batteries and swapped batteries as well as a certain amount of energy reserve requirement. At time t, the electric energy of swapping available EV batteries can be determined by the number of swapping available EV batteries as:
Wevba ðtÞ ¼ Nevba ðtÞWevb
(9)
Considering the effect of newly fully-charged batteries and swapped batteries, the variation of electric energy of swapping available EV batteries can be described as:
Wevba ðt þ 1Þ ¼ Wevba ðtÞ Wev ðtÞ þ Wevbn ðt þ 1Þ Wevba ðt þ TÞ ¼ Wevba ðtÞ
tþT1 X
s¼t
Wev ðsÞ þ
tþT X
s ¼ tþ1
Wevbn ðsÞ
should have a certain amount of energy reserve besides meeting the current energy demand for battery swapping. It means the EV batteries should meet the battery swapping demand for an additional period tr in the future. And there is:
Wevbr ðt; tr Þ ¼
tþðt r 1Þ X
s¼t
Wev ðsÞ
Wevba ðtÞ Wevbr ðt; tr Þ
(12)
(13)
Relations of variables in the battery swapping service model are illustrated in Fig. 4. 3.3. Power distribution model
(10) (11)
Considering the availability of battery swapping service and forecasting errors of battery swapping demand, the EVB system
This model dynamically determines the charging power of EVB system Pevb(t) and the power supplied by the power grid Pg(t), according to the electric energy of swapping available EV batteries Wevba(t) and the output of PV system Ps(t). 3.3.1. Relations of variables in power distribution model According to the number of EV batteries waiting for charging, the maximum charging power of the EVB system at time t Pevbm(t) can be described as:
Pevbm ðtÞ ¼ ðNevbs Nevba ðtÞÞ$Pdc2a
(14)
At time t, the EV batteries being charged can be classified into two parts: ones that start to be charged at time t and the others that start before time t but haven’t completed charging. It means the EVB system’s charging load contains the newly-added charging load Pevbn(t) and existing charging load Pevbe(t). So there is
Pevb ðtÞ ¼ Pevbn ðtÞ þ Pevbe ðtÞ
(15)
where Pevbe(t) has a fixed relationship with Pevbn(t):
Pevbe ðtÞ ¼
Fig. 2. Efficiency curve of transformers.
t 1 X
s ¼ tTþ1
Pevbn ðsÞ
(16)
The electric energy of newly fully charged EV batteries at time t þ T Wevbn(t) can be expressed by the newly-added charging power at time t as:
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Fig. 4. Relations of variables in the battery swapping service model.
Wevbn ðt þ TÞ ¼ Pevbn ðtÞ$T
(17)
3.3.2. Process of power distribution According to the battery swapping model, the following formula should be guaranteed:
Wevba ðt þ TÞ Wevbr ðt þ T; tr Þ
(18)
For Wevba(t þ T), Wevbn(t þ T) is controllable to achieve the goal of battery swapping service (see formula (9)), which can be adjusted by setting the number of EV batteries that start charging at time t based on the lack of energy. To be specific, there are two conditions.
power grid. The required power of EVB system Pevbr(t) can be calculated by the lack of energy and charging cycle T.
Pevbr ðtÞ ¼
Wevbr ðt þ T; tr Þ Wevba ðtÞ þ
tþT1 X
s¼t
!, Wev ðsÞ
tþT1 X
s ¼ tþ1
Wevbn ðsÞ
T
If the energy reserve requirement can be met by the PV system independently, it means that the remaining power is still greater than the required power of the EVB system Pevbr(t):
Ps ðtÞ$h1 $h2 Pevbe ðtÞ Pevbr ðtÞ 3.3.2.1. EVB system can meet the energy reserve requirement.
Wevba ðtÞ þ
tþT1 X
s ¼ tþ1
Wevbn ðsÞ
tþT1 X
s¼t
Wev ðsÞ Wevbr ðt þ T; tr Þ
In this case, EV batteries are charged by the PV system independently. To utilize the output power of PV system as much as possible, the number of EV batteries to be charged should be determined by the output power of PV system and the maximum charging power of EVB system. Consequently, the charging power of EVB system can be expressed as:
(21)
(22)
In this case, there is no need to purchase any electric energy from the power grid. Besides, the energy generated by the PV system should be utilized to the greatest extent. It will follow the same power distribution rule as the above condition, shown in (19) and (20). Additionally, there is a precondition for this case:
Pevbm ðtÞ Pevbe ðtÞ Pevbr ðtÞ
(23)
And there is no need to purchase any electric energy from the power grid.
which means the EV batteries waiting to be charged at the station should be abundant all the time. However, if the energy reserve requirement cannot be met by the PV system independently, it means that the output power of the PV system is less than the sum of existing charging power Pevbe(t) and required power Pevbr(t), that is:
Pg ðtÞ ¼ 0
Ps ðtÞ$h1 $h2 Pevbe ðtÞ < Pevbr ðtÞ
Pevb ðtÞ ¼ minðPevbm ðtÞ; Ps ðtÞ$h1 $h2 Þ
(19)
(20)
3.3.2.2. EVB system cannot meet the energy reserve requirement.
Wevba ðtÞ þ
tþT1 X
s ¼ tþ1
Wevbn ðsÞ
tþT1 X
s¼t
Wev ðsÞ < Wevbr ðt þ T; tr Þ
In this case, the lack of energy should be compensated immediately. In order to utilize PV energy as much as possible, the output power of PV system should be given priority to charge EV batteries. And the remaining energy demand should be supplied by the
(24)
In this case, it is necessary to purchase electricity from the power grid. The charging power of EVB system should be the sum of Pevbe(t) and Pevbr(t). The power purchased from the power grid should be the difference between the charging power of EVB system and the output power of PV system.
Pevb ðtÞ ¼ Pevbe ðtÞ þ Pevbr ðtÞ
(25)
Pg ðtÞ ¼ ðPevb ðtÞ Ps ðtÞ$h1 $h2 Þ=ðh2 $ht ðtÞ$hac ðtÞÞ
(26)
Flow chart of the energy exchange strategy is shown in Fig. 5.
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
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N. Liu et al. / Energy xxx (2013) 1e14
Fig. 5. Flow chart of energy exchange strategy.
of the PV system, EV batteries, MOD1, MOD2, MOD3, transformers and electricity purchased from the grid.
4. Mathematical model of capacity optimization 4.1. Objective functions
4.1.1.1. Annual cost of PV system. To achieve the maximum benefits of economy and environment, it is supposed to minimize the system annual cost and maximize PUPT. Details about these two objective functions are given as follows. 4.1.1. System annual cost The objective function of the system annual cost is constructed as follows.
min C ¼ Cs þ Cevb þ Cdc1 þ Cdc2 þ Cac þ Cd þ Cg
(27)
where C is the system total annual cost of the PV-based BSS; Cs, Cevb, Cdc1, Cdc2, Cac, Cd and Cg respectively represent the total annual cost
Cs ¼ aPr Npvs Npvp
r0 ð1 þ r0 Þm þ u Npvp ð1 þ r0 Þm 1
(28)
where a is the unit price of PV cells (RMB/kW); u(Npvp) is the annual maintenance and operation cost of the PV system; m is the system lifetime; r0 is the discount rate. 4.1.1.2. Annual cost of EV batteries. The total cost of EV batteries can be divided into three parts: 1) initial cost of purchasing EV batteries for the construction of the PV-based BSS; 2) additional cost of EV batteries used for complementing the capacity of eliminated
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batteries due to their lower-than-normal capacity [23,24]; 3) annual maintenance and operation cost of the EV batteries.
Cevb ¼
bWevb Nevb þ
m cW P evb Nevb þ bWevbt ðiÞ i¼1
!
ð1 þ r0 Þi
r0 ð1 þ r0 Þm þ uðNevb Þ ð1 þ r0 Þm 1
(29)
where b is the unit price of EV batteries (RMB/kWh); c is the unit cost of the capacity test (RMB/kWh); Wevbt(i) is the capacity of EV batteries to be complemented at year i (kWh); u(Nevb) is the annual maintenance and operation cost of EV batteries. 4.1.1.3. Annual cost of MOD1 and MOD2.
r0 ð1 þ r0 Þm þ uðNdc1 Þ ð1 þ r0 Þm 1
(30)
r0 ð1 þ r0 Þm þ uðNdc2 Þ ð1 þ r0 Þm 1
(31)
Cdc1 ¼ dNdc1
Cdc2 ¼ eNdc2
where d and e are unit price of MOD1 and MOD2 (RMB/10 kW); Ndc1 and Ndc2 are the number of modules in MOD1 and MOD2; u(Ndc1) and u(Ndc2) are the annual maintenance and operation cost of MOD1 and MOD2. 4.1.1.4. Annual cost of MOD3.
Cac ¼ fNac
r0 ð1 þ r0 Þm þ uðNac Þ ð1 þ r0 Þm 1
(32)
where f is the unit price of MOD3 (RMB/10 kW); Nac is the number of modules in MOD3; u(Nac) is the annual maintenance and operation cost of MOD3. 4.1.1.5. Annual cost of grid-connected system.
Cd ¼ gSta Nt
r0 ð1 þ r0 Þm þ uðNt Þ ð1 þ r0 Þm 1
(33)
where g is the unit price of transformers (RMB/kVA); Nt is the number of transformers; Sta is the rated apparent power of a transformer (kVA); u(Nt) is the annual maintenance and operation cost of transformers. 4.1.1.6. Annual cost of
Cg ¼
8760 X
cg ðtÞPg ðtÞDt
purchasing electricity from
the grid.
(34)
t ¼1
where cg(t) is the unit price of electricity (RMB/kWh); Dt is the time interval. 4.1.2. The percentage of utilized PV energy in total energy (PUPT) PUPT is determined by the utilized PV energy and the total charging energy of the EVB system. The objective function is constructed as:
P8760 max PUPT ¼
t¼1
P Pevb ðtÞ$Dt=h2 ht ðtÞhac ðtÞ 8760 t ¼ 1 Pg ðtÞ$Dt P8760 t ¼ 1 Pevb ðtÞ$Dt=h2 (35)
7
4.2. Constraints 4.2.1. Constraints on the external parameters and the construction scale Npvp, Nevb, Ndc1, Ndc2, Nac and Nt are the decision variables of the capacity optimization model that need to be solved out. The number of PV cells is restricted by the limited area of the PV-based BSS. Besides, the number of EV batteries, converters and transformers shall be given an appropriate upper limit according to the battery swapping demand, thereby narrowing the search scale for the optimal solution.
0 Npvp Npvp:max 0 Nevb Nevb:max 0 Ndc1 Ndc1:max 0 Ndc2 Ndc2: max 0 Nac Nac: max 0 Nt Nt: max
(36)
4.2.2. Operation constraints 4.2.2.1. Additional constraints on decision variables. According to the results of the power distribution model, it is necessary to add constraints to the number of converters and transformers.
Pdc Ndc1 Pr Npvs Npvp
(37)
Pdc Ndc2 maxðPevb ðtÞÞ=h2
(38)
Pac Nac ht ðtÞmax Pg ðtÞ
(39)
Sta Nt max Pg ðtÞ ðcos 4$gÞ
(40)
where cos4 and g are the power factor and load rate of transformers respectively. 4.2.2.2. Constraints on system power balance. The charging power of EVB system is supposed to be equal to the sum of the output power of PV system and the power supplied by the power grid all the time. Consequently, the following equality constraint should be satisfied.
Pevb ðtÞ=h2 ¼ Ps ðtÞ$h1 þ Pg ðtÞ$ht ðtÞ$hac ðtÞ
(41)
4.2.3. Constraints on battery swapping service The number of EV batteries available for swapping is supposed to be less than the total amount of EV batteries at the station, that is
0 Nevba ðtÞ Nevbs
(42)
According to formula (23) introduced in the power distribution model, it should be ensured that the EV batteries waiting to be charged are abundant at any time. Therefore, further constraint is described as
ðNevbs Nevba ðtÞÞ$Pdc2a Pevbe ðtÞ þ Pevbr ðtÞ
(43)
5. Problem solving process of the capacity optimization model According to the capacity optimization model, the problem needed to be solved can be expressed as:
ðmin C; max PUPTÞ ¼ fc Npvp ; Nevb ; Ndc1 ; Ndc2 ; Nac ; Nt
(44)
This capacity optimization model is a nonlinear multi-object optimal problem containing several decision variables. NSGA-II
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
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algorithm is used to solve this type of problems [25e27]. Specific solving process of this capacity optimization model is shown in Fig. 6. During the process, the primary difficulties are the calculation of objective functions, including system annual cost and PUPT. For any PV-based BSS, the data listed as follows are needed before calculating the objective functions: 1) statistical data of a whole year’s solar radiation and the temperature of the area that BSS plans to be located; 2) forecasting data of daily battery swapping demand for EVs that BSS will serve for; 3) specific parameters of the components in the BSS, such as unit price, lifetime, efficiency curve and rated power etc.; 4) upper and lower limit for each decision variable given the battery swapping demand and location area of the BSS. The specific calculation process is introduced as follows.
3) Calculate the electric energy of swapping available EV batteries at time t þ 1, according to formula (10) in the battery swapping model. 4) Let t ¼ t þ 1, repeat 1)e3) until all the charging power and purchased power of the EVB system for the whole year are calculated. 5) Check the constraints on the decision variables by (37)e(40), and correct the variables that fail to satisfy the constraints. 6) Calculate the capacity that needs to be complemented by the EVB system within the planning years m, named as Wevbt(i), according to the limited charging cycles of EV batteries (i ¼ 1,2,.,m). 7) Calculate the system annual cost and PUPT by (27)e(35).
1) Calculate the output power of PV system Ps(t), according to the statistical data of a whole year’s solar radiation, temperature and the number of PV cells in parallel Npvp. 2) Calculate the charging power of EVB system Pevb(t) and the power purchased from the power grid Pg(t) based on the power distribution model.
6. Case study 6.1. Study object and basic data Take the planning of PV-based BSS in a certain district (north latitude 32 460 ) as an example to optimize its capacity. Solar
Fig. 6. Flow chart of solving the optimization model based on NSGA-II.
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radiation and temperature of typical days are shown in Figs. 7 and 8 respectively. In the future, the main types of EVs can be divided into buses, taxis, commuter vehicles and private cars. Therefore, energy demand for battery swapping can be analyzed according to the above four types. Suppose the number of EVs provided battery swapping service by the BSS is 100 and the number of buses, taxis, commuter vehicles and private cars are 5, 10, 10 and 75 respectively. And the corresponding rated energy capacities of EV batteries are 72 kWh, 48 kWh, 24 kWh and 24 kWh. EV batteries used in taxis and buses can be considered to be formed by two and three EV batteries with rated energy capacity of 24 kWh. Based on the investigation and forecasting, the energy demand for battery swapping for workdays and holidays is shown in Fig. 9. The unit price of electricity can be divided into three levels according to the peak, flat and valley period of the day, as shown in Table 1. The values of parameters of the components used in the system are listed in Table 2. It is noted that the prices of components are based on the data offered by the public or inquiry from the manufacturers in China. These prices may not be equal in different countries, using for research only. Fig. 8. Variation of temperature of typical days.
6.2. Analysis of optimal solutions 6.2.1. Pareto optimal solutions Pareto front and its extreme solutions obtained by NSGA-II are shown in Fig. 10 and Table 3, respectively. As shown in Fig. 10, the result of the Pareto front provides abundant information for mutual compromise between economic and environmental benefits. Each point in the Pareto front corresponds to a fixed value of system annual cost and PUPT. This means that each point represents a definite capacity optimization solution. Moreover, it can be clearly seen from the figure that, advisable solutions can be divided into economy preferred solutions (0e43.83%) and environment preferred solutions (43.83%e95%). Once PUPT exceeds 95%, the cost will increase dramatically, which is not advisable. If designer emphasizes on the economic benefits, they can set a smaller value of system annual cost and then get the correspond value of PUPT. Likewise, if the priority is given to the utilization of renewable energy resources, the higher PUPT will be their choice. Therefore, there are a number of optimal solutions derived from the multi-objective optimization method. In the actual design for PV-based BSS, the final “optimal” solution can be chosen following the expectation of the BSS owner and designer. For example, if 10%, 50% and 80% of PUPT are expectations for different designers, the
Fig. 7. Variation of solar radiation of typical days.
related closest optimal solutions can be selected, as show in Table 4. Finally, BSS owner and designer can make a reasonable and suitable decision with the flexible scheme.
6.2.2. Variations of the capacities of system components The relations between the capacities of system components and PUPT are shown in Fig. 11. It can be seen that the rated power of PV system and MOD1 increase with the augment of PUPT. The rated power of MOD1 is determined by the lower limit of the number of modules in MOD1 ðPse ðqÞNpvs Npvp =Pdc Þ, mentioned in the additional constraints on the decision variables, shown as formula (45).
Pdc Ndc1 Pr Npvs Npvp
(45)
For EVB system, EV batteries have to play the role in balancing the system power as there is no other type of batteries dedicated to store energy. After meeting certain charging demand of EVB
Fig. 9. Daily energy demand for battery swapping in the PV-based BSS.
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Table 1 Unit price of electricity. Levels
Time period
Unit price of purchasing electricity (RMB/kWh)
Peak level Flat level Valley level
7:00e11:00, 19:00e23:00 11:00e19:00 23:00e7:00 (next day)
0.0225 0.0140 0.0057
system, the excess power of PV system will increase with the augment of PUPT. Therefore, to balance the increasing excess power, the rated capacity of EVB system will inevitably increase. According to the additional constraints on the decision variables, the lower limit of the number of modules in MOD2 ðmaxðPe Þ=ðh2 $Pdc ÞÞ is determined by the maximum charging power of EVB system Pevbm(t). When PUPT is small, it means the PV system cannot meet the charging demand independently. Hence, purchasing electricity from the power grid is required. In this case, Pevbm(t) is determined by the energy reserve requirement which is only related to tr. Therefore, the rated power of MOD2 remains unchanged. When PUPT increases to a certain extent, Pevbm(t) is determined by the output power of PV system. Therefore, the rated power of MOD2 increases. Finally, there are three quantified results can be obtained. 1) With the variation of PUPT, the rated power of PV system keeps almostly the same with the rated power of MOD1. 2) When PUPT is smaller than 43.83%, the number of EV batteries versus the number of charging modules is about 4.8:1. When PUPT gets lager than 43.83%, this ratio became lower and it will get the minimum 2:1 with PUPT reaching 100%. 3) When PUPT is smaller than 43.83%, the ratio between the rated power of PV system and MOD2 keeps growing from 0 to 1.56:1. When PUPT exceeds this point, this ratio decreases and its minimum can reach 1.23:1.
6.2.3. Analysis of system power distribution In order to better analyze the effectiveness of the power distribution model, an optimal solution (PUPT is 79.90%, system annual cost is 7.5253 106 RMB) is selected from the Pareto front. The distribution of the output power of the PV system, utilized power of the PV system, charging power and purchased power of EVB system for the two typical days in summer and winter is shown in Fig. 12. Several conclusions can be obtained from the results. 1) The charging power of EVB system is satisfied by both the supply of the PV system and the power grid.
Table 2 System parameter values.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
System parameters
Values
unit price of PV cells lifetime of PV cells (system lifetime) rated power capacity of DC/DC modules unit price of DC/DC modules efficiency of DC/DC modules self-discharge rate of EV batteries rated energy capacity of EV batteries unit price of EV batteries rated power capacity of AC/DC modules unit price of AC/DC modules rated capacity of transformers unit price of transformers power factor of transformers load rate of transformers
7000 (RMB/kW) 20 years 10 kW 8000 (RMB/10 kW) 97% 0.0001 24 kWh 120,000 (RMB/kWh) 10 kW 25,000 (RMB/10 kW) 400 kVA 120,000 (RMB/kVA) 0.95 0.6
Fig. 10. Pareto front obtained by NSGA-II.
2) During the daytime with adequate sunshine, the output of the PV system is utilized to a great extent. It can independently satisfy the charging demand of EVB system. Reserved fullycharged EV batteries can even satisfy the battery swapping demand at night. So there is no need to get any electricity from the power grid till midnight. Purchasing electricity from the grid only occurs after midnight due to insufficient energy reserve and lower electricity price. 3) With larger radiation intensity and longer duration of sunshine, the output energy of the PV system in summer is larger than that in winter. At the same time, the difference between summer and winter in the charging power of EVB system is small. Therefore, PUPT in summer is smaller than that in winter.
6.2.4. Analysis of the energy of EVB system The energy of EVB system can be analyzed from the same optimal solution used in the analysis of system power distribution. For the same time period, the distribution of the energy demand for battery swapping, energy reserve requirement and storage energy of EVB system are shown in Fig. 13. It can be noted that the storage energy of EVB system is always more than the energy demand for battery swapping and no less than the energy reserve requirement. Hence, EVB system can satisfy the energy demand for battery swapping all the time. At night without any power generated by the PV system, the charging power is supplied by the power grid independently. At this time, the energy storage just needs to satisfy the energy reserve requirement when the economic benefits are considered. During the daytime with adequate solar energy, the charging power is mainly supplied by the PV system. To improve PUPT, the energy storage is far more than the energy reserve requirement at night. 6.2.5. Variation of marginal electricity price for battery swapping Considering the development of PV-based BSS, its profitability should also be given adequate attention. The price should not only
Table 3 Extreme solutions in Pareto optimal set. System annual cost (RMB) Minimum system annual cost Maximum PUPT
6
6.0444 10 1.0503 107
PUPT (%) 0 99.88
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N. Liu et al. / Energy xxx (2013) 1e14 Table 4 System capacity optimization solutions for different PUPT (Select PUPT as 10.39%, 50.08 %and 79.90% respectively). PUPT
Name
Optimization results
Rated energy
10.39%
Number of PV cells in parallel Number of EVBs Number of DC/DC modules 1 Number of DC/DC modules 2 Number of AC/DC modules Number of transformers System annual cost Number of PV cells in parallel Number of EVBs Number of DC/DC modules 1 Number of DC/DC modules 2 Number of AC/DC modules Number of transformers System annual cost Number of PV cells in parallel Number of EVBs Number of DC/DC modules 1 Number of DC/DC modules 2 Number of AC/DC modules Number of transformers System annual cost
40 173 13 36 37 2 6.1303 106 (RMB) 199 180 62 40 37 2 6.5980 106 (RMB) 317 220 98 76 37 2 7.5253 106 (RMB)
123 kW 4152 kWh 130 kW 360 kW 370 kW 800 kVA e 610 kW 4320 kWh 620 kW 400 kW 370 kW 800 kVA e 974 kW 5280 kWh 980 kW 760 kW 370 kW 800 kVA e
50.08%
79.90%
ensure the profit of operators, but also help reduce EV users’ expenditure compared to using internal-combustion-engine vehicles [28]. Therefore, the electricity price related to PUPT should be properly determined. Define the electricity price that ensures profitability for a certain PUPT as marginal electricity price. Based on the Pareto optimal solutions, the marginal electricity price for each PUPT is obtained. The relation between marginal electricity price and PUPT is shown in Fig. 14. From the result, we can find out that the growth rate of the marginal price is relatively lower when PUPT varies from 0 to 43.83%. In contrast, the growth rate of the marginal price is much higher when PUPT varies from 43.83% to 100%. Therefore,
11
considering the economic reasons, it is more feasible to select an optimal solution with PUPT no more than 43.83%. The result is consistent with the turning point of Pareto optimal solutions. 6.2.6. Influence of energy reserve time on capacity optimization The energy reserve time tr directly influences the energy reserve requirement of EVB system, thereby the system capacity optimization. To analyze the specific influence of tr on the system capacity optimization, tr is taken as 3 h, 5 h and 7 h respectively. 6.2.6.1. Comparison of the Pareto optimal solutions. Based on the results of capacity optimization for different energy reserve time, related Pareto front can be obtained, shown as Fig. 15. It can be found that system annual cost increases with the augment of tr. It is because the augment of tr will make the rated capacity of EVB system increase, inevitably leading to the augment of system annual cost. 6.2.6.2. Comparison of the capacities of system components. Rated capacities of system components for different tr are shown in Fig. 16. It can be seen that tr mainly influences the rated capacity of EVB system and MOD2. For EVB system, its rated capacity increases with the augment of tr, which directly determines the energy reserve requirement. For MOD2, its rated power is determined by the maximum charging power of EVB system Pevbm(t). When PUPT is small, Pevbm(t) is mainly related to tr. As a result, the rated power of MOD2 increases with the augment of tr. When PUPT gets larger to a certain extent, Pevbm(t) is determined by the rated power of the PV system, which has little to do with tr. Consequently, the rated power of MOD2 is basically the same for different tr. 6.2.6.3. Comparison of marginal electricity price. The relation between marginal electricity price and energy reserve time tr is shown in Fig. 17. It can be seen that the marginal electricity price
Fig. 11. Relations between the capacities of system components and PUPT.
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Fig. 12. System power distribution for the two days randomly selected in summer and winter respectively.
Fig. 13. System energy distribution for the two days randomly selected in summer and winter respectively.
increases with the increase of tr. And the variations of the marginal prices under different reserve time have common increase rules. The parameter of energy reserve time is set to guarantee the availability of battery swapping service. According to the
aforementioned results, the value of the energy reserve time will have a significant influence on the economic benefits. Hence, considering hourly energy status of the EVB system, it is sufficient to set the energy reserve time at 3 h for the BSS in this case study.
Fig. 14. Relation between marginal electricity price and PUPT.
Fig. 15. Influence of energy reserve time on the Pareto front (Select tr as 3 h, 5 h and 7 h respectively).
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Fig. 16. Influence of energy reserve time on the capacities of system components (Select tr as 3 h, 5 h and 7 h respectively).
7. Conclusions The contribution of this paper is mainly on a multi-objective capacity optimization method for the components of the PVbased BSS, including the PV system, DC/DC converters, AC/DC converters, transformers and EV batteries. For an actual design of
PV-based BSS, there are a number of optimal solutions can be derived, which are divided into economy preferred and environment preferred solutions. The final scheme for capacities of components can be chosen following the expectation of the BSS owner and designer. By the analysis of case study, some interesting results have been obtained. There is an apparent turning point (PUPT ¼ 43.83%) between the solutions of economy preferred and environment preferred. For the economy preferred solutions, the rated power of the PV system keeps growing with the increase of PUPT. The number of EV batteries and charging modules remains unchanged (the ratio is about 4.8:1), which mainly depends on the battery swapping demand. For the environment preferred solutions, the rated power of the PV system still keeps growing with the increase of PUPT. However, in order to maximally utilize the energy of PV system, the number of EV batteries and charging modules deployed in the BSS also increases. Finally, the ratio between the number of EV batteries and charging modules will get the minimum about 2:1. Considering EVs are still in the developing stage, it is more feasible to select an optimal solution from the economy preferred solutions. The parameter of energy reserve time is set to guarantee the availability of battery swapping service. The value has a significant influence on economic benefits. It is sufficient to set the energy reserve time as 3 h for the BSS in the case. Acknowledgments
Fig. 17. Influence of energy reserve time on the marginal electricity price (Select tr as 3 h, 5 h and 7 h respectively).
This work is supported by the Key Project of the National Research Program of China (No. 2011BAG02B14) and the National Natural Science Foundation of China (No. 51277067).
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment Nian Liu*, Zheng Chen, Jie Liu, Xiao Tang, Xiangning Xiao, Jianhua Zhang School of Electrical and Electronic Engineering, North China Electric Power University, Beinong Road 2#, Changping District, 102206 Beijing, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 June 2013 Received in revised form 28 October 2013 Accepted 30 October 2013 Available online xxx
With the rapid development of EVs (electric vehicles), the integration of PV (photovoltaic) generation with EV charging infrastructure can effectively improve the efficiency of clean energy utilization and carbon emission reduction. How to optimize the capacities of components in the PV-based BSS (battery switch stations) is still unsettled. This paper focuses on the mathematical model of the problem. With consideration of battery swapping requirement and maximally utilizing PV energy, an energy exchange strategy is introduced for the PV-based BSS, including battery swapping service model and power distribution model. Towards benefits of economy and environment, objective functions of capacity optimization are modeled with the purpose of minimizing annual cost and maximizing the percentage of utilized PV energy in total energy. The constraints include the construction scale, power balance and battery swapping service etc. Based on the energy exchange strategy, the optimization model is solved by NSGA-II algorithm. Finally, taking the planning of a PV-based BSS in a certain district as example, optimized capacities of PV panels, EV batteries, EV chargers and grid-connected modules can be obtained. From the analysis of the results, the method can provide a foundation for the plan and design of the PV-based BSSs. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Battery switch station Capacity optimization Energy exchange strategy Photovoltaic generation
1. Introduction In the transport sector, EV (electric vehicles) have been regarded as a type of environmentally friendly vehicles. It has been established as an effective way to promote the development of EVs to realize low-carbon economic transition and ensure energy security by many countries. However, EVs need to be connected to the electric power grid for charging and there are still many barriers remaining to be considered. Firstly, according to the prior studies, the indirect emissions of EVs are sensitive to the generation mix of a particular region’s electric power system [1e4]. If the power generation of the grid is dominated by coal-fired power plants, the emission advantage for EVs is not obvious. Secondly, with large scale use of EVs, it will need more investment on the capacities of generation, transmission and distribution due to the boosting charging requirements of EVs. As a renewable and clean energy, solar PV (photovoltaic) can be produced anywhere, including the urban areas for EV applications. The direct integration of PV with EV charging infrastructure can be a suitable way to effectively improve * Corresponding author. Tel.: þ86 10 80790940; fax: þ86 10 51971652. E-mail address: [email protected] (N. Liu).
the emission reduction of EVs and reduce the dependence on the power grid [5e9]. There have been many studies on the integration of PV with EV charging facilities. The technical feasibility of directly charging vehicle batteries with solar PV panels is provided in Refs. [7,8]. These two studies provide a proof of concept for this approach, demonstrating the safety and viability of this charging scheme. The idea that solar PV arrays built over parking lots to provide daytime charging for commuter vehicles is proposed in Ref. [6], which broadly sketches out what such a system would look like and assesses the potential energy production from a single parking space. A system with bidirectional, highly efficient, DC/DC EV charger placed between the high-voltage DC bus of a PV inverter and EV battery is presented in Ref. [5]. The system partially alleviates the overload of distribution system feeder by providing EV batteries with fast charging. In addition, the charger is capable of diverting fast changes in the PV output to the battery. Similarly, a concept of bi-directional battery charger for PHEV/EV with PV system and related algorithms are proposed in Ref. [10]. In order to integrate PHEV (plug-in hybrid vehicles) with an existing residential PV system, an approach for the control and optimization of power flow is proposed in Ref. [11]. With PHEVs serving as an energy storage
0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.10.090
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Nomenclature EV PV EVB BSS PUPT Nevba(t) Pr Ps(t) Pdc Pdc2(t) Pdc2a Pac Pevb(t) Pevbm(t) Pevbn(t) Pevbe(t)
electric vehicle photovoltaic electric vehicle battery battery switch station percentage of utilized PV energy in total energy number of swapping available EV batteries at time t rated power of a PV cell (KW) output power of PV arrays at time t (KW) rated power of a single DC/DC module charging power of MOD2 at time t average charging power of MOD2 for a whole cycle T rated power of a single AC/DC module charging power of EVB system at time t maximum charging power of EVB system at time t newly-added charging power at time t existing charging power at time t
unit, the integrated system provides flexible and efficient control of power flow with the coordination of PCU (power conditioning unit) and controller. Similarly, a residential PV system for PHEV load is designed in Ref. [12]. A power management algorithm is introduced to control the power flow between the grid and EV battery according to load profile. In order to maximize the use of solar and wind energy in transportation, a stochastic optimization algorithm, which may eventually be used by electric energy suppliers to coordinate charging of EDVs (electric-drive vehicles), is presented in Ref. [13]. Summarizing the aforementioned studies, most of them focus on the systems that integrate PV with EV battery chargers. Related control strategies and evaluations are proposed to prove the feasibility of the system. To promote the development of EVs, it is necessary to build infrastructures that can charge EVs in a short time. BSS (battery switch station) is one of the solutions to this problem [14e16], in which the automated switch platform will replace the depleted batteries with fully-charged batteries. The depleted batteries will be placed in a storage room and recharged to be available for other drivers [17]. Consequently, this paper mainly concentrates on the plan and design of the integrated system of PV and BSS. Before the construction of a PV-based BSS, it needs to design the electrical structure of the system and determine the capacities of primary components including PV panels, EV batteries, DC/DC EV chargers and grid-connected AC/DC modules. Generally, considering the solar irradiation, temperature and EV battery swapping requirements in a specific area, the capacities of the components should be suitable to provide enough fully-charged batteries for swapping service. On the basis of service availability, the construction cost of the system is the primary problem to be considered by investors. Besides, in order to reduce the emission, the PUPT (percentage of utilized PV energy in total energy) should be advanced as far as possible. However, the benefits between economy and environment are always contradictory. An economic and environmental analysis model for EVs operated under different conditions is proposed in Ref. [18], and the feasibility of the model is also tested using case studies. If we want to reduce the emission, more PV panels need to be purchased, and more EV batteries should be reserved due to the solar irradiance intermittency. Although the electricity purchased from the power grid is reduced, the total investment will inevitably increase in the additional cost of PV panels and EV batteries.
Pevbr(t) Pg(t) Wevb Wevba(t)
required power of EVB system power supplied by power grid at time t rated energy capacity of a single EV battery (kWh) electric energy of the swap available EV batteries at time t Wevbn(t) electric energy of newly fully charged EV batteries at time t Wevbt(i) capacity of EVB system to be complemented at year i(kWh) Wev ðtÞ energy exchange demand during period [t, t þ 1] Wevbr ðt; tr Þ energy reserve demand of EVB system within a certain period tr in the future at time t h1 energy conversion efficiency of MOD1 h2 energy conversion efficiency of MOD2 hac(t) energy conversion efficiency of MOD3 ht(t) energy conversion efficiency of transformers tr energy reserve time for EVB system
For the above reasons, this paper proposes a multi-objective capacity optimization approach for the components of the PVbased BSS, which includes the benefits of economy and environment as two objectives to be optimized. The content of this paper is organized as follows. Section 2 describes the system structure and function of the components of the PV-based BSS. In Section 3, an energy exchange strategy is introduced. Section 4 establishes a mathematical model for capacity optimization, aiming at minimizing system annual cost and maximizing PUPT. In Section 5, problem solving process of the multi-objective capacity optimization model is introduced. Case study and related analysis of results are presented in Section 6. Finally, conclusions are given in Section 7. 2. System structure and function of the PV-based BSS 2.1. System structure The PV-based BSS system established in this paper is mainly composed of PV system, EVB system, grid-connected system and central control system (see Fig. 1). 2.2. Function of system components 1) PV system is composed of PV arrays and related DC/DC modules (abbreviation as MOD1). PV arrays, composed of PV cells in series and parallel, convert solar energy directly into electric energy, connecting to the DC bus through MOD1. And the maximum power generated by PV arrays has a fixed relationship with the rated power of MOD1. Define h1 as the energy conversion efficiency of MOD1; Vmpp as the PV cell voltage at the maximum power point; Impp as the PV cell current at the maximum power point; Tc as the operating temperature of PV cells ( C); GT as the hourly irradiance on a tilted surface (W/m2); Pr as the rated power of a PV cell; Npvs as the number of PV cells in series, which is determined by both the range of operating voltage of MOD1 and Vpmp; Npvp as the number of PV cells in parallel, and its value determines the total rated capacity of PV arrays; Ps(t) as the output power of PV arrays at time t, details of the calculation can be acquired from Ref. [19]. So there is:
Tc ¼ f1 ðNOCT; Ta ; GT Þ
(1)
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Fig. 1. System structure.
Vmpp ; Impp ¼ f2 ðVoc ; Isc ; Vmax ; Imax ; Tc Þ
(2)
Wevb ¼ h2 $
ZtþT Pdc2 ðtÞdt
(6)
t
Ps ðtÞ ¼ f3 h1 ; Vmpp ; Impp ; Npvs ; Npvp ; 0 Ps ðtÞ < Pr Npvs Npvp (3) where NOCT (normal operating cell temperature) is usually between 42 C and 46 C; Ta is the ambient temperature of the location area; Voc means the open circuit voltage of PV cell; Vmax means the maximum voltage of PV cell at the reference operating conditions; Isc means the short circuit current of PV cell; Imax means the maximum current of PV cell at the reference operating conditions. 2) EVB system is composed of EV batteries and related DC/DC modules (abbreviation as MOD2). The PV-based BSS provides fullycharged EV batteries for EVs. The replaced EV batteries will be placed in a storage room and recharged to be available for other drivers. Therefore, for EV batteries of the BSS, some are on the EVs while the others are at the station. Define h2 as the energy conversion efficiency of MOD2; Nevb as the total number of EV batteries; Nevbs as the number of EV batteries at the station; Nevbc as the number of EV batteries being charged; Nevbv as the number of EV batteries on the EVs.
Nevb ¼ Nevbs þ Nevbv
(4)
Nevbs Nevbc
(5)
During the whole charging cycle T, each EV battery should be charged by only one MOD2. Define Pdc as the rated power of a single MOD2; Pdc2(t) as the charging power of MOD2 at time t; Wevb as the rated energy capacity of an EV battery (kWh).
The charging power may be not constant during the charging cycle. From the battery side, a conventional lithium-ion battery charging is characterized by two main phases: constant current and constant voltage. Recently, constant power charging became popular in large vehicle battery packs [20]. Hence, if the constant power charging is used, the charging power will be unchanged. If the conventional charging method is utilized, the charging power of an EV battery is time-vary according to the SOC (state of charge) [21,22]. The SOC mainly increases in the period of constant-current, which takes up most of the time of charging process. Besides, the charging power changes with a small increase in this period. Therefore, to simplify the calculation, this paper uses the average charging power Pdc2a to describe the demand for charging of an EV battery.
Pdc2a ¼ ðWevb =TÞ=h2
(7)
Therefore, the charging power of the EVB system at time t can be described as:
Pevb ðtÞ ¼ Nevbc $Pdc2a
(8)
3) The grid-connected system is mainly composed of transformers and related AC/DC modules (abbreviation as MOD3). Transformers are used to transform the electric energy from the grid into the energy that matches the operating voltage of MOD3. MOD3 are used as the components that transmit the power from the grid to the system by converting AC to DC. Define ht(t) and hac(t) as the energy conversion efficiency of transformers and MOD3; Pg(t) as the power supplied by the power grid at time t; Pac as the rated power of a single MOD3. As the efficiency of transformers ht(t)
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and efficiency of AC/DC inverters hac(t) are not constant and vary by the load rate, their variations are provided in Figs. 2 and 3 respectively. 3. Energy exchange strategy of the PV-based BSS 3.1. Basic principles The main load of the BSS is the EV batteries waiting to be recharged, which are removed from EVs and placed in a storage room. During the operation, there are two basic principles that need to be followed. One is the PV-based BSS should provide the battery swapping service for EVs all the time. The other is, in order to reduce the carbon emissions of EVs, EVB system should be charged by the PV system as much as possible. Only when the PV system cannot meet the charging demand of EVB system, would the charging power of EV batteries be conditionally supplied by the power grid. Consequently, the system energy exchange strategy can be divided into battery swapping service model and power distribution model. Fig. 3. Efficiency curve of AC/DC converters.
3.2. Battery swapping service model This model mainly describes the variation of the electric energy of swapping available EV batteries Wevba(t), while taking a series of factors into consideration, including the effect of newly fullycharged batteries and swapped batteries as well as a certain amount of energy reserve requirement. At time t, the electric energy of swapping available EV batteries can be determined by the number of swapping available EV batteries as:
Wevba ðtÞ ¼ Nevba ðtÞWevb
(9)
Considering the effect of newly fully-charged batteries and swapped batteries, the variation of electric energy of swapping available EV batteries can be described as:
Wevba ðt þ 1Þ ¼ Wevba ðtÞ Wev ðtÞ þ Wevbn ðt þ 1Þ Wevba ðt þ TÞ ¼ Wevba ðtÞ
tþT1 X
s¼t
Wev ðsÞ þ
tþT X
s ¼ tþ1
Wevbn ðsÞ
should have a certain amount of energy reserve besides meeting the current energy demand for battery swapping. It means the EV batteries should meet the battery swapping demand for an additional period tr in the future. And there is:
Wevbr ðt; tr Þ ¼
tþðt r 1Þ X
s¼t
Wev ðsÞ
Wevba ðtÞ Wevbr ðt; tr Þ
(12)
(13)
Relations of variables in the battery swapping service model are illustrated in Fig. 4. 3.3. Power distribution model
(10) (11)
Considering the availability of battery swapping service and forecasting errors of battery swapping demand, the EVB system
This model dynamically determines the charging power of EVB system Pevb(t) and the power supplied by the power grid Pg(t), according to the electric energy of swapping available EV batteries Wevba(t) and the output of PV system Ps(t). 3.3.1. Relations of variables in power distribution model According to the number of EV batteries waiting for charging, the maximum charging power of the EVB system at time t Pevbm(t) can be described as:
Pevbm ðtÞ ¼ ðNevbs Nevba ðtÞÞ$Pdc2a
(14)
At time t, the EV batteries being charged can be classified into two parts: ones that start to be charged at time t and the others that start before time t but haven’t completed charging. It means the EVB system’s charging load contains the newly-added charging load Pevbn(t) and existing charging load Pevbe(t). So there is
Pevb ðtÞ ¼ Pevbn ðtÞ þ Pevbe ðtÞ
(15)
where Pevbe(t) has a fixed relationship with Pevbn(t):
Pevbe ðtÞ ¼
Fig. 2. Efficiency curve of transformers.
t 1 X
s ¼ tTþ1
Pevbn ðsÞ
(16)
The electric energy of newly fully charged EV batteries at time t þ T Wevbn(t) can be expressed by the newly-added charging power at time t as:
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Fig. 4. Relations of variables in the battery swapping service model.
Wevbn ðt þ TÞ ¼ Pevbn ðtÞ$T
(17)
3.3.2. Process of power distribution According to the battery swapping model, the following formula should be guaranteed:
Wevba ðt þ TÞ Wevbr ðt þ T; tr Þ
(18)
For Wevba(t þ T), Wevbn(t þ T) is controllable to achieve the goal of battery swapping service (see formula (9)), which can be adjusted by setting the number of EV batteries that start charging at time t based on the lack of energy. To be specific, there are two conditions.
power grid. The required power of EVB system Pevbr(t) can be calculated by the lack of energy and charging cycle T.
Pevbr ðtÞ ¼
Wevbr ðt þ T; tr Þ Wevba ðtÞ þ
tþT1 X
s¼t
!, Wev ðsÞ
tþT1 X
s ¼ tþ1
Wevbn ðsÞ
T
If the energy reserve requirement can be met by the PV system independently, it means that the remaining power is still greater than the required power of the EVB system Pevbr(t):
Ps ðtÞ$h1 $h2 Pevbe ðtÞ Pevbr ðtÞ 3.3.2.1. EVB system can meet the energy reserve requirement.
Wevba ðtÞ þ
tþT1 X
s ¼ tþ1
Wevbn ðsÞ
tþT1 X
s¼t
Wev ðsÞ Wevbr ðt þ T; tr Þ
In this case, EV batteries are charged by the PV system independently. To utilize the output power of PV system as much as possible, the number of EV batteries to be charged should be determined by the output power of PV system and the maximum charging power of EVB system. Consequently, the charging power of EVB system can be expressed as:
(21)
(22)
In this case, there is no need to purchase any electric energy from the power grid. Besides, the energy generated by the PV system should be utilized to the greatest extent. It will follow the same power distribution rule as the above condition, shown in (19) and (20). Additionally, there is a precondition for this case:
Pevbm ðtÞ Pevbe ðtÞ Pevbr ðtÞ
(23)
And there is no need to purchase any electric energy from the power grid.
which means the EV batteries waiting to be charged at the station should be abundant all the time. However, if the energy reserve requirement cannot be met by the PV system independently, it means that the output power of the PV system is less than the sum of existing charging power Pevbe(t) and required power Pevbr(t), that is:
Pg ðtÞ ¼ 0
Ps ðtÞ$h1 $h2 Pevbe ðtÞ < Pevbr ðtÞ
Pevb ðtÞ ¼ minðPevbm ðtÞ; Ps ðtÞ$h1 $h2 Þ
(19)
(20)
3.3.2.2. EVB system cannot meet the energy reserve requirement.
Wevba ðtÞ þ
tþT1 X
s ¼ tþ1
Wevbn ðsÞ
tþT1 X
s¼t
Wev ðsÞ < Wevbr ðt þ T; tr Þ
In this case, the lack of energy should be compensated immediately. In order to utilize PV energy as much as possible, the output power of PV system should be given priority to charge EV batteries. And the remaining energy demand should be supplied by the
(24)
In this case, it is necessary to purchase electricity from the power grid. The charging power of EVB system should be the sum of Pevbe(t) and Pevbr(t). The power purchased from the power grid should be the difference between the charging power of EVB system and the output power of PV system.
Pevb ðtÞ ¼ Pevbe ðtÞ þ Pevbr ðtÞ
(25)
Pg ðtÞ ¼ ðPevb ðtÞ Ps ðtÞ$h1 $h2 Þ=ðh2 $ht ðtÞ$hac ðtÞÞ
(26)
Flow chart of the energy exchange strategy is shown in Fig. 5.
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Fig. 5. Flow chart of energy exchange strategy.
of the PV system, EV batteries, MOD1, MOD2, MOD3, transformers and electricity purchased from the grid.
4. Mathematical model of capacity optimization 4.1. Objective functions
4.1.1.1. Annual cost of PV system. To achieve the maximum benefits of economy and environment, it is supposed to minimize the system annual cost and maximize PUPT. Details about these two objective functions are given as follows. 4.1.1. System annual cost The objective function of the system annual cost is constructed as follows.
min C ¼ Cs þ Cevb þ Cdc1 þ Cdc2 þ Cac þ Cd þ Cg
(27)
where C is the system total annual cost of the PV-based BSS; Cs, Cevb, Cdc1, Cdc2, Cac, Cd and Cg respectively represent the total annual cost
Cs ¼ aPr Npvs Npvp
r0 ð1 þ r0 Þm þ u Npvp ð1 þ r0 Þm 1
(28)
where a is the unit price of PV cells (RMB/kW); u(Npvp) is the annual maintenance and operation cost of the PV system; m is the system lifetime; r0 is the discount rate. 4.1.1.2. Annual cost of EV batteries. The total cost of EV batteries can be divided into three parts: 1) initial cost of purchasing EV batteries for the construction of the PV-based BSS; 2) additional cost of EV batteries used for complementing the capacity of eliminated
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batteries due to their lower-than-normal capacity [23,24]; 3) annual maintenance and operation cost of the EV batteries.
Cevb ¼
bWevb Nevb þ
m cW P evb Nevb þ bWevbt ðiÞ i¼1
!
ð1 þ r0 Þi
r0 ð1 þ r0 Þm þ uðNevb Þ ð1 þ r0 Þm 1
(29)
where b is the unit price of EV batteries (RMB/kWh); c is the unit cost of the capacity test (RMB/kWh); Wevbt(i) is the capacity of EV batteries to be complemented at year i (kWh); u(Nevb) is the annual maintenance and operation cost of EV batteries. 4.1.1.3. Annual cost of MOD1 and MOD2.
r0 ð1 þ r0 Þm þ uðNdc1 Þ ð1 þ r0 Þm 1
(30)
r0 ð1 þ r0 Þm þ uðNdc2 Þ ð1 þ r0 Þm 1
(31)
Cdc1 ¼ dNdc1
Cdc2 ¼ eNdc2
where d and e are unit price of MOD1 and MOD2 (RMB/10 kW); Ndc1 and Ndc2 are the number of modules in MOD1 and MOD2; u(Ndc1) and u(Ndc2) are the annual maintenance and operation cost of MOD1 and MOD2. 4.1.1.4. Annual cost of MOD3.
Cac ¼ fNac
r0 ð1 þ r0 Þm þ uðNac Þ ð1 þ r0 Þm 1
(32)
where f is the unit price of MOD3 (RMB/10 kW); Nac is the number of modules in MOD3; u(Nac) is the annual maintenance and operation cost of MOD3. 4.1.1.5. Annual cost of grid-connected system.
Cd ¼ gSta Nt
r0 ð1 þ r0 Þm þ uðNt Þ ð1 þ r0 Þm 1
(33)
where g is the unit price of transformers (RMB/kVA); Nt is the number of transformers; Sta is the rated apparent power of a transformer (kVA); u(Nt) is the annual maintenance and operation cost of transformers. 4.1.1.6. Annual cost of
Cg ¼
8760 X
cg ðtÞPg ðtÞDt
purchasing electricity from
the grid.
(34)
t ¼1
where cg(t) is the unit price of electricity (RMB/kWh); Dt is the time interval. 4.1.2. The percentage of utilized PV energy in total energy (PUPT) PUPT is determined by the utilized PV energy and the total charging energy of the EVB system. The objective function is constructed as:
P8760 max PUPT ¼
t¼1
P Pevb ðtÞ$Dt=h2 ht ðtÞhac ðtÞ 8760 t ¼ 1 Pg ðtÞ$Dt P8760 t ¼ 1 Pevb ðtÞ$Dt=h2 (35)
7
4.2. Constraints 4.2.1. Constraints on the external parameters and the construction scale Npvp, Nevb, Ndc1, Ndc2, Nac and Nt are the decision variables of the capacity optimization model that need to be solved out. The number of PV cells is restricted by the limited area of the PV-based BSS. Besides, the number of EV batteries, converters and transformers shall be given an appropriate upper limit according to the battery swapping demand, thereby narrowing the search scale for the optimal solution.
0 Npvp Npvp:max 0 Nevb Nevb:max 0 Ndc1 Ndc1:max 0 Ndc2 Ndc2: max 0 Nac Nac: max 0 Nt Nt: max
(36)
4.2.2. Operation constraints 4.2.2.1. Additional constraints on decision variables. According to the results of the power distribution model, it is necessary to add constraints to the number of converters and transformers.
Pdc Ndc1 Pr Npvs Npvp
(37)
Pdc Ndc2 maxðPevb ðtÞÞ=h2
(38)
Pac Nac ht ðtÞmax Pg ðtÞ
(39)
Sta Nt max Pg ðtÞ ðcos 4$gÞ
(40)
where cos4 and g are the power factor and load rate of transformers respectively. 4.2.2.2. Constraints on system power balance. The charging power of EVB system is supposed to be equal to the sum of the output power of PV system and the power supplied by the power grid all the time. Consequently, the following equality constraint should be satisfied.
Pevb ðtÞ=h2 ¼ Ps ðtÞ$h1 þ Pg ðtÞ$ht ðtÞ$hac ðtÞ
(41)
4.2.3. Constraints on battery swapping service The number of EV batteries available for swapping is supposed to be less than the total amount of EV batteries at the station, that is
0 Nevba ðtÞ Nevbs
(42)
According to formula (23) introduced in the power distribution model, it should be ensured that the EV batteries waiting to be charged are abundant at any time. Therefore, further constraint is described as
ðNevbs Nevba ðtÞÞ$Pdc2a Pevbe ðtÞ þ Pevbr ðtÞ
(43)
5. Problem solving process of the capacity optimization model According to the capacity optimization model, the problem needed to be solved can be expressed as:
ðmin C; max PUPTÞ ¼ fc Npvp ; Nevb ; Ndc1 ; Ndc2 ; Nac ; Nt
(44)
This capacity optimization model is a nonlinear multi-object optimal problem containing several decision variables. NSGA-II
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algorithm is used to solve this type of problems [25e27]. Specific solving process of this capacity optimization model is shown in Fig. 6. During the process, the primary difficulties are the calculation of objective functions, including system annual cost and PUPT. For any PV-based BSS, the data listed as follows are needed before calculating the objective functions: 1) statistical data of a whole year’s solar radiation and the temperature of the area that BSS plans to be located; 2) forecasting data of daily battery swapping demand for EVs that BSS will serve for; 3) specific parameters of the components in the BSS, such as unit price, lifetime, efficiency curve and rated power etc.; 4) upper and lower limit for each decision variable given the battery swapping demand and location area of the BSS. The specific calculation process is introduced as follows.
3) Calculate the electric energy of swapping available EV batteries at time t þ 1, according to formula (10) in the battery swapping model. 4) Let t ¼ t þ 1, repeat 1)e3) until all the charging power and purchased power of the EVB system for the whole year are calculated. 5) Check the constraints on the decision variables by (37)e(40), and correct the variables that fail to satisfy the constraints. 6) Calculate the capacity that needs to be complemented by the EVB system within the planning years m, named as Wevbt(i), according to the limited charging cycles of EV batteries (i ¼ 1,2,.,m). 7) Calculate the system annual cost and PUPT by (27)e(35).
1) Calculate the output power of PV system Ps(t), according to the statistical data of a whole year’s solar radiation, temperature and the number of PV cells in parallel Npvp. 2) Calculate the charging power of EVB system Pevb(t) and the power purchased from the power grid Pg(t) based on the power distribution model.
6. Case study 6.1. Study object and basic data Take the planning of PV-based BSS in a certain district (north latitude 32 460 ) as an example to optimize its capacity. Solar
Fig. 6. Flow chart of solving the optimization model based on NSGA-II.
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radiation and temperature of typical days are shown in Figs. 7 and 8 respectively. In the future, the main types of EVs can be divided into buses, taxis, commuter vehicles and private cars. Therefore, energy demand for battery swapping can be analyzed according to the above four types. Suppose the number of EVs provided battery swapping service by the BSS is 100 and the number of buses, taxis, commuter vehicles and private cars are 5, 10, 10 and 75 respectively. And the corresponding rated energy capacities of EV batteries are 72 kWh, 48 kWh, 24 kWh and 24 kWh. EV batteries used in taxis and buses can be considered to be formed by two and three EV batteries with rated energy capacity of 24 kWh. Based on the investigation and forecasting, the energy demand for battery swapping for workdays and holidays is shown in Fig. 9. The unit price of electricity can be divided into three levels according to the peak, flat and valley period of the day, as shown in Table 1. The values of parameters of the components used in the system are listed in Table 2. It is noted that the prices of components are based on the data offered by the public or inquiry from the manufacturers in China. These prices may not be equal in different countries, using for research only. Fig. 8. Variation of temperature of typical days.
6.2. Analysis of optimal solutions 6.2.1. Pareto optimal solutions Pareto front and its extreme solutions obtained by NSGA-II are shown in Fig. 10 and Table 3, respectively. As shown in Fig. 10, the result of the Pareto front provides abundant information for mutual compromise between economic and environmental benefits. Each point in the Pareto front corresponds to a fixed value of system annual cost and PUPT. This means that each point represents a definite capacity optimization solution. Moreover, it can be clearly seen from the figure that, advisable solutions can be divided into economy preferred solutions (0e43.83%) and environment preferred solutions (43.83%e95%). Once PUPT exceeds 95%, the cost will increase dramatically, which is not advisable. If designer emphasizes on the economic benefits, they can set a smaller value of system annual cost and then get the correspond value of PUPT. Likewise, if the priority is given to the utilization of renewable energy resources, the higher PUPT will be their choice. Therefore, there are a number of optimal solutions derived from the multi-objective optimization method. In the actual design for PV-based BSS, the final “optimal” solution can be chosen following the expectation of the BSS owner and designer. For example, if 10%, 50% and 80% of PUPT are expectations for different designers, the
Fig. 7. Variation of solar radiation of typical days.
related closest optimal solutions can be selected, as show in Table 4. Finally, BSS owner and designer can make a reasonable and suitable decision with the flexible scheme.
6.2.2. Variations of the capacities of system components The relations between the capacities of system components and PUPT are shown in Fig. 11. It can be seen that the rated power of PV system and MOD1 increase with the augment of PUPT. The rated power of MOD1 is determined by the lower limit of the number of modules in MOD1 ðPse ðqÞNpvs Npvp =Pdc Þ, mentioned in the additional constraints on the decision variables, shown as formula (45).
Pdc Ndc1 Pr Npvs Npvp
(45)
For EVB system, EV batteries have to play the role in balancing the system power as there is no other type of batteries dedicated to store energy. After meeting certain charging demand of EVB
Fig. 9. Daily energy demand for battery swapping in the PV-based BSS.
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Table 1 Unit price of electricity. Levels
Time period
Unit price of purchasing electricity (RMB/kWh)
Peak level Flat level Valley level
7:00e11:00, 19:00e23:00 11:00e19:00 23:00e7:00 (next day)
0.0225 0.0140 0.0057
system, the excess power of PV system will increase with the augment of PUPT. Therefore, to balance the increasing excess power, the rated capacity of EVB system will inevitably increase. According to the additional constraints on the decision variables, the lower limit of the number of modules in MOD2 ðmaxðPe Þ=ðh2 $Pdc ÞÞ is determined by the maximum charging power of EVB system Pevbm(t). When PUPT is small, it means the PV system cannot meet the charging demand independently. Hence, purchasing electricity from the power grid is required. In this case, Pevbm(t) is determined by the energy reserve requirement which is only related to tr. Therefore, the rated power of MOD2 remains unchanged. When PUPT increases to a certain extent, Pevbm(t) is determined by the output power of PV system. Therefore, the rated power of MOD2 increases. Finally, there are three quantified results can be obtained. 1) With the variation of PUPT, the rated power of PV system keeps almostly the same with the rated power of MOD1. 2) When PUPT is smaller than 43.83%, the number of EV batteries versus the number of charging modules is about 4.8:1. When PUPT gets lager than 43.83%, this ratio became lower and it will get the minimum 2:1 with PUPT reaching 100%. 3) When PUPT is smaller than 43.83%, the ratio between the rated power of PV system and MOD2 keeps growing from 0 to 1.56:1. When PUPT exceeds this point, this ratio decreases and its minimum can reach 1.23:1.
6.2.3. Analysis of system power distribution In order to better analyze the effectiveness of the power distribution model, an optimal solution (PUPT is 79.90%, system annual cost is 7.5253 106 RMB) is selected from the Pareto front. The distribution of the output power of the PV system, utilized power of the PV system, charging power and purchased power of EVB system for the two typical days in summer and winter is shown in Fig. 12. Several conclusions can be obtained from the results. 1) The charging power of EVB system is satisfied by both the supply of the PV system and the power grid.
Table 2 System parameter values.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
System parameters
Values
unit price of PV cells lifetime of PV cells (system lifetime) rated power capacity of DC/DC modules unit price of DC/DC modules efficiency of DC/DC modules self-discharge rate of EV batteries rated energy capacity of EV batteries unit price of EV batteries rated power capacity of AC/DC modules unit price of AC/DC modules rated capacity of transformers unit price of transformers power factor of transformers load rate of transformers
7000 (RMB/kW) 20 years 10 kW 8000 (RMB/10 kW) 97% 0.0001 24 kWh 120,000 (RMB/kWh) 10 kW 25,000 (RMB/10 kW) 400 kVA 120,000 (RMB/kVA) 0.95 0.6
Fig. 10. Pareto front obtained by NSGA-II.
2) During the daytime with adequate sunshine, the output of the PV system is utilized to a great extent. It can independently satisfy the charging demand of EVB system. Reserved fullycharged EV batteries can even satisfy the battery swapping demand at night. So there is no need to get any electricity from the power grid till midnight. Purchasing electricity from the grid only occurs after midnight due to insufficient energy reserve and lower electricity price. 3) With larger radiation intensity and longer duration of sunshine, the output energy of the PV system in summer is larger than that in winter. At the same time, the difference between summer and winter in the charging power of EVB system is small. Therefore, PUPT in summer is smaller than that in winter.
6.2.4. Analysis of the energy of EVB system The energy of EVB system can be analyzed from the same optimal solution used in the analysis of system power distribution. For the same time period, the distribution of the energy demand for battery swapping, energy reserve requirement and storage energy of EVB system are shown in Fig. 13. It can be noted that the storage energy of EVB system is always more than the energy demand for battery swapping and no less than the energy reserve requirement. Hence, EVB system can satisfy the energy demand for battery swapping all the time. At night without any power generated by the PV system, the charging power is supplied by the power grid independently. At this time, the energy storage just needs to satisfy the energy reserve requirement when the economic benefits are considered. During the daytime with adequate solar energy, the charging power is mainly supplied by the PV system. To improve PUPT, the energy storage is far more than the energy reserve requirement at night. 6.2.5. Variation of marginal electricity price for battery swapping Considering the development of PV-based BSS, its profitability should also be given adequate attention. The price should not only
Table 3 Extreme solutions in Pareto optimal set. System annual cost (RMB) Minimum system annual cost Maximum PUPT
6
6.0444 10 1.0503 107
PUPT (%) 0 99.88
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
N. Liu et al. / Energy xxx (2013) 1e14 Table 4 System capacity optimization solutions for different PUPT (Select PUPT as 10.39%, 50.08 %and 79.90% respectively). PUPT
Name
Optimization results
Rated energy
10.39%
Number of PV cells in parallel Number of EVBs Number of DC/DC modules 1 Number of DC/DC modules 2 Number of AC/DC modules Number of transformers System annual cost Number of PV cells in parallel Number of EVBs Number of DC/DC modules 1 Number of DC/DC modules 2 Number of AC/DC modules Number of transformers System annual cost Number of PV cells in parallel Number of EVBs Number of DC/DC modules 1 Number of DC/DC modules 2 Number of AC/DC modules Number of transformers System annual cost
40 173 13 36 37 2 6.1303 106 (RMB) 199 180 62 40 37 2 6.5980 106 (RMB) 317 220 98 76 37 2 7.5253 106 (RMB)
123 kW 4152 kWh 130 kW 360 kW 370 kW 800 kVA e 610 kW 4320 kWh 620 kW 400 kW 370 kW 800 kVA e 974 kW 5280 kWh 980 kW 760 kW 370 kW 800 kVA e
50.08%
79.90%
ensure the profit of operators, but also help reduce EV users’ expenditure compared to using internal-combustion-engine vehicles [28]. Therefore, the electricity price related to PUPT should be properly determined. Define the electricity price that ensures profitability for a certain PUPT as marginal electricity price. Based on the Pareto optimal solutions, the marginal electricity price for each PUPT is obtained. The relation between marginal electricity price and PUPT is shown in Fig. 14. From the result, we can find out that the growth rate of the marginal price is relatively lower when PUPT varies from 0 to 43.83%. In contrast, the growth rate of the marginal price is much higher when PUPT varies from 43.83% to 100%. Therefore,
11
considering the economic reasons, it is more feasible to select an optimal solution with PUPT no more than 43.83%. The result is consistent with the turning point of Pareto optimal solutions. 6.2.6. Influence of energy reserve time on capacity optimization The energy reserve time tr directly influences the energy reserve requirement of EVB system, thereby the system capacity optimization. To analyze the specific influence of tr on the system capacity optimization, tr is taken as 3 h, 5 h and 7 h respectively. 6.2.6.1. Comparison of the Pareto optimal solutions. Based on the results of capacity optimization for different energy reserve time, related Pareto front can be obtained, shown as Fig. 15. It can be found that system annual cost increases with the augment of tr. It is because the augment of tr will make the rated capacity of EVB system increase, inevitably leading to the augment of system annual cost. 6.2.6.2. Comparison of the capacities of system components. Rated capacities of system components for different tr are shown in Fig. 16. It can be seen that tr mainly influences the rated capacity of EVB system and MOD2. For EVB system, its rated capacity increases with the augment of tr, which directly determines the energy reserve requirement. For MOD2, its rated power is determined by the maximum charging power of EVB system Pevbm(t). When PUPT is small, Pevbm(t) is mainly related to tr. As a result, the rated power of MOD2 increases with the augment of tr. When PUPT gets larger to a certain extent, Pevbm(t) is determined by the rated power of the PV system, which has little to do with tr. Consequently, the rated power of MOD2 is basically the same for different tr. 6.2.6.3. Comparison of marginal electricity price. The relation between marginal electricity price and energy reserve time tr is shown in Fig. 17. It can be seen that the marginal electricity price
Fig. 11. Relations between the capacities of system components and PUPT.
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
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N. Liu et al. / Energy xxx (2013) 1e14
Fig. 12. System power distribution for the two days randomly selected in summer and winter respectively.
Fig. 13. System energy distribution for the two days randomly selected in summer and winter respectively.
increases with the increase of tr. And the variations of the marginal prices under different reserve time have common increase rules. The parameter of energy reserve time is set to guarantee the availability of battery swapping service. According to the
aforementioned results, the value of the energy reserve time will have a significant influence on the economic benefits. Hence, considering hourly energy status of the EVB system, it is sufficient to set the energy reserve time at 3 h for the BSS in this case study.
Fig. 14. Relation between marginal electricity price and PUPT.
Fig. 15. Influence of energy reserve time on the Pareto front (Select tr as 3 h, 5 h and 7 h respectively).
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
N. Liu et al. / Energy xxx (2013) 1e14
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Fig. 16. Influence of energy reserve time on the capacities of system components (Select tr as 3 h, 5 h and 7 h respectively).
7. Conclusions The contribution of this paper is mainly on a multi-objective capacity optimization method for the components of the PVbased BSS, including the PV system, DC/DC converters, AC/DC converters, transformers and EV batteries. For an actual design of
PV-based BSS, there are a number of optimal solutions can be derived, which are divided into economy preferred and environment preferred solutions. The final scheme for capacities of components can be chosen following the expectation of the BSS owner and designer. By the analysis of case study, some interesting results have been obtained. There is an apparent turning point (PUPT ¼ 43.83%) between the solutions of economy preferred and environment preferred. For the economy preferred solutions, the rated power of the PV system keeps growing with the increase of PUPT. The number of EV batteries and charging modules remains unchanged (the ratio is about 4.8:1), which mainly depends on the battery swapping demand. For the environment preferred solutions, the rated power of the PV system still keeps growing with the increase of PUPT. However, in order to maximally utilize the energy of PV system, the number of EV batteries and charging modules deployed in the BSS also increases. Finally, the ratio between the number of EV batteries and charging modules will get the minimum about 2:1. Considering EVs are still in the developing stage, it is more feasible to select an optimal solution from the economy preferred solutions. The parameter of energy reserve time is set to guarantee the availability of battery swapping service. The value has a significant influence on economic benefits. It is sufficient to set the energy reserve time as 3 h for the BSS in the case. Acknowledgments
Fig. 17. Influence of energy reserve time on the marginal electricity price (Select tr as 3 h, 5 h and 7 h respectively).
This work is supported by the Key Project of the National Research Program of China (No. 2011BAG02B14) and the National Natural Science Foundation of China (No. 51277067).
Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090
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Please cite this article in press as: Liu N, et al., Multi-objective optimization for component capacity of the photovoltaic-based battery switch stations: Towards benefits of economy and environment, Energy (2013), http://dx.doi.org/10.1016/j.energy.2013.10.090