applied sciences Article
Modeling and Solving Method for Supporting ‘Vehicle-to-Anything’ EV Charging Mode Tian Mao 1, * 1 2
*
ID
, Xin Zhang 2 and Baorong Zhou 1
State Key Laboratory of HVDC, Electric Power Research Institute, China Southern Power Grid, Guangzhou 510663, China;
[email protected] School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;
[email protected] Correspondence:
[email protected]; Tel.: +86-186-6469-7058
Received: 29 May 2018; Accepted: 13 June 2018; Published: 27 June 2018
Abstract: Electric vehicles (EVs) are an attractive solution to make traditional transportation energy-efficient and environmentally friendly. EVs are also considered an important element to bring new opportunities for power grids. In addition to the role of a pure load, along with the development of discharging technology for batteries, EVs can deliver energy back to power grids or another power consumption entity or community, performing various discharging activities such as vehicle-to-home (V2H), vehicle-to-building (V2B), vehicle-to-vehicle (V2V), vehicle-to-grid (V2G), etc. These charging scenarios can be uniformly named the ‘Vehicle-to-anything’ (V2A) charging mode. The paradigm of this charging mode has already been given; however, the modeling and solving approaches are still insufficient. Therefore, the analysis and modeling of V2A are investigated herein. The aim is to propose a generic model suitable for different applications of V2A in different places. The characteristics of the V2A charging mode are given and analyzed first. Then a model that can adapt to the V2A scenario is illustrated. The optimization problem is transformed and solved as an INLP (integer nonlinear programming) problem. The effectiveness of the approach is verified with simulation results. The outcome also indicates that V2A applications have great potential for lowering power consumption costs; for instance, a reduction of 4.37% in energy expense can be achieved in a case study with EV discharging enabled for a household. Keywords: charging; discharging; electric vehicle; INLP; vehicle-to-anything
1. Introduction Electric vehicles (EVs) are an attractive transportation option that provides appealing benefits by reducing the use of fossil fuels with high energy efficiency and combatting CO2 emissions. As an alternative to traditional petrol or diesel vehicles, EVs are now receiving unprecedented interest from numerous users, investors, and countries [1,2]. According to a recent report on the global electric car stock, worldwide sales of EVs have hit a new record with over 0.75 million in 2016 and the transition to electric road transport is likely to keep growing over the coming decades [3]. The fast development of EVs has also attracted researchers into power systems. EVs should rely on power grids in procuring energy for voyage support. To accommodate the charging of EVs, certain infrastructures such as charging stations, a communication link, and a control interface and system must be developed or implemented. The penetration of massive EVs will also challenge the operation of the power system, since the additional load of EV charging may potentially amplify the daily peak of power load curve and induce some adverse impacts including voltage drops, frequency oscillations, power congestion [4,5], etc.
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Besides the load impact, it is also expected that an EV can direct energy back into the power grid by utilizing the discharging activity of the EV battery. This envisaged technology is well known as Vehicle-to-Grid (V2G) technology [6]. With V2G enabled, EVs can act as moving energy banks, capable of procuring energy from the power grid and also injecting energy back when necessary. Therefore, the power flow of V2G can be unidirectional (charging only) or bidirectional [7], and EV owners have the opportunity to earn extra profit through charging their cars at low-price time slots while selling energy back to power grid during periods with high power prices. The discharging ability also enables EVs to participate in other various charging/discharging activities such as home energy management (V2H, Vehicle-to-Home) [8], building energy management (V2B, Vehicle-to-Building) [9], and charging station energy management (V2V, Vehicle-to-Vehicle). In essence, these discharging behaviors are operated to compensate for the power demand from other loads, thus achieving the optimization of energy consumption and operational costs for certain power consumption entities or communities (home, building, charging station, residential area, and so on). The above EV discharging activities, including V2H, V2B, V2V, and V2G, can be uniformly named the ‘Vehicle-to-anything’ (V2A) charging mode [10]. In [10], a thorough discussion of V2A scenarios is given, including the challenges and opportunities involved in this technology. To support the various charging/discharging activities of V2A, communication infrastructures and technologies are needed for essential information exchange [11,12]. In addition, it is also advised to develop and apply the ‘Vehicle-to-anything’ app for EV energy management [13]. Previous studies gave some basic concepts/future expectations of V2A [10–13], or only focused on the partial application of this charging mode (V2H, V2G, or V2B) [8,9], while the modeling and supporting approach for a more comprehensive utilization of V2A technology is still insufficient. In order to support the V2A scenarios, its charging activities are investigated. The aim herein is to develop a solving model that can adapt to V2A technology. The main contributions of this work lie in: (1) (2)
(3)
Based on basic findings of V2H, V2B, V2V, and V2G, all the applications of V2A are considered and a generic model that can adapt to V2A is proposed; Besides the consideration of EV charging satisfaction for EV user, battery degradation that can affect EV charging/discharging behaviors is also considered in the model through the evaluation via battery charging/discharging cycles; In the proposed model, each of the EV behaviors (including the status of charging, V2H, V2B, V2V, and V2G) is assigned a single Boolean vector and the created model is then transformed into an INLP (integer nonlinear programming) problem. An intelligent module with treatment for easing the calculated variables is also designed to guide the optimization for different applications of V2A.
The remaining paper is organized as follows: the paradigm of V2A charging mode is presented in Section 2. The modeling and solving approach is described in Section 3. Then the simulation results to verify the model and solving approach are illustrated in Section 4. The conclusions are given in Section 5. 2. V2A Charging Mode Due to the inherent mobility of vehicles, the charging activities of EV customers are hard to predict. EV owners can choose to park their cars in private garages when they return home, in their company charging places during weekdays, or in commercial parking stations for traveling purposes, to procure energy to refill EV batteries. When EVs are connected to the power grid, the power grid provides a channel for griddable EVs to perform ‘Grid-to-vehicle’ (G2V) charging. With the discharging capability enabled in the near future, EVs are also envisaged to perform various V2A activities, including V2H, V2B, V2V, and V2G. An overview of the V2A paradigm is given in Figure 1. The demonstrated architecture consists of a power grid operator, smart home, smart building, charging
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system elements. EVs are parked in different places and can be controlled to perform various discharging activities, in detail: V2H for home usage, V2B for building energy management, V2V station, AC transmission link, otherinbasic power system elements. EVs are among different EVs in EVcommunication charging station, channel, and V2G and arranged different places. parked inAll different places and can be controlled to perform various discharging activities, in detail: the power consumption/supply units are supervised by the grid operator, which depends V2H for usage, of V2B for building energy management, V2V among different EVs in EV charging on home the support bidirectional communications. The details of the V2A charging mode are Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 16 introduced below. station, and V2G arranged in different places. system elements. EVs are parked in different places and can be controlled to perform various discharging activities, in detail: V2H for home usage, V2B for building energy management, V2V among different EVs in EV charging station, and V2G arranged in different places. All the power consumption/supply units are supervised by the grid operator, which depends on the support of bidirectional communications. The details of the V2A charging mode are introduced below.
Figure1.1.Overview Overview of Figure of V2A V2Aparadigm. paradigm.
2.1. V2H Charging Scenario
All the power consumption/supply units are supervised by the grid operator, which depends When an EV needs power refilling, the most convenient approach for EV users to recharge their on the support of bidirectional communications. The details of the V2A charging mode are cars is to connect EVs to home private charging piles. Meanwhile, it is assumed that EV and the introduced below.
other household appliances (e.g., air conditioner, washing machine, etc.) are all managed and Figure 1. Overview of V2ASystem). paradigm.Under this condition, V2H can be controlled through a HEMS (Home Energy Management 2.1. V2H Charging Scenario operated. V2H refers to the power compensation from the EV battery to other home loads, e.g., air 2.1. V2H Scenario conditioner, machine, water heater, and convenient so on, as shown in Figure EV users owners choose their When anCharging EVwashing needs power refilling, the most approach for2.EV tocan recharge to perform V2H in response to price variations; for instance, they can charge their cars when theother cars is to connect to home private charging piles. Meanwhile, it isfor assumed that EV and their the When anEVs EV needs power refilling, the most convenient approach EV users to recharge power price is low and discharge their cars during high-price time slots. In this manner, EV users cars is appliances to connect EVs to air home private charging piles. Meanwhile, is assumed that EV the household (e.g., conditioner, washing machine, etc.)itare all managed andand controlled can achieve the goal of paying(e.g., less for bills. washing machine, etc.) are all managed and other household appliances airenergy conditioner,
through a HEMS (Home Energy Management System). Under this condition, V2H can be operated. controlled through a HEMS (Home Energy System). Under thisloads, condition, can be V2H refers to the power compensation from Management the EV battery to other home e.g., V2H air conditioner, operated. V2H refers to the power compensation from the EV battery to other home loads, e.g., air washing machine, water heater, and so on, as shown in Figure 2. EV owners can choose to perform conditioner, washing machine, water heater, and so on, as shown in Figure 2. EV owners can choose V2H in response to price variations; for instance, they can charge their cars when the power price is to perform V2H in response to price variations; for instance, they can charge their cars when the low and discharge their cars during high-price time slots. In this manner, EV users can achieve the power price is low and discharge their cars during high-price time slots. In this manner, EV users goal of bills. canpaying achieveless the for goalenergy of paying less for energy bills.
Figure 2. Paradigm of V2H.
Figure 2. Paradigm of V2H.
Figure 2. Paradigm of V2H.
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Generally, V2H V2H endows endows EV EV with with the the following following features: features: (1) (1) V2H V2H typically typically involves involves only only one one Generally, EV for a single house; (2) V2H can help reduce household power consumption bills; (3) V2H can EV for a single house; (2) V2H can help reduce household power consumption bills; (3) V2H can smooth the thedaily daily load profile a single family; (4)can V2H can with interact with the utilization of smooth load profile of a of single family; (4) V2H interact the utilization of household household distributed power resources, thus improving the energy efficiency of a house; (5) since distributed power resources, thus improving the energy efficiency of a house; (5) since a household isa a basic forcan a gird, V2H can the alsodevelopment enhance the of development of the smart grid. ahousehold basic unit is for a gird,unit V2H also enhance the smart grid. 2.2. V2B V2B Charging Charging Scenario Scenario 2.2. V2B isisdefined definedasasthe the energy transfer of EV battery to a building, a building in a V2B energy transfer of EV battery to a building, e.g., ae.g., building locatedlocated in a school school or a company, for supporting its internal loads [9], as shown in Figure 3. Through V2B, the or a company, for supporting its internal loads [9], as shown in Figure 3. Through V2B, the operation operation cost of the managed building can be lowered. Meanwhile, as a countermeasure, V2B can cost of the managed building can be lowered. Meanwhile, as a countermeasure, V2B can be arranged to be arranged to mitigate themismatch potentialbetween power day-ahead mismatch scheduling between day-ahead scheduling energy mitigate the potential power energy demand and real-time demand and real-time power consumption [14]. power consumption [14].
Figure 3. 3. Paradigm Paradigm of of V2B. V2B. Figure
EV users can perform V2B when they park their cars in a smart garage of a single building; this EV users can perform V2B when they park their cars in a smart garage of a single building; charging mode is attractive in several aspects: (1) V2B can help facilitate the participation of this charging mode is attractive in several aspects: (1) V2B can help facilitate the participation of buildings in demand side management; to be more specific, it can reduce the on-peak load of buildings in demand side management; to be more specific, it can reduce the on-peak load of buildings buildings through load shifting operation; (2) V2B can be operated for emergency backup purposes, through load shifting operation; (2) V2B can be operated for emergency backup purposes, to generate to generate power for power restoration of buildings when outage management is needed; (3) power for power restoration of buildings when outage management is needed; (3) besides the energy besides the energy regulation of buildings, V2B also provides extra profit for EV owners; (4) V2B is regulation of buildings, V2B also provides extra profit for EV owners; (4) V2B is simpler than V2G, simpler than V2G, and is regarded as a more near-term alternative to V2G [9]. and is regarded as a more near-term alternative to V2G [9]. 2.3. V2V Charging Scenario 2.3. V2V Charging Scenario V2V means the energy transaction among different EVs at an EV aggregator, an EV charging V2V means the energy transaction among different EVs at an EV aggregator, an EV charging station, or a community [10,15]. In Figure 4, the V2V operation of an EV charging station is station, or a community [10,15]. In Figure 4, the V2V operation of an EV charging station is demonstrated. All EVs can interact with each other, controlled by the centralized controller demonstrated. All EVs can interact with each other, controlled by the centralized controller deployed deployed by the charging station. The charging station acts as an aggregator and is responsible for by the charging station. The charging station acts as an aggregator and is responsible for the group the group coordination of EV charging/discharging. The energy of EVs can be first distributed coordination of EV charging/discharging. The energy of EVs can be first distributed among each other, among each other, and then can be arranged to interact with the power grid for overall energy and then can be arranged to interact with the power grid for overall energy demand procurement. demand procurement. Through the adoption of V2V, the power energy reserve within an aggregator or community can be maintained, which can offload the power demand from the power grid to the aggregated area. The application of V2V can bring the following benefits: (1) V2V can help coordinate the energy consumption within a community, thus facilitating the coordination of EVs and the power
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grid; (2) the execution of V2V involves very few power transmission losses; (3) with V2V operation, the charging efficiency of EVs can be greatly improved, while the power demand of a community can also be offloaded; (4) V2V can facilitate the utilization of renewable energy resources within a community the development of the smart grid. Appl. Sci. grid 2018, 8,and x FOR PEER REVIEW 5 of 16 Distribution network
Grid operator AC Link
Information link
V2 G
EV
V2
Charging station
V
EV
V 2V
EV
V2
V2 G
EV
EV Charging
Charging
V
EV
EV
Figure 4. Paradigm of V2V.
Figure 4. Paradigm of V2V.
Through the adoption of V2V, the power energy reserve within an aggregator or community
2.4. V2G Scenario can Charging be maintained, which can offload the power demand from the power grid to the aggregated area. The application of V2V can bring the following benefits: (1) V2V can help coordinate the V2G signifies the discharging power released from EVs to the power grid, as shown in Figure 5. energy consumption within a community, thus facilitating the coordination of EVs and the power The given framework consists of residential households, a battery swapping station, distributed grid; (2) the execution of V2V involves very few power transmission losses; (3) with V2V operation, renewable energy resources, an EV charging station, smart buildings, smart home, and other essential the charging efficiency of EVs can be greatly improved, while the power demand of a community powercan grid Based practical applications and voltage levels,energy the energy distribution alsoelements. be offloaded; (4) on V2V can facilitate the utilization of renewable resources within a can be categorized clusters [10]: of thethe first cluster communityinto grid three and the development smart grid. performs charging/discharging for EVs at low-voltage networks such as at home or building parking lots; the second cluster implements 2.4. V2G Charging Scenario EV charging/discharging at charging stations, particularly for fast power exchange of EVs at medium-voltage networks; the thirdpower cluster is EV from batteries are swapped at battery swapping V2G signifies the discharging released EVs tothat the power grid, as shown in Figure 5. stations discharged batteries are collectively recharged. It should be noted that the third role Thewhile giventhe framework consists of residential households, a battery swapping station, distributed energy resources, an EV charging station, smart buildings, smart home, and other is notrenewable advised for V2G operation. essential power grid elements. applications and voltage levels, energy The discharging capability of aBased singleon EV,practical however, is normally limited due to itsthe small capacity. distribution be potential categorizedof V2G, into athree the coordinated first cluster and performs To explore the fullcan storage groupclusters of EVs [10]: is usually governed charging/discharging for EVs at low-voltage networks such as at home or building parking lots; the through an internal agent, e.g., an EV charging station or an EV aggregator [16]. The EV user can second cluster implements EV charging/discharging at charging stations, particularly for fast power choose an aggregator for V2G participation via signing a contract, while the aggregator can obtain exchange of EVs at medium-voltage networks; the third cluster is EV batteries that are swapped at regulation revenues through incentives offered by the power operators. recharged. A thorough battery swapping stationsthe while the discharged batteries are collectively It review should of be V2G can benoted found in [6] and the opportunities offered by V2G are briefly summarized below: that the third role is not advised for V2G operation. (1) V2G be operated in various places, residential areas,limited commercial The can discharging capability of a single EV, e.g., however, is normally due to parking its small lots, and work places, as displayed in Figure 5; (2) of with V2G participation of massive EVs, adequate capacity. To explore the full storage potential V2G, a group of EVs is usually coordinated and an internalfor agent, e.g., an EV charging station(3) or V2G an EVactivity aggregator The EV to powergoverned supply through can be provided a power regulation service; has [16]. the potential userthe canpower choosestability, an aggregator forefficiency, V2G participation via signing a contract, while aggregator can improve energy and reliability of power grids; (4)the V2G can be arranged obtain regulation revenues through the incentives offered by the power operators. A thorough to coordinate with distributed renewable energy resources; (5) V2G is considered an important element review of V2G can be found in [6] and the opportunities offered by V2G are briefly summarized for the realization of smart grid. below: The above activities constitute the paradigm of the V2A charging mode. Based on the above (1) V2G can be operated in various places, e.g., residential areas, commercial parking lots, and introduction, a single EV can perform activities depending the parking places,power normally: work places, as displayed in Figuredifferent 5; (2) with V2G participation of on massive EVs, adequate (1) G2V, V2H, and V2G at home; (2) G2V, V2B, and V2G in building garages; (3) G2V, V2V, and V2G at supply can be provided for a power regulation service; (3) V2G activity has the potential to improve a commercial the powercharging stability,station. energy efficiency, and reliability of power grids; (4) V2G can be arranged to coordinate with distributed renewable energy resources; (5) V2G is considered an important element for the realization of smart grid.
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The above activities constitute the paradigm of the V2A charging mode. Based on the above introduction, a single EV can perform different activities depending on the parking places, normally: (1) G2V, V2H, and V2G at home; (2) G2V, V2B, and V2G in building garages; (3) G2V, 6 of 16 Appl. Sci. 2018, 8, 48 V2V, and V2G at a commercial charging station.
Figure 5. 5. Paradigm Figure ParadigmofofV2G. V2G.
3. Modeling for V2A Charging Mode
3. Modeling for V2A Charging Mode
The aim of this paper is to develop a generic model that can support the various charging The aim ofofthis paper is to develop a generic model can support the various charging activities activities V2A applications. Therefore, all thethat charging statuses, including charging, of V2A applications.and Therefore, all the charging statuses, including charging,for V2H/V2B/V2V, and V2H/V2B/V2V, V2G should be determined at each timeslot. Meanwhile, the development of V2G the be proposed model, at theeach following assumptions are used: The EV vehicles studied pure EVs; should determined timeslot. Meanwhile, for(1) the development of the are proposed model, (2) reactiveassumptions power exchange not considered at the currentstudied stage; (3)are thepure price EVs; for EV(2) charging and the following areisused: (1) The EV vehicles reactive power other loads is different from the V2G power price for incentive purposes [17], i.e., the power load exchange is not considered at the current stage; (3) the price for EV charging and other loads is different price ϑL,t and the V2G power price ϑV2G,t are two different price signals; (4) the charging/discharging from the V2G power price for incentive purposes [17], i.e., the power load price ϑL,t and the V2G power is assumed to be the rated power of the EV battery. power price ϑV2G,t are two different price signals; (4) the charging/discharging power is assumed to In addition, EV charging decisions must be given on the basis of predefined objectives. In this be the rated power the EV battery. work, the powerofconsumers are supposed to be price followers, i.e., EVs or the load consumption In addition, EV charging be given on theto basis predefined objectives. In this unit would make decisions decisions about EV must charging in response priceofsignals released by power work, the power consumers are supposed to be price followers, i.e., EVs or the load consumption system operators.
unit would make decisions about EV charging in response to price signals released by power 3.1.operators. Constraints system Other than charging for a whole day, an EV usually completes its power refilling within a
3.1. Constraints certain period, while its charging/discharging should be subject to constraints from both user power
demand andcharging battery technical limitations: Other than for a whole day, an EV usually completes its power refilling within a certain
period, its charging/discharging should be subject to constraints from both user power demand (1) while Constraint of battery SOC (State-of-charge) and battery technical limitations: i Soc Soc i Soc i Soc i t ST ，i SE EV ,min
(1)
EV , t
EV ,max
(1)
EV
Constraint of battery SOC (State-of-charge) SociEV,min ≤ SociEV,t ≤ SociEV,max ≤ SociEV ∀t ∈ ST, ∀i ∈ SE SociEV,t = SociEV,tstart +
−
t i PEV ∑ i ηdi CEV t=t
t i ηci PEV ∑ i CEV t=t
Si,c EV,t
start
i,dV2V i,dV2G (Si,dV2H + Si,dV2B EV,t EV,t + S EV,t + S EV,t ),
start
i s.t. t, tstart ∈ TEV
(1)
(2)
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where SociEV,min and SociEV,max are typically set to 20% and 90% to prolong the lifetime of the EV battery [18]; ST is normally set to 24 with a one-hour time resolution for a whole day; and SE is usually set to 1 for a single household. (2)
Energy requirement from EV user
The charging activity of a single EV during its charging period should satisfy the energy desire of the EV user for traveling purposes: SociEV,t
−
end
= SociEV,tstart +
tend i PEV ∑ i ηdi CEV t=t
tend i ηci PEV ∑ i CEV t=t
Si,c EV,t
start
(3)
i,dV2V i,dV2G (Si,dV2H + Si,dV2B EV,t EV,t + S EV,t + S EV,t )
start
i s.t. tend ∈ TEV
SociEV,tend − SociEV,exp ≤ ∆, ∆ → 0+ .
(3)
(4)
Constraint for EV charging statuses
The charging and discharging of an EV cannot contradict each other. Namely, at each time slot, EV should be idling, charging, or in one of the V2A discharging activities, i.e., ( Si,c EV,t
(4)
+ Si,dV2H EV,t
+ Si,dV2B EV,t
+ Si,dV2V EV,t
+ Si,dV2G EV,t
=
0 1
idling . either charging or discharging
(5)
Consideration of the lifetime of the EV battery
To prolong the lifetime of the EV battery, the charging degradation should also be considered, and it can be quantified through EV charging/discharging cycles [19]: i2 h i,disC i,disC i,c Γi = (Si,c EV,t+1 − S EV,t+1 ) − ( S EV,t − S EV,t )
(6)
i,dV2G i,dV2V i,dV2H + Si,dV2B Si,disC EV,t + S EV,t + S EV,t , EV,t+1 = S EV,t
(7)
where Si,disC EV,t denotes the discharging status of the ith EV. (5)
Constraint for special charging conditions
Under the condition of V2V charging scenario, the number of EVs transferring energy to other vehicles must be equal to the number of EVs procuring energy from other cars. This indicates that the number of EVs performing the charging activity should be no less than the number of EVs performing the V2V activity at each timeslot, i.e., i,c i,dV2V ∑ SEV,t − ∑ SEV,t ≥ 0.
i∈SE
(8)
i∈SE
3.2. Objective Function The optimization goal for EV charging is to minimize the running costs of a power consumption unit (i.e., a home or a building), or maximize the profit of a power operation unit (e.g., an EV aggregator). The objective function of the above target can be given as: min
F (U ) = ∑ Pb,t ϑL,t t∈ TB
+ ∑
i,c i − Si,dV2H Pi − Si,dV2B Pi − Si,dV2V Pi ) ϑ ∑ (SEV,t PEV EV EV EV L,t EV,t EV,t EV,t
i∈SE t∈ T i
EV
− ∑
∑
i∈SE t∈ T i
EV
i SidV2G EV,t PEV ϑV2G,t
.
(9)
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For the final EV charging state limited by the energy desire from EV users, the constraint Equation (4) can be added to Equation (9) with an additional penalty function; the consideration Equation (6) for EV battery life can be also handled with the above method [17,19]. Then the objective function changes to: 2
min G(U ) = F (U ) + ∑ ρi (SociEV,t − SociEV,exp ) end i ∈SE h i2 i,c i,disC i,disC , + ∑ λi (SEV,t+1 − SEV,t+1 ) − (Si,c − S ) EV,t EV,t
(10)
i ∈SE
s.t. constraints (1), (2), (3), (5), (7), (8)
where ρi denotes the penalty coefficient for EV charging satisfaction quantified through the deviation of final SOC state from the desired SOC; λi represents the penalty coefficient for EV battery degradation quantified through EV charging/discharging cycles. In addition, the following limit should be guaranteed to ensure that the discharging power of V2H, V2B and V2V will not pour into the power grid: i,dV2H i i,dV2B i i,dV2V i i Pb,t + ∑ (Si,c EV,t PEV − S EV,t PEV − S EV,t PEV − S EV,t PEV ) > 0 .
(11)
i t∈ TEV
3.3. Problem Transformation and Solving Method For the above EV charging model, only the charging and discharging statuses are waiting to be solved. Therefore, the charging/discharging statuses are assigned as variables, with five Boolean state vectors attributed to the charging, V2H, V2B, V2V, and V2G statuses, respectively, for a single EV. Meanwhile, the constraints for EV charging are nonlinear. Based on existing studies, the proposed model can be transformed into the INLP (Integer Nonlinear Programming) optimization form [20,21], which can be expressed as: subject to :
minimize Fobj ( x ), Heq ( x ) = beq Gieq ( x ) ≤ bieq , lb ≤ x ≤ ub x∈Z
(12)
where Fobj ( x ) represents the objective goal; Heq ( x ) denotes the equal constraints constrained by the value set beq ; Gieq ( x ) signifies the unequal constraints with limit set bieq ; lb and ub denote the bounded lower and upper box constraints for x; and vector x should be subject to integer space Z. Taking all five Boolean state vectors into account, the computational effort for the INLP model would be enormous. For example, there would be 5 × 24 variables for a single EV. To ease the calculation burden, the variables for an EV can be preprocessed at the initialization stage. The control signals outside the EV charging period can be set to 0 to reduce the solved variables, as shown in Figure 6. Moreover, some variables can be predetermined based on practical charging scenarios. Specifically, all the discharging variables can be set to 0 when discharging activity is forbidden, while the state variables for V2H, V2B, and V2V can be partially determined based on the charging places discussed in Section 2. Since there are different charging places involved, an intelligent module is designed to guide the optimization for different applications of V2A, as displayed in Figure 7. The datasets including market prices, parking places, EV data, preference for charging/discharging activities in the charging location, and other essential information are collected at the initial stage. Based on the data obtained, the charging and V2A choices are determined, and the optimization problem is transformed into an INLP model, which will then be solved to finalize the solutions of charging/discharging statuses for the penetrated EV(s). It should be noted that the combinations of charging/discharging behaviors for different occasions can be adjusted based on practical demands.
the charging and V2A choices are determined, and the optimization problem is transformed into an location, and which other essential collected the initial Based on the data obtained, INLP model, will theninformation be solved toare finalize the at solutions of stage. charging/discharging statuses for the charging and V2A It choices andcombinations the optimization problem is transformed into an the penetrated EV(s). shouldare bedetermined, noted that the of charging/discharging behaviors INLP model,occasions which will then be solvedbased to finalize the solutions of charging/discharging statuses for for different can be adjusted on practical demands. the penetrated EV(s). It should be noted that the combinations of charging/discharging behaviors scheduling problem can be solved through many kinds of algorithms and tools; in this Appl. Sci.The 2018,EV 8, 48 9 of 16 for different occasions can be adjusted based on practical demands. work, the optimization tool CVX [22] is utilized to work out the solutions of EV charging. The EV scheduling problem can be solved through many kinds of algorithms and tools; in this work, the optimization tool CVX [22] is utilized to work out the solutions of EV charging.
Figure 6. Treatment for control variables of a single EV. Figure 6. Treatment for control variables of a single EV. Figure 6. Treatment for control variables of a single EV.
Figure 7. Optimization process for different V2A applications. Figure 7. Optimization process for different V2A applications. 4. Simulation Cases Figure 7. Optimization process for different V2A applications.
In this work, the model of V2A is given, which includes four discharging activities: V2H, V2B, 4. Simulation Cases V2V, For illustration, the charging for amany household, andand a commercial Theand EV V2G. scheduling problem can be solvedcases through kinds aofbuilding, algorithms tools; in this In this work, the model ofThe V2Aproposed is given, charging which includes four discharging activities: V2H, V2B, parking station are presented. model is coded and studied on a work, the optimization tool CVX [22] is utilized to work out the solutions of EV charging.MATLAB V2V, and V2G. For illustration, the charging cases for a household, a building, and a commercial platform. parking station are presented. The proposed charging model is coded and studied on a MATLAB 4. Simulation Cases platform. In this work, the model of V2A is given, which includes four discharging activities: V2H, V2B, V2V, and V2G. For illustration, the charging cases for a household, a building, and a commercial parking station are presented. The proposed charging model is coded and studied on a MATLAB platform.
4.1. Basic Parameters The EVs simulated are supposed to be private vehicles with unified capacity of 24 kWh and nominal charging power of 3.3 kW. The charging and discharging efficiency are all set to 0.98.
4.1. Basic Parameters The EVs simulated are supposed to be private vehicles with unified capacity of 24 kWh and nominal charging power of 3.3 kW. The charging and discharging efficiency are all set to 0.98. Furthermore, as EV users may arrive and depart the charging piles at random times, their charging Appl. Sci. 2018, 8, 48 10 of 16 behaviors should be predicted. Based on existing studies, the charging pattern of EVs can be captured through some stochastic methods [23,24]. In this work, Truncated Gaussian Distribution Furthermore, EV users the maycharging arrive andactivities depart theofcharging piles at random times, theirof charging [23,24] is used toassimulate EV customers, with the ranges initial and behaviors should be predicted. Based on existing studies, the charging pattern of EVs can be expected SOC values given in Table 1. Moreover, for the household case, the EV captured charging is through some stochastic methods [23,24]. In this work, Truncated Gaussian Distribution [23,24] is assumed to be performed during the night due to home user working/living habits [8]; for the used to simulate the charging activities of EV customers, with the ranges of initial and expected SOC building and charging station scenarios, EVs are supposed to park during the daytime, with ranges values given in Table 1. Moreover, for the household case, the EV charging is assumed to be performed of plugging-in and unplugging times displayed in Table 1. In addition, the penalty coefficients ρi during the night due to home user working/living habits [8]; for the building and charging station and scenarios, λi are uniformly set to 1.5 to and 0.15 for the caseswith in Sections to 4.4. For the evaluation of EVs are supposed park during the test daytime, ranges of4.2 plugging-in and unplugging battery degradation, 4.5addition, is giventhe to penalty simulate the influences penalty coefficients ρi and λi times displayed in Section Table 1. In coefficients ρi and λof i are uniformly set to 1.5 and on EV charging/discharging. 0.15 for the test cases in Section 4.2 to Section 4.4. For the evaluation of battery degradation, Section 4.5 is given to simulate the influences of penalty coefficients ρi and λi on EV charging/discharging. Table 1. Simulation parameters. Table 1. Simulation parameters.
Parameter Parameter tstart range of EV tendtstart range ofofEV range EV i of EV end range SoctEV,t (range) i i Soc EV,tstart (range) Soc EV,exp (range) SociEV,exp (range) i SocEV,min i start
Soc EV,min
Value [8:00,Value 15:00] [13:00, [8:00, 22:00] 15:00] [13:00,0.65] 22:00] [0.2, [0.2, 0.65] [0.6, 0.95] [0.6, 0.95] 0.2 0.2
Parameter i Parameter SocEV,max i i (kW) PSoc EV EV,max i i (kW) CPEVEV(kWh) i (kWh) i CEV ηic ηci ηid ηd
Value Value 0.9 3.3 0.9 3.3 24 24 0.98 0.98 0.98 0.98
The simulated EV numbers for the test building and charging station are set at 5 and 10, The simulated EV numbers for the test building and charging station are set at 5 and 10, respectively. The test signals for the power load price ϑL,t and the V2G power price ϑV2G,t are given in respectively. The test signals for the power load price ϑL,t and the V2G power price ϑV2G,t are given Figure 8. As stated before, the two price signals are differentiated for incentive purposes of EV in Figure 8. As stated before, the two price signals are differentiated for incentive purposes of EV charging/discharging activity in inresponse loadprofiles profiles[17]. [17]. Meanwhile, charging/discharging activity responseto to power power load Meanwhile, the the two two priceprice vectors are just presupposed forfor testing purpose, prices are arefixed fixedvalues. values.As Ascan can be vectors are just presupposed testing purpose,which whichmeans means the the prices seen,bethere two priceprice periods (11:00–13:00 and L,t to mitigate the seen,are there arehigh-power two high-power periods (11:00–13:00 and18:00–20:00) 18:00–20:00) for for ϑ ϑL,t to mitigate morning and evening peak loads; there is one period (17:00–21:00) with high ϑ V2G,t to motivate the morning and evening peak loads; there is one period (17:00–21:00) with high ϑV2G,t motivate EV EV discharging since the power demand the evening canheavy be heavy to increased residentialloads discharging since the power demand in theinevening can be duedue to increased residential loads (cooking, lighting, air conditioning, etc. when people return home after work) [25]. In addition, the (cooking, lighting, air conditioning, etc. when people return home after work) [25]. In addition, basicfor loads the household, the building, charging stationare arepresented presented in basicthe loads the for household, the building, andand thethe charging station in Figure Figure9.9.
Figure forsimulation. simulation. Figure8.8.Price Price signals signals for
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Figure 9. Basic load profiles for simulation: left axis for the building and household load; right axis Figure 9. 9. Basic Basic load loadprofiles profiles for simulation: left axis for the building and household load; right axis Figure for the charging station load.for simulation: left axis for the building and household load; right axis for for the charging station load. the charging station load.
4.2. Simulation Results for the Household 4.2. Simulation Results for the Household 4.2. Simulation Results for the Household The optimization goal for the EV charging of a household is to optimize the energy The optimization goal for the EV charging of a household is to optimize the energy The optimization goalelectricity for the EV charging a household tominimized. optimize theThe energy management management so that the cost of the of home user canisbe EV is set to plug management so that the electricity cost of the home user can be minimized. The EV is set to plug so that electricity of the canthe be minimized. The EV is setFor to plug into the power grid into thethe power grid cost during thehome nightuser when EV user returns home. comparison, a scenario into the power grid during the night when the EV user returns home. For comparison, a scenario during night when returns home.isFor comparison, scenario where discharging of the where the discharging of the theEV EVuser is not allowed also simulated.a The simulation outcome for where discharging of the EV is not allowed is also simulated. The simulation outcome for the EV is not allowed also simulated. The simulation outcome for the household is given in Figure 10. household is givenisin Figure 10. household is given in Figure 10.
Figure 10. Outcome for the EV management of the household: (a) load details with discharging; (b) Figure 10. Outcome Outcomefor forthe theEV EVmanagement managementofof the household: load details with discharging; Figure 10. the household: (a) (a) load details with discharging; (b) load details without discharging; basic household load refers to the household load without EV load (b) load details without discharging; basic household load refers to the household load without EV load details without discharging; basic household load refers to the household load without EV load profile; the optimized load profile refers to the basic household load plus the aggregated EV load profile; the optimized profile refers basichousehold householdload loadplus plus the the aggregated aggregated EV profile; the optimized loadload profile refers to to thethe basic EV charging/discharging result based on the proposed model. charging/discharging result based based on on the the proposed proposed model. model. charging/discharging result
According to the results, for the case of EV charging with discharging ability permitted, in According to the results, for the case of EV charging with discharging ability permitted, in response to the price signals, the EV is arranged to perform charging for power refilling during response to the price signals, the EV is arranged to perform charging for power refilling during lower price timeslots (i.e., 16:00–17:00, and 2:00–4:00) while choose to discharge for V2G when the lower price timeslots (i.e., 16:00–17:00, and 2:00–4:00) while choose to discharge for V2G when the
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According to the results, for the case of EV charging with discharging ability permitted, in response to the price signals, the EV is arranged to perform charging for power refilling during lower price Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 16 timeslots (i.e., 16:00–17:00, and 2:00–4:00) while choose to discharge for V2G when the V2G price is Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 16 attractive (at 21:00) and perform V2H when the load price is high (during the time period 18:00–20:00). V2G price is attractive (at 21:00) and perform V2H when the load price is high (during the time This EV charging/discharging is smartly regulated on theisprice In addition, V2G demonstrates price is attractive 21:00) and perform V2H when the based load price hightuples. (during period 18:00–20:00). This(atdemonstrates EV charging/discharging is smartly regulated basedthe ontime the the power consumption costs for the household are 101.09 p. u. and 105.71 p. u., respectively, with and period 18:00–20:00). This demonstrates EV charging/discharging is smartly regulated based on the price tuples. In addition, the power consumption costs for the household are 101.09 p. u. and 105.71 without EV discharging, indicating a reduction costs of 4.37% in household energy expense withp.V2A enabled. price tuples. In addition, the power consumption for the are 101.09 u. and 105.71 p. u., respectively, with and without EV discharging, indicating a reduction of 4.37% in energy This that thewith discharging activity can help minimize the overall powerofconsumption cost p. u.,proves respectively, and without indicating a can reduction 4.37%the in overall energy expense with V2A enabled. This provesEV thatdischarging, the discharging activity help minimize of the household. expense with V2A enabled. Thishousehold. proves that the discharging activity can help minimize the overall power consumption cost of the The energy statecost for of thethe EVhousehold. battery is demonstrated in Figure 11. As demonstrated, the energy power consumption The energy state for the EV battery is demonstrated in Figure 11. As demonstrated, the energy desire of the home user is the well achieved without SOC bound violations. The above outcome indicates energy state batterywithout is demonstrated in Figure 11. As energy desireThe of the home userfor is wellEV achieved SOC bound violations. Thedemonstrated, above outcomethe indicates that the charging model can smartly support EV charging/discharging activities for home usage. desire the home user can is well achieved without SOC bound violations. The above outcome indicates that theofcharging model smartly support EV charging/discharging activities for home usage. that the charging model can smartly support EV charging/discharging activities for home usage.
Figure 11. Energy state of the managed EV. Figure 11. Energy state of the managed EV. Figure 11. Energy state of the managed EV.
4.3. Simulation Results for the Building 4.3. Simulation Results Results for for the 4.3. Simulation the Building Building The simulation outcome for EV management of the building is given in Figure 12. As The outcome EV EV management of theofbuilding is givenisingiven Figurein12.Figure As presented, The simulation simulation outcomefor for management thecompensate building As presented, EVs are managed to perform V2B activity to for the daily load 12. of the EVs are managed to perform V2B activity to compensate for the daily load of the building at the time presented, EVs are managed to perform V2B activity to compensate for the daily load of the building at the time slots 11:00–13:00 and 19:00–20:00. It is also observed that no V2G activity is slots 11:00–13:00 and slots 19:00–20:00. It is and also 19:00–20:00. observed that noalso V2G activity isthat organized during the building atduring the time 11:00–13:00 It is no of V2G is organized the simulated time window. The reason is thatobserved the load profile theactivity building simulated time window. The reason is that the load profile of the building during the daily time when organized during thewhen simulated time window. The reasonhigh. is that the load in profile of the building during the daily time EVs are connected is apparently Therefore, response to the price EVs arethe connected is when apparently high. Therefore, in response to the price signals, the prior choice during daily time EVs are connected is apparently high. Therefore, in response to the price signals, the prior choice for the building is to perform V2B activity to lower the load consumption for for the building is to perform V2B activity to lower the load consumption for the reduction of the signals, the prior for the building is tocost. perform activitythat to lower the load consumption for the reduction of choice the overall power energy ThisV2B indicates the charging model can also overall power energy cost. This indicates thatcost. the charging model that can also effectively support thealso EV the reduction of the overall power energy This indicates the charging model can effectively support the EV charging/discharging decisions for EVs parked in a building. charging/discharging for EVs parked in a building. effectively support thedecisions EV charging/discharging decisions for EVs parked in a building.
Figure 12. Outcome for EV charging of the building: basic building load refers to the building load Figure 12. 12. Outcome for EV EVthe charging of the theload building: basic building refers to the theload building load Figure for charging of building: building load refers to building without EVOutcome load profile; optimized profilebasic refers to theload basic building plus load the without EV load profile; the optimized load profile refers to the basic building load plus the without EV EV loadcharging/discharging profile; the optimizedresult load profile refers the basicmodel. building load plus the aggregated aggregated based on theto proposed aggregated EV charging/discharging result based on the proposed model. EV charging/discharging result based on the proposed model.
4.4. Simulation Results for the EV Charging Station 4.4. Simulation Results for the EV Charging Station The simulation outcome for EV management of the EV charging station is given in Figure 13. The simulation outcome EV management of the to EVperform chargingV2V station is given in Figure 13. As demonstrated, some of thefor parked EVs are operated activity at 11:00–13:00 to As demonstrated, some of the parked EVs are operated to perform V2V activity at 11:00–13:00 to support the charging demand of other EVs before their departure from the charging station. With support the charging demand of other EVs before their departure from the charging station. With this operation, the power energy cost can be reduced since the power prices during 11:00–13:00 are thishighest operation, the the power energy can be one reduced power prices during are the during whole day. cost Moreover, of thesince EVs the is managed to deliver its 11:00–13:00 battery energy
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4.4. Simulation Results for the EV Charging Station The simulation outcome for EV management of the EV charging station is given in Figure 13. As demonstrated, some of the parked EVs are operated to perform V2V activity at 11:00–13:00 to support the charging demand of other EVs before their departure from the charging station. With this operation, the power energy cost can be reduced since the power prices during 11:00–13:00 are the Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 16 highest during the whole day. Moreover, one of the EVs is managed to deliver its battery energy to Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 16 the grid 18:00atwhen V2G is attractive. This indicates that the proposed to the(V2G) grid at (V2G) 18:00 the when theprice V2Gprovided price provided is attractive. This indicates that the model can also meet can the regulation demand of charging, V2V, and V2GV2V, for anand EV V2G charging station in proposed model also meet the regulation demand of charging, for an to the grid (V2G) at 18:00 when the V2G price provided is attractive. This indicates that EV the response to price signals. charging response to price proposedstation modelincan also meet thesignals. regulation demand of charging, V2V, and V2G for an EV charging station in response to price signals.
Figure 13. Outcome for EV charging of the charging station: basic charging station load refers to the
Figure 13. Outcome for EV charging of the charging station: basic charging station load refers to the charging station loadfor without EV load profile; the optimized profile refers to the basic charging Figurestation 13. Outcome EV charging the charging station: load basic station the charging load without EV loadof profile; the optimized loadcharging profile refers toload the refers basic to charging station load plus the aggregated EV charging/discharging result based on the proposed model. charging station load without EV load profile; the optimized load profile refers to the basic charging station load plus the aggregated EV charging/discharging result based on the proposed model. station load plus the aggregated EV charging/discharging result based on the proposed model.
4.5. Consideration for the Issue of Battery Degradation
4.5. Consideration for the Issue of Battery Degradation
4.5. Consideration the Issue of Battery As modeled for in Equations (6) andDegradation (10), the issue of battery degradation is quantified through Asevaluation modeled in Equations (6) and (10), the issue ofvalues battery isisquantified through the the of EV charging/discharging cycles. The ofdegradation penalty coefficient for the charging As modeled in Equations (6) and (10), the issue of battery degradation quantified through evaluation of EV charging/discharging cycles. The values of penalty coefficient for the charging cycles cycles of EVs are therefore simulated to investigate the influence of battery degradation. For the evaluation of EV charging/discharging cycles. The values of penalty coefficient for the charging convenience, theare values of λi are uniformly forinfluence all EVs. The chargingdegradation. scenario theFor EVconvenience, charging of EVs are of therefore simulated to investigate the ofinfluence battery cycles EVs therefore simulated toset investigate the of batteryofdegradation. For is withofdifferent and thefor simulation outcome including the total and is the station values of analyzed λi are uniformly set uniformly forλiall EVs. The scenario of the EV station convenience, the values λi are set allcharging EVs. The charging scenario of charging the EVload charging economic for the sideλis presented in Figure 14. The analyzed different λi operator anddifferent the simulation outcome including thecharging/discharging total load and stationwith is profit analyzed with i and the simulation outcome including theeconomic total behaviors loadprofit and for of EVs are given in Figure 15. Since no EV selects discharging under the case , the details of in 0 economicside profit the operator side is14. presented in Figure 14. The charging/discharging i the operator is for presented in Figure The charging/discharging behaviors of EVsbehaviors are given of EVs are given in Figure 15. Since no EV selects under the caseofEV , the details of EV behaviors for EV this scenario are therefore omitted here. Figure 15. Since no selects discharging under thedischarging case λi = 0, the details i 0behaviors for this EV behaviors for this scenario are therefore omitted here. scenario are therefore omitted here.
Figure 14. Simulation results of the charging station with different λi: the load profiles in the big frame the results load curve changes to be more with fluctuate with the increase of λi; theinprofit of Figuredemonstrate 14. Simulation of the charging station different λi: the load profiles the big Figure 14. Simulation results of indicates the charging station with different λithe : the load profiles in the big the operator in the small frame the profit can be improved with increase of λ i. frame demonstrate the load curve changes to be more fluctuate with the increase of λi; the profit of
frame demonstrate the load curve changes to be more fluctuate with the increase of λi ; the profit of the the operator in the small frame indicates the profit can be improved with the increase of λi. operator in be theseen smallfrom frame indicates the profit can be improved the to increase of λless As can Figure 15, with the increase of λi, EVs with choose perform i . discharging due to the increased penalty for battery charging/discharging cycles. The users smartly choose to As can be seen from Figure 15, with the increase of λi, EVs choose to perform less discharging perform charging or discharging at adjacent time slots when λ i increases, or even give up due to the increased penalty for battery charging/discharging cycles. The users smartly choose to discharging when or Figure 14, the load profile to fluctuate λi 1 . Based on at perform charging adjacent time slots whentends λi increases, or more even when give up i discharging
dischargingwhile whenthei power on Figurecost 14, changes the load to profile tends when to fluctuate more when λi decreases, consumption be higher the demand for the 1 . Based lifecycle of EV batteries changes is higher (i.e., with higher λ i). The battery degradation is therefore decreases, while the power consumption cost changes to be higher when the demand for the
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14 of 16 that can affect the charging/discharging behavior of EVs and the operational costs of the power consumption entity.
Figure 15. Details of the aggregated EV charging/discharging profiles for the charging station with Figure 15. Details of the aggregated EV charging/discharging profiles for the charging station with different λi: (a–e): λi = 0, 0.1, 0.2, 0.3 and 0.5 respectively; with the increase of λi, EVs choose to different λi : (a–e): λi = 0, 0.1, 0.2, 0.3 and 0.5 respectively; with the increase of λi , EVs choose to perform perform less discharging. less discharging.
5. Conclusions As can be seen from Figure 15, with the increase of λi , EVs choose to perform less discharging due A generic model that can fit the various activities of V2A application has been presented in this to the increased penalty for battery charging/discharging cycles. The users smartly choose to perform paper. With the proposed model, the decisions of charging/discharging statuses including charging, charging or discharging at adjacent time slots when λ increases, or even give up discharging when V2H, V2B, V2V, and V2G of EVs under the guidancei of power price signals for different parking λi places = 1. Based onsupported. Figure 14, The the load profile tends to fluctuate when λi decreases, the power can be battery degradation issue has more also been considered. As while demonstrated consumption cost changes to be higher when the demand for the lifecycle of EV batteries changes by the simulation results, the proposed model can be utilized to help minimize the power energy is higher (i.e., higher λi ). The battery therefore an V2A important concern can affect cost of thewith power consumption entity ordegradation community is involved with applications in that response to thethe charging/discharging of EVs and the costs of the powerinconsumption entity. price signals releasedbehavior by the grid operator. Foroperational instance, a reduction of 4.37% energy expenses can be achieved in a case study with EV discharging enabled for a household. This also reflects that 5. Conclusions EVs are prone to perform less discharging when the demand for the lifecycle of EV batteries is higher. Since model power that prices can different charging/discharging behaviors in EVs, future work A generic can fitinduce the various activities of V2A application has been presented in this should be focused on price tuning for regulating EV charging/discharging behaviors. The constraints paper. With the proposed model, the decisions of charging/discharging statuses including charging, of power gridsand can V2G also be to fitthe theguidance proposedofmodel into more practical applications. V2H, V2B, V2V, of studied EVs under power price signals for different parking places can be supported. The battery degradation issue has also been considered. As demonstrated by the Author Contributions: T.M. conducted the investigation, designed the methodology and completed the simulation results, model canonbe toidea helpand minimize the power of the original draft; X.Z. the and proposed B.Z. gave suggestions theutilized proposed simulation cases; T.M.energy and X.Z.cost revised power consumption entity or community involved with V2A applications in response to the price the paper based on comments from the reviewers; T.M. checked the proofreading. signals released by the grid operator. For instance, a reduction of 4.37% in energy expenses can be Acknowledgments: This paper was supported by the project “Research on power system planning theory achieved in aproportion case study EV discharging for a household. ThisSouthern also reflects EVs with high of with intermittent renewable enabled energy resources” of the China Powerthat Grid are(CSGTRC-K163007). prone to perform less discharging when the demand for the lifecycle of EV batteries is higher. Since power prices can induce different charging/discharging behaviors in EVs, future work should be Conflicts of Interest: The authors declare no conflict of interest. focused on price tuning for regulating EV charging/discharging behaviors. The constraints of power grids can also be studied to fit the proposed model into more practical applications.
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Author Contributions: T.M. conducted the investigation, designed the methodology and completed the original draft; X.Z. and B.Z. gave suggestions on the proposed idea and simulation cases; T.M. and X.Z. revised the paper based on comments from the reviewers; T.M. checked the proofreading. Acknowledgments: This paper was supported by the project “Research on power system planning theory with high proportion of intermittent renewable energy resources” of the China Southern Power Grid (CSGTRC-K163007). Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature t i ST SE SociEV,min SociEV,max SociEV,t SociEV,tstart SociEV,tend SociEV,exp SociEV i PEV i CEV i ηc ηdi Si,c EV,t
Si,dV2H EV,t
Si,dV2B EV,t
Si,dV2V EV,t Si,dV2G EV,t tstart tend i TEV TB Pbt ϑV2G,t ϑL,t ρi λi
Time index EV index Time interval set EV set at a power consumption unit Lower SOC limit for the ith EV Upper SOC limit for the ith EV SOC state of the ith EV at time t SOC value at plugging-in time of ith EV SOC value at plugging-out time of ith EV Expected SOC value of ith EV from the car owner Nominal battery SOC of the ith EV Nominal charging power of the ith EV Battery capacity of the ith EV Charging efficiency of the ith EV Discharging efficiency of the ith EV Charging status (0 or 1) at time t of the ith EV V2H status (0 or 1) at time t of the ith EV V2B status (0 or 1) at time t of the ith EV V2V status (0 or 1) at time t of the ith EV V2G status (0 or 1) at time t of the ith EV Charging start time Charging end time Working period of the ith EV Time period of basic load for a power consumption unit Basic power load at time t for a power consumption unit V2G power price at time t Power load price at time t Penalty coefficient for energy desire of the ith EV Penalty coefficient for charging cycles of the ith EV
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