# Multiobjective Model for Microgrids Integrating Electric Vehicles to Grid and Building Based on Interest Balance

Authors: Xiaolin Chu; Peng Wang; Dong Yang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Microgrids allow energy exchange among multiple interconnected microgrids for greater energy efficiency and collective economic interest. However, in some cases, the benefit of some microgrids within the network may not be uncertain. In view of the increasing development of electric vehicles (EVs), a multiobjective model is proposed to improve the performance of microgrids by integrating electric vehicles-to-grid (V2G) and vehicles-to-building (V2B) based on global and individual benefit balance. Two reference models are built to verify the validity of the proposed method, and models are formulated as mixed integer linear programming formats solved by the weighting method. A set of parameters of microgrids are adopted to model the driver behaviors (e.g., available hours of EV), energy transactions (e.g., electricity), performance factor (e.g., emission factor), distributed energy (e.g., solar panel), and energy load of five commercial buildings (e.g., hotel) located in Shanghai. Simulation results demonstrate the effectiveness of the operation decision models in the energy management of microgrids under neutral, proeconomic, proenvironmental, and proenergy weighting scenarios. The case study results specify that the proposed method can achieve operational cost, CO2 emission, and primary energy consumption reductions for each microgrid, with total benefits declining slightly.


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## Body

## 1. Introduction

Global energy consumption has been continuously increasing due to population growth, economic development, and accelerated urbanization in recent years. As a larger proportion of energy consumption, electricity demand is expected to increase by almost 28% from 23,300 terawatt-hours (TWh) in 2020 to almost 30,000 TWh by 2030 [1]. To accommodate a reliable supply of power to customers, the power grid’s infrastructure needs to be upgraded and expanded, which might lead to high capital investments and serious environmental pollution. To deal with these issues, the microgrid technology has been developed rapidly in recent years which consist of distributed energy sources (e.g., renewable energy resources, power generators, and storage system) and energy loads [2]. The microgrid can provide a good opportunity to effectively improve energy utilization and reduce environmental pollution and is expected to play a significant role in building smart cities in many countries [3–5].The microgrid can be defined as an electricity bounded area of distributed network that aggregates locally distributed generation sources (e.g., solar power generation) along with energy storage devices (e.g., electric storage) and controllable loads (e.g., electricity load) so as to form a self-sufficient energy system [6]. Following the increase in electricity demand, the energy efficiency of a microgrid may be restricted due to the limited capacity of locally distributed generation sources in a bounded area. Based on the development of Internet technology, different microgrids can operate collaboratively to improve efficiency and reliability as well as economy by exchanging energy with each other, which is regarded as microgrids technology [7, 8]. In the past few decades, extensive research has been tried to obtain energy efficient operation strategies for individual microgrid and microgrids.As for an individual microgrid, existing works mainly focus on optimizing energy dispatch with the aim to maximize economic benefit [9, 10], environmental benefit, and reliability [11]. For example, due to the high energy utilization efficiency of combined cooling, heating, and power (CCHP) systems, authors in [12] use a novel two-stage coordinated control approach to solve the CCHP microgrid energy management problem with the objective to minimize cost. In order to reduce operation costs, reduce gas emissions, and increase consumer satisfaction, the authors in [13] present a practical multiobjective dynamic optimal dispatch model incorporating energy storage and user experience. At the same time, in view of the increasing development of EVs, vehicle-to-grid (V2G) and vehicle-to-building (V2B) technologies are proposed to overcome fluctuations in the voltage and frequency caused by EVs’ charging [14–16]. In V2G and V2B bidirectional communication, EVs can supply electricity to a power grid/building with the utilization of bidirectional converters under plugged-in EVs. The authors in [17] focus on balancing the interests between microgrids and EV battery swapping stations and propose a new bilevel optimal scheduling model under multistakeholder scenarios. Furthermore, the authors in [18] extend the mathematical model to coordinate flexible demand response and multiple renewable uncertainties. However, the interest conflict among microgrids is ignored.Due to the economic performance and power generation reliability of microgrids, the collaborative operation among microgrids has recently drawn the attention of the researcher. The operation process of microgrids is more complex, as multiple renewable energy sources are complemented and multiple types of energy are exchanged [19]. Several efforts (e.g., framework development, modelling, and solution methods) are made to study microgrids in order to take full advantage of the services and benefits [20–22]. The authors in [23] study the energy sharing and trading on a novel spatiotemporal energy network through V2B and V2G interaction and evaluate the techno-economic-environmental potentials of the proposed energy network. Stochastic and robust optimization-based collaborative operation approaches for microgrids are formulated to derive the energy scheduling scheme, whose objective is to minimize the total microgrids’ operation costs under uncertain factors [19, 24]. Multiobjective optimization dispatch for microgrids with EV charging is studied to achieve minimized operation cost, greenhouse gas emission reductions, and enhanced reliability of services [25]. These operation decision models mainly focus on maximizing collective benefits by aggregating all the entities into the overall microgrid system as one unit, while the benefit of individual microgrid is not considered.However, the individual interest of each microgrid may be damaged if only the benefits of microgrids are focused. The conflicts of interests will lead to microgrids being disbanded when the microgrid’s operators are heterogeneous (i.e., independent) and profit-driven entities. To address this problem, balancing the collective and individual economic benefits should be focused on obtaining a scheduling energy strategy to implement microgrids with coordinated operations [26, 27]. A mathematical decision framework is presented in [28] to research the transactive energy management of microgrids under the local energy transaction market. Furthermore, chance-constrained models using a transactive energy structure are proposed to manage energy exchange in microgrids considering uncertainty, and simulation results prove that microgrids can gain both collective and individual economic benefits based on the mechanism [29]. However, methods balancing global and local benefits of microgrids with multiple perspectives came from real-world problems are missing. And decision makers’ preferences are less focused on the microgrid optimization problem.To bridge these research gaps, we propose the multiobjective model for the microgrids integrating V2G and V2B based on interest balance to ensure individual microgrid’s benefit. EVs can be utilized as dynamically configurable dispersed energy storages to balance the energy supply and demand in microgrids. The objectives of microgrids are to minimize collective cost (COST), carbon dioxide emission (CDE), and primary energy consumption (PEC) and ensure individual microgrid’s benefit. Three multiobjective models are formulated to examine the performance of variation, and different weight combinations are assumed to represent the preference of decision maker. The first reference model focuses on minimizing collective interests under no energy exchange among microgrids, buildings, and charging station (CS). The second reference model is to achieve collaborative Internet in microgrids integrating V2G and V2B, when energy can freely exchange among microgrids, buildings, and charging stations. The proposed model aims to maximize both the global and local interests of microgrids integrating V2G and V2B. In the case study, four scenarios are investigated for the microgrids in Shanghai under different importance levels of operators. In summary, the contributions of this research lie in three aspects: (1) A multiobjective mathematical decision framework is proposed to balance interest among individual microgrids and is discussed with reference problems; (2) the weighting method is used to solve the multiobjective models, and the weighting scenarios are set according to the decision markers’ preferences; and (3) multidimensional experiments are analyzed in the case study to illustrate the models’ scalability.The rest of the paper is structured as follows: Section2 describes the technical roadmap and problem description; in Section 3, a multiobjective collaborative model is built to describe the energy sharing in the microgrids; in Section 4,reference decision models are proposed; in Section 5,the numerical results from the case studies for the presented multiobjective energy management system of microgrids under different weighting scenarios are reported; and in Section 6,several conclusions are drawn.


## 2. Problem Description

In this research study, a modelling framework is developed to study the energy management of microgrids. The layout of the proposed network is presented in Figure1, and the overall system is comprised of the power grid and multiple microgrids. Each microgrid consists of an end user (e.g., building), a CCHP system, a photovoltaic (PV) panel, and a charging station. Electric vehicles arriving at charging stations are in two-way power exchange with the power grid and end users based on V2G and V2B technologies. In addition, localized cooling networks and microgrids are established to enable electricity and cooling energy transfer within microgrids, which are depicted as solid lines with green and blue colors in Figure 1, respectively.Figure 1
System layout of the proposed microgrids.The specific layout of the proposed network is displayed in Figure2, in which each microgrid can share and exchange electric and cooling energy with other microgrids through wires and pipes within the network, respectively. The microgrid is comprised of a power grid, building, and charging station. The building, as the end user, is equipped with a CCHP system and PV panels. Due to its higher efficiency and lower emissions, the stationary Solid Oxide Fuel Cell (SOFC) is deployed as the prime mover of a CCHP system to generate electricity. Heating energy can be produced by a recovery system, and fuel can be converted to heat by an auxiliary boiler to satisfy cooling and heating demand. The CS has the capacity to charge multiple EVs simultaneously, using power from its PV panels, power grid, building, and other microgrids. The microgrid network connects with the power grid and can be enabled to feed-in or purchase electricity from the grid.Figure 2
Overall schematic of the microgrids integrating V2G and V2B.The solid line in green color in Figure2 represents electricity flow. The electric load of building in each microgrid is supplied by CCHP, utility grid, PV, CS, and other microgrids. The electric load of electric vehicles in each microgrid is satisfied by the utility grid, PV, buildings, and other microgrids. The solid lines with blue color and red color in Figure 2 show cooling flow and heating flow, respectively. The cooling load of the building in each microgrid is supplied by an absorption chiller in a CCHP system and in other microgrids by cooling piping. The heating load is satisfied by the heat pump and CCHP systems.As shown in Figures1 and 2, the goal of this study is to gain the optimal energy management strategy for the power grid, EVs, CCHP system, PV, and energy transaction with balancing global and individual benefits. By adopting the optimal strategy, the total proposed system and each microgrid economic, environmental, and energy performance can be maximized under the constraints of equipment features, buildings’ loads, EVs characteristics (e.g., EV battery balance and energy demand). The COST, CDE, and PEC of the system optimal strategy are explored under the following four different weighting scenarios to provide a better view of performances in the case studies: neutral, proeconomic, proenvironmental, and proenergy.


## 3. Mathematic Model for the Microgrids

In this section, a mixed integer linear programming (MILP) model is formulated to minimize the economic cost, environmental pollution, and energy consumption by obtaining the optimal strategy for the microgrids integrating V2G and V2B technologies. The model is established from a systematic perspective by considering the interrelationships among the multiple microgrids. The notations of indexes, parameters, and variables applied in the model are displayed in Table1. All the parameters and variables are nonnegative.Table 1
Indexes, parameters, and variables applied in the proposed model.
NomenclatureAbbreviationsCOSTCostCDECarbon dioxide emissionPECPrimary energy consumptionCCHPCombined cooling, heating, and powerSOFCSolid oxide fuel cellSRISolar radiation indexPVPhotovoltaicEVElectric vehicleCSCharging stationSubscripttIndex of the slotted interval,t=1,2,⋯,Ti/jNumber of microgrid,i/j=1,2,⋯,IvIndex for the EVs,v=1,2,...,VParametersPNGNatural gas price ($/kWh)PmaintMaintenance price of devices ($/kWh)PtimElectricity price form power grid at timet ($/kWh)PtexSelling price of electricity to power grid at timet ($/kWh)αNGCarbon dioxide emission factor for natural gas (kg/kWh)αgridCarbon dioxide emission factor for power grid (kg/kWh)δNGPrimary energy conversion parameter for natural gasδgridPrimary energy conversion parameter for power gridδsolarPrimary energy conversion parameter for solarCAPgridThe limit of power grid (kWh)CAPifcThe capacity of SOFC in microgridi (kWh)CAPiboThe capacity of boiler in microgridi (kWh)CAPiacThe capacity of absorption chiller in microgridi (kWh)CAPiecThe capacity of electric chiller in microgridi (kWh)CAPihpThe capacity of heat pump in microgridi (kWh)CAPibpvThe capacity of building’s PV in microgridi (kWh)CAPicspvThe capacity of CS’s PV in microgridi (kWh)CAPi,vevThe capacity of CS’s EVv in microgrid i (kWh)SRtSolar radiation at timetEi,tbelElectric load of building in microgridi at time tQi,tbhlHeating load of building in microgridi at time tQi,tbclCooling load of building in microgridi at time tηbpvElectricity generation efficiency of building’s PVηfcElectricity generation efficiency of SOFCηreHeating generation efficiency of SOFCηacCooling generation efficiency of absorption chillerηecCooling generation efficiency of electric chillerηboHeating generation efficiency of boilerηhpHeating generation efficiency of heat pumpηcspvElectricity generation efficiency of CS’s PVSOCi,vevminMinimal electricity store rate of EVv in microgrid iSOCi,vevmaxMaximal electricity store rate of EVv in microgrid iSOCi,viniInitial battery electricity rate of EVv in microgrid iSOCi,vdesDemand electricity level at departure time of EVv in microgrid i∆t1 h time intervalαi,vcminMinimal charging limit of EVv in microgrid iαi,vcmaxMaximal charging limit of EVv in microgrid iαi,vdcminMinimal discharging limit of EVv in microgrid iαi,vdcmaxMaximal discharging limit of EVv in microgrid iLwireTransmission loss of electricityLpipeTransmission loss of coolingParametersMA big enough numberContinuous decision variables (in timet)NGi,tfcNatural gas consumption of SOFC in microgridiNGi,tboNatural gas consumption of boiler in microgridiEi,tfcElectricity generation of SOFC in microgridiEi,tbpvElectricity generation of building’s PV in microgridiEi,tcspvElectricity generation of CS’s PV in microgridiEi,tgbElectricity flow from power grid to building in microgridiEi,tgcsElectricity flow from power grid to CS in microgridiEi,tbgElectricity flow from building in microgridi to power gridEi,tcsgElectricity flow from CS in microgridi to power gridEi,tcsbElectricity flow from CS to building in microgridiEi,tecThe electricity generated by electric chiller in microgridiEi,thpThe electricity consumption by heat pump in microgridiEi,j,tmbtrElectricity exchanged from microgridi to building in microgrid jEi,tbcsElectricity exchanged from building to CS in the microgridiEi,tcsgElectricity exchanged from CS to power grid in microgridiEi,tcsbElectricity exchanged from CS to building in microgridiEi,tcsElectricity needed by CS in microgridiEi,j,tmcstrElectricity exchanged from microgridi to CS in microgrid jEi,v,tevcElectric energy charged to EVv in microgrid iEi,v,tevdcElectric energy discharged from EVv in microgrid iEi,v,tevElectric energy stored in EVv in microgrid iQi,tboHeat generated from boiler in microgridiQi,thpHeat generated from heat hump in microgridiQi,teccCooling generated by electric chiller in microgridiQi,taccCooling generated by absorption chiller in microgridiQi,treHeating recovered from SOFC in microgridiQi,tachHeating consumption by absorption chiller in microgridiQi,j,tmbtrCooling exchanged from microgridi to building in microgrid jBinary decision variables (in timet)xi,v,tevcCharging state of EVv in microgrid ixi,v,tevdcDischarging state of EVv in microgrid ixi,tim1 if electricity imported from power grid to microgridi; 0 otherwisexi,tex1 if electricity exported to power grid from microgridi; 0 otherwisexi,j,tmb1 if electricity flow from microgridi to building in microgrid j; 0 otherwisexi,j,tmcs1 if electricity flow from microgridi to CS in microgrid j; 0 otherwisexi,j,tmbc1 if cooling flow from microgridi to building in microgrid j; 0 otherwise


### 3.1. Constraints

#### 3.1.1. Power Grid Capacity Constraints

The power purchased from the utility grid to building (Ei,tgb) and charging station (Ei,tgcs) is restricted by the capacity of the utility grid (CAPgrid) as follows:(1)Ei,tgb+Ei,tgcs≤CAPgrid,∀i,∀t,where i and t are the number of microgrids and time, respectively.


#### 3.1.2. Building Operation Decision Model

(a)
Electric Load Balance Constraints. The electrical balance showed in equation (2) means that the electric supply should be equal to demand at time t for building in microgrid i. The electric supply on the left side consists of electricity generated by solar PV (Ei,tbpv), SOFC (Ei,tfc), purchased from the grid (Ei,tgb), the charging station (Ei,tcsb) as well as other microgrids (Ej,i,tmbtr). The right (demand) side items of the electricity include electricity consumption by EC (Ei,tec) and HP (Ei,thp), electricity sold back to the utility grid (Ei,tbg), building electric load (Ei,tbel), electricity transmitted to CS (Ei,tbcs), and other microgrids (Ei,j,tmbtr). The transmission loss of electric energy within the microgrids is considered by implementing the factor of Lwire.(2)Ei,tbpv+Ei,tfc+Ei,tgb+Ei,tcsb+∑jEj,i,tmbtr×1−LwireEi,tec+Ei,thp+Ei,tbg+Ei,tbel+Ei,tbcs+∑jEi,j,tmbtr,∀i,t,j≠i.(b)
Thermal Load Balance Constraints. The heating balance is displayed in equation (3), where recovered heat (Qi,tre) from the SOFC power generation plus heating supply from the boiler (Qi,tbo) and heat pump (Qi,thp) are used to satisfy the heating consumption of absorption chiller (Qi,tach) and the building heating load (Qi,tbhl) in microgrid i. Similarly, the cooling balance showed in equation (4) means that the cooling energy supply should be equal to electric demand at time t for building in microgrid i. The left (supply) side of the cooling demand includes the cooling generated by absorption chiller (Qi,tacc) and electric chiller (Qi,tecc) plus transmitted from other microgrids (Qj,i,tmbtr). The right (demand) side of the cooling demand includes the building’s cooling demand (Qi,tbcl) and transmits to other microgrids (Qi,j,tmbtr). Lpipe represents the transmission loss of cooling energy within the microgrids.(3)Qi,tre+Qi,tbo+Qi,thp=Qi,tach+Qi,tbhl,∀i,t,j,(4)Qi,tacc+Qi,tecc+Qj,i,tmbtr=Qi,tbel+Qi,j,tmbtr1−Lpipe,∀i,t,j≠i.(c)
Constraints for PV. Electricity generated by PV panel (Ei,tbpv) can be calculated by its size (CAPibpv) multiplying by electricity generation efficiency (ηbpv) and solar radiation (SRt) in microgrid i as follows:(5)Ei,tbpv≤CAPibpv×ηbpv×SRt,∀i,t,i.(d)
Constraints for CCHP. The electric/thermal output of SOFC (Ei,tfc), boiler (Qi,tbo), absorption chiller (Qi,tacc), electric chiller (Qi,tecc), and heat pump (Qi,thp) must be not more than the corresponding installed capacities (CAP) in microgrid i as given in equations (6)–(10). The energy conversion efficiencies are given in equations (11)–(16), where η shows the energy efficiency of various devices in the CCHP system.(6)Ei,tfc≤CAPifc∀i,t,(7)Qi,tbo≤CAPibo∀i,t,(8)Qi,tacc≤CAPiac∀i,t,(9)Qi,tecc≤CAPiec∀i,t,(10)Qi,thp≤CAPihp∀i,t,(11)Ei,tfc=ηfc×NGi,tfc∀i,t,(12)Qi,tre=ηre×Ei,tfc∀i,t,(13)Qi,tacc=ηac×Qi,tach∀i,t,(14)Qi,tecc=ηec×Ei,tec∀i,t,(15)Qi,tbo=ηbo×NGi,tbo∀i,t,(16)Qi,thp=ηhp×Ei,thp∀i,t.


#### 3.1.3. Electric Vehicle Charging Station Operation Decision Model

(a)
Electric Load Balance Constraints. Constraint in equation (17) represents that the supply and demand of electricity should be equal at time t for CS in microgrid i. For microgrid i, the energy suppliers include purchased from utility grid (Ei,tgcs), transmitted from building (Ei,tbcs), generated by CS’s PV (Ei,tcspv), and transmitted from other microgrids j (Ej,i,tmcstr). The energy demand includes electricity sold back to the utility grid (Ei,tcsg), transmitted to other buildings (Ei,tcsb), requested energy to charge EVs (Ei,tcs), and transmitted to other microgrid j (Ei,j,tmcstr). Constraint (18) means that electricity requested energy to charge EVs equals to the EVs’ charging minus discharging energy.(17)Ei,tgcs+Ei,tbcs+Ei,tcspv+∑jEj,i,tmcstr×1−Lwire=Ei,tcsg+Ei,tcsb+Ei,tcs+∑jEi,j,tmcstr∀i,t,(18)Ei,tcsev=∑vEi,v,tevc−Ei,v,tevdc∀i,t.(b)
Constraints for PV. Similarly, electricity generated by CS’s PV panel (Ei,tcspv) is restrained by its capacity (CAPicspv) times electricity generating efficiency (ηcspv) and solar radiation (SRt) in microgrid i.(19)Ei,tcspv≤CAPicspv×ηcspv×SRt∀i,t.(c)
Constraints for Electric Vehicles. For the EVs, Ti,vaandTi,vua represent the EV v arriving and leaving the CS in microgrid i, which are assumed as available and unavailable time, respectively. During the EV parking time (available time), the thermal energy stored in EVs (Ei,v,t+1ev) is bounded as shown in equation (20) and can be calculated by charging energy minus discharging energy as displayed in equations (21) and (22). Constraint (23) guarantees the electricity level of EV (Ei,v,t−1ev) which can meet the owner’s desired electricity level when the EV leaves the CS. Equation (24) designates that EVs cannot be in charging (xi,v,tevc) and discharging (xi,v,tevdc) states at the same time. Constraints (25) and (26) are used to guarantee that the EV battery charging and discharging electricity are limited by their maximum and minimum charging and discharging rate, respectively.(20)CAPi,vev×SOCi,vevmin≤Ei,v,tev≤CAPi,vev×SOCi,vevmax∀i,v,Ti,va≤t≤Ti,vua,(21)Ei,v,t+1ev=CAPi,vev×SOCi,vini+Ei,v,t+1evc−Ei,v,t+1evdc×Δt∀i,v,t=Ti,va,(22)Ei,v,t+1ev−Ei,v,tev=Ei,v,t+1evc−Ei,v,t+1evdc×Δt∀i,v,Ti,va<t<Ti,vua,(23)Ei,v,t−1ev≥CAPi,vev×SOCi,vdes∀i,v,t=Ti,vua,(24)xi,v,tevc+xi,v,tevdc≤1∀i,v,Ti,va<t<Ti,vua,(25)CAPi,vev×αi,vcmin×xi,v,tevc≤Ei,v,tevc≤CAPi,vev×αi,vcmax×xi,v,tevc∀i,v,Ti,va<t<Ti,vua,(26)CAPi,vev×αi,vdcmin×xi,v,tevdc≤Ei,v,tevdc≤CAPi,vev×αi,vdcmax×xi,v,tevdc∀i,v,Ti,va<t<Ti,vua.


#### 3.1.4. Constraints for Grid Exchange

Constraint (27) indicates that electricity cannot be imported from and exported to power grid at the same time for the microgrid. Equation (28) ensures that electricity from utility grid and CS are restricted by maximum capacity. Similarly, equation (29) states that electricity feed-in utility grid and CS are restricted by maximum capacity.(27)xi,tim+xi,tex≤1∀i,t,(28)Ei,tbg+Ei,tcsg≤xi,tex×CAPgrid∀i,t,(29)Ei,tgb+Ei,tgcs≤xi,tim×CAPgrid∀i,t.


#### 3.1.5. Constraints for Networking

The constraint expressed in equations (30), (33), and (36) indicates that electricity/cooling feed-in and import cannot happen simultaneously. Note that xi,j,tmb and xi,j,tmcs are binary variables to represent the electricity from buildings and CS in microgrids i to j exchange status, respectively. The transmission of electricity energy (Ei,j,tmbtr, Ej,i,tmbtr) restricted by exchange status is defined in equations (31), (32), (34), and (35). xi,j,tmbc is binary variable to control the cooling in building from microgrids i to j exchange status. Constraints (37) and (38) ensure that the transmission of cooling energy (Qi,j,tmbtr, Qj,i,tmbtr) is limited by exchange status. M is a big number, normally adopted in mixed integer programming.(30)xj,i,tmb+xi,j,tmb≤1∀i,t,j≠i,(31)Ej,i,tmbtr≤M×xj,i,tmb∀i,t,j≠i,(32)Ei,j,tmbtr≤M×xi,j,tmb∀i,t,j≠i,(33)xj,i,tmcs+xi,j,tmcs≤1∀i,t,j≠i(34)Ej,i,tmcstr≤M×xj,i,tmcs∀i,t,j≠i,(35)Ei,j,tmcstr≤M×xi,j,tmcs∀i,t,j≠i,(36)xj,i,tmbc+xi,j,tmbc≤1∀i,t,j≠i,(37)Qj,i,tmbtr≤M×xj,i,tmbc∀i,t,j≠i,(38)Qi,j,tmbtr≤M×xi,j,tmbc∀i,t,j≠i.


### 3.2. Objectives

In this study, three objectives are evaluated from the economic, environmental, and energy saving perspective, respectively.


#### 3.2.1. Operational Cost (COST)

The collective interest of the microgrids can be formulated as equation (39a), which is to minimize the sum of each microgrid’s energy cost as equation (39b). As shown in equation (39b), the energy cost of each microgrid can be subdivided into cost associated with natural gas (the first term), maintenance cost of equipment (the second term), costs associated with power grids (the third term), and revenue associated with utility grids (the last term).(39a)minfCOST=∑iCOSTi,(39b)COSTi=PNG×∑tNGi,tfc+NGi,tbo+Pmaint×∑tEi,tfc+Ei,tbpv+Ei,tcspv+Qi,tbo+Qi,thp+Qi,tecc+Qi,tacc+Ptim×∑tEi,tgb+Ei,tgcs−Ptex×∑tEi,tbg+Ei,tcsg∀i.


#### 3.2.2. Carbon Dioxide Emission (CDE)

Greenhouse gases from the power generation combusting fuel deteriorate the environment, in which global warming is one of the crucial issues. The CDE is selected as the environmental index, and the collective environmental benefit of the microgrids can be built as equation (40a), with the aim of minimizing the sum of each microgrid’s CDE as equation (40b). As displayed in equation (40b), the CDE of each microgrid can be estimated by the emissions from natural gas consumption (the first term) and purchased electricity from the utility grid (the second term).(40a)minfCDE=∑iCDEi,(40b)CDEi=αNG×∑tNGi,tfc+NGi,tbo+αgrid×∑tEi,tgb+Ei,tgcs.


#### 3.2.3. Primary Energy Consumption (PEC)

The collective energy benefit of the microgrids can be formulated as equation (41a), which is to minimize the sum of each microgrid’s PEC as equation (41b). The PEC of each microgrid includes primary energy consumption of natural gas (the first term), utility grid (the second term), and PV panel (the last term), as shown in equation (41b).(41a)minfPEC=∑iPECi,(41b)PECi=δNG×∑tNGi,tfc+NGi,tbo+δgrid×∑tEi,tgb+Ei,tgcs+δsolar×∑tEi,tbpv+Ei,tcspv.


### 3.3. Multiobjective Optimization

The multiobjective optimization (MOO) algorithm is substantially different from single-objective optimization since there are various but conflicting evaluation indicators in MOO. The weighting method uses weights to represent the goals preferred by decision makers [30], which is adopted to solve the proposed model after normalization in this paper.


#### 3.3.1. Normalization of Indicators

In equation (42), three indicators have different units and characteristics, in which f represents an objective and fnon shows the normalized objective calculated by(42)fnon=1,f≤f−,f−f−f+−f−,f−≤f≤f+,0,f≥f+,where f−=minf and f+=maxf.


#### 3.3.2. Weighting Method

After normalization of these indicators and using the weighting method, the multiobjective model can be transformed into the following single-objective model:(43)minf=ω1fCOST,non+ω2fCDE,non+ω3fPEC,non,where ω represents the weight of objective, which will determine the solution of the fitness function and show the performance priority. Different weighting scenarios represent the preferences of decision makers in different contexts.


## 3.1. Constraints

### 3.1.1. Power Grid Capacity Constraints

The power purchased from the utility grid to building (Ei,tgb) and charging station (Ei,tgcs) is restricted by the capacity of the utility grid (CAPgrid) as follows:(1)Ei,tgb+Ei,tgcs≤CAPgrid,∀i,∀t,where i and t are the number of microgrids and time, respectively.


### 3.1.2. Building Operation Decision Model

(a)
Electric Load Balance Constraints. The electrical balance showed in equation (2) means that the electric supply should be equal to demand at time t for building in microgrid i. The electric supply on the left side consists of electricity generated by solar PV (Ei,tbpv), SOFC (Ei,tfc), purchased from the grid (Ei,tgb), the charging station (Ei,tcsb) as well as other microgrids (Ej,i,tmbtr). The right (demand) side items of the electricity include electricity consumption by EC (Ei,tec) and HP (Ei,thp), electricity sold back to the utility grid (Ei,tbg), building electric load (Ei,tbel), electricity transmitted to CS (Ei,tbcs), and other microgrids (Ei,j,tmbtr). The transmission loss of electric energy within the microgrids is considered by implementing the factor of Lwire.(2)Ei,tbpv+Ei,tfc+Ei,tgb+Ei,tcsb+∑jEj,i,tmbtr×1−LwireEi,tec+Ei,thp+Ei,tbg+Ei,tbel+Ei,tbcs+∑jEi,j,tmbtr,∀i,t,j≠i.(b)
Thermal Load Balance Constraints. The heating balance is displayed in equation (3), where recovered heat (Qi,tre) from the SOFC power generation plus heating supply from the boiler (Qi,tbo) and heat pump (Qi,thp) are used to satisfy the heating consumption of absorption chiller (Qi,tach) and the building heating load (Qi,tbhl) in microgrid i. Similarly, the cooling balance showed in equation (4) means that the cooling energy supply should be equal to electric demand at time t for building in microgrid i. The left (supply) side of the cooling demand includes the cooling generated by absorption chiller (Qi,tacc) and electric chiller (Qi,tecc) plus transmitted from other microgrids (Qj,i,tmbtr). The right (demand) side of the cooling demand includes the building’s cooling demand (Qi,tbcl) and transmits to other microgrids (Qi,j,tmbtr). Lpipe represents the transmission loss of cooling energy within the microgrids.(3)Qi,tre+Qi,tbo+Qi,thp=Qi,tach+Qi,tbhl,∀i,t,j,(4)Qi,tacc+Qi,tecc+Qj,i,tmbtr=Qi,tbel+Qi,j,tmbtr1−Lpipe,∀i,t,j≠i.(c)
Constraints for PV. Electricity generated by PV panel (Ei,tbpv) can be calculated by its size (CAPibpv) multiplying by electricity generation efficiency (ηbpv) and solar radiation (SRt) in microgrid i as follows:(5)Ei,tbpv≤CAPibpv×ηbpv×SRt,∀i,t,i.(d)
Constraints for CCHP. The electric/thermal output of SOFC (Ei,tfc), boiler (Qi,tbo), absorption chiller (Qi,tacc), electric chiller (Qi,tecc), and heat pump (Qi,thp) must be not more than the corresponding installed capacities (CAP) in microgrid i as given in equations (6)–(10). The energy conversion efficiencies are given in equations (11)–(16), where η shows the energy efficiency of various devices in the CCHP system.(6)Ei,tfc≤CAPifc∀i,t,(7)Qi,tbo≤CAPibo∀i,t,(8)Qi,tacc≤CAPiac∀i,t,(9)Qi,tecc≤CAPiec∀i,t,(10)Qi,thp≤CAPihp∀i,t,(11)Ei,tfc=ηfc×NGi,tfc∀i,t,(12)Qi,tre=ηre×Ei,tfc∀i,t,(13)Qi,tacc=ηac×Qi,tach∀i,t,(14)Qi,tecc=ηec×Ei,tec∀i,t,(15)Qi,tbo=ηbo×NGi,tbo∀i,t,(16)Qi,thp=ηhp×Ei,thp∀i,t.


### 3.1.3. Electric Vehicle Charging Station Operation Decision Model

(a)
Electric Load Balance Constraints. Constraint in equation (17) represents that the supply and demand of electricity should be equal at time t for CS in microgrid i. For microgrid i, the energy suppliers include purchased from utility grid (Ei,tgcs), transmitted from building (Ei,tbcs), generated by CS’s PV (Ei,tcspv), and transmitted from other microgrids j (Ej,i,tmcstr). The energy demand includes electricity sold back to the utility grid (Ei,tcsg), transmitted to other buildings (Ei,tcsb), requested energy to charge EVs (Ei,tcs), and transmitted to other microgrid j (Ei,j,tmcstr). Constraint (18) means that electricity requested energy to charge EVs equals to the EVs’ charging minus discharging energy.(17)Ei,tgcs+Ei,tbcs+Ei,tcspv+∑jEj,i,tmcstr×1−Lwire=Ei,tcsg+Ei,tcsb+Ei,tcs+∑jEi,j,tmcstr∀i,t,(18)Ei,tcsev=∑vEi,v,tevc−Ei,v,tevdc∀i,t.(b)
Constraints for PV. Similarly, electricity generated by CS’s PV panel (Ei,tcspv) is restrained by its capacity (CAPicspv) times electricity generating efficiency (ηcspv) and solar radiation (SRt) in microgrid i.(19)Ei,tcspv≤CAPicspv×ηcspv×SRt∀i,t.(c)
Constraints for Electric Vehicles. For the EVs, Ti,vaandTi,vua represent the EV v arriving and leaving the CS in microgrid i, which are assumed as available and unavailable time, respectively. During the EV parking time (available time), the thermal energy stored in EVs (Ei,v,t+1ev) is bounded as shown in equation (20) and can be calculated by charging energy minus discharging energy as displayed in equations (21) and (22). Constraint (23) guarantees the electricity level of EV (Ei,v,t−1ev) which can meet the owner’s desired electricity level when the EV leaves the CS. Equation (24) designates that EVs cannot be in charging (xi,v,tevc) and discharging (xi,v,tevdc) states at the same time. Constraints (25) and (26) are used to guarantee that the EV battery charging and discharging electricity are limited by their maximum and minimum charging and discharging rate, respectively.(20)CAPi,vev×SOCi,vevmin≤Ei,v,tev≤CAPi,vev×SOCi,vevmax∀i,v,Ti,va≤t≤Ti,vua,(21)Ei,v,t+1ev=CAPi,vev×SOCi,vini+Ei,v,t+1evc−Ei,v,t+1evdc×Δt∀i,v,t=Ti,va,(22)Ei,v,t+1ev−Ei,v,tev=Ei,v,t+1evc−Ei,v,t+1evdc×Δt∀i,v,Ti,va<t<Ti,vua,(23)Ei,v,t−1ev≥CAPi,vev×SOCi,vdes∀i,v,t=Ti,vua,(24)xi,v,tevc+xi,v,tevdc≤1∀i,v,Ti,va<t<Ti,vua,(25)CAPi,vev×αi,vcmin×xi,v,tevc≤Ei,v,tevc≤CAPi,vev×αi,vcmax×xi,v,tevc∀i,v,Ti,va<t<Ti,vua,(26)CAPi,vev×αi,vdcmin×xi,v,tevdc≤Ei,v,tevdc≤CAPi,vev×αi,vdcmax×xi,v,tevdc∀i,v,Ti,va<t<Ti,vua.


### 3.1.4. Constraints for Grid Exchange

Constraint (27) indicates that electricity cannot be imported from and exported to power grid at the same time for the microgrid. Equation (28) ensures that electricity from utility grid and CS are restricted by maximum capacity. Similarly, equation (29) states that electricity feed-in utility grid and CS are restricted by maximum capacity.(27)xi,tim+xi,tex≤1∀i,t,(28)Ei,tbg+Ei,tcsg≤xi,tex×CAPgrid∀i,t,(29)Ei,tgb+Ei,tgcs≤xi,tim×CAPgrid∀i,t.


### 3.1.5. Constraints for Networking

The constraint expressed in equations (30), (33), and (36) indicates that electricity/cooling feed-in and import cannot happen simultaneously. Note that xi,j,tmb and xi,j,tmcs are binary variables to represent the electricity from buildings and CS in microgrids i to j exchange status, respectively. The transmission of electricity energy (Ei,j,tmbtr, Ej,i,tmbtr) restricted by exchange status is defined in equations (31), (32), (34), and (35). xi,j,tmbc is binary variable to control the cooling in building from microgrids i to j exchange status. Constraints (37) and (38) ensure that the transmission of cooling energy (Qi,j,tmbtr, Qj,i,tmbtr) is limited by exchange status. M is a big number, normally adopted in mixed integer programming.(30)xj,i,tmb+xi,j,tmb≤1∀i,t,j≠i,(31)Ej,i,tmbtr≤M×xj,i,tmb∀i,t,j≠i,(32)Ei,j,tmbtr≤M×xi,j,tmb∀i,t,j≠i,(33)xj,i,tmcs+xi,j,tmcs≤1∀i,t,j≠i(34)Ej,i,tmcstr≤M×xj,i,tmcs∀i,t,j≠i,(35)Ei,j,tmcstr≤M×xi,j,tmcs∀i,t,j≠i,(36)xj,i,tmbc+xi,j,tmbc≤1∀i,t,j≠i,(37)Qj,i,tmbtr≤M×xj,i,tmbc∀i,t,j≠i,(38)Qi,j,tmbtr≤M×xi,j,tmbc∀i,t,j≠i.


## 3.1.1. Power Grid Capacity Constraints

The power purchased from the utility grid to building (Ei,tgb) and charging station (Ei,tgcs) is restricted by the capacity of the utility grid (CAPgrid) as follows:(1)Ei,tgb+Ei,tgcs≤CAPgrid,∀i,∀t,where i and t are the number of microgrids and time, respectively.


## 3.1.2. Building Operation Decision Model

(a)
Electric Load Balance Constraints. The electrical balance showed in equation (2) means that the electric supply should be equal to demand at time t for building in microgrid i. The electric supply on the left side consists of electricity generated by solar PV (Ei,tbpv), SOFC (Ei,tfc), purchased from the grid (Ei,tgb), the charging station (Ei,tcsb) as well as other microgrids (Ej,i,tmbtr). The right (demand) side items of the electricity include electricity consumption by EC (Ei,tec) and HP (Ei,thp), electricity sold back to the utility grid (Ei,tbg), building electric load (Ei,tbel), electricity transmitted to CS (Ei,tbcs), and other microgrids (Ei,j,tmbtr). The transmission loss of electric energy within the microgrids is considered by implementing the factor of Lwire.(2)Ei,tbpv+Ei,tfc+Ei,tgb+Ei,tcsb+∑jEj,i,tmbtr×1−LwireEi,tec+Ei,thp+Ei,tbg+Ei,tbel+Ei,tbcs+∑jEi,j,tmbtr,∀i,t,j≠i.(b)
Thermal Load Balance Constraints. The heating balance is displayed in equation (3), where recovered heat (Qi,tre) from the SOFC power generation plus heating supply from the boiler (Qi,tbo) and heat pump (Qi,thp) are used to satisfy the heating consumption of absorption chiller (Qi,tach) and the building heating load (Qi,tbhl) in microgrid i. Similarly, the cooling balance showed in equation (4) means that the cooling energy supply should be equal to electric demand at time t for building in microgrid i. The left (supply) side of the cooling demand includes the cooling generated by absorption chiller (Qi,tacc) and electric chiller (Qi,tecc) plus transmitted from other microgrids (Qj,i,tmbtr). The right (demand) side of the cooling demand includes the building’s cooling demand (Qi,tbcl) and transmits to other microgrids (Qi,j,tmbtr). Lpipe represents the transmission loss of cooling energy within the microgrids.(3)Qi,tre+Qi,tbo+Qi,thp=Qi,tach+Qi,tbhl,∀i,t,j,(4)Qi,tacc+Qi,tecc+Qj,i,tmbtr=Qi,tbel+Qi,j,tmbtr1−Lpipe,∀i,t,j≠i.(c)
Constraints for PV. Electricity generated by PV panel (Ei,tbpv) can be calculated by its size (CAPibpv) multiplying by electricity generation efficiency (ηbpv) and solar radiation (SRt) in microgrid i as follows:(5)Ei,tbpv≤CAPibpv×ηbpv×SRt,∀i,t,i.(d)
Constraints for CCHP. The electric/thermal output of SOFC (Ei,tfc), boiler (Qi,tbo), absorption chiller (Qi,tacc), electric chiller (Qi,tecc), and heat pump (Qi,thp) must be not more than the corresponding installed capacities (CAP) in microgrid i as given in equations (6)–(10). The energy conversion efficiencies are given in equations (11)–(16), where η shows the energy efficiency of various devices in the CCHP system.(6)Ei,tfc≤CAPifc∀i,t,(7)Qi,tbo≤CAPibo∀i,t,(8)Qi,tacc≤CAPiac∀i,t,(9)Qi,tecc≤CAPiec∀i,t,(10)Qi,thp≤CAPihp∀i,t,(11)Ei,tfc=ηfc×NGi,tfc∀i,t,(12)Qi,tre=ηre×Ei,tfc∀i,t,(13)Qi,tacc=ηac×Qi,tach∀i,t,(14)Qi,tecc=ηec×Ei,tec∀i,t,(15)Qi,tbo=ηbo×NGi,tbo∀i,t,(16)Qi,thp=ηhp×Ei,thp∀i,t.


## 3.1.3. Electric Vehicle Charging Station Operation Decision Model

(a)
Electric Load Balance Constraints. Constraint in equation (17) represents that the supply and demand of electricity should be equal at time t for CS in microgrid i. For microgrid i, the energy suppliers include purchased from utility grid (Ei,tgcs), transmitted from building (Ei,tbcs), generated by CS’s PV (Ei,tcspv), and transmitted from other microgrids j (Ej,i,tmcstr). The energy demand includes electricity sold back to the utility grid (Ei,tcsg), transmitted to other buildings (Ei,tcsb), requested energy to charge EVs (Ei,tcs), and transmitted to other microgrid j (Ei,j,tmcstr). Constraint (18) means that electricity requested energy to charge EVs equals to the EVs’ charging minus discharging energy.(17)Ei,tgcs+Ei,tbcs+Ei,tcspv+∑jEj,i,tmcstr×1−Lwire=Ei,tcsg+Ei,tcsb+Ei,tcs+∑jEi,j,tmcstr∀i,t,(18)Ei,tcsev=∑vEi,v,tevc−Ei,v,tevdc∀i,t.(b)
Constraints for PV. Similarly, electricity generated by CS’s PV panel (Ei,tcspv) is restrained by its capacity (CAPicspv) times electricity generating efficiency (ηcspv) and solar radiation (SRt) in microgrid i.(19)Ei,tcspv≤CAPicspv×ηcspv×SRt∀i,t.(c)
Constraints for Electric Vehicles. For the EVs, Ti,vaandTi,vua represent the EV v arriving and leaving the CS in microgrid i, which are assumed as available and unavailable time, respectively. During the EV parking time (available time), the thermal energy stored in EVs (Ei,v,t+1ev) is bounded as shown in equation (20) and can be calculated by charging energy minus discharging energy as displayed in equations (21) and (22). Constraint (23) guarantees the electricity level of EV (Ei,v,t−1ev) which can meet the owner’s desired electricity level when the EV leaves the CS. Equation (24) designates that EVs cannot be in charging (xi,v,tevc) and discharging (xi,v,tevdc) states at the same time. Constraints (25) and (26) are used to guarantee that the EV battery charging and discharging electricity are limited by their maximum and minimum charging and discharging rate, respectively.(20)CAPi,vev×SOCi,vevmin≤Ei,v,tev≤CAPi,vev×SOCi,vevmax∀i,v,Ti,va≤t≤Ti,vua,(21)Ei,v,t+1ev=CAPi,vev×SOCi,vini+Ei,v,t+1evc−Ei,v,t+1evdc×Δt∀i,v,t=Ti,va,(22)Ei,v,t+1ev−Ei,v,tev=Ei,v,t+1evc−Ei,v,t+1evdc×Δt∀i,v,Ti,va<t<Ti,vua,(23)Ei,v,t−1ev≥CAPi,vev×SOCi,vdes∀i,v,t=Ti,vua,(24)xi,v,tevc+xi,v,tevdc≤1∀i,v,Ti,va<t<Ti,vua,(25)CAPi,vev×αi,vcmin×xi,v,tevc≤Ei,v,tevc≤CAPi,vev×αi,vcmax×xi,v,tevc∀i,v,Ti,va<t<Ti,vua,(26)CAPi,vev×αi,vdcmin×xi,v,tevdc≤Ei,v,tevdc≤CAPi,vev×αi,vdcmax×xi,v,tevdc∀i,v,Ti,va<t<Ti,vua.


## 3.1.4. Constraints for Grid Exchange

Constraint (27) indicates that electricity cannot be imported from and exported to power grid at the same time for the microgrid. Equation (28) ensures that electricity from utility grid and CS are restricted by maximum capacity. Similarly, equation (29) states that electricity feed-in utility grid and CS are restricted by maximum capacity.(27)xi,tim+xi,tex≤1∀i,t,(28)Ei,tbg+Ei,tcsg≤xi,tex×CAPgrid∀i,t,(29)Ei,tgb+Ei,tgcs≤xi,tim×CAPgrid∀i,t.


## 3.1.5. Constraints for Networking

The constraint expressed in equations (30), (33), and (36) indicates that electricity/cooling feed-in and import cannot happen simultaneously. Note that xi,j,tmb and xi,j,tmcs are binary variables to represent the electricity from buildings and CS in microgrids i to j exchange status, respectively. The transmission of electricity energy (Ei,j,tmbtr, Ej,i,tmbtr) restricted by exchange status is defined in equations (31), (32), (34), and (35). xi,j,tmbc is binary variable to control the cooling in building from microgrids i to j exchange status. Constraints (37) and (38) ensure that the transmission of cooling energy (Qi,j,tmbtr, Qj,i,tmbtr) is limited by exchange status. M is a big number, normally adopted in mixed integer programming.(30)xj,i,tmb+xi,j,tmb≤1∀i,t,j≠i,(31)Ej,i,tmbtr≤M×xj,i,tmb∀i,t,j≠i,(32)Ei,j,tmbtr≤M×xi,j,tmb∀i,t,j≠i,(33)xj,i,tmcs+xi,j,tmcs≤1∀i,t,j≠i(34)Ej,i,tmcstr≤M×xj,i,tmcs∀i,t,j≠i,(35)Ei,j,tmcstr≤M×xi,j,tmcs∀i,t,j≠i,(36)xj,i,tmbc+xi,j,tmbc≤1∀i,t,j≠i,(37)Qj,i,tmbtr≤M×xj,i,tmbc∀i,t,j≠i,(38)Qi,j,tmbtr≤M×xi,j,tmbc∀i,t,j≠i.


## 3.2. Objectives

In this study, three objectives are evaluated from the economic, environmental, and energy saving perspective, respectively.


### 3.2.1. Operational Cost (COST)

The collective interest of the microgrids can be formulated as equation (39a), which is to minimize the sum of each microgrid’s energy cost as equation (39b). As shown in equation (39b), the energy cost of each microgrid can be subdivided into cost associated with natural gas (the first term), maintenance cost of equipment (the second term), costs associated with power grids (the third term), and revenue associated with utility grids (the last term).(39a)minfCOST=∑iCOSTi,(39b)COSTi=PNG×∑tNGi,tfc+NGi,tbo+Pmaint×∑tEi,tfc+Ei,tbpv+Ei,tcspv+Qi,tbo+Qi,thp+Qi,tecc+Qi,tacc+Ptim×∑tEi,tgb+Ei,tgcs−Ptex×∑tEi,tbg+Ei,tcsg∀i.


### 3.2.2. Carbon Dioxide Emission (CDE)

Greenhouse gases from the power generation combusting fuel deteriorate the environment, in which global warming is one of the crucial issues. The CDE is selected as the environmental index, and the collective environmental benefit of the microgrids can be built as equation (40a), with the aim of minimizing the sum of each microgrid’s CDE as equation (40b). As displayed in equation (40b), the CDE of each microgrid can be estimated by the emissions from natural gas consumption (the first term) and purchased electricity from the utility grid (the second term).(40a)minfCDE=∑iCDEi,(40b)CDEi=αNG×∑tNGi,tfc+NGi,tbo+αgrid×∑tEi,tgb+Ei,tgcs.


### 3.2.3. Primary Energy Consumption (PEC)

The collective energy benefit of the microgrids can be formulated as equation (41a), which is to minimize the sum of each microgrid’s PEC as equation (41b). The PEC of each microgrid includes primary energy consumption of natural gas (the first term), utility grid (the second term), and PV panel (the last term), as shown in equation (41b).(41a)minfPEC=∑iPECi,(41b)PECi=δNG×∑tNGi,tfc+NGi,tbo+δgrid×∑tEi,tgb+Ei,tgcs+δsolar×∑tEi,tbpv+Ei,tcspv.


## 3.2.1. Operational Cost (COST)

The collective interest of the microgrids can be formulated as equation (39a), which is to minimize the sum of each microgrid’s energy cost as equation (39b). As shown in equation (39b), the energy cost of each microgrid can be subdivided into cost associated with natural gas (the first term), maintenance cost of equipment (the second term), costs associated with power grids (the third term), and revenue associated with utility grids (the last term).(39a)minfCOST=∑iCOSTi,(39b)COSTi=PNG×∑tNGi,tfc+NGi,tbo+Pmaint×∑tEi,tfc+Ei,tbpv+Ei,tcspv+Qi,tbo+Qi,thp+Qi,tecc+Qi,tacc+Ptim×∑tEi,tgb+Ei,tgcs−Ptex×∑tEi,tbg+Ei,tcsg∀i.


## 3.2.2. Carbon Dioxide Emission (CDE)

Greenhouse gases from the power generation combusting fuel deteriorate the environment, in which global warming is one of the crucial issues. The CDE is selected as the environmental index, and the collective environmental benefit of the microgrids can be built as equation (40a), with the aim of minimizing the sum of each microgrid’s CDE as equation (40b). As displayed in equation (40b), the CDE of each microgrid can be estimated by the emissions from natural gas consumption (the first term) and purchased electricity from the utility grid (the second term).(40a)minfCDE=∑iCDEi,(40b)CDEi=αNG×∑tNGi,tfc+NGi,tbo+αgrid×∑tEi,tgb+Ei,tgcs.


## 3.2.3. Primary Energy Consumption (PEC)

The collective energy benefit of the microgrids can be formulated as equation (41a), which is to minimize the sum of each microgrid’s PEC as equation (41b). The PEC of each microgrid includes primary energy consumption of natural gas (the first term), utility grid (the second term), and PV panel (the last term), as shown in equation (41b).(41a)minfPEC=∑iPECi,(41b)PECi=δNG×∑tNGi,tfc+NGi,tbo+δgrid×∑tEi,tgb+Ei,tgcs+δsolar×∑tEi,tbpv+Ei,tcspv.


## 3.3. Multiobjective Optimization

The multiobjective optimization (MOO) algorithm is substantially different from single-objective optimization since there are various but conflicting evaluation indicators in MOO. The weighting method uses weights to represent the goals preferred by decision makers [30], which is adopted to solve the proposed model after normalization in this paper.


### 3.3.1. Normalization of Indicators

In equation (42), three indicators have different units and characteristics, in which f represents an objective and fnon shows the normalized objective calculated by(42)fnon=1,f≤f−,f−f−f+−f−,f−≤f≤f+,0,f≥f+,where f−=minf and f+=maxf.


### 3.3.2. Weighting Method

After normalization of these indicators and using the weighting method, the multiobjective model can be transformed into the following single-objective model:(43)minf=ω1fCOST,non+ω2fCDE,non+ω3fPEC,non,where ω represents the weight of objective, which will determine the solution of the fitness function and show the performance priority. Different weighting scenarios represent the preferences of decision makers in different contexts.


## 3.3.1. Normalization of Indicators

In equation (42), three indicators have different units and characteristics, in which f represents an objective and fnon shows the normalized objective calculated by(42)fnon=1,f≤f−,f−f−f+−f−,f−≤f≤f+,0,f≥f+,where f−=minf and f+=maxf.


## 3.3.2. Weighting Method

After normalization of these indicators and using the weighting method, the multiobjective model can be transformed into the following single-objective model:(43)minf=ω1fCOST,non+ω2fCDE,non+ω3fPEC,non,where ω represents the weight of objective, which will determine the solution of the fitness function and show the performance priority. Different weighting scenarios represent the preferences of decision makers in different contexts.


## 4. Operation Decision Models for Transactive Energy Management

To carry out this analysis, the proposed model (i.e., model III) balancing global and local benefits is compared with two reference models (i.e., models I and II). Reference model I is presented to search for the total benefit for all the microgrids that are disconnected and operated separately, which is used to compare the performance of the microgrids with single microgrid operation. The global microgrids are obtained in the reference model II integrating V2G and V2B, when each microgrid can freely connect with other microgrids to share information and exchange energy in the transactive energy work.


### 4.1. Reference Model I

The mathematic model is formulated as reference model andfI is the total performance for the microgrids. Constraint (45) ensures that there is no energy exchange among microgrids, buildings, and charging stations.Reference model I:(44)minfI=ω1×fI,COST,non+ω2×fI,CDE,non+ω3×fI,PEC,non,(45)s.txj,i,tmb=0xi,j,tmb=0;xj,i,tmcs=0;xi,j,tmcs=0;xj,i,tmb=0;xi,j,tmb=0,∀i,t,j≠i.Equations (45) and (1)–(38) compose the constraints for reference model I jointly.


### 4.2. Reference Model II

In this operation model, reference model II is built to study the operation decisions for the microgrids with the aim to obtain global microgrids benefit, when energy can freely exchange among microgrids. In this model, maximizing the global collective benefit of the microgrids is the focus and a MILP model is formulated to obtain the operation decisions for the microgrids.Reference model II:(46)minfII=ω1×fII,COST,non+ω2×fII,CDE,non+ω3×fII,PEC,non.Equations (1)–(38) compose the constraints for reference model II.


### 4.3. Model III

Although the reference model II can minimize the collective interests, the individual interests of each microgrid may not be ensured. That is to say, some microgrids may have to spend more if they join the clusters. For a profit-driven entity (i.e., the microgrid’s owner), to guarantee each microgrid achieves cost savings in the clusters, reference model II is extended to model III by introducing a constraint in equation (48). α, β, and δ are parameters to indicate the percentage of interest saving regarded as the same level. Furthermore, equations (48)–(50) can be modified to be constraints to guarantee the microgrid’s economic, environmental, and energy benefits when microgrid i decision markers pay attention to achieving individual interests.Model III:(47)minfIII=ω1×fIII,COST,non+ω2×fIII,CDE,non+ω3×fIII,PEC,non,(48)s.t.fiIII,COST,non≤fiI,COST,non×1−α∀i,(49)fiIII,CDE,non≤fiI,CDE,non×1−β∀i,(50)fiIII,PEC,non≤fiI,PEC,non×1−δ∀i,Constraints in equations (1)–(38)


## 4.1. Reference Model I

The mathematic model is formulated as reference model andfI is the total performance for the microgrids. Constraint (45) ensures that there is no energy exchange among microgrids, buildings, and charging stations.Reference model I:(44)minfI=ω1×fI,COST,non+ω2×fI,CDE,non+ω3×fI,PEC,non,(45)s.txj,i,tmb=0xi,j,tmb=0;xj,i,tmcs=0;xi,j,tmcs=0;xj,i,tmb=0;xi,j,tmb=0,∀i,t,j≠i.Equations (45) and (1)–(38) compose the constraints for reference model I jointly.


## 4.2. Reference Model II

In this operation model, reference model II is built to study the operation decisions for the microgrids with the aim to obtain global microgrids benefit, when energy can freely exchange among microgrids. In this model, maximizing the global collective benefit of the microgrids is the focus and a MILP model is formulated to obtain the operation decisions for the microgrids.Reference model II:(46)minfII=ω1×fII,COST,non+ω2×fII,CDE,non+ω3×fII,PEC,non.Equations (1)–(38) compose the constraints for reference model II.


## 4.3. Model III

Although the reference model II can minimize the collective interests, the individual interests of each microgrid may not be ensured. That is to say, some microgrids may have to spend more if they join the clusters. For a profit-driven entity (i.e., the microgrid’s owner), to guarantee each microgrid achieves cost savings in the clusters, reference model II is extended to model III by introducing a constraint in equation (48). α, β, and δ are parameters to indicate the percentage of interest saving regarded as the same level. Furthermore, equations (48)–(50) can be modified to be constraints to guarantee the microgrid’s economic, environmental, and energy benefits when microgrid i decision markers pay attention to achieving individual interests.Model III:(47)minfIII=ω1×fIII,COST,non+ω2×fIII,CDE,non+ω3×fIII,PEC,non,(48)s.t.fiIII,COST,non≤fiI,COST,non×1−α∀i,(49)fiIII,CDE,non≤fiI,CDE,non×1−β∀i,(50)fiIII,PEC,non≤fiI,PEC,non×1−δ∀i,Constraints in equations (1)–(38)


## 5. Case Study

To validate the economic, environmental, and energy criteria of the proposed system using the multiobjective models built, the microgrids in Shanghai, China, are investigated as a case study. In this research, the decision time interval is set at 1 h. The microgrids consisting of five public building categories (i.e., hotel, office, hospital, school, and supermarket) are selected for analysis in the case. The typical weekday hourly energy demand profiles including electric, heating, and cooling of each building in the transition season are plotted in Figure3 [31]. The TOU energy prices are displayed in Figure 4 [26], and the solar radiation indexes are presented in Figure 5 [32].Figure 3
Typical weekday electricity heating and cooling demand profiles of five buildings in the microgrids located in Shanghai.Figure 4
The energy price.Figure 5
The solar radiation indexes.For the charging stations, each parking area is set with a maximum capacity of five EVs. Moreover, it is assumed each CS is in full-state during corresponding time interval set to be in Table2. The EVs arrive at the CS with 20% battery charged and leave with 100% charged battery. Furthermore, other parameters related to the models are given in Table 3.Table 2
The EVs arriving and leaving time of five buildings in the microgrids.
OfficeSupermarketHotelSchoolHospitalArriving time8 : 0018 : 001 : 007 : 001 : 00Leaving time17 : 0023 : 008 : 0019 : 0024 : 00Table 3
Description of parameter settings [29, 30, 32–35].
CategoryNotationValueTechnical inputηfc0.45ηre0.37ηac1ηec4ηbo0.85ηhp3.5ηbpv0.18ηcspv0.18Lwire0.05Lpipe0.06SOCi,vevmin0.10SOCi,vevmax1αi,vcmin0.05αi,vcmax0.25αi,vdcmin0.05αi,vdcmax0.25SOCi,vini0.2SOCi,vevd1Capacity inputCAPi,vev30 kWhCAPgrid700 kWCAPibpv1000 m2CAPifc580 kWCAPibo1500 kWCAPiac1200 kWCAPiec1200 kWCAPihp1200 kWCAPicspv200 m2Economic inputPmaint0.0015 $/kWhEnvironment inputαNG0.18 kg/kWhαgrid0.95 kg/kWhEnergy inputδNG1.047δsolar0.9δgrid3.336A computer with an Intel (R) Core (™) i5-8265U CPU @1.60 GHz processor and 8 GB memory running Windows 10 on a 64 bit operating system is used for all experiments. The proposed multiobjective optimization method of transactive energy management is implemented in Python 3. The optimization programming language is adopted to code the mathematical models in IBM ILOG CPLEX v12.8 optimizer. Through the Python API, the optimization models are solved by IBM Decision Optimization CPLEX (DOcplex) Modelling for Python. To verify the models’ scalability and feasibility, three operation decision models under four weighting scenarios are examined for economic, environmental, and energy performance in the objective function.


### 5.1. Neutral Scenario

In the neutral scenario, equal weights (i.e.,ω1=ω2=ω3=1/3) are adopted in the operation decision models and represent equal importance for the three objectives. After running the reference models I-II and model III, the economic and environmental as well as energy performances of each microgrid are recorded in Table 4, and the three models run for 316 seconds. The total COST, CDE, and PEC for the microgrids under reference model I are $3,350.44, 18.46 tons, and 12.49∗104, respectively. It is demonstrated that reference model II can achieve about 22% CDE reduction and 12% PEC saving compared with reference model I. Despite the COST of reference models I and II is about the same, each microgrid cost saving level is different. Model III is adopted to obtain an optimal energy strategy while balancing global and single-cost interests with α=0, when the microgrid’s entity focuses on economic performance. In addition, β and δ are set to be 0. The results of reference models and model III are shown in Table 4, and the saving/reduction in economic, environmental, and energy performance of each microgrid under different operation models is displayed in Figure 6.Table 4
Performances of each microgrid in the microgrids for reference models I-II and model III in the neutral scenario.
Microgrid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1429.88452.39429.883.311.931.832.001.651.592447.36478.84447.363.052.051.922.031.711.643705.30716.52705.303.503.083.042.542.322.294834.35763.31834.354.203.233.552.842.412.595933.55946.04933.554.404.064.083.082.892.90Overall3350.443357.103350.4418.4614.3514.4212.4910.9811.01Figure 6
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the neutral scenario: (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)As shown in Table4, the objective function of three models (i.e., fI,fII,andfIII) under neutral scenario can be known with 0.67, 0.67, and 0.014. Therefore, the proposed method can achieve economic, environmental, and energy benefits simultaneously. In Figure 6, the economic interest of each microgrid can be ensured in the presented model III when the cost of 1-th, 2-th, 3-th, and 5-th microgrid is larger than reference models I. Compared with reference I, the PEC and CDE reduction levels of each microgridare similar in model III and reference model II. Subgraphs (a), (b), and (c) in Figure 6 also show that the economic interests have been equilibrated best. Therefore, as shown in Table 4 and Figure 6, the proposed microgrids integrating V2G and V2B formulated multiobjective model can obtain multibenefits and achieve a balance between global and individual benefits under a neutral scenario.


### 5.2. Proeconomic Scenario

In the proeconomic scenario,ω1=0.8 and ω2=ω3=0.1 are set to represent the proenvironmental attitude and are used in operation decision models. Table 5 displays the performance of each microgrid under three operation models, and the three models run for 309 seconds. In the reference model II under proeconomic scenario, the centralize collective operation can achieve about 6% COST saving, 9% CDE reduction, and 4% PEC reduction compared with the reference model I. However, the economic benefits of each microgrid may be not ensured, for example, the COST and CDE as well as PEC of 2-th microgrid increased. For proeconomic microgrid entity, constraint ensuring economic benefit are added to the proposed model III. Model III is adopted to guarantee each microgrid can have cost saving with minimum level. α is set up to be an average percentage (i.e., 6%) based on the overall COST saving, and β as well as δ are set be 0.Table 5
Performances of each microgrid in the microgrids for reference models I-II and model III in the proeconomic scenario.
Microgrid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1353.585286.347326.443.893.073.072.342.312.312362.474426.674340.733.703.443.112.412.372.183611.778674.822575.074.204.574.142.953.032.934804.252650.213756.004.413.644.182.972.642.805867.95773.5815.874.884.524.753.363.153.29Overall3000.0392811.5562814.1121.0819.2419.2514.0313.5013.51As shown in Table5, the value of fI,fII,andfIII under proeconomic weighting scenario can be known with 1, 0, and 0.038. Therefore, the proposed method can get multibenefits similar to reference model II and superior to reference model I under microgrids running alone. In Figure 7, the COST and PEC of 3-th microgrid are higher than operation separately, which represent that the benefit is damaged. Subgraphs (a), (b), and (c) in Figure 7 also show that the economic interests have been equilibrated best. Therefore, as shown in Table 5 and Figure 7, the proposed microgrids integrating V2G and V2B formulated multiobjective model can obtain multibenefits and achieve balance between global and individual benefits under a proeconomic weighting scenario.Figure 7
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the proeconomic scenario. (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)


### 5.3. Proenvironmental Scenario

In the proenvironmental scenario,ω2=0.8 and ω1=ω3=0.1 are set to represent the proenvironmental attitude and adopt in the operation decision models. Table 6 displays the performances of each microgrid in microgrids, and the three models run for 311 seconds. In the reference model II under proenvironmental scenario, the centralized collective operation can achieve 22% CDE reduction and 12% PEC reduction when each microgrid’s environmental pollution emission is reduced by different percentages. In order to balancing global and single benefit, model III is adopted to guarantee that each microgrid can have CDE reduction with same level. Based on the overall CDE reduction, β is set up to be 21% when there is no optimal solution with average level (i.e., 22%). In addition, α as and δ are set be 0.Table 6
Performances of each microgrid in the microgrids for reference models I-II and model III in the proenvironmental scenario.
Microgrid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1429.88449.36605.623.311.922.612.001.642.042447.50475.87519.183.052.032.222.041.711.823705.30715.60645.633.503.072.772.542.312.134832.90765.81781.134.193.253.312.862.412.455933.55950.47814.324.404.083.473.082.902.54Overall3349.133357.13365.8818.4514.3514.3812.5210.9710.98In Table6, the values of fI,fII,andfIII under proenvironmental weighting scenario can be obtained with 0.67, 0.1586, and 0.338. Therefore, the multibenefits of the presented model III are inferior to reference II when ignoring individual benefits but also better than reference model I when considering microgrids running alone. Figure 8 shows that CDE reduction level of each microgrid in the proposed method is balanced than other models. As shown in Table 6 and Figure 8, although the benefits of microgrids reduced compared with neglecting interest balance, the proposed microgrids integrating V2G and V2B formulated multiobjective models can achieve balance between global and individual benefits under proenvironmental weighting scenario.Figure 8
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the proenvironmental scenario. (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)


### 5.4. Proenergy Scenario

In the proenergy scenario, the reference models and model III are solved withω3=0.8 and ω1=ω2=0.1, which represents the proenergy attitude. Table 7 shows the performance of each microgrid in the microgrids, and the three models run for 322 seconds. In the reference model II under proenergy scenario, the centralized collective operation can achieve 12% CDE saving, 24% CDE reduction, and 9% PEC reduction, when each microgrid’s PEC is reduced by a different percentage. Furthermore, Model III is adopted to guarantee that each microgrid can achieve PEC reduction at the same level. Based on the overall PEC reduction, δ is set up to be 8% when there is no optimal solution with average percentage (i.e., 9%). In addition, α and β are set be 0.Table 7
Performances of each microgrid in the microgrids for reference models I-II and model III in the proenergy scenario.
Micro-grid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1533.98452.39480.533.311.932.061.901.651.722547.91478.84487.943.502.052.091.941.711.743798.04721.68696.073.503.102.992.462.332.264926.34760.90795.044.273.223.372.732.402.4951020.91943.29898.904.404.053.853.002.882.76Overall3827.183357.103358.4818.9814.3514.3612.0410.9710.97In Table7, the values of fI,fII,andfIII under proenvironmental weighting scenario can be calculated with 1, 0, and 0.0017. Therefore, the multibenefits of formulated model III is similar with reference model II and better than reference I. The energy interest of each microgrid is achieved outstanding compared with reference models I and II (see Figure 9). As shown in Table 7 and Figure 9, the proposed microgrids integrating V2G and V2B formulated multiobjective model can achieve balance global and individual benefit under the proenergy weighting scenario, when the interest of microgrids basically guaranteed.Figure 9
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the proenergy scenario. (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)


## 5.1. Neutral Scenario

In the neutral scenario, equal weights (i.e.,ω1=ω2=ω3=1/3) are adopted in the operation decision models and represent equal importance for the three objectives. After running the reference models I-II and model III, the economic and environmental as well as energy performances of each microgrid are recorded in Table 4, and the three models run for 316 seconds. The total COST, CDE, and PEC for the microgrids under reference model I are $3,350.44, 18.46 tons, and 12.49∗104, respectively. It is demonstrated that reference model II can achieve about 22% CDE reduction and 12% PEC saving compared with reference model I. Despite the COST of reference models I and II is about the same, each microgrid cost saving level is different. Model III is adopted to obtain an optimal energy strategy while balancing global and single-cost interests with α=0, when the microgrid’s entity focuses on economic performance. In addition, β and δ are set to be 0. The results of reference models and model III are shown in Table 4, and the saving/reduction in economic, environmental, and energy performance of each microgrid under different operation models is displayed in Figure 6.Table 4
Performances of each microgrid in the microgrids for reference models I-II and model III in the neutral scenario.
Microgrid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1429.88452.39429.883.311.931.832.001.651.592447.36478.84447.363.052.051.922.031.711.643705.30716.52705.303.503.083.042.542.322.294834.35763.31834.354.203.233.552.842.412.595933.55946.04933.554.404.064.083.082.892.90Overall3350.443357.103350.4418.4614.3514.4212.4910.9811.01Figure 6
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the neutral scenario: (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)As shown in Table4, the objective function of three models (i.e., fI,fII,andfIII) under neutral scenario can be known with 0.67, 0.67, and 0.014. Therefore, the proposed method can achieve economic, environmental, and energy benefits simultaneously. In Figure 6, the economic interest of each microgrid can be ensured in the presented model III when the cost of 1-th, 2-th, 3-th, and 5-th microgrid is larger than reference models I. Compared with reference I, the PEC and CDE reduction levels of each microgridare similar in model III and reference model II. Subgraphs (a), (b), and (c) in Figure 6 also show that the economic interests have been equilibrated best. Therefore, as shown in Table 4 and Figure 6, the proposed microgrids integrating V2G and V2B formulated multiobjective model can obtain multibenefits and achieve a balance between global and individual benefits under a neutral scenario.


## 5.2. Proeconomic Scenario

In the proeconomic scenario,ω1=0.8 and ω2=ω3=0.1 are set to represent the proenvironmental attitude and are used in operation decision models. Table 5 displays the performance of each microgrid under three operation models, and the three models run for 309 seconds. In the reference model II under proeconomic scenario, the centralize collective operation can achieve about 6% COST saving, 9% CDE reduction, and 4% PEC reduction compared with the reference model I. However, the economic benefits of each microgrid may be not ensured, for example, the COST and CDE as well as PEC of 2-th microgrid increased. For proeconomic microgrid entity, constraint ensuring economic benefit are added to the proposed model III. Model III is adopted to guarantee each microgrid can have cost saving with minimum level. α is set up to be an average percentage (i.e., 6%) based on the overall COST saving, and β as well as δ are set be 0.Table 5
Performances of each microgrid in the microgrids for reference models I-II and model III in the proeconomic scenario.
Microgrid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1353.585286.347326.443.893.073.072.342.312.312362.474426.674340.733.703.443.112.412.372.183611.778674.822575.074.204.574.142.953.032.934804.252650.213756.004.413.644.182.972.642.805867.95773.5815.874.884.524.753.363.153.29Overall3000.0392811.5562814.1121.0819.2419.2514.0313.5013.51As shown in Table5, the value of fI,fII,andfIII under proeconomic weighting scenario can be known with 1, 0, and 0.038. Therefore, the proposed method can get multibenefits similar to reference model II and superior to reference model I under microgrids running alone. In Figure 7, the COST and PEC of 3-th microgrid are higher than operation separately, which represent that the benefit is damaged. Subgraphs (a), (b), and (c) in Figure 7 also show that the economic interests have been equilibrated best. Therefore, as shown in Table 5 and Figure 7, the proposed microgrids integrating V2G and V2B formulated multiobjective model can obtain multibenefits and achieve balance between global and individual benefits under a proeconomic weighting scenario.Figure 7
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the proeconomic scenario. (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)


## 5.3. Proenvironmental Scenario

In the proenvironmental scenario,ω2=0.8 and ω1=ω3=0.1 are set to represent the proenvironmental attitude and adopt in the operation decision models. Table 6 displays the performances of each microgrid in microgrids, and the three models run for 311 seconds. In the reference model II under proenvironmental scenario, the centralized collective operation can achieve 22% CDE reduction and 12% PEC reduction when each microgrid’s environmental pollution emission is reduced by different percentages. In order to balancing global and single benefit, model III is adopted to guarantee that each microgrid can have CDE reduction with same level. Based on the overall CDE reduction, β is set up to be 21% when there is no optimal solution with average level (i.e., 22%). In addition, α as and δ are set be 0.Table 6
Performances of each microgrid in the microgrids for reference models I-II and model III in the proenvironmental scenario.
Microgrid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1429.88449.36605.623.311.922.612.001.642.042447.50475.87519.183.052.032.222.041.711.823705.30715.60645.633.503.072.772.542.312.134832.90765.81781.134.193.253.312.862.412.455933.55950.47814.324.404.083.473.082.902.54Overall3349.133357.13365.8818.4514.3514.3812.5210.9710.98In Table6, the values of fI,fII,andfIII under proenvironmental weighting scenario can be obtained with 0.67, 0.1586, and 0.338. Therefore, the multibenefits of the presented model III are inferior to reference II when ignoring individual benefits but also better than reference model I when considering microgrids running alone. Figure 8 shows that CDE reduction level of each microgrid in the proposed method is balanced than other models. As shown in Table 6 and Figure 8, although the benefits of microgrids reduced compared with neglecting interest balance, the proposed microgrids integrating V2G and V2B formulated multiobjective models can achieve balance between global and individual benefits under proenvironmental weighting scenario.Figure 8
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the proenvironmental scenario. (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)


## 5.4. Proenergy Scenario

In the proenergy scenario, the reference models and model III are solved withω3=0.8 and ω1=ω2=0.1, which represents the proenergy attitude. Table 7 shows the performance of each microgrid in the microgrids, and the three models run for 322 seconds. In the reference model II under proenergy scenario, the centralized collective operation can achieve 12% CDE saving, 24% CDE reduction, and 9% PEC reduction, when each microgrid’s PEC is reduced by a different percentage. Furthermore, Model III is adopted to guarantee that each microgrid can achieve PEC reduction at the same level. Based on the overall PEC reduction, δ is set up to be 8% when there is no optimal solution with average percentage (i.e., 9%). In addition, α and β are set be 0.Table 7
Performances of each microgrid in the microgrids for reference models I-II and model III in the proenergy scenario.
Micro-grid indexCOST ($)CDE (tons)PEC (∗104)Reference model IReference model IIModel IIIReference model IReference model IIModel IIIReference model IReference model IIModel III1533.98452.39480.533.311.932.061.901.651.722547.91478.84487.943.502.052.091.941.711.743798.04721.68696.073.503.102.992.462.332.264926.34760.90795.044.273.223.372.732.402.4951020.91943.29898.904.404.053.853.002.882.76Overall3827.183357.103358.4818.9814.3514.3612.0410.9710.97In Table7, the values of fI,fII,andfIII under proenvironmental weighting scenario can be calculated with 1, 0, and 0.0017. Therefore, the multibenefits of formulated model III is similar with reference model II and better than reference I. The energy interest of each microgrid is achieved outstanding compared with reference models I and II (see Figure 9). As shown in Table 7 and Figure 9, the proposed microgrids integrating V2G and V2B formulated multiobjective model can achieve balance global and individual benefit under the proenergy weighting scenario, when the interest of microgrids basically guaranteed.Figure 9
Saving performances of each microgrid in the microgrids for reference models I-II and model III in the proenergy scenario. (a) COST. (b) CDE. (c) PEC.
(a)(b)(c)


## 6. Conclusion

In this research, the multiobjective model is formulated to conduct a research on the transactive energy management for the microgrids integrating EVs. The COST, CDE, and PEC are selected as the economic, environmental, and energy indexes, respectively. Three different operation models are proposed to analyze the energy management in microgrids. The reference model I is formulated to maximize the total benefit with no exchange among microgrids. The reference model II is proposed to maximize collective interest under exchanging electricity and cooling energy among microgrids. The proposed model III is adopted to maximize collective interest within a satisfactory level of individual benefit. In the case study, microgrids located in Shanghai under different weighting scenarios are analyzed, and the mathematical models are solved by IBM’s commercial solver CPLEX in Python with running average about 315 seconds. The experimental results indicate that proposed method can ensure benefit of each microgrid under weighting scenarios (i.e., decision maker’s preference), when the multiple interest of microgrids is close to ignoring interest balance. For example, each microgrid have cost saving more than 6% under proeconomic weighting scenario. Therefore, the proposed method can be used to ensure the sustainable development for microgrids.In this study, energy supply and demand are assumed as predetermined. However, they are influenced by many factors, such as extreme weather, equipment failure, and traffic congestion. In the future study, the energy management can be analyzed considering various uncertainties (e.g., solar radiation, energy load, and EV driving schedules). Robustness programming can be used in formulating stochastic optimization problems of microgrids. In addition, with the expansion of the scale of microgrids, the intelligent optimization algorithm can be adjusted and adopted to solve the microgrids’ mathematical models.



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*Source: 4578868-2022-12-27.xml*