diesel multi-generation energy systems

Sustainable Cities and Society 48 (2019) 101592

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Bi-level optimization of design, operation, and subsidies for standalone solar/diesel multi-generation energy systems

T

⁎

Xi Luo , Jiaping Liu, Yanfeng Liu, Xiaojun Liu State Key Laboratory of Green Building in Western China, School of Building Services Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Bi–level optimization Solar subsidies Multi–generation energy system Demand response

Unlike grid–tied energy systems, wherein uniform renewable energy subsidies can be applied directly, the standalone multi-generation energy systems integrated with renewable energy in remote areas deserve to be subsidized specifically according to the local natural resources and energy demands. To establish an effective subsidy policy, the impacts of electrical and thermal subsidies for renewable energy on the system performance need to be investigated effectively, from the perspective of various stakeholders. In this study, a bi–level optimization model is proposed to obtain optimal design, operation, and subsidies for a standalone multi-generation energy system situated on a remote island; the system incorporates solar energy, fossil energy, and storage. Herein, the social cost to the society is set as the upper-level objective, and the private cost to the residents is set as the lower-level objective. The results indicate that production-based incentives of solar electrical energy and solar thermal energy jointly impact the design and operation of the energy system to minimize the social and private costs simultaneously; moreover, the demand response could further increase the flexibility of system operation, thus decreasing the system cost to a larger extent.

1. Introduction 1.1. Background The environmental concerns and limited reserves of fossil fuels have motivated energy planners and policy makers to deploy more alternative energy sources for energy supply using efficient combinations of heat and power units. In remote areas such as isolated islands, the demand for renewable energy is stronger because the costs of the distribution system for non-renewable energy carriers are unfavorable (Lorestani & Ardehali, 2018). Encouraging renewable energy investment is the key for policy makers to promote renewable energy; however, investors are generally not keen on renewable energy. The primary reason is the challenge of investment recovery owing to the high initial investment cost of renewable energy technologies. Although rational system designs and operation strategies facilitate reduction in the initial system cost, they are insufficient for the energy system to attain a satisfactory level of renewable penetration rate. As renewable energy exhibits environmental advantages over conventional energy, the corresponding environmental externalities function as a barrier to renewable energy development. To correct the market distortion, it is necessary for policy makers to design incentive mechanisms to promote

⁎

renewable energy. As uniform subsidies are determined based on the average case within a large range, standalone multi-generation energy systems integrated with renewable energy deserve to be subsidized specifically according to local natural resources and energy demands. Therefore, the system design and operation strategy in conjunction with government subsidies impact the economic effectiveness and feasibility of standalone multi-generation energy system projects in remote areas, following the problem to determine the optimal values of these design parameters. 1.2. Previous researches Numerous researchers have investigated the design optimization of multi-generation energy system integrated with renewable energies; meta-heuristic methods are commonly used to solve these optimization problems. For example, Yang et al. developed a mathematical model of a combined cooling, heating, and power (CCHP) system and adopted particle swarm optimization to obtain the optimum values of the design parameters (Yang & Zhai, 2018). Arandian et al. examined the effects of environmental emissions in the optimal combination and allocation of renewable and non-renewable combined heating and power (CHP) technologies in heat and electricity distribution networks based on an

Corresponding author. E-mail address: [email protected] (X. Luo).

https://doi.org/10.1016/j.scs.2019.101592 Received 4 December 2018; Received in revised form 5 May 2019; Accepted 5 May 2019 Available online 06 May 2019 2210-6707/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

Subscripts

Latin Symbols

DG PV PVT AC EC EES WT EESC EESD s a ACI ACO CL L FUEL O&M CAP e th cell solar,elec solar,th CO2 sys trans i,trans o,trans

P Q PBI n G COP C E f F l SOC N T r A p t F U d C S m V k

electrical power (kW) thermal power (kW) production-based incentive ($/kWh) number of units solar irradiance (W/m2) coefficient of performance economic cost ($) environmental cost ($) lower level objective function value upper level objective function value lifetime (y) state of charge (%) capacity of storage system (kWh) temperature(℃) discount rate (%) area (m2) price ($) time-step (h) upper level objective function value heat loss coefficient (W/m2K) day specific heat capacity (J /kg℃) subsidy ($) mass (kg) volume (m3) proportionality coefficient (m3/m2)

Greek Symbols

Acronyms

η ρ δ κ τα

DR FL SSC

efficiency (%) density (kg/m3) environmental impact (gCO2/kWh) diesel fuel consumption (l) transmission and absorption coefficient

diesel generator photovoltaic photovoltaic/thermal absorption chiller electric chiller electricity energy storage water tank electrical energy storage charge electrical energy storage discharge single array absorption chiller input absorption chiller output cooling load electrical load diesel fuel operation and maintenance capital cost electrical thermal cell solar electrical solar thermal carbon dioxide system transferred transferred in transferred out

demand response fixed-load social cost of carbon dioxide

attention in recent years (Aghaei & Alizadeh, 2013; Chen et al., 2018; Jing, Bai, & Wang, 2012; Motevasel, Seifi, & Niknam, 2013; Wu, Mavromatidis, Orehounig, & Carmeliet, 2017; Zhang, Evangelisti, Lettieri, & Papageorgiou, 2015; Zheng et al., 2018). However, multiobjective optimization only balances several variables at the same level; the hierarchical decision-making framework, which is typical in actual engineering applications, cannot be reflected in single-level multi-objective optimization. Thus, bi-level optimization is developed to solve the problem. Bi-level optimization is effective for addressing the decision making problems wherein each decision maker at two hierarchical levels independently regulates a set of decision variables, and their decisions are affected by each other (Jin, Li, & Nie, 2018). Although bilevel programming problems are NP (non-deterministic polynomial)hard, a number of methodologies have been developed to solve bi-level programming problems. These can be mainly classified into three categories (Han, Zhang, Hu, & Lu, 2016): the vertex enumeration approach (Shi, Lu, & Zhang, 2005), the Karush-Kuhn-Tucker (KKT) approach (Bahramara, Parsa Moghaddam, & Haghifam, 2016; Wu et al., 2018), and the penalty function approach (White & Anandalingam, 1993). Bi-level optimization also provides an opportunity to combine mathematical programming methods and meta-heuristic methods. For example, Evins proposed a methodology to address the design and operation of a building and its energy system at three levels: building design, system design, and system operation. The optimization techniques used are a multi-objective genetic algorithm in the design stage

improved particle swarm optimization algorithm (Arandian & Ardehali, 2017). Maleki designed a hybrid energy system integrated with solar and wind by multiple metaheuristic approaches; these include genetic algorithm, particle swarm optimization algorithm, and improved bee algorithm (Maleki, Hafeznia, Rosen, & Pourfayaz, 2017; Maleki, 2018). With regard to the operation optimization, mathematical programming methods and meta-heuristic methods are the most frequently-used optimization algorithms. In a study by Zheng et al., a mixed integer nonlinear programming (MINLP) multi-objective optimization model was developed for operational planning of a highly integrated CCHP system in urban China (Zheng et al., 2018). Ondeck et al. described a novel simultaneous optimization of design and operating strategies for a CHP plant with photovoltaic (PV) integration as a utility producer for a residential neighborhood (Ondeck, Edgar, & Baldea, 2017). Lorestani et al. developed a simulation model for optimizing an autonomous CHP system incorporating photovoltaic/thermal (PVT) panels and wind turbines; the model was developed by a new evolutionary particle swarm optimization algorithm (Lorestani & Ardehali, 2018). Wang et al. proposed an energy smart hybrid community renewable energy system that considered both the thermal and electricity market at the level of a large community (Wang, Abdollahi, Lahdelma, Jiao, & Zhou, 2015). Because of the limitations of single-objective optimization in addressing practical problems wherein several aspects of performance are important, multi-objective optimization has received particular 2

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multi-level optimization (Stojiljković, 2017). However, there are few examples of previous research applying hierarchical optimization processes to subsidy-related optimization of these energy systems. Another commonly omitted problem is that many of the aforementioned studies examine the subsidies according to only the electrical generation of energy systems, whereas the inherent values of thermal production from renewable energies are not reflected. The answers to the following questions are not forthcoming from previous research works: Is it necessary to introduce thermal subsidy apart from electrical subsidy when the energy system generate solar electrical energy and solar thermal energy simultaneously? How does the solar electrical subsidy and solar thermal subsidy interact with each other to impact the optimization results of a multi-generation energy system? What is the optimal subsidy for a standalone multi-generation energy system, and how can it be estimated? In this study, a bi-level optimization aimed at minimizing the social and private costs is developed to obtain accurate design, operation, and solar subsidies of a standalone multi-generation energy system, the system herein comprises various supply-side technologies including PV, PVT, and diesel generator (DG). In the proposed system, PV and PVT panels are used to reduce fossil energy consumption; their optimal capacity ratio is determined according to the electrical and cooling demands of the consumers. Considering the social and individual interests, the impacts of solar electrical subsidy and solar thermal subsidy on the system performance are investigated to provide a basis for governments to develop subsidy policies. For comparison, the model is constructed in a demand response scenario and a fixed-load scenario. The remainder of this study is organized as follows: Section 2 introduces the proposed energy system. Section 3 explains the mathematical model of the energy system and the optimization approach. The results of the simulation and optimization are presented and discussed in Section 4. Finally, Section 5 presents the conclusions of the study.

and mixed integer linear programming (MILP) in the operation stage (Evins, 2015). Stojiljković presented a methodology to formulate the multi-objective bi-level optimization of energy supply systems; herein, upper-level decision makers decided on the design and policy using scatter search method, and the plant operation was defined at the lower level using MILP (Stojiljković, 2017). Over the past several years, interest in the determination and optimization of renewable energy subsidies has increased. For example, Zhang et al. proposed a real option model for estimating the optimal subsidy for a renewable energy power generation project; they used a stochastic process to describe the market price of electricity, carbon dioxide price, and investment cost (Zhang, Zhou, Zhou, & Chen, 2017). Andor et al. derived the optimal subsidization of renewable energies in electricity markets; the results indicated that generation subsidies should correspond to the externalities of electricity generation and investment subsidies should correspond to the externalities of capacity (Andor & Voss, 2016). Yang et al. employed a dynamic control model to study the welfare effects of a subsidy game for renewable energy investment between two neighboring regions (Yang, Nie, Liu, & Shen, 2018). He et al. established an optimization model of China’s energy prices, taxes, and subsidy policies based on the dynamic computable general equilibrium (He, Liu, Du, Zhang, & Pang, 2015). Yang et al. established a duopoly model incorporating renewable energy enterprises and traditional energy enterprises based on the market, with both complete and asymmetric information (Yang, Chen, & Nie, 2016). Jeon et al. proposed a method of optimizing financial subsidies and public research and development investments for renewable energy technologies using system dynamics and a real option model (Jeon, Lee, & Shin, 2015).

1.3. Contributions In summary, a considerable number of models have been developed to optimize the energy system and subsidy mechanism. However, the subsidy optimization is always separated from the accurate system design in these studies; therefore, the unit generation costs from historical data are used in most of the subsidy optimization studies, rather than the cost computed from the specific system model. Although this is practical from a macroscopic perspective, the establishment of subsidy policies for remote areas should be correlated with the capacity and scheduling of standalone systems. This is because the natural resources and energy demands of remote areas vary across regions; the highly location-specific characteristics of remote areas render the average cost and uniform subsidies inapplicable. Moreover, certain remote regions such as the national borders have higher self-sufficiency requirement of energy supply; therefore, the local subsidy should be specially adapted to the system design and operation to maximize the local social welfare. In these particular areas, energy system optimization should be a part of the subsidy design optimization process, because the system cost may significantly depend on the subsidy policy, imposing the necessity for

2. System description In this study, the proposed solar/diesel multi-generation energy system is assumed to be installed on a remote tropical island in the South China Sea. The island includes a residential population of approximately 100 fishermen. Owing to the tropical monsoon climate, space heating is not necessary on the island. Therefore, the primary energy demands consist of only the cooling and electrical demands. Two typical days are used in this study to presents the weather variation in the dry season (from November to April) and wet season (from May to October). Fig. 1 illustrates the typical electrical and cooling loads of the island in these two seasons during a 24-h time interval. The cooling demand of the island is simulated and computed by (EnergyPlus (2019)) with the cooling set point of 25℃. In the simulation model, 50 houses with an area of 1000 ft2 each are grouped as an aggregated node to obtain the cooling demand curve of the entire island. The number of occupants in each house is assumed to be two (Luo, Zhu, Liu, & Liu,

Fig. 1. Electrical and cooling demands of the island based on hourly resolution of typical days in dry and wet seasons. 3

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2018). The electrical loads are obtained from the building energy load profile estimator of Solar Advisor Model (SAM) (SAM, 2019). Owing to seasonal and temporal variation, solar energy cannot reliably satisfy the energy demand. Therefore, standalone systems integrate conventional-energy-based prime movers in conjunction with renewables. Fig. 2 illustrates the proposed solar/diesel multi-generation energy system for the island. The energy system consists of PVT panels, PV panels, DGs, absorption chillers (AC), and electric chillers (EC). Storage systems including electrical energy storage (EES) and water tank are also integrated into the system. As shown in Fig. 2, PVT and PV panels are employed to generate electricity to satisfy the electrical demand of the island. If solar power is in short supply, the DGs start to operate and compensate the power shortage; under excess solar power, the surplus is stored in the EES system. The PVT panels also provide thermal energy to be converted to cooling energy via the ACs. When the AC output is insufficient to satisfy the cooling requirement, the shortage is supplemented by the ECs.

ηtht = ταPVT (1 − ηet, PVT ) −

(4) t t Uloss (Tcell , PVT − Ta )

(5)

where ταPVT denotes the transmission and absorption coefficient of the PVT panel, Uloss denotes the heat loss coefficient, and Tat is the ambient temperature. The output power from a PV panel of area APV at time t is expressed as (Guangqian, Bekhrad, Azarikhah, & Maleki, 2018; Maleki, 2018) t t t PPV , s = APV G ηe, PV

(6)

t ηet, PV = ηr , PV ηpc [1 − NT (Tcell , PV − Tref )]

(7)

where ηet, PV represents the efficiency of the PV panels, ηr , PV is the reference module efficiency, ηpc is the power conditioning efficiency, and t NT is the photovoltaic panel efficiency temperature coefficient. Tcell , PV is the cell temperature and can be calculated as follows (Guangqian et al., 2018; Maleki, 2018):

3. Methodology

t t ⎡ NOCT − 20 ⎤ Gt Tcell , PV = Ta + 800 ⎣ ⎦

3.1. System modeling

(8)

where NOCT is the nominal cell operating temperature. The electrical power from the PVT array, thermal power from the PVT array, and electrical power from the PV array at time-step t can be calculated by

The generated electrical power and electrical efficiency of a PVT panel at time step t can be calculated by the following equations (Yousefi, Ghodusinejad, & Kasaeian, 2017): t t t PPVT , s = APVT G ηe, PVT

(1)

t t PPVT , a = nPVT PPVT , s

t ηet, PVT = ηref , PVT (1 − βref , PVT (Tcell , PVT − Tref ))

(2)

t QPVT ,a

Gt

where APVT denotes the total area of a PVT panel, denotes the solar radiation on an unit area of a panel, ηet, PVT denotes the electrical efficiency of the panel, ηref , PVT denotes the reference electrical efficiency of the panel, βref , PVT denotes the power temperature coefficient of the panel, Tref denotes the reference temperature, and t denotes the timet step. Tcell , PVT is the PV cell temperature; it depends on the environmental conditions and can be estimated as (Yousefi et al., 2017) t t t Tcell , PVT = 30 + 0.0175(G − 300) + 1.14(Ta − 25)

Gt

=

t nPVT QPVT ,s

t t PPV , a = nPV PPV , s

(9) (10) (11)

where nPVT denotes the number of PVT panels in the array and nPV denotes the number of PV panels in the array. The water tank is used as the thermal energy storage system in this study. Pressurized water is stored in the tank and transfers the input energy into the generator of the AC. The working fluid is pressurized water at 5 bar, a pressure level that permits water to remain in the liquid phase up to 150 ℃ (Bellos, Tzivanidis, Symeou, & Antonopoulos, 2017). Note that in this study, the water tank is considered as a mixed node; moreover, the thermal energy that cannot be utilized is permitted

(3)

The generated thermal power and thermal efficiency of a PVT panel can be expressed as follows (Yousefi et al., 2017):

Fig. 2. Diagram of the solar/diesel multi-generation energy system. 4

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overcome the barriers arising from externalities (Bhattacharyya, 2011); one of these is the provision of subsidies. Subsidies can be defined as the difference between the price that would exist in a market in the absence of distortion and the price charged to consumers, at a specified time (Bhattacharyya, 2011). In this study, subsidies are in the form of production-based incentive (PBI), such that the energy system can operate perfectly and allocate resources efficiently. Therefore, two objectives need to be achieved in the process of system optimization: (i) minimize the private costs to the residents, and (ii) minimize the social costs to the society. To balance the assessment criteria, bi-level optimization is introduced in this study. Bi-level optimization divides a problem into sections; each section is addressed using the most appropriate evaluation and optimization processes (Evins, 2015). Two important assumptions of this study for constructing the bi-level optimization model are as follows: (i) on the premise of minimizing the annualized system social cost, the government could minimize subsides, and (ii) residents are concerned only about their own interests. Under these assumptions, the government will search for all the feasible combinations of solar power PBI (PBIsolar , elec ) and solar thermal PBI (PBIsolar , th ). Corresponding to each pair of PBIsolar , elec and PBIsolar , th , the residents optimize the size and operation of the system to lower their net cost after receiving subsidies from the government. Optimal values of PBIsolar , elec and PBIsolar , th that minimize the optimal social cost can be determined. From the government’s perspective, the goal is to induce the residents to design and operate the system optimally with the least cost. Therefore, it is necessary and feasible to determine a pair of PBIsolar , elec and PBIsolar , th in the feasible set that minimizes the subsidies borne by the government. Thus, the complete optimization procedure is as follows: step 1, minimize the annualized system private cost of the residents to obtain the optimal system design and operation for each feasible pair of PBIsolar , elec and PBIsolar , th ; step 2, search for the feasible pairs of PBIsolar , elec and PBIsolar , th that minimize the annualized system social cost based on the optimized system design and operation in step 1; step 3, minimize the cost borne by the government to obtain the optimal PBIsolar , elec and PBIsolar , th . The flowchart of the proposed optimization model is shown in Fig. 4. The basic function of a bi-level optimization assumes the following structure (Luo et al., 2018):

to be dumped using heat exchangers for hot water cooling. Thus the energy balance equation of the water tank can be calculated by

Cp ρVWT

dTWT t t t = (QPVT , a − Q ACI − Qdumped ) Δt dt

(12)

where Cp is the specific heat capacity of the pressurized water, ρ is the t t Δt is the water density, TWT is the temperature of the water tank, Q ACI thermal energy delivered to the AC during the time interval Δt , and t Qdumped Δt is the thermal energy dumped during the time interval Δt . VWT is the volume of the water tank and proportional to the area of the PVT array. kPVT,WT is the proportionality coefficient. The relationship between VWT and PVT area can be expressed as

VWT = nPVT APVT kPVT , WT

(13)

In this study, PVT panels generate electrical and thermal energy from solar radiation with the tilt angle of 20° and azimuth of 180°. The meteorological data used in this study is of Qionghai, a city near the South China Sea, and derived from the EnergyPlus simulation software website (Weather Data, 2019).The detailed global horizontal irradiation (GHI) variations during typical days during the dry and wet seasons are illustrated in Fig. 3. EES is adopted to increase the operational flexibility and energy efficiency of the system by enabling the buffering of insufficient or excess energy generation. The state-of-charge (SOC) of the EES at timestep t is as follows (Lorestani & Ardehali, 2018): t t−1 SOCEES = SOCEES +

t PEESC ΔtηEESC

nEES NEES

−

t PEESD Δt ηEESD nEES NEES

(14)

where NEES is the nominal capacity, ηEESC is the corresponding charge efficiency, and ηEESD is the discharge efficiency of the EES. All the efficiencies are assumed to be constant, and the self-discharge rate of the EES is not considered in this study. The diesel consumption by the DGs can be calculated as (RodríguezGallegos et al., 2018) t t nominal κFUEL = nDG (a⋅PDG + b⋅PDG ) Δt

(15)

where nDG is the number of DGs in the system, a and b are constants that t depend on the quality of the DGs, PDG is the output power of an innominal dividual DG at time-step t , and PDG is the nominal power of an individual DG. It is assumed that the outputs of devices of similar type are equal at each time-step. The outputs of the ACs and ECs are modeled as follows (Guajardo & Jörnsten, 2015): t t Q ACO = Q ACI ⋅COPAC

(16)

t t QEC = PEC ⋅COPEC

(17)

minF (x , y ) x

s.t.x ∈ X = {x: H (x ) ≤ 0} y = arg minf (x , y ) y

s.t.g (x , y ) ≤ 0, y ∈ Y = {y: G (y ) ≤ 0}

(18)

where COPAC and COPEC are the coefficients of performance of the AC and EC, respectively. In this study, COPAC and COPEC are assumed to be constant. The cost and technical information of these components are presented in Tables 1 and 2. 3.2. System optimization The owner of the energy system should be determined prior to optimization; this is because the rationality of the optimization result correlates highly with the optimization objective, which varies across owners. For example, the objective pertains more to the general welfare of the whole society if the public sector undertakes the project; meanwhile, the private sector is more concerned with its self-interest. In this study, it is assumed that the residents of the island are the project investors who bear all the system costs. It is apparent that the residents will minimize the use of renewable energy to lower the system cost; however, this conduct negatively affects the social benefits. A number of support mechanisms have been used to promote renewable energy to

Fig. 3. Typical GHI variations of the island during dry and wet seasons within a 24-h time interval. 5

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where p, n, and l are the unit price, number, and life span of the t component, respectively. r is the benchmark discount rate, κFUEL is the

Table 1 Costs of key components.

diesel fuel consumption at time-step t ,

Device

Size

Cost

PVT panel PV panel

1.49 m2 0.18 kW

Diesel generator

10 kW

Absorption chiller Electric chiller Electrical energy storage Water tank

10 kW 10 kW 10 kWh

415.4 $/m2 (Lorestani & Ardehali, 2018) 1776 $/ kW (Al-Ugla, El-Shaarawi, Said, & Al-Qutub, 2016) 500 $/kW (Rodríguez-Gallegos et al., 2018) 516 $/kW (Al-Ugla et al., 2016) 400 $/kW (Al-Ugla et al., 2016) 280 $/kWh (Lorestani & Ardehali, 2018) 1137 $/m3 (Bellos et al., 2017)

Uloss ταPVT ηref

9.12 W/m2K 0.9 15 %

βref

0.43% /℃

ηpc

1

t t t QEC + Q ACO = QCL

(26)

t SOCEES,min ≤ SOCEES ≤ SOCEES,max

(27)

t TWT ,min ≤ TWT ≤ TWT ,max

(28)

365

t t t xEESC nEES PEESC,min ≤ PEESC ≤ xEESC nEES PEESC ,max

(32)

t xEESD nEES PEESD,min

(33)

0≤

(20)

CO & M = CCAP⋅ηO & M

(22)

365

Ssolar , th

365

d=1 t=1

⎠

ξit, k

≤

(35)

ni, k,max x it, k

ni, k,max (x it, k

− 1) ≤

(36)

ξit, k

≤ n i, k

(37)

(38)

PLt , trans

is the electrical demand after DR at time t . The transferwhere rable load refers to the load that can be shifted depending on the requirements of the consumers, such as for the use of washing machines, electric heaters, and disinfection cabinets. At any time-step, the load transferred in and out should satisfy the following constraints:

(23)

24

⎛ ⎞ t t = ⎜ ∑ ∑ (QPVT , a − Qdumped ) Δt ⎟ PBIsolar , th = = d 1 t 1 ⎝ ⎠

(34)

t t t t t t t PPV , a + PPVT , a + nDG PDG + PEESD = PL, trans + PEC + PEESC

24

⎞ t ∑ ∑ PPVT , a Δt ⎟ PBIsolar , elec

≤

t xEESD nEES PEESD,max

This study assumes that the SOC and water tank temperature at time zero are equal to those at the end of the planning horizon. The installation of each component is limited by the optimization search space, which is listed in Table 3. Traditionally, the energy demand has to be satisfied by modulating the supply side. For comparison, demand response (DR) management, which is an effective method for adjusting the load curves for a smoother system operation, is considered in the model to investigate its effects on the system performance improvement. The optimization with and without DR management is called the DR scenario and fixed-load (FL) scenario, respectively (Table 4). To adapt to the DR scenario, Eq. (25) in the FL scenario is converted to the following form:

(19)

(21)

24

≤

t PEESD

ξit, k = x it, k ni, k

24

365

(30)

Notably, the above optimization model is a MINLP problem. Considering the computational complexity, the optimization model is transformed into a MILP problem by introducing new variables ξit, k as follows:

⎛ ⎞ t CFUEL = ⎜ ∑ ∑ κFUEL Δt ⎟ pFUEL 1 1 = = d t ⎝ ⎠

⎛ t Ssolar , elec = ⎜ ∑ ∑ PPV , a Δt + ⎝ d=1 t=1

(29)

(31)

t t xEESC + xEESD ≤1

r (1 + r )li

i

≤

t xEC nEC QEC ,max

t t t xAC nAC Q ACO,min ≤ Q ACO ≤ xAC nAC Q ACO,max

n i, k +

∑ pi ni⋅ (1 + r )li − 1

t QEC

is the binary variable defined as the operating state of the where component. Because the charging and discharging of the EES cannot occur simultaneously, the following constraints hold:

3.2.1. Lower level The objective in the lower level is to minimize the cost borne by the system investors, i.e., the residents of the island. The objective function, denoted by, is the sum of the annualized capital cost, fuel cost, and maintenance cost of the system. The solar subsidies inclusive of the electrical and thermal incentives offset part of the cost; therefore, the final expression for f is as follows:

CCAP =

≤

≤

t xDG PDG,max

x it

where F is the objective of the master optimization, and f is the objective of the slave optimization. x and y are the variables at the master and slave levels, respectively.

f = CCAP + CFUEL + CO & M − Ssolar , elec − Ssolar , th

≤

t PDG

t xEC nEC QEC,min

15.5% 3.7 × 10−3 /℃ 43 ℃ 50 L/m2 2.5 0.7 0.246 l/kWh 0.084 l/kWh 0.85 0.85

ηr − PV NT NOCT kPVT , WT COPEC COPAC a b ηEESC ηEESD

(25)

t xDG PDG,min

2

1.49 m 1.28 m2 25 ℃

t t t t t t t PPVT , a + PPV , a + nDG PDG + PEESD = PL + PEC + PEESC

For a stable operation, the output of each device at any time-step is constrained as follows:

Value (Unit)

APVT APV Tref

is the capital recovery

factor, and ηO & M is the ratio of the operation and maintenance costs to the annualized capital cost of the system. PBIsolar , elec is the PBI of solar electrical energy, and PBIsolar , th is the PBI of solar thermal energy. In the following equations, Eq. (25) represents the electrical balance of the multi-generation energy system. Eq. (26) is the constraint that must be satisfied for the cooling demands in each time interval.

Table 2 Technical characteristics of key components (Al-Ugla et al., 2016; Das, Al-Abdeli, & Kothapalli, 2018; Guangqian et al., 2018; Lorestani & Ardehali, 2018; Maleki, 2018; Rodríguez-Gallegos et al., 2018; Settino et al., 2018; Talmatsky & Kribus, 2008). Parameter

r (1 + r )li (1 + r )li − 1

(24) 6

t t PLt , trans = PLt + PLi , trans − PLo, trans

(39)

t t t t fit PLt ait,min ≤ PLi , trans ≤ f i PL ai,max

(40)

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Fig. 4. Flowchart of the bi-level optimization model. n

Table 3 Optimization search space.

n

∑ PLit ,trans Δt= ∑ PLot ,trans Δt t=1

Component

Range

PVT panel PV panel Diesel generator Absorption chiller Electric chiller Electrical energy storage PBIsolar , elec PBIsolar , th

0–10,000 units 0–10,000 units 0–50 units 0–50 units 0–50 units 0–100 units 0–0.20 $/kWh,elec 0–0.20 $/kWh,th

t=1

3.2.2. Upper level The upper optimization objective is to minimize the annualized social cost of the system; it includes the annualized economic and environmental costs of the standalone solar/diesel multi-generation energy system. The mathematical objective function of the social cost is described as follows:

F = Csys + Esys f ot PLt aot,min

≤

fit + f ot ≤ 1

t PLo , trans

≤

f ot PLt aot,max

(43)

(44)

where Csys denotes the annualized economic cost and Esys denotes the annualized environmental cost. The annualized economic cost consists of the capital cost, fuel cost, and maintenance cost of the system.

(41)

(42)

Csys = CCAP + CFUEL + CO & M

where PLt , trans is the power demand after the load transfer at time-step t ; t t PLi , trans and PLo, trans are the loads transferred in and out, respectively, at time step t ; ait, min and ait, max are the rates of the minimum and maximum feasible loads, respectively, transferred to the original load at time-step t ; aot, min and aot, max are the rates of the minimum and maximum feasible loads, respectively, transferred out from the original load at time-step t ; and fit and f ot are the binary values indicating the transfer direction. In this study, ait, min , ait, max , aot, min and aot, max are assumed to be constant. The detailed technical characteristics of the system is shown in Table 4. Within a specified period, the load transferred in must equal the load transferred out. The following equation presents these relationships:

(45)

The second part of the social cost is the annualized environmental cost that varies considerably across energy technologies. Because renewable energy reduces the emission of carbon dioxide and other greenhouse gases when compared with traditional fossil fuel, the cost of the carbon dioxide emitted by the system is identified as the environmental cost in this study and expressed as follows:

Esys = EDG + Esolar , elec + Esolar , th + EEES 365

24

⎛ ⎞ t EDG = ⎜ ∑ ∑ nDG PDG Δt ⎟ δDG⋅pCO2 ⎝ d=1 t=1 ⎠ 7

(46)

(47)

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high computing cost, the variables in the upper level are constrained to a limited stepwise range. The optimization method in the upper level is grid search, and the search space of the PBIs is discretized into a 20 × 20 matrix with equal increments of 0.01 $/kWh,elec and 0.01 $/kWh,th. Therefore, it is feasible to optimize the system with regards to each combination of PBIsolar , elec and PBIsolar , th . This discretization lowers the computation cost of the multi-level optimization, it is also practical because excessive precision is not necessary for governments in formulating subsidy polices. Finally, the PBIsolar , elec and PBIsolar , th that minimize the system social cost with the least sum of Ssolar , elec and Ssolar , th is selected from the results of the bi-level optimization, as the optimal PBIsolar , elec and PBIsolar , th .

Table 4 Technical characteristics of the multi-generation energy system.

365

Parameter

Value

lEES lPVT lPV lEC lAC lWT lDG pFUEL ηO & M r ηEESC ηEESD PDG, max PDG, min PEESC , max PEESC , min PEESD, max PEESD, min QEC , max QEC , min Q ACO, max Q ACO, min SOCEES, min SOCEES, max ai, min ai, max ao, min ao, max TWT , min TWT , max

5y 25 y 25 y 12 y 20 y 25 y 15 y 0.91 $/l 2% 8% 0.85 0.85 12 kW 3 kW 2 kW 0 kW 2 kW 0 kW 10 kW 1 kW 10 kW 1 kW 0.2 1 0 0.2 0 0.2 90 ℃ 150 ℃

24

365

4. Results and discussion 4.1. Optimal system design In this study, the annualized system social costs with 20 × 20 combinations of PBIsolar , elec and PBIsolar , th are minimized to obtain the optimal design, operation, and subsidies of a solar/diesel multi-generation energy system. If the subsidies are excessively low, the renewable energy penetration rate would be below expectation, and the environmental benefit of such systems cannot be completely exploited. If the subsidies are excessively high, the final system design would deviate from the optimal configuration, and the government would be required to bear the unnecessary cost. In this study, the minimum annualized social cost of the system in the FL scenario is $ 210,430 (PBIsolar , elec = 0.04 $/kWh,elec, PBIsolar , th = 0.01 $/kWh,th), whereas the cost in the DR scenario is $ 194,030 (PBIsolar , elec = 0.05 $/kWh,elec, PBIsolar , th = 0 $/kWh,th). The optimal component capacities of the system in the FL and DR scenarios are presented in Table 5. As illustrated, the application of DR results in a decrease in the capacities of the DG, PVT, and AC; however, it increases the capacities of the PV, EES, and EC. This result indicates that in the DR scenario, more electrical energy is generated from the PV to satisfy the energy demand of the residents.

24

⎛ ⎞ ⎛ ⎞ t t Esolar , elec = ⎜ ∑ ∑ PPV , a Δt ⎟ δPV , elec⋅pCO2 + ⎜ ∑ ∑ PPVT , a Δt ⎟ δPVT , elec⋅pCO2 ⎝ d=1 t=1 ⎠ ⎝ d=1 t=1 ⎠ (48) 365

24

⎛ ⎞ t Esolar , th = ⎜ ∑ ∑ QPVT , a Δt ⎟ δsolar , th⋅pCO2 = = d 1 t 1 ⎝ ⎠ EEES = mEES δEES⋅pCO2 ⋅

r (1 + r )li (1 + r )li − 1

4.2. Optimal system operation (49)

Fig. 5 shows the load profiles with and without the demand response. It is evident that the demand response shifts the power demand from the peak hour in the evening to the middle of the day. The purpose is to make the load profiles more consistent with the generation curves of solar power and thus increase the utilization rate of solar energy. The most preferable system operating schedules for the two scenarios are presented in Fig. 6. In the FL scenario, a substantially large part of the electricity load is supplied by the DGs from 7 PM to 8 AM owing to the low solar radiation. After 8 AM, technologies using solar energy can be used, causing the DGs to reduce their output. Compared with the system operation in the wet season, the DGs operate for a shorter time during the typical day in the dry season. This is because the optimal capacities of the PVT, PV, and EES are designed with the whole year’s load profiles and oversized for the energy demand during the dry

(50)

where mEES is the mass of EES; δDG , δPV , elec , δPVT , elec , δPVT , th , and δEES are the environmental impacts of diesel–electric generation, solar–power generation by PV, solar-power generation by PVT, solar-thermal generation by PVT, and EES, respectively; these are 600 gCO2/kWh,elec (Guerrero-Lemus & Martínez-Duart, 2012), 36.6 gCO2/kWh,elec (Settino et al., 2018), 59.8 gCO2/kWh,elec (Settino et al., 2018), 8 gCO2/kWh,th (Settino et al., 2018), and 900 gCO2/kg (Settino et al., 2018), respectively. In this study, pCO2 is the societal cost (SCC) of carbon dioxide. SCC is the monetary value of the damage caused by the emission of an additional ton of carbon dioxide to the environment, or the damage prevented by reducing carbon dioxide emissions by a ton. Owing to the established adverse effects of carbon dioxide emissions, numerous studies have attempted to estimate SCC, and there is substantial variation in the results. Generally, SCC ranges between 10 $/t and 150 $/t depending on the estimation method (Garnaut, 2011; Holland et al., 1998; Hope, 2011; Tol, 2005; Watkiss, Downing, Handley, & Butterfield, 2005). The model proposed in this study derives a SCC of 50 $/t. This study utilized the ILOG’s CPLEX optimization solver (IBM, 2019) to solve the MILP model, which is formulated in (MATLAB (2019)); therefore, global optimality is guaranteed. Considering the

Table 5 Optimal component units of the solar/diesel multi-generation energy system. Device

Diesel generator PVT panel PV panel Electrical energy storage Absorption chiller Electric chiller

8

Number of units FL scenario

DR scenario

5 1078 414 57 16 3

3 948 865 61 15 6

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Fig. 5. Impacts of demand response on electrical load profiles. Fixed-load scenario Demand response scenario

be replaced with PV panels to lower the cost. Because the DR further increases the solar power generating capacity and the capacity of the EES, DGs are not used in the dry season. For a solar/diesel multi-generation energy system with AC and EC as cooling generation units, EC generally operates when there is inadequate thermal energy, typically in the morning or evening. However, in this study, the EC mainly operates when solar radiation is the highest (Fig. 7). This can be attributed to the difference between the cost of the PV and PVT. As noted previously, the cooling demand (particularly at midday) determines the minimal thermal energy from PVT and minimum number of PVT. If the cooling demand during this time interval could be lowered, certain capacity of the expensive PVT could be replaced with inexpensive PV. According to the assumption in this study, the cooling demand cannot be changed or transferred. However, the AC output could be decreased by increasing the EC output, thus reducing the thermal energy demand during this time interval. As the capacity ratio of PV to PVT is higher in the DR scenario,

season. Therefore, the capacities of these components are generally large enough to ensure the relatively low power supply in the dry season, saving the fuel cost of DGs. In the DR scenario, the load profile has been reshaped so that the electrical demand is more centralized toward the middle of the day. However, the cooling load remains unchanged; therefore, the ratio of the electrical demand to the cooling demand dramatically increases during this time interval. The result is that the share of the electrical power generated from the PV increases, whereas that from the PVT decreases (Fig. 5). This change can also be reflected by the optimal PBIsolar , elec and PBIsolar , th in the two scenarios; these are (PBIsolar , elec = 0.04, PBIsolar , th = 0.01) in the FL scenario and (PBIsolar , elec = 0.05, PBIsolar , th = 0) in the DR scenario. This phenomenon is consistent because the PVT panels produce electrical and thermal energy simultaneously; owing to this, PVT is cost-efficient when both energy demands exist. However, if the electrical demand keeps increasing and cooling demand remains unchanged, the price advantages of PV panels gradually become prominent, and a few PVT panels would

Fig. 6. Electrical balances for an optimal system in different scenarios: (a) Fixed-load scenario; (b) Demand response scenario. Fixed-load scenario Demand response scenario 9

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Fig. 7. Cooling balances for an optimal system in different scenarios: (a) Fixed-load scenario; (b) Demand response scenario. Fixed-load scenario Demand response scenario

Fig. 8. Impacts of PBI on system configuration: (a) Fixed-load scenario; (b) Demand response scenario.

the EC output is higher and more centralized at midday when compared with that in the FL scenario.

4.3. Impacts of subsidies on system design To investigate the impacts of solar subsides on the system configuration, the capacity of PV and PVT with different PBIsolar , elec and PBIsolar , th are depicted in Fig. 8. As is evident, nPV increases and nPVT 10

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increase the capacities of PV, EES, and EC. This is because the load profile was centralized in the middle of the day in the DR scenario, creating conditions in which the less expensive PV capacity expands. The study implies that optimal subsidies could encourage more social capital to shift from traditional energy to renewable energy. The cost-benefit analysis of the government is absent in this study and will be included in future work. The external investors will also be introduced in future to investigate the impacts of market competition on renewable energy subsidies, via game theory.

Table 6 Comparison of optimal annualized system social costs in the four scenarios. Scenario

PV + PVT + DG PVT + DG PV + DG DG Only

Annualized system social cost FL ($)

DR ($)

210,430 211,510 256,720 315,620

194,030 195,700 239,550 303,550

Acknowledgements

decreases with the increase in PBIsolar , elec ; meanwhile, nPV decreases and nPVT increases with the increase in PBIsolar , th . When PBIsolar , th remains at a low level, the increase in PBIsolar , elec significantly influences the capacity of PV and PVT. As PBIsolar , th increases, the variation in nPVT and nPV decreases accordingly; this indicates that the renewable energy penetration rate is gradually approaching the highest feasible value. Another observation from Fig. 6 is that the impact of PBIs on the capacity of PV and PVT in the DR scenario is smaller than that in the FL scenario. This is because DR is an effective method that can change the load profile to minimize the annualized system social cost. When DR applies, there is less room left for subsidies to decrease the cost; therefore, the effect would be less apparent.

This research was supported by China Postdoctoral Science Foundation (2018M643807XB) and Shaanxi Department of Science and Technology (2018ZDCXL–SF–03–04). References Aghaei, J., & Alizadeh, M.-I. (2013). Multi-objective self-scheduling of CHP (combined heat and power)-based microgrids considering demand response programs and ESSs (energy storage systems). Energy, 55, 1044–1054. https://doi.org/10.1016/j.energy. 2013.04.048. Al-Ugla, A. A., El-Shaarawi, M. A. I., Said, S. A. M., & Al-Qutub, A. M. (2016). Technoeconomic analysis of solar-assisted air-conditioning systems for commercial buildings in Saudi Arabia. Renewable and Sustainable Energy Reviews, 54, 1301–1310. https:// doi.org/10.1016/j.rser.2015.10.047. Andor, M., & Voss, A. (2016). Optimal renewable-energy promotion: Capacity subsidies vs. Generation subsidies. Resource and Energy Economics, 45, 144–158. https://doi. org/10.1016/j.reseneeco.2016.06.002. Arandian, B., & Ardehali, M. M. (2017). Effects of environmental emissions on optimal combination and allocation of renewable and non-renewable CHP technologies in heat and electricity distribution networks based on improved particle swarm optimization algorithm. Energy, 140, 466–480. https://doi.org/10.1016/j.energy.2017. 08.101. Bahramara, S., Parsa Moghaddam, M., & Haghifam, M. R. (2016). A bi-level optimization model for operation of distribution networks with micro-grids. International Journal of Electrical Power & Energy Systems, 82, 169–178. https://doi.org/10.1016/j.ijepes. 2016.03.015. Bellos, E., Tzivanidis, C., Symeou, C., & Antonopoulos, K. A. (2017). Energetic, exergetic and financial evaluation of a solar driven absorption chiller – A dynamic approach. Energy Conversion and Management, 137, 34–48. https://doi.org/10.1016/j. enconman.2017.01.041. Bhattacharyya, S. C. (2011). Energy economics. London: Springerhttps://doi.org/10.1007/ 978-0-85729-268-1. Chen, X., Zhou, H., Li, W., Yu, Z., Gong, G., Yan, Y., et al. (2018). Multi-criteria assessment and optimization study on 5 kW PEMFC based residential CCHP system. Energy Conversion and Management, 160, 384–395. https://doi.org/10.1016/j.enconman. 2018.01.050. Das, B. K., Al-Abdeli, Y. M., & Kothapalli, G. (2018). Effect of load following strategies, hardware, and thermal load distribution on stand-alone hybrid CCHP systems. Applied Energy, 220, 735–753. https://doi.org/10.1016/j.apenergy.2018.03.068. EnergyPlus Availabe online: www.github.com/NREL/EnergyPlus (Accessed on 1 July). Evins, R. (2015). Multi-level optimization of building design, energy system sizing and operation. Energy, 90, 1775–1789. https://doi.org/10.1016/j.energy.2015.07.007. Garnaut, R. (2011). The garnaut review 2011: Australia in the global response to climate change. Cambridge University Press. Guajardo, M., & Jörnsten, K. (2015). Common mistakes in computing the nucleolus. European Journal of Operational Research, 241, 931–935. https://doi.org/10.1016/j. ejor.2014.10.037. Guangqian, D., Bekhrad, K., Azarikhah, P., & Maleki, A. (2018). A hybrid algorithm based optimization on modeling of grid independent biodiesel-based hybrid solar/wind systems. Renewable Energy, 122, 551–560. https://doi.org/10.1016/j.renene.2018. 02.021. Guerrero-Lemus, R., & Martínez-Duart, J. M. (2012). Renewable energies and CO2. London: Springerhttps://doi.org/10.1007/978-1-4471-4385-7. Han, J., Zhang, G., Hu, Y., & Lu, J. (2016). A solution to bi/tri-level programming problems using particle swarm optimization. Information Sciences, 370-371, 519–537. https://doi.org/10.1016/j.ins.2016.08.022. He, Y. X., Liu, Y. Y., Du, M., Zhang, J. X., & Pang, Y. X. (2015). Comprehensive optimisation of China’s energy prices, taxes and subsidy policies based on the dynamic computable general equilibrium model. Energy Conversion and Management, 98, 518–532. https://doi.org/10.1016/j.enconman.2015.03.010. Holland, M., Berry, J., Forster, D., Watkiss, P., Boyd, R., Lee, D., et al. (1998). ExternE Externalities of energy. Methodology, Volume 7 update; 1999. Hope, C. (2011). The social cost of Co2 from the Page09 model. Social Science Electronic Publishing. IBM ILOP CPLEX Optimizer. Availabe online: www.imb.com/software/commerce/ optimization/cplex-optimizer (Accessed on 13 July 2018). Jeon, C., Lee, J., & Shin, J. (2015). Optimal subsidy estimation method using system dynamics and the real option model: Photovoltaic technology case. Applied Energy,

4.4. Comparison of different configurations Finally, the minimal annualized system social costs with different system configurations are presented in Table 6 for comparison. There are four scenarios with different configurations of energy generation units: Scenario 1, wherein PVT, PV, and DG are available; Scenario 2, wherein PVT and DG are available; Scenario 3, wherein PV and DG are available; and Scenario 4, wherein only DG is available. The results demonstrate that the combination of PVT and PV is the best option and that the system with only DG is most expensive; this establishes that systems incorporating multiple technologies are superior to those with only one technology. 5. Conclusions In this study, we develop a method for obtaining the optimal subsidy mechanism that ensures the rationality of the design and operation of a standalone solar/diesel multi-generation energy system that supplies residential cooling and electrical loads on a remote island. A bilevel optimization methodology is proposed to minimize the annualized social and private costs of the energy system. The primary conclusions are as follows: Government financial support plays an important role in promoting the introduction of renewable energy technologies into the market and reducing the economic gap with conventional energy technologies. To achieve the best performance, it is necessary to formulate a subsidy policy adapted to the characteristic of the renewable energy technologies; moreover, both PBIsolar , elec and PBIsolar , th are required to induce the residents to design and operate the multi-generation energy system in an optimal manner. A solar/diesel multi-generation energy system utilizes multi-energy sources synthetically and efficiently based on system integration. Therefore, more degrees-of-freedom are introduced. Hybridized with conventional energy technologies, the utilization rate of renewable energies can be improved in a more flexible manner. A good example in this study is that the AC output could be decreased by increasing the EC output; thereby, the thermal energy demand during this time interval can be reduced and the PV capacity increased. DR could minimize the system social cost by reshaping the load profiles; this is because the optimal capacity ratio of PV to PVT is highly related to the energy demands. In this study, the application of DR results in a decrease in the capacities of the DG, PVT, AC, and an in 11

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supply systems aided by problem-specific heuristics. Energy, 137, 1231–1251. https://doi.org/10.1016/j.energy.2017.06.037. Talmatsky, E., & Kribus, A. (2008). PCM storage for solar DHW: An unfulfilled promise? Solar Energy, 82, 861–869. https://doi.org/10.1016/j.solener.2008.04.003. Tol, R. S. J. (2005). The marginal damage costs of carbon dioxide emissions: An assessment of the uncertainties. Energy Policy, 33, 2064–2074. https://doi.org/10.1016/j. enpol.2004.04.002. Wang, H., Abdollahi, E., Lahdelma, R., Jiao, W., & Zhou, Z. (2015). Modelling and optimization of the smart hybrid renewable energy for communities (SHREC). Renewable Energy, 84, 114–123. https://doi.org/10.1016/j.renene.2015.05.036. Watkiss, P., Downing, T., Handley, C., & Butterfield, R. (2005). The impacts and costs of climate change. Environmental Policy Collection. Weather Data by Region. Availabe online: www.energyplus.net/weather-region/asia_ wmo_region_2/CHN%20%20 (Accessed on 20 September). White, D. J., & Anandalingam, G. (1993). A penalty function approach for solving bi-level linear programs. Journal of Global Optimization, 3, 397–419. https://doi.org/10. 1007/BF01096412. Wu, R., Mavromatidis, G., Orehounig, K., & Carmeliet, J. (2017). Multiobjective optimisation of energy systems and building envelope retrofit in a residential community. Applied Energy, 190, 634–649. https://doi.org/10.1016/j.apenergy.2016.12.161. Wu, C., Gu, W., Xu, Y., Jiang, P., Lu, S., & Zhao, B. (2018). Bi-level optimization model for integrated energy system considering the thermal comfort of heat customers. Applied Energy, 232, 607–616. https://doi.org/10.1016/j.apenergy.2018.09.212. Yang, Y.-c., Nie, P.-y., Liu, H.-t., & Shen, M.-h. (2018). On the welfare effects of subsidy game for renewable energy investment: Toward a dynamic equilibrium model. Renewable Energy, 121, 420–428. https://doi.org/10.1016/j.renene.2017.12.097. Yang, D.-x., Chen, Z.-y., & Nie, P.-y. (2016). Output subsidy of renewable energy power industry under asymmetric information. Energy, 117, 291–299. https://doi.org/10. 1016/j.energy.2016.10.089. Yang, G., & Zhai, X. (2018). Optimization and performance analysis of solar hybrid CCHP systems under different operation strategies. Applied Thermal Engineering, 133, 327–340. https://doi.org/10.1016/j.applthermaleng.2018.01.046. Yousefi, H., Ghodusinejad, M. H., & Kasaeian, A. (2017). Multi-objective optimal component sizing of a hybrid ICE+PV/T driven CCHP microgrid. Applied Thermal Engineering, 122, 126–138. https://doi.org/10.1016/j.applthermaleng.2017.05.017. Zhang, D., Evangelisti, S., Lettieri, P., & Papageorgiou, L. G. (2015). Optimal design of CHP-based microgrids: Multiobjective optimisation and life cycle assessment. Energy, 85, 181–193. https://doi.org/10.1016/j.energy.2015.03.036. Zhang, M. M., Zhou, D. Q., Zhou, P., & Chen, H. T. (2017). Optimal design of subsidy to stimulate renewable energy investments: The case of China. Renewable and Sustainable Energy Reviews, 71, 873–883. https://doi.org/10.1016/j.rser.2016.12. 115. Zheng, X., Wu, G., Qiu, Y., Zhan, X., Shah, N., Li, N., et al. (2018). A MINLP multiobjective optimization model for operational planning of a case study CCHP system in urban China. Applied Energy, 210, 1126–1140. https://doi.org/10.1016/j.apenergy. 2017.06.038.

142, 33–43. https://doi.org/10.1016/j.apenergy.2014.12.067. Jin, S. W., Li, Y. P., & Nie, S. (2018). An integrated bi-level optimization model for air quality management of Beijing’s energy system under uncertainty. Journal of Hazardous Materials, 350, 27–37. https://doi.org/10.1016/j.jhazmat.2018.02.007. Jing, Y.-Y., Bai, H., & Wang, J.-J. (2012). Multi-objective optimization design and operation strategy analysis of BCHP system based on life cycle assessment. Energy, 37, 405–416. https://doi.org/10.1016/j.energy.2011.11.014. Lorestani, A., & Ardehali, M. M. (2018). Optimization of autonomous combined heat and power system including PVT, WT, storages, and electric heat utilizing novel evolutionary particle swarm optimization algorithm. Renewable Energy, 119, 490–503. https://doi.org/10.1016/j.renene.2017.12.037. Luo, X., Zhu, Y., Liu, J., & Liu, Y. (2018). Design and analysis of a combined desalination and standalone CCHP (combined cooling heating and power) system integrating solar energy based on a bi-level optimization model. Sustainable Cities and Society, 43, 166–175. https://doi.org/10.1016/j.scs.2018.08.023. Maleki, A. (2018). Design and optimization of autonomous solar-wind-reverse osmosis desalination systems coupling battery and hydrogen energy storage by an improved bee algorithm. Desalination, 435, 221–234. https://doi.org/10.1016/j.desal.2017.05. 034. Maleki, A., Hafeznia, H., Rosen, M. A., & Pourfayaz, F. (2017). Optimization of a gridconnected hybrid solar-wind-hydrogen CHP system for residential applications by efficient metaheuristic approaches. Applied Thermal Engineering, 123, 1263–1277. https://doi.org/10.1016/j.applthermaleng.2017.05.100. MATLAB Availabe online: www.mathworks.cn/products/matlab (Accessed on 12 June 2018). Motevasel, M., Seifi, A. R., & Niknam, T. (2013). Multi-objective energy management of CHP (combined heat and power)-based micro-grid. Energy, 51, 123–136. https://doi. org/10.1016/j.energy.2012.11.035. Ondeck, A., Edgar, T. F., & Baldea, M. (2017). A multi-scale framework for simultaneous optimization of the design and operating strategy of residential CHP systems. Applied Energy, 205, 1495–1511. https://doi.org/10.1016/j.apenergy.2017.08.082. Rodríguez-Gallegos, C. D., Yang, D., Gandhi, O., Bieri, M., Reindl, T., & Panda, S. K. (2018). A multi-objective and robust optimization approach for sizing and placement of PV and batteries in off-grid systems fully operated by diesel generators: An Indonesian case study. Energy, 160, 410–429. https://doi.org/10.1016/j.energy. 2018.06.185. Syste Advisor Model (SAM). Availabe online: www.sam.nrel.gov (Accessed on 28 June 2018). Settino, J., Sant, T., Micallef, C., Farrugia, M., Spiteri Staines, C., Licari, J., et al. (2018). Overview of solar technologies for electricity, heating and cooling production. Renewable and Sustainable Energy Reviews, 90, 892–909. https://doi.org/10.1016/j. rser.2018.03.112. Shi, C., Lu, J., & Zhang, G. (2005). An extended kth-best approach for linear bilevel programming. Applied Mathematics and Computation, 164, 843–855. https://doi.org/ 10.1016/j.amc.2004.06.047. Stojiljković, M. M. (2017). Bi-level multi-objective fuzzy design optimization of energy

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