Multi-Objective Capacity Configuration of PV-Energy Storage Systems in Low-Carbon Buildings with Electric Vehicles: A Bi-Level Optimization Approach

Abstract

To support low-carbon smart buildings, this study proposes a multi-objective capacity optimization method for PV-energy storage systems considering the flexibility potential of orderly electric vehicle (EV) charging loads. First, an orderly EV charging model based on price-guided charging quantifies the flexibility potential of EV charging loads. Then, a bi-level multi-objective capacity configuration model is proposed. In the upper level, the building operator minimizes both economic and carbon emission costs, jointly optimizing PV-energy storage capacity configuration and EV charging prices. In the lower level, EV users optimize their charging schedules to minimize their charging costs in response to the charging prices. To solve this bi-level multi-objective problem, the two objectives are normalized and weighted into a single-objective function, and then a heuristic solution method based on a genetic algorithm is developed. Case study results show that the proposed mode reduces building economic cost and electricity-related carbon emissions, demonstrating the benefits of incorporating carbon emissions into demand-side optimization under the “dual-carbon” targets.

1. Introduction

Against the backdrop of global efforts to address climate change, the development of low-carbon buildings has become an important pathway for promoting the energy transition and achieving the “dual-carbon” targets. According to statistics from the International Renewable Energy Agency, building-related carbon emissions account for 28% of global carbon emissions, with energy consumption and emissions during the operational stage being the dominant contributors [1]. In China, in 2024, carbon emissions from building operations accounted for 22.1% of the national total. Among operational emissions from public buildings, urban residential buildings, and rural residential buildings, the shares of indirect emissions associated with electricity consumption reached as high as 78.3%, 49.5%, and 77.3% [2], respectively, indicating significant potential for emission reduction. Meanwhile, clean energy supply and storage technologies represented by distributed photovoltaic (PV) systems and energy storage, driven by improved technological maturity, enhanced safety, and continuously declining costs, are promoting the transition of end-users from passive electricity consumers to active energy managers [3,4]. In some microgrids and user-side applications, energy self-sufficiency has even been achieved [5]. Users can effectively reduce energy costs and carbon emissions by deploying PV and energy storage systems in and around buildings and optimizing their energy consumption in response to electricity price signals, thereby creating broader opportunities for achieving the “dual-carbon” targets [6,7]. Therefore, it is particularly important to optimize the capacity configuration of PV-storage systems in buildings by jointly considering economic performance and carbon emissions, thereby promoting the development of low-carbon buildings.

A growing body of research has focused on the coordinated configuration and operation of distributed PV and energy storage in smart buildings. Both [8,9] aimed to reduce operation costs and carbon emission costs by coordinating electrical energy storage, thermal energy storage, and hydrogen storage to optimize building energy use. However, they differ in their treatment of carbon objectives. The former imposes a zero-carbon electricity constraint, while the latter one considers the carbon objective separately from the economic objective and assigns it a specific weight. Ref. [10] showed that, after integrating electrical and thermal energy storage, the carbon emissions can be reduced by 28% while costs decrease by 7%. The joint configuration of PV and energy storage can further enhance building electrification and reduce both economic and carbon emission costs [11]. In [12], a building energy system incorporating PV, heat pumps, thermal storage, and battery energy storage achieved a 16.3% reduction in the levelized cost of electricity (LCOE) and a 20.9% reduction in carbon emissions compared with a PV-only system. The system in [13], which includes rooftop PV, battery storage, and cold thermal storage, demonstrated that a configuration with 40% PV penetration and an energy storage investment cost of 0.006 USD/kWh can reduce costs by 27.3%, outperforming configurations with either standalone PV or standalone energy storage. In studies focusing solely on energy storage operation or the impacts of specific factors on operational performance, the storage capacity is often predefined, such as the actually installed capacity [14], a value equal to the maximum net load [15], or a fixed proportion of PV capacity [16]. While this approach simplifies the optimization problem, the predefined capacity may not be optimal in terms of economic and carbon performance and may make it difficult to recover the investment cost even after operational optimization [17]. Joint optimization of capacity configuration and system operation can yield more appropriate solutions [18,19]. Despite these advances, in PV-energy storage capacity configuration, carbon objectives are typically incorporated through rigid constraints or subjectively assigned weights, making it difficult to explicitly characterize different low-carbon preferences and their impacts on resource configuration.

Meanwhile, with the increasing penetration of electric vehicles (EVs), large-scale EV charging demand in smart buildings not only imposes additional load pressure on building operation but also provides new opportunities for low-carbon and cost-effective energy management. As typical flexible loads, EV charging features temporal flexibility and controllability. While satisfying users’ travel demands, EV charging behavior can be guided through price signals or dispatch instructions to achieve peak shaving and valley filling, as well as to facilitate the utilization of PV generation [20]. Moreover, EV adoption also offers significant potential for reducing global emissions, with every 1% increase in EV penetration leading to a 0.096% reduction in global carbon emissions [21]. EV charging loads and their associated flexibility have been incorporated into building energy system models. In [22], a smart building energy system with vehicle-to-grid (V2G) capability is modeled as a Markov Decision Process, and reinforcement learning is employed to minimize operating costs. In [23], EVs are treated as flexible loads, and an optimization model is established to minimize system operating costs while considering battery state of charge (SOC) constraints and degradation costs. In [24], coordinated optimization of grid electricity purchase, PV generation, stationary energy storage, and EV charging/discharging is performed with the objective of minimizing the total system operating cost. The authors of [25] consider the dispatchable potential of EV charging stations around buildings and shows that incorporating EVs increases load coverage by 12.08%, improves grid flexibility by 29.63%, reduces annual electricity costs by 18.70%, and decreases the levelized cost of electricity by 6.24%, while also demonstrating significant benefits in terms of economic performance, carbon emissions, and storage capacity.

With the widespread adoption of time-of-use (TOU) electricity pricing, its effectiveness in regulating building loads and PV-storage operation has been well demonstrated [26]. The impact of TOU pricing on flexible loads, particularly EVs, has also been extensively studied. In [27], the impact of TOU pricing on the electricity costs for EVs parked in residential buildings is analyzed. Under TOU pricing, the effects of uncertainties in EV driving parameters [28] and users’ willingness to respond and its impact on charging power [29] have also been investigated. In these studies, the electricity price signal is typically derived from external grid TOU tariffs or other predefined fixed prices (hereinafter referred to as external prices, OPs), which serve as a common signal for both buildings and EVs. While OP reflects grid electricity prices and the upstream grid’s expectations for building electricity consumption and can effectively guide system operation and investment decisions, it does not reflect the internal energy status of the building system and may, therefore, be insufficient for effectively guiding EV charging within the building. To address this issue, Ref. [30] proposed a hybrid game-based energy system in which a Stackelberg game between the energy system operator and the building integrated energy system (BIES) allocates cooperative benefits through energy trading prices. Under the guidance of OP, heuristic intelligent algorithms are used to determine the energy transaction price between ESO and the BIES. Such an optimization-driven dynamic pricing idea has also been applied at the distribution network level to guide building users toward more desirable electricity consumption patterns and properly reward buildings for providing frequency regulation and other response services. By accounting for diverse objectives and resource states, dynamic electricity prices can provide more adaptive price signals than fixed TOU tariffs. The authors of [31] couple the load layer (including machine-learning-based industrial flexible loads and transparent residential loads) and the electricity-selling layer into a single-layer MINLP model via the Karush–Kuhn–Tucker (KKT) conditions, to obtain the optimal dynamic electricity prices for the electricity retailer and compare them with a fixed electricity price. The results show that although the fixed electricity price determined based on the upper-level wholesale prices can minimize the cost of the electricity retailer, it also yields the lowest revenue. By contrast, dynamic electricity pricing increases the profit of the electricity retailer by 130%. The authors of [32] develop a user-behavior model, which can be combined with the upper-level grid operator model to form a solvable MINLP problem to determine dynamic electricity prices. Compared with the scenario adopting fixed TOU, the grid operation cost and users’ electricity consumption cost decreased by 3.72% and 25.9%, respectively. A similar price-maker bi-level model has also been applied in frequency regulation ancillary service markets. In [33], a market platform is designed where the upper level represents an AVPP, which procures power services from lower-level ancillary service providers and sells them to the transmission system operator (TSO) for arbitrage. The upper and lower levels act as the price maker and price takers, respectively, and the model is solved by coupling the two levels through KKT optimality conditions. Compared with the fixed-price scenario, the dynamic market-clearing price scenario increases the upper-level profit by 27.9%, while enhancing the flexibility contribution of lower-level resources by 61.1%. The prices reflect both the profit-seeking behavior of participants and the respective energy states of the participating resources. The bi-level model solved via heuristic algorithms can preserve information privacy between the two levels, whereas bi-level models reformulated using KKT conditions can obtain the global optimum. Accordingly, these two approaches have their respective advantages and limitations. Based on similar principles, such an approach can also be applied to buildings or charging stations to guide the charging behavior of EVs. However, existing studies on integrated optimization of buildings and EVs primarily rely on OP and rarely consider an interactive pricing mechanism that reflects the internal energy state of the building and EV users’ response behavior.

In summary, despite extensive research efforts, three gaps remain. First, in PV-energy storage capacity configuration, carbon objectives are typically incorporated through rigid constraints or subjectively, making it difficult to reflect different low-carbon preferences in resource configuration. Second, coordination between the building energy operator and EV users primarily relies on external grid prices that do not reflect the internal energy state of the building, with limited consideration of interactive pricing mechanisms. Third, the flexibility potential of EV charging loads is not explicitly quantified and incorporated in PV-storage capacity optimization, potentially limiting opportunities to reduce storage investment and carbon emissions. In this context, to fully exploit the flexibility potential of EV charging loads and to optimize PV-energy storage capacity configuration considering EV flexibility, this study proposes a multi-objective capacity optimization method for PV-energy storage systems that jointly consider economic and carbon objectives. The proposed method incorporates the flexibility potential of existing EV charging loads in buildings, enabling the coordinated low-carbon and cost-effective configuration of PV-storage systems. Case study results demonstrate the effectiveness of the proposed approach. The main contributions of this study are summarized as follows:

(1) A multi-objective capacity optimization model for PV-storage systems is developed based on a bi-level optimization framework that explicitly accounts for the flexibility potential of EV charging loads. The proposed model explores both optimal PV-storage configuration strategies and building-EV cooperation mechanisms. Specifically, the upper-level model represents the building energy operator, aiming to minimize both the economic cost and the carbon emission cost, thereby achieving joint optimization of PV-storage capacity configuration and EV charging prices. The lower-level mode represents EV users, who optimize their charging schedules to minimize their total charging cost in response to the charging prices set by the building operator.

(2) An efficient solution algorithm based on a genetic algorithm (GA) is developed for the bi-level multi-objective optimization model. An efficient solution algorithm is developed. First, a weighted-sum method is employed to convert the multi-objective problem into a single-objective optimization problem. Then, a heuristic solution framework is developed, where the upper-level model and lower-level model are, respectively, solved by GA and commercial solvers through iterative updates of EV charging prices.

The remainder of this paper is organized as follows. Section 2 presents the methodology. Section 3 presents the solution method. Section 4 presents case studies, and Section 5 draws the main conclusions.

2. Methodology

2.1. Model Framework

This study focuses on the development of low-carbon and cost-effective smart buildings through the joint optimal capacity configuration of PV-energy storage systems. Figure 1 illustrates the energy and information flow architecture of the considered building energy system. The building’s electricity demand consists of inherent building loads and EV charging loads, while distributed PV and energy storage systems are newly installed within the building. The building operator serves as the central decision maker for system planning and operation and is responsible for coordinating the power dispatch of inherent building loads, EV charging loads, distributed PV, and energy storage systems. Meanwhile, the operator determines the charging prices for orderly EV charging based on grid electricity prices and the internal operational conditions of the building energy system.

In consideration of the different objectives between EV users and the building operator, the coordinated operation of the building energy system and orderly EV charging is formulated using a bi-level optimization framework. In the upper level, the building operator aims to minimize the total economic cost and carbon emission cost, thereby jointly optimizing PV-storage capacity configuration and EV charging prices, the latter of which are then communicated to the lower level. In the lower level, EV users optimize their charging schedules to minimize their charging costs in response to the received charging prices and feed the resulting charging schedules back to the upper level.

Ultimately, through the optimal capacity configuration of PV-storage systems and the implementation of price-guided orderly EV charging, the building achieves low-carbon and cost-effective operation.

2.2. EV Orderly Charging Model

With the continuous growth in EV adoption, a substantial number of EV charging loads have emerged in commercial and office buildings. A key consideration in implementing orderly EV charging is to properly account for users’ willingness to respond. User response behavior is influenced by multiple factors, including charging cost, charging safety, travel convenience, individual behavioral habits, and psychological factors, among which economic considerations are among the primary driver of charging decisions.

This study focuses on a slow-charging scenario in buildings, where EVs are modeled as flexible loads with flexible charging time windows. For simplification, V2G operation/EV discharging is not considered in this study. A price-driven orderly EV charging model is developed. Specifically, the parameters of each EV in the building are defined $\left\{E_{\mathrm{EV},n,d},t_{\mathrm{in},n,d},t_{\mathrm{out},n,d},SO{C}_{\mathrm{EV},n,d}^{\mathrm{in}},SO{C}_{\mathrm{EV},n,d}^{\exp }\right\}$.

Considering that the parking duration of EVs in buildings is generally longer than the time required to fulfil their charging demand, the charging demand can be flexibly scheduled within the parking period. By optimizing the temporal scheduling of charging activities during the parking interval, the flexibility potential of EV charging loads as controllable loads can be effectively exploited, thereby supporting low-carbon and cost-effective operation of building energy systems.

In the process of implementing orderly EV charging, the charging demand of EV users must be satisfied as a fundamental requirement. Therefore, the following constraints are formulated for orderly EV charging:

$$SO{C}_{\mathrm{EV},n,d}^{\exp }\le SO{C}_{\mathrm{EV},n,d,t}\le SO{C}_{\mathrm{EV},n,d}^{\max },t=t_{\mathrm{out},n,d}$$

(1)

$$0\le P_{\mathrm{EV},n,d,t}\le {\delta }_{\mathrm{EV},n,d,t}{P}_{\mathrm{EV}}^0,\forall n=1,\dots ,N_{\mathrm{EV}},d=1,\dots ,D,t=1,\dots ,T$$

(2)

$${\delta }_{\mathrm{EV},n,d,t}\le {\mu }_{\mathrm{EV},n,d,t},\forall n=1,\dots ,N_{\mathrm{EV}},d=1,\dots ,D,t=1,\dots ,T$$

(3)

$${\displaystyle \sum _{n=1}^{N_{EV}}{\delta }_{\mathrm{EV},n,d,t}}\le N_{cp},\forall n=1,\dots ,N_{\mathrm{EV}},d=1,\dots ,D,t=1,\dots ,T$$

(4)

where ${\delta }_{\mathrm{EV},n,d,t}=1$ indicates that the EV is charging in the current time interval, and otherwise it is not charging. ${\mu }_{\mathrm{EV},n,d,t}$ is an input parameter, where a value of 1 indicates that the vehicle is parked within the building charging area and is available for charging, while 0 indicates that it is outside the feasible charging region. Constraint (1) represents that the SOC at the departure interval of EV n should be equal to or larger than the target SOC. And since V2G is not considered and EVs can only be at charging status, Constraint (1) naturally constrains that SOC at each interval does not exceed the allowable maximum SOC. Constraint (2) defines the charging power of EV n at time interval t. Constraint (3) specifies the charging availability constraint, indicating whether EV n is in an allowable time interval for charging. Constraint (4) states that the number of EVs at charging status should not exceed the number of available installed charging piles.

2.3. Optimal Configuration Model of PV-Storage Systems Considering Orderly EV Charging

This study adopts a typical-day-based operational simulation approach, in which one representative day is selected for each of the four seasons (spring, summer, autumn, and winter) to formulate a multi-objective capacity planning model that satisfies operational constraints of each typical day while minimizing the annual total economic cost and carbon emission cost. Specifically, the proposed multi-objective capacity configuration model is formulated within a bi-level optimization framework, and its structure is illustrated in Figure 1.

2.3.1. Multi-Objective Capacity Configuration Model for PV-Storage Systems

(1) Objective function

In PV-energy storage capacity configuration, the objective of the building energy operator is to achieve both the minimum carbon emission cost $C_{\mathrm{carb}}$ and economic cost $C_{\mathrm{fina}}$. The economic cost includes the investment cost of the PV-storage system $C_{\mathrm{inv}}$, the total operation and maintenance cost of the PV-storage system $C_{\mathrm{o}\&\mathrm{m}}$, the cost of electricity purchased from the grid $C_{\mathrm{g}}$, the cost of curtailed PV power $C_{\mathrm{curt}}$, and the revenue from EV charging $C_{\mathrm{EV}}$.

$$\min f\left(C_{\mathrm{carb}},C_{\mathrm{fina}}\right)$$

(5)

$$C_{\mathrm{carb}}={\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\pi }_d{e}_{\mathrm{carb}}{P}_{\mathrm{g},d,t}\Delta t}}$$

(6)

$$C_{\mathrm{fina}}=C_{\mathrm{inv}}+C_{\mathrm{g}}+C_{\mathrm{curt}}+C_{\mathrm{o}\&\mathrm{m}}-C_{\mathrm{EV}}$$

(7)

$$C_{\mathrm{inv}}=c_{\mathrm{bess}}^{\mathrm{inv}}{E}_{\mathrm{bess}}^{\mathrm{N}}+c_{\mathrm{pv}}^{\mathrm{inv}}{P}_{\mathrm{pv}}^{\mathrm{N}}$$

(8)

$$C_{\mathrm{o}\&\mathrm{m}}=c_{\mathrm{bess}}^{\mathrm{o}\&\mathrm{m}}{P}_{\mathrm{bess}}^{\mathrm{N}}+c_{\mathrm{pv}}^{\mathrm{o}\&\mathrm{m}}{P}_{\mathrm{pv}}^{\mathrm{N}}$$

(9)

$$C_{\mathrm{g}}={\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\pi }_d{c}_{\mathrm{g},d,t}{P}_{\mathrm{g},d,t}\Delta t}}$$

(10)

$$C_{\mathrm{curt}}={\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\pi }_d{c}_{\mathrm{curt}}{P}_{\mathrm{curt},d,t}\Delta t}}$$

(11)

$$C_{\mathrm{EV}}={\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{n=1}^{N_{\mathrm{EV}}}{\pi }_d{R}_{d,t}^{\mathrm{EV}}{P}_{\mathrm{EV},n,d,t}\Delta t}}}$$

(12)

The electricity price for EV charging $R_{d,t}^{\mathrm{EV}}$ is determined by the building operator based on the building’s internal operation conditions and the characteristics of EV charging loads. EV users’ response to the price depends on their economic considerations, charging demands and parking schedules. As a vital variable coupling the building model and the EV model, the $R_{d,t}^{\mathrm{EV}}$ serves as the key decision variable in the interaction between the upper and lower levels. Setting a lower charging price at a certain time interval t enables the building to encourage EV users for charging yet reduces the building operator’s charging revenue. In contrast, setting a higher charging price discourages EV users from charging during that interval, thereby shifting charging demand to other periods. In this case, by accepting a lower charging revenue during certain time intervals according to the sufficiency or shortage of its inherent energy resources, the building can improve its overall profit over the entire time horizon and reduce EV users’ charging costs. This motivates the introduction of dynamically optimized EV charging prices in this study and also explains the mechanism through which mutual economic benefits can be achieved.

(2) Constraints

The constraints of the proposed multi-objective PV-storage capacity configuration model for the building are as follows:

(a) Power balance constraint

$$\begin{array}{l}{P}_{\mathrm{g},d,t}+\left(P_{\mathrm{pv}}^{\mathrm{N}}+P_{\mathrm{pv}}^0\right){\tilde{P}}_{\mathrm{pv},d,t}-P_{\mathrm{curt},d,t}+P_{\mathrm{bess},d,t}^{\mathrm{d}}=\\ P_{\mathrm{l},d,t}+P_{\mathrm{bess},d,t}^{\mathrm{c}}+{\displaystyle \sum _{n=1}^{N_{\mathrm{EV}}}{P}_{\mathrm{EV},n,d,t}},\forall d=1,\dots ,D, t=1,\dots ,T\end{array}$$

(13)

Constraint (13) ensures that the internal power balance between supply and demand is satisfied at any time interval within the building.

(b) PV power curtailment constraint

$$0\le P_{\mathrm{curt},d,t}\le \left(P_{\mathrm{pv}}^{\mathrm{N}}+P_{\mathrm{pv}}^0\right){\tilde{P}}_{\mathrm{pv},d,t},\forall d=1,\dots ,D, t=1,\dots ,T$$

(14)

Constraint (14) restricts the PV power curtailment at any time interval to be within its upper and lower bounds.

(c) Energy storage charging and discharging power constraints

$$\left\{\begin{array}{c}0\le P_{\mathrm{bess},d,t}^{\mathrm{d}}\le P_{\mathrm{bess}}^{\mathrm{N}}\\ 0\le P_{\mathrm{bess},d,t}^{\mathrm{c}}\le P_{\mathrm{bess}}^{\mathrm{N}}\end{array}\right.,\forall d=1,\dots ,D, t=1,\dots ,T$$

(15)

$$\left\{\begin{array}{l}0\le P_{\mathrm{bess},d,t}^{\mathrm{d}}\le u_{\mathrm{bess},d,t}M\hfill \\ 0\le P_{\mathrm{bess},d,t}^{\mathrm{c}}\le \left(1-u_{\mathrm{bess},d,t}\right)M\hfill \end{array}\right.,\forall d=1,\dots ,D, t=1,\dots ,T$$

(16)

$$E_{\mathrm{bess},d,t}=E_{\mathrm{bess},d,t-1}+\left({\eta }_{\mathrm{bess}}^{\mathrm{c}}{P}_{\mathrm{bess},d,t}^{\mathrm{c}}-P_{\mathrm{bess},d,t}^{\mathrm{d}}/{\eta }_{\mathrm{bess}}^{\mathrm{d}}\right)\Delta t,\forall d=1,\dots ,D, t=1,\dots ,T$$

(17)

$$SO{C}_{\mathrm{bess}}^{\min }{E}_{\mathrm{bess}}^{\mathrm{N}}\le E_{\mathrm{bess},d,t}\le SO{C}_{\mathrm{bess}}^{\max }{E}_{\mathrm{bess}}^{\mathrm{N}},\forall d=1,\dots ,D, t=1,\dots ,T$$

(18)

$$E_{\mathrm{bess},d,0}=E_{\mathrm{bess},d,T}\forall d=1,\dots ,D$$

(19)

where $u_{\mathrm{bess},d,t}=1$ indicates that the storage system is in discharging mode, and otherwise it is in charging mode. Constraint (15) limits the charging and discharging power of the energy storage system at any time interval to be less than its rated power. Constraint (16) ensures that the energy storage system cannot charge and discharge simultaneously at any time interval. Constraint (17) describes the relationship between the stored energy and the charging/discharging power of the energy storage system. Constraint (18) ensures that the stored energy of the energy storage system at any time interval must remain within its allowable minimum and maximum SOC limits. Constraint (19) ensures that the state of charge of the energy storage system at the initial and terminal time intervals of a typical day is the same.

2.3.2. EV Charging Response Model

EV users in the building provide a certain degree of charging flexibility through the temporal shifting of charging demand, which can effectively facilitate PV generation accommodation and peak-load reduction during high-price periods within the building energy system. Within this framework, EV users optimize their charging power across time intervals with the objective of minimizing their total charging cost:

$$\min C_{\mathrm{EV}}={\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{n=1}^{N_{\mathrm{EV}}}{\pi }_d{R}_{d,t}^{\mathrm{EV}}{P}_{\mathrm{EV},n,d,t}\Delta t}}}$$

(20)

Meanwhile, the EV charging constraints specified in Equations (1)–(4) are satisfied.

3. Solution Method

The proposed PV-energy storage capacity configuration model for the building is formulated as a bi-level multi-objective mixed-integer linear programming (MILP) problem, which is difficult to solve directly. To address this issue, a weighted-sum method is first employed to transform the bi-objective optimization problem into a single-objective problem. However, the resulting single-objective model remains a bi-level program with binary variables at the lower level, which prevents direct reformulation. To tackle this challenge, a GA-based solution approach is developed.

3.1. Single-Objective Model Reformulation

Existing studies have proposed optimization strategies for power systems or demand-side users that simultaneously consider the dual objectives of carbon emissions and economic performance. Common approaches include the Pareto optimality method [34,35] and the ε-constraint method [36]. In this study, the building is modeled as an individual decision-making entity with two optimization objectives. A key consideration in formulating the proposed model is that carbon emission costs and economic costs differ considerably in magnitude from other economic costs. Nevertheless, in practical scenarios, decision makers may attach comparable importance to carbon reduction and economic performance. Although relatively straightforward, the weighted-sum method is adopted in this study to eliminate the influence of differences in objective scales and enable their relative importance to be appropriately represented.

The weighted-sum method is adopted to convert the bi-objective optimization problem into a single-objective formulation. First, to eliminate the influence of scale differences among two objectives on the optimization results, both the economic objective and the carbon emission objective are normalized. The established model is first solved by considering only the economic objective to obtain the minimum economic cost, which is used as the lower bound for normalization of $C_{\mathrm{fina}}$. The upper bound of $C_{\mathrm{fina}}$ is obtained from the reference case without PV-energy storage capacity expansion or EV charging optimization, in which the building relies on power exchange with the main grid. Thus, the economic objective $C_{\mathrm{fina}}$ is normalized into the interval [0, 1]. Similarly, the carbon emission cost $C_{\mathrm{carb}}$ is normalized using its upper and lower bounds obtained following the same procedure.

$$\min f=\alpha {\displaystyle \frac{C_{\mathrm{carb}}-C_{\mathrm{carb}}^{\min }}{C_{\mathrm{carb}}^{\max }-C_{\mathrm{carb}}^{\min }}}+\beta {\displaystyle \frac{C_{\mathrm{fina}}-C_{\mathrm{fina}}^{\min }}{C_{\mathrm{fina}}^{\max }-C_{\mathrm{fina}}^{\min }}}$$

(21)

where $\alpha +\beta =1$. The capacity configuration model transformed by Equation (21) is formulated as a single-objective optimization problem.

$$\max \mathsf{\epsilon }=(f_{\mathrm{dp}}-f)(C_{\mathrm{EV},\mathrm{dp}}-C_{\mathrm{EV}})$$

(22)

where the disagreement point of the bilateral negotiation is defined based on the optimization outcomes when two levels independently optimize their respective objectives using their available resources. Specifically, the two levels interact with power exchange based on the TOU tariff instead of optimizing the EV charging price.

$$R_{\min }\le R_{d,t}^{\mathrm{EV}}\le c_{\mathrm{g},d,t}$$

(23)

It should be noted that V2G participation of EVs is not considered in this study. Thus, Constraint (23) is introduced to impose bounds on the EV to ensure reasonable daytime EV charging behavior within the building.

3.2. GA-Based Solution Method for the Bi-Level Optimization Model

In the proposed bi-level optimization model, the lower-level orderly EV charging optimization problem (i.e., Equation (20), Constraints (1)–(4) and (23)) contains a large number of binary variables, preventing the direct application of KKT- or strong-duality-based reformulation methods. Furthermore, to preserve the information privacy of the lower-level EV users, in practical implementation, the lower level only feeds back its charging power to the upper level. As a result, conventional reformulation methods based on KKT conditions or strong-duality-based reformulation, which are typically used to convert a bi-level model into an equivalent single-level problem, cannot be directly applied.

To address this issue, a GA-based solution framework is developed to solve the bi-level optimization model, as illustrated in Figure 2. The main solution procedure is as follows. First, the upper-level model initializes a population of EV charging price schemes $R_{d,t}^{\mathrm{EV}}$. Given the charging prices, the lower-level orderly EV charging problem is a MILP, which can be directly solved, yielding the optimal EV charging power profile in response to the given charging prices. Subsequently, the obtained EV charging response is fed back to the upper-level model, which then performs coordinated optimization of PV-storage capacity configuration and charging prices based on the updated EV charging demand. In summary, the decision variables optimized by the GA, i.e., the chromosome, are the charging prices $R_{d,t}^{\mathrm{EV}}$. With the proposed solution framework, both the lower-level EV problem and the upper-level building problem can be solved as MILPs for a given charging price scheme, which can be solved directly using commercial solvers such as Gurobi.

During the iterative process, the Nash product between the building operator and EV users is adopted as the fitness function of the GA, and the GA evolves the population toward maximizing the Nash product. The algorithm proceeds through population initialization, selection, crossover, and mutation operations and iterates until the predefined convergence criteria are satisfied. Finally, the optimal PV-storage capacity configuration and EV charging price scheme are obtained.

4. Case Studies

4.1. Case Data

EV charging data are extracted from [28], which reports a survey on EV travel and charging behavior at the campus of Beijing University of Technology, showing that the average EV arrival and departure times are 08:07 and 18:37, respectively. The arrival SOC follows a normal distribution of N (0.59, 0.21). The arrival SOC values sampled based on the normal distribution are shown in Figure 3. The sampled arrival SOC parameters are used as the initial SOC of each EV in Equation (1). This study focuses on an office building on the campus, and the maximum building load of 90 kW is adopted based on data in [28]. In this study, EVs are assumed to remain parked at the building from 08:00 to 18:00, and their charging loads are available for scheduling during this period. The departure SOC of each EV is limited to the interval [0.8, 0.95].

The EV battery capacity is set to 60 kWh, based on the specifications of the Tesla Model Y, and the charging pile power is set to 7 kW, based on Tesla’s third-generation wall-mounted connector. The charging efficiency is assumed to be 95%. In this case study, 30 EVs and 10 charging piles are considered. The cost parameters of the PV and energy storage systems are adopted from [37]. The PV investment cost is 3815.1 CNY/kW, with a lifetime of 25 years and an annual operation and maintenance cost of 38.15 CNY/kW. The energy storage system has a charge/discharge rate of 0.25 and an efficiency of 95%, with an investment cost of 3851.1 CNY/kWh, a lifetime of 15 years, and an annual operation and maintenance cost of 96.28 CNY/kW. The PV power curtailment penalty is set to 0.3 CNY/kWh. The carbon emission cost coefficient of grid electricity purchase is set to 0.01013 CNY/kWh, with reference to the typical value of 0.0102 CNY/kWh in the North China Power Grid. This value is also consistent with a grid emission factor of approximately 0.85 kg CO₂/kWh and a carbon price of approximately 0.012 CNY/kg CO₂. The Big-M parameter in Equation (16) is set to 1 × 10⁷.

The typical seasonal electricity load curves and corresponding data for Beijing can be obtained from [38]. Since this study does not focus on the development of representative-day construction methods, four representative days, one for each season, are selected following previous work using representative days for capacity expansion planning models. Specifically, the load profiles on 1 March, 1 June, 1 September, and 1 December are selected and normalized to obtain representative daily load factors. These factors are then multiplied by the maximum load of the BUT building to generate the load profiles shown in Figure 4. All data are aligned to Beijing Time (UTC+8). The per-unit PV power output profiles are extracted from the MERRA-2-based dataset in [39] using the grid cell covering the BUT campus (39.8744° N, 116.4857° E). The unit-capacity PV generation profile is shown in Figure 5, and the time-of-use electricity price is shown in Figure 6.

The upper-level optimization problem is solved by the ga function in MATLAB (Global Optimization Toolbox, version corresponding to MATLAB R2023b). The EV model and building model are solved by Gurobi (version 13.0.0). Detailed parameters of GA and Gurobi are provided in Appendix A.

4.2. Results and Discussion

To highlight the effectiveness of the proposed multi-objective PV-storage capacity configuration method considering the flexibility potential of EV charging loads, six comparative cases are designed, as summarized in

Table 1. Case settings.

Case	Energy Storage + PV Generation	Electric Vehicles (with Optimized ${\mathit{R}}_{\mathit{d},\mathit{t}}^{\mathbf{EV}}$)	Economic Objective	Carbon Emission Objective
I	√	√	√	√
II	√	√	√	×
III	√	×	√	√
IV	√	×	√	×
V	√	×	×	√
VI	×	×	√	√

Note: √ indicates that the factor is considered, while × indicates that the factor is not considered.

.

Cases I and II correspond to the proposed PV-storage capacity configuration framework considering EV charging flexibility, where Case I considers both carbon emission and economic objectives, while Case II considers only the economic objective. Cases III and IV represent PV-storage configurations without EV charging optimization, where EVs charge according to the TOU tariff. Case III includes both objectives and Case IV considers only the economic objective. Cases I–IV are designed to evaluate the impact of the utilization of EV charging flexibility in building load regulation as well as the influence of single-objective versus multi-objective optimization on PV-storage configuration. Case V considers only the carbon emission objective in the PV-storage configuration, while Case VI represents a multi-objective building operation scenario without PV-storage capacity planning and without considering EV flexibility. It should be noted that all cases are considered for theoretical demonstration since some engineering constraints that may limit the installation of PV-energy storage systems are not considered, e.g., the available rooftop or installation area, maximum PV installation capacity. The presented methodology for PV-energy storage capacity planning can be easily extended to more realistic application scenarios by adding additional scenario-specific constraints without altering the model features and the applicability of the proposed solution algorithms.

The PV-storage configuration results and corresponding cost performance under different cases are presented in

Table 2. PV-storage configuration results under different cases.

Case	Energy Storage Capacity (kWh)	Energy Storage Power (kW)	PV Capacity (kW)
I	32.888	8.222	309.869
II	16.922	4.231	301.349
III	175.739	43.935	286.980
IV	19.944	4.986	254.209
V	4075.146	1018.789	164,225

and

Table 3. Building costs and their components under different cases.

Case	Costs (104 CNY)
	${\mathit{C}}_{\mathbf{inv}}$	${\mathit{C}}_{\mathbf{o}\&\mathbf{m}}$	${\mathit{C}}_{\mathbf{g}}$	${\mathit{C}}_{\mathbf{curt}}$	${\mathit{C}}_{\mathbf{fina}}$	${\mathit{C}}_{\mathbf{carb}}$	${\mathit{C}}_{\mathbf{EV}}$ *
I	10.562	1.261	38.041	0.994	46.543	0.497	4.315
II	9.664	1.190	39.027	0.920	46.506	0.503	4.295
III	15.533	1.518	35.641	0.416	47.594	0.509	5.514
IV	8.377	1.018	41.129	0.526	45.536	0.539	5.514
V	5062.764	636.327	0	5166.322	10,859.899	0	5.514
VI	0	0	58.578	0	53.064	0.631	5.514

* Note: The value for C_EV represents the buildings’ revenue from EV charging.

, respectively.

From Table 2 and Table 3, it can be observed that, compared with Case VI, Case I, which jointly optimizes PV-storage capacity configuration and orderly EV charging, significantly reduces both the total economic cost and carbon emission cost of the building, with reductions of 12.28% and 21.24%, respectively. This result demonstrates the potential of smart buildings in achieving cost reduction and decarbonization under the dual-carbon targets.

Comparisons of Case I with Case II and Case III with Case IV, jointly considering economic cost and carbon emission cost, allow the decarbonization objective to be explicitly incorporated under the “dual carbon” goals, elevating the importance of carbon emissions to a level comparable with economic objectives. A reduction in carbon emissions (1.19%) can be achieved with 0.08% increases in economic performance. In contrast, pursuing a zero-carbon electricity supply alone leads to oversized PV-storage configurations and substantial PV curtailment, resulting in building economic costs that are several-times higher.

In addition, EV charging loads within the building exhibit significant flexibility potential. By optimizing EV charging schedules, the required PV-storage capacity can be effectively reduced. Comparing Case I and Case III further indicates that optimized EV charging yields considerable economic benefits. By reducing peak EV charging demand and shifting charging loads toward periods with abundant PV generation, the required energy storage system capacity can be reduced. Based on the results in Table 2, the rated power of energy storage decreases from 43.935 kW in Case III to 8.222 kW in Case I with a reduction of 35.713 kW, which is about 51.02% of the total rated power of building charging piles. This coordination contributes to a reduction in the total building cost of CNY 10,510 and a reduction in EV charging cost of CNY 11,996 compared with the TOU scenario. The specific charging costs for each EV are compared in Figure 7. In contrast, Case V results in excessively large capacities of energy storage and PV generation, which may be impractical for buildings with a peak load of only 90 kW. This is because Case V minimizes the carbon emission cost without considering economic costs. Since grid electricity purchases are assumed to be the only source of operational carbon emissions, optimization tends to eliminate grid electricity purchases through PV capacity far exceeding the building’s peak load.

In terms of the detailed operational simulation results for each typical day, the energy storage system exhibits relatively limited charging and discharging activity in spring, autumn, and winter. In these three seasons, PV power curtailment is almost negligible. In contrast, during the summer representative day, due to higher PV generation, the energy storage system exhibits more frequent switching between charging and discharging during daytime operation, and PV curtailment becomes more pronounced, as shown in Figure 8, Figure 9, Figure 10 and Figure 11.

Figure 12 shows the EV charging power profiles before and after optimization. The optimized EV charging price is illustrated in Figure 13. We can observe that the EV charging price first decreases and then increases, reaching its minimum at 11:00 and the maximum at 15:00. This pattern is mainly attributed to abundant PV generation during the daytime. Accordingly, the EV charging profile is redistributed across the scheduling period. The optimized EV charging demand is mainly concentrated during 09:00 and14:00 and around 18:00, exhibiting a bimodal pattern with one major peak and one minor peak.

The solution process of the proposed building PV-storage capacity configuration model is illustrated in Figure 14. It can be observed that the GA-based optimization converges after 41 iterations, reaching a stable solution. During the iterative process, a solution close to the final converged value is already achieved after 20 iterations, and subsequent iterations only exhibit minor variations until the convergence criterion is reached.

To further investigate the convergence performance, nine independent runs are conducted and statistically analyzed, as illustrated in Figure 15 and Figure 16. The average computation time of the model is about 7063 s. The carbon emission cost shows limited fluctuation. However, the building economic cost and EV charging cost exhibit greater variations across runs, which correspond to different allocations of the cooperative benefits under varying electricity prices. Nevertheless, the total cooperative benefits remain relatively stable. Energy storage and flexible EV charging provide partially substitutable temporal flexibility, which leads to greater variability in the optimized energy storage capacity across runs compared with PV capacity. The degree of variation and convergence degree of the charging price differ across time intervals, while its intra-day trend remains similar across independent runs, where low prices in the morning encourage EV charging, whereas high prices in the afternoon discourage EV charging. Overall, the adopted GA-based solution approach is effective in solving the established bi-level model.

4.3. Sensitivity Analysis

The optimal PV-storage capacity configuration in the building is influenced by multiple technical and economic parameters. To further verify the effectiveness of the proposed method under different parameter settings, this section conducts a sensitivity analysis on key parameters, including objective weighting coefficients, unit investment costs of distributed PV and energy storage systems, and PV curtailment penalty.

Figure 17a,b illustrate the variations in energy storage capacity and PV capacity under different combinations of economic and carbon objective weights, respectively. Since the economic cost objective and the carbon emission cost objective have been normalized in this study, and the two weights are allowed to vary independently in the model, this two-dimensional sensitivity analysis can reflect the influence of different decision-making preferences on system capacity configuration.

As shown in Figure 17a, the energy storage capacity is relatively sensitive to changes in objective weights. When the economic weight is high, the overall storage capacity remains low, indicating that greater emphasis on the economic objective limits the deployment of energy storage. When the economic weight is low and the carbon weight is high, the storage capacity increases significantly, suggesting that under a low-carbon-dominated scenario, the system tends to deploy more energy storage to improve PV accommodation, reduce PV curtailment, and decrease carbon emissions associated with grid electricity purchases.

As shown in Figure 17b, PV capacity exhibits a trend similar to that of energy storage capacity. When the economic weight is high, PV capacity remains low because of its investment cost. When the carbon weight is high and the economic weight is low, PV capacity increases markedly, indicating that PV, as the main low-carbon energy supply technology, becomes more favorable as greater emphasis is placed on the carbon objective.

Overall, Figure 17 shows that PV and energy storage capacity configurations have a synergistic relationship. In the region with low economic weight and high carbon weight, the system forms a “high PV capacity–high energy storage capacity” configuration pattern. In contrast, in the region with high economic weight, the optimal capacities of both types of equipment remain relatively low. This indicates that the proposed model can reasonably characterize the trade-off between economic performance and low-carbon performance and adjust the PV-storage capacity configuration in response to different objective preferences.

Figure 18a,b illustrate the impacts of variations in PV investment cost, PV curtailment penalty, and energy storage cost parameters on energy storage capacity and PV capacity, respectively. Overall, the capacities of both types of equipment exhibit systematic response patterns to changes in key parameters.

For energy storage capacity, the energy storage-related parameters have the greatest influence. When the storage-related parameters decrease, the optimal energy storage capacity increases substantially. As these parameters increase, the storage capacity declines rapidly and remains at a relatively low level when approaching the baseline value. This indicates that energy storage configuration is primarily influenced by its own investment and operating costs. Only when the cost of energy storage decreases does the system tend to deploy a larger storage capacity. Meanwhile, an increase in the PV curtailment penalty cost leads to a slight increase in energy storage capacity, suggesting that energy storage provides flexibility in improving PV accommodation and reducing PV curtailment.

For PV capacity, PV investment cost has the most direct influence. As the PV investment cost increases, the optimal PV capacity generally decreases, indicating that PV configuration is strongly influenced by the unit installation cost. When the energy storage-related parameters decrease, PV capacity also increases accordingly. This suggests that lower storage costs enhance the system’s ability to shift surplus PV generation across time and mitigate temporal mismatches between generation and load demand, thereby making a larger PV capacity economically more favorable. In contrast, the impact of PV curtailment penalty cost on PV capacity is relatively limited. This indicates that, under the current model constraints, the curtailment penalty mainly improves PV accommodation by affecting storage configuration and operational scheduling, rather than directly driving a substantial increase in PV capacity.

Overall, the sensitivity analysis results in Figure 18 demonstrate a clear coupled relationship between PV and energy storage capacity configuration. PV capacity is mainly affected by PV investment cost, while energy storage capacity is primarily influenced by storage-related parameters. At the same time, improved storage economics can enhance PV accommodation capability and thereby support a higher level of PV deployment. These results indicate that the proposed optimization model can effectively capture the trade-off among investment costs, PV curtailment costs, and operational flexibility capability in PV-storage systems.

5. Conclusions

This study focuses on low-carbon smart buildings and develops a multi-objective capacity optimization model for PV-energy storage considering the flexibility potential of orderly EV charging loads. The proposed model is formulated as a bi-level multi-objective optimization framework. The upper level represents the building operator, aiming to simultaneously minimize economic cost and carbon emission cost. The lower level represents EV users, who optimize their charging schedules in response to the charging prices set by the building operator with the objective of minimizing their individual charging costs. To solve the proposed model, an objective normalization and weighted-sum method is first developed to convert the bi-objective optimization problem into a single-objective formulation using a weighted-sum approach. Furthermore, a GA-based solution framework is proposed for the bi-level optimization model.

Case study results demonstrate the effectiveness of the proposed model and solution method. The results demonstrate that incorporating carbon emission reduction objectives into PV-storage capacity planning significantly reduces the building’s carbon emission level, highlighting the low-carbon operational characteristics and emission reduction potential of smart buildings under dual-carbon targets. Meanwhile, the flexible regulation potential of orderly EV charging effectively reduces the required capacity of the PV-storage system, thereby decreasing both the total economic cost and carbon-related cost of the building system, as well as reducing EV charging costs.

Overall, this study provides a theoretical foundation for the coordinated planning of PV-energy storage and EV resources in low-carbon buildings. Future work will extend the proposed framework to incorporate V2G operation and uncertainties in EV resources. In addition, the current study represents seasonal operation using four representative days and does not explicitly capture inter-day variability. Future research will investigate more advanced representative-day construction methods that account for both intra-day load profiles and inter-day variations, particularly under prolonged extreme weather conditions, to improve the temporal representation of capacity planning models.