Virtual Energy Storage System Scheduling for Commercial Buildings with Fixed and Dynamic Energy Storage

Abstract

This study presents a virtual energy storage system (VESS) scheduling method that strategically integrates fixed and dynamic energy storage (ES) solutions to optimize energy management in commercial buildings. Fixed ES, such as batteries, provides stable flexibility but is expensive and can be inefficiently operated. In contrast, dynamic ES can be utilized as needed but requires validation of their flexibility. By combining fixed ES with dynamic ES utilizing vehicle-to-grid (V2G) capabilities, this approach enhances grid stability and manages energy costs more effectively. Empirical validation using real-world data from Korea demonstrates significant improvements in total net benefits by reducing energy costs, which are crucial for the economic sustainability of commercial energy use. Additionally, the analysis of Pearson’s linear correlation coefficient with demand identifies where benefits occur in the scheduling process. The integrated system reduces the need for costly upgrades to the utility grid, suggesting a strategic advantage for large-scale adoption. This study establishes a framework for the broader implementation of such integrated systems, highlighting the potential for substantial improvements in energy efficiency, reduced carbon emissions, and enhanced grid reliability.

1. Introduction

1.1. Motivation

The commercial sector is a major consumer of energy, representing a significant portion of the global energy demand. According to the International Energy Agency (IEA), buildings were responsible for approximately 30% of global final energy consumption and 26% of global energy-related emissions in 2022 [1]. This substantial impact highlights the critical need to advance energy efficiency in commercial buildings as a strategic response to economic and environmental challenges.

With increasing energy costs and environmental concerns becoming more pressing, there is an urgent need to enhance energy efficiency and foster sustainable practices in commercial buildings [2]. Addressing inefficiencies in energy consumption and adopting energy storage technologies are critical steps toward reducing carbon emissions and advancing sustainable energy initiatives. The integration of energy-efficient systems and energy storage solutions in buildings is a key strategy for environmental conservation [3].

Energy storage systems (ESSs) are essential for optimizing energy consumption in buildings. By storing surplus energy during periods of low demand and releasing it during peak times, these systems mitigate the burden on electrical grids and improve energy efficiency within the premises [4]. However, the high upfront costs of ESSs present a significant barrier to their adoption in commercial settings. Overcoming this financial challenge is crucial for the broader uptake of these technologies [5].

The concept of shared energy storage models offers a promising solution to this challenge. Virtual energy storage systems (VESSs) allow multiple users or entities to share communal energy storage facilities. This collaborative model maximizes the efficiency of storage, diminishes the cost burden on individual participants, and enhances the overall effectiveness of stored energy utilization [6]. By leveraging the shared approach of a VESS, businesses and consumers can access energy storage solutions in a more economically feasible manner.

1.2. Prior Works

The widespread adoption of renewable energy sources in power grids presents several challenges for power system operators. The integration of energy storage systems (ESSs) has emerged as a promising solution [7]. ESSs are utilized in various applications, including interfacing within energy Internet ecosystems [8], smoothing output power in microgrids [9], and enhancing stability for virtual synchronous generators [10]. ESSs also enhance building energy reliability, reduce costs, support grid stability through frequency and voltage regulation, optimize renewable energy use, lower carbon footprints, and provide backup power during outages [5]. However, the initial capital investment required to procure and install ESSs can be substantial, particularly for large-scale systems capable of providing considerable energy storage capacity. This upfront cost burden poses a financial challenge to building owners and operators [11].

VESSs have emerged as a promising approach to address the cost barriers associated with ESS implementation in buildings. VESSs enable multiple users within a building or community to collectively use a single energy storage unit, thereby minimizing the initial capital expenditure [12]. Li et al. [13] developed a cost–benefit analysis framework for shared energy storage systems, emphasizing the economic advantages of collective energy management in reducing both operational and capital costs. Zhu and Ouahada [14] introduced a novel algorithm for the dynamic management of shared energy storage, significantly improving reliability and performance by adapting to real-time energy demands. Jasim et al. [15] proposed a demand response strategy for buildings equipped with VESSs, optimizing energy use and reducing peak loads on the grid, thus enhancing overall grid stability.

Furthermore, understanding and incorporating user behavior into the design and operation of VESSs has also been explored. Mediwaththe et al. [16] developed a user-centric model for VESSs that accounts for individual user preferences and behaviors to optimize energy usage and enhance system efficiency. This approach not only improves user satisfaction but also contributes to more balanced and efficient energy consumption patterns. Gailani and Crosbie [17] analyzed the impact of different regulatory scenarios on the adoption and effectiveness of VESSs, providing insights into how policy adjustments could foster wider implementation.

The integration of vehicle-to-grid (V2G) technology offers a compelling opportunity to enhance energy storage capabilities within buildings. V2G enables electric vehicles (EVs) to serve as mobile energy storage units, storing excess energy from the grid and feeding it back during peak demand periods [18]. One key advantage of V2G is its ability to leverage existing infrastructure—EVs and their batteries—for energy storage, minimizing the need for additional dedicated storage systems. This approach reduces upfront capital costs and maximizes resource utilization, aligning with circular economy principles by repurposing existing resources [19].

V2G also presents unique opportunities for revenue generation and cost offsetting through grid services and energy trading. EV owners can participate in demand response programs or provide ancillary services to the grid, earning incentives or payments for their contributions. In buildings, V2G-enabled EV fleets can be aggregated to provide significant storage capacity and demand flexibility, enhancing the economic viability of energy storage investments and potentially generating additional revenue streams for building owners and operators [20].

Furthermore, V2G integration promotes energy resilience and grid stability by diversifying storage options and enhancing grid flexibility. Building energy management systems can optimize energy use and mitigate grid disturbances by utilizing distributed energy resources such as EVs, solar panels, and stationary batteries. V2G-enabled buildings can function as microgrids, capable of islanding from the main grid during emergencies or blackouts, providing critical backup power with stored energy from EVs [21].

The integration of EVs and ESSs in households holds significant promise for reducing home energy costs and enhancing overall energy efficiency. Homeowners can optimize energy usage, store excess renewable energy, and leverage the flexibility of EV batteries to manage electricity demand more effectively [22]. The combination of ESSs and EVs offers a synergistic solution for energy reduction and optimization. Integrating ESSs and EVs into energy management systems provides numerous advantages, including grid stability, demand response capabilities, and enhanced renewable energy integration. By leveraging EV battery storage capacity and bidirectional energy flow flexibility, this integration enables efficient energy management, cost reduction, and environmental sustainability. Thus, the integration of ESSs and EVs is foundational to modern energy management practices, paving the way for a more resilient, efficient, and sustainable energy future [23].

However, existing research on the combination of ESSs and EVs in buildings has primarily focused on utilizing individual energy storage systems and EVs separately. There is a notable lack of studies exploring the integration of EVs as a source of virtual energy storage in conjunction with fixed shared energy storage systems. To address this gap, our study proposes a novel approach for scheduling energy in commercial buildings by integrating fixed ESSs and EVs. By leveraging the complementary strengths of fixed and mobile storage systems, this combined approach aims to optimize energy management strategies, thereby enhancing the efficiency and effectiveness of commercial building operations.

1.3. Contribution

The main contributions of this study can be summarized as follows:

• Integration of fixed and dynamic ESSs: This study proposes an approach for integrating both fixed and dynamic ESSs within a VESS scheduling framework. Unlike traditional methods that typically focus on either fixed or dynamic storage independently, this study demonstrates the enhanced efficiency and efficacy of combining these systems. By integrating fixed batteries and dynamic V2G capabilities, the proposed model optimizes energy usage within commercial buildings and enhances grid stability and energy cost management. This dual approach allows greater flexibility and resilience in energy management, adapting to both predictable energy demands and peak load fluctuations more effectively than standalone systems.
• Experimental results and discussions regarding a real dataset: The use of real-world data from Korea in the simulation process validates the practical applicability of the proposed scheduling method and enhances its relevance and utility for real-world scenarios. This methodological rigor ensures that the scheduling strategy is not only theoretically sound but also empirically effective, providing a replicable model for other researchers and practitioners in the field. These findings highlight the potential for significant reductions in energy costs and peak demand charges, which are crucial for the economic sustainability of energy use in commercial settings. Moreover, the demonstrated capability of the combined VESS in reducing the need for extensive and costly upgrades to utility grids presents a compelling case for policymakers to consider supportive policies and incentives for integrated energy storage solutions. This could lead to the broader adoption of such systems, ultimately contributing to enhanced energy efficiency, reduced carbon emissions, and greater energy independence on a larger scale.

2. System Description

In this study, we explore the deployment of a VESS in a commercial building comprising multiple units. The VESS integrates both fixed and dynamic ES solutions to enhance the energy efficiency of the participating units, markedly reducing electricity costs. Fixed ES relies on stationary batteries that offer reliable energy reserves. Concurrently, dynamic ES harnesses energy from parked EVs, contributing to the adaptability of the system. The interplay between the participant units and the service provider is managed through clearly defined contractual agreements that stipulate the responsibilities and limits of all parties involved. As depicted in Figure 1, the VESS for commercial buildings is structured around four principal components: the building energy service provider (BESP), participant units, fixed ES, and EV charging stations.

In Figure 1, The components marked with green, orange, and blue icons correspond to the virtual energy storage, commercial building, and grid areas, respectively. Additionally, solid lines represent power flow, while dashed lines indicate information flow.

2.1. Building Energy Service Provider

The BESP fulfills a critical function within the VESS, orchestrating the energy flows between the participating units and energy producers. It employs advanced decision-making algorithms to determine the scheduling of the participants in line with the strategic objectives and operational constraints of the VESS. The primary aim is to ensure that energy distribution across building units is conducted smoothly, efficiently, and in an optimized manner.

The BESP operates on a service-oriented basis and offers access to a fixed ES capacity, which includes a fleet of stationary batteries. These batteries provide a reliable and regulated energy supply, particularly during peak demand periods or those related to electricity tariffs. By commercializing access to this fixed ES capacity, the BESP contracts service prices with the participating units, establishing a mutually beneficial economic relationship that incentivizes energy conservation and efficiency.

Although fixed ES implementation costs are shouldered by the BESP, they are considered marginal in the context of a long-term implementation scenario, as envisioned in this study. Such costs are expected to be offset by long-term operational savings and potential revenue generated through the service model.

In contrast, the dynamic ES, which encompasses the energy storage potential of EVs, is managed individually by EV owners. This component introduces a flexible and adaptive energy reserve that complements the fixed ES. The BESP facilitates the integration of this dynamic ES into the energy portfolio of the building but does not directly incur costs or receive benefits. However, it plays a pivotal role in coordinating the availability of EVs for energy storage and ensuring that this dynamic resource is effectively utilized within the VESS framework.

2.2. Participant Unit

Participant units stand to gain economically by engaging with a VESS, primarily through a reduction in their electricity bills, compared to scenarios where no ESS is utilized. By adopting an electricity tariff model, such as Time-of-Use (ToU), the electricity bill for a participant unit $u$, $B_u\left(·\right)$, is calculated as follows:

$$\begin{array}{rr}{B}_u\left(·\right)& =p_d\underset{t\in \mathcal{T}}{\mathrm{m}\mathrm{a}\mathrm{x}} d_{u,t}+{\displaystyle \sum _{t\in \mathcal{T}}}{p}_{e,t}{d}_{u,t},\end{array}$$

(1)

where $\mathcal{T}=\{1,\cdots ,t,\cdots ,T\}$ represents the scheduling period, such as one month, $d_{u,t}$ indicates the demand for unit $u$ at time $t$, $\underset{t\in \mathcal{T}}{\mathrm{m}\mathrm{a}\mathrm{x}} d_{u,t}$ denotes the peak demand among the scheduling period $\mathcal{T}$, $p_d$ denotes the demand price for the billing period, and $p_{e,t}$ indicates the energy price at time $t$.

When unit $u$ employs fixed ES, denoted by $e_{u,t}^F$, and dynamic ES, denoted by $e_{u,t}^D$, the electricity bill of unit $u$ utilizing fixed and dynamic ES, $B_u\left(e_{u,t}^F,e_{u,t}^D\right)$, is modified as

$$\begin{array}{r}{B}_u\left(e_{u,t}^F,e_{u,t}^D\right)=p_d\underset{t\in \mathcal{T}}{\mathrm{m}\mathrm{a}\mathrm{x}}\left(d_{u,t}-e_{u,t}^F-e_{u,t}^D\right)+{\displaystyle \sum _{t\in \mathcal{T}}}{p}_{e,t}\left(d_{u,t}-e_{u,t}^F-e_{u,t}^D\right).\end{array}$$

(2)

Participant units incur costs through service fees associated with the utilization of both fixed and dynamic ES. The cumulative cost for a participant unit $u$ over a given scheduling period, $C_u\left(E_u^F,e_{u,t}^D\right)$, is represented by

$$\begin{array}{r}{C}_u\left(E_u^F,e_{u,t}^D\right)={\displaystyle \sum _{t\in \mathcal{T}}}{p}_s^F{E}_u^F+{\displaystyle \sum _{t\in \mathcal{T}}}{p}_{s,t}^D \left|e_{u,t}^D\right|,\end{array}$$

(3)

where $E_u^F$ denotes the allocated fixed ES capacity for unit $u$, $p_s^F$ denotes the per-unit service price for the fixed ES, and $p_{s,t}^D$ denotes the per-unit service prices for the dynamic ES unit at time $t$.

Equation (3) outlines that the fixed ES capacity, which is the battery capacity, is assigned to unit u for the entire scheduling period. In contrast, the dynamic ES capacity is billed at each decision point within that period. This differentiation is caused by the predictable nature of fixed ES capacity as opposed to the variable availability of dynamic ES capacity, which depends on the presence of EVs at any given time.

Considering the costs associated with the usage of ES, the net benefit for a participant unit u utilizing the VESS, $N_u\left(e_{u,t}^F,e_{u,t}^D\right)$, is computed as

$$\begin{array}{r}{N}_u\left(e_{u,t}^F,e_{u,t}^D\right)=B_u\left(·\right)-B_u\left(e_{u,t}^F,e_{u,t}^D\right)-C_u\left(E_u^F,e_{u,t}^D\right)\end{array}.$$

(4)

$B_u\left(·\right)$ represents the electricity bill of unit u without employing ES, $B_u\left(e_{u,t}^F,e_{u,t}^D\right)$ refers to the modified electricity bill of unit u accounting for the use of both fixed and dynamic ES, and $C_u\left(e_{u,t}^F,e_{u,t}^D\right)$ denotes the cost incurred for the services of fixed and dynamic ES. The net benefit of unit u utilizing the VESS, $N_u\left(e_{u,t}^F,e_{u,t}^D\right)$, is calculated as the gains obtained from using the VESS minus the costs of usage.

2.3. Fixed Energy Storage

Fixed ES refers to a designated ES capacity that is permanently installed within a building and utilized collectively by various units. This often encompasses conventional battery storage systems that store a specific quantity of energy that is then dispatched based on the proposed scheduling method.

The cost-efficiency of fixed ES is directly related to its capacity. As the capacity of fixed ES expands, the per-unit cost generally declines owing to the benefits of economies of scale. Let $E^F$ denote the capacity of the fixed ES. The unit service price for employing fixed ES throughout the scheduling duration associated with the ESS is mathematically formulated as [24]

$$p_s^F=T \left[{\alpha }_1\exp \left(-{\alpha }_2{E}^F\right)+{\alpha }_3\right],$$

(5)

where ${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_3$ are parameters intrinsic to the cost characteristics of fixed ES. In Equation (5), the exponential term reflects the levelized cost of storage (LCOE) [25], which decreases as the capacity increases, whereas the multiplicative factor $T$ represents the duration of service provision.

2.4. Dynamic Energy Storage

In this study, dynamic ES refers to the use of EVs as flexible energy storage systems capable of rapidly responding to fluctuations in energy demand and supply. This dynamic utilization involves tapping the batteries of electric vehicles to store and release energy.

EV owners gain financial benefits from participating in the VESS. They can monetize the energy stored in their vehicle batteries by discharging it during periods of high demand, thereby obtaining a higher price for the energy provided. Consequently, the service price for dynamic ES is directly linked to the EV charging tariff. For this analysis, it is assumed that the EV charging tariff, denoted as $p_{s,t}^D$, remains constant throughout the scheduling period and is represented as [26]

$$p_{s,t}^D=p_{EV}.$$

(6)

The model can be easily extended to accommodate variable pricing over time, allowing for adjustments based on temporal changes in energy demand and tariff rates.

3. Virtual Energy Storage Scheduling Method

3.1. Objective Function

The principal objective of VESS scheduling for a commercial building is to maximize social welfare, which is defined here as the total net benefit accrued by all participating units. The objective function of the VESS scheduling problem, $\mathcal{O}\left(e_{u,t}^F,e_{u,t}^D\right)$, that quantifies this overarching goal is formulated as follows:

$$\mathcal{O}\left(e_{u,t}^F,e_{u,t}^D\right)=\sum _{u\in \mathcal{U}}{N}_u\left(e_{u,t}^F,e_{u,t}^D\right),$$

(7)

where $N_u\left(e_{u,t}^F,e_{u,t}^D\right)$ represents the net benefit for each participant unit u, derived from the use of both fixed (F) and dynamic (D) energy storage options at time t, and $\mathcal{U}=\{1,\cdots ,u,\cdots ,U\}$ is the set of all participant units within the building.

This function of Equation (7) aims to optimize energy usage across all units by effectively scheduling the discharge and charge cycles of fixed and dynamic ES. It integrates the financial, operational, and environmental aspects of energy management to ensure that the energy supply is economically beneficial while aligning with sustainability objectives.

3.2. Fixed ES Constraint

The scheduling of a VESS must adhere to resource constraints to ensure efficient and sustainable energy management. The critical constraint is related to the fixed ES capacity and is denoted as $E^F$. The sum of the capacities allocated to all participating units must not exceed the total fixed ES capacity. The fixed ES capacity constraint is expressed as [7]

$$\sum _{u\in \mathcal{U}}{E}_u^F\le E^F,$$

(8)

where $E_u^F$ represents the fixed ES capacity allocated to each unit u.

Moreover, the operation of fixed ES at each participant unit u during any given time t must be within the allocated capacity. The operational conditions for ES, utilized as a battery, include a charging and discharging rate (C-rate) of 0.5. This results in the following power constraints [7]:

$$-0.5 E_u^F\le e_{u,t}^F\le 0.5 E_u^F, \forall t\in \mathcal{T},\forall u\in \mathcal{U}.$$

(9)

Additionally, the state-of-charge (SoC) of the battery, which is affected by accumulated actions up to time t, starting from an initial state $s_{u,0}^F$, must not exceed the maximum allowable SoC, represented by $E_u^F$. This is expressed as [7]

$$0\le s_{u,0}^F+{\displaystyle \sum _{i=0}^t}{e}_{u,i}^F\le E_u^F, \forall t\in \mathcal{T},\forall u\in \mathcal{U}.$$

(10)

This constraint ensures that the capacity of the battery is optimally utilized without overcharging or deep discharging, thereby maintaining its longevity and efficiency.

3.3. Dynamic ES Constraint

Dynamic ES, which involves EVs in a V2G service, is limited by the flexibility of the V2G.

Predicting the flexibility of V2G involves analyzing historical data on the charging and discharging behaviors of EVs, such as the duration and frequency at which they are connected to the grid and available for energy services. These data are essential for estimating the potential energy contributions of EVs to the grid.

From existing research [27], the available V2G flexibility at a charging station (CS) equipped with m chargers, $V_t$, can be quantified as

$$V_t=E^D\Delta E\hspace{0.17em}m\hspace{0.17em}{\rho }_t\left[1-P_b\left({\rho }_t,m\right)\right],$$

(11)

where $E^D$ denotes the charging power of the charger installed at the CS, $\Delta E$ indicates the participation time of EVs in the V2G service, ${\rho }_t$ symbolizes the utilization rate of the CS, and $P_b\left({\rho }_t,m\right)$ represents the blocking probability, which indicates the likelihood that an EV cannot access a charger due to all chargers being occupied.

The blocking probability is calculated using the formula [28]

$$P_b\left({\rho }_t,m\right)=\frac{{\rho }_t{}^m/m!}{\sum _{i=0}^m{\rho }_t{}^i/i!}.$$

(12)

To maximize the participation of the EVs in the V2G program, it is necessary to manage the blocking probability of the CS with the following constraint [27]:

$$P_b\left({\rho }_i^{+},m\right)-P_b\left({\rho }_i,m\right)\le {\gamma }_{Th},i\in \{t,t+1,\cdots ,T\},$$

(13)

where ${\rho }_i^{+}$ denotes the adjusted utilization rate that reflects the increased EV charging time due to participation in V2G services.

Thus, the dynamic ES capacity for a given time period is defined as

$$E_t^D=E^D\Delta E^{\mathrm{*}}\hspace{0.17em}m\hspace{0.17em}{\rho }_t\left[1-P_b\left({\rho }_t,m\right)\right],$$

(14)

where $\Delta E^{\mathrm{*}}$ indicates the maximum V2G service time adjusted by the blocking probability. Equation (14) expresses how the dynamic ES capacity varies with both the historical usage patterns and the current utilization rate of the charging station.

According to the established operational constraints for dynamic ES derived from the V2G capabilities, the available dynamic ES that the participant units can utilize is strictly regulated. This regulation ensures that the dynamic interaction between EVs and the power grid remains within the capacity provided by the V2G service. This constraint is mathematically expressed as follows:

$$0\le {\displaystyle \sum _{u\in \mathcal{U}}}{e}_{u,t}^D\le E_t^D, \forall t\in \mathcal{T}.$$

(15)

Unlike fixed ES, which is allocated individually to participant units, Equation (15) expresses that dynamic ES operates on an aggregated basis. This collective management approach is fundamentally different because dynamic ES capitalizes on the variable and mobile nature of EV batteries. In practice, this means that the energy stored in EVs is pooled and managed as a common resource, which participant units draw from or contribute to based on real-time requirements and availability.

The aggregation of dynamic ES allows for greater flexibility and efficiency in managing energy flows. This enables the system to respond more effectively to fluctuations in the energy demand and supply across buildings or grids. For example, during times of peak demand, energy can be dynamically drawn from multiple EVs connected to the system. Conversely, during off-peak times, these vehicles can be collectively recharged, thereby optimizing both the energy usage and cost efficiency.

This method of aggregated usage contrasts with fixed ES, in which each unit has a predetermined storage capacity that is not shared with the other units. Fixed capacity typically contains stationary batteries installed within a building that are used exclusively by the unit to which they are assigned. Although reliable, these systems lack the dynamic scalability and flexibility provided by the pooled resources of dynamic ES.

3.4. VESS Scheduling Method with Fixed and Dynamic ESs

The proposed scheduling method for the VESS, which incorporates both fixed and dynamic ES, was formulated to maximize social welfare, which is defined as the total net benefit from energy savings across all participant units. The optimization problem is expressed as follows:

$$\begin{array}{rr}\hfill \underset{e_{u,t}^F,e_{u,t}^D}{\mathrm{m}\mathrm{a}\mathrm{x}}& \mathcal{O}\left(e_{u,t}^F,e_{u,t}^D\right)={\displaystyle \sum _{u\in \mathcal{U}}}{N}_u\left(e_{u,t}^F,e_{u,t}^D\right)\hfill \\ \hfill \mathrm{subject} \mathrm{to}& {\displaystyle \sum _{u\in \mathcal{U}}}{E}_u^F\le E^F,\hfill \\ & -0.5 E_u^F\le e_{u,t}^F\le 0.5 E_u^F, \forall t\in \mathcal{T},\forall u\in \mathcal{U},\hfill \\ & 0\le s_{u,0}^F+{\displaystyle \sum _{i=0}^t}{e}_{u,i}^F\le E_u^F, \forall t\in \mathcal{T},\forall u\in \mathcal{U},\hfill \\ & 0\le {\displaystyle \sum _{u\in \mathcal{U}}}{e}_{u,t}^D\le E_t^D, \forall t\in \mathcal{T}.\hfill \end{array}$$

(16)

Equation (16) outlines the optimization framework, presenting a convex problem with the objective of maximizing electricity bill savings by strategically allocating fixed and dynamic ES resources during each billing period. The convex nature of the problem suggests that it can be effectively solved using iterative methods, such as the gradient descent technique, which ensures convergence to the global optimum [29]. Additionally, to solve the problem, predicted information for future power demand and EV profiles is utilized. This predictive approach allows for the efficient scheduling of resources based on anticipated demand and availability. However, for real-time operation of the scheduled resources, compensation for uncertainties at each time point is necessary. The model does not currently address these real-time uncertainties, which presents a limitation in its practical application.

The VESS scheduling methods described in Equation (16) comprehensively address the dual aspects of fixed and dynamic ES by leveraging the unique benefits of each type. For fixed ES, using a shared large-capacity battery system enables significant economies of scale. By assigning the specific capacity of this shared battery to individual users for the scheduling duration, the unit cost of energy storage can be substantially reduced. This is a critical advantage, as it not only lowers the financial barriers associated with adopting energy storage technologies but also enhances the overall economic feasibility of the VESS.

In contrast, dynamic ES exploits the benefits of multi-user diversity. By allowing flexible and real-time sharing of energy resources among multiple users, primarily through the use of EVs in a V2G framework, dynamic ES can adaptively respond to fluctuations in energy demand and supply. This dynamic utilization optimizes grid stability and energy efficiency, providing a robust mechanism for harnessing the intermittent and unpredictable nature of renewable energy sources.

Collectively, these strategies highlight a sophisticated approach to managing ES in the context of a commercial building. The integration of fixed and dynamic ES capitalizes on economic efficiency and operational flexibility while contributing significantly to the sustainability goals of ES. By ensuring that energy storage is both cost-effective and dynamically responsive, this VESS scheduling method supports a broader transition toward smarter and more sustainable energy infrastructures.

4. Results and Discussion

4.1. Experimental Environment

To evaluate the proposed VESS scheduling method, a simulation was conducted on a building comprising 24 units. The energy demand data for this simulation were sourced from the Korea Micro Grid Energy Project (K-MEG) and recorded with a 1-h resolution [30]. Figure 2 illustrates the average daily demand distribution across these building units, providing insights into the consumption patterns that are critical for optimizing energy storage and usage.

To calculate electricity bills in this simulation, the ToU tariff applied was that of the medium general demand-metered service provided by the Pacific Gas and Electric Company (PG&E). Under this tariff, the energy prices for the mid-peak and on-peak periods are considered equal, as detailed in

Table 1. ToU tariff of Pacific Gas and Electric Company.

Demand Price (USD/kW)	Energy Price (USD/kWh)
	Off-Peak	Mid-Peak	On-Peak
24.10	0.27	0.20	0.20

[31].

In the simulation, fixed ES was implemented using lithium-ion batteries, reflecting one of the most common choices in current energy storage systems. The cost parameters associated with the fixed ES service, denoted as α1, α2, and α3, were set to 0.17, 0.0004, and 0.043, respectively, to calculate the service price according to the levelized cost of storage (LCOE) formula detailed in [24].

For dynamic ES, the service price was determined based on the average rate of the Business Electric Vehicle tariff proposed by the PG&E, which is 0.15 USD/kWh [32]. This rate effectively reflects the economic considerations associated with utilizing electric vehicles as part of a VESS.

The flexibility offered by dynamic ES was facilitated through a CS with specifics on the EVs used for dynamic ES sourced from the Korea Environment Corporation (KEC) [33], as depicted in Figure 3. The selected charging station was equipped with four DC chargers, each capable of delivering a charging power of 50 kWh. In Figure 3a, the maximum utilization of the CS is approximately 1.6, which suggests that during peak times, an average of 1.6 EVs simultaneously utilize each of the four available CSs. Figure 3b illustrates the associated blocking probability at times of maximum utilization, which was quantified as approximately 0.06. This indicates that out of every 100 EVs that arrive at the CS intending to charge, approximately 6 EVs are unable to do so because all the chargers are occupied. This blocking probability is a critical metric as it quantifies the likelihood of service denial, which is a crucial factor in assessing the adequacy of the charging station infrastructure to satisfy the demand.

To clarify the parameters used in our simulations, we have summarized them in

Table 2. Simulation parameters.

Parameter	Value	Description
Parameters related to BESP
Scheduling period	One month	Value according to the billing cycle
Parameters related to participant units
Demand of unit	Measured value	Recorded value by the K-MEG project [30]
Electricity tariff	A-10 of PG&E	Announced tariff for medium general demand-metered service [31]
Parameters related to fixed ES
Battery cost parameters	α1 = 0.17, α2 = 0.0004, and α3 = 0.043	Fitting value of the Li-ion battery’s LCOE [24]
Battery capacity	10~500 kWh	Variable to measure performance under different conditions.
Parameters related to dynamic ES
EV profile	Measured value	Recorded value by the KEC [33]
EV tariff	BEV of PG & E	Announced tariff for business electricity vehicle [32]
Charging power of chargers	50 kW	Specification of fast charger [27]
Number of CSs	3, 4, 5	Variable to measure performance under different conditions.
Blocking probability threshold	0.02~1.00	Variable to measure performance under different conditions.

below.

The total net benefit, defined in Equation (7) and used as the objective function of the scheduling problem in Equation (16), is selected as the system performance metric. In the simulation, the scheduling period is assumed to be one month. Therefore, the total net benefit is measured on a monthly basis. This assumption allows for a detailed analysis of the VESS scheduling method’s performance within a practical timeframe, reflecting the typical billing cycle in commercial settings.

To validate the effectiveness of the proposed scheduling method, a comparative analysis with existing methods is necessary. However, methodologies that combine fixed and dynamic ES approaches in the same environment have not yet been developed. Therefore, we compare the proposed method with two existing scenarios: a fixed-ES-only scenario and a dynamic-ES-only scenario. This comparison allows us to evaluate the performance of the proposed method, which integrates both fixed and dynamic ES systems, against established approaches.

By conducting this comparative analysis, we aim to demonstrate the advantages and improvements offered by the combined fixed and dynamic ES approach over traditional methods that utilize either fixed or dynamic ES in isolation. The performance metrics and simulation results will highlight the benefits of integrating these two types of ES, providing a comprehensive evaluation of the proposed scheduling method.

4.2. Fixed-ES-Only Scenario

The operation of fixed ES within the proposed VESS is subject to capacity limitations, as defined in Equations (9) and (10), respectively. Figure 4 illustrates the impact of varying fixed ES capacities ranging from 10 to 500 kWh on the objective of maximizing social welfare, measured as the total net benefit to all participating units.

As shown in Figure 4, the total net benefit increases linearly as the fixed ES capacity increases to 200 kWh. Beyond this point, the rate of increase in the net benefits begins to decrease. This diminishing return indicates that, while participants gain maximum benefits up to a fixed ES capacity of 200 kWh, additional capacity beyond this threshold results in smaller incremental gains relative to the service fees incurred for using fixed ES. This suggests an optimal capacity threshold at which the cost–benefit ratio of fixed ES utilization stabilizes.

This result also highlights the limitations of using fixed ES. When a fixed ES capacity is allocated, costs are incurred for the entire scheduling period. Participant units need to consider these costs when purchasing capacity. However, there is an inherent limitation in the utilization of fixed ES during periods when it is not being fully used. This underutilization during off-peak times means that fixed ES may not always be cost-effective, emphasizing the need for careful capacity planning and optimization to ensure that fixed ES provides maximum economic benefit.

To further explore the characteristics driving the gains from fixed ES,

Table 3. Pearson’s linear correlation coefficient between the participants’ demand profiles and their purchased fixed ES capacities, $E_u^F$.

200 kWh Fixed ES Capacity Case			500 kWh Fixed ES Capacity Case
Average Demand	Peak Demand	${\mathit{E}}_{\mathit{u}}^{\mathit{F}}$	Average Demand	Peak Demand	${\mathit{E}}_{\mathit{u}}^{\mathit{F}}$
0.21	0.77	1.00	0.38	0.88	1.00

presents the results of calculating the Pearson’s linear correlation coefficient (PLCC) between the participants’ demand profiles and their purchased fixed ES capacities, $E_u^F$ [34].

The data reveal a strong correlation, with coefficients between the participants’ peak demand and the capacity of fixed ES they procure ranging from 0.77 to 0.88. This high correlation underscores the fact that participants primarily invest in fixed ES to mitigate the costs associated with high-demand prices, which are significantly more substantial than variable energy prices. Notably, as the fixed ES capacity increases to 500 kWh, the correlation with the peak demand strengthens compared with that at 200 kWh, indicating that users with higher peak demands tend to utilize larger fixed ES capacities more intensively.

4.3. Dynamic-ES-Only Scenario

Equation (13) shows that the operational scope of dynamic ES is constrained by the blocking probability threshold. The blocking probability, which indicates the likelihood that an EV cannot be charged because all chargers are occupied, significantly affects the system’s performance. This probability is also affected by the number of available CSs in Equation (12).

Figure 5 illustrates how changes in the blocking probability threshold and number of CSs affect the total net benefit. The results show that as the blocking probability threshold increases (indicating a relaxation in the blocking constraint) and the number of CSs increases, the total net benefit also increases.

Specifically, with four charging stations, increasing the blocking probability threshold from 0.02 to 0.1 results in a net benefit increase from 882.5 to 2260.3, which is an approximately 156% increase. Adding one more CS under the same conditions boosts the total net benefit to $3092.4, a further increase of approximately 250%.

Additionally, compared to the results shown in Figure 4, Figure 5 does not exhibit discontinuous changes in the total net benefit. This difference is attributed to the nature of dynamic ES, which allows for the purchase of the required capacity at the needed time, unlike fixed ES, which requires upfront allocation for the entire period. This flexibility in dynamic ES usage results in a smoother increase in net benefits.

These findings underscore the critical role of the number of CSs in enhancing the performance of dynamic ES systems. The data demonstrate that both increasing the blocking probability threshold and adding more charging stations significantly boost the total net benefit, highlighting the importance of strategic planning in the deployment of dynamic ES infrastructure.

Table 4. Pearson’s linear correlation coefficient between the participants’ demand profiles and their total purchased dynamic ES capacities, ${\sum }_{t\in \mathcal{T}}{e}_{u,t}^D$ with four charging stations.

0.04 Blocking Probability Threshold			0.08 Blocking Probability Threshold
Average Demand	Peak Demand	${\displaystyle \sum _{\mathit{t}\in \mathcal{T}}}{\mathit{e}}_{\mathit{u},\mathit{t}}^{\mathit{D}}$	Average Demand	Peak Demand	${\displaystyle \sum _{\mathit{t}\in \mathcal{T}}}{\mathit{e}}_{\mathit{u},\mathit{t}}^{\mathit{D}}$
−0.33	−0.44	1.00	−0.40	−0.54	1.00

explores the characteristics driving the gains from dynamic ES, similar to the analysis performed for the fixed-ES-only scenario. It presents the results of calculating PLCC between the participants’ demand profiles and their total purchased dynamic ES capacity ${\sum }_{t\in \mathcal{T}}{e}_{u,t}^D$ with four CSs.

Unlike fixed ES, which allows for controlled operation regardless of external conditions, the capacity available from dynamic ES is highly dependent on the state of the EVs. The results indicate a weak negative correlation between the dynamic ES capacity and demand profile characteristics. This suggests that in the operation of dynamic ES, the availability and state of EVs have a more significant impact on performance than the participants’ actual energy needs.

4.4. Combining Fixed ES and Dynamic ES Scenario

The proposed VESS scheduling method aims to optimize the combined operation of fixed and dynamic ES to maximize social welfare. This scenario investigates the interplay between these two types of ES and their collective impact on the total net benefit for participants.

Figure 6 illustrates the variation in the total net benefits as the constraints on fixed ES and dynamic ES change, demonstrating how these combined systems can be coordinated to enhance performance. Figure 6a,b presents the results for scenarios with four and five CSs, respectively, illustrating the different VESS configurations.

In Figure 6a,b, the axes are defined to reflect the changes in net benefits due to the interaction between fixed and dynamic ES. The y-axis (‘a’ direction along the y-axis) measures changes in the total net benefits due to the inclusion of dynamic ES, as compared to the scenario where only fixed ES is used. This axis provides insights into the additional benefits of dynamic ES over and above the baseline established by fixed ES alone. Moreover, the x-axis (‘b’ direction along the x-axis) measures changes in total net benefits due to the inclusion of fixed ES, as compared to the scenario where only dynamic ES is utilized. This axis highlights the incremental benefits that fixed ES brings to a system initially optimized only for dynamic ES.

The results depicted in Figure 6 strongly indicate that the combined VESS operation of fixed and dynamic ES yields greater total net benefits compared to scenarios where only fixed ES or only dynamic ES are used. Specifically, the total net benefit with 200 kWh fixed ES only and dynamic ES only with 0.04 blocking probability scenarios is $1660.4 and $1338.3, as shown in Figure 4 and Figure 5, respectively. By combining fixed ES and dynamic ES with 4 CSs, the total net benefit increases to $2767.1. This enhancement represents a 66.7% increase from the fixed-ES-only scenario and a 106.8% increase from the dynamic-ES-only scenario. This confirms the effectiveness of the proposed VESS scheduling method, which strategically integrates both storage types to optimize overall system performance.

In Figure 6a, the increase in the total net benefits is symmetrically distributed about the origin, as indicated by the gray arrows. This symmetry suggests that fixed and dynamic ES contribute comparably to the gains realized in the combined operational scenario. The balanced enhancement from both storage types underscores the well-coordinated integration within the VESS, leading to a harmonized increase in net benefits.

Conversely, Figure 6b exhibits a more pronounced increase in total net benefits in the ‘b’ direction. This indicates that in scenarios with a higher number of CSs, dynamic ES plays the predominant role in improving the total net benefits. The difference between Figure 6a,b arises primarily from the number of CSs. As the number of CS increases, as shown in Figure 5, the flexibility provided by dynamic ES also increases. This enhanced flexibility enables dynamic ES to have a more substantial impact on VESS scheduling in the scenarios depicted in Figure 6b, contributing to a steeper increase in benefits.

The results from Figure 6 suggest that the combined approach of using fixed and dynamic ES benefits from resource diversity, which enhances overall performance. The change in the direction of the gray arrow between Figure 6a,b highlights how the dominant resource and the direction of resource utilization can shift based on the available resources. This study presents the relationship between these resources and their combined utilization, but future research should focus on analyzing the impact of unit resource amounts on system performance. Such research could evaluate which resources have a dominant impact and develop methods for optimal resource composition, further improving the system’s efficiency and effectiveness.

Overall, the combined use of fixed and dynamic ES demonstrates a scalable and flexible approach, offering higher efficiency and economic gains compared to using either fixed or dynamic ES alone. The results suggest that careful adjustment of the blocking probability threshold and fixed ES capacity is crucial for maximizing total net benefits.

In exploring the synergistic effects of combined fixed and dynamic ES within the VESS,

Table 5. Pearson’s linear correlation coefficient between the participants’ demand profiles and their total purchased fixed ES capacity $E_u^F$ and dynamic ES capacities, ${\sum }_{t\in \mathcal{T}}{e}_{u,t}^D$ with four charging stations.

200 kWh Fixed ES Capacity and 0.04 Blocking Probability Threshold
Average Demand	Peak Demand	${\mathit{E}}_{\mathit{u}}^{\mathit{F}}$	Average Demand	Peak Demand	${\displaystyle \sum _{\mathit{t}\in \mathcal{T}}}{\mathit{e}}_{\mathit{u},\mathit{t}}^{\mathit{D}}$
0.38	0.81	1.00	0.27	0.28	1.00

plays a crucial role by quantifying the relationship between participants’ demand profiles and their capacity purchases from both types of ES.

Unlike the dynamic-ES-only scenario presented in Table 4, where a weak negative correlation is observed, Table 5 reveals a positive correlation between the demand profiles and dynamic ES purchase capacity in the combined VESS scheduling scenario. This shift suggests that when dynamic ES is integrated with fixed ES, the purchased capacity is more closely aligned with the actual demand patterns, particularly during peak usage periods.

Furthermore, when compared with the fixed-ES-only scenario results in Table 3, the combined VESS scheduling exhibits a stronger correlation with the demand profiles, particularly with the peak demand profile. This enhanced correlation indicates that the combined scheduling strategy can control and reduce peak demands more effectively than scenarios that utilize fixed or dynamic ES independently. Effective peak demand management is crucial for reducing participant costs and mitigating operational stress on utility grids, which typically face higher costs during peak periods.

The results in Table 5 suggest that the proposed combined VESS scheduling strategy increases the net benefits for participant units by optimizing the energy costs associated with peak demand and provides broader benefits to the utility grid. By smoothing peak loads more efficiently, the combined system helps reduce the necessity for costly peak-time energy production and contributes to overall grid stability and sustainability.

4.5. Discussion Summary

From the results of the scenarios explored in Section 4.2, Section 4.3 and Section 4.4, it is clear that integrating both fixed and dynamic ES optimizes the VESS scheduling more effectively than using either system in isolation. Based on these findings, the following key points can be highlighted for the VESS operation:

• Net benefit dynamics: The total net benefits are directly proportional to the combined capacity of the fixed and dynamic ES. As shown in Figure 6, the VESS scheduled under the combined scenario achieves higher benefits owing to the optimized resource utilization and cost efficiency compared to the scenarios where only one type of ES is used. This implies that the synergy between the fixed and dynamic ES significantly enhances the performance of the system.
• Operational efficiency: The operational efficiency of a VESS varies significantly across different setups. In scenarios that utilize only fixed ES, efficiency hinges on matching storage capacity precisely with demand because both oversizing and undersizing can introduce cost inefficiencies. For dynamic ES setups, efficiency is more variable and heavily dependent on the availability and capacity of the charging infrastructure, which can be mitigated by increasing the number of CSs. However, combining fixed and dynamic ES offers the best of both systems, optimizing operational efficiency by using fixed ES for stability and dynamic ES for flexibility. This combination minimizes energy waste and enhances the ability of the system to respond adaptively to demand fluctuations, thereby showcasing a superior operational model.
• Demand management: Demand management capabilities differ across various VESS scenarios. Fixed ES systems effectively manage base and peak loads within their capacity but lack the flexibility to respond to demands beyond their static limits. Conversely, dynamic ES systems, reliant on EV availability and charging behaviors, tend to struggle with peak demand management when used in isolation because of their dependence on external factors. The integration of both fixed and dynamic ES into a combined system proves to be the most effective, leveraging dynamic ES for its responsiveness to sudden peaks and fixed ES for consistent baseline load management, thereby ensuring a comprehensive demand response strategy.
• Implications for the utility grid and social welfare: The combined VESS operation effectively reduces peak demand, which directly benefits the utility grid by lowering the need for costly peak-time energy production and deferring new infrastructure investments. Moreover, as the combined system enhances the efficiency of both fixed and dynamic ES, it promotes a higher level of social welfare improvement across participating units and broader energy networks.

The results of this study demonstrate the potential benefits of integrating fixed and dynamic energy storage systems (ESSs) into commercial buildings. However, there are several limitations to this research that need to be acknowledged:

• Real-time operation: Our approach focuses on the scheduling of flexible resources and derives solutions as an optimization problem. For real-time operation of the scheduled resources, compensation for uncertainties at each time point is necessary. The model does not currently address these real-time uncertainties.
• Economic impact analysis: The study uses total net benefit to evaluate the economic impact. However, this metric can be influenced by fluctuations in electricity market prices, which may affect the overall benefits. The variability of market conditions needs to be considered for a more comprehensive economic analysis.
• VESS integration into the utility grid: The integration of VESS into the utility grid may introduce additional constraints related to grid stability and operational limitations. These constraints could affect the feasibility and effectiveness of VESS operations, especially during peak demand periods.

According to these limitations, the following future research directions are suggested:

• Integration of renewable energy sources: The potential for integrating renewable energy sources, such as solar and wind, with fixed and dynamic ES within the VESS can be explored. This study focuses on effectively storing the excess energy generated during peak production times and utilizing it during demand peaks or low production periods to enhance sustainability and reduce reliance on non-renewable energy sources. Additionally, real-time uncertainty compensation methods should be developed to address the variability in renewable energy generation.
• Scalability and modular system design: Investigate the scalability of VESS by implementing modular designs that can be easily expanded or adjusted based on the increase in energy demands or changes in the user base. This includes studying the impacts of scaling up on system performance, cost efficiency, and infrastructure requirements. Future research should also consider the integration of uncertainty compensation mechanisms to ensure robust real-time operations as the system scales.
• Economic and regulatory impact analysis: Comprehensive studies can be conducted on the economic impacts of widespread VESS adoption, including cost–benefit analysis, return on investment, and effects on electricity market prices. Sensitivity analyses should be performed to understand how varying market conditions influence the total net benefit. Additionally, frameworks for assessing the regulatory challenges and opportunities should be developed to facilitate the broader deployment of VESS.
• Impact on utility grids: The long-term impacts of large-scale VESS integration on utility grids, including grid stability, load balancing, and the potential to reduce peak load pressures, need to be analyzed. Improvements in these areas will help understand how VESS can be optimized to support the existing grid infrastructure and contribute to grid modernization. Future research should also explore the implications of VESS integration on utility grids, considering constraints such as grid stability and operational limitations. Analyzing how these constraints affect VESS operations will provide insights into optimizing the system for enhanced grid reliability and performance.
• Real-time application of study results: As mentioned in the limitations, our study focuses on scheduling and does not explicitly consider real-time operation. However, the problem addressed can be reformulated as a sequential decision making (SDM) problem, as indicated by the benefit model used in our objective function. Our problem can be tackled using techniques such as dynamic programming or reinforcement learning-based approaches to facilitate real-time operation [35]. Future research should explore this reformulation to enable real-time implementation, addressing the uncertainties at each decision point and optimizing operations dynamically.

5. Conclusions

This study developed an optimized VESS scheduling method for commercial buildings that incorporates both fixed and dynamic ES systems. The VESS model included three main components: fixed ES, dynamic ES, and a utility grid—creating a comprehensive framework for energy management in commercial settings. The VESS scheduling problem, which integrates constraints from both fixed and dynamic systems, was formulated as a mixed-integer linear problem, allowing for optimal solutions through computational techniques, such as gradient methods and dual decomposition. The simulation results, utilizing a real dataset from Korea, demonstrated that the combined VESS scheduling of fixed and dynamic ES provided substantial benefits in terms of total net benefit and operational efficiency. Specifically, the integration of these systems resulted in improved energy cost management and enhanced grid reliability compared with scenarios that utilize only one type of storage system. Furthermore, the combined system showed a significant increase in total net benefits, proving the effectiveness of integrating multiple ES systems.

The basic framework established for the VESS, fixed ES, and dynamic ES can be extended to more complex scenarios. Future research could explore real-time operation scenarios that include active units and their uncertainty, such as prosumers with distributed renewable generators, which would add a layer of complexity and relevance to the VESS model. Additionally, problems related to ownership and the economically optimal sizing of VESS capacities warrant further investigation. Finally, the utility grid model can be expanded to include more detailed power system requirements to provide a more nuanced understanding of grid dynamics and energy management strategies.