Day-Ahead Nonlinear Optimization Scheduling for Industrial Park Energy Systems with Hybrid Energy Storage

Jiacheng Guo; Yimo Luo; Bin Zou; Jinqing Peng

doi:10.1016/j.eng.2024.10.006

Engineering ›› 2025, Vol. 46 ›› Issue (3) :349 -366. DOI: 10.1016/j.eng.2024.10.006

Research Energy System Engineering—Article

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Day-Ahead Nonlinear Optimization Scheduling for Industrial Park Energy Systems with Hybrid Energy Storage

Jiacheng Guo ^a^,^b
, Yimo Luo ^a^,^b
, Bin Zou ^a^,^b^,^*
, Jinqing Peng ^a^,^b^,^*

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Abstract

Hybrid energy storage can enhance the economic performance and reliability of energy systems in industrial parks, while lowering the industrial parks’ carbon emissions and accommodating diverse load demands from users. However, most optimization research on hybrid energy storage has adopted rule-based passive-control principles, failing to fully leverage the advantages of active energy storage. To address this gap in the literature, this study develops a detailed model for an industrial park energy system with hybrid energy storage (IPES-HES), taking into account the operational characteristics of energy devices such as lithium batteries and thermal storage tanks. An active operation strategy for hybrid energy storage is proposed that uses decision variables based on hourly power outputs from the energy storage of the subsequent day. An optimization configuration model for an IPES-HES is formulated with the goals of reducing costs and lowering carbon emissions and is solved using the non-dominated sorting genetic algorithm II (NSGA-II). A method using the improved NSGA-II is developed for day-ahead nonlinear scheduling, based on configuration optimization. The research findings indicate that the system energy bill and the peak power of the IPES-HES under the optimization-based operational strategy are reduced by 181.4 USD (5.5%) and 1600.3 kW (43.7%), respectively, compared with an operation strategy based on proportional electricity storage on a typical summer day. Overall, the day-ahead nonlinear optimal scheduling method developed in this study offers guidance to fully harness the advantages of active energy storage.

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Keywords

Industrial park energy system / Hybrid energy storage / Active energy storage / Configuration optimization / Day-ahead optimal scheduling

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Jiacheng Guo, Yimo Luo, Bin Zou, Jinqing Peng. Day-Ahead Nonlinear Optimization Scheduling for Industrial Park Energy Systems with Hybrid Energy Storage. Engineering, 2025, 46(3): 349-366 DOI:10.1016/j.eng.2024.10.006

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1. Introduction

The Chinese government has pledged to achieve a carbon peak and is striving to reach carbon neutrality [1]. However, the life-cycle energy consumption of buildings in China accounts for 45.5% of the nation’s total energy consumption, while buildings’ in China life-cycle carbon emissions account for 50.9% of nation’s carbon emissions [2]. Industrial parks, which represent significant energy and carbon emissions in both the building and industrial sectors, play a pivotal role in advancing toward China’s goals of a carbon peak and carbon neutrality [3]. The current energy systems of industrial parks have the issues of high energy consumption and large carbon emissions during the operational stage. A high penetration of renewable energy utilization is an effective means to achieve low-carbon, zero-energy operations in industrial parks [4]. Nonetheless, renewable energy sources inherently exhibit intermittency and volatility, and the unpredictable load demands within industrial parks might lead to a low utilization of renewables.

Energy storage acts as a bridge between the supply and demand sides and is crucial for increasing the renewable energy utilization in industrial parks, thereby contributing to the realization of low-carbon, zero-energy objectives [5]. However, existing energy-storage technologies have inherent advantages and disadvantages. As the penetration rate of renewable energy increases on the supply side and various load demands increase on the demand side, the limitations of the flexibility of a single type of energy storage become increasingly evident, making this type of energy storage less effective within industrial parks. Some reports have indicated that hybrid energy-storage systems, which comprise both thermal energy storage and electrical energy storage, can effectively leverage the strengths of different energy-storage methods [6]. These systems have significant benefits in meeting the multiple energy demands of industrial parks and reducing the overall cost of energy-storage systems. They are particularly suitable for industrial park scenarios with cooling, heating, and electric load demands. Coupling a hybrid energy-storage system with an industrial park energy-supply system to constitute an industrial park energy system with hybrid energy storage (IPES-HES) can significantly improve the economic benefits and renewable energy utilization and decrease the carbon emissions of industrial parks [7]. Studies have indicated that optimizing the scheduling of IPES-HESs is the key to achieving efficient, reliable, and economical operation [4]. However, the complexity of IPES-HESs, which encompass renewable energy utilization, energy storage, and utility grid components, poses significant challenges when optimizing a system’s operational scheduling. Therefore, research is needed on the operational scheduling for IPES-HESs to enhance their economic efficiency and decrease carbon emissions.

The development of device models with high reliability and robustness serves as the theoretical foundation for optimizing the operational scheduling of IPES-HESs [8], [9]. Most energy system models for industrial parks are based on real-time energy-balance constraints and have established thermodynamic models (Table 1 [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]) [10]. Chen et al. [11] developed thermodynamic models for energy device such as compressed-air energy storage and thermal/cold storage tanks to accurately characterize the operational features of a system. To address issues related to the heating and cooling load supply, Wang et al. [12] devised a detailed thermodynamic model for IPES-HESs. However, the aforementioned models primarily focused on the thermodynamic characteristics of energy device, neglecting the electrical parameters.

Other studies have established unified models (Table 1); for example, the energy hub model considers the heterogeneous energy flows of cooling, heating, and electricity during their production, conversion, storage, and usage processes. Jin et al. [13] used a unified model of energy device and linearly simplified the thermodynamic characteristics of the associated energy device to reduce the model’s complexity and solving difficulty. Yin and Liu [14] developed detailed models for photovoltaics (PVs) and hybrid energy storage to enhance the reliability of IPES-HESs’ electricity supply. Currently, the system models used for IPES-HESs tend to simplify energy device through linearization; this approach lacks detailed modeling and fails to accurately represent the real-time operational characteristics of an industrial park.

A reasonable operational strategy is crucial for improving the renewable energy utilization and economic efficiency and lowering the carbon emissions of an IPES-HES [15], [16]. Thus far, most studies have employed rule-based control methods to synergistically manage IPES-HESs (Table 1) [17], [18]. Le et al. [19] adopted an operational strategy of maximizing the self-consumption ratio (SCR) to control the operation of an IPES-HES, which decreased the industrial park’s carbon emissions. To address the problem of the high costs associated with electricity storage, some scholars have suggested leveraging power-to-heat (P2H)/power-to-cooling (P2C) technologies to transform electrical energy into heating/cooling energy for storage, thereby improving the economic efficiency and decreasing the carbon emissions of IPES-HESs [20], [21]. Erdmann et al. [22] integrated storage batteries with P2H technologies (i.e., thermal energy storage) for storing PV power generation, achieving a 46% reduction in carbon emissions. Di Somma et al. [23] proposed a hybrid energy-storage operation strategy based on time-of-use electricity pricing, which reduced the annual total cost of the system by 21%–36% compared with the baseline strategy. However, the aforementioned rule-based passive control strategies do not consider the energy characteristics of industrial parks at future time points, which results in low energy-storage utilization and an inability to reduce the peak grid-connected power (GCP), diminishing the advantages of active energy storage.

Appropriate methods for optimizing scheduling further improve the operational efficiency of IPES-HESs. Most previous studies have simultaneously considered device configuration and operation strategies for scheduling optimization, obtaining static system schemes (Table 1) [24]. He et al. [25] established coordinated optimization of an IPES-HES based on a nonlinear programming model, achieving enhanced economic performance and reliability for the system. However, a static system scheme neglects the dynamic demands of operational scheduling and does not meet the actual scheduling requirements. To address this issue, some researchers have proposed multi-stage optimization scheduling methods (Table 1) [26], which prioritize device configuration optimization followed by system scheduling optimization, effectively improving the system’s operational efficiency [27]. Naserabad et al. [28] utilized a non-dominated sorting genetic algorithm II (NSGA-II) for the optimal scheduling of IPES-HESs, significantly enhancing the exergy efficiency, total cost ratio, and carbon index of secondary school buildings. Forough and Roshandel [29] employed mixed-integer convex programming for the day-ahead optimization scheduling of an IPES-HES, increasing the renewable energy utilization by 12.9%. However, these simplified linear optimization scheduling methods cannot accurately reflect the actual operational conditions of an energy system.

The literature review above indicates that applying hybrid energy storage can effectively enhance the comprehensive benefits of IPES-HESs. There has been substantial advancement in the research related to IPES-HESs. However, several challenges still exist that urgently need to be addressed: ① Most studies have only established linear models for IPES-HESs, which do not accurately characterize the nonlinear operational characteristics of the energy device. ② Most studies have employed rule-based operation strategies that entail passive control of the hybrid energy storage, thus failing to fully utilize the active-energy-storage advantages. ③ Most studies have implemented simplified linear optimization scheduling based on configuration optimization, which does not accurately reflect the actual operational conditions of a hybrid energy-storage system.

To address these issues, this study presents the following work: ① A nonlinear refined model for an IPES-HES is developed that can accurately characterize the operating characteristics of various devices (e.g., battery degradation, thermal loss in thermal energy storage, and efficiency changes of a dual-purpose chiller (DPC)). ② An operational strategy for active energy storage is proposed, which employs the hourly power output from energy storage on the next day as the decision variable. ③ A nonlinear day-ahead optimization scheduling method with the improved NSGA-II is proposed, based on configuration optimization.

The other sections of this study are organized as follows: Section 2 establishes the IPES-HES model, Section 3 proposes optimization methods for the IPES-HES, Section 4 introduces the case study, Section 5 presents the results and discussion, and Section 6 presents the main conclusions of this study.

2. System description

2.1. An IPES-HES

The structure of the IPES-HES is shown in Fig. 1. It consists of PVs, a DPC, lithium batteries, a thermal storage tank (TST), chilled water storage (CWS), and the utility grid. The area of the industrial park studied in this paper is relatively small, and thermal losses from the heating network and heat exchange are proportionally accounted for. We assume that there is no transmission delay in the heating networks. PV panels are installed on the building rooftops and surrounding areas of the industrial park to generate clean energy. The electric load of the industrial park is met through PVs, the utility grid, and lithium batteries. The cooling load of the industrial park is jointly served by the DPC and CWS. The users’ heating needs are fulfilled by the DPC and TST. The operational strategy of the IPES-HES is presented in Section 2.2. Detailed modeling of each device within the IPES-HES is discussed in Section 2.3, while the linear models used for comparison are presented in Appendix A.

In most industrial parks in China, the electric load is supplied by the utility grid, the cooling load is addressed by chiller units for cooling, and the heating load is met by chiller units for heating or by a centralized heating system. This type of energy-supply system is called a “separate production system” and is the reference system in this study. In this study, the utility grid caters to the electricity demands of the industrial users, and the DPC meets both the cooling and heating needs of the industrial park. In the reference system, the utility grid is used to meet the electric loads of the industrial park, and DPCs are employed to address both the cooling and heating loads of the industrial park users. This reference system does not include PV and energy storage systems.

2.2. The system operational strategy

2.2.1. Rule-based operational strategies

We examine three main types of rule-based operational strategy for the IPES-HES:① an operational strategy based on electricity-only storage, ② an operational strategy based on electricity-priority storage, and ③ an operational strategy based on proportional electricity storage.

(1)An operational strategy based on electricity-only storage. The PV electricity generation is priority to serve the electricity demands of the industrial park, which include both its electric load and the power require for the DPC. Surplus PV electricity generation is preferentially stored using lithium batteries. The remaining electricity is integrated into the utility grid, when the lithium batteries are fully charged. Power from lithium battery discharge and the utility grid are used to fill the electricity gap, when the PV power generation is less than the electric load of the industrial park. The DPC is used to meet both the cooling and heating loads of the industrial park.

(2)An operational strategy based on electricity-priority storage. If the lithium batteries are fully charged in summer and winter, the remaining PV power generation is converted into cooling and heating energy, using P2C and P2H technologies, and is stored in the CWS and the TST. The remaining electricity-supply strategy is the same as strategy 1. The surplus PV power in the system is partially stored in the lithium batteries and partially in the TST through P2H technologies. The distribution ratio between these two forms of storage is referred to as the “P2H ratio.” The heating load of the industrial park is jointly provided by the DPC heating and the heat discharge from the TST. The DPC and CWS are utilized to meet the cooling load of the industrial park.

(3)An operational strategy based on proportional electricity storage. When the IPES-HES has surplus electricity during summer and winter, a portion is proportionally allocated to the lithium battery storage. The remaining PV generation is converted into cooling and heating energy through P2C and P2H technologies and is stored in the CWS and TST. The remaining electricity-supply strategy is the same as strategy 1. The strategy for supplying cooling and heating loads in the industrial park is the same as strategy 2.

2.2.2. Optimization-based operational strategy

To further realize the economic, carbon-reducing, and load-flexibility advantages of the IPES-HES, the hourly power outputs of the lithium batteries, TST, and CWS for the following day are used as decision variables for the day-ahead optimal scheduling of the IPES-HES. Details of the optimization process are provided in Section 3.2.

2.3. Mathematical models for the devices

This study establishes detailed models for the PVs, lithium batteries, TST, CWS, DPC, and so forth. The detailed modeling process for each energy device is provided in Appendix A.

3. Mathematical modeling and method

3.1. System configuration optimization

3.1.1. Performance indicators

This study uses the cost-reduction ratio (CRR) as the economic performance indicator for the IPES-HES. The CRR is defined as the percentage decrease in the system’s annual energy bill compared with that of the reference system, calculated using Eq. (1) [30].

(1)

CRR = \frac{C_{ref,annual} - C_{IPES-HES,annual}}{C_{ref,annual}} \times 100 %

(2)

C_{annual} = C_{bat,aging} + \sum_{t = 1}^{n_{1}} [\sum_{j = 1} c_{equ, j} (t) + \sum_{j = 1} c_{om, j} (t) + c_{grid,buy} (t) - c_{grid,sell} (t)]

where C_ref,annual and C_{IPES-HES,annual} are the annual energy bill of the reference system and the IPES-HES, in USD; C_bat,aging is the aging cost of lithium batteries in USD; c_equ,_j(t) and c_om,_j(t) are the initial investment and maintenance costs of the jth device at time t, respectively, in USD; c_grid,buy(t) and c_grid,sell(t) are the cost of electricity purchase and the revenue from electricity sales for a certain energy-supply system, respectively, in USD; and n₁ is the optimization time, which is set to 8760 h in this study.

The initial investment and maintenance costs for the jth device at time t are calculated using Eqs. (3), (4), respectively.

(3)

c_{equ, j} (t) = P_{equ,nom, j} \times c_{ini, j} \times Δ t / L_{equ, j}

(4)

c_{om, j} (t) = P_{om, j} (t) \times c_{om, j}

where P_equ,nom is the rated power of the certain device in kW, c_ini is the unit initial investment of the certain device in USD·kW⁻¹, Δt is the time step in h, L_equ is the lifetime of the certain device in years, P_om is the output power of the certain device in kW·h, and c_om is the unit maintenance cost of the certain device in USD·(kW·h)⁻¹.

The cost of electricity purchase and the revenue from the electricity sales of a certain energy supply system at time t are calculated using Eqs. (5), (6), respectively.

(5)

c_{grid,buy} (t) = γ_{grid,buy} (t) \times E_{grid,buy} (t) \times Δ t

(6)

c_{grid,sell} (t) = γ_{grid,sell} \times E_{grid,sell} (t) \times Δ t

where E_grid,buy(t) and E_grid,sell(t) are the electricity of purchase and sales in a certain energy supply system at time t, respectively, in kW·h; γ_grid,buy is the time-of-use tariffs of the utility grid [31] in USD·(kW·h)⁻¹; and γ_grid,sell is the feed-in tariff of the PVs [30] in USD·(kW·h)⁻¹.

The environmental benefits of the IPES-HES are evaluated in terms of the carbon-abatement ratio (CAR). The CAR is defined as the reduction in carbon emissions of a certain system compared with the reference system, calculated using Eq. (7) [32].

(7)

CAR = \frac{{CE}_{ref,annual} - {CE}_{IPES-HES,annual}}{{CE}_{ref,annual}} \times 100 %

(8)

{CE}_{annual} = \sum_{t = 1}^{n_{1}} [ce \times E_{grid,buy} (t) \times Δ t]

where CE_ref,annual and CE_{IPES-HES,annual} are the annual carbon emissions of the reference system and the IPES-HES, respectively, in kg; and ce is the unit carbon emissions from the utility grid [31], in kg·(kW·h)⁻¹.

The SCR refers to the proportion of PV generation used to meet the electricity demand of the buildings in the industrial park compared with the total PV power generation [33]. This ratio reflects the efficiency of the onsite utilization of PV generation. A higher SCR means that the large-scale grid-connected PV power can be reduced, improving the stability of the utility grid. The self-sufficiency ratio (SSR) is the proportion of the electricity demand of the buildings in the industrial park met by the PV generation relative to buildings’ total electricity consumption [34]. A higher SSR indicates a lower reliance on electricity purchased from the utility grid. The SCR and the SSR are commonly used to evaluate the benefits of PV utilization in IPES-HESs and are calculated using Eqs. (9), (10), respectively [33], [34].

(9)

SCR = \frac{E_{PV,annual} - E_{grid,sell,annual}}{E_{PV,annual}}

(10)

SSR = \frac{E_{PV,annual} - E_{grid,sell,annual}}{E_{PV,annual} + E_{grid,buy,annual} - E_{grid,sell,annual}}

(11)

E_{PV,annual} = \sum_{t = 1}^{n_{1}} [N_{PV} \times P_{PV} (t) \times Δ t]

(12)

E_{grid,sell,annual} = \sum_{t = 1}^{n_{1}} [E_{grid,sell} (t) \times Δ t]

(13)

E_{grid,buy,annual} = \sum_{t = 1}^{n_{1}} [E_{grid,buy} (t) \times Δ t]

where E_PV,annual, E_{grid,sell,annual}, and E_{grid,buy,annual} are the annual PV power generation, electricity sales, and electricity purchases of the system, respectively, in kW·h; P_PV(t) is the power generation of the PV in kW; and N_PV is the installed area of PV panels in m².

3.1.2. Decision variables

The number of PV installations determines the scale of renewable energy utilization in the IPES-HES. Under high PV penetration, a substantial amount of PV power generation being fed into the utility grid could have a significant adverse impact. Appropriate capacities of the lithium batteries, TST, and CWS can effectively improve the system’s renewable energy utilization rate and economic benefits, without leading to idling in energy storage. A rational arrangement of the storage capacity and discharge power can further enhance the system’s comprehensive benefits and PV utilization. Hence, during the device-configuration optimization stage, the selected decision variables include the number of PV panels; the rated capacity, charging power, and discharging power of the lithium batteries; the radius, height-to-diameter ratio, heat-storage power, and heat-release power of the TST; the radius, height-to-diameter ratio, cold storage power, and heat-release power of the CWS; and the P2H ratio (x_P2H) and P2C ratio (x_P2C).

3.1.3. Constraint conditions

During the operation of the IPES-HES, it is necessary to maintain a power balance with the utility grid and a supply balance for the cooling, heating, and electric loads of the users:

Balance of electric load supply:

(14)

N_{PV} \times P_{PV} (t) + E_{grid,buy} (t) + P_{bat,dis} (t) = E_{user} (t) + P_{DPC} (t) + P_{P2C} (t) + P_{P2H} (t) + P_{bat,ch} (t) + E_{grid,sell} (t)

where P_bat,ch(t) and P_bat,dis(t) are the charging and discharging power of the lithium batteries, respectively, in kW; E_user(t) is the electric load of the industrial park users in kW; P_DPC(t) is the electric power in the DPC in kW; and P_P2H(t) and P_P2C(t) are the electricity power for the processes of converting P2H and P2C, respectively, in kW.

Balance of heating load supply:

(15)

Q_{DPC,heating} (t) + Q_{TST,dis} (t) = Q_{user} (t) + Q_{TST,ch} (t)

where Q_DPC,heating(t) is the heating supply of the DPC in kW; Q_TST,ch(t) and Q_TST,dis(t) are the charging and discharging power of the TST, respectively, in kW; and Q_user(t) is the heating load of the industrial park users in kW.

Balance of cooling load supply:

(16)

C_{DPC,cooling} (t) + C_{CWS,dis} (t) = C_{user} (t) + C_{CWS,ch} (t)

where C_DPC,cooling(t) is the cooling supply of the DPC in kW; C_CWS,ch(t) and C_CWS,dis(t) are the charging and discharging power of the CWS, respectively, in kW; and C_user(t) is the cooling load of the industrial park users in kW.

3.1.4. Solution method

NSGA-II [35], [36] is one of the most popular heuristic algorithms at present. It introduces improvements such as tournament selection, fast non-dominated sorting, and elitist strategy, and possesses several advantages in solving multi-objective optimization problems, including fast operation speed and good convergence of results [37], [38]. The technique for order of preference by similarity to the ideal solution (TOPSIS) [39] is a common method for comprehensive evaluation within a group. It is widely adopted in multi-objective decision-making in energy systems due to its advantages, which include independence from subjectivity and easy operation [40], [41]. In this research, we utilized NSGA-II for optimization and the TOPSIS method for decision-making to perform configuration optimization on the IPES-HES. The detailed optimization process is shown in Fig. 2.

Step 1: Generation, calculation, and sorting of the initial population. The population size, iteration number, and crossover and mutation probabilities of NSGA-II are set. The optimization ranges of decision variables such as the number of PV panels and the rated capacity of the lithium batteries are determined. Initial values of various decision variables are randomly generated and substituted into the fitness function for calculation, to obtain the fitness value (i.e., the optimization objective value) of each individual. The initial population (i.e., the first-generation population) undergoes fitness function calculation. Based on the obtained fitness values, non-dominated sorting and crowding distance calculations are performed, resulting in a parent population that is sorted by rank and crowding distance.

Step 2: Calculating the annual benefit value of the IPES-HES. Step 2.1: basic parameter setting of the system. The values of each decision variable are obtained from the initialization step of NSGA-II. The annual cost-saving ratio and carbon-emission–reduction ratio is set as the optimization objectives. The user hourly load and meteorological parameters are inputted, and the relevant technical, economic, and carbon-emission parameters of each device are set. Step 2.2: hourly calculation. The power output of devices such as PVs and the DPC is calculated. The expenses, including battery degradation and grid power purchases, are calculated. The primary energy consumption and carbon-emission values of the system are calculated. Step 2.3: annual calculation. The annual energy bill and the carbon emissions of the reference system and the IPES-HES are calculated, obtaining the annual benefit value of the system. Step 2.4: acquisition of the fitness values. All individual calculations are completed in sequence to obtain the fitness values in the population.

Step 3: Optimization of configuration in the IPES-HES. Parents suitable for reproduction are selected through tournament selection. Crossover and mutation operations are performed using the simulated binary crossover and polynomial mutation methods, respectively, to obtain the child population. The child population is then substituted into the fitness function, Steps 2.1–2.4 are performed in sequence, and the fitness values of all children are obtained. The parent and child populations are merged, quick non-dominated sorting is performed, and the crowding distance of each individual in each non-dominated layer is calculated. Individuals are selected to form a new parent population based on non-dominance relationships and individual crowding distances. The cycles are iterated until all cycles are completed.

Step 4: Obtaining device configurations that satisfy the user preferences. After completing all cycle iterations, the Pareto-optimal frontier solution set of the IPES-HES is obtained. The weights of each optimization target value are set according to the user preferences. The TOPSIS method is used to make decisions on the Pareto-optimal frontier solution set. The optimal device configuration and benefit value of the IPES-HES that meet the user preferences are obtained.

3.2. Multi-objective operation optimization

3.2.1. Performance indicators

In the operation stage, the daily energy bill, peak GCP, and daily grid-connected volume are chosen as the benefit indicators of the IPES-HES. This is done to leverage the advantages of active energy storage as much as possible, while taking into account the economic benefits of the system.

The system’s daily energy bill has five components: the battery degradation costs, initial investment of devices, device maintenance expenses, expenditure on purchased electricity, and income from electricity sales. These are calculated using Eq. (17) [30].

(17)

C_{IPES-HES,day} = C_{bat,aging} + \sum_{t = 1}^{n_{2}} [\sum_{j = 1} c_{equ, j} (t) + \sum_{j = 1} c_{om, j} (t) + c_{grid,buy} (t) - c_{grid,sell} (t)]

where C_IPES-HES,day is system’s daily energy bill in USD, n₂ is the optimization time, is set to 24 h in this study.

By minimizing the system’s GCP, it is effectively possible to avoid the large-scale injection of PV power generation into the utility grid, which can have significant adverse effects. The minimization of the GCP for the IPES-HES can be calculated using Eq. (18) [42]:

(18)

GCP (t) = \min (| P_{grid,sell} (t) |)

where GCP(t) is the minimizing the system’s GCP in kW.

The daily SCR effectively reflects the renewable energy utilization and the potential to achieve zero carbon in the IPES-HES [33]. In this study, the SCR is selected as the evaluation indicator for assessing the renewable energy utilization.

3.2.2. Decision variables

The output power of the energy-storage device is determined through day-ahead optimization, enabling the active energy storage. This approach further enhances the advantages of hybrid energy storage in terms of economic benefits, peak shaving and valley filling, and renewable energy utilization. During the operation stage, the output power of the lithium batteries, TST, and CWS on the next day are chosen as the decision variables.

3.2.3. Constraint conditions

During the operation stage, the real-time cooling, heating, and electric balance constraints among the IPES-HES, the utility grid, and the users are met. Simultaneously, the output power of the energy storage cannot exceed its constraint, as illustrated by the example of lithium batteries (Eqs. (19), (20)). The heat-discharge power of the TST cannot exceed the user’s heating load (Eq. (21)), and the cooling-discharge power of the CWS cannot exceed the user’s cooling load (Eq. (22)).

(19)

P_{bat,ch} (t) \leq \min \{P_{bat,ch,max}, \frac{E_{bat,nom} \times {SOC}_{bat,max} - E_{bat} (t - 1)}{f_{bat,ch} \times Δ t}\}

(20)

P_{bat,dis} (t) \leq \min \{P_{bat,dis,max}, \frac{(E_{bat} (t - 1) - E_{bat,nom} \times {SOC}_{bat,min}) \times f_{bat,dis}}{Δ t}\}

(21)

Q_{TST,dis} (t) \leq Q_{user} (t)

(22)

Q_{CWS,dis} (t) \leq C_{user} (t)

where E_bat,nom is the rated capacity of lithium batteries in kW·h, P_bat,ch,max and P_bat,dis,max are the rated charging power and rated discharging power of lithium batteries, respectively in kW, SOC_bat,max and SOC_bat,min are the maximum and minimum states of charge (SOC) of lithium batteries, respectively, and E_bat(t – 1) is the quantity of electricity stored in the lithium batteries at the time t − 1, in kW·h.

3.2.4. Solution method

This optimization scheduling method can effectively improve the advantages of active hybrid energy storage. The detailed process is shown in Fig. 3.

Step 1: generate initial values of the output power in the energy-storage device. Parameters such as the population size and iteration number of NSGA-II are determined. The rated charge–discharge power of each energy-storage device is obtained from the configuration optimization of the IPES-HES. Initial values for the hourly output power of each energy-storage device are randomly generated. If the generated values do not meet the output constraints of the energy-storage device, new decision variables are randomly regenerated until the generated decision variable values meet the output power constraints of the energy storage. The generated decision-variable values are substituted into the fitness function for calculation, thereby obtaining the fitness values corresponding to all individuals. All individuals are then subjected to nondominated sorting and crowding distance calculation, and the sorted parent population is obtained.

Step 2: calculate the daily benefits of the IPES-HES. First, the foundational parameters required for optimization scheduling are imported. The next-day hourly output power of each energy-storage device obtained in step 1 is imported. The next day’s hourly user loads and meteorological parameter data are predicted, and the hourly electricity price of the next day is determined. Next, the hourly operational conditions of the system are calculated. The hourly output power of the PVs and DPC are obtained. The hourly battery-aging costs and electricity-purchase expenditures of the system are calculated. Next, the hourly interactive power and zero-carbon potential of the system are calculated. Then, the system’s daily performance values are calculated. The IPES-HES’s daily energy bill, peak GCP, and daily grid-connected electricity are calculated. Finally, the fitness values for all individuals are obtained. All individual calculations are completed in turn, thus obtaining the fitness values of all individuals.

Step 3: day-ahead optimization scheduling of the IPES-HES. A competitive bidding method is used to select individuals suitable for reproduction, and a random generation method is used for crossover and mutation operations to obtain the offspring population. If the child individuals generated after the crossover or mutation operation do not meet the constraints of the energy-storage output power, the crossover or mutation operation is redone to generate new individuals, until the generated child individuals meet the power output constraints of the energy storage. The child population is substituted into the fitness function, and calculations are performed in turn according to step 2, thereby obtaining the fitness values of all offspring individuals. The remaining steps are detailed in step 3 of Section 3.1.4.

Step 4: obtain the scheduling results based on active energy storage. After the calculations in steps 2 and 3 have been completed, the Pareto optimal solution set for the IPES-HES is obtained. According to user preferences, the weights of each optimization objective are set, and the TOPSIS method is used to make decisions on the solution set. The day-ahead optimal scheduling of the IPES-HES based on active energy storage is thus obtained.

4. Case study

The hourly meteorological data for a typical year in Beijing, China, is presented in Fig. S2 in Appendix A. This region falls within a typical cold climatic zone, with annual average, maximum, and minimum temperatures of 12.65, 37.20, and −14.20 °C, respectively. The abundant solar resources in Beijing are marked by the annual accumulation of solar irradiance, reaching up to 5042.7 MJ·m⁻², along with 1014 h during which the solar irradiance exceeds 500 W·m⁻². The solar resource distribution also exhibits seasonality, exemplified by May’s solar irradiance of 593.6 MJ·m⁻², which is 2.71 times higher than that recorded in December.

The hourly cooling, heating, and electric loads of a certain industrial park over a typical year are presented in Fig. S3 in Appendix A. The annual accumulated cooling, heating, and electric loads of the industrial park are 26.62 kW·h·m⁻², 24.04 kW·m⁻², and 36.04 kW·m⁻², respectively. The variability of the cooling and heating loads of the industrial park is significantly larger than that of its electric load, with peak loads reaching 9647.6, 7302.1, and 2561.1 kW, respectively.

The time-of-use electricity pricing and feed-in tariffs in Beijing are presented in Fig. S4 in Appendix A. The technical, economic, and environmental parameters of the IPES-HES are detailed in Table S1 in Appendix A, and the optimization ranges for each decision variable during the configuration optimization stage are provided in Table S2 in Appendix A. It is assumed that the rooftops and surrounding open spaces in the industrial park can be fully covered with PV panels. The lithium batteries can meet the average electricity demand of users for up to 6 h. The TST can meet 4 h of heating demand on a typical winter day, while the CWS can meet 4 h of cooling demand on a typical summer day. The charging and discharging power of each energy storage device is between 0.25 and 0.50 times its rated capacity. The optimization range of the P2H/C ratio is between 0 and 1.

To validate the effectiveness of the refined energy device modeling and the nonlinear operation optimization method presented in this paper, we designed seven research cases. Case 1: linear energy device model + operational strategy based on electricity-only storage; Case 2: linear energy device model + operational strategy based on electricity-priority storage; Case 3: linear energy device model + operational strategy based on proportional electricity storage; Case 4: nonlinear energy device model + operational strategy based on electricity-only storage; Case 5: nonlinear energy device model + operational strategy based on electricity-priority storage; Case 6: nonlinear energy device model + operational strategy based on proportional electricity storage; Case 7: nonlinear energy device model + optimization-based operational strategy + Case 6’s configuration.

5. Results and discussion

5.1. Configuration optimization results

During the configuration optimization stage, the IPES-HES is optimized, with the CRR and CAR as the optimization objectives. The Pareto solution sets for the optimization results of each case are shown in Fig. 4. As shown, the optimization results of each case converge, and the obtained Pareto optimal sets are reasonable. The Pareto solution sets for Cases 1–3 overlap significantly and are superior to those for Cases 4–6. The economic and carbon-reduction benefits of the IPES-HES decrease as the factors considered during device modeling increase. Under detailed modeling, the overall carbon-reduction benefit of the industrial park energy system that only stores electricity (Case 4) exceeds that of the IPES-HES (Cases 5 and 6). The cycling efficiency and energy quality of the electrical storage are higher than those of the thermal energy storage. Considering only the electrical storage, the lithium batteries capacity in Case 4 is greater than those in Cases 5 and 6, thus improving the carbon-reduction effect of the IPES-HES. Hybrid energy storage improves the economic benefits of the IPES-HES (Cases 5 and 6), compared with the Case 4, which only stores electricity; the TST and CWS are more affordable and have a longer lifespan, reducing the investment and operational costs of the IPES-HES compared with the use of lithium batteries.

Table 2 describes the device configurations and benefit index values for each case after the NSGA-II optimization and TOPSIS decision-making. As shown in the table, each case fully utilizes the PV panel installations to the maximum extent (40 000 m²) because the unit cost of the PVs is cheap (0.5–0.6 USD·W⁻¹). Compared with Case 1, capacities of the lithium batteries in Cases 2 and 3 decreases by 655 kW·h (8.5%) and 565 kW·h (7.3%), respectively. Capacities of the lithium batteries in Cases 5 and 6 decreases by 2595 kW·h (35.5%) and 2867 kW·h (39.2%), respectively, when compared with Case 4. When the nonlinear aging of the lithium batteries is considered, the batteries’ operational cost increases significantly, resulting in a decrease in the installed capacity. The IPES-HES utilizes a TST and CWS to replace a portion of the lithium battery capacity, thereby increase the system’s economic benefit. The capacity of the TST and CWS in the IPES-HES increases substantially, when the detailed modeling of the devices is included. For example, compared with Case 2, the capacities of the TST and CWS in Case 5 increase by 6112 kW·h (3.05 times) and 7342 kW·h (1.75 times), respectively.

The energy efficiency ratio and the coefficient of performance of the DPC decrease in both summer and winter, while the aging costs of the lithium batteries increase significantly, when the detailed modeling of the devices is included. As a result, the economic and carbon-reduction benefits of the IPES-HES exhibit a declining trend. For example, the CRR, CAR, and SCR of Case 4 decrease by 8.2%, 6.9%, and 3.9%, respectively, compared with those of Case 2. Both the coefficient of performance (winter) and the energy efficiency coefficient (summer) of the DPC decrease when the detailed modeling of the devices is considered. As the energy consumption of the DPC increases, the economic benefits of the IPES-HES are expected to decline. The CRR of Cases 5 and 6 increases by 3.6% (0.21 USD·m⁻²) and 6.2% (0.36 USD·m⁻²), respectively, compared with that of Case 4. The costs of the TST and CWS are much lower than those of the lithium batteries. By substituting the TST and CWS for some of the lithium battery capacity, the economic benefits of the IPES-HES can be effectively enhanced.

Table 3 details the composition of the energy bill expenditures for each case. The IPES-HES effectively reduces the energy expenditures of the park users (as referred to in Table 2, Table 3), compared with the reference system. The cost of electricity purchases constitutes the largest portion of the energy bills for the IPES-HES, with the electricity purchase cost accounting for 65% of the entire system’s costs in Case 5. Operational costs for the lithium batteries represent a significant expenditure in the IPES-HES, reaching 4.541 × 10⁵ USD in Case 4. The batteries’ operational costs significantly increase, after accounting for the nonlinear aging of the lithium batteries. For example, the operational cost for the lithium batteries in Case 4 reaches up to 58.6 USD·(kW·h)⁻¹, which is 1.49 times greater than that in Case 1. The IPES-HES obtains income from selling electricity to the utility grid. For example, the revenue from electricity sales in Case 5 accounts for 11.9% of the system’s energy bill.

5.2. Benefit analysis of each case

Fig. 5 illustrates the monthly benefit values of each case. The primary energy consumption, carbon emissions, and purchased electricity for each case are mainly concentrated from December through February and from July to August. More specifically, in January, the primary energy consumption, carbon emissions, and purchased electricity for Case 5 are 55 287.3 MW·h, 1109.7 t, and 1945.7 MW·h, respectively. In summer (July–August) and winter (December–February), the park users have substantial cooling and heating load demands. Between December and February, the primary energy consumption, carbon emissions, and purchased electricity for Cases 4–6 are higher than those for Cases 1–3. However, from June to September, the opposite is observed. The detailed modeling of the devices leads to a decrease in the coefficient of performance of the DPC and an increase in its energy efficiency coefficient, compared with the linear simplified model of the devices. The detailed modeling of the devices causes the energy consumption of the IPES-HES to increase in winter and decrease in summer. Throughout the year, each case has PV grid-connected requirements, with the most pronounced occurrence being observed from March to May. From March to May, Beijing (China) experiences enriched solar energy resources. The daytime solar power generation markedly surpasses the energy consumption of the industrial park, leading to a significant amount of PV power generation that needs to be uploaded to the utility grid.

The monthly energy bills of each case and their monthly proportion of the annual total are illustrated in Fig. 6. The energy bill for each case study exhibits a seasonal distribution: Expenditures are higher in winter and summer, but lower in spring and autumn. This phenomenon can be attributed to the park’s large load demand in the summer and winter months and its small load demand in spring and autumn. Concurrently, the IPES-HES capitalizes on the rich solar energy resources in summer to mitigate the system’s expenses, leading to summer energy bills being lower than the winter expenditures. The detailed modeling of devices alters the monthly expenditure structure of the IPES-HES to a certain extent. For example, Case 6’s energy bills for December to February account for 40.5% of the annual total, marking a 3.9% increase compared with Case 3. Conversely, Case 6’s expenditures from June to August constitute 24.1% of the yearly energy bill, representing a 2.7% decrease in relation to Case 3. Following the detailed modeling of the DPC, its coefficient of performance decreases, while its energy efficiency coefficient increases. As a result, the IPES-HES purchases more electricity during the winter and less during the summer, altering the system’s energy bill expenditure structure.

The monthly acquired electricity for the lithium batteries, P2H, and P2C in each case, as well as their monthly proportion of the annual total, are illustrated in Fig. 7. As illustrated in the figure, Cases 5 and 6 have significantly increased amounts of PV power generation, which is converted into heating and cooling energy for storage through P2H and P2C. Concurrently, in comparison with Case 4, Cases 5 and 6 have less energy being stored in lithium batteries. When the nonlinear aging of the lithium batteries is taken into account, their operational costs exhibit a significant increase. The TST and CWS are employed to replace a portion of the battery capacity, to enhance the economic efficiency of the IPES-HES. As depicted in Figs. 7(b)–(g), the proportion of monthly storage electricity relative to the annual total for each case follows a consistent trend. This indicates that considering the nonlinear aging of lithium batteries does not affect the trend of the monthly storage electricity proportion relative to the annual total.

After analyzing and discussing the annual and monthly benefits of each case, we further selected Cases 4 and 6 as research cases and conducted an hourly benefit analysis. Fig. 8 illustrates the hourly energy bill, carbon emissions, and interactive power of the reference system, Case 4, and Case 6. The hourly energy bill trends for Cases 4 and 6 are largely similar, with both cases seeing increased energy bills in December–January and July–August. At the same time, the overall energy bills for Case 4 are higher than those for Case 6. Case 4 considers only lithium batteries as energy-storage device, and the batteries’ high operating cost reduces the economic benefits of the IPES-HES. The overall carbon emissions of the IPES-HES decrease in electricity-only storage (Case 4), but this does not reduce the industrial park’s instantaneous carbon emission intensity, compared with the reference system. For example, the peak carbon emission intensities for both Cases 4 and 6 are 2981.2 kg·h⁻¹, which are consistent with that of the reference system (2909.8 kg·h⁻¹). During winter nights, the industrial park experiences its peak demand in both electric and heating loads. As solar energy resources are not available at night, the IPES-HES relies on purchasing electricity from the utility grid to satisfy its needs, which prevents a reduction in the industrial park’s instantaneous carbon emission intensity. Cases 4 and 6 have significant interactive power with the utility grid, and the annual peak grid-connection power exceeds the annual peak purchased power. For example, the peak instantaneous grid-connection power and power purchase for Case 6 are 6805.0 and 5227.5 kW, respectively. A large amount of PV power generation is uploaded to the utility grid, when the solar irradiance is high and the industrial park’s load is low. The hybrid energy storage of the IPES-HES can utilize a portion of the PV generation to minimize the uploading electricity to the utility grid. However, when the hybrid energy storage adopts a passive storage strategy based on the maximum SCR, it is prevented from fully leveraging its advantages of utilizing the peak solar generation.

5.3. Analysis of various scheduling schemes

We further conducted day-ahead optimal dispatches for the IPES-HES, with the aim of mitigating the electricity of the PV grid connection and reducing the system’s cost, based on the configuration optimization. The optimization objectives were to minimize the grid-connection power, cumulative grid-connection volume, and system energy bill. The decision variables involved the hourly power output for the subsequent day from each energy storage device. A detailed procedure is provided in Section 3.2. January 21, April 25, and July 15 were chosen as typical days for winter, spring, and summer, respectively, for optimization research.

In this section, Cases 4, 6, and 7 are selected for the analysis of day-ahead optimization scheduling. Case 4 represents an industrial park energy system with only electricity storage, while Case 6 represents an IPES-HES. Both cases use the same operation strategy to compare the differences in the benefits of the IPES-HES versus the industrial park energy system with only electricity storage. Case 7 has the same system configuration as Case 6 but employs an optimization-based operational strategy. The potential advantages of the method proposed in this study for day-ahead optimization scheduling are demonstrated through a comparative analysis of Cases 4, 6, and 7. The scheduling interval for the day-ahead optimization is set to 1 h, considering factors such as the coordinated operation of different energy forms, the use of time-of-use pricing in the electricity market, and the complexity of the optimization calculations.

In this section, the optimization method proposed in this study is compared with the commonly used mathematical programming method (MPM) [42], [43]. The MPM was implemented on the Matlab platform and solved using the commercial solver Gurobi. The population size of the improved NSGA-II was set to 100 individuals, and the number of iterations was 200 generations. The simulations were conducted on an ASUS desktop computer with a Windows 10 64-bit operating system, a 12th Gen Intel Core i7-12700F processor, and a 32 GB DDR4 3600 MHz memory. The optimization results for the two optimization scheduling methods under different typical days are shown in Table 4. The optimization times of the proposed method are 2.32 and 2.06 s on typical summer and winter days, respectively, which are 0.32 s (12.1%) and 0.17 s (7.6%) faster than those of the MPM. On a typical summer day, the proposed method has a lower daily energy bill and lower carbon emissions, at 3.08 × 10³ USD and 15.47 t, respectively, which are 160 USD (4.9%) and 0.67 t (4.2%) less than those of the MPM. The day-ahead optimization scheduling method demonstrates certain advantages in terms of the computation time and system benefits, in comparison with the MPM.

Table 5 presents the benefits of each case on a typical summer day. The peak grid-connection power for Case 7 is 2062.4 kW, which is 1608.8 kW (43.8%) and 1600.3 kW (43.7%) less than those of Cases 4 and 6, respectively. In Cases 4 and 6, the hybrid energy storage stops storing solar power generation at 11:00 and 13:00, respectively, while in Case 7, it continues to store PV power generation until 16:00, as depicted in Fig. 9. The optimization-based operational strategy can adjust the hourly power output of the hybrid energy storage, facilitating active energy storage. The zero-carbon potential for Cases 4, 6, and 7 increases by 9.4%, 9.8%, and 10.2%, respectively, while the SCR improve by 12.3%, 12.4%, and 14.0%, respectively, compared with those of the systems without storage. However, the IPES-HES must purchase a significant amount of electricity from the utility grid during the night, and nearly 30% of the solar power generation needs to be fed into the utility grid during the day. In the future, researchers can integrate load flexibility into the IPES-HES for study, thereby enhancing the renewable energy utilization of the IPES-HES.

Table 6 presents the benefits of each case on a typical spring day. The amount of electricity sold in Case 4 decreases by 2.39 MW·h compared to Case 6, but the maximum grid-connection power for both cases is 6804.6 kW. Under rule-based operational strategies, increasing the lithium battery capacity can enhance the PV utilization ratio of the system, but it is difficult to address the issue of maximum solar grid-connection power. The maximum grid-connection power for Case 7 is 5364.3 kW, which is reduced by 1440.3 kW (21.2%) compared with Case 6. The energy balance for each case on a typical spring day is shown in Fig. 10. Case 7 actively sells electricity to the utility grid between 11:00 and 14:00 and frees up the energy storage capacity to store the peak PV power generation from 14:00 to 15:00, as shown in Fig. 10(c). The daily energy bill for Case 7 is 1.44 × 10³ USD, which is 2.05 × 10³, 0.41 × 10³, and 21.4 USD less than those of the reference system, Case 4, and Case 6, respectively. On this typical day, the zero-carbon potential for Cases 4, 6, and 7 is 57.7%, 50.3%, and 52.6%, respectively, while the SCR are 45.9%, 39.8%, and 40.3%, respectively. On this typical day, the solar power generation profile and the industrial park load curve are highly mismatched. The use of hybrid energy storage can address the mismatch between PV power generation and user load to some extent. However, the IPES-HES still encounters the issues of the extensive grid-connection capacity of renewable energy and high carbon emissions.

The benefit values for each case on a typical winter day are presented in Table 7. The daily energy bill of Case 7 decreases by 1.58 × 10³ USD (21.7%), 0.93 × 10³ USD (14.0%), and 0.53 × 10³ USD (8.5%), respectively, compared with the reference system, Case 4, and Case 6. The peak of the GCP for Case 7 is 326.4 kW, which is 252.2 and 35.8 kW lower than those of Cases 4 and 6, respectively. The energy balance for each case on a typical winter day is shown in Fig. 11. As shown in the Fig. 11, Cases 4 and 6 utilize a passive storage strategy for dispatching the hybrid energy storage. Compared with Cases 4 and 6, the optimization-based operational strategy (in Case 7) fully leverages the active-energy-storage advantage for the operation scheduling of the IPES-HES. In response to the low off-peak electricity price during the hours of 0:00–6:00, Case 7 utilizes hybrid energy storage for electricity and heating storage, and then provides electricity and heating discharge to users during the morning period of 7:00–11:00. This operational strategy not only increases the economic benefits of the IPES-HES but also ensures that energy-storage capacity is released to store excess PV power generation during the day.

6. Conclusions

This paper reported on the development of an IPES-HES based on detailed energy device modeling. Rule-based and optimization-based operational strategies for hybrid energy storage were proposed. A multi-objective configuration optimization model and a day-ahead scheduling optimization model for the IPES-HES were established. The primary conclusions are as follows:

The IPES-HES effectively improved the economic efficiency and carbon-reduction of the industrial park, compared with the reference system in which the electric load and cooling and heating loads were supplied by the utility grid and the DPC, respectively. The CRR and CAR of the system, which were based on detailed energy device modeling, were significantly lower than those of the energy device with linear modeling. The detailed energy device modeling revealed that a portion of the lithium batteries’ capacity could be replaced by the TST and CWS, increasing the economic efficiency of the IPES-HES.

When the detailed energy device modeling was taken into account, the coefficient of performance of the DPC decreased; as a result, the electricity purchase, carbon emissions, and system energy bills of the IPES-HES increased, compared with the linear energy device model. The proportion of electrical energy being converted into heating and cooling energy storage using P2H and P2C technologies increased, after considering the nonlinear aging of the lithium batteries. System configuration optimization enhanced the annual benefits of the IPES-HES but could not reduce the instantaneous peak carbon emissions, system energy bill, or interactive power of the system.

By fully leveraging the active-energy-storage advantages, the system costs and the peak GCP of the IPES-HES were reduced. For example, on a typical summer day, the lithium batteries and CWS were used for active electricity storage and cooling storage, respectively. The daily energy bill in Case 7 (the active energy storage case) was reduced by 661.4 USD (15.6%) and 181.4 USD (5.5%), compared with those in Cases 4 and 6 (the sole electrical-storage case and the hybrid energy-storage case), respectively. Concurrently, the peak GCP in active energy storage case (in Case 7) decreased by 1608.8 kW (43.8%) and 1600.3 kW (43.7%) in comparison with those in Cases 4 and 6, respectively.

Acknowledgments

This work was supported by National Key Research and Development Program of China (2022YFB4201003), the National Natural Science Foundation of China (52278104 and 52108076), and the Science and Technology Innovation Program of Hunan Province (2023RC1042).

Compliance with ethics guidelines

Jiacheng Guo, Yimo Luo, Bin Zou, and Jinqing Peng declare that they have no conflict of interests or financial conflicts to disclose.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2024.10.006.

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