System-Level Techno-Economic Optimization of Decarbonized Industrial Thermal Energy Systems via Active Load Restructuring

Abstract

In cold-region industrial parks, prolonged heating seasons and intensive hot water demands trigger severe temporal mismatches between stochastic renewable generation and rigid thermal requirements. To address this, a multidimensional synergistic optimization framework for industrial thermal energy systems is proposed. The physical architecture integrates wind, solar, and shallow geothermal energy with hybrid storage, establishing thermodynamic boundaries. Concurrently, a customized solver is developed for the coupled electro-thermal scheduling problem. At its core, the active load restructuring strategy (ALRS) exploits the thermal inertia of thermal storage tanks and leverages the high coefficient of performance of ground source heat pumps. ALRS restructures the all-day hot water supply load to nighttime windows characterized by abundant wind power and off-peak tariffs, achieving profound source–load temporal decoupling and transforming rigid thermal demands into cross-period virtual flexible assets. Assessments demonstrate that the proposed strategy reduces typical-day electricity costs by 82.51%. Compared to a grid-dependent rigid baseline, comprehensive daily operational and carbon emission costs decrease by 71.9% and 90.2%, respectively. This study demonstrates the potential of translating thermal flexibility into coordinated energy management and provides a system-level reference for the low-carbon operation of industrial thermal energy systems.

1. Introduction

Driven by the global transition toward clean and low-carbon energy systems [1,2,3], industrial parks, as primary carriers of high energy consumption and carbon emissions (accounting for approximately 31% of national industrial carbon emissions) [4,5], constitute not only the core of regional energy consumption but also critical nodes for urban decarbonization [6]. Particularly, for industrial parks in cold regions, the superimposition of high-intensity electrical demands, prolonged heating periods, and massive hot water requirements [7] induces intricate electro-thermal coupling features, rendering conventional single-energy systems inadequate [8]. Consequently, constructing integrated energy systems (IESs) with high renewable penetration has become a consensus [9,10,11]. Characterized by wide distribution and stable temperatures, shallow geothermal energy [12,13,14], combined with ground source heat pump (GSHP) technology [15,16], not only provides a high-quality heat source for industrial decarbonization but also establishes a solid foundation for the green evolution of energy structures.

However, as the penetration of renewable energy continues to increase [17,18,19], its inherent stochasticity significantly amplifies the system’s demand for flexible regulation resources [20,21], exacerbating the source–load temporal mismatch. In typical industrial parks, electrical and thermal loads exhibit strong daytime inflexibility, compelling the system to maintain a high-load state during peak periods. Conversely, wind power generation possesses an inverse-peaking characteristic [22], highly coinciding with nighttime off-peak load and tariff windows. This temporal asynchrony traps the park in a dual dilemma: substantial supply–demand gaps and high procurement costs during daytime hours, and severe wind curtailment risks at night due to the lack of effective cross-period regulation measures. This structural contradiction between operational costs and resource utilization has become the primary bottleneck hindering cost-effective decarbonization in industrial parks.

In addressing large-scale, inter-temporal energy management in integrated energy parks, existing pathways exhibit limitations: the investment costs and cycle life of battery energy storage systems (BESSs) constrain their economic viability in long-duration scenarios [23,24]; thermal-storage devices are often employed primarily as buffering units, leaving their thermal inertia insufficiently exploited for active cross-period restructuring [25,26]; and passive demand response utilizing building thermal inertia is restricted by strict thermal comfort boundaries, yielding limited regulation depth [27,28]. Recent studies have further demonstrated that flexible demand and hybrid electro-thermal storage can substantially enhance multi-energy flexibility and reduce dependence on dedicated electrical storage. Under the reported operating conditions, flexible loads accounting for approximately 18–23% of total electrical demand were reported to provide an alternative to BESSs [29]. Meanwhile, integrated-energy-system assessment has increasingly extended beyond eco-nomic dispatch toward coordinated economic, environmental, and resource-related performance evaluation [30].

Theoretically, integrating GSHPs with time-of-use (TOU) tariffs to shift space heating (SH) loads into off-peak periods appears economically sound. However, engineering deductions reveal that due to the sheer magnitude of SH loads and rigid thermal demands, concentrating this heating unavoidably triggers a drastic surge in instantaneous peak loads. This not only precipitates a non-linear escalation in equipment capital expenditure due to required capacity oversizing, but short-term, high-intensity heat extraction also exacerbates local soil cold accumulation, ultimately leading to severe ground thermal imbalance.

Accordingly, for cold-region industrial parks during the heating season, a key unresolved issue is how to construct a targeted electro-thermal architecture and corresponding operating mechanism that can reconcile the strong temporal mismatch among renewable generation, time-of-use electricity prices, and rigid electro-thermal demands. Such a framework should coordinate electrical and thermal flexibility according to their distinct physical characteristics, avoid the excessive capacity and ground thermal stress associated with large-scale SH shifting, and improve renewable energy utilization and reduce peak-period grid dependence without altering the required end-use thermal service.

To fundamentally resolve the source–load temporal mismatch and circumvent the aforementioned limitations, an active load restructuring strategy (ALRS) is proposed in this paper. Methodologically, unlike conventional demand-response approaches that directly modify end-use demand, the ALRS preserves the required thermal-service profile and restructures the timing of suitable thermal energy production through physical buffering, thereby achieving source–load temporal decoupling without transferring the adjustment burden to end users. Architecturally, the park’s SH and hot water supply (HWS) are supplied by dedicated GSHPs, capitalizing on their high thermodynamic conversion efficiency to reduce baseline comprehensive thermal provision costs. Based on the functionally decoupled thermal topology, the SH is directly supplied by a dedicated GSHP without temporal restructuring, whereas the HWS utilizes the TST-GSHP for temporal restructuring to achieve the decoupling of thermal energy production and consumption. This strategy exhibits multidimensional coordination advantages, manifested by its capability to adapt to diverse operational scenarios: during periods of abundant nighttime wind power, it superimposes the GSHP’s high coefficient of performance (COP) and off-peak tariffs to minimize operational costs while promoting local wind power accommodation; conversely, even in the absence of surplus nighttime wind, the daily HWS load can be restructured into the nighttime off-peak tariff window to reduce heat supply costs and alleviate main-grid stress. This synergistic optimization approach, integrating the underlying physical topology with top-level management strategies, exploits the endogenous flexibility of thermal inertia. Overall, the proposed coordination improves the utilization of local energy flexibility and supports economic operation and decarbonization under the modeled conditions.

In summary, this paper develops a strategy-led active energy management approach to alleviate the source–load temporal mismatch that constrains the economic operation and decarbonization of industrial parks. The core contributions are summarized as follows:

•

Proposing an ALRS driven by temporal restructuring for industrial heating applications. By harnessing the thermal inertia potential, rigid thermal demands are restructured into virtual flexible assets, thereby enabling source–load temporal decoupling and cross-period energy coordination.

•

Establishing a sustainable multi-energy complementary architecture. Centered on a functionally decoupled GSHP and hybrid electrical–thermal storage, this architecture integrates multiple renewable energy sources and provides the physical basis for implementing the ALRS and coordinated energy dispatch.

•

Developing a customizing system-level digital solver for the coupled electro-thermal scheduling problem. The solver provides a problem-oriented computational framework for obtaining feasible operating decisions under prescribed system constraints.

•

Executing a comprehensive techno-economic and environmental assessment. The quantitative analysis evaluates the operational, economic, and environmental effects of the proposed strategy and provides a system-level reference for the decarbonization of cold-region industrial parks.

2. ALRS-Driven System Architecture and Operational Framework

2.1. System Topology and Energy Flow Analysis

To address the dynamic electro–thermal load characteristics and TOU pricing mechanisms in cold-region industrial parks, a decarbonized microgrid architecture coupling wind, solar, and shallow geothermal energy with an electro-thermal hybrid storage system is constructed. The corresponding system topology and energy flows are depicted in Figure 1.

Electrical subsystem: High-penetration wind turbines (WTs) and photovoltaic (PV) systems are deployed to establish a multi-source synergistic generation foundation. To mitigate the stochastic fluctuations of renewable outputs and load volatility, a BESS is incorporated. Furthermore, a bidirectional power exchange mode with the main grid is adopted, ensuring instantaneous power balance while enhancing the operational economy and resilience of the system.

Thermal subsystem: To accommodate the differential load profiles of space heating (high-flow with low-to-medium temperature) and hot water supply (low flow with high temperature), a decoupled thermal supply architecture is established. This architecture strictly adheres to the principles of cascaded utilization by decoupling the distinct temperature requirements and flow dynamics of the thermal subsystems.

•

SH: A dedicated GSHP for SH (SH-GSHP) is implemented in a parallel topology comprising dual units to counter significant day–night thermal demand fluctuations. Guided by a synergistic load-matching strategy, the system autonomously modulates the number of active units to ensure that the heat pumps consistently operate within their optimal part-load efficiency ranges.

•

HWS: A dedicated GSHP for HWS (HWS-GSHP) is coupled with a TST. Leveraging the massive thermal buffering capacity of the TST, this topology achieves temporal decoupling between the primary thermal output and terminal load demand.

Electro-thermal coupling and synergistic response: As the core electro-thermal hubs, GSHP units drive high-efficiency conversion between heterogeneous energy flows. To mitigate multi-timescale volatilities, the hybrid storage architecture integrates the high-power density of the BESS with the high-energy density of the TST. Within this architecture, the BESS suppresses high-frequency stochastic electrical fluctuations, thereby stabilizing the operational boundary for the TST to execute large-capacity, cross-period thermal shifting. This coordinated allocation establishes a robust physical foundation for decarbonizing park heating processes.

2.2. Core Operational Strategy of the ALRS

To overcome the intense temporal coupling constraint inherent in the conventional supply-follows-load paradigm, the ALRS based on time shift is proposed. Leveraging the thermal inertia of the TST, the strategy decouples heat production from real-time thermal demand, converting rigid thermal loads into flexible adjustable electric power to fully respond to TOU tariffs.

Let $Q_{\mathrm{load},\mathrm{hws}}(t)$ denote the real-time hot water demand. Within the ALRS, the thermal generation $Q_{\mathrm{gshp},\mathrm{hws}}(t)$ of the HWS–GSHP is restructured from a passively following variable into an independently controllable one. Notably, the rigid thermal demand is strictly preserved as a boundary condition throughout this restructuring process. Based on the principle of energy conservation, the restructured equivalent flexible electrical power $P_{\mathrm{flex}}(t)$ is expressed as:

$$Q_{\mathrm{gshp},\mathrm{hws}}(t)=Q_{\mathrm{load},\mathrm{hws}}(t)+\left[Q_{\mathrm{tank}}^{\mathrm{in}}(t)-Q_{\mathrm{tank}}^{\mathrm{out}}(t)\right]$$

(1)

$$P_{\mathrm{flex}}(t)={\displaystyle \frac{Q_{\mathrm{gshp},\mathrm{hws}}(t)}{{\mathrm{COP}}_{\mathrm{hws}}}}$$

(2)

By coordinating the thermal charging and discharging states of the TST, the system dynamically switches between the following two operational modes (Figure 2):

TST accumulation mode: The HWS–GSHP operates at high load during off-peak periods ($Q_{\mathrm{tank}}^{\mathrm{in}}(t)\gg Q_{\mathrm{load},\mathrm{hws}}(t),\forall t\in {\mathcal{T}}_{\mathrm{off}-\mathrm{peak}}$). The system utilizes low-cost electricity for thermal pre-charging and stores thermal energy in the TST, enabling cross-period temporal restructuring.

TST release mode: The HWS–GSHP unit is either on standby or maintained at minimal output during on-peak and mid-peak tariff periods (${\mathcal{T}}_{\mathrm{on}-\mathrm{peak}}$, ${\mathcal{T}}_{\mathrm{mid}-\mathrm{peak}}$). The real-time thermal demand is solely satisfied by the TST discharge $Q_{\mathrm{tank}}^{\mathrm{out}}(t)$, effectively avoiding high-price electricity and achieving grid-side peak shifting.

2.3. Mathematical Modeling of Subsystems

To execute the proposed ALRS and facilitate system-level synergistic optimization, the dynamic electro-thermal interactions of the supportive physical equipment must be mathematically quantified. A quasi-steady-state modeling approach is applied to quantify the dynamic electro-thermal interactions and constraints across subsystems. Setting $\mathrm{\Delta }t=1\mathrm{h}$ and $T=24\mathrm{h}$ balances computational accuracy and efficiency. For conciseness, subsequent formulations focus exclusively on state-decision interactions, with the static parameters defined in the Nomenclature.

2.3.1. Renewable Energy Generation Models

(1)

Wind generation model

The dynamic active power output of the WT is primarily governed by the real-time wind speed at the hub height [25]. This nonlinear power conversion characteristic is formulated as:

$$P_{\mathrm{wt}}(t)=\left\{\begin{array}{ll}0,\hfill & v(t)<v_{\mathrm{in}}\mathrm{or}v(t)>v_{\mathrm{out}}\hfill \\ P_{\mathrm{r}}{\displaystyle \frac{v(t)-v_{\mathrm{in}}}{v_{\mathrm{r}}-v_{\mathrm{in}}}},\hfill & v_{\mathrm{in}}\le v(t)<v_{\mathrm{r}}\hfill \\ P_{\mathrm{r}},\hfill & v_{\mathrm{r}}\le v(t)\le v_{\mathrm{out}}\hfill \end{array}\right.$$

(3)

where $P_{\mathrm{wt}}(t)$ is the active power output; $v_{\mathrm{in}}$, $v_{\mathrm{r}}$, and $v_{\mathrm{out}}$ are the cut-in, rated, and cut-out wind speeds, respectively; $P_{\mathrm{r}}$ is the rated power; and $v(t)$ is the real-time wind speed.

(2)

PV generation model

The PV power output exhibits irradiance–temperature coupling [31]. To account for the effect of ambient temperature on conversion efficiency in cold climates, a nominal operating cell temperature (NOCT) model is utilized for real-time power correction [32]:

$$P_{\mathrm{pv}}(t)={\mathrm{\eta }}_{\mathrm{pv}}{S}_{\mathrm{pv}}I(t)\left[1-{\alpha }_T\left(T_{\mathrm{cell}}(t)-T_{\mathrm{ref}}\right)\right]$$

(4)

$$T_{\mathrm{cell}}(t)=T_{\mathrm{amb}}(t)+{\displaystyle \frac{I(t)}{0.8}}\times (\mathrm{NOCT}-20)$$

(5)

where $P_{\mathrm{pv}}(t)$ is the corrected power output; $I(t)$ is the solar irradiance on the tilted plane; $T_{\mathrm{cell}}(t)$ and $T_{\mathrm{amb}}(t)$ are the cell and ambient temperatures, respectively.

2.3.2. GSHP Model

The index $i\in \left\{\mathrm{sh},\mathrm{hws}\right\}$ designates the SH-GSHP and HWS-GSHP units, respectively. Considering the intraday scheduling horizon and the relatively slow ground thermal response over this timescale [33], ${\mathrm{COP}}_i$ is represented by a nominal value and treated as constant within the scheduling horizon. This approximation is intended to characterize the average short-term conversion efficiency of the GSHP rather than to imply invariant performance over seasonal or long-term operation. Recent long-term studies have further demonstrated that ground-temperature disturbance can induce COP degradation under sustained GSHP operation [34]; the influence of COP variation on energy consumption and electricity cost is therefore further assessed analytically in Section 5.6.2 [33,35]. The power conversion relationship is expressed as follows:

$$Q_{\mathrm{soil},i}(t)=Q_{\mathrm{gshp},i}(t)-P_{\mathrm{gshp},i}(t)=({\mathrm{COP}}_i-1)·P_{\mathrm{gshp},i}(t)$$

(6)

where ${\mathrm{COP}}_i$ denotes the nominal coefficient of performance of GSHP unit $i$ over the intraday scheduling horizon; $P_{\mathrm{gshp},i}(t)$, $Q_{\mathrm{gshp},i}(t)$, and $Q_{\mathrm{soil},i}(t)$ are the input electric power, thermal power, and soil-side heat extraction power of unit $i$, respectively.

To represent the operating limits of the GSHP and avoid excessive ground-side heat extraction, operational boundaries and daily cumulative heat extraction limits are established:

$$u_i(t)P_i^{\min }\le P_{\mathrm{gshp},i}(t)\le u_i(t)P_i^{\max }$$

(7)

$${\displaystyle \sum _{t=1}^T{\displaystyle \sum _i{Q}_{\mathrm{soil},i}}}(t)\le {\mathrm{\Gamma }}_{\max }$$

(8)

where $u_i(t)\in \{0,1\}$ denote the binary on/off status indicator, and ${\mathrm{\Gamma }}_{\max }$ is the maximum daily heat extraction.

2.3.3. Electro-Thermal Hybrid Storage Models

(1)

BESS model

To capture its rapid electrical buffering characteristics alongside self-discharge and power conversion losses, the discrete-time dynamic energy balance and operational boundaries of the BESS [36] are mathematically formulated as:

$$E_{\mathrm{bat}}(t)=E_{\mathrm{bat}}(t-1)(1-{\mathrm{\sigma }}_{\mathrm{bat}})+\mathrm{\Delta }t\left({\mathrm{\eta }}_{\mathrm{bat}}^{\mathrm{ch}}{P}_{\mathrm{bat}}^{\mathrm{ch}}(t)-{\displaystyle \frac{P_{\mathrm{bat}}^{\mathrm{dis}}(t)}{{\mathrm{\eta }}_{\mathrm{bat}}^{\mathrm{dis}}}}\right)$$

(9)

$$\mathrm{SOC}(t)={\displaystyle \frac{E_{\mathrm{bat}}(t)}{E_{\mathrm{bat}}^{\mathrm{cap}}}}$$

(10)

$$\left\{\begin{array}{l}0\le Q_{\mathrm{tank}}^{\mathrm{in}}(t)\le Q_{\mathrm{tank}}^{\max }\\ 0\le Q_{\mathrm{tank}}^{\mathrm{out}}(t)\le Q_{\mathrm{tank}}^{\max }\\ H_{\mathrm{tank}}^{\min }\le H_{\mathrm{tank}}(t)\le H_{\mathrm{tank}}^{\max }\end{array}\right.$$

(11)

where $E_{\mathrm{bat}}(t)$ and $\mathrm{SOC}(t)$ are the stored electrical energy and state of charge (SOC), respectively; $P_{\mathrm{bat}}^{\mathrm{ch}}(t)$ and $P_{\mathrm{bat}}^{\mathrm{dis}}(t)$ are the charging and discharging powers; $Q_{tank}^{max}$ is the maximum allowable thermal charging/discharging rate.

To circumvent the myopic end-of-horizon effect and ensure cross-day cyclic sustainability, an initial-to-terminal state consistency constraint is imposed: $E_{\mathrm{bat}}(0)=E_{\mathrm{bat}}(T)$.

(2)

TST model

Acting as the core medium for thermal inertia utilization, the cross-period energy balance and operational boundary constraints of the TST are formulated based on a lumped-parameter method [36]:

$$H_{\mathrm{tank}}(t)=H_{\mathrm{tank}}(t-1)·(1-{\mathrm{\sigma }}_{\mathrm{tank}})+\mathrm{\Delta }t·\left({\mathrm{\eta }}_{\mathrm{tank}}^{\mathrm{in}}{Q}_{\mathrm{tank}}^{\mathrm{in}}(t)-{\displaystyle \frac{Q_{\mathrm{tank}}^{\mathrm{out}}(t)}{{\mathrm{\eta }}_{\mathrm{tank}}^{\mathrm{out}}}}\right)$$

(12)

$$\left\{\begin{array}{l}0\le Q_{\mathrm{tank}}^{\mathrm{in}}(t)\le u_{\mathrm{tank}}^{\mathrm{in}}(t)Q_{\mathrm{tank}}^{\max }\hfill \\ 0\le Q_{\mathrm{tank}}^{\mathrm{out}}(t)\le u_{\mathrm{tank}}^{\mathrm{out}}(t)Q_{\mathrm{tank}}^{\max }\hfill \\ u_{\mathrm{tank}}^{\mathrm{in}}(t)+u_{\mathrm{tank}}^{\mathrm{out}}(t)\le 1\hfill \\ H_{\mathrm{tank}}^{\min }\le H_{\mathrm{tank}}(t)\le H_{\mathrm{tank}}^{\max }\hfill \end{array}\right.$$

(13)

where $H_{\mathrm{tank}}(t)$ is the stored thermal energy in the tank; $Q_{\mathrm{tank}}^{\mathrm{in}}(t)$ and $Q_{\mathrm{tank}}^{\mathrm{out}}(t)$ represent the thermal charging and discharging powers; and $u_{\mathrm{tank}}^{\mathrm{in}}(t),u_{\mathrm{tank}}^{\mathrm{out}}(t)\in \{0,1\}$ are the binary operational states indicators.

3. Synergistic Optimization Modeling and Customized Digital Solver

3.1. Economic Cost Modeling and Objective Functions

To establish a rigorous economic assessment, the systemic expenditures are decoupled into capital expenditure (CAPEX) and operational expenditure (OPEX):

(1)

CAPEX denotes the one-time initial investment cost of each facility.

$$\mathrm{CAPEX}={\displaystyle \sum _{k\in K}{c}_{\mathrm{inv},k}}·S_k$$

(14)

where $c_{\mathrm{inv},k}$ denotes the unit capital investment cost of asset $k$, and $S_k$ is the installed capacity.

(2)

Fixed OPEX encompasses routine maintenance, insurance, and administrative overheads that are independent of hourly dispatch. For consistent use in the operational economic assessment, the annualized capital cost and fixed operation and maintenance (OM) cost are converted into an equivalent unit-energy cost coefficient ${\xi }_k$:

$${\xi }_k={\displaystyle \frac{c_{\mathrm{inv},k}·\mathrm{CRF}+c_{\mathrm{OM},k}}{h_{\mathrm{eq},k}}}$$

(15)

$${\mathrm{CRF}}_k={\displaystyle \frac{r{(1+r)}^{N_k}}{{(1+r)}^{N_k}-1}}$$

(16)

where ${\mathrm{CRF}}_k$ is the capital recovery factor; $r$ is the benchmark discount rate; $N_k$ is the asset service lifetime; $c_{\mathrm{OM},k}$ is the annual fixed OM cost; and $h_{\mathrm{eq},k}$ is the annual equivalent full-load utilization hours.

The comprehensive cost $F$ includes the levelized energy production cost $C_{\mathrm{LCOE}}$, the main grid interaction cost $C_{\mathrm{grid}}$, the carbon emission cost $C_{\mathrm{carbon}}$, and the virtual penalty cost $C_{\mathrm{penalty}}$. Specifically, $C_{\mathrm{LCOE}}$ accounts for the annualized capital and fixed O&M expenditures allocated to unit energy production and supply. Moreover, penalty terms are introduced to discourage violations of selected scheduling constraints, while the prescribed operating bounds and model-specific feasibility treatments are applied to maintain physically admissible solutions, as shown in Equation (21).

It should be emphasized that the electricity required to operate the GSHPs is incorporated into the electrical power balance (Equation (22)) and cleared through renewable generation and the main grid interactions. To avoid double-counting the GSHP costs, the levelized cost of the heat coefficient ${\xi }_{\mathrm{gshp},\mathrm{i}}$ excludes the electricity expenses incurred during the operation of the heat pumps.

$$\min F=C_{\mathrm{LCOE}}+C_{\mathrm{grid}}+C_{\mathrm{carbon}}+C_{\mathrm{penalty}}$$

(17)

$$C_{\mathrm{LCOE}}={\displaystyle \sum _{t=1}^T\left[{\xi }_{\mathrm{wt}}{P}_{\mathrm{wt}}(t)+{\xi }_{\mathrm{pv}}{P}_{\mathrm{pv}}(t)+{\xi }_{\mathrm{gshp},\mathrm{i}}{Q}_{\mathrm{gshp},i}(t)+{\xi }_{\mathrm{bat}}\left(P_{\mathrm{bat}}^{\mathrm{ch}}(t)+P_{\mathrm{bat}}^{\mathrm{dis}}(t)\right)\right]}·\mathrm{\Delta }t$$

(18)

$$C_{\mathrm{grid}}={\displaystyle \sum _{t=1}^T\left(c_{\mathrm{buy}}(t)·P_{\mathrm{grid}}^{\mathrm{buy}}(t)-c_{\mathrm{sell}}(t)·P_{\mathrm{grid}}^{\mathrm{sell}}(t)\right)}·\mathrm{\Delta }t$$

(19)

$$C_{\mathrm{carbon}}={\displaystyle \sum _{t=1}^T\left(P_{\mathrm{grid}}^{\mathrm{buy}}(t)·\mathrm{\Delta }t·{\gamma }_{\mathrm{grid}}·{\alpha }_{\mathrm{carbon}}\right)}$$

(20)

$$\begin{array}{l}{C}_{\mathrm{penalty}}={\displaystyle \sum _{t=1}^T\left[{\lambda }_{\mathrm{bal}}\mathrm{\Delta }P{(t)}^2+{\lambda }_{\mathrm{sim}}·{\mathrm{\Theta }}_{\mathrm{bat}}(t)+{\lambda }_{\mathrm{SOC}}·{\mathrm{\Omega }}_{\mathrm{SOC}}(t)\right]}\\ +{\lambda }_{\mathrm{end}}·|SOC(T)-SO{C}_{\mathrm{target}}|\end{array}$$

(21)

where $P_{\mathrm{grid}}^{\mathrm{buy}}(t)$ and $P_{\mathrm{grid}}^{\mathrm{sell}}(t)$ denote the active power purchased from and sold to the main grid, respectively; $\mathrm{\Delta }P(t)$ is the source–load power imbalance; ${\mathrm{\Theta }}_{\mathrm{bat}}(t)$ and ${\mathrm{\Omega }}_{\mathrm{soc}}(t)$ represent the violation quantities of the BESS mutually exclusive constraint and the SOC operational constraint, and $\mathrm{SOC}(T)$ is the actual terminal state.

3.2. Electro-Thermal Coupling and Operational Constraints

To ensure system stability, the active power supply–demand balance (Equation (22)) and the mutually exclusive grid interaction constraints (Equation (23)) must be strictly maintained. Simultaneously, the SH constraint is defined as $Q_{\mathrm{gshp},\mathrm{sh}}(t)=Q_{\mathrm{load},\mathrm{sh}}(t)$, while the dynamic hot water balance is governed by Equation (1).

$$P_{\mathrm{grid}}^{\mathrm{buy}}(t)+P_{\mathrm{wt}}(t)+P_{\mathrm{pv}}(t)+P_{\mathrm{bat}}^{\mathrm{dis}}(t)=P_{\mathrm{load}}^{\mathrm{base}}(t)+P_{\mathrm{gshp}}\left(t\right)+P_{\mathrm{bat}}^{\mathrm{ch}}(t)+P_{\mathrm{grid}}^{\mathrm{sell}}(t)$$

(22)

$$\left\{\begin{array}{l}0\le P_{\mathrm{grid}}^{\mathrm{buy}}(t)\le u_{\mathrm{grid}}(t)·P_{\mathrm{grid}}^{\max }\\ 0\le P_{\mathrm{grid}}^{\mathrm{sell}}(t)\le (1-u_{\mathrm{grid}}(t))·P_{\mathrm{grid}}^{\max }\end{array}\right.$$

(23)

where $P_{\mathrm{gshp}}(t)=P_{\mathrm{gshp},\mathrm{sh}}(t)+P_{\mathrm{gshp},\mathrm{hws}}(t)$ represents the total power consumption of the GSHP units; $P_{\mathrm{load}}^{\mathrm{base}}(t)$ is the base electrical load; and $u_{\mathrm{grid}}(t)\in \{0,1\}$ is the binary status variable.

3.3. Customized Digital Solver for High-Dimensional Electro-Thermal Optimization

Owing to the severe non-convexity and high-dimensionality [37] introduced by electro-thermal coupling and complicated operational constraints, standard heuristic solvers are highly susceptible to premature convergence [38,39]. To ensure the reliability of the synergistic optimization, an enhanced solver, denoted as PLIW-SCGS-PSO, which integrates a piecewise linear time-varying inertia weight (PLIW) and a swarm centroid guidance strategy (SCGS), is customized for this architecture.

3.3.1. Mathematical Formulation of the Tailored Heuristic Solver

Specifically, to efficiently balance global exploration and local exploitation, the PLIW $\omega (k)$ sustains a higher value during the initial phase ($k\le K_{\mathrm{bp}}$) for broad space traversal, executing an accelerated linear decay in the late phase ($k>K_{\mathrm{bp}}$) to accelerate convergence. Concurrently, to prevent premature stagnation stemming from over-reliance on individual historical bests, the SCGS is equivalent to a high-dimensional low-pass filter by introducing the $d$-dimensional geometric centroid ${\overline{P}}_d$ of the entire swarm’s historical best positions into the velocity update vector.

$$\omega (k)=\left\{\begin{array}{ll}{\omega }_{\max }-{\displaystyle \frac{k}{K_{\mathrm{bp}}}}({\omega }_{\max }-{\omega }_{\mathrm{bp}}),\hfill & k\le K_{\mathrm{bp}}\hfill \\ {\omega }_{\mathrm{bp}}-{\displaystyle \frac{k-K_{\mathrm{bp}}}{K_{\max }-K_{\mathrm{bp}}}}({\omega }_{\mathrm{bp}}-{\omega }_{\min }),\hfill & k>K_{\mathrm{bp}}\hfill \end{array}\right.$$

(24)

$${\overline{P}}_d={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^{N}p}bes{t}_{i,d}$$

(25)

$$v_{i,d}^{k+1}=\omega (k)v_{i,d}^k+c_1{r}_1({\overline{P}}_d-x_{i,d}^k)+c_2{r}_2(gbes{t}_d-x_{i,d}^k)$$

(26)

where $k$ is the current iteration number; $K_{\max }$ is the maximum iteration limit; $K_{\mathrm{bp}}$ is the predefined breakpoint iteration; $\omega (k)$ is the dynamic inertia weight at iteration $k$; $x_{i,d}^k$ and $v_{i,d}^k$ represent the position and velocity of particle $i$ in dimension $d$ at iteration $k$; $pbes{t}_{i,d}$ and $gbes{t}_d$ denote the personal and global best positions, respectively.

3.3.2. Modular Execution Framework and Physical Boundary Enforcement

Beyond the mathematical formulation of the heuristic engine, as illustrated in Figure A1 in the Appendix A, the proposed customized digital solver is not a mere mathematical optimum-seeking tool, but a system-level computing platform explicitly tailored for complex, non-convex electro-thermal coupled architectures. Within its execution framework, this platform deeply integrates multidimensional parameter initialization, electro-thermal system modeling, and an underlying heuristic search engine (PLIW-SCGS-PSO). Concurrently with the efficient generation of the globally optimal synergistic scheme, its embedded data analysis and multidimensional visualization modules explicitly illustrate the swarm evolutionary characteristics, ALRS temporal restructuring profiles, equipment operational trajectories, and economic and environmental assessments throughout the optimization process. Furthermore, by decoupling the physical equipment modeling from the underlying search engine, this platform is highly modular, endowing the framework with robust scalability, enabling the framework to seamlessly accommodate larger and more complex industrial energy systems.

Furthermore, to guarantee the physical robustness and engineering feasibility of the synergistic optimization scheme under complex operating conditions, the developed solver strictly enforces dual hard and soft constraints throughout the entire iterative process. Initially, hard constraints are imposed by employing a boundary absorption strategy that forcibly resets out-of-bounds particles back into the feasible domain, ensuring that the solutions strictly adhere to the operational limits of the equipment. Subsequently, during the fitness evaluation stage, soft constraints—realized via static penalty functions—are applied to the stringent electro-thermal power balance and mutually exclusive operational states, such as grid power exchanges and the charging/discharging cycles of the BESS, effectively guiding the swarm to circumvent physically infeasible regions. Crucially, the optimization framework incorporates a dedicated SOC trajectory correction module for the energy storage system, enforcing consistency between the initial and terminal states. This state-anchoring strategy effectively overcomes the end effect inherent in finite-horizon optimization and fundamentally eradicates the cross-day energy overdraft of the BESS, thereby guaranteeing the scientific validity and rigor of long-term comprehensive system assessments.

4. Case Study

4.1. Simulation Scenarios and System Parameters

(1)

Simulation scenario

A typical park in northern China during the heating season is selected as the case study. Based on local meteorological data (Figure 3), this scenario presents two primary operational bottlenecks, serving as the baseline to validate the proposed optimization approach.

Temporal generation–demand mismatches: Daytime PV output peaks (6048 kW) during the noon off-peak load period, yet its effective duration is insufficient to meet the prolonged daytime power demand, requiring additional grid electricity procurement. Conversely, wind power exhibits an anti-peaking characteristic. Its high nocturnal output (>2500 kW) coincides with the night load valley (1250 kW), leading to wind curtailment. Addressing this mismatch solely by deploying a large-capacity BESS increases investment and operational costs.

Rigid electro-thermal demand: Under the conventional supply-follows-load mode, the uninterruptible electro-thermal requirement leads to high electricity procurement costs (Figure 3a and Figure 4a). However, the thermal load fluctuates within a narrow margin (466–921 kW). This bounded variation diminishes the demand for capacity redundancy, enabling the effective implementation of the ALRS through optimized GSHP and TST configurations.

(2)

Parameter configuration

As detailed in

Table 1. Technical specifications and operational parameters of system components.

Symbol	Value	Symbol	Value	Symbol	Value	Symbol	Value
$P_{\mathrm{wt}}^{\mathrm{rate}}(\mathrm{kW})$	3000	NOCT (°C)	45	$E_{\mathrm{bat}}(\mathrm{kWh})$	4000	$P_{\mathrm{tank}}^{\max }(\mathrm{kW})$	1200
$v_{\mathrm{in}}(\mathrm{m}/\mathrm{s})$	3.0	$P_{\mathrm{grid}}^{\max }(\mathrm{kW})$	5000	$P_{\mathrm{bat}}^{\max }(\mathrm{kW})$	1000	${\mathrm{\eta }}_{\mathrm{tank}}^{\mathrm{in}},{\mathrm{\eta }}_{\mathrm{tank}}^{\mathrm{out}}(-)$	0.98
$v_{\mathrm{r}}(\mathrm{m}/\mathrm{s})$	11.3	${\mathrm{COP}}_{\mathrm{sh}}(-)$	4.4	$SO{C}_{\min }(-)$	0.2	$T_{\mathrm{tank}}^{\min }$ (°C)	40
$v_{\mathrm{out}}(\mathrm{m}/\mathrm{s})$	25	${\mathrm{COP}}_{\mathrm{hws}}(-)$	3.2	$SO{C}_{\max }(-)$	0.95	$T_{\mathrm{tank}}^{\max }$ (°C)	85
$P_{\mathrm{pv}}^{\mathrm{rate}}(\mathrm{kW})$	6300	$P_{\mathrm{sh}}^{\max }(\mathrm{kW})$	450	$SO{C}_{\mathrm{target}}(-)$	0.5	$H_{\mathrm{tank}}^{\min }(\mathrm{kWh})$	250
${\alpha }_T$ (1/°C)	0.0045	$P_{\mathrm{hws}}^{\max }(\mathrm{kW})$	500	${\mathrm{\eta }}_{\mathrm{bat}}^{\mathrm{ch}},{\mathrm{\eta }}_{\mathrm{bat}}^{\mathrm{dis}}(-)$	0.9	$H_{\mathrm{tank}}^{\max }(\mathrm{kWh})$	4700
$T_{\mathrm{ref}}(°\mathrm{C})$	25	${\mathrm{\Gamma }}_{\max }(\mathrm{kWh})$	18,000	${\mathrm{\sigma }}_{\mathrm{bat}}({\mathrm{h}}^{-1})$	0.001	${\mathrm{\sigma }}_{\mathrm{tank}}({\mathrm{h}}^{-1})$	0.015

, the grid power-exchange limit is determined with reference to the rated capacity of industrial distribution transformers. The rated capacities of renewable generation and energy storage units are predetermined considering load demand, safety margins, and economic feasibility. Specifically, the WT operating wind speed thresholds are acquired from the engineering procurement technical specifications of commercial 3 MW units. Meanwhile, the operational parameters for PV, BESS, GSHP, and TST are con-figured with reference to commercial equipment technical datasheets and literature benchmarks. The principal techno-economic parameters, operating boundaries, and the resulting equivalent unit-energy cost coefficients calculated using Equations (15) and (16) are summarized in Appendix A 

Table A1. Comprehensive techno-economic parameters of the multi-energy system components.

Equipment	Capacity	Unit CAPEX	Total CAPEX (Million CNY)	Lifetime (Years)	Fixed OM	Equivalent Hours	LCOE ${\mathit{\xi }}_{\mathit{k}}$ (CNY/kWh)
WT	3000 kW	4500 CNY/kW	13.5	20	88 CNY/kW	2400	0.2
PV	6300 kW	4000 CNY/kW	25.2	20	50 CNY/kW	1100	0.36
SH-GSHP	3960 kWth	3000 CNY/kW	11.88	20	45 CNY/kW	1700	0.18
HWS-GSHP	1600 kWth	3000 CNY/kW	4.8	20	45 CNY/kW	2360	0.13
BESS	4000 kW	1100 CNY/kWh	4.4	15	16.5 CNY/kW	418	0.31
TST *	4700 kW	100 CNY/kWh	0.47	20	-	-	-

* For the TST, only the initial CAPEX is considered, and no separate levelized cost is assigned during operational dispatch.

.

The industrial TOU electricity tariffs in

Table 2. Industrial time-of-use (TOU) electricity tariffs.

Tariff Type	Time Period	Electricity Price (CNY/kWh)
Off-peak	23:00–07:00	0.427
Mid-peak	07:00–09:00 12:00–16:00 21:00–23:00	0.800
On-peak	09:00–12:00 16:00–21:00	1.146

are based on the prevailing local electricity price, while the feed-in tariff 0.82 CNY/kWh is adopted as the regional benchmark electricity-selling price used in this study. Accordingly, the resulting grid-export revenues should be interpreted under this assumed selling-price condition. The carbon assessment parameters (${\gamma }_{\mathrm{grid}}$ and ${\alpha }_{\mathrm{carbon}}$) are set to $0.56{\mathrm{t}\mathrm{CO}}_2/\mathrm{MWh}$ and $120{\mathrm{CNY}/\mathrm{t}\mathrm{CO}}_2$, respectively, representing the grid-emission factor and carbon-price coefficient used in the present assessment.

4.2. Definition of Comparative Baselines

To quantify the techno-economic and environmental benefits of the proposed electro-thermal synergistic optimization approach, two comparative scenarios are established. The detailed configurations of the rigid baseline (Scenario 1) and the proposed approach (Scenario 2) are systematically outlined in

Table 3. Detailed configurations of the comparative scenarios.

Dimension	System Element	Scenario 1 (Baseline)	Scenario 2 (Optimized)
Architecture Layer	Energy Supply	Grid-dependent	Multi-energy complementary
	Thermal Device	Electric boiler	GSHP–TST
Strategy Layer	Load Management	Rigid demand operation	ALRS
	Operational Logic	Passive (Supply- -follows-load)	Active (Source–grid–load –storage synergy)
Algorithm Layer	Optimization Solver	Rule-based control	Customized solver
	Optimization Objective	Cost-blind execution	Comprehensive cost minimization

.

5. Results and Discussion

Unless otherwise specified, all optimization-related results in this section, except those in Section 5.3, are obtained from the same representative run and are used to illustrate the complete scheduling process and its system-level outcomes. Statistical validation of the stochastic search engine, including repeated runs, benchmark comparisons, convergence analysis, and ablation studies, is presented separately in Section 5.3.

5.1. Effectiveness Validation of the ALRS in Industrial Heating Systems

To evaluate ALRS efficacy, thermal load profiles are compared. The baseline thermal load profiles (Figure 4a) constructed from the park’s recorded daily heat consumption and industrial operating schedules. The daily demands for space heating and hot water total 13,875 kWh (750 kW peak) and 2460 kWh (114 kW peak), respectively. Unlike the synchronous supply–demand tracking in baseline mode, the ALRS restructures the heat-production schedule for HWS toward nighttime off-peak periods, as illustrated in Figure 4b. The prescribed end-use thermal demand profiles are largely maintained, while the timing of HWS heat production is shifted through thermal storage. Unlike conventional thermal demand response that utilizes building thermal mass to modulate indoor conditions within a permissible comfort band [40], the proposed ALRS does not directly modify the end-use thermal demand. Furthermore, compared with strategies in which the TST is used primarily as a local thermal buffer [41], the ALRS utilizes its thermal inertia for cross-period HWS heat-production scheduling. This decouples the timing of thermal energy production from end-use HWS demand and extends the scheduling flexibility across tariff periods. This strategy fundamentally upgrades the TST into a dispatchable virtual flexible asset. Consequently, the ALRS deeply decouples the rigid supply-follows-load constraints, alleviating daytime grid pressure and expanding the regulation window for cross-period arbitrage.

The impacts of different strategies on operational costs are further elucidated in

Table 4. Techno-economic performance comparison of different operational strategies.

Strategy	Electricity Cost (CNY)	Savings Rate (%)
Baseline	2792.53	Ref.
TST only	1562.97	44.03
GSHP only	872.67	68.75
ALRS (Integrated GSHP–TST)	488.43	82.51

. The standalone TST or GSHP configurations show smaller cost reductions than the combined ALRS configuration. This comparison indicates that coordinating GSHP conversion efficiency with the temporal flexibility provided by the TST can improve the alignment between energy conversion and lower-tariff operating periods, thereby enhancing the economic performance of the integrated system.

In conclusion, based on extrapolation of the representative-day results to a 120-day heating season, the ALRS is estimated to yield cumulative operational electricity cost savings of 276,492 CNY. This seasonal estimate is intended to indicate the potential economic benefit of load restructuring under the assumed representative operating conditions, while the limitations of typical-day extrapolation are discussed separately in Section 5.7.

5.2. Performance of the Customized Digital Solver

To solve the non-convex multi-energy model, the customized digital solver employs PLIW-SCGS-PSO as its embedded stochastic search engine. During the initial exploration phase (iterations 0–250), a quasi-static decay slope (−0.0006) maintains a relatively high inertia weight to support broader exploration of the normalized search space, as shown in Figure 5a. At iteration 250, a state transition shifts the slope to −0.003, gradually directing the search toward stronger local exploitation. Throughout the iteration process, the SCGS introduces swarm-level guidance derived from historical personal-best information to complement the swarm-level search process. Combined with principal component analysis dimensionality reduction visualization, the diversity and iterative evolution dynamics of the swarm within the feature space are detailed in Figure 6 and Figure 7.

The convergence trajectory in Figure 5b illustrates the evolution of the best-found objective value during this representative optimization run. The convergence trajectory in Quantitatively, the representative run yields a reduction in the comprehensive objective value from an initial swarm best of 34,188 CNY to a final best-found value of 27,358 CNY, corresponding to a 20.0% reduction. The resulting schedule satisfies the prescribed electro-thermal balance and operating constraints of the current model. It is worth noting that the virtual penalty cost is always 0.0 CNY, with each of its subcomponents maintained at 0.0 CNY. These results characterize the numerical search process and feasible scheduling outcome of the representative case, rather than the statistical performance of the stochastic search engine.

5.3. Statistical Validation and Reproducibility of the Customized Digital Solver

The customized digital solver developed in this study is a problem-oriented optimization framework integrating model construction, physical constraint handling, stochastic search, and post-optimization analysis. Within this framework, PLIW-SCGS-PSO serves as the embedded stochastic search engine rather than representing the entire solver. Therefore, this subsection focuses on its statistical behavior and reproducibility under repeated runs, without claiming mathematical global optimality or universal superiority over other metaheuristics.

Before the formal validation, a preliminary screening was conducted for the two acceleration coefficients, with $c1=\left\{1.2,1.5,1.8\right\}$ and $c2=\left\{1.5,1.8,2.1\right\}$. The resulting nine combinations were evaluated through five pilot runs using an independent tuning seed set. The mean objective value was used as the primary selection criterion, with the coefficient of variation (CV) as an auxiliary stability indicator. The selected configuration was fixed before formal validation, and the complete parameter settings are summarized in

Table 5. Parameter settings used for the statistical validation of the PLIW-SCGS-PSO search engine.

Symbol	Value	Symbol	Value	Symbol	Value	Symbol	Value
$N$	300	${\mathrm{\omega }}_{bp}$	0.75	$K_{\max }$	400	$c_1,c_2$	1.2, 2.1
${\mathrm{\omega }}_{\min }$	0.3	${\mathrm{\omega }}_{\max }$	0.9	$K_{\mathrm{bp}}$	250	$V_0$ *	0.05

* $V_0$ denotes the initial velocity amplitude used to sample the initial particle velocities from $U\left(-V_0,V_0\right)$.

.

For reproducibility, all stochastic experiments were carried out for the same scheduling problem. The formal comparison consisted of 30 independent runs using seeds 70,001–70,030, with the same run-indexed seed applied to each compared algorithm. A separate seed set of 80,001–80,030 was used for the ablation study. Parallel computing was used only to accelerate independent runs, while the reported computational time corresponds to each individual optimization task. Final feasibility was assessed by directly checking the original physical constraints within prescribed numerical tolerances rather than by requiring the penalty term to be exactly zero.

Standard PSO and GA were selected as representative baseline algorithms and were evaluated under the same scheduling model, objective function, constraints, search space, and comparable computational budget. The statistical comparison is presented in

Table 6. Statistical comparison of the optimization algorithms over 30 independent runs.

Algorithm	Best (CNY)	Worst (CNY)	Mean (CNY)	Std (CNY)	CV (%)	Avg. Time (s)	Feasibility (%)
Standard-PSO	26,186.65	30,654.77	28,768.43	1088.01	3.78	52.76	100
Standard GA	25,522.95	26,758.03	26,161.01	321.02	1.23	37.75	100
PLIW-SCGS-PSO	26,936.44	32,309.12	29,452.15	1237.66	4.20	47.80	100

. The results show that GA provides the best overall objective-value performance and the lowest run-to-run variability in the present problem, while standard PSO also performs more favorably than PLIW-SCGS-PSO in terms of the average objective value. Thus, the benchmark does not support a claim of universal superiority for the embedded PLIW-SCGS-PSO search engine, but instead provides an objective assessment of its numerical performance in the present scheduling problem.

The corresponding mean convergence trajectories and distributions of the final best-found objective values are shown in Figure 8. The multi-run results demonstrate clear differences among the compared stochastic methods, which are also supported by the Friedman and pairwise Wilcoxon tests. These results confirm that the relative performance of metaheuristic search methods is problem-dependent and that a single convergence trajectory should not be interpreted as evidence of mathematical global optimality.

To separately examine the effects of PLIW and SCGS, a four-variant ablation study was performed under otherwise unchanged computational settings, as summarized in

Table 7. Ablation analysis of the PLIW and SCGS mechanisms over 30 independent runs.

Variant	PLIW	SCGS	Best (CNY)	Mean (CNY)	Std (CNY)	CV (%)	Feasibility (%)
Standard-PSO	×	×	26,676.19	29,165.51	1034.21	3.55	100
PLIW-PSO	✓	×	25,461.30	28,399.10	1275.93	4.49	100
SCGS-PSO	×	✓	26,862.69	30,354.60	1340.38	4.42	100
PLIW-SCGS-PSO	✓	✓	26,165.37	29,682.74	1150.72	3.88	100

Note: “✓” indicates that the corresponding mechanism is incorporated in the variant, whereas “×” indicates that it is not incorporated.

. PLIW provides the clearest positive contribution to objective-value reduction in the present problem, whereas SCGS alone does not produce the same improvement. The combined variant performs better than the SCGS-only variant but does not outperform the PLIW-only variant, indicating that the contribution of SCGS is more dependent on the characteristics of the constrained scheduling problem.

Overall, the repeated-run experiments provide a reproducible statistical assessment of the stochastic search component used in the customized digital solver. The contribution of this work is therefore positioned as the development of a problem-oriented customized digital optimization framework for electro-thermal scheduling, rather than as the universal superiority of a standalone metaheuristic algorithm.

The benchmark results also indicate that the modular solver framework is not tied to a single search strategy; therefore, integrating alternative or adaptive search engines that are better matched to the characteristics of the scheduling problem may further improve solution quality and computational performance.

5.4. Dynamic Operational Characteristics Analysis

Under the ALRS, the system shifts from baseline supply-follow-load operation to coordinated source–grid–load–storage dispatch, as illustrated in Figure 9a,b. The optimization approach utilizes TOU tariff differentials. During nighttime off-peak periods, the BESS charges to shift part of the grid electricity purchases to lower-price periods; conversely, during daytime on-peak periods, the BESS discharges to reduce external power purchase costs. Furthermore, during periods of surplus PV generation, source–grid–load–storage coordination enables surplus electricity to be exported to the grid under the assumed grid-export and electricity-selling conditions, as detailed in Figure 9a. This price-signal-driven bidirectional power interaction illustrates the modeled response of the integrated system to time-varying electricity prices while satisfying the prescribed operating constraints.

The dynamic evolution of the SOC under operational constraints reflects the interaction between economic dispatch and battery operating limits within the representative scheduling horizon. As depicted in Figure 9c, the SOC varies with source–load–price conditions while remaining within the prescribed operating range of 0.20–0.95. This indicates that the available storage flexibility is utilized without violating the SOC limits. At the end of the operational cycle, the terminal SOC returns to the specified target value (0.50). Satisfying this terminal constraint reduces the end-of-horizon effect of the finite-horizon optimization and avoids obtaining artificial short-term cost reductions through excessive depletion of stored energy at the end of the representative scheduling cycle. These results characterize the BESS operation within the representative scheduling case and do not imply long-term battery-performance validation.

5.5. Comprehensive Assessment of Techno-Economic and Environmental Benefits

•

In the baseline scenario, the system operates on a passive supply-follows-load logic, with electro-thermal demands relying entirely on grid power purchases. The superposition of peak loads and on-peak tariffs drives the operational costs above 7000 CNY/h (Figure 10). In contrast, the optimized scenario establishes a bidirectional energy interaction mechanism. During the surplus PV generation window (10:00–14:00), electricity exports to the grid provide an economic return of approximately 4000 CNY/h under the assumed electricity-selling conditions. For the representative day (Figure 11a), the daily comprehensive operational cost and carbon emissions decrease by 71.9% and 90.2%, respectively. These improvements are associated with the coordinated operation of the system architecture and ALRS under the adopted scheduling framework. Architecture-level configuration: the integration of wind–solar–shallow geothermal energy complementarity and hybrid electrical–thermal storage enhances the available system flexibility for coordinated energy dispatch and temporal load restructuring.

•

Strategy-level restructuring: the ALRS utilizes the thermal inertia of the TST together with the conversion efficiency of the GSHP to shift HWS heat production toward nighttime periods with favorable wind availability and off-peak tariffs, thereby enabling source–load temporal decoupling and cross-period coordination.

Beyond the representative-day analysis, an indicative seasonal estimate is obtained by extrapolating the representative operating conditions over the 120-day heating season, as shown in Figure 11b. This extrapolation is intended to provide an approximate indication of seasonal techno-economic and environmental performance rather than a validated continuous-season simulation. Under the assumption that the representative-day operating pattern remains applicable and that nonlinear disturbances caused by extreme weather and seasonal load variations are not explicitly considered, the extrapolated results correspond to a comprehensive operational saving of approximately $8.2\times {10}^6$ CNY over the heating season. The carbon emission-related cost reduction remains above 90% under the same representative-day extrapolation assumption, indicating the potential for substantial environmental benefits.

For the remaining non-heating period, a simplified annualization assumption is adopted only for the investment payback calculation. Considering weather intermittency, the renewable arrays and domestic hot water GSHPs are assumed to operate under simplified representative conditions, resulting in an estimated gross revenue of approximately $1.01\times {10}^6$ CNY from surplus renewable electricity sales. This value is therefore used only as an indicative annualized estimate rather than as a result derived from continuous year-round simulation.

After deducting the annual fixed maintenance cost of $0.90\times {10}^6$ CNY/year from the estimated aggregate revenues, the resulting annualized net operational saving is approximately $8.31\times {10}^6$ CNY/year. Based on the CAPEX estimate reported in Table A1, this annualized saving corresponds to a preliminary static payback period of approximately 7.25 years and a discounted payback period of approximately 9.80 years. These payback results provide an indicative economic assessment under the stated annualization assumptions and should not be interpreted as a validated long-term investment forecast.

5.6. Sensitivity and Robustness Analysis

To further evaluate the sensitivity of the main results, two complementary perspectives are considered. A numerical sensitivity analysis is performed to investigate the response of the system to electricity price and carbon tax fluctuations. Meanwhile, considering the constant-COP approximation adopted in the GSHP model, an analytical sensitivity assessment is conducted to quantify the direct influence of COP deviations on GSHP electricity consumption and the associated electricity cost.

5.6.1. Numerical Sensitivity to Electricity Price and Carbon Tax Fluctuations

Practical system operation is subject to market-related and policy-related uncertainties, particularly fluctuations in electricity prices and carbon taxes. To examine the response of the proposed framework to these external variations, electricity prices and carbon taxes are jointly scaled by a coefficient $\lambda \in [0.8,1.2]$, while the remaining system parameters are kept unchanged. Figure 12 presents the resulting variations in operational and environmental costs. Under the baseline scenario, both cost components vary approximately linearly with $\lambda$. In contrast, the optimized scenario exhibits smaller absolute cost variations over the investigated range. Across the tested values of $\lambda$, the optimized case maintains lower operational and environmental costs than the baseline case, indicating that the economic and environmental benefits remain evident under the considered price and carbon tax variations.

5.6.2. Analytical Sensitivity Assessment of the GSHP COP Assumption

As clarified in Section 2.3.2, the COP adopted in the GSHP model represents a nominal short-term value within the intraday scheduling horizon. Nevertheless, variations in ground thermal conditions and operating states may cause the actual COP to deviate from its nominal value. To quantify the direct influence of this approximation, an analytical sensitivity assessment is performed based on the GSHP energy-conversion relationship in Equation (6).

According to Equation (6), for a prescribed thermal output, the electrical input of GSHP unit $i$ varies inversely with ${\mathrm{COP}}_i$. To quantify deviations from the nominal value, a uniform relative COP deviation $\delta$ is considered over the scheduling horizon, such that $CO{P}_{i^{\prime }}=(1+\delta )CO{P}_i$. Under an unchanged GSHP thermal-output profile, the corresponding electrical input ratio and relative change are given by ${\displaystyle \frac{{P^{\prime }}_{\mathrm{gshp},i}(t)}{P_{\mathrm{gshp},i}(t)}}={\displaystyle \frac{1}{1+\delta }}$, ${\displaystyle \frac{\mathrm{\Delta }{P}_{\mathrm{gshp},i}}{P_{\mathrm{gshp},i}}}={\displaystyle \frac{1}{1+\delta }}-1$.

As shown in

Table 8. Analytical sensitivity of GSHP electricity consumption and associated electricity cost to COP variations.

Relative COP Deviation $\mathit{\delta }$	Relative Change in GSHP Electricity Consumption	Relative Change in Associated Electricity Cost *
−10%	+11.11%	+11.11%
−5%	+5.26%	+5.26%
0%	0%	0%
+5%	−4.76%	−4.76%
+10%	−9.09%	−9.09%

* The electricity cost variation represents the direct analytical effect under an unchanged GSHP thermal-output profile and electricity price profile. Secondary effects associated with system redispatch are not included.

, GSHP electricity consumption exhibits a nonlinear inverse dependence on COP. A 10% reduction in COP increases the required GSHP electricity consumption by approximately 11.11%, whereas a 10% increase in COP reduces it by approximately 9.09%. For smaller deviations of ±5%, the corresponding changes are +5.26% and −4.76%, respectively. Under an unchanged GSHP thermal-output profile and electricity price profile, the associated electricity cost follows the same proportional tendency. These results demonstrate that deviations from the nominal COP directly affect the absolute electricity consumption and associated electricity cost of the GSHP, with COP degradation producing a slightly stronger adverse effect than the benefit obtained from an equivalent percentage improvement in COP.

It should be emphasized that this assessment quantifies the direct sensitivity of GSHP electricity consumption and its associated electricity cost to COP deviations rather than the full system-level response after re-optimization. In the coupled electro-thermal system, time-varying COP may additionally affect energy storage operation, grid interaction, and the scheduling of other devices. Such secondary redispatch effects are beyond the scope of the present analytical assessment and are explicitly acknowledged in Section 5.6.

5.7. Limitations and Future Work

While the proposed framework demonstrates cost-effectiveness and operational flexibility in the present case study, its scope is specifically anchored to the heating season of cold-region industrial parks. Necessary modeling simplifications introduce the following boundaries.

First, relying on typical-day models rather than continuous long-term simulations inadequately captures extreme weather and seasonal load fluctuations, potentially overestimating overall benefits. Although the analytical influence of GSHP COP variations is evaluated in Section 5.6, the present short-term model does not explicitly capture the dynamic coupling between ground thermal conditions and time-varying GSHP performance, including borehole thermal interference and soil temperature recovery.

Moreover, the battery model omits degradation characteristics like capacity fading and cycle aging, meaning actual operational costs may exceed current estimates. The present model also does not explicitly include alternating current (AC) power flow constraints, such as voltage limits and network losses, which may affect power transfer capability and operating costs in practical distribution networks [42].

To address these limitations, future work will incorporate dynamic GSHP performance, battery degradation, and AC power flow constraints, while considering broader representative weather, renewable generation, load, and storage capacity scenarios. Extending the temporal horizon from representative-day analysis to seasonal and annual simulations will further improve the assessment of long-term system performance and engineering applicability.

6. Conclusions

This study systematically evaluates the techno-economic and environmental performance of industrial IES in cold regions, addressing the urgent need for innovative and efficient thermal energy solutions. By implementing a multidimensional synergistic optimization approach, the potential source–load temporal mismatch often encountered in renewable-driven decarbonization transition pathways is alleviated to a certain extent. The primary conclusions are summarized as follows:

Source–load decoupling achieved by the ALRS: The proposed ALRS transforms rigid thermal demands into cross-period virtual flexible assets. By achieving source–load temporal decoupling, this strategy reduces the typical-day electricity cost by 82.51% and yields estimated cumulative savings of 276,492 CNY throughout the heating season. This suggests that active temporal restructuring of the electro-thermal coupling relationship can serve as an important mechanism for translating thermodynamic flexibility into operational economic benefits.

System integration and physical boundaries: A decarbonized industrial IES architecture integrating wind, solar, shallow geothermal energy, and hybrid storage has been evaluated within the present system framework. Through multi-energy complementation, this architecture mitigates reliance on the main grid, indicating that coordinated source-side restructuring and multi-energy integration provide a physical basis for the system-level optimization considered in this study.

Dedicated system-level digital solver: The proposed solver provides a problem-oriented framework for converting the coupled electro-thermal scheduling model into feasible operating decisions under prescribed system constraints. The representative results confirm the practical applicability of this problem-oriented solver, while the repeated validation also indicates that its modular structure allows alternative search engines to be incorporated when better suited to specific scheduling characteristics.

Techno-economic and environmental assessment: The synergistic optimization approach achieves a 71.9% reduction in daily comprehensive operational costs and a 90.2% decrease in carbon emissions. This quantitative evidence suggests that the coordinated restructuring of industrial thermal loads and multi-energy resources can contribute to cost reduction and decarbonization under the assumptions and operating conditions considered in this study provides a system-level reference for further development of low-carbon industrial energy systems.