The U-IEH-C framework and the proposed optimization model for economically synergistic decarbonization scheduling, described by Eqs. (1)–(24), include internal nonlinearities primarily arising from CHP cogeneration systems. These nonlinearities result from the presence of quadratic and non-convex terms. To ensure computational tractability, the nonlinear components are linearized using piecewise linearization and McCormick relaxation techniques, enabling the use of Mixed-Integer Linear Programming (MILP) solvers. Consequently, the original Mixed-Integer Nonlinear Programming (MINLP) formulation is transformed into an MILP model that preserves the essential solution characteristics while ensuring efficient and reliable computation.
The complete modeling and solution procedures are implemented in Python using the Pyomo optimization library, and numerical computations are performed with the COIN-OR Branch and Cut (CBC) solver. The overall process, from model formulation (Layers A–E) to solution analysis, is illustrated in Fig. 2.
The study considers four integrated U-IEH-C units managed by a central market coordinator (see Fig. 1). The conceptual framework, expanded in the schematic representation shown in Fig. 3, illustrates the multi-cluster architecture of the system and the complementary integration of its components. Each U-IEH comprises a CHP unit, renewable generation resources (wind turbines and photovoltaic panels), multiple storage systems including ESS, TSS, and HT, as well as fleets of PLEVs and PLHVs. Supporting infrastructure includes U-DPLs and U-HRSs.
Day-ahead energy trading is coordinated through a decentralized scheduling mechanism, whereby each U-IEH independently determines its electricity and hydrogen offers and submits them to the central coordinator. A scenario-based stochastic optimization framework underpins the solution methodology, ensuring robust handling of system uncertainties. Detailed procedures for scenario generation and reduction are provided in Appendix E of the supplementary material. Simulation inputs and parameters are reported in36,37 and are therefore not repeated here. Additional graphical results and supplementary analyses are presented in Appendix F of the supplementary material.
Workflow of the proposed U-IEH-C optimization and solution process.
System configuration of the U-IEH-C framework with coordinated market interactions.
Multi-carrier optimal dispatch
This section presents the results of DICE within the U-IEH-C framework, considering uncertainties related to wholesale electricity prices, solar radiation, wind speed, and electrical and thermal loads. The hourly power exchanges between each U-IEH and the coordinating center are illustrated in Fig. 4. Positive values indicate electricity exports, whereas negative values represent imports. The results indicate an inverse relationship between wholesale electricity purchases and market prices: all U-IEHs increase imports during low-price periods, while exports predominantly occur during high-price intervals. U-IEH Nos. 1 and 4 import electricity during peak hours, whereas U-IEH Nos. 2 and 3 export surplus energy during hours t = 21–23.
Additional visualizations of temperature contour variations and the density distribution of power exchanges are provided in Figs. F.1 and F.2, respectively (see Appendix F of the supplementary material).
Power exchanges between the coordinating center and each U-IEH.
For electrical power balancing, Fig. 5 presents the hourly optimal power dispatch profile for U-IEH No. 1 to U-IEH No.4. These figures illustrate the optimal hourly power dispatch profiles using a heatmap-based representation.
Based on the results, the figures illustrate the optimal hourly power dispatch profiles of the U-IEHs. CHP type 1 units primarily supply U-IEH Nos. 2 and 3, whereas U-IEH Nos. 1 and 4 are mainly supplied by CHP type 2 units. Prior to the highest market price period, electricity procurement from the market remains more economical than internal generation across all systems. Consequently, CHP units are activated once market prices increase significantly (around t = 12), particularly under higher load conditions that require internal generation. For U-IEH Nos. 1 and 4, the continuous operation of CHP type 2 units during t = 5–6 results from their marginal costs being lower than the prevailing market prices.
All U-IEHs strategically utilize ESSs to exploit price volatility. Charging occurs during low-price periods, while discharging is concentrated during high-price intervals, notably around t = 4–6 and 16–22, with recharging observed at t = 22–24.
The operation of P2H₂ technology is closely linked to hydrogen demand and market conditions. During early morning hours, when hydrogen demand is low and electricity prices are reduced, surplus electricity is converted into hydrogen for storage. At t = 18, stored hydrogen is reconverted into electricity, coinciding with elevated market prices. In addition, PLEVs operating as mobile storage units exhibit behavior analogous to ESSs, smoothing intraday fluctuations. The proportional contribution of each energy carrier and transfer pathway to the overall power energy balance is depicted in Fig. 6, which presents system-wide energy flow distributions.
Heatmap contour plots of optimal heat dispatch patterns for the U-IEHs are presented in Figs. F.3–F.6 (see Appendix F of the supplementary material), offering further spatiotemporal insight into operational performance.
Hourly optimal power dispatch profile and Energy Carrier Contributions to U-IEHs. (a) Hourly optimal power dispatch in U-IEH No. 1, (b) Unit-level contributions to the electrical power balance of the U IEH No. 1., (c). Hourly optimal power dispatch in U-IEH No. 2., (d) Unit-level contributions to the electrical power balance of the U IEH No. 2, (e) Hourly optimal power dispatch in U-IEH No. 3., (f) Unit-level contributions to the electrical power balance of the U IEH No. 3, (g) Hourly optimal power dispatch in U-IEH No. 4., (h) Unit-level contributions to the electrical power balance of the U IEH No. 4.
For thermal balancing, Fig. 6 presents the hourly optimal heat dispatch profile for U-IEH No. 1 to U-IEH No.4. These figures illustrate the optimal heat dispatch profiles of each U-IEH-C component. In addition to electricity and hydrogen, thermal demand plays a critical role in system operation. During morning hours characterized by low electricity prices, P2H technology operates to generate heat that is subsequently stored in TSSs for later use. All U-IEHs, except U-IEH No. 1, utilize P2H₂ due to substantial morning heat demand.
Heat supply is provided by either GBs or CHP units. GBs are preferred in U-IEH Nos. 1 and 2 because of lower operational costs; however, CHP units are activated when GB capacity is insufficient. In contrast, U-IEH Nos. 3 and 4 are equipped with higher-capacity CHP units that primarily satisfy thermal demand, with GBs serving as auxiliary units.
TSS units provide additional operational flexibility by charging during low-demand periods and discharging during high-demand intervals, particularly during hours t = 5 and 6 when electricity prices increase. Heatmap contour plots of optimal heat dispatch patterns for the U-IEHs are presented in Figs. F.7–F.10 (see Appendix F of the supplementary material), offering further spatiotemporal insight into operational performance.
Hourly optimal thermal dispatch and Whisker visualization in U-IEHs. (a) Hourly optimal thermal dispatch in U-IEH No. 1., (b) Whisker visualization of energy heat balance distribution in U-IEH No. 1., (c) Hourly optimal thermal dispatch in U-IEH No. 2., (d) Whisker visualization of energy heat balance distribution in U-IEH No. 2., (e) Hourly optimal thermal dispatch in U-IEH No. 3., (f) Whisker visualization of energy heat balance distribution in U-IEH No. 3., (e) Hourly optimal thermal dispatch in U-IEH No. 4., (g) Whisker visualization of energy heat balance distribution in U-IEH No. 4.
For the hydrogen hub, Fig. 7 illustrates the operational dynamics of hydrogen storage and procurement within the U‑IEH network. HTs are charged during early morning hours when electricity prices are low. During peak demand periods, which coincide with elevated electricity prices, stored hydrogen is discharged. Between t = 15 and 21, P2H₂ operation is suspended due to high electricity prices; during this interval, hydrogen demand is met from storage, and any remaining deficit is supplied through purchases from U‑HRSs to maintain system reliability.
The dynamic interaction between hydrogen storage discharge and U‑HRS procurement across the U‑IEH network is depicted in Fig. 9(a–b). The SoC trajectories of individual HTs reflect the combined effects of on‑site hydrogen production via P2H₂ and external hydrogen procurement from U‑HRSs. During early morning periods characterized by low electricity prices, hydrogen production and storage are maximized. As electricity prices and hydrogen demand increase throughout the day, stored hydrogen is deployed to satisfy system requirements. When real‑time hydrogen production becomes economically unfavorable, the system relies on stored hydrogen and supplementary U‑HRS transactions.
Hydrogen storage and procurement dynamics in the U‑IEH network. (a) Hourly SoC profile of HTs across U‑IEHs., (b) Hourly hydrogen purchases from U‑HRSs by U‑IEHs.
The operation of demand response for electrical and thermal loads in U-IEH No. 1 is presented in Figs. 8 and 9. The analysis demonstrates the application of the FEDM framework, under which end users participate in demand-side management through incentive-based mechanisms associated with dynamic electricity pricing and renewable energy utilization.
During peak price periods (hours 12–22), FEDM enables demand shifting toward off-peak hours (hours 1–11 and 24). This load rescheduling reduces total energy procurement costs by at least 10%, indicating effective alignment between consumption patterns and real-time market conditions. Thermal load management exhibits comparable flexibility. In coordination with power-to-heat (P2H) technology, FEDM supports adaptive responses to price volatility. In U-IEH No. 1, higher electricity prices during hours 13–21 coincide with increased thermal demand; under these conditions, Gas Boilers (GBs) are dispatched to efficiently supply peak thermal loads.
The corresponding results for the remaining hubs are provided in the supplementary figures. The implementation of FEDM for electrical load demand in U-IEH Nos. 2, 3, and 4 is illustrated in Figs. F.11–F.13 (see Appendix F of the supplementary material), respectively, while the implementation of FEDM for thermal load demand in U-IEH Nos. 2, 3, and 4 is shown in Figs. F.14–F.16 (see Appendix F of the supplementary material). These figures are included for reference and demonstrate consistent demand response behavior across all U-IEHs.
The Implementation of FEDM for electrical load demand in U-IEH No. 1.
The Implementation of FEDM for thermal load demand in U-IEH No. 1.
Financial analysis
A detailed comparison of operating costs (purchased hydrogen and electricity, CHP costs, and GBs costs) and benefits (CET and GCT revenues, and electricity sales) is presented in Fig. 10 for each U-IEH-C unit and for the aggregated system. The results indicate that CHP plants constitute the dominant component of total operating cost, accounting for approximately 93.25% of the overall expenditure and playing a critical role in system economics.
The remaining costs are distributed among hydrogen purchases (7.37%), condenser operation (7.21%), and participation in the electricity market (69.3%), reflecting the diversity of operational strategies adopted across the U-IEHs. These findings suggest that improving CHP efficiency, optimizing hydrogen procurement strategies, and enhancing boil GBs er operation represent key avenues for cost reduction. Furthermore, the substantial contribution of electricity market participation to total costs highlights the importance of real-time market optimization within the energy management strategy, as well as the need to maintain diversified trading capabilities.
Component-wise operating cost matrix for U-IEH-C.
The financial impact of demand response is further illustrated in Fig. 11. The integration of FEDM in electrical load management results in significant operational cost savings of 16.21% and 16.53% for U-IEH Nos. 1 and 2, respectively. In contrast, U-IEH Nos. 3 and 4 derive greater benefits from the application of SESS, achieving cost reductions of 39.54% and 36.62%, respectively.
Temporal impact of flexible resource integration on operating costs across individual U-IEHs.
Trade market incentives analysis
Market-oriented mechanisms, namely CET and GCT, play a significant role in enhancing the operational and economic performance of the U-IEH-C system. The dynamic operational effects of these mechanisms for all U-IEHs are illustrated in Fig. 12.
Under the CET framework, each U-IEH is allocated emission allowances within a cap-and-trade structure. Entities emitting less than their assigned quota may sell surplus allowances, whereas those exceeding their limits must purchase additional permits. The hourly pattern shown in Fig. 12 indicates that U-IEHs utilize this mechanism most effectively during periods of high emission potential, particularly between 12:00 and 18:00. During these intervals, increased market activity enables U-IEHs with emission costs exceeding their allocated credits to purchase allowances, while those with surplus permits can sell them, thereby improving both financial performance and environmental compliance.
The GCT mechanism promotes renewable energy generation and utilization by issuing certificates for electricity produced from RES and supplied to the system. As reflected by lower values during early morning hours (between 1:00 and 6:00), U-IEHs capitalize on off-peak periods to enhance renewable penetration and accumulate green certificates.
Impact of CET and GCT transactions on U-IEH operational performance.
Sensitivity analysis
A detailed sensitivity analysis is conducted to evaluate the robustness of the proposed operational strategy within the U-IEH-C system. This analysis examines the sensitivity of operating costs and overall performance to variations in key configuration parameters. The objective is to identify critical system vulnerabilities and assess the financial implications of deviations from the baseline configuration. The selected stress factors and corresponding scenarios are summarized in Table 4.
A stress test incorporating practical operational disturbances is performed to evaluate the resilience of the U-IEH-C scheduling approach. In each scenario, profit is defined as the difference between total operating costs (purchased electricity and hydrogen, CHP costs, and GBs costs) and total revenues (electricity sales and CET/GCT incentives). The break-even profit is reported as $4,837 (see Table 5).
Figure 13 presents the financial trajectory under different stress scenarios, enabling a comparative assessment of the incremental impact of each stress factor on overall profitability. Demand surges and renewable generation shortfalls (S1 and S3) significantly affect system costs and revenues. However, increased system utilization and favorable market conditions offset these effects, resulting in substantial net profit gains.
The influence of hydrogen price shocks (S2) on profitability remains limited, as hydrogen represents a relatively small share of total operating costs. Similarly, the impact of electricity market price increases (S4) on profit is minimal, indicating effective internal hedging mechanisms.
Incremental profit changes of the U-IEH-C system under different stress scenarios.
Welfare assessment analysis
To evaluate how structural perturbations propagate through the U-IEH-C architecture and influence social–environmental performance, the ESW layer was assessed under the five stress scenarios defined in Table 3. All ten hydrogen-oriented ESW indicators were normalized relative to the baseline case (S0 = 1.00). The normalized responses of these indicators under individual and combined stress conditions are presented in Fig. 14. In addition, Fig. 14(b) reports the percentage deviation of each ESW indicator from the baseline across all stress scenarios, enabling a comparative interpretation of welfare sensitivity.
Under S1 (Demand Surge, + 10%), increased aggregate load intensifies CHP dispatch and electricity imports. This structural shift reduces the GHPR because a larger share of demand is met through conventional cogeneration rather than electrolytic hydrogen. Simultaneously, Hydrogen Storage Utilization Rate (HSUR) rises due to greater reliance on buffer capacity to hedge intraday peaks. The moderate decline in HEOR reflects higher marginal emissions associated with load-following thermal units. From a system-structure perspective, this scenario reveals the dependence of welfare gains on renewable surplus availability. urban demand growth without parallel expansion of RES capacity erodes hydrogen-driven decarbonization benefits; coordinated planning of demand growth and renewable expansion is therefore essential.
In S2 (Hydrogen Price Shock, + 20%), the economic attractiveness of purchased hydrogen declines. The system compensates by shifting toward in-situ P2H₂ production when electricity prices permit. As a result, GHPR remains relatively resilient, while HECR deteriorates because cost savings from hydrogen substitution diminish. This indicates that welfare performance is more sensitive to hydrogen market structure than to physical infrastructure. Structurally, the multi-vector flexibility of U-IEH-C dampens the shock through internal conversion pathways. Stable hydrogen pricing mechanisms or long-term contracts are necessary to preserve affordability-related welfare metrics.
The S3 (Renewable Energy Shortfall, − 15% PV/WT) scenario exerts the strongest structural pressure on welfare. Reduced renewable input lowers green hydrogen production capacity, directly decreasing GHPR and ECHT due to fewer green certificates and emission offsets. Increased reliance on CHP weakens HEOR and slightly affects SEHA, as disadvantaged districts may experience higher marginal energy costs. This scenario demonstrates that welfare gains are tightly coupled to renewable penetration rather than hydrogen technology alone. resilience of urban hydrogen strategies depends on diversification of renewable sources and storage scaling to buffer supply volatility.
Under S4 (Electricity Market Price Rise, + 12%), demand response and storage coordination become economically valuable. Indicators related to load flexibility, including HLSC and HECR, remain comparatively stable because FEDM and P2H coupling enable strategic temporal shifting. The structural interaction between electricity markets and hydrogen conversion units functions as a hedge mechanism. Welfare degradation is limited, illustrating that market-integrated flexibility enhances socio-environmental robustness. Enabling dynamic pricing and flexible participation frameworks strengthens welfare stability in volatile markets.
The S5 (Combined Worst-Case) scenario exposes systemic interdependencies. Simultaneous demand growth, renewable shortfall, hydrogen price increase, and market price escalation collectively reduce GHPR and ECHT to their minimum observed levels (0.37 and 0.44). The decline is causally linked to constrained renewable input, elevated marginal costs, and intensified thermal dispatch. However, social-access indicators such as SEHA and PAHUM remain above 0.68, reflecting structural equity embedded in decentralized energy access and distributed infrastructure (U-HRSs, U-DPLs).
Across all stress scenarios, three structural insights emerge. First, welfare sensitivity is driven primarily by renewable availability rather than hydrogen price fluctuations, indicating that green hydrogen penetration remains structurally dependent on sustained RES input. Second, the presence of multi-vector storage and sector-coupled conversion pathways dampens welfare volatility by absorbing market and supply disturbances. Third, decentralized clustering of U-IEHs preserves equity-oriented indicators, maintaining social accessibility even under systemic stress.
These findings imply that effective urban hydrogen integration requires coordinated policy support, including sustained renewable expansion to protect green hydrogen penetration, price-stabilization mechanisms in both hydrogen and electricity markets, strengthened carbon and GCT frameworks to safeguard emission-offset incentives, and distributed infrastructure planning to ensure equitable hydrogen access during adverse operating conditions.
Relative welfare deviation from baseline under stress conditions. (a) Eco-social welfare performance under structured stress scenarios, (b) normalized ESW indicators across stress scenarios.
