Multi-Objective Optimal Dispatch of Integrated Energy Systems Guided by Dynamic Carbon Emission Factors

Abstract

Regional integrated energy systems (RIES) represent a promising approach for the energy transition and sustainable development, leveraging the flexible, coordinated operation of a multienergy system. With the growing penetration of renewable energy sources and the increasing complexity of energy management, the optimization of RIES necessitates the integration of demand response (DR) mechanisms. The optimization problems are increasingly characterized by multiobjective optimization. This study proposes a novel bilevel multiobjective optimization model for RIES, designed to minimize operational costs, reduce carbon emissions, and enhance load stability simultaneously. The model utilizes dynamic carbon emission factors, derived from the carbon emission flow (CEF) calculation, and time-of-use (TOU) energy pricing as DR signals. The Pareto front for demand-side strategies is obtained using the NSGA-II algorithm, coordinated with an upper-level economic dispatch solved by GUROBI, thereby balancing system and user benefits and identifying the optimal trade-offs among these conflicting objectives. Validation through integrated case studies with a 30-bus power, 20-node gas, and 8-node heat system demonstrates that multiobjective optimization with DR significantly improves economic and environmental performance: achieving a 10.29% cost reduction and a 1.42% carbon decrease, load variation was effectively managed, with electric and thermal load reductions of 3.50% and 6.50%, respectively. However, maintaining system load stability comes at the expense of fully achieving economic and low-carbon objectives, highlighting the critical trade-offs inherent in multiobjective optimization.

1. Introduction

The surge in global energy demand growth has exacerbated energy security concerns and environmental pressures, solidifying the international consensus on transitioning to low-carbon energy systems. Energy systems currently face critical challenges, including high energy intensity, low integrated efficiency, excessive carbon emissions, and inadequate interaction between supply side and demand-side, all demanding urgent solutions. Consequently, achieving high efficiency, cleanliness, and low-carbon development has become the predominant direction of energy advancement. As a primary source of carbon emission, the power sector must urgently move beyond the traditional “generation-follows-load” dispatch paradigm, prioritizing flexible load-regulation methods like demand response and energy storage. The temperature control targets set by the 2016 Paris Agreement further necessitate that energy systems reduce carbon intensity through structural optimization and technological innovation. Therefore, the development of integrated energy systems (IES), capable of accommodating distributed energy resources and diversified energy demands, emerges as an objective requirement for energy transition. Such systems achieve deep integration of energy and information technologies through synergistic design. Specifically, at the regional level, the integration of power grids, natural gas networks, and district heating systems into unified Regional Integrated Energy Systems (RIES) is critical for enhancing overall energy utilization efficiency, reducing costs, and achieving multiobjective optimization. This multienergy complementarity enables RIES to leverage diverse energy vectors for systemic optimization. Given these imperatives, the optimization of RIES, particularly when coupled with demand-side response mechanisms, has become a focal research area in both academia and industry in recent years.

2. Literature Review

The optimization of RIES primarily depends on two aspects: the modeling approaches and solution methods. Regarding the modeling approaches, current IES research primarily employs physical modeling based on energy mechanisms and matrix modeling based on topological structure. Most IES configurations couple electricity with one or more other energy carriers (e.g., thermal or gas). This necessitates establishing energy flow relationships among various equipment, considering the inherent characteristics of different energy forms and their conversion processes. Regarding the solution methods, RIES optimization problems are typically addressed using a diverse range of algorithms. Mathematical programming , and heuristic algorithms , are commonly used tools in current research. Building on this, the collaborative optimization of RIES using multiparameter, multistage, multilevel, , and multiobjective , approaches has become a standard practice.

In recent years, the traditional single-objective “minimum cost” optimization approach has constrained the further development of RIES. While economic analysis remains essential, energy planning necessitates a broader perspective. Consequently, more comprehensive multiobjective optimization that coordinates economic, reliability, and environmental objectives has garnered significant attention in current RIES research, despite the challenge of balancing conflicting priorities. Methods for solving multiobjective optimization models in IES are broadly categorized into a priori and a posteriori approaches. A priori methods convert multiple objectives into a single objective using techniques such as weighted coefficients and penalty factors. In contrast, a posteriori methods obtain the Pareto optimal frontier of IES models in a single run, demonstrating high applicability in multiobjective optimization. Numerous methodologies exist for achieving multiobjective optimization in modern energy systems, including weighted sum, ε-constraint, and evolutionary approaches. While weighted scalarization and ε-constraint approaches demonstrate computational efficiency for certain applications, their inherent dependence on a priori weight assignments and exhaustive parameter tuning fundamentally limits comprehensive exploration of the Pareto optimal frontier. In contrast, evolutionary algorithms offer superior flexibility for multiobjective optimization, enabling effective exploration of extensive solution spaces, management of nonconvexity, and generation of diverse trade-off solutions. Widely adopted algorithms include Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and the Nondominated Sorting Genetic Algorithm II (NSGA-II), among others. NSGA-II is particularly suited for problems with nonconvex objective spaces and mixed-integer variables, making it a common and effective choice for multiobjective optimization in energy system scheduling, , a rationale that informs our methodological selection in this study. The technique for order preference by similarity to ideal solution (TOPSIS) provides a transparent mechanism to select a final compromise solution based on definable weights, aligning with the study’s policy-analysis focus.

In energy systems, power plants are the primary source of direct carbon emissions, while electricity consumers are responsible for the indirect emissions associated with their power consumption. The rapid advancements in renewable energy technologies intensify power system volatility. While the auxiliary services (e.g., demand response or energy storage systems) are essential for safeguarding the grid stability, maintaining the system integrity, and increasing the renewable penetration rates, they also reveal the limitations of conventional annual average carbon emission factors in addressing high spatiotemporal-resolution requirements. Consequently, the introduction of the carbon emission flow (CEF) theory becomes imperative. On one hand, it facilitates precise allocation of carbon accountability to the load side, thereby guiding demand-responsive behaviors to reduce emissions and foster a low-carbon, sustainable transition of RIES; on the other hand, by building upon Kang’s foundational carbon flow calculation method for power networks and its extension to multienergy systems (which determines carbon emission obligations associated with energy consumption), CEF theory establishes a novel optimization scheduling paradigm for RIES targeting carbon emission minimization. Through this framework, energy utilization efficiency is enhanced, operational costs are reduced, and carbon emissions are mitigated, ultimately driving low-carbon economic operations.

Based on the preceding literature review, critical unresolved issues persist in the modeling and optimization of RIES, which require addressing the following key aspects:

• 1Multiobjective conflicts: economic objectives prioritize minimizing energy supply costs, while low-carbon targets necessitate dispatching higher-cost clean energy or incurring carbon costs. Concurrently maintaining the supply stability introduces a three-way conflict, demanding careful trade-offs among the economic efficiency, the emission reduction, and the system stability.
• 2The absence of carbon-driven coordination: the source-side resources (renewable units, gas turbines), the storage systems, and the load-side demand lack closed-loop coordination mechanisms driven by carbon signaling in the scheduling operations.
• 3Static carbon flow quantification: the conventional fixed emission factor methodology fails to capture the dynamic spatiotemporal variations in carbon emissions during energy transmission.

To address the aforementioned limitations, this paper proposes a bilevel coordinated low-carbon economic optimization model for multienergy systems. This model is designed to explore the energy flexibility mechanisms among multiple agents within RIES; to balance the multiobjective trade-offs; and to schedule demand response by using the time-of-use (TOU) energy pricing and dynamic carbon emission factors. The principal innovations and contributions of the proposed model are outlined as follows:

• 1A bilevel optimization framework integrating the carbon flow and demand response is proposed. The upper-level model is optimized via the NSGA-II algorithm, while the lower-level model is solved using the GUROBI solver. For balancing the multiobjective trade-offs, the technique for order preference by similarity to ideal solution (TOPSIS) method is selected for decision-making in the present study.
• 2A dual-incentive demand response signaling mechanism based on the TOU energy prices and dynamic carbon emission factors. Dynamic emission factors derived from carbon flow calculations and real-time energy prices jointly serve as demand response signals. This dual-incentive approach avoids the singular response objectives, ensuring simultaneous consideration of end-user economic efficiency and low-carbon requirements.
• 3A synergistic triobjective optimization. Economic efficiency, low-carbon performance, and system stability are coordinately optimized within RIES. This advances sustainable energy system development while enhancing grid resilience and operational reliability.

This paper is organized as follows: Section details the formulated bilevel energy scheduling and coordinated optimization model. Section 3 proposes the bilevel optimization flowchart and the solving process. Section 4 validates the proposed model through comprehensive case studies comparing multiple benchmark scenarios. Section 5 derives key conclusions and future perspectives.

3. Bi-Level Coordinated Low-Carbon Economic Optimization Model

This study develops a scheduling model for regional electricity-heat-gas integrated energy systems, dynamically dispatching distributed generation units, multienergy coupling facilities, and energy storage systems. The CEF tracking captures the real-time variations in the carbon factors across the RIES. These spatiotemporal dynamic emission factors serve as guiding signals for the low-carbon economic demand response, achieving the multiobjective co-optimization in electricity-dominant regional energy infrastructures.

3.1. Modeling of RIES

Figure illustrates the RIES architecture through the three integrated functional domains: the energy supply comprising conventional thermal/gas turbines coupled with renewable wind/PV systems and multienergy conversion facilities like heat pumps and combined heat and power (CHP) units, the electrical storage facilities providing critical grid stabilization, and the end-user electricity-heat-gas loads, collectively forming an interconnected energy ecosystem where the generation, storage, and consumption interact dynamically.

1.

Schematic of the structure and energy flow of the RIES.

The model of wind power generation equipment is depicted in eq .

$$P_{WT}(t)=\{\begin{array}{l}0,v(t)<v_m\\ \frac{v^3-v_m^3}{v_s^3-v_m^3}\times P_{WT}^r,v_m\le v(t)<v_r\\ P_{WT}^r,v_r\le v(t)<v_{out}\\ 0,v(t)\ge v_{out}\end{array}$$ 1

Where P_WT (t) is the prediction of the wind power generator at time t; v is the actual wind speed in the current environment; v_in and v_out are respectively the cut-in and cut-out wind speeds of the fan; v_r is the rated wind speed of the fan; $P_{WT}^r$ is the rated output power.

The model of photovoltaic power generation equipment is depicted in eq .

$$\{\begin{array}{l}{P}_{PV}(t)=N_{PV}{I}_{PV}(t)V_{PV}(t)f_T{f}_s\\ I_{PV}(t)=I_{sc}(\frac{R_{ad}}{R_{ad,rated}}-1)+I_{pm}\\ V_{PV}(t)=V_{pm}(1+0.0593\lg \left(\frac{R_{ad}(t)}{R_{ad,rated}}\right))\\ f_T=1-(T_{real}^{PV}(t)-T_{rated})/200\\ T_{real}^{PV}(t)=T_{ae}+30R_{ad}(t)/800\end{array}$$ 2

Where P_PV(t) is the prediction of photovoltaic power generation at time t; N_PV is the number of panels; I_sc , I_pm and I _PV (t) are the short-circuit current, peak current, and real-time current at time t, respectively; V_PV (t) and V_pm are the real-time voltage at time t and the peak voltage; f_T and f_s are the respective correction coefficients of temperature and dust; R_ad (t) and R_ad,rated are the real-time light intensity at time t and the rated light intensity; T_ae , $T_{real}^{PV}(t)$ , and T_rated are the ambient temperature, the actual temperature of the photovoltaic panel at time t and the rated temperature.

The cogeneration facility simultaneously produces electrical power and thermal energy through natural gas consumption. Its operation mode can be expressed as

$$H_{CHP}(t)=P_{CHP}(t)·\frac{{\eta }_{CH{P}_h}}{{\eta }_{CH{P}_p}}$$ 3

Where ηCHP_h and ηCHP _p are the heat and electric output efficiencies of the cogeneration unit, which the ratio ηCHP_h : ηCHP _p is assumed to be a constant of 1.0 : 1.1 in this study; H_CHP(t) is the output thermal power of the cogeneration unit at time t; P_CHP (t) is the output electric power of the cogeneration unit at time t.

Functioning as multienergy coupling facilities, gas turbine generates electric energy by consuming natural gas:

$${\mathit{P}}_{GT}(t)={\eta }_{GT}\times LCV\times G_{GT}(t)$$ 4

Where P_GT (t) is the electrical energy generated by the gas turbines at time t; η_GT is the power generation efficiency of the gas turbines; LCV is the calorific value of natural gas; and G_GT(t) is the amount of natural gas consumed by the gas turbines at time t.

The heat output of the heat pump is converted from the electrical energy drawn from the power system:

$$H_{HP}(t)=COP\times P_{HP}(t)$$ 5

Where H_HP (t) is the output heating power of the heat pump; COP is the coefficient of performance of the heat pump; P_HP (t) is the power consumed by the heat pump at time t.

Combining renewable energy generation with energy storage technologies effectively reduces the volatility of renewable energy electricity and enhances the renewable energy utilization efficiency of RIESs. The mathematical model of its operational mode is described by the following equation (also can be found in ref ).

$$SOC(t)=(1-{\mu }_{ES})SOC(t-1)+P_{ES}^{char}(t)\mathrm{\Delta }t{\eta }_{ES}^{char}-\frac{P_{ES}^{dis}(t)\mathrm{\Delta }t}{{\eta }_{ES}^{dis}}$$ 6

Where SOC(t) is the electric energy stored by the energy storage equipment at time t; μ_ES is the self-discharge rate of the power storage system; $P_{ES}^{char}(t)$ and $P_{ES}^{dis}(t)$ are the charging and discharging power of the power storage system at time t; ${\eta }_{ES}^{dis}$ and ${\eta }_{ES}^{char}$ are the discharging and charging efficiency of the power storage system.

3.2. Constraints

3.2.1. Power Balance Constraints for IES

The constraints for electricity load balancing are as follows:

$$\sum P_{g,i}(t)+P_{WT}(t)+P_{PV}(t)+P_{ES}^{dis}(t)/{\eta }_{ES}^{dis}-P_{ES}^{char}(t)+P_{CHP}(t)-P_{HP}(t)+\sum P_{DR,k}(t)=P_{load}(t)$$ 7

$$H_{CHP}(t)+H_{HP}(t)=H_{load}(t)$$ 8

Where P _g,i (t) is the output power of the i-th conventional unit; P_DR,k(t) is the load variation of the demand response for the k-th category; P_load(t) and H_load (t) are the electricity load and the heat load.

3.2.2. Operational Constraints of Equipment within RIES

$$P_{g,i}^{min}\le P_{g,i}(t)\le P_{g,i}^{max}$$ 9

$$P_{GT,j}^{min}\le P_{GT,j}(t)\le P_{GT,j}^{max}$$ 10

$$P_{CHP}^{min}\le P_{CHP}(t)\le P_{CHP}^{max}$$ 11

$$P_{hp}^{min}\le P_{HP}(t)\le P_{HP}^{max}$$ 12

$$SO{C}_{ES}^{min}\le SO{C}_{ES}(t)\le SO{C}_{ES}^{max}$$ 13

$$0\le P_{ES}^{dis}(t)\le P_{ES}^{max}$$ 14

$$0\le P_{ES}^{char}(t)\le P_{ES}^{max}$$ 15

Where the subscripts max and min denote the upper and lower operational power boundaries of the corresponding equipment. In addition, the charging and discharging processes for the energy storage systems are mutually exclusive.

3.2.3. Slope Rate Constraint

The output power is constrained within a defined operational range via ramp rate limitations, thereby preventing the thermal stress damage of the turbine components from high-temperature steam exposure. The constraints can be referred to ref .

3.2.4. Demand Response

$$P_{DR,k}^{min}\le P_{DR,k}(t)\le P_{DR,k}^{max}$$ 16

Where $P_{DR,k}^{min}$ and $P_{DR,k}^{max}$ are the minimum and maximum dispatchable volumes for the k-th type of demand response load, respectively.

3.3. CEF Model

Accurate power flow calculation, which determines steady-state operating conditions under given network configurations, system parameters, and boundary constraints, is fundamental for CEF calculation. Building upon these power flow results, CEF dynamically traces carbon source-sink distribution by quantifying coupling relationships between power flow distribution and generator emission intensities. Both power flow calculation and CEF calculation are topology-dependent. Furthermore, CEF calculation is further governed by variations in the generator emission characteristics.

Per energy conservation principles, the carbon emission factor at any network node equals the weighted average of factors from all injected energy streams. The calculation formula of the node carbon emission factor is

$${\rho }_{b,t}=\frac{\sum _{i\in T{G}_b}{P}_{i,t}{\rho }_i+\sum _{(l,b)\in L^{b+}}|f_{lb,t}|{\rho }_{lb,t}}{\sum _{i\in T{G}_b}{P}_{i,t}+\sum _{(l,b)\in L^{b+}}|f_{lb,t}|},\forall b$$ 17

Where ρ _b,t is the carbon emission factor of node b at time t; TG_b is the set of generating units on node b; L^{b +} is the set of inflow branches of node b; P_i,t is the output power of generator i; ρ_i is the carbon emission factor of the i-th generator; f_lb,t is the branch flow on line l–b at time t; ρ_lb,t is the carbon emission factor of branches on line l–b at time t.

In this iterative framework, the CEFs are calculated ex-post based on the dispatch result from the upper-level optimization. These CEFs then serve as fixed parameters in the lower-level demand response optimization for the subsequent iteration, forming a sequential (open-loop) coordination mechanism.

3.4. Electricity-Heat-Gas Network Model

Heating networks, gas supply networks, and transmission grids function as integrated components within RIES, with detailed modeling methodologies referenced in existing literature. ,

3.5. Objective Function

3.5.1. Upper-Level Optimization

The fundamental operational paradigm for RIES is to reduce the economic expenditures subject to the constraint of ensuring the safe operation of all integrated equipment. Consequently, the upper-level subproblem focuses on minimizing the comprehensive economic cost, operating under given load profiles, and the optimal combination of equipment output at each time period is obtained using the GUROBI solver. The comprehensive economic cost of RIES comprises equipment operating costs, costs of energy purchases, battery degradation and maintenance expenses, the start–stop cost of devices, and the penalties of solar curtailment and wind curtailment.

$$\min F_1=\sum _{t=1}^{24}(F_{G,t}+F_{buy,t}+F_{ES,t}+F_{ss,t}+F_{pen,t})$$ 18

Where F₁ is the comprehensive economic cost of upper-level optimization; F_G,t is the equipment operating costs of RIES at time t; F_buy,t is the cost of gas purchases at time t; F_ES,_t is the degradation and maintenance cost of energy storage; F_ss,t is the start–stop cost of devices; F_pen,t is the penalty for solar curtailment and wind curtailment.

$$\{\begin{array}{l}{E}_{\mathrm{G},t}=\sum _{i=1}^{N_{\mathrm{g}}}(c_{g,1,i}{P_{g,i}(t)}^2+c_{g,2,i}{P}_{g,i}(t)+c_{g,3,i})\\ F_{buy,t}=c_{\mathrm{g}\mathrm{a}\mathrm{s}}{G}_t^{\mathrm{g}\mathrm{a}\mathrm{s}}\\ F_{ES,t}=c_{ES}(P_{ES}^{dis}(t)‐P_{ES}^{char}(t))+c_m(P_{ES}^{dis}(t)‐P_{ES}^{char}(t))+{\pi }_{ES}{u}_{ES,ss,t}\\ F_{ss,t}=\sum _{i=1}^{N_{\mathrm{G}}}{c}_{g,ss,i}(1‐u_{\mathrm{G}i,t‐1})u_{\mathrm{G}i,t}\\ F_{pen,t}=c_{\mathrm{p}\mathrm{e}\mathrm{n},\mathrm{P}\mathrm{V}}(P_{PV}(t)‐P_{PV}^{con}(t)+c_{pen,WT}(P_{WT}(t)‐P_{WT}^{con}(t)\end{array}$$ 19

Where N_g is the number of conventional units; c _g,1,i , c _g,2,i and c _{g,3, i} are the power generation cost coefficients of the i-th conventional unit, respectively; c _gas is the cost coefficient corresponding to the natural gas consumed by the system; $G_t^{\mathrm{gas}}$ is the natural gas consumption during period t; c_ES is the cost coefficient of energy storage; c_m is the maintenance cost coefficient of energy storage; π _ES is the degradation cost coefficient of energy storage; u_ES,ss,t is the start–stop state of the energy storage at time t; c_g,ss,i is the start–stop cost coefficient of the i-th conventional unit; u_g,t is the start–stop state of the i-th conventional unit at time t; c _pen,PV and c_pen,WT are penalty cost coefficients of solar curtailment and wind curtailment respectively; $P_{PV}^{con}(t)$ and $P_{WT}^{con}(t)$ are the consumptions of solar and wind power in the power system, respectively.

3.5.2. Lower-Level Optimization

The lower-level optimization focuses on the demand-side response of end-users within the RIES. Given the time-varying electricity prices and heat prices provided by the system operator, as well as the dynamic carbon emission factors derived from the upper-level dispatch results, users adjust their electricity and heat consumption profiles to minimize their own comprehensive costs while contributing to system-wide low-carbon and stable operation. The decision variables are the demand response quantities for electricity and heat, categorized into curtailable loads and shiftable loads.

$$\min F_{2,DR}=\sum _{k=1}^K\sum _{t=1}^{24}(w_{p,t}{P}_{load}(t)+w_{h,t}{H}_{load}(t)-c_{DR,k}{P}_{DR,k}(t))$$ 20

$$\min F_{2,carbon}=\sum _{t=1}^{24}(E{F}_{p,t}{P}_{load}(t)+E{F}_{h,t}{H}_{load}(t))$$ 21

$$\min F_{2,load}=\frac{\sum _{t=1}^{24}{(P_{load}(t)-\overline{P_{load}})}^2}{24}$$ 22

Where _F2,DR is the cost of DR; w_p,t and w_h,t are the time-of-use prices of electricity and heat; c _DR,k is the compensation cost coefficient of the k-th DR; F_buy,t is the cost of gas purchases at time t; K is the number of types of demand response; F _2,carbon is the total carbon emission of RIES; EF_p,t and EF_h,t are the dynamic electricity and heat carbon emission factor respectively; F_{2, load} is the variance of real-time electricity load throughout a day.

Minimizing load variance serves critical practical purposes beyond mathematical optimization. A smoother load profile directly reduces the demand for fast-responding regulation reserves, alleviates stress on frequency control systems by minimizing sudden power imbalances, and mitigates wear-and-tear on conventional generators from excessive ramping. This objective thus translates to enhanced grid stability, and reduced operational risks, aligning the optimization framework with real-world power system security and economic imperatives.

4. Solution Method

The overall optimization problem is structured as a coordinated bilevel framework, combining a single-objective upper-level problem with a multiobjective lower-level problem, rather than a monolithic triobjective optimization. The upper-level performs economic dispatch using the GUROBI solver to minimize operational costs under given load profiles. The lower-level employs the NSGA-II algorithm to generate a Pareto front that captures the trade-offs among user energy cost, carbon emissions, and load stability, in response to the price and carbon signals from the upper level. These two layers are coordinated through an iterative heuristic process, exchanging updated load profiles and carbon emission factors until convergence.

Multiobjective optimization allows for the individual optimization of each objective function; however, identifying a single solution that perfectly satisfies all objectives simultaneously is extremely challenging, particularly when these objectives are in conflict with one another. The fundamental difference between multiobjective and single-objective optimization is the lack of a unique optimal solution; instead, a set of Pareto optimal solutions exists. The Nondominated Sorting Genetic Algorithm II (NSGA-II) enhances the overall benefits in energy system scheduling by effectively balancing convergence and solution diversity in multiobjective optimization. Due to its low computational complexity and robust capability in managing mixed variables, NSGA-II provides robust solutions for complex engineering optimizations and has been widely implemented across various energy systems.

This study establishes a bilevel optimization model for the RIES, which is solved using a combination of the GUROBI and NSGA-II algorithm. The optimization yields a Pareto frontier solution set, upon which the TOPSIS method is applied for decision-making. Through the iterative coordination between the upper and lower levels, this framework achieves a trade-off-balanced system configuration and operational planning (Figure ). The weights assigned to the economic, carbon, and stability objectives in the TOPSIS method are scenario-specific, reflecting different policy priorities (e.g., carbon-focused, economy-focused, or balanced). They are set to illustrate the potential outcomes under distinct stakeholder perspectives. Adjustments must be made based on different application scenarios.

2.

RIES bilevel optimization process.

4.1. Step 1: System Initialization

Input the forecasted local wind and solar generation profiles, the nodal topology of electricity-heat-gas networks, and the trienergy load demands. Initialize the RIES optimization model with key parameters, including the NSGA-II population size, the TOPSIS weighting criteria, and the equipment operational constraints.

4.2. Step 2: Upper-Level Optimization

Perform the power balance calculations while adhering to network constraints (e.g., the voltage limits, the pipeline pressures). GUROBI is used to minimize the total operational costs. Output the optimal dispatch schedules for generation, conversion, and storage devices.

4.3. Step 3: Dynamic Carbon Accounting

Calculate the node-specific carbon emission factors using the CEF theory, and conduct an electricity-heat network power flow analysis to capture the spatiotemporal variations in emissions.

4.4. Step 4: Lower-Level Multi-Objective Optimization

Input the upper-level results and the dynamic carbon factors. Predict demand response behaviors with a focus on user economics, carbon reduction, and load stability. Solve the multiobjective optimization using NSGA-II to obtain the Pareto frontiers, then apply TOPSIS to select the optimal solution. Output the optimized electricity-heat load profiles.

4.5. Step 5: Iterative Convergence

Evaluate the deviations between the optimized and initial loads. If the convergence criterion is not met, feed the updated loads back into Step 2. The process continues until a balanced equipment configuration and operational schedule are achieved.

4.6. Step 6: Comparative Validation

Simulate three preference-oriented schemes under typical daily operations to validate the model’s effectiveness by evaluating the performance of the electricity, heat, and gas subsystems.

5. Case Studies

5.1. System Configuration

The selected RIES in this study comprises the 30-bus power system, the 20-node natural gas system, and the 8-node thermal system, as illustrated in Figure . Figure illustrates the predicted wind and PV generation output for a typical day. Figure depicts the electricity, heat, and gas loads required by users in the system. The RIES is required to provide electricity and heat to users throughout the day, adopting TOU electricity and heat prices. The key electrical equipment parameters required in the RIES are listed in Tables –. (Table ) Data for the thermal and natural gas network modeling are provided in Appendix A.

3.

Topology of the RIES.

4.

Renewable energy generation data on a typical day.

5.

Electric, heating, and gas load on a typical day.

1. RIES Equipment Parameters.

Unit	Type of power generation	$P_g^{max}$ /MW	$P_g^{min}$ /MW	a/(CNY/(MW)2)	b/(CNY/(MW))	c/(CNY)	Max slope rate (MW/h)
G1	Coal	150	50	0.0375	20	375.5	72
G2	Coal	120	30	0.175	17.5	352.3	48
G3	Coal	100	25	0.625	10	316.5	60
G4	Natural gas	80	20	0.0834	32.5	329.2	60
G5	Natural gas	60	15	0.25	30	276.4	48

3. Energy Storage Parameters.

Energy storage capacity (MW)	Maximum hourly charge/discharge capacity (MW)	Charge loss coefficient	Discharge loss coefficient
500	200	0.98	0.96

2. HP Parameters.

$P_{HP}^{max}$ (MW)	$P_{HP}^{min}$ (MW)	COP
100	0	3

This section designs three scenarios to validate the feasibility and the effectiveness of the proposed algorithm.

Scenario 1: This scenario employs a single-layer optimization framework, focusing solely on economic objectives without considering demand response (DR) mechanisms. This scenario serves as a benchmark and is solved using the Gurobi solver.

Scenario 2: This scenario introduces a bilevel optimization framework, incorporating DR mechanisms and optimizing for both economic and low-carbon objectives. In this structure, the upper-level problem is handled by the Gurobi solver, while the lower-level problem is solved using the NSGA-II algorithm.

Scenario 3: Building upon Scenario 2, this scenario further integrates load stability into the optimization objectives, forming a bilevel optimization framework with economic, low-carbon, and load stability goals. The upper-level problem continues to be solved by Gurobi, and the lower-level problem by the NSGA-II algorithm.

Given that the natural gas network in this study does not feature complex equipment configurations or fluctuations in emission factors, the analysis and the discussion of the results will primarily focus on the electricity and the thermal systems.

5.2. Results and Discussion

Figure presents a heatmap illustrating the real-time electricity carbon emission factors for each node within the RIES. The electricity carbon emission factors are intrinsically determined by both the node’s geographical location and the real-time generator dispatch configuration. As shown in Figure , nodes 8 and 21–30 exhibit consistently lower carbon emission factors compared to other nodes. This reduction is primarily attributed to the RIES’s design, where gas-fired generator units predominantly supply power to the regions of nodes 21–30, and renewable energy sources (wind power) are exclusively dedicated to node 8. These configurations collectively establish a lower-carbon regional power structure, leading to comparatively smaller carbon emission factors than other nodes primarily supplied by coal-fired units. Furthermore, during the three time periods, 1:00–6:00, 12:00–14:00, and 21:00–24:00, the overall carbon emission factor is lower than in other time slots. This is because the RIES electricity system integrates a greater share of renewable energy during the nighttime hours, characterized by surging wind power generation, and during the midday hours, which experience peak photovoltaic output.

6.

Heatmap visualization of real-time nodal carbon emission factors in Scenario 3.

However, since user locations cannot be arbitrarily altered, the adoption of overly granular carbon emission factors could impede the equitable distribution of carbon responsibility. This would inevitably impose an undue emission burden on end-users situated far from renewable energy generation facilities. Consequently, this optimization study adopts a unified system-wide carbon emission factor for real-time carbon accounting.

The exclusive pursuit of either low-carbon objectives or economic efficiency may impose substantial burdens on energy systems. The aggregate system costs, carbon emissions, and load variation metrics for the RIES under investigation are comprehensively detailed in Table . As quantified, the aggregate system costs register at 4.54 × 10⁵ CNY for Scenario 1, 4.27 × 10⁵ CNY for Scenario 2, and 4.07 × 10⁵ CNY for Scenario 3, a progressive reduction pattern. Notably, Scenario 3 achieves the lowest total cost, reflecting a 10.29% reduction compared to Scenario 1 and a 4.77% decrease relative to Scenario 2. Convergence of the heuristic iterative coordination process was consistently achieved within 30 iterations across all scenarios, validating the practical robustness of the proposed framework in resolving conflicts between the economic dispatch layer and the multiobjective demand response layer (Tables –).

4. Running Results of Three Scenarios.

			Load variation (MW)		Load variance
Scenario	Total cost (CNY)	Carbon emissions (t)	Electricity	Heat	Electricity	Heat
Scenario 1	453,636.90	7,910.27	/	/	5,197.48	18.59
Scenario 2	427,327.78	7,033.10	–3.84%	–3.90%	7,420.80	67.84
Scenario 3	406,942.05	7,797.86	–6.18%	–5.80%	2,564.08	22.07

A1. Basic Parameters of Gas Source.

Gas source node	Lower limits of flow/Mm3	Upper limits of flow/Mm3
1	0.90	1.7391
2	0	1.26
5	0	0.72
8	1.00	2.3018
13	0	0.27
14	0	1.44

A3. DR Compensation Cost Coefficient.

Type		Compensation cost coefficient/(CNY/MWh)
Electricity	Curtailable load	150
	Shiftable load	100
Heat	Curtailable load	75
	Shiftable load	50

Scenario 1 exhibited the highest carbon emissions, primarily due to the absence of electricity demand response implementation. In contrast, the carbon emissions in Scenario 2 were significantly reduced, which is mainly attributed to its carbon reduction measures not accounting for load stability. Figure presents a comparison of the electric and thermal loads for Scenarios 2 and 3, both before and after optimization. It is evident that while Scenario 2 achieved substantial emission reductions, it also exhibited significant load fluctuations. Conversely, Scenario 3 strikes a balance among economic benefits, carbon emissions, and load stability. It not only reduced system costs and carbon emissions but also ensured stable operational states by maintaining a smoother load profile. Figure and Figure , respectively, illustrate the power output distribution of conventional units and the dynamic balance of the electric load across the three scenarios. Analysis of the information presented in these figures reveals that the demand response strategy in Scenario 2 is implemented by shifting or curtailing load without prioritizing load stability, coupled with a reliance on energy storage systems to compensate for the load instability. Furthermore, the overall power output of conventional units in Scenario 2 also exhibited a slight downward trend. Given that conventional units constitute the primary source of carbon emissions in this RIES, these combined factors led to Scenario 2 achieving the lowest overall carbon emissions among the three scenarios. A carbon market perspective further enriches the comparison among scenarios. Assuming a carbon price of 90 CNY/tCO₂, the 877.17 t reduction in Scenario 2 could yield about 78,945 CNY in revenue. This partially offsets its operational cost disadvantage. This highlights that carbon pricing can reshape the economic trade-offs between strategies, underscoring the importance of incorporating market signals when evaluating dispatch models that balance cost, emissions, and stability.

7.

Comparison of load profiles before and after optimization in different scenarios: (a) electricity load in Scenario 2, (b) heat load in Scenario 2, (c) electricity load in Scenario 3, and (d) heat load in Scenario 3.

8.

Power output distribution of conventional units in three different scenarios: (a) Scenario 1, (b) Scenario 2, and (c) Scenario 3.

9.

Dynamic balance of electrical load in three different scenarios: (a) Scenario 1, (b) Scenario 2, and (c) Scenario 3.

The integration of various demand response signals enhances optimization opportunities for RIES. Figure depicts the real-time electric load fluctuations for Scenarios 2 and 3 when both TOU pricing and dynamic carbon emission factors are implemented. When TOU electricity tariffs and carbon emission factors are used together as demand response signals, these two incentive mechanisms can produce complex synergistic or conflicting interactions. Typically, when both signals are at high levels, the electric load is anticipated to rise; conversely, when both are at low levels, the load is expected to decrease. However, in scenarios where the high and low levels of these signals are misaligned, the actual system operation requires trade-offs among multiple objectives, resulting in nondeterministic patterns of change. Scenario 2, which overlooks load stability constraints, shows disordered optimization results. Specifically, between 1:00 and 5:00, load fluctuations alternate between positive and negative deviations, rather than following consistent patterns. Notably, at 10:00, when both the power price and carbon emission factors peak, the load unexpectedly experiences an increase. In contrast, Scenario 3 demonstrates stable and orderly demand response fluctuations throughout the optimization period. The optimization outcome in Scenario 3 mainly concentrates on load reduction. From 1:00 to 5:00, both the power price and carbon emission factors are kept at constant levels, while the electric load during this interval shifts from a decrease to an increase. This particular load profile aims to reduce the peak-to-trough difference in electricity demand, aligning with the optimization goal of minimizing overall load fluctuations. From 6:00 to 24:00, both the power price and emission factors are generally higher than in the previous period. Consequently, all load changes during this time are reductions, though their extent varies significantly. Specifically, substantial load reduction is implemented during periods characterized by peak power prices and elevated carbon emission factors, such as between 10:00 and 19:00. Slight load reduction occurs during the period of shoulder power price and comparatively lower carbon emission factor (e.g., 13:00–14:00).

10.

TOU, carbon emission factors, and electrical load variations in different scenarios: (a) Scenario 2, (b) Scenario 3.

6. Conclusion

This study proposes a comprehensive optimization planning framework for RIES, which incorporates dynamic carbon emission factors and demand response. The aim is to minimize system costs and carbon emissions while maintaining load stability. The multiobjective optimization problem is solved using the NSGA-II, with the TOPSIS method employed to select the optimal solution from the Pareto front. Results demonstrate that the multiobjective optimization of RIES effectively reduces both system costs and carbon emissions. However, ensuring stable system operation often requires a trade-off, necessitating a compromise between economic efficiency and low-carbon objectives.

To thoroughly analyze these multiobjective trade-offs, three different scenarios are established. The key findings are summarized as follows:

• 1Demand response consistently reduces the load. Regardless of whether system load stability is incorporated as an optimization objective, it leads to a 3.50–6.50% reduction in both the electric and thermal loads.
• 2Explicitly incorporating load stability as a lower-level optimization objective significantly impacts system performance. Specifically, the carbon emission reduction rate declines markedly from −11.09% in Scenario 2 to −1.42% in Scenario 3. Conversely, the system costs decrease even further, falling from −5.80% to −10.29% over the same scenarios. These results indicate inherent conflicts among the different optimization objectives, demonstrating that achieving balance requires careful trade-offs based on specific system priorities.
• 3Ancillary services, including energy storage and demand response, are pivotal in mitigating load volatility. Comparisons of the optimization results across different scenarios reveal that the conventional generation units tend to maintain their stable operation, demonstrating significantly less flexible regulation capabilities compared to the energy storage systems when responding to abrupt load variations.

A2. Heat Medium Flow Rate of 8-Node Thermal System.

Inflow node	Outflow node	Flow velocity/(kg/s)
1	2	388.10
2	3	339.22
2	5	24.44
2	7	24.44
3	4	143.58
3	6	97.82
3	8	97.82

With the rapid advancement of renewable energy technologies, future research should prioritize the integration of uncertainty modeling into planning and optimization frameworks. A crucial first step in this direction is to formally distinguish between and model two key types of variability: predictable, time-varying dynamics (such as the diurnal patterns of energy prices and carbon factors addressed in this study) and inherent stochastic uncertainty (such as renewable generation forecast errors). Such integration will improve the reliability and resilience of energy systems while also driving innovation in energy management strategies. To effectively address prediction inaccuracies in wind and solar power generation, stochastic programming and robust optimization methods should be adopted. Furthermore, in response to the rapidly growing electricity demand from electric vehicle (EV) charging stations, it is essential to develop grid-interactive charging pile models. These models should systematically assess the load-shaping potential of EV charging networks and investigate regulatory mechanisms that allow charging infrastructure to partially substitute traditional energy storage systems. Such efforts will contribute significantly to building more resilient and adaptive regional integrated energy systems (RIES).

Appendix A

See Tables –.

Y.L.: writing-original draft, writing-review and editing, visualization, validation, software, methodology, formal analysis, investigation, data curation, and conceptualization. Z.L.: writing-review and editing, writing-original draft, conceptualization, and supervision. H.Q.: investigation and project administration. Z.L.: investigation and project administration. X.L.: writing-review and editing. G.L.: resources and funding acquisition. Q.W.: resources and funding acquisition. P.W.: resources and funding acquisition. J.Y.: resources and funding acquisition. S.Y.: project administration, supervision, and funding acquisition.

The authors declare no competing financial interest.