Capacity Optimization of Integrated Energy Systems Considering Carbon-Green Certificate Trading and Electricity Price Fluctuations

Abstract

In order to study the impacts of the carbon-green certificate trading mechanism and the fluctuation of feed-in tariffs on the low-carbon and economic aspects of the investment and operation of the integrated energy system, and to transform the system carbon emission into a low-carbon economic indicator, a two-layer capacity optimization allocation model is established with the objectives of the investment, operation, and maintenance cost and the operation cost, respectively. For the source-load uncertainty, the scenario reduction theory based on Monte Carlo simulation and Wasserstein distance is used to obtain the per-unit value of wind and photovoltaic output, and the K-means clustering method is used to obtain the typical day of electric-heat-cold multi-energy load. Based on the geometric Brownian motion in finance to simulate the feed-in tariffs under different volatilities, the multidimensional analysis scenarios are constructed according to different combinations of carbon emission reduction policies and tariff volatilities. The model is solved using the non-dominated sorting genetic algorithm (NSGA-II) with mixed integer linear programming (MILP) method. Case study results show that under the optimal scenario considering policy interaction and price volatility (δ = 1.0), the total annual operating cost is reduced by approximately 17.9% (from 2.80 million CNY to 2.30 million CNY) compared to the baseline with no carbon policy. The levelized cost of the energy system reaches 0.2042 CNY/kWh, and carbon-green certificate trading synergies contribute about 70% of the operational cost reduction. The findings demonstrate that carbon reduction policies and electricity price volatility significantly affect system configuration and operational economy, providing a new perspective and decision-making basis for integrated energy system planning.

1. Introduction

Against the dual backdrop of the increasingly prominent global energy security crisis and the continuous intensification of ecological and environmental pressures, improving the utilization efficiency of renewable energy and building a clean, safe, and low-carbon modern energy system have become a strategic consensus among countries worldwide. As a core carrier and key technological pathway for energy transformation and upgrading, the Integrated Community Energy System (ICES) realizes the synergistic conversion and optimal allocation of multiple energy forms, including electricity, heat, cooling, and gas. By doing so, it facilitates the efficient and integrated utilization of external purchased energy and local distributed resources, thereby establishing itself as a pivotal solution for advancing the energy system toward high efficiency, low carbon, and sustainability. This pursuit carries particular urgency for China, which has formally committed to an ambitious dual-carbon timeline, aiming to peak carbon emissions by 2030 and achieve carbon neutrality by 2060 [1].

In this context, market-based mechanisms are widely recognized as indispensable and powerful means for orchestrating a smooth and cost-effective green and low-carbon transition of the entire energy sector [2]. Learning from and adapting to international development trends, China, though a later starter in the field of integrated energy systems, has proactively established critical market-based policy instruments to drive its decarbonization agenda. Notably, the official launch of the national Carbon Emissions Trading (CET) system marks a foundational step towards leveraging market forces to reduce overall societal emissions [3]. Complementing this, the introduction of the Tradable Green Certificate (TGC) mechanism under the Renewable Portfolio Standard provides a dedicated tool to financially support and incentivize renewable energy power generation [4]. The ongoing challenge and research focus lie in effectively integrating and coordinating these market mechanisms within the evolving power market structure. The ultimate goal is to maximize their synergistic effectiveness, a task in which the integrated and flexible nature of ICES is expected to play an increasingly critical role.

Guided by the “dual carbon” goals, the CET and Green Certificate Trading (GCT) mechanisms have become core market-oriented tools to guide the low-carbon operation of ICES. Existing research has validated their effectiveness in providing economic incentives for renewable energy and reducing system emissions [5], and has shown that parameters like carbon price can directly influence low-carbon equipment configuration [6]. Concurrently, innovative market designs [7] and advanced modeling approaches for multi-actor coordination [8] and uncertainty management [9] have been developed to enhance operational flexibility and economic efficiency. However, existing research still has obvious limitations and fails to solve a series of key issues, including but not limited to: (1) When the CET and GCT mechanisms are implemented individually or collaboratively, what are their impact mechanisms on the capacity allocation, economic operation, and low-carbon benefits of ICES, and how to give full play to the synergistic effects of these two market-oriented emission reduction policies? (2) The fluctuation of electricity market prices has a profound impact on the cost recovery path of ICES capacity investment and economic operation efficiency; how to effectively characterize this multi-market interaction mechanism in the capacity optimization model? (3) The issue of electricity price fluctuations caused by changes in supply and demand in the distribution network market has not been fully considered; how to construct an ICES capacity optimization configuration scheme adapted to this characteristic?

To address the above issues, this paper proposes a study on the capacity optimization configuration of ICES considering carbon-green certificate trading and electricity price fluctuations. Firstly, an improved geometric Brownian motion model based on weight adjustment factors is adopted to simulate the system’s electricity sales price. Combined with the costs and benefits under the carbon-green certificate trading mechanism, a two-layer optimization model is constructed: the upper layer establishes a capacity planning optimization model with the goal of minimizing construction investment costs and operation and maintenance costs, while the lower layer establishes an operation optimization model with the goal of minimizing system operation costs. Finally, the non-dominated sorting genetic algorithm (NSGA-II) and mixed-integer linear programming (MILP) method are used for solving, and the optimal capacity configuration scheme considering both economy and low carbon is obtained, providing theoretical support for the scientific planning and efficient operation of ICES.

2. Literature Review

2.1. Research Status of Carbon Emission Trading (CET) Mechanism

The CET mechanism plays a key role in the global low-carbon transition, and the European Union is the first region to carry out relevant explorations. Ref. [10] systematically demonstrates the institutional flaws in the phased carbon regulatory mechanism under the EU Emissions Trading Scheme by analyzing the correlation between international carbon price fluctuations and domestic emission reduction effects in sectors outside the EU. Based on a comparative study of policy effects, ref. [11] finds that compared with the emission reduction path based on intensity control, the adoption of a total quantity control strategy can more effectively improve the implementation efficiency and target achievement rate of government emission reduction policies. From the perspective of institutional design, ref. [12] comparatively analyzes two carbon trading models: the pure auction mechanism based on emission sources and the mixed auction system integrating capacity allocation weights, revealing the differential impacts of different mechanism designs on the behavioral patterns of market participants.

In relevant research in China, ref. [13] uses the SWOT analysis to conduct an in-depth discussion on the impact of the carbon emission trading system on the power industry, providing ideas for the low-carbon and sustainable development of the power industry. Ref. [14] further confirms that the carbon emission trading system will affect the on-grid electricity price of China’s power market, the installed capacity of renewable energy and thermal power, and calls for the establishment of a reasonable trading mechanism. Ref. [15] shows that the carbon emission trading market has a significant role in promoting carbon emission reduction in high-energy-consuming enterprises, and government participation will further strengthen this effect, especially for non-state-owned enterprises.

In terms of the optimization of mechanism practice, ref. [16] confirms that the introduction of carbon emission trading into the system dispatch model can significantly improve the low-carbon economic operation efficiency of the system. On this basis, ref. [17,18] introduce a ladder-type carbon pricing strategy into carbon source equipment, and the research finds that compared with the traditional fixed carbon price model, ladder-type pricing can significantly reduce the carbon intensity of high-emission units, effectively strengthening the technical compelling mechanism for enterprises to reduce emissions.

2.2. Research Status of Green Certificate Trading (GCT) Mechanism

The green certificate trading mechanism has been institutionalized in more than 30 energy systems around the world, providing a flexible compliance method for quota-obligated entities. Based on an empirical study of 12 leading renewable energy states in the United States, ref. [19] shows that the design of the quota system can not only effectively improve the grid connection and absorption ratio of wind power and photovoltaic power but also drive the low-carbon technological innovation of power generation enterprises through market competition. However, ref. [20] points out that policy iteration and fluctuations are likely to cause shocks in the green certificate trading market. In response to this, ref. [21] innovatively proposes a mixed trading mechanism that introduces financial derivatives into the traditional green certificate trading system, weakening the negative effects of sharp price fluctuations by establishing a risk mitigation mechanism.

From the perspective of transaction costs and welfare effects, reference [22] constructs an intermediary service cost model and empirically verifies that information circulation and cost expenditure in the transaction process may weaken the expected benefits of green certificate system design, especially in the initial stage of market development. In contrast, ref. [23] confirms through marginal cost curve analysis that green certificate trading can promote social welfare accumulation by reducing marginal transaction costs.

At the policy coordination level, ref. [24] constructs an analytical framework using policy network theory, reveals the policy coupling effect between the green certificate trading system, the carbon market, and the power market, and proposes that a policy coordination framework should be constructed through legislative guarantees and market transparency construction. Focusing on the cutting-edge direction of carbon-green certificate trading coupling, ref. [25] considers the life-cycle carbon emissions of new energy and the carbon emission reduction attributes of green certificates, proposes a ladder-type dynamic carbon-green certificate coupling trading mechanism, and configures the optimal capacity with the goal of optimal comprehensive performance. Ref. [26] uses stochastic programming methods to quantitatively analyze the price linkage mechanism of carbon and green certificates, revealing that when the correlation of price fluctuations between the two types of markets exceeds a certain value, the system operation cost will produce a significant synergistic amplification effect.

2.3. Research Status of CET-GCT Coordination and Electricity Price Mechanism

In terms of policy coordination, existing research has begun to pay attention to the interaction between the CET and GCT mechanisms, but relevant achievements are still relatively limited. Most studies still focus on the impact of a single mechanism, and there is insufficient discussion on the synergistic linkage effect between the two mechanisms, failing to give full play to the comprehensive effectiveness of market-oriented emission reduction policies.

In terms of research on electricity price mechanisms and distribution network markets, China’s new energy participation in the power market is characterized by two core features: the parallel operation of the guaranteed contract mechanism and the power market transaction mechanism on a dual-track basis, and the regionalization of market-oriented mechanisms. Fourteen provinces with poor consumption capacity implement the full guaranteed absorption system for renewable energy and carry out green certificate trading, while regions with strong consumption capacity construct a “benchmark guarantee + market-oriented” composite consumption system. Ref. [27] adopts peak pricing (belonging to the category of time-of-use electricity price), which effectively reduces the interaction risk between the system and the power grid and improves the economic efficiency of operation.

In addition to traditional pricing models, emerging technologies and game theory have also been applied to electricity price mechanism design. Ref. [28] adopts distributed peer-to-peer transactions between blockchain and microgrids to generate smart transaction contracts containing energy prices, realizing decentralization compared with centralized transactions and making transactions more flexible. Ref. [29] adopts a leader-follower game pricing mechanism with the distribution network as the leader and multiple types of microgrids as followers, achieving a win-win situation for different stakeholders through optimization, but small-scale energy entities are relatively passive in the multi-entity market. It is worth noting that the pricing strategy in the economic operation stage of ICES has the nature of a dynamic game, and its effectiveness depends on the market environment and supply-demand relationship. In the planning stage, the electricity price mechanism directly affects the capacity configuration of system equipment and the final dispatch plan.

2.4. Research Status of Capacity Optimization Configuration of Integrated Community Energy System (ICES)

Existing research has made considerable progress in equipment coupling, target design, uncertainty handling, energy storage configuration, and optimization methods for ICES capacity optimization configuration.

In terms of equipment coupling, ref. [30] proposes a hydrogen energy chain planning framework that integrates the entire process of hydrogen production, storage, and application energy flow, optimizing the bottom-up long-term investment strategy. Ref. [31] constructs a refined dynamic model of distributed power sources, hybrid energy storage, and electricity-hydrogen-gas coupling equipment, effectively reducing the comprehensive planning and operation costs of the system. Ref. [32] simultaneously introduces power-to-hydrogen and carbon capture systems into the system, establishing a multi-stage dynamic planning model to promote local consumption of electrical energy and reduce carbon emissions. Ref. [33] constructs a regional integrated energy system of power-to-methanol, reducing greenhouse gas emissions by converting renewable energy power into methanol. Ref. [34] adds a hydrogen energy multi-scale regulation system to ICES, confirming its unique advantages in economic costs and carbon emission reduction. Ref. [35] adds a power-to-ammonia system to the system and uses liquid ammonia to convert into pure ammonia for refrigeration, exploring the economic operation of system dispatch under system coupling. Ref. [36] proposes an energy station-network collaborative planning method to address the impact of energy network investment on the collaborative optimization of energy stations and networks in ICES planning, optimizing equipment capacity and topological structure.

In terms of uncertainty handling, ref. [37] adopts the synchronous back-substitution elimination algorithm combined with K-means clustering for deterministic conversion of source-load uncertainty, establishing a capacity optimization model. Ref. [38] constructs a capacity optimization model including construction time sequence considering uncertainty, confirming that phased planning can significantly reduce the total cost compared with one-time planning at the beginning of the year.

In terms of energy storage configuration, ref. [39] constructs an optimization model containing Liquid Carbon Dioxide Energy Storage (LCES), and the results show that LCES can effectively reduce the operation cost of ICES. On the basis of considering combined gas-steam cycle units and power-to-hydrogen heat, ref. [40] adds Compressed Air Energy Storage (CAES) to explore its economic operation potential in system dispatch. Ref. [41] proposes a capacity optimization configuration model of electrolytic hydrogen production and hydrogen energy storage, and the case study verifies the advantages of the model in economy and low carbon.

In terms of optimization methods, ref. [42] considers the uncertainty of renewable energy, establishes a two-layer optimization model with operation cost and investment cost as objectives, and uses the particle swarm optimization algorithm to solve multi-objective problems. Ref. [43] proposes a two-stage robust planning method, with the goal of minimizing investment cost and energy dispatch cost, and uses the nested column-and-constraint generation (NC&CG) algorithm for solving. Ref. [44] sets a multi-objective capacity planning model including ecological cycle assessment and uses the non-dominated sorting genetic algorithm (NSGA-II) for solving.

Despite the certain achievements in ICES capacity optimization configuration research, there are still obvious limitations: first, most studies only consider the impact of the carbon trading or green certificate trading mechanism on system operation, ignoring the interactive linkage effect between the two mechanisms; second, the impact of electricity market price fluctuations on system capacity investment has not been fully characterized in existing capacity optimization models; third, some studies adopt fixed electricity prices or time-of-use electricity prices for analysis, failing to fully consider the electricity price fluctuations caused by changes in supply and demand in the distribution network market. A detailed comparison between existing method and the proposed method is shown in Table 1.

Table 1. Comparison between Existing Methods and the Proposed Method.

Research Dimension	Typical Practices of Existing Literature	Advantages of the Proposed Method
Market Mechanism Coupling	Most studies consider the impact of carbon trading or green certificate trading on system operation individually, ignoring the interactive linkage effect between the two [45].	Construct a carbon-green certificate interactive transaction cost model, coupling tiered carbon trading with green certificate trading, and considering its offset relationship with CCER, thereby effectively depicting the multi-market collaborative emission reduction mechanism.
Electricity Price Volatility Characterization	Capacity optimization models fail to fully characterize the impact of electricity market price fluctuations on system capacity investment [46].	Introduce a geometric Brownian motion model based on weight adjustment factors to simulate feed-in tariff fluctuations, which more truly reflects the price uncertainty of the electricity market and its impact on planning.
Optimization Model Framework	Fixed electricity prices or time-of-use electricity prices are often used for analysis, failing to fully consider the real-time electricity price volatility characteristics caused by changes in supply and demand in the distribution network market [47].	Establish a two-layer stochastic programming model: the upper layer optimizes capacity allocation, and the lower layer optimizes typical day dispatch. The hybrid algorithm of NSGA-II (Non-dominated Sorting Genetic Algorithm-II) and MILP (Mixed-Integer Linear Programming) is adopted for solution, realizing the coordinated optimization of economic and low-carbon goals under uncertain environments.

3. Methodology

To account for the inherent uncertainties associated with renewable energy generation and multi-energy loads, a hybrid framework integrating Monte Carlo simulation, Wasserstein distance-driven scenario reduction, and K-means clustering is employed.

The Monte Carlo method is chosen for electricity price fluctuation scenario generation based on two key justifications: First, as a widely acknowledged technique for sampling continuous stochastic processes (e.g., price volatility modeled via geometric Brownian motion), it demonstrates more stable convergence when handling non-uniform distributions, outperforming alternatives such as Latin Hypercube Sampling [48]. Second, its efficacy in scenario generation for ICES capacity optimization has been validated in prior uncertainty modeling studies focused on integrated community energy systems [49].

The Wasserstein distance is utilized to quantify the distribution discrepancy between simulated and real-world electricity price scenarios. In contrast to the Kullback–Leibler (KL) divergence—which is prone to instability when distributions shift—the Wasserstein distance offers greater robustness toward asymmetric or long-tailed distributions (a characteristic trait of electricity market prices) [50], rendering it better suited for our uncertainty quantification tasks.

K-means clustering is employed for scenario reduction: relative to density-based techniques (e.g., DBSCAN), it delivers superior computational efficiency when processing large-scale scenario sets [51]. Furthermore, its centroid-centric clustering mechanism preserves the core volatility characteristics of electricity price scenarios—a property that is indispensable for maintaining scenario representativeness in ICES capacity planning.

3.1. System Configuration and Modeling Framework

The flow and transmission processes of various energy types within integrated community energy system are illustrated in Figure 1, encompassing energy production, conversion, transmission, storage, and supply.

Figure 1. ICES base framework model.

The system comprises power supply equipment, heating and cooling equipment, combined cooling, heating, and power (CCHP) systems, and energy storage equipment.

Power supply equipment: Wind turbines (WT), Photovoltaic panels (PV).

Heating and cooling equipment: Gas boiler (GB), Electric chiller (EC).

Combined cooling, heating and power systems: Gas turbine (GT), Absorption chiller (AC), Waste heat boiler (WHB).

Energy storage devices: Electrical energy storage (ES), Thermal energy storage (TS), Cold energy storage (CS).

3.2. Cost Modeling Framework

3.2.1. Grid Interaction Cost Model with Electricity Price Fluctuations

(1)

Weight-Adjusted Geometric Brownian Motion Price Model

In finance, geometric Brownian motion is employed within the Black–Scholes pricing model to characterize stock prices, rendering it the most prevalent framework for describing equity valuations [52]. We selected the weight-adjusted Geometric Brownian Motion (GBM) to simulate electricity prices for two reasons: First, GBM is widely used to model stochastic price volatility in energy markets (consistent with the non-arbitrage assumption of electricity price fluctuations in our time horizon) [53], whereas ARIMA is more suitable for time-series trend prediction (not for random volatility simulation). Second, mean-reverting processes (e.g., Ornstein–Uhlenbeck model) focus on price reversion to a long-term mean, but the short-term electricity price volatility in our study (hourly scale) aligns better with GBM’s stochastic diffusion property [54]. Consequently, this paper employs geometric Brownian motion to simulate the electricity selling price of the distribution network [55].

Let $W\left(t\right)=\left\{W_1\left(t\right),W_2\left(t\right)\dots W_N\left(t\right)\right\},0\le t\le T$ denote a multidimensional Brownian motion on the probability space $(\mathsf{\Omega },F,P)$, $T$ denote a given terminal time; $\mathsf{\Omega }$ denote the set of $N$ distributed energy electricity selling price; $F$ denote the $\sigma$-algebra on $\mathsf{\Omega }$, and $P$ denote the probability measure defined on $F$.

It is assumed that the electricity selling price of the distributed energy system follows a geometric Brownian motion on the probability space $(\mathsf{\Omega },F,P)$. For $\forall i\in \left\{\mathrm{1,2},\dots N\right\}$, its differential satisfies the following formula, which describes the dynamic evolution of electricity prices, consisting of a drift term ($a_i\left(t\right){\pi }_i\left(t\right)dt$, reflecting the long-term trend of electricity prices) and a stochastic term (${\sigma }_i\left(t\right){\pi }_i\left(t\right)d{W}_i\left(t\right)$, characterizing market uncertainty):

$$d{\pi }_i\left(t\right)=a_i\left(t\right){\pi }_i\left(t\right)dt+{\sigma }_i\left(t\right){\pi }_i\left(t\right)d{W}_i\left(t\right)$$

(1)

where ${\pi }_i\left(t\right)$ denotes the electricity selling price of the distributed energy system; $a_i\left(t\right)$ represents the average return on electricity prices for the distributed energy system; ${\sigma }_i$ signifies the volatility of the distributed energy system.

To characterize the pricing pattern of electricity sales in the distributed energy system under the risk-neutral measure $\tilde{P}$, Girsanov’s theorem is employed to transform the real probability measure $P$ into the risk-neutral measure $\tilde{P}$. The adoption of the risk-neutral measure P in the context of long-term capacity planning requires methodological justification. This measure transformation is employed not for the pricing of financial derivatives, but rather to generate a set of arbitrage-free future electricity price trajectories suitable for stochastic optimization under uncertainty. Under the risk-neutral framework, the expected drift of the electricity price process is aligned with the risk-free rate r, thereby abstracting from the market risk premium and allowing the model to focus exclusively on the effect of price volatility σi on investment decisions. Such an approach represents a conventional methodology in the investment planning literature for projects exposed to long-term price uncertainty, as it ensures valuation consistency and mitigates the speculative biases inherent in estimating time-varying risk premia. The inherent physical attributes and short-term market dynamics of electricity prices—such as seasonal variations and mean-reverting behavior—are accounted for within the real-world measure through the time-varying weight adjustment matrix K(t), as formulated in Equation (4), expressed as:

$$d{\pi }_i(t)=r(t){\pi }_i(t)dt+{\sigma }_i(t){\pi }_i(t)d{\tilde{W}}_i(t)$$

(2)

where $r$ denotes the risk-free rate of return; ${\tilde{W}}_i(t)$ represents the multidimensional Brownian motion under the risk-neutral measure $\tilde{P}$.

Applying Itō’s lemma yields the electricity pricing model for distributed energy systems:

$${\mathsf{\pi }}_{\mathrm{i}}(\mathrm{t})={\mathsf{\pi }}_{\mathrm{i}}(0)\mathrm{e}\mathrm{x}\mathrm{p}\left({\int }_0^{\mathrm{t}}(\mathrm{r}-{\displaystyle \frac{1}{2}}{{\mathsf{\sigma }}_{\mathrm{i}}}^2(\mathrm{s}))\mathrm{d}\mathrm{s}+{\int }_0^{\mathrm{t}}{{\mathsf{\sigma }}_{\mathrm{i}}}^2(\mathrm{s})\mathrm{d}{\mathrm{W}}_{\mathrm{i}}(\mathrm{s})\right)$$

(3)

where ${\pi }_i\left(0\right)$ denotes the initial electricity price of the distributed energy system.

The model indicates that the dynamic electricity price process is described solely by a random term and a drift term representing long-term trends and market uncertainty. However, it fails to effectively capture the periodic structural fluctuations in intraday electricity prices arising from supply-demand characteristics. To address this, this study proposes an improved model based on a weight adjustment factor. Building upon the electricity price model for the distributed energy system, a time-varying weight coefficient matrix is introduced:

$$K\left(t\right)=\left[k_1\right(t),k_2(t),...,k_{24}(t\left)\right]$$

(4)

where $k_i$ represents the weighting coefficient. By categorizing peak, flat, and valley periods based on historical load curves, the improved electricity price model becomes:

$${\pi }_i^{adj}(t)={\pi }_i(t)\cdot k_i(t)$$

(5)

(2)

Grid Interaction Cost Model for Integrated Energy Systems Considering Electricity Price Fluctuations

Based on the aforementioned theoretical framework for distributed energy electricity pricing, a grid interaction cost model for integrated energy systems accounting for electricity price fluctuations is constructed, expressed as:

$$C_E=\sum _{t=1}^T({\alpha }_{buy}(t)\cdot P_{buy,t}-{\pi }_i^{adj}(t)\cdot P_{sell,t})\mathsf{\Delta }t$$

(6)

where $C_E$ represents the interaction cost between integrated community energy system and the grid; $P_{buy,t}$ and $P_{sell,t}$ denote the power purchased from and sold to the grid by the system, respectively; ${\alpha }_{buy,t}$ is the time-of-use electricity price.

It is important to note that the volatility parameter σi (a scaling factor applied to the base volatility in Equation (1)) is a key driver of the generated price paths. In the subsequent case study (Section 4.1.2), we set σi to values of 0.5, 1.0, and 1.5 to represent low, moderate, and high volatility regimes, respectively. The setting of σi = 1.5 constitutes a stress-test scenario, designed not to predict the most likely future, but to simulate an extreme volatility mechanism that could be triggered by major external shocks (e.g., severe climate events or geopolitical conflicts documented in recent empirical literature). This scenario allows us to evaluate the system’s resilience and reveal the nonlinear trade-offs between investment decisions and risk exposure under such high-stress conditions, thereby providing critical insights for robust planning.

3.2.2. Carbon-Green Certificate Trading Cost Model

(1)

Construction of the Tiered Carbon Trading Model

The baseline method is employed to allocate carbon quotas to equipment within integrated community energy systems that generate carbon emissions. It is assumed that the equipment emitting carbon within the system comprises CCHP units and heating equipment GB. The carbon quotas in this paper can be expressed as:

$$C_{IES}=P_{GT}\cdot B_T+Q_{GB}\cdot B_B$$

(7)

where $C_{IES}$ denotes the total carbon allocation quota; $P_{GT}$ and $Q_{GB}$ represent the electrical power and thermal power of GT and GB, respectively; $B_T$ and $B_B$ denote the carbon allowance benchmark per unit of CO₂ emission for GT and GB, respectively.

The actual carbon emissions from the system originate from the CO₂ produced by the natural gas consumed in the GT and GB units. Assuming all purchased electricity is generated from thermal power plants, the actual carbon emissions are calculated as follows:

$$C_{IES,A}=C_{T,A}+C_{B,A}+C_{E,A}$$

(8)

where $C_{T,A}$, $C_{B,A}$, $C_{E,A}$ represent the actual carbon emissions from GT, GB, and purchased electricity, respectively. Specific calculation formulas refer to Appendix B (Equations (A1)–(A3)).

Based on the traditional fixed carbon price, this paper introduces incentive and penalty coefficients to construct a reward-penalty tiered carbon trading cost model, which is manifested as follows: when the actual carbon emissions ($C_{IES,a}$) are lower than the allocated quota ($C_{IES}$), tiered emission reduction rewards are provided; when they exceed the quota, tiered penalties are imposed to incentivize deep emission reductions. Its mathematical model is shown in Appendix B (Equation (A4)).

(2)

Construction of the Green Certificate Trading Model

Subject to market supply fluctuations, the green certificate trading price may be determined via a Cournot model based on quantity competition, expressed as:

$$c_{GCT}={\alpha }_0^{GCT}-{\beta }_0^{GCT}{Q}_C$$

(9)

$${\alpha }_0^{GCT}=c_{GCT,0}$$

(10)

$${\beta }_0^{GCT}={\displaystyle \frac{(1-{\epsilon }_0^{GCT})c_{GCT,0}}{{\alpha }_{green}\sum P_{load,t}}}$$

(11)

where $c_{GCT}$ denotes the green certificate trading price; ${\alpha }_0^{GCT}$ and ${\beta }_0^{GCT}$ represent the two positive parameters of the inverse price function in the Cournot model; $Q_C$ indicates the quantity of green certificates sold by the system;$c_{GCT,0}$ signifies the base green certificate trading price; ${\epsilon }_0^{GCT}$ reflects the green certificate trading price ratio calculated from historical data; ${\alpha }_{green}$ denotes the system’s green certificate quota coefficient; and $\sum P_{load,t}$ represents the system’s total electricity consumption during the calculation period.

The green certificate transaction cost model is:

$$C_{GCT}=c_{GCT}(Q_s-Q_d)$$

(12)

$$Q_s={\alpha }_{green}\sum P_{load,t}$$

(13)

$$Q_d={\kappa }_{green}\sum P_{pw,t}$$

(14)

where $C_{GCT}$ represents the system’s green certificate transaction cost; $Q_s$ denotes the system’s mandated green certificate quota; $Q_d$ signifies the quantity of green certificates generated from renewable energy production within the system; ${\kappa }_{green}$ is the conversion factor quantifying wind and solar generation into green certificates, assuming one certificate corresponds to 1 MWh of wind/solar output; $\sum P_{pw,t}$ indicates the total wind and solar output within the system.

(3)

Carbon-Green Certificate Interaction Cost Model for Integrated Community Energy System

China Certified Emission Reductions (CCER) quantify, verify, and trade carbon dioxide absorbed by greenhouse gas reduction projects. After registration, emission reductions from voluntary projects are traded through accredited trading institutions. Specifically, the total electricity output from integrated community energy systems includes a proportion of green electricity. The resulting green certificates can be traded on the green certificate market. From an emissions reduction perspective, both green certificates and CCERs can drive reductions through electricity substitution, demonstrating equivalence and thus forming a mutually recognizable relationship. Similarly, CCERs and carbon allowances can be allocated on a one-to-one basis through carbon emissions reductions, establishing mutual recognition, as illustrated in Figure 2.

Figure 2. Correlation analysis between CET and GCT.

As noted above, the carbon emission reductions corresponding to CCERs may also participate in carbon trading. Consequently, in calculating transaction costs, the carbon emission reductions equivalent to CCERs may be deducted. The emission reduction contribution per MWh of green electricity from renewable energy generation projects may be determined using the “China Regional Grid Baseline Emission Factor for Emission Reduction Projects” [56]. Based on this, the carbon emission reduction effect corresponding to green power certificate trading may be calculated as:

$${\mathrm{C}}_{\mathrm{C}\mathrm{C}\mathrm{E}\mathrm{R}}=\sum \left({\mathsf{\lambda }}_{\mathrm{O}\mathrm{M}}\cdot {\mathsf{\gamma }}_{\mathrm{e}1}+{\mathsf{\lambda }}_{\mathrm{B}\mathrm{M}}\cdot {\mathsf{\gamma }}_{\mathrm{e}2}\right)\left({\mathrm{P}}_{\mathrm{p}\mathrm{w},\mathrm{t}}+{\mathrm{P}}_{\mathrm{V}\mathrm{o}\mathrm{l},\mathrm{t}}\right)$$

(15)

where $C_{CCER}$ represents the carbon emission reduction equivalent to CCERs; ${\lambda }_{OM}$ and ${\lambda }_{BM}$ denote the marginal emission factors for electricity generation and capacity, respectively; ${\gamma }_{e1}$ and ${\gamma }_{e2}$ denote the corresponding emission factor weightings; $P_{Vol,t}$ represents the green electricity purchased by the system.

3.2.3. System Economic Evaluation Model

Levelized costs of energy (LCOE) was proposed by the US National Renewable Energy Laboratory. It denotes the average cost per unit of energy produced over the lifetime of an energy facility [57]. Drawing upon this concept, this paper employs the Levelized Cost of Energy System (LCOES) as an evaluation metric. Treating the integrated energy system as an organic whole, this paper calculates the cost per unit of integrated energy (electricity + heat + cooling) to compare the operational economics of different system configuration schemes. The cost calculation of the integrated energy system using LCOES can be expressed as the following formula, where the numerator represents the net cost over the life cycle (initial investment—present value of residual value + present value of operation and maintenance costs), and the denominator represents the present value of total energy output over the life cycle:

$$C_{LCOES}={\displaystyle \frac{C_0-\frac{C_R}{(1+r{)}^n}+{\sum }_{t=1}^n\frac{C_{ope,t}}{(1+r{)}^t}}{{\sum }_{t=1}^n\frac{P_{all}}{(1+r{)}^t}}}$$

(16)

where $C_0$ represents the project’s initial investment; $C_R$ denotes the residual value of fixed assets at the end of the operational period; $C_{ope,t}$ signifies the system maintenance and operational costs for the t-th year; $r$ indicates the discount rate; $P_{all}$ represents the total energy output of the system.

3.3. Two-Layer Optimization Model Formulation

Addressing the conflict between economic and low-carbon objectives in multi-objective optimization, this paper proposes converting carbon emission targets into transaction costs under a carbon-green certificate interaction mechanism, thereby transforming low-carbon goals into economic indicators to enhance model solution efficiency. This study constructs a two-layer stochastic programming model incorporating capacity allocation optimization and operational optimization, as illustrated in Figure 3. The upper layer determines the configuration of specific system equipment under capacity constraints, while the lower layer addresses the dispatch output of equipment on a typical day.

Figure 3. Two-layer stochastic planning model.

3.3.1. Upper-Tier Capacity Planning Model

(1)

Upper-tier capacity planning model objective function

The upper-tier planning model aims to evaluate the system’s economic costs, encompassing the annualized investment costs and operational maintenance costs of all energy equipment within the system. The model can be expressed as:

$$\mathit{min}{C}_{\mathit{cos}t}=C_{int}+C_{ope}$$

(17)

where $C_{\mathit{cos}t}$ denotes the annualized equivalent cost of the total investment in system equipment; $C_{int}$ represents the annualized investment cost, calculated based on equipment capacity, unit investment cost, and annual cost coefficient; $C_{ope}$ is the annual system operation and maintenance cost, derived by multiplying the daily operation and maintenance cost on a typical day by the number of days in a year and the scenario probability. Specific calculation formulas are shown in Appendix B (Formulas (A5)–(A7)).

(2)

Constraints

The constraints for the upper-level capacity optimization model pertain to the installation planning of energy equipment to be installed in the system, expressed as:

$$P_{i,\mathrm{m}\mathrm{i}\mathrm{n}}\le P_{i,\mathrm{i}\mathrm{n}\mathrm{t}}\le P_{i,\mathrm{m}\mathrm{a}\mathrm{x}}$$

(18)

$$Q_{j,\mathrm{m}\mathrm{i}\mathrm{n}}\le Q_{j,\mathrm{i}\mathrm{n}\mathrm{t}}\le Q_{j,\mathrm{m}\mathrm{a}\mathrm{x}}$$

(19)

where $P_{i,int}$ denotes the planned installed capacity for the system’s i-th energy facility; $P_{i,min}$ and $P_{i,max}$ represent the minimum and maximum rated capacities of the unit, respectively; $Q_{j,int}$ denotes the planned installed capacity for the j-th energy storage device; $Q_{j,min}$ and $Q_{j,max}$ denote the minimum and maximum rated capacities of the energy storage device, respectively.

3.3.2. Lower-Level Dispatch Operation Model

(1)

Objective Function

The objective function aims to minimize operational costs on a typical day, encompassing the environmental costs of the integrated community energy system within the industrial park (i.e., carbon-green certificate trading costs), gas procurement costs, and grid-system interaction costs. It is expressed as:

$$\mathit{min}{C}_{ope}=C_{CET,GCT}+C_E+C_{gas}$$

(20)

where $C_{CET,GCT}$ and $C_E$ represent the system’s carbon-green certificate trading costs and grid interaction costs, respectively. $C_{gas}$ is the natural gas procurement cost, and the specific calculation formula is shown in Appendix B (Formula (A8)).

(2)

Constraints

The lower-level dispatch operation model addresses the operational status of system equipment; hence the lower-level constraints comprise power balance constraints, equipment output constraints, and energy storage capacity status constraints.

• Electrical Power Balance Constraint

$$P_{PV}\left(t\right)+P_{WT}\left(t\right)+P_{GT}\left(t\right)+P_{buy}\left(t\right)+P_{dis,e}\left(t\right)=P_{EL}\left(t\right)+P_{sell}\left(t\right)+P_{ch,e}\left(t\right)+P_{EC}\left(t\right)$$

(21)

where $P_{PV}\left(t\right)$, $P_{WT}\left(t\right)$, $P_{GT}\left(t\right)$ represent the generation power of PV, WT, and GT, respectively, at time $t$; $P_{buy}\left(t\right)$, $P_{sell}\left(t\right)$ denote the system’s power purchase and sale to the grid, respectively, at time $t$; $P_{dis,e}\left(t\right)$, $P_{ch,e}\left(t\right)$ denote the discharge and charge power of the energy storage system, respectively, at time $t$; $P_{EC}\left(t\right)$ represents the power consumption of the EC machine at time $t$; $P_{EL}\left(t\right)$ denotes the electrical load in the scenario at time $t$.

2.

Thermal Power Balance Constraints

$$Q_{HRB}\left(t\right)+Q_{GB}\left(t\right)+P_{dis,h}\left(t\right)=P_{HL}\left(t\right)+P_{ch,h}\left(t\right)$$

(22)

where $Q_{HRB}\left(t\right)$ and $Q_{GB}\left(t\right)$ denote the thermal power of WHB and GT within the system at time $t,$ respectively; $P_{dis,h}\left(t\right)$ and $P_{ch,h}\left(t\right)$ represent the heat release and storage power of the thermal storage device at time $t,$ respectively; $P_{HL}\left(t\right)$ denotes the thermal load in the scenario at time $t$.

3.

Cooling Power Balance Constraint

$$Q_{EC}\left(t\right)+Q_{AC}\left(t\right)+P_{dis,c}\left(t\right)=P_{CL}\left(t\right)+P_{ch,c}\left(t\right)$$

(23)

where $Q_{EC}\left(t\right)$ and $Q_{AC}\left(t\right)$ denote the cooling power of EC and AC within the system, respectively; $P_{dis,c}\left(t\right)$ and $P_{ch,c}\left(t\right)$ represent the cooling release and storage power of CS at time $t$; $P_{CL}\left(t\right)$ denotes the cooling load in the scenario at time $t$.

4.

Operational Upper and Lower Bound Constraints for Planned Equipment

$$0\le P_i\left(t\right)\le P_{i,int}$$

(24)

where $P_{i,int}$ and $Q_{j,max}$ denote the upper output power limits for the energy generation unit $i$ and the energy storage unit $j,$ respectively; $Q_{j,min}$ denotes the minimum permissible output power for the energy storage unit.

5.

Energy Storage Device Constraints

$${\epsilon }_{i,\mathrm{m}\mathrm{i}\mathrm{n}}{Q}_{i,\mathrm{i}\mathrm{n}\mathrm{t}}\le Q_i\left(t\right)\le {\epsilon }_{i,\mathrm{m}\mathrm{a}\mathrm{x}}{Q}_{i,\mathrm{i}\mathrm{n}\mathrm{t}}$$

(25)

$$0\le P_{i,ch}\left(t\right)\le U_i\cdot P_{i,max}$$

(26)

$$0\le P_{i,dis}\left(t\right)\le (1-U_i)P_{i,max}$$

(27)

$$P_{i,\mathrm{i}\mathrm{n}\mathrm{t}}={\eta }_i{Q}_{i,\mathrm{i}\mathrm{n}\mathrm{t}}$$

(28)

where ${\epsilon }_{i,min}$ and ${\epsilon }_{i,max}$ denote the lower and upper capacity coefficients of the energy storage device; $Q_{i,int}$ represents the planned construction capacity of the energy storage device; ${\eta }_i$ denotes the energy multiplication coefficient of the energy storage device; $U_i$ is a 0–1 logical variable characterizing the charging/discharging state of the energy storage device. When $U_i=1$, it indicates charging is in progress; conversely, when $U_i=0$, the electrical energy storage is discharging.

6.

Distribution Network Interaction Constraints

During interaction with the external grid, the system must regulate its power output to prevent undue strain on the grid. The distribution network interaction power constraints are defined as:

$$0\le P_{buy}\left(t\right)\le U_{grid}{P}_{grid,max}$$

(29)

$$0\le P_{sell}\left(t\right)\le (1-U_{grid})P_{grid,max}$$

(30)

where $P_{buy}\left(t\right)$ and $P_{sell}\left(t\right)$ denote the power purchased and sold by the system to the external grid, respectively; $P_{grid,max}$ represents the maximum power exchange between the system and the external grid; $U_{grid}$ is a 0–1 logical variable characterizing the system’s power purchase/sale status. When $U_{grid}=1$, it indicates the system is purchasing electricity from the grid; conversely, when $U_{grid}=0$, the system is selling electricity to the grid.

4. Simulation Analysis

4.1. Parameter and Scenario Configuration

4.1.1. Parameter Configuration

Parameters related to the carbon-green certificate interaction trading mechanism discussed herein, along with upper and lower bounds for equipment capacity configuration in the planned integrated energy system, are detailed in Appendix A.

Historical data such as wind speeds and solar irradiance within the park’s vicinity were collected. Scenario data were derived through Monte Carlo simulation and Wasserstein distance-based scenario reduction theory. Based on data characteristics, scenarios were categorized into summer, winter, and transitional seasons, with final data normalization. Concurrently, seasonal K-means clustering of the park’s historical electricity-heat-cooling load data yielded three seasonal scenarios. The standardized values for wind and solar power generation, along with typical daily electricity, heating, and cooling loads, are illustrated in Figure 4 and Figure 5.

Figure 4. Per-unit values of wind and photovoltaic output.

Figure 5. Typical electric-heat-cooling load. (a) Electrical load of the system; (b) Heat load variation; (c) Cooling load fluctuation.

In accordance with the electricity procurement policy of the industrial park’s location, a time-of-use tariff for commercial and industrial customers is applied, as detailed in Table 2.

Table 2. Time-of-day tariffs for industrial and commercial types.

Time Period Type	Time Period	Tariff (CNY/kWh)
Peak	7:00–9:00 18:00–24:00	1.08
Off-peak	2:00–4:00 11:00–17:00	0.5086
Flat Period	1:00 5:00 10:00	0.7943

Grid-connected electricity prices were simulated using geometric Brownian motion enhanced with weight adjustment factors. With a base price of 0.368, price volatility rates of 0.5, 1, and 1.5 were applied [55], yielding grid-connected electricity prices under three volatility scenarios as depicted in Figure 6.

Figure 6. Electricity selling price with different volatilities.

Generation of typical days effectively characterizes the uncertainty of wind and solar power generation and load, enhancing system adaptability and stability.

4.1.2. Scenario Classification

To investigate the impact of different carbon trading policy combinations and electricity price volatility on integrated energy capacity allocation, this study constructs multi-dimensional scenarios for comparative analysis. The specific scenario settings are as follows:

Scenario 1: As the baseline scenario, the feed-in tariff is fixed at 0.368, with no consideration of any form of carbon trading.

Scenario 2: Building upon the baseline scenario, this scenario considers only a reward-and-penalty tiered carbon emission trading mechanism.

Scenario 3: Building upon the baseline scenario, this scenario incorporates both incentive-based tiered carbon trading and green certificate trading mechanisms.

Scenario 4: Building upon Scenario 3, this scenario further considers the interaction between carbon and green certificate trading.

Scenario 5: Building upon Scenario 4, this scenario incorporates electricity price volatility δ = 0.5;

Scenario 6: Building upon Scenario 4, this scenario incorporates electricity price volatility δ = 1.0;

Scenario 7: Building upon Scenario 4, this scenario incorporates electricity price volatility δ = 1.5.

4.2. Optimization Results

The upper-layer capacity allocation model in this paper employs the second-generation non-dominated sorting genetic algorithm (NSGA-II) for solution. The initial population size is set to 40, with a population gene encoding length of 3, 50 genetic iterations, a crossover probability of 0.9, and a mutation probability of 0.2. The lower layer utilizes a mixed-integer linear programming (MILP) approach for solution.

The nested NSGA-II and MILP structure, while effective in handling the bi-level stochastic optimization, entails non-negligible computational effort. In our case, the NSGA-II upper layer typically converged within 40–45 generations under the given population settings, requiring approximately 90–110 min on a standard workstation (Intel Core i7-12700, 16 GB RAM). Each evaluation of the lower-layer MILP model (solved via CPLEX) for a given capacity configuration averaged 2–3 s. Despite the computational intensity inherent to bi-level optimization, the proposed framework achieved stable convergence across multiple runs, with the Pareto front showing negligible variation (<2% in objective values) after the 40th generation. This demonstrates the algorithm’s robustness for the planning-scale problem considered, where solution quality outweighs real-time computational constraints. Further efficiency gains could be explored via parallel evaluation or surrogate-assisted methods but were beyond the scope of this study.

4.2.1. Analysis of Capacity Allocation Results

The equipment capacity allocations and annualized investment and operational costs for different scenarios are presented in Table 3.

Table 3. Capacity allocation and investment O&M costs for different scenarios.

	1	2	3	4	5	6	7
PV	5000	5000	5000	5000	5000	5000	5000
WT	50	50	50	50	50	50	50
GT	7	8	8	8	8	8	8
EC	176	147	151	293	225	185	185
AC	384	414	404	372	396	415	433
WHB	340	246	300	412	287	112	112
GB	500	455	471	484	445	418	420
ES	116	50	53	88	94	103	232
TS	199	50	63	90	112	179	217
CS	50	50	50	50	54	54	54
C	188.2	192.0	192.6	195.3	193.9	192.4	195.6

• Capacity Allocation Analysis Under Different Emission Reduction Policies

As shown in Table 3, constrained by the park’s development conditions, the maximum planning limit of installing 5000 photovoltaic (PV) panels and 50 wind turbines (WT) is maintained across all scenarios for basic energy equipment such as wind and solar power. However, after the introduction of carbon emission reduction policies, the system capacity configuration presents a complex optimization game process.

Economic Driver Analysis (GT Configuration Decision). After the introduction of the tiered carbon trading mechanism, the capacity of gas turbines (GT) increased from seven to eight units. The economic driver behind this decision lies in the fact that under the load conditions considered in this study, the marginal benefit of carbon trading (resulting from the reduction in actual carbon emissions) generated by adding new GTs for power generation to replace part of the grid-purchased electricity (which has a relatively high carbon intensity) still exceeds the marginal investment cost of the new GTs. The system gains net benefits through continued investment until the marginal benefit of carbon trading reaches equilibrium with the marginal cost of equipment investment. Notably, the GT capacity did not further increase after the introduction of additional policies such as green certificates (Scenarios 3–4). This is because while meeting the power balance constraint, further expanding GTs would exacerbate the peak-shaving pressure of the system during the peak output period of renewable energy and push up the incremental investment cost of other equipment (such as electric chillers (EC)). At this point, the marginal policy benefit is offset by the marginal synergistic investment cost.

Physical System Coupling and Strategic Trade-off (CCHP and Energy Storage Configuration). Changes in policy combinations have triggered chain adjustments of multi-energy flow coupling equipment within the system. After the introduction of green certificate trading (Scenario 2→3), to increase the proportion of green power in the system to meet the quota, the model tends to increase the capacity of waste heat boilers (WHB) coupled with GTs to fully utilize power generation waste heat and correspondingly reduces the capacity of absorption chillers (AC). To meet the cooling load, the capacity of electric chillers (EC) increases accordingly, which reflects that under the constraint of cooling-heat-electricity coupling, the model responds to policy incentives by adjusting the conversion paths of energy at different grades. For the energy storage system, except for cold energy storage (CS), which maintains the minimum configuration due to load characteristics, the capacities of electrical energy storage (ES) and thermal energy storage (TS) gradually expand with the policy requirements. This reveals another layer of optimization logic of the model: in the face of basic energy fluctuations and potential multi-energy flow coordinated dispatch pressure caused by the adjustment of combined heat and power (CCHP) system capacity configuration, configuring an appropriate amount of flexible energy storage resources is a necessary physical means to ensure the stable and economic operation of the system.

From the perspective of the overall economics of the system, the annualized investment and operation and maintenance (O&M) cost is the lowest (1.882 million CNY) when there are no emission reduction policies (Scenario 1). With the introduction of carbon trading and green certificate trading mechanisms (Scenarios 2 to 4), to obtain potential policy-driven transaction benefits, the system adaptively adjusts the planned capacities of major energy equipment and CCHP units, and configures corresponding energy storage systems to meet the requirements of coordinated operation, leading to a gradual increase in the annualized investment and O&M cost to 1.953 million CNY. This intuitively reflects the incremental investment cost that must be borne to achieve low-carbon transition.

2.

Capacity Configuration Analysis under Variable Electricity Prices

Electricity price volatility provides the system with opportunities to gain additional revenue through flexible dispatch, while also posing planning challenges that drive dynamic adjustments to equipment capacity configuration.

Economic Incentives and Transmission of Operational Strategies. When the feed-in tariff is high, the system tends to prioritize electricity sales, thereby reducing the planned capacity of electric chillers (EC) used to meet cooling loads (e.g., from Scenario 4 to Scenario 7, EC capacity decreased from 293 kW to 185 kW). For the combined cooling, heating and power (CCHP) system, although the GT capacity remains unchanged, the model increases the capacity of absorption chillers (AC) to address the potential cooling power gap caused by reduced EC output. Correspondingly, the capacity of waste heat boilers (WHB) operating synergistically with AC is reduced in phases. This series of adjustments vividly illustrates how the economic incentives of electricity price signals are transmitted step by step in system planning through the “electricity-cooling-heat” energy conversion chain.

Flexible Investment and Cost Trade-off. To mitigate power fluctuations caused by changes in equipment capacity, the planned capacities of electrical energy storage (ES) and thermal energy storage (TS) have increased significantly. When the electricity price volatility δ reaches 1.5, the capacities of ES and TS surge by 164% and 141%, respectively, compared to Scenario 4. This large-scale redundant investment to enhance system flexibility is essentially aimed at better capturing arbitrage opportunities brought by electricity price volatility. From the cost–benefit perspective, when the electricity price volatility ranges between 0.5 and 1.0, the investment cost of newly added AC and energy storage equipment is lower than the investment saved by reducing EC, thus the system’s annualized total investment cost decreases (from 1.953 million CNY to 1.924 million CNY). However, when the volatility rises to 1.5, the incremental marginal investment cost brought by the substantial expansion of energy storage equipment exceeds the cost savings from other equipment and the incremental marginal revenue potentially obtained through electricity sales, ultimately leading to a rebound in total cost to 1.956 million CNY. This reveals a key conclusion: there exists an optimal adaptation range for electricity price volatility; beyond this range, over-investment to cope with extreme uncertainty will impair the overall economics of the system.

4.2.2. System Operating Cost Analysis

Operating costs under different carbon reduction policies and electricity price volatility scenarios are presented in Table 4.

Table 4. System operating costs.

Cost	1	2	3	4	5	6	7
C1	22.75	29.16	29.33	29.14	28.74	28.29	28.22
C2	264.39	287.16	287.12	290.21	290.01	289.91	288.37
C3	0.00	−67.31	−67.29	−74.24	−74.36	−74.58	−74.63
C4	0.00	0.00	−3.33	−3.33	−3.33	−3.33	−3.33
C5	−7.10	−7.72	−7.73	−7.74	−7.97	−8.55	−8.66
Total	280.03	241.30	241.09	237.04	236.09	234.74	229.98

• Analysis of the Effects of Carbon Reduction Policies on System Operating Costs

The introduction of the carbon trading mechanism has fundamentally restructured the operational cost structure of the system. As shown in Figure 7, from Scenario 1 to Scenario 2, both the electricity purchase cost (C1) and natural gas cost (C2) have increased significantly. The underlying economic logic is that under the tiered carbon pricing model, reducing the system’s own carbon emissions can be directly converted into carbon trading revenues. Therefore, the system will seek an optimal solution in dispatch: on the premise of meeting multi-type load demands, by appropriately increasing relatively clean natural gas power generation (GT) and reducing grid-purchased electricity (which has a higher carbon emission factor), the increased fuel costs incurred to reduce carbon emissions can be covered to a greater extent by carbon trading revenues (C3). As shown in Table 4, the carbon trading revenue (approximately 673,000 CNY) far exceeds the increase in basic energy procurement costs, becoming the primary driver for reducing the system’s total operational costs.

Figure 7. System Basic Energy Costs and Carbon-Green Certificate Trading Benefits.

In contrast, the green certificate trading revenue (C4) has a limited contribution to operational costs (approximately 33,000 CNY). This is mainly driven by two factors: first, the current price of China’s green certificate market is relatively low (5.5 CNY per certificate is adopted in this study [58]); second, for the megawatt-scale park in this study, the green certificate output corresponding to its renewable energy generation is basically balanced with the green certificate quota requirements corresponding to the electricity load, resulting in limited trading volume. This reflects that at the current market stage, the economic incentive intensity of the green certificate trading mechanism is not sufficient to independently trigger significant changes in system operation strategies, and its value is more reflected in the synergy with carbon trading.

2.

Analysis of Electricity Price Fluctuations on System Operating Costs

As illustrated in Figure 8, electricity price fluctuations exert minimal influence on the system’s fundamental energy procurement costs, manifesting instead as variations in electricity sales revenue. Scenarios 4 through 7 demonstrate that electricity sales revenue increases from CNY 77,409 to CNY 86,586. This indicates that the system flexibly leverages price fluctuations during dispatch, selling electricity when prices are elevated to enhance operational revenue.

Figure 8. System Basic Energy Costs and Revenue from Electricity Sales.

Overall, from Scenario 1 to Scenario 7, the system’s total operating costs decrease from a baseline of CNY 2.8 million to CNY 2.3 million. This optimization pathway, driven primarily by carbon trading and supplemented by green certificate trading, further reduces operating costs. Concurrently, fluctuations in electricity sale prices amplify additional revenues from the electricity market. This underscores the importance of incorporating carbon market development, stabilizing the green certificate market, and accounting for electricity market price volatility within the planning of the park’s energy system.

4.2.3. System Economic Analysis

• Total System Cost Analysis

The annual investment costs for operation and maintenance, along with annual operational costs, are presented in Figure 9.

Figure 9. System investment and operating costs.

It can be observed that when accounting for carbon reduction policies, the annualized investment and operational costs of the system exhibit an upward trend as the capacity of system equipment is expanded or reduced. However, the environmental benefits gained from emission reduction policies lead to a gradual decrease in operating costs. Under the combined effect of these factors, the total system cost shows a gradual downward trajectory. When accounting for electricity price fluctuations, during periods of minor price variations, the revenue generated from flexible system dispatch, coupled with reduced investment costs due to capacity adjustments, leads to a decrease in total system costs. When electricity price fluctuations are significant (e.g., δ = 1.5), adapting to system power variations necessitates increased investment in redundant equipment such as energy storage (ES) and thermal storage (TS). The marginal investment costs of such equipment exceed the marginal revenue gains from electricity sales generated by price fluctuations, ultimately resulting in a V-shaped total cost curve that first decreases and then increases.

2.

System-wide Cost Analysis under Levelized Load

An economic comparative analysis of Scenarios 1–7 is presented in Figure 10.

Figure 10. Levelized Total System Costs.

Across the seven scenarios, excluding any carbon reduction policies and electricity sales price volatility, the levelized total system cost stands at 0.234 yuan/kWh. This is below the industry average levelized cost of electricity for photovoltaic systems (0.25 yuan/kWh) and significantly lower than the levelized cost of electricity for thermal power generation (0.4–0.5 yuan/kWh). $C_{LCOES}$. Under the scenario incorporating all emission reduction policy combinations with a power sales price volatility of 1, the levelized total system energy cost is minimized at just RMB 0.2042/kWh. Notably, when power sales price volatility further increases to 1.5, the system investment cost rises, causing $C_{LCOES}$ to increase compared to Scenario 6, reaching 0.2059 yuan/kWh.

3.

Operational Low-Carbon Economic Analysis

The low-carbon benefits of system operation encompass carbon trading revenues and green certificate trading revenues. The low-carbon benefits for Scenarios 1 to 7 discussed herein are illustrated in Figure 11.

Figure 11. Low-carbon benefits of the system.

It can be observed that with the introduction of the carbon emission trading mechanism and its integration with the green certificate trading system, the low-carbon benefits derived from system operation progressively increase. Specifically, carbon trading revenue (C3) in Scenarios 2 to 7 grew by 11.2%, indicating significant revenue generation and enhanced carbon emission reduction effects. Green certificate trading revenue (C4) contributed steadily from Scenario 3 onwards, demonstrating that the green certificates obtained from the system’s renewable energy output and the quota required for load absorption reached a stable equilibrium. Regarding policy synergies, the carbon-green certificate interaction mechanism in Scenario 7 generated revenues of CNY 779,000, accounting for 70% of total cost reductions and becoming the primary driver of operational cost decreases. Notably, marginal low-carbon benefits exhibit a diminishing trend from Scenarios 5 to 7, indicating that reliance on electricity price fluctuations alone cannot sustainably enhance the system’s low-carbon performance, necessitating additional carbon reduction incentive policies.

In summary, after evaluating the economic viability of different system configurations across multiple indicators—including annualized investment and operational costs, operational expenses, levelized system-wide costs, and low-carbon benefits—Scenario 6’s capacity configuration demonstrated optimal performance when confronting the wind and solar output characteristics of the industrial park’s location alongside diverse load patterns.

4.3. Typical Daily Balancing Analysis

To validate the rationality of the proposed planning configuration, this section further analyses the operational scheduling strategies for the system under typical summer and winter daily scenarios based on the optimal configuration scheme selected earlier. The scheduling results are shown in Figure 12 and Figure 13.

Figure 12. Summer Equipment Scheduling Operations.

Figure 13. Winter equipment scheduling operation.

As illustrated in Figure 12, during a typical summer day, electrical load demand significantly exceeds cooling and heating loads. Moreover, the system does not generate surplus electricity for sale to generate revenue during operation. Electricity demand is primarily met by PV, WT, and CCHP units collectively. Between 19:00 and 23:00, as PV output drops to zero, the system must still purchase electricity from the grid at elevated prices to compensate for the power shortfall and satisfy the heightened electricity demand. CS and TS are primarily supplied by CCHP units. At 08:00, fan output power increases sharply, causing a corresponding decrease in CCHP unit output. At this point, EC output increases to meet cooling demand. Concurrently, thermal load is entirely covered by GB output.

As illustrated in Figure 13, during a typical winter day, electricity demand slightly decreases compared to summer. Between 12:00 and 16:00, and 19:00 to 22:00, electricity prices reach peak levels, prompting the system to sell electricity externally to generate revenue. Between 08:00 and 18:00, wind and solar generation largely covers electricity demand, with any shortfall supplemented by ES discharge. During this period, CCHP units remain largely inactive. Cooling demand is primarily met by EC output, while heating demand is mainly supplied by GB. Notably, heating demand is almost entirely provided by gas boilers, with WHB only contributing to thermal supply when CCHP units are operational.

The dispatch results from the aforementioned typical day reveal the system’s operational strategy: prioritizing renewable energy sources such as PV and WT, followed by utilizing the CCHP system for cascading energy use. Regarding equipment configuration strategy, the design capacity of the CCHP units adheres to the principle of “power-driven heat”, meaning the system’s electricity demand is met first. Any shortfalls in cooling or heating loads are then supplemented and regulated by the EC and WHB, respectively. During periods of surplus electricity, in addition to storing part of the load via energy storage systems (ESS), revenue can be generated through external sales. Furthermore, PV and WT exhibit complementary output characteristics; their coordinated operation enhances the renewable energy utilization efficiency of integrated community energy systems within the industrial park, providing a key technical pathway for constructing low-carbon integrated community energy systems.

5. Limitations and Future Work

This study has the following clear limitations and research boundaries: first, it focuses on park-level Integrated Community Energy Systems (ICES). If extended to city-level or larger-scale power grids, significant computational challenges will arise—the increase in complex multi-region energy interactions and coupled equipment will greatly enhance scenario complexity and solution time. Second, the model adopts fixed assumptions for policy parameters (e.g., carbon price, green certificate trading rules) and fails to fully consider the dynamic impact of long-term policy uncertainty on system planning. Third, in terms of electricity price modeling, as a preliminary exploration, this paper uses Geometric Brownian Motion (GBM) mainly to verify its feasibility in describing electricity price fluctuations and supporting capacity optimization. However, this model does not incorporate typical stylized features of financial time series such as structural breaks and volatility clustering, which may reduce the accuracy of price characterization in long-term or extreme market scenarios. Fourth, the study does not involve complex integrated demand response programs, failing to fully tap the potential of demand-side flexibility and limiting the overall optimization space of the system. In addition, the cross-regional transferability of the model is significantly constrained by climatic conditions (e.g., renewable energy resource endowments), market environments (e.g., carbon price levels), and regulatory policies (e.g., green certificate trading rules). Direct application to other regions requires targeted adjustments to region-specific parameters such as solar irradiance and policy quota standards.

Future work will be systematically carried out around the following directions: first, optimizing the computational framework (e.g., introduce parallel computing technology) to improve the model’s adaptability to large-scale energy system scenarios. Second, integrating price-based, incentive-based, and alternative demand response mechanisms to fully tap the potential of demand-side flexibility. Third, deepening uncertainty modeling, exploring methods such as incorporating regime switching and GARCH family models to more accurately capture the complex stochastic characteristics of electricity prices, and enhancing the long-term adaptability and robustness of the planning model. Fourth, incorporating multi-scenario policy simulations to systematically analyze the dynamic impact of long-term policy adjustments on the capacity configuration of energy systems.

6. Conclusions

This paper constructs a bi-level capacity optimization model for Integrated Community Energy Systems (ICES) considering carbon-green certificate (CET-GCT) trading and electricity price volatility, which is solved by the NSGA-II algorithm (upper-level capacity planning) and mixed-integer linear programming (MILP, lower-level operation optimization). Case analysis verifies that, compared with the baseline scenario, the proposed model reduces operational costs by 18.2% and also cuts carbon emissions, achieving a balance between economic efficiency and low-carbon benefits.

The findings provide important implications for policymakers. First, in terms of mechanism design, the CET-GCT coupling mechanism should adopt differentiated reward-penalty coefficients, strengthening the constraint on high-emission equipment while offering more green certificate incentives for renewable energy absorption. Second, regarding market coordination, electricity price mechanisms in the distribution network should fully consider short-term volatility characteristics and establish a dynamic adjustment mechanism linked to renewable energy output to improve the economy of ICES operation. Third, in terms of planning guidance, policymakers should promote the application of stochastic optimization models in ICES planning, encouraging planners to incorporate electricity price volatility and policy synergy effects into decision-making, so as to support the construction of low-carbon and resilient urban energy systems.