A joint trading mechanism for energy credits and electricity in virtual power plants

Abstract

With the urgent need to achieve carbon neutrality goals and the rapid development of distributed energy resources, traditional electricity markets face challenges in effectively integrating environmental and economic values, lacking unified mechanisms to simultaneously clear energy and environmental transactions. This study proposes an energy credits–electricity joint trading mechanism for virtual power plants that achieves co-equilibrium through explicit coupling between energy and environmental value markets. First, a multi-dimensional energy credit quantification model is established, integrating energy type, time period, trading volume, and behavioral characteristics to differentiate environmental contributions. An optional reputation assessment enhancement covering prediction accuracy, fulfillment reliability, response timeliness, trading frequency, and anomaly behavior can be integrated for virtual power plant (VPP) operators requiring behavioral differentiation. Second, a unified joint clearing model is constructed that co-optimizes energy and credit trading, employing the alternating direction method of multipliers (ADMM) to decompose large-scale optimization problems into parallelizable prosumer and market coordination subproblems. Simulation results across single-day, multi-day (5-day cycle), and seasonal scenarios demonstrate that the mechanism successfully distinguishes prosumer performance: renewable energy prosumers accumulate substantial positive credits (136.2 credits over 5 days), while fossil fuel users incur credit deficits (−25.1 credits single-day), achieving system-level carbon credit balance over multi-day settlement cycles. The proposed mechanism effectively realizes the principle of “green contributors benefit, polluters pay” and provides a practical pathway for integrating environmental value in electricity markets.

1 Introduction

As the urgency of global climate change response intensifies, energy systems are undergoing unprecedented structural transformation. The rapid development of distributed energy resources (DERs) provides important technological pathways for achieving carbon neutrality goals, while virtual power plants (VPPs), by aggregating massive distributed resources into a unified dispatchable resource through advanced information and communication technologies (Nosratabadi et al., 2017), can fully promote the accommodation of distributed generation resources (Liu J. et al., 2023) and have become an important component of modern power system transformation (Ullah et al., 2024; Gao et al., 2024).

Traditional electricity markets face two critical challenges in integrating environmental value:

First, markets operate with separate mechanisms: energy trading and environmental transactions (e.g., carbon markets and green certificates) function independently with different clearing rules, time scales, and participants. This separation prevents the mutual influence between economic and environmental signals, leading to suboptimal outcomes in which energy dispatch decisions fail to reflect environmental costs (Al-Abdulqader et al., 2025; Zeng et al., 2023; Reshetnikova et al., 2023).

Second, environmental value is not precisely quantified: although carbon pricing policies exist (Al-Abdulqader et al., 2025), current approaches apply uniform rates that ignore the heterogeneity of prosumer contributions, such as renewable energy quality, reliability, and behavioral performance. This one-size-fits-all method fails to provide differentiated incentives for green energy production (Kasaei et al., 2017; Maanavi et al., 2019).

Existing VPP (Esfahani et al., 2019; Wang et al., 2016; Yang et al., 2019; Vieira and Zhang, 2021; Sousa-Dias et al., 2024; Li et al., 2018; Baringo and Rahimiyan, 2020; Sun et al., 2024; Ma et al., 2021; Zhang et al., 2023; Pena-Bello et al., 2022; Mallaki et al., 2020; Boyd et al., 2010; Maneesha and Swarup, 2021; Liu D. et al., 2023) research can be categorized into three main streams, each exhibiting specific limitations in achieving deep integration of environmental value and energy market operations:

Esfahani et al. (2019), Wang et al. (2016), and Yang et al. (2019) explored commercial VPP concepts and market participation mechanisms, focusing primarily on economic optimization. Li et al. (2018), Baringo and Rahimiyan (2020), and Sun et al. (2024) investigated bidding strategies and two-stage market participation (day-ahead and real-time), coordinating distributed resources through price signals. However, these approaches concentrate exclusively on energy market optimization without incorporating environmental value quantification into the market-clearing framework. As a result, prosumers lack explicit economic incentives to prioritize renewable generation over fossil-based alternatives, limiting the environmental effectiveness of VPP operations.

Recent research has begun incorporating environmental considerations. Liu D. et al. (2023) proposed a two-stage electricity-carbon joint trading mechanism in which VPPs participate sequentially in electricity and carbon markets with weekly cycles. Zhang et al. (2023) developed an optimal dispatch model incorporating both carbon trading and green certificate trading mechanisms, demonstrating improved economic and environmental performance. Similarly, studies have explored integrated electricity-carbon-green certificate (ECG) markets using bi-level optimization frameworks, in which the upper level optimizes VPP bidding strategies, and the lower level performs market clearing.

However, a critical limitation persists: these approaches treat environmental value and energy trading as separate sequential processes rather than unified joint clearing. Specifically:

Two-stage separation: VPPs first participate in energy markets and then separately engage in carbon/green certificate transactions.

Bi-level hierarchy: Upper-level VPP optimization, followed by lower-level market clearing, rather than simultaneous co-optimization.

Post-hoc environmental accounting: Carbon costs and green certificates are calculated after energy dispatch decisions, lacking bidirectional coupling.

This separation prevents the achievement of co-equilibrium, where energy and environmental value markets clear simultaneously, resulting in suboptimal resource allocation and weakened environmental incentives.

Vieira and Zhang (2021) and Sousa-Dias et al. (2024) explored peer-to-peer (P2P) energy trading frameworks with smart contracts and trust mechanisms, while Mallaki et al. (2020) introduced reputation systems for energy-reliability markets. These mechanisms successfully address behavioral reliability in energy transactions. However, they do not extend reputation or behavioral performance to environmental credit allocation, failing to link prosumer behavior with differentiated environmental incentives. Consequently, high-quality renewable energy producers and reliable market participants receive the same environmental credit treatment as less reliable actors.

Regarding solution methodologies, ADMM has been extensively applied to distributed VPP optimization problems, including P2P energy trading, multi-microgrid coordination, and transmission and distribution network (TSO-DSO) market clearing (Boyd et al., 2010; Maneesha and Swarup, 2021). For instance, recent studies have employed ADMM for distributed energy dispatch, market bidding optimization, and transactive energy management. However, existing ADMM applications focus exclusively on single-commodity market clearing (energy-only or ancillary services), in which only one market type is cleared at a time.

These gaps hinder the effective realization of market-based environmental incentives in VPP operations, motivating the development of a truly integrated joint trading mechanism.

2 Energy credit mechanism for environmental value quantification

The energy credit mechanism proposed in this article serves as the core component for environmental value quantification in VPP operations. To enhance the mechanism’s effectiveness, a reputation assessment system can be optionally integrated to differentiate prosumer performance by incentivizing accurate forecasting, reliable execution, timely responses, and active market participation while penalizing anomalous behavior. However, implementing such a reputation system requires comprehensive operational data collection and may raise concerns regarding data privacy and regulatory compliance.

Importantly, the joint energy credit clearing mechanism operates independently of the reputation system. The core clearing model and ADMM-based solution achieve co-optimization of energy and credit markets without requiring reputation scores. The reputation enhancement is entirely optional and can be adopted by VPP operators based on their specific contexts. For completeness, the detailed reputation calculation methodology is provided in Supplementary Appendix SA. When the optional reputation enhancement is adopted, data collection and privacy considerations are detailed in Supplementary Appendix SA.1.

2.1 Calculation and trading model of energy credits

2.1.1 Credit calculation model

The credit obtained by Prosumer for using energy type in time period is calculated using a multi-dimensional weighting method shown in Equation 1:where is the usage amount of energy type by Prosumer in time period (kW).

is the basic credit conversion coefficient for energy type , reflecting the environmental value differences of different energy sources, as defined in Equations 2, 3:where is the renewable energy certificate price (yuan/MWh); is the initial credit price (yuan/credit); is the carbon emission coefficient of gas turbines (tCO₂/MWh); is the carbon emission rights price (yuan/tCO₂); and are adjustment coefficients for renewable energy resources and fossil energy, respectively; and and are the corresponding scaling coefficients.

The prosumer type coefficient is used to distinguish the credit generation capabilities of different types of prosumers.

2.1.2 Credit trading mechanism

Prosumers can trade credits through the credit market. Gas turbine users are typically credit demanders, and their credit demand is calculated using Equation 7:where is the gas turbine generation of Prosumer in time period (kW); is the credit demand coefficient corresponding to unit gas turbine generation; and is the current surplus of credit.

Renewable energy resources are typically credit suppliers, and their credit supply is determined using Equation 8 based on credit surplus and market price:where is the supply ratio function related to the credit price.

The credit trading price on day is dynamically adjusted using Equation 9 according to market supply and demand relationships:where is the price adjustment coefficient and and are the total credit demand and total supply on day , respectively.

2.1.3 Credit penalty mechanism

For prosumers whose credit demand cannot be fully satisfied, the system implements a penalty mechanism. The penalty mainly targets gas turbine users, and the penalty cost is calculated using Equation 10:where is the unmet credit demand of Prosumer and is the penalty coefficient, satisfying .

This penalty mechanism embodies the principle of “polluter pays,” prompting high-carbon emission users to actively reduce carbon emissions or purchase sufficient credits to compensate for their environmental impact.

Through the above design, the reputation-based energy credits calculation model establishes a dynamic coupling relationship between reputation values and credit generation. It not only effectively quantifies the environmental value of green energy but also constrains prosumer behavior through the reputation mechanism, incentivizes the production and consumption of green energy, and provides strong support for the sustainable development of virtual power plants.

3 Energy credits–electricity joint trading mechanism

To fully leverage the energy credit mechanism and achieve unified management of energy value and environmental value, this chapter proposes an energy credits–electricity joint trading mechanism. This mechanism is designed for a community-level virtual power plant within the distribution network. It operates in the day-ahead market timeframe to determine the optimal dispatch and trading plan for the next 24 h. This mechanism unifies the clearing problems of energy and credit markets through modeling, decomposes large-scale optimization problems into parallelizable subproblems using the alternating direction method of multipliers (ADMM), and achieves collaborative optimization of energy trading and credit trading.

3.1 Joint clearing problem modeling

3.1.1 Objective function

The objective function of joint clearing aims to maximize the overall system benefits, including energy market benefits, credit market benefits, and the coupling benefits between them. It is important to clarify the ownership and operational model adopted in this study. The VPP is defined as a cooperative aggregation (grand coalition) of prosumers, rather than a profit-oriented commercial entity owned by a single operator. In this framework, the VPP operator functions as a “community manager” who coordinates the market to maximize the collective social welfare of the entire alliance (i.e., the sum of benefits for all prosumers), as formulated in Equations 11–14.

where , , and represent the objective functions for the energy market, the credit market, and the energy credit coupling terms, respectively. represents the trading decision of Prosumer for energy type in time period (kW), . Positive values indicate selling energy to the market, while negative values indicate purchasing energy from the market. represents the credit trading decision of Prosumer (credits), . Positive values indicate selling credits to the market, while negative values indicate purchasing credits from the market. is the utility function of Prosumer for energy type ; is the corresponding cost function. is the credit utility function of Prosumer ; is the credit cost function. is the coupling weight coefficient; is the credit conversion coefficient for energy type .

3.1.2 Cost model and constraint conditions of the energy market

The operational costs of gas turbine generation include fuel consumption and maintenance expenses, which are typically modeled as a quadratic function of output power using Equation 15.

Additionally, to quantify the battery aging and operation costs, an equivalent degradation cost model is adopted. The degradation cost is proportional to the energy throughput (charging and discharging amount), expressed as Equation 16:

which is consistent with prior VPP scheduling that accounts for energy-storage degradation costs (Borisoot et al., 2023).

where represents the degradation cost of the energy storage system for Prosumer at time ; is the unit degradation cost coefficient (depreciation cost) per kW of power throughput; and and are the charging and discharging power, respectively.

Consequently, this cost term is incorporated into the prosumer’s total energy cost function in Equation 12, ensuring that the optimization strategy accounts for battery cycle life.

Thermostatically controlled loads (e.g., HVAC systems) provide demand-side flexibility by adjusting power consumption within acceptable temperature bounds. The indoor temperature dynamics are modeled using Equation 17:where is the indoor temperature at time t, is the outdoor temperature, and C(i) are the equivalent thermal resistance (K/kW) and thermal capacitance (kWh/K) representing building thermal characteristics, is the coefficient of performance (COP) of the heating/cooling system, P(i,t,TCL) is the thermostatically controlled load (TCL) power consumption (kW), and Δt is the time step.

The indoor temperature must remain within the comfort range defined by Equation 18:where and define the acceptable temperature bounds for Prosumer i.

The constraint conditions of the energy trading are formulated as Equations 19–30, including load constraints (Equation 19), renewable energy output constraints (Equations 20, 21), gas turbine operation constraints (Equations 22, 23), energy storage operation constraints (Equations 24–28), power balance constraints (Equation 29), and prosumer trading capacity constraints (Equation 30).

Load constraintswhere is the load power of Prosumer in time period (kW) and and are the lower and upper limits of the load power, respectively.

Renewable energy output constraintswhere and are the forecasted outputs of photovoltaic and wind power, respectively; and are output power of photovoltaic and wind power, respectively. and are the sets of photovoltaic and wind power prosumers, respectively.

Gas turbine operation constraintswhere is the power of the gas turbine; and are the gas turbine generation lower and upper limits, respectively; is the ramping constraint; and is the set of gas turbine prosumers.

Energy storage operation constraintswhere and are the charging and discharging power of energy storage (kW), respectively; and are the charging and discharging power upper limits, respectively; and is the set of energy storage prosumers. Equation 26 ensures that energy storage does not charge and discharge simultaneously. is the state of charge of energy storage; and are the state of charge lower and upper limits, respectively; and are the charging and discharging efficiencies, respectively; is the energy storage capacity (kWh); and is the time step.

Power balance constraints

Prosumer trading capacity constraintswhere and are the trading lower and upper limits of Prosumer for energy type , respectively.

3.1.3 Constraint conditions of the credit market

The constraint conditions of the credit trading are formulated as Equations 31–33, including credit trading constraints (Equations 31, 32) and the gas turbine user credit demand constraint (Equation 33).

Credit trading constraintswhere and are the credit trading lower and upper limits of Prosumer , respectively; and is the lower limit of credit surplus.

Gas turbine user credit demand constraintswhere is the credit demand coefficient for gas turbine generation.

3.2 ADMM-based solution algorithm

3.2.1 ADMM algorithm principle

The ADMM is an effective distributed optimization algorithm, particularly suitable for solving large-scale optimization problems with a separable structure. The joint clearing problem can be reformulated into the standard ADMM form as Equation 34:where represents the prosumer decision variables; represents the market coordination variables; is the prosumer objective function; is the market coordination objective function; and represents the market clearing constraints.

Equation 35 shows the corresponding Lagrangian function:where is the Lagrange multiplier and is the penalty parameter.

3.2.2 ADMM decomposition strategy

In each iteration of ADMM, each Prosumer must solve the subproblem of Equation 36:

where is the objective function of Prosumer ; is the ADMM penalty term; is the penalty parameter; and and are the auxiliary variables and Lagrange multipliers at the iteration, respectively.

Equations 37, 38 present the update formula for Lagrange multipliers:where is the relaxation parameter.

3.2.3 Convergence criteria

The convergence of the ADMM algorithm is determined by primal and dual residuals. The algorithm is considered converged when the conditions shown as Equations 39–42 are satisfied:where , , , and are the absolute and relative tolerances for primal and dual residuals, respectively; and are the primal residuals; and are the dual residuals, which are calculated using Equations 43–46:

3.2.4 Adaptive parameter adjustment

To improve the convergence speed of the algorithm, the adaptive parameter adjustment strategy using Equations 47, 48 is adopted to adjust the penalty parameter and relaxation parameter:where and are adjustment factors; is the balance factor; ; ; and , , and are the upper limit, lower limit, and adjustment step of the relaxation parameter, respectively.

Through the above joint trading mechanism, the system achieves deep integration of energy trading and credit trading, not only improving market operation efficiency but also promoting green energy accommodation and system stable operation through reputation mechanisms and credit mechanisms. The distributed nature of the ADMM algorithm enables efficient solution of large-scale optimization problems.

4 Case study and result discussion

To validate the effectiveness of the proposed reputation-based energy credits–electricity joint trading mechanism, comprehensive simulations are conducted on a virtual power plant system comprising four prosumers with heterogeneous distributed energy resources. This section first presents the simulation configuration and original data, followed by a detailed analysis of carbon credit dynamics, sensitivity studies, and economic performance evaluation.

4.1 Simulation configuration and original data

The simulation system represents a community-scale virtual power plant consisting of four prosumers equipped with different combinations of distributed generation, energy storage, and flexible loads. The system operates under a multi-day carbon credit settlement mechanism, in which energy trading and carbon credit allocation are jointly optimized through the proposed ADMM-based clearing algorithm. Three simulation scenarios are designed to evaluate system performance under different temporal scales and seasonal conditions:

Scenario 1: Single-day operation (24 h) for baseline analysis.

Scenario 2: Multi-day operation (120 h) with a 5-day carbon credit settlement cycle.

Scenario 3: Seasonal variations (120 h) across spring, summer, and winter conditions.

4.2 Prosumer configuration

The four prosumers represent typical participants in a community energy system, as detailed in Table 1. Prosumer 1 operates exclusively with renewable generation (photovoltaic (PV) + energy storage (ES)), representing an environmentally conscious household. Prosumer 2 relies on dispatchable gas turbine generation (micro-turbine (MT) + ES) to meet higher load demands, representing a commercial facility. Prosumer 3 functions as a pure energy storage operator, providing flexibility services to the community. Prosumer 4 operates a hybrid system (PV + MT + ES) with moderate renewable penetration, representing a mixed-use building.

The load scale and PV scale factors represent the relative sizing of each prosumer’s load demand and PV generation compared to the baseline profiles, accounting for building characteristics and occupancy patterns.

4.3 System parameters

To ensure the accuracy and credibility of the simulation, the physical parameters (carbon trading price, emission factors, storage efficiency, and electricity pricing) and mechanism design hyperparameters (reputation weights, credit adjustment coefficients, penalty coefficients, and ADMM algorithm settings) are calibrated based on established market data and literature, as documented in references (Boyd et al., 2010; International Carbon Action Partnership (ICAP), 2025; U.S. Environmental Protection Agency, 2024; Kaczorowska et al., 2020; Wang et al., 2021; Li et al., 2024; Gong et al., 2024).

The carbon credit pricing mechanism is calibrated based on China’s renewable energy certificate (REC) market and national carbon emission trading system (ETS). Table 2 summarizes the key environmental parameters.

The technical parameters for distributed energy resources are configured according to typical commercial specifications, as shown in Table 3.

The electricity pricing follows a time-of-use tariff structure reflecting typical urban grid conditions in China. The ADMM algorithm parameters presented in Table 4 are tuned to balance convergence speed and solution quality for the multi-day, multi-prosumer optimization problem.

4.4 Load and generation profiles

4.4.1 Baseline profiles

The baseline operational data for the 24-h simulation cycle are illustrated in Figure 1, which presents the electricity pricing structure, load demand pattern, and photovoltaic generation forecast that form the foundation of the optimization model. It is important to note that the load and PV generation profiles used in this study are typical operational curves derived from the reference data in Wang et al. (2024). In this article, raw data profiles were smoothed to filter out high-frequency stochastic fluctuations. This simplification was intentionally adopted to clearly verify the feasibility of the proposed joint trading mechanism and to visualize the coupling relationship between energy flow and carbon credits without the interference of random noise. While smoothed, the profiles retain the critical peak-valley characteristics representative of actual prosumers, which is sufficient for the proof-of-concept analysis of the proposed strategy.

4.5 Seasonal adjustments

For Scenario 3, the baseline profiles are modified according to seasonal characteristics, as summarized in Table 5.

The seasonal scaling factors are applied to the baseline profiles to reflect (1) solar irradiance variations due to weather patterns and sun angle, (2) heating/cooling load changes driven by temperature differences, and (3) occupancy pattern shifts across seasons.

4.6 Single-day simulation analysis

This section presents a detailed analysis of a typical 24-h operation to demonstrate the mechanism’s effectiveness in coordinating heterogeneous distributed resources and implementing carbon credit accounting.

4.6.1 System-level operation

Figure 2 illustrates the system-wide power balance and energy composition. The total load exhibits a typical double-peak pattern, reaching maximum values of 82 kW at 13:00 and 90 kW at 18:00. PV generation operates during daylight hours (08:00–20:00) with peak output of 18 kW, while MT generation provides dispatchable backup during the evening peak (19:00–21:00) with maximum output of 25 kW.

The net grid power reveals bidirectional interaction: the system exports up to 60 kW during midday surplus periods and imports up to 78 kW during evening peaks. The 24-h energy composition shows grid electricity comprising 74.2%, PV generation 17.3%, and MT generation 8.5%, demonstrating effective renewable integration despite intermittency constraints.

4.6.2 Individual prosumer dispatch strategies

Figure 3 presents the dispatch strategies of four representative prosumers with distinct asset configurations:

Prosumer 1 (PV + ES): Maximizes PV self-consumption during daytime, charges storage during surplus periods, and discharges during evening hours to minimize grid dependence.

Prosumer 2 (MT + ES): Operates MT during evening peak periods (18:00–21:00) for price arbitrage, while charging storage during valley hours and discharging during peaks.

Prosumer 3 (ES only): Conducts pure energy arbitrage without local generation, charging during low-price periods and discharging during peaks.

Prosumer 4 (PV + MT + ES): Achieves the highest operational flexibility by combining renewable generation (10:00–18:00), dispatchable MT (18:00–21:00), and storage arbitrage.

The heterogeneous strategies validate the mechanism’s adaptability to diverse participant portfolios while providing differentiated incentives based on carbon intensity.

4.6.3 Carbon credit flow analysis

Figure 4 quantifies energy consumption patterns and resulting carbon credit dynamics. Prosumer 2 exhibits the highest consumption at 300 kWh with the lowest renewable fraction, while Prosumer 4 achieves 27% renewable penetration through its hybrid PV + MT configuration.

The carbon credit balance reveals clear differentiation: Prosumer 1 accumulates +26.6 credits through exclusive PV/storage operation, while Prosumer 2 incurs −25.1 credits due to MT fossil fuel consumption. Prosumer 3 experiences −1.6 credits from grid electricity’s carbon intensity, and Prosumer 4 maintains +1.8 credits despite MT operation, benefiting from substantial PV generation offset.

This 51.7-point differential between the highest and lowest performers creates substantial economic incentives for renewable investment and emission reduction, validating the mechanism’s “green contributors benefit, polluters pay” principle.

4.7 Multi-temporal scale simulation

To validate the effectiveness of the proposed carbon credit settlement mechanism over extended periods, a 5-day simulation is conducted with periodic carbon credit balancing. Unlike the single-day scenario, this multi-day case allows daily imbalances in carbon credits, which are settled at the end of the 5-day cycle.

4.7.1 Carbon credit evolution

Figure 5 illustrates the carbon credit dynamics over the 5-day period. As shown in Figure 5a, Prosumer 1 (equipped with PV + ES) steadily accumulates positive credits, reaching 136.2 points by day 5, benefiting from its renewable generation capacity. Conversely, Prosumer 2 (MT + ES) experiences continuous credit depletion, ending at −129.8 points due to its reliance on carbon-intensive microturbine generation. Prosumers 3 (ES only) and 4 (PV + MT + ES) maintain relatively balanced positions, with final balances near zero (−2.4 points for Prosumer 4).

The daily carbon credit generation and consumption patterns shown in Figure 5b reveal significant day-to-day variations. Prosumer 1 consistently generates 20–33 points per day, while Prosumer 2 consumes 15–42 points per day, with peak consumption occurring on days 1 and 5. This temporal imbalance underscores the need for flexible settlement mechanisms that accommodate operational uncertainties while ensuring long-term carbon accountability.

4.7.2 System-level carbon balance

Figure 6 presents the community-wide carbon credit dynamics. The daily generation versus consumption comparison shown in Figure 6a shows that carbon credit generation fluctuates between 20 points and 50 points per day, while consumption ranges from 15 points to 65 points. The net balance (indicated by the black line) exhibits substantial volatility, varying from −40 points on day 1 to +32 points on day 5. This variability reflects the stochastic nature of renewable generation and load demand across different days.

Figure 6b tracks the cumulative net balance over the 5-day period. Starting at −38 points on day 1, the cumulative deficit improves gradually, reaching approximately 0 points by day 5. Notably, the annotation indicates “External Purchase: 0.0 points,” confirming that the community achieves carbon credit balance over the 5-day cycle without requiring external carbon purchases. This validates the effectiveness of the proposed multi-day settlement mechanism in maintaining system-level carbon neutrality despite significant daily fluctuations.

4.7.3 Economic performance

Figure 7 analyzes the economic outcomes of the 5-day operation. The revenue structure shown in Figure 7a shows that all prosumers incur net costs, primarily driven by energy procurement expenses (blue bars). The small orange portions represent carbon credit trading revenue, which is minimal compared to energy costs. Prosumer 2 faces the highest total cost (approximately 600 yuan) due to its dependence on both grid purchases and MT operation.

Figure 7b highlights the carbon credit penalty costs, where Prosumer 1 bears the largest penalty (approximately 9.8 yuan), despite having a positive cumulative credit balance. This counterintuitive result occurs because the penalty mechanism penalizes interim imbalances before the final 5-day settlement, incentivizing smoother daily credit profiles rather than extreme day-to-day variations.

The net economic performance shown in Figure 7c demonstrates substantial cost variations across prosumers, ranging from approximately −370 yuan (Prosumer 1) to −610 yuan (Prosumer 2). The average cost line indicates a mean expenditure of approximately −460 yuan per prosumer, reflecting the community’s overall operational expenses when considering both energy and carbon credit trading costs.

4.7.4 Energy utilization analysis

Figure 8 analyzes the energy consumption patterns and renewable penetration. The 5-day total energy composition shown in Figure 8a reveals distinct energy portfolios across prosumers. Prosumer 1 achieves the highest renewable share with approximately 35% PV generation, while the remaining 65% comes from grid electricity. Prosumer 2 relies primarily on grid purchases with a modest MT contribution. Prosumer 3, lacking any generation assets, depends entirely on grid electricity. Prosumer 4, with its hybrid PV + MT + ES configuration, demonstrates a more balanced energy portfolio with notable contributions from all three sources (PV, MT, and grid).

The daily renewable energy penetration shown in Figure 8b exhibits remarkable stability, fluctuating only between 16.4% and 17.4% with an average of 16.8% across all 5 days. This consistency indicates effective day-ahead scheduling that maintains stable renewable integration despite daily variations in load and PV generation. The tight clustering around the average baseline demonstrates the robustness of the proposed energy management strategy in maintaining predictable renewable utilization patterns.

4.8 Seasonal analysis

To evaluate the robustness of the proposed mechanism under varying environmental conditions, a 5-day simulation is conducted across three representative seasons: spring, summer, and winter. Each season exhibits distinct characteristics in terms of load patterns, PV generation capacity, and ambient temperature, providing a comprehensive assessment of system adaptability.

4.8.1 Seasonal load and PV characteristics

Figure 9 illustrates the typical daily load and PV generation profiles for each season on day 3. Spring conditions shown in Figure 9a demonstrate moderate load demand with peak values of approximately 120 kW and balanced PV generation reaching 18 kW during midday hours. The ambient temperature of 18 °C results in relatively stable energy consumption patterns without extreme heating or cooling requirements.

Summer characteristics shown in Figure 9b reveal significantly elevated load demand, peaking at approximately 200 kW due to intensive air conditioning loads under 32 °C ambient temperature. Despite higher solar irradiation, the PV generation peaks at similar levels (∼18 kW) as spring, creating a notable supply-demand mismatch during afternoon hours when cooling loads remain high while solar generation begins to decline.

Winter operation shown in Figure 9c shows distinct dual-peak load patterns, with morning and evening peaks reaching 180–200 kW driven by heating demand in the 5 °C environment. Critically, PV generation is substantially reduced, peaking at only 18 kW and exhibiting a compressed generation window. This temporal mismatch between peak heating demand and limited solar availability presents the most challenging scenario for renewable energy utilization.

4.8.2 Seasonal performance comparison

Figure 10 quantifies the system-level performance across seasons. The carbon credit balance shown in Figure 10a shows that all three seasons achieve near-zero net balances over the 5-day cycle, validating the effectiveness of the periodic settlement mechanism. Spring maintains excellent balance with generation (131 points) nearly matching consumption (132 points). Summer exhibits the highest carbon credit activity with 155 points generated and 159 points consumed, resulting in a minor deficit of approximately 4 points. Winter demonstrates a slight surplus of 17 points (151 points generated versus 134 consumed), likely due to increased reliance on grid electricity rather than carbon-intensive MT generation during peak heating periods.

The renewable energy penetration shown in Figure 10b reveals significant seasonal variation. Spring achieves the highest penetration at 14.9%, benefiting from favorable solar conditions and moderate load levels. Summer penetration drops to 9.3% despite strong solar irradiation, as the dramatically increased cooling loads dilute the relative contribution of PV generation. Winter records the lowest penetration at 8.4%, reflecting both reduced solar availability and increased heating demands. The average penetration across seasons stands at 10.9%, indicating consistent but modest renewable integration that remains relatively stable despite substantial environmental variations.

These seasonal results demonstrate that while the proposed carbon credit mechanism successfully maintains system-level balance across diverse operating conditions, the inherent seasonal variability in load patterns and renewable generation creates significant fluctuations in renewable penetration rates. The winter season, in particular, highlights the challenge of maintaining high renewable energy utilization when solar resources are limited and energy demands are increased.

5 Conclusion

This study successfully constructs and validates an energy credits–electricity joint trading mechanism for virtual power plants, effectively addressing the critical challenge of integrating environmental value quantification with energy market operations. The proposed unified joint clearing framework achieves simultaneous co-equilibrium between energy and environmental value markets, fundamentally different from existing sequential or hierarchical approaches. The multi-dimensional energy credit quantification model integrates energy type, temporal characteristics, trading scale, and behavioral performance into differentiated environmental incentives, while the ADMM-based decomposition strategy enables efficient distributed solution of large-scale optimization problems.

Simulation results across diverse operational scenarios validate the mechanism’s effectiveness. Single-day analysis demonstrates clear differentiation: renewable energy prosumers (Prosumer 1) accumulate positive credits (+26.6 credits) through exclusive PV/storage operation, while fossil fuel users (Prosumer 2) incur credit deficits (−25.1 credits) requiring compensation. Multi-day simulations over 5-day settlement cycles show renewable users achieving cumulative credit accumulation (136.2 credits) while maintaining system-level carbon credit balance, validating the mechanism’s temporal flexibility. Seasonal analysis across spring, summer, and winter conditions demonstrates stable performance with renewable penetration ranging from 8.4% to 14.9%, confirming robustness to environmental variations. The credit differentiation span of more than 50 points between the highest and lowest performers creates substantial economic incentives for renewable investment and emission reduction, effectively realizing the principle of “green contributors benefit, polluters pay.”

The research provides a practical implementation blueprint for environmental value integration in electricity markets. The modular design allows VPP operators to deploy the mechanism according to their operational context, with core joint clearing functionality and optional reputation enhancement. This flexibility makes the mechanism adaptable to different regulatory frameworks and infrastructure capabilities, providing policymakers with a tool for designing precise environmental incentives.

Despite achieving positive results, certain limitations remain for future research. The current simulation operates under idealized conditions, while practical applications will face challenges such as communication delays, stochastic renewable generation, and heterogeneous participant capabilities. Future work should focus on incorporating uncertainty modeling, developing fault-tolerant mechanisms, conducting systematic sensitivity analysis of design parameters, investigating scalability under extreme participation scenarios, and exploring integration pathways with existing market structures and regulatory frameworks.

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