Research on the Low-Carbon Economic Operation Optimization of Virtual Power Plant Clusters Considering the Interaction Between Electricity and Carbon

Abstract

Under carbon emission constraints, to promote low-carbon transformation and achieve the aim of carbon peaking and carbon neutrality in the energy sector, this paper constructs an operational optimization model for the coordinated operation of a virtual power plant cluster (VPPC). Considering the resource characteristics of different virtual power plants (VPPs) within a cooperative alliance, we propose a multi-VPP interaction and sharing architecture accounting for electricity–carbon interaction. An optimization model for VPPC is developed based on the asymmetric Nash bargaining theory. Finally, the proposed model is solved using an alternating-direction method of multipliers (ADMM) algorithm featuring an improved penalty factor. The research results show that P2P trading within the VPPC achieves resource optimization and allocation at a larger scale. The proposed distributed ADMM solution algorithm requires only the exchange of traded electricity volume and price among VPPs, thus preserving user privacy. Compared with independent operation, the total operation cost of the VPPC is reduced by 20.37%, and the overall proportion of new energy consumption is increased by 16.83%. The operation costs of the three VPPs are reduced by 1.12%, 20.51%, and 6.42%, respectively, while their carbon emissions are decreased by 4.47%, 5.80%, and 5.47%, respectively. In addition, the bargaining index incorporated in the proposed (point-to-point) P2P trading mechanism motivates each VPP to enhance its contribution to the alliance to achieve higher bargaining power, thereby improving the resource allocation efficiency of the entire alliance. The ADMM algorithm based on the improved penalty factor demonstrates good computational performance and achieves a solution speed increase of 15.8% compared to the unimproved version.

1. Introduction

1.1. Literature Review

In recent years, the traditional centralized energy architecture has been gradually transitioning toward decentralization and flexibility [1]. The rapid development of distributed energy resources (DERs)—such as renewable energy systems, energy storage units, and flexible loads—has introduced both opportunities and challenges to power systems [2]. However, the dispersed and intermittent nature of DERs complicates their coordinated management. In this context, the virtual power plant (VPP) has emerged as a solution. By aggregating DERs and leveraging advanced communication and control technologies, VPPs enable unified management and scheduling of diverse resources [3], enhancing integration efficiency and collaborative optimization. Additionally, participation in electricity market transactions allows VPPs to generate additional revenue for internal resources, positioning them as a critical link between distributed energy and centralized grids.

VPP planning, operation, and business models have become key research foci. Regarding operational mechanisms, reference [4] proposed a decision-making model for VPP operation that incorporates price-based demand response (DR). This model integrated pumped hydro storage and battery storage as energy storage devices, while also considering renewable energy sources. Similarly, reference [5] optimized the operational costs of a VPP by employing a combined energy storage system utilizing both battery storage and pumped hydro storage, concurrently accounting for two types of renewable energy: wind power and photovoltaic (PV) power. Reference [6] designed a VPP model for spot market participation and developed a two-stage optimization approach to address electricity price volatility risks. To improve VPP economic and environmental performance, extensive research has focused on dispatch optimization. For instance, reference [7] introduced a multi-energy coupling VPP method incorporating energy storage, carbon capture (CCS), and power-to-gas (P2G) systems. Reference [8] optimized DER aggregation within VPPs to enhance operational efficiency. Reference [9] proposed a scheduling model for a rural VPP. This VPP internally aggregates rural biomass energy resources, distributed renewable energy sources, and demand-responsive loads. Reference [10] developed a two-stage optimization model for VPP scheduling. The upper-level optimizes the collaborative power generation from supply-side generating units, while the lower-level focuses on the optimized scheduling of demand response on the load side. Reference [11] established a multi-objective operation optimization model for VPPs. This model aims to simultaneously enhance operational economics and distribution grid security. Reference [12] proposed a multi-objective model balancing revenue, grid losses, and peak-valley mitigation. The existing literature primarily emphasizes single-VPP internal optimization, demonstrating VPPs’ advantages in cost reduction and renewable energy integration. However, as power systems and energy markets evolve, standalone VPP operations reveal their limitations [13]. Reference [14] proposed an optimal scheduling strategy for multi-VPP games considering carbon trading costs. Reference [15] developed a cooperative game optimization model for multi-VPPs that explicitly accounts for interactions between VPPs while balancing coalition and individual interests, solving it using a merge-and-split-based game algorithm. Reference [16] proposed a bi-level game methodology for VPP dispatch utilizing multiple regional integrated energy systems. Nevertheless, these approaches largely overlook the profit-maximization objectives of microgrid operators as rational individual entities. Reference [17] employed Nash bargaining theory to investigate point-to-point (P2P) transactions between VPPs, constructing a transaction game model for interconnected VPPs. Compared to Stackelberg methods, this approach simultaneously addresses individual benefits and social welfare while enhancing Pareto optimality. Reference [18] further considered loss risks and carbon flow, formulating a cooperative game model for multi-VPPs based on Nash negotiation, and allocated benefits among VPPs using the Shapley value. Collectively, these studies validate the feasibility of employing Nash bargaining theory to represent supply–demand interactions.

Furthermore, most of the aforementioned literature employs centralized algorithms. While such algorithms offer high computational efficiency, they may incur risks associated with information leakage. Reference [19] employed the Alternating-Direction Method of Multipliers (ADMM) algorithm to solve the optimal operation problem for a multi-regional energy system. Reference [20] developed a multi-VPP scheduling optimization model based on multi-tiered game theory, incorporating load demand response mechanisms. Additionally, the ADMM algorithm was utilized to solve the formulated model. Reference [21] proposed a hierarchical control architecture for VPPs. Furthermore, an integrated spectral clustering–ADMM algorithm was introduced to enhance the model’s convergence efficiency. Reference [22] formulated a multi-VPP management mechanism based on an adaptive ADMM method. It was highlighted that the distributed algorithm effectively protects the data privacy of alliance members without compromising solution accuracy.

It can be seen that current research on VPPC has problems in aspects such as user privacy protection and solution efficiency. Based on this, on the basis of constructing the framework of VPPC, this paper uses the Nash negotiation model and asymmetric bargaining theory, starting from the two aspects of overall benefits and individual benefits, decomposes the operation optimization problem of VPPC into two subproblems that are easy to solve—the decision-making of VPP transaction volume and the decision-making of VPP transaction price—and uses the distributed algorithm of the improved ADMM to solve the model, taking into account both user privacy protection and solution efficiency.

1.2. Contributions

Through the analysis of existing research, it is evident that the fundamental economic dispatch problem of VPPs has been effectively addressed. However, current studies on multi-VPP interactions primarily focus on electrical energy exchange, with limited consideration given to carbon emission rights trading—a critical component in the context of global low-carbon energy transitions. Furthermore, most of the existing literature employs centralized algorithms to solve multi-VPP dispatch optimization models, which inadequately safeguards the privacy of participating entities. In view of these limitations, this paper considers different types of VPPC, including power-source-dominant, load-dominant, and hybrid configurations, and proposes an optimization framework that simultaneously accounts for electricity and carbon interactions. Building upon this foundation, the asymmetric bargaining theory is applied to decompose the Nash bargaining model of VPPC into two interconnected subproblems: minimizing the overall cost of the coalition while simultaneously minimizing individual VPP costs. To address transaction privacy concerns in VPPC operations, an improved ADMM algorithm incorporating a penalty factor correction parameter is developed, enhancing both computational efficiency and data protection. The proposed model is subsequently solved and validated using this enhanced algorithm. The main contributions of this work are as follows:

• Electricity–carbon interactive architecture:

A novel multi-VPP interaction framework enabling simultaneous electrical energy and carbon emission rights trading, extending traditional single-dimensional resource sharing to dual-dimensional coordination among heterogeneous VPPs.

• Privacy-preserving distributed optimization:

A Nash bargaining-based operation model that requires only trading volume and price data exchange between VPPs, effectively protecting core private parameters (e.g., cost functions, resource constraints) of alliance members.

• Improved ADMM algorithm:

An improved distributed solving method with adaptive penalty factors, achieving 23% faster convergence in test cases while maintaining solution accuracy compared to conventional ADMM.

2. Framework of VPPC

The VPPC framework proposed in this paper is designed to integrate diverse energy resources, achieve system-wide optimization, and ensure efficient electricity distribution and utilization. To demonstrate this framework, we analyze a cooperative alliance comprising three VPPs as a case study. Each VPP within the alliance incorporates some or all of the following components: wind turbines (WTs), PV systems, electrical energy storage (EES), thermal energy storage (TES), gas turbines (GTs), waste heat boilers (WHBs), carbon capture systems (CCSs), as well as electrical and thermal loads.

In this study, VPP1 represents a load-type virtual power plant characterized by aggregating a large number of electrical loads while relying on limited supply-side resources, including a small amount of renewable generation and GTs. The absence of a WHB prevents heat–electricity decoupling, resulting in electrical energy shortages and relatively low operational flexibility. In contrast, VPP2 operates as a power-source-type VPP where renewable energy output significantly exceeds internal load demand, creating surplus electricity but facing renewable energy curtailment issues. VPP3 serves as a balanced hybrid-type system with relatively equal supply and demand, equipped with a WHB for flexible operation, though its limited renewable penetration requires supplementary fossil-fuel generation. These distinct resource configurations enable complementary advantages through cluster coordination: VPP1 and VPP3 can assist VPP2 in renewable energy absorption while reducing their own fossil-fuel consumption, thereby achieving optimal resource allocation and carbon emission reduction through power interactions within the VPP coalition. Notably, the interaction between VPPs extends beyond electricity exchange to include carbon emission rights trading, while heat interaction is excluded due to the technical challenges of heat pipeline transportation and the dispersed nature of VPP resources. As shown in Figure 1, the proposed VPPC operational architecture allows any VPP to flexibly engage in electricity and carbon trading with external systems including the main power grid, gas networks, and carbon markets. Each VPP operates under independent operator control, while a central cluster operator coordinates energy-sharing information exchange and facilitates inter-VPP coordination.

3. Distributed Operation Model of VPPC Based on Nash Negotiation

3.1. Nash Bargaining Model of Cooperative Game

3.1.1. Basic Principle of Nash Negotiation

The Nash negotiation theory can, on the premise of taking into account both individual and collective interests, find an equilibrium solution by maximizing the Nash product, enabling each VPP to obtain Pareto optimal benefits. To ensure the fairness of the negotiation process and its results, Nash negotiation emphasizes that all participants can improve their own utility through negotiation, that is, the income after cooperation must be greater than the breakdown point of the negotiation; otherwise, they will not participate in the cooperation. Based on this, each VPP can reach a consensus in the process of determining the interaction volume and price of electricity and carbon emissions, as shown in Equation (1).

$$\left\{\begin{array}{c}\max {\displaystyle \prod _{i=1}^I(U_i-U_i^0)}\\ \mathrm{s}.\mathrm{t}. U_i-U_i^0\ge 0\end{array}\right.$$

(1)

In the formula, $U_i$ is the benefit of player $i$ after participating in the cooperation, $U_i^0$ is the benefit of player $i$ before participating in the cooperation. The Nash negotiation breakdown point usually refers to the solution in the worst-case scenario. In this paper, it refers to the optimal benefit of each VPP when there is no energy interaction. When the benefit is less than the negotiation breakdown point, it means that the income obtained by the VPP from participating in the alliance is lower than that of independent operation, and at this time, the VPP withdraws from the cooperation.

3.1.2. Nash Negotiation Model of VPPC

The Nash negotiation model in Equation (1) is difficult to solve directly. According to Reference [23], Equation (1) can be equivalently decomposed into two subproblems: the optimal alliance benefit (Subproblem 1) and the optimal individual benefit (Subproblem 2). Subproblem 1 aims to maximize the alliance benefit, focusing on the overall benefit. Through the solution, the bargaining index of each VPP $P_i$, the alliance gain, and the electricity quantity of each VPP through P2P transactions are transmitted to Subproblem 2. Subproblem 2 aims to maximize the individual benefit of the VPP, focusing on individual rationality. By substituting the variables output by Subproblem 1, the P2P transaction price is solved.Relationship between Subproblems 1 and 2 is shown as Figure 2.

This decomposition is fundamentally motivated by the need to resolve the inherent complexity of simultaneously optimizing interdependent physical power flows and economic prices. This joint optimization renders the original problem highly non-convex and resistant to direct solution. Drawing upon established mathematical equivalence proven in reference [23], we recognize that the Nash bargaining solution, maximizing the product of individual net gains, can be equivalently achieved by first maximizing the sum of these gains (the total coalition surplus) and then ensuring this surplus is distributed proportionally according to each participant’s bargaining power.

The core conceptual workflow and variable transmission mechanism driving the equivalence are as follows:

Subproblem 1: This stage acts as the physical optimizer, focusing solely on maximizing the collective benefit achievable through the coordinated operation of the VPPC, before setting specific transaction prices. It operates independently of detailed price negotiations between individual pairs. Crucially, by solving this physically constrained optimization (typically a linear or quadratic program), Subproblem 1 determines the optimal P2P energy exchange volumes, the total achievable coalition gain, and, as a natural by-product of its Lagrangian solution (specifically, the optimal dual variables associated with power balance or resource constraints per VPP), the intrinsic bargaining indices. These bargaining indices quantify the marginal value contribution of each VPP i to the overall coalition optimum, effectively reflecting their relative ‘scarcity value’ or leverage within the collaborative network at the optimal physical operating point. P2P energy exchange volumes, total achievable coalition gain, and bargaining indices are the primary outputs passed from Subproblem 1 to Subproblem 2.

Subproblem 2: Leveraging the fixed physical solution (energy exchange volumes, total achievable coalition gain, bargaining indices) from Stage 1, this stage acts as the fairness enforcer. Its objective is to establish the P2P transaction prices that distribute the already-realized total achievable coalition gain among the VPPs in a manner that is both individually rational and proportionally fair, precisely according to the bargaining indices derived in Stage 1. It accomplishes this by maximizing the weighted sum of the logarithms of individual net gains. The solution to this optimization explicitly yields the proportional fairness condition. The actual P2P transaction prices emerge as the mechanism satisfying this condition, ensuring the division of total achievable coalition gain respects the relative bargaining power (bargaining indices) signified by the physical solution’s dual variables. No physical quantities are altered at this stage; P2P transaction prices are the primary output.

This decomposition achieves equivalence to the original Nash bargaining problem because of the following:

• Subproblem 1 guarantees the solution lies on the Pareto frontier (i.e., no other feasible physical schedule yields a higher total gain total achievable coalition gain), satisfying the collective optimality requirement.
• Subproblem 2, using the bargaining indices derived from Subproblem 1’s KKT conditions (which encode sensitivity at the optimum), ensures the distribution of total achievable coalition gain adheres to the proportional fairness inherent in the Nash product. The combined solution therefore satisfies the necessary optimality conditions for the original problem.

3.2. Calculation of the Individual Benefits of VPPs Under the Cooperative Alliance

3.2.1. Objective Function

From an overall perspective, the total operation optimization cost of VPPi includes several parts such as the interaction cost with the external market $C_{i,buy}^{grid}$, the cost of P2P transactions with other VPPs in the alliance $C_{i,buy}^{P2P}$, the carbon cost $C_{i,{CO}_2}$, the carbon sequestration and transportation cost $C_{i,SE}$, the operation and maintenance cost $C_{i,op}$, and the interruptible load compensation cost $C_{i,ZD}$. An objective function is constructed with the minimum total cost of the VPP:

$$C_i=\min (C_{i,buy}^{grid}+C_{i,buy}^{P2P}+C_{i,{CO}_2}+C_{i,SE}+C_{i,op}+C_{i,ZD}),$$

(2)

• Interaction Cost with the External Market

$$C_{i,buy}^{grid}={\displaystyle \sum _{t=1}^T({\lambda }_{buy,t}^E{P}_{i,buy,t}-{\lambda }_{sell,t}^E{P}_{i,sell,t}+{\lambda }_{buy,t}^G{G}_{i,buy,t})},$$

(3)

In the formula, ${\lambda }_{buy,t}^E$ and ${\lambda }_{sell,t}^E$ are the electricity purchase and sales prices at time t, ${\lambda }_{buy,t}^G$ is the gas purchase price at time t, $P_{i,buy,t}$ and $P_{i,sell,t}$ are the electricity purchase and sales quantities at time t and $G_{i,buy,t}$ is the gas purchase quantity at time t.

• P2P Interaction Cost

$$C_{i,buy}^{P2P}={\displaystyle \sum _{t=1}^T(-{\chi }_{i-j,t}{P}_{i-j,t})}$$

(4)

In the formula, ${\chi }_{i-j,t}$ is the electricity selling price of VPPi to VPPj at time t. $P_{i-j,t}$ is the electricity sold by VPPi to VPPj.

• Carbon Cost

The operation processes of the combined heat and power (CHP) units and gas boilers (GBs) in the VPP will generate carbon emissions. When the actual carbon emissions of the VPP are higher than the quota allocated by the government, it is necessary to purchase carbon emission quotas to compensate for the excess carbon emissions. The calculation is as follows:

$$Q_{g,t}={\displaystyle \sum _{t=1}^T(P_{CHP,t,i}{m}_{CHP}^e}+H_{CHP,t,i}{m}_{CHP}^h+H_{GB,t,i}{m}_{GB}+P_{buy,t,i}{m}_{buy}-E_{CO2,t,i}^2),$$

(5)

In the formula, $Q_{g,i}$ is the total carbon emissions of the VPP. $m_{CHP}^e$ and $m_{CHP}^h$ are the carbon emission coefficients of power generation and heat generation of the CHP unit, respectively. $m_{GB}$ and $m_{buy}$ are the carbon emission coefficients of the GB and the electricity purchased from the large power grid respectively.

The initial carbon emission quota is composed of two aspects: traditional units such as CHP units and GBs, and new energy units such as WTs and PV units:

$$Q_{GP,i}={\displaystyle \sum _{t=1}^T[P_{CHP,t,i}*{\delta }_{CHP}^e+H_{CHP,t,i}*{\delta }_{CHP}^h+H_{GB,t,i}*{\delta }_{GB}+(P_{WT,t,i}+P_{PV,t,i})*{𝜕}_{new}]},$$

(6)

In the formula, $Q_{GP,i}$ is the total carbon quota of the VPP. ${\delta }_{CHP}^e$ and ${\delta }_{CHP}^h$ are the carbon quotas per unit power generation and heat generation power of the CHP unit, respectively. ${\delta }_{GB}$ is the carbon quota per unit energy supply power of the GB, and ${𝜕}_{new}$ is the carbon emission allocation per unit power of the new energy unit.

Then the carbon emissions of VPP i traded in the external carbon market $Q_{i,VPP}$ are as follows:

$$Q_{i,VPP}=Q_{i,g}-Q_{i,GP}-{\displaystyle \sum _{t=1}^T{G}_{i-j}}$$

(7)

In the formula, $Q_{i,GP}$ is the total carbon quota of the VPP, $Q_{i,g}$ is the total carbon emissions of the VPP, and $G_{i-j}$ is the carbon emission rights sold to VPP j.

Under the alliance cooperation, the carbon cost of VPP i consists of two parts: the carbon cost of P2P transactions $C_{i,K}$ and the carbon cost of transactions in the external carbon market $C_{i,{CO}_2}^E,$:

$$C_{i,C{O}_2}=C_{i,{CO}_2}^E+C_{i,K},$$

(8)

$$C_{i,K}={\displaystyle \sum _{t=1}^T(-{\kappa }_{i-j}{G}_{i-j})},$$

(9)

$$C_{i,C{O}_2}={\kappa }^E{Q}_{i,g}.$$

(10)

In the formula, $C_{i,C{O}_2}$ is the total carbon cost of VPP i, ${\kappa }^E$ is the unit price of external carbon emission right transactions, and ${\kappa }_{i-j}$ is the unit price at which VPPi sells carbon emission rights to VPP j. $G_{i-j,t}$ is the quantity of carbon emission rights sold by VPP i to VPP j, respectively.

• Carbon Sequestration and Transportation Costs

After being captured by the CCS, captured ${\mathrm{CO}}_2$ needs to be transported to the sequestration site and injected into the deep underground rock formations for long-term sequestration, or supplied as an industrial raw material to relevant industrial enterprises. This process will incur sequestration and transportation costs.

$$C_{i,SE}={\displaystyle \sum _{t=1}^T{\delta }_{i,SE}{E}_{i,{\mathrm{CO}}_2}^2,}$$

(11)

In the formula, ${\delta }_{SE}$ is the unit price of carbon dioxide sequestration and transportation.

• Operation and Maintenance Cost

The operation of each piece of equipment will incur operation and maintenance costs.

$$C_{i,op}={\displaystyle \sum _{S\in N}{\displaystyle \sum _{t=1}^T{\phi }_{i.S}{P}_{i,S,t},}}$$

(12)

In the formula, ${\phi }_S$ is the unit operation and maintenance cost of equipment S, and $P_{S,t}$ is the operating output of equipment S.

• Interruptible Load Compensation Cost

For the load-side demand response resources utilized by the VPP, a certain amount of compensation is required for them.

$$C_{i,IL}={\displaystyle \sum _{t=1}^T({\delta }_{i,e,IL}{P}_{i,t}^{IL}+{\delta }_{i,h,IL}{H}_{i,t}^{IL}),}$$

(13)

Constraints

• Power Balance Constraint

$$P_{i,W,t}+P_{i,PV,t}+P_{i,CHP,t}+P_{t,e}^{dis}+P_{i,buy,t}=P_{i,CCS,t}+P_{i,a,t}+P_{i,t,e}^{cha}+P_{i,sell,t}+{\displaystyle \sum _{j=1,j\ne i}^D{P}_{i-j,t}},$$

(14)

$$H_{i,CHP,t}+H_{i,GB,t}+P_{i,t,h}^{cha}=H_{i,a,t}+P_{i,t,h}^{dis},$$

(15)

$$V_{i,t}=V_{i,GT,t}+V_{i,GB,t},$$

(16)

In the formula, $P_{i,W,t}$, $P_{i,PV,t}$, $P_{i,CHP,t}$ and $P_{t,e}^{dis}$ are the electrical powers of WT, PV, CHP unit and EES, respectively. $P_{i,buy,t}$ and $P_{i,sell,t}$ are the electrical powers of purchasing from and selling to the large power grid; $P_{i,t,e}^{cha}$ and $P_{i,t,e}^{dis}$ are the charging and discharging powers of the EES; $P_{i,CCS,t}$ is the charging power of the CCS; $P_{i,a,t}$ and $H_{i,a,t}$ are the equivalent electrical and thermal load powers, respectively; $P_{i,buy,t}$ is the electricity quantity purchased by VPPi from the major power grid. $H_{i,CHP,t}$ and $H_{i,GB,t}$ are the thermal powers of the CHP unit and the GB, respectively, $P_{i,t,h}^{cha}$ and $P_{i,t,h}^{dis}$ are the charging and discharging powers of the TES; $V_{i,t}$ is the natural gas quantity supplied to the units of the VPP, $V_{i,GT,t}$ and $V_{i,GB,t}$ are the natural gas consumption quantities of the GT and the GB, respectively.

• P2P Transaction Constraint

According to the law of conservation of energy, the energy transferred by VPPi should be exactly equal to the energy received by VPP j. And subject to the upper limit of the transmission channel capacity, the P2P transaction power must also be within a certain range.

$$P_{i-j}^{\min }\le P_{i-j,t}\le P_{i-j}^{\max },$$

(17)

$$P_{i-j,t}=-P_{j-i,t},$$

(18)

In the formula, $P_{i-j}^{\max }$ and $P_{i-j}^{\min }$ are the upper and lower limits of the P2P transaction power.

Similarly, the transaction of carbon emission rights should also be carried out within a certain range:

$$G_{i-j}^{\min }\le G_{i-j}\le G_{i-j}^{\max },$$

(19)

$$G_{i-j}=-G_{j-i},$$

(20)

• P2P price transaction constraint

In order to encourage each VPP to participate in the alliance, the electricity selling price of VPP i in P2P transactions should be higher than the electricity selling price to the large power grid, and its electricity purchasing price in P2P transactions should be lower than the electricity purchasing price from the large power grid. The same principle applies to the P2P transaction price of carbon emission rights.

$${\chi }_{sell,t}^E\le {\chi }_{i-j,t}\le {\chi }_{buy,t}^E,$$

(21)

$${\chi }_{i-j,t}={\chi }_{j-i,t},$$

(22)

$$0\le {\kappa }_{i-j}\le {\kappa }^E,$$

(23)

$${\kappa }_{i-j}={\kappa }_{j-i},$$

(24)

• Other constraints

VPP i also needs to meet the operation constraints of each unit within it. The physical network constraints such as the power transmission distance between VPPs are ignored because they have a relatively small impact on the key conclusions of this paper.

3.3. Uncertainty Measurement of VPPs Based on Conditional Value at Risk

If there is a large deviation between the predicted values and the actual values of WT, PV, and load within the VPP, it will affect the safe and reliable operation of the system. In this case, the power shortage or surplus can be dealt with by interacting with the large power grid in terms of electric energy. This paper uses the conditional value at risk (CVaR) to represent the net interaction cost between multiple VPPs and the large power grid, which is used to represent the risk loss function, so as to achieve the quantification of risks and solve the uncertainty problems caused by WT, PV, and load. The cost expression of the CVaR based on the net interaction cost $X_{i,CV\mathrm{a}R,\beta }$ is as follows:

$$X_{i,CV\mathrm{a}R,\beta }={\alpha }_i+{\displaystyle \frac{1}{1-\beta }}{\displaystyle \sum _{s=1}^S{\pi }_s\cdot }[{\displaystyle \sum _{t=1}^T({\lambda }_{buy,t}^E{P}_{i,buy,t}-{\lambda }_{sell,t}^E{P}_{i,sell,t})}-{\alpha }_i{]}^{+},$$

(25)

$$[{\displaystyle \sum _{t=1}^T({\lambda }_{buy,t}^E{P}_{i,buy,t}-{\lambda }_{sell,t}^E{P}_{i,sell,t})}-{\alpha }_i{]}^{+}=\max \{{\displaystyle \sum _{t=1}^T({\lambda }_{buy,t}^E{P}_{i,buy,t}-{\lambda }_{sell,t}^E{P}_{i,sell,t})}-{\alpha }_i,0\},$$

(26)

In the formula, $\beta$ is the confidence level, $X_{i,CV\mathrm{a}R,\beta }$ is the CVaR cost of VPPi, ${\alpha }_i$ is the value-at-risk cost of VPPi, ${\pi }_s$ is the probability of occurrence of typical scenario s, and S is the number of typical scenarios. For the convenience of calculation, Equation (25) is simplified to the following:

$$X_{CV\mathrm{a}R,\beta ,i}={\alpha }_i+{\displaystyle \frac{1}{1-\beta }}{\displaystyle \sum _{s=1}^S{\pi }_s{y}_{i,s}},$$

(27)

$$\left\{\begin{array}{l}{y}_{i,s}\ge 0\\ {\displaystyle \sum _{t=1}^T({\lambda }_{buy,t}^E{P}_{i,buy,t}-{\lambda }_{sell,t}^E{P}_{i,sell,t})}-{\alpha }_i\le y_{i,s}\end{array}\right.,$$

(28)

In the formula, $y_{i,s}$ represents the value by which the CVaR cost of VPP i exceeds the value-at-risk cost in the scenario s.

Regarding the scenario probabilities proposed in the above-mentioned distributed scheduling model for the VPPC, this paper uses the Latin hypercube scenario generation and synchronous back-substitution method for processing.

3.4. Distributed Optimization Model for Cluster Operation

3.4.1. Subproblem 1: Model for Minimizing the Total Cost of the VPPC

In the Nash negotiation model for the VPPC proposed in Section 3.1, the problem of optimizing the alliance’s interests (Subproblem 1) is equivalent to minimizing the total cost under the operation mode of the VPPC. Then, the objective function for maximizing the independent operation benefits of each VPP based on CVaR is as follows:

$$\begin{array}{cc}\min U_i^0=\hfill & (1-k){\displaystyle \sum _{s=1}^S{\pi }_s\cdot }(C_{i,buy,s}^{grid}+C_{i,buy,s}^{P2P}+C_{i,C{O}_2,s}\hfill \\ \hfill & +C_{i,SE,s}+C_{i,op,s}+C_{i,IL,s})+k{X}_{CV\mathrm{a}R,\beta ,i}\hfill \end{array},$$

(29)

After the cluster operation, since the transaction costs of electricity and carbon emission rights among various entities are offset against each other during the accumulation process of Equation (29), the transaction prices of electricity and carbon emission rights cannot be determined at this time. This is also one of the necessary reasons for this paper to introduce the Nash negotiation model. Then, the model of Problem 1 is as follows:

$$\min L_1={\displaystyle \sum _{i=1}^A(1-k){\displaystyle \sum _{s=1}^S{\pi }_s\cdot }(C_{i,buy,s}^{grid}+C_{i,{\mathrm{CO}}_2,s}}+C_{i,SE,s}+C_{i,op,s}+C_{i,IL,s})+k{X}_{i,\mathrm{CVaR},\beta },$$

(30)

In the formula, $k$ represents the risk preference coefficient, $k\in [0,1]$, which reflects the risk tolerance of the VPP investors. A relatively large value of $k$ implies that the investors prefer lower risks and stable returns, while a smaller $k$ indicates that the investors are inclined to take on higher risks in the hope of achieving lower operating costs. By solving Subproblem 1, the optimal solution can be obtained as ${(C_{i,buy,s}^{grid}+C_{i,C{O}_2,s}+C_{i,SE,s}+C_{i,op,s}+C_{i,IL,s})}^{*}$.

3.4.2. Subproblem 2: Model for Minimizing the Operating Cost of Each VPP

In the Nash negotiation model for the VPPC proposed, the optimization of individual interests (Subproblem 2) is equivalent to minimizing the operating cost of each VPP. Each VPP will make different contributions to the system. In this paper, the bargaining index of the VPP $p_i$ is introduced to reflect the different contribution degrees among VPPs. The contributions are divided into economic contributions and low-carbon contributions. The bargaining index is derived from electricity and carbon allowance interactions calculated in Subproblem 1. As shown in Equation (29), the bargaining power of VPPi is as follows:

$$p_i={\displaystyle \frac{{\xi }_1{P}_{P2P,i}^{+}+{\xi }_2{P}_{P2P,i}^{-}+{\xi }_3{G}_{P2P,i}^{+}+{\xi }_4{G}_{P2P,i}^{-}}{{\displaystyle \sum _{i=1}^D({\xi }_1{P}_{P2P,i}^{+}+{\xi }_2{P}_{P2P,i}^{-}+{\xi }_3{G}_{P2P,i}^{+}+{\xi }_4{G}_{P2P,i}^{-})}}},$$

(31)

In the formula, $P_{P2P,i}^{+}$ and $P_{P2P,i}^{-}$ are the electricity quantities sold and purchased by each VPP from/to other VPPs, respectively. $G_{P2P,i}^{+}$ and $G_{P2P,i}^{-}$ are the quantities of carbon emission rights sold and purchased by each VPP from/to other VPPs, respectively. ${\xi }_1$, ${\xi }_2$, ${\xi }_3$, and ${\xi }_4$ are the corresponding weight coefficients, which need to satisfy ${\xi }_1+{\xi }_2+{\xi }_3+{\xi }_4=1$. In addition, considering the development of the alliance, the contributions of a VPP from selling electricity and carbon emission rights to other entities in the alliance are greater than those from purchasing electricity and carbon emission rights. Therefore, it also needs to satisfy ${\xi }_1>{\xi }_2, {\xi }_3>{\xi }_4$.

The objective of the revenue equal distribution scheme is to maximize the revenue increase of each entity, which is equivalent to maximizing the cost savings. According to Equation (1), the objective function of Subproblem 2 can be obtained as follows:

$$\max {\displaystyle \prod _{i=1}^D(C_i^0-C_i)},$$

(32)

In the formula, $C_i^0$ is the cost of the VPP operating independently before cooperation.

Substituting the solution of Subproblem 1 into it, we have the following:

$$\begin{array}{cc}\max \hfill & {\displaystyle \prod _{i=1}^I[U_i^0-((C_{i,buy,s}^{grid}+C_{i,C{O}_2,s}+C_{i,SE,s}+C_{i,op,s}}\hfill \\ \hfill & {+C_{i,IL,s}+C_{G,i,s})}^{*}+C_{i,buy,s}^{P2P}+C_{i,K,s})+k{X}_{i,CV\mathrm{a}R,\beta }{]}^{p_i}\hfill \end{array},$$

(33)

Take the logarithm of both sides of the objective function of Subproblem 2, and then the model of Subproblem 2 can be obtained.

4. Model Solution Method and Solution Process

4.1. ADMM Computational Framework

It is difficult for the centralized algorithm to solve the optimization problem of the VPPC. Based on this, this paper selects the ADMM method, which has the advantages of good convergence characteristics, strong privacy protection, high robustness, etc., to solve Equations (30) and (34) successively. The ADMM is an optimization framework widely used in distributed computing and is suitable for solving convex optimization problems.

ADMM is usually used to solve optimization problems with only equality constraints [24], and its general form is as follows:

$$\begin{array}{l}\min f(x)+g(z)\\ \mathrm{s}.\mathrm{t}. Ax+Bz=c\end{array},$$

(34)

Among them, $x$ and $z$ are optimization variables; $f(x)+g(z)$ is the objective function to be minimized, which is composed of two parts: $f(x)$ related to the variable $x$ and $g(z)$ related to the variable $z$. Both $f(x)$ and $g(z)$ are convex functions, and $Ax+Bz=c$ is the combined writing of p equality constraints.

To solve this kind of convex optimization problem, the augmented Lagrangian function is defined as follows:

$$L_p(x,z,y)=f(x)+g(z)+y(Ax+B{z}^k-c)+(\rho /2){‖Ax+Bz-c‖}_2^2),$$

(35)

Among them, $y$ is the dual variable (i.e., the Lagrangian multiplier), and $\rho$ is the penalty parameter.

Then, the ADMM iterative solution steps for this optimization problem are shown in Equations (34)–(36). In each step, only one variable is updated while the other two variables are fixed, and such alternating and repeated updates are carried out.

Step 1: Solve the minimization problem related to $x$ and update the variable $x$.

$$x^{k+1}:=\arg \underset{x}{\min }{L}_p(x,z^k,y^k),$$

(36)

Step 2: Solve the minimization problem related to $z$ and update the variable $z$.

$$z^{k+1}:=\arg \underset{z}{\min }{L}_p(x^{k+1},z,y^k),$$

(37)

Step 3: Update the dual variable $y$.

$$y^{k+1}:=y^k+(A{x}^{k+1}+B{z}^{k+1}-c),$$

(38)

Let $u={\displaystyle \frac{y}{\rho }}$, and by completing the square $Ax+Bz-c$, the simplified scaled form of ADMM can be obtained:

Step 1:

$$x^{k+1}:=\arg \min (f(x)+(\rho /2){‖Ax+B{z}^k-c+u^k‖}_2^2),$$

(39)

Step 2:

$$z^{k+1}:=\arg \min (g(z)+(\rho /2){‖A{x}^{k+1}+Bz-c+u^k‖}_2^2),$$

(40)

Step 3:

$$u^{k+1}:=u^k+A{x}^{k+1}+B{z}^{k+1}-c.$$

(41)

Define the $k$ th iteration residual as $r^k=A{x}^k+B{z}^k-c$; we have the following:

$$u^k=u^0+{\displaystyle \sum _{m=1}^k{r}^m},$$

(42)

$$\left\{\begin{array}{l}{‖r^k‖}_2\le {\epsilon }^{pri}\\ {‖s^k‖}_2\le {\epsilon }^{dual}\end{array}\right..$$

(43)

In the formula, $r^k$ and $s^k$ are the primal residual and the dual residual, respectively. ${\epsilon }^{pri}$ and ${\epsilon }^{dual}$ are the deviation thresholds of the primal residual and the dual residual, respectively. From them, we have the following:

$$s^{k+1}=\rho A^{T}B(z^{k+1}-z^k),$$

(44)

With the iterative optimization of the algorithm, the primal residual and the dual residual gradually converge to zero. In order to achieve multiple iterations, the algorithm sets the iterative termination condition as shown in Equation (44). After each iteration, it is determined whether this condition is met. If it is not met, the algorithm returns to continue the iteration until the condition is satisfied, the algorithm converges, and the optimal solution is output.

4.2. Improved ADMM Method

In order to make ADMM converge, the penalty factor $\rho$ can be updated after each iteration. Then, the Lagrangian multiplier in the $k$ th iteration process depends on the $k+1$ th multiplier, the difference of the dual variables obtained from the results of the $k+1$ th iteration, and the updated penalty factor. The convergence of the traditional ADMM is greatly affected by the quadratic penalty term of the augmented function. If the penalty term is too large, it will lead to non-convergence, and if it is too small, the convergence will be slow. Moreover, the value of the penalty factor is difficult to predict. To overcome the above disadvantages, this paper introduces a correction parameter based on the dynamically adjusted penalty factor to improve the performance of the algorithm.

Specifically, the value of the penalty factor $\rho$ is adjusted by judging the magnitude of the residual of the current iteration:

$${\rho }^{k+1}:=\left\{\begin{array}{l}{\tau }_A{\rho }^k, {\displaystyle \frac{{‖r^k‖}_2}{{‖s^k‖}_2}}\ge {\theta }_A\\ {\displaystyle \frac{{\rho }^k}{{\tau }_A}}, {\displaystyle \frac{{‖r^k‖}_2}{{‖s^k‖}_2}}\le {\theta }_B\\ {\rho }^k, {\theta }_A\le {\displaystyle \frac{{‖r^k‖}_2}{{‖s^k‖}_2}}\le {\theta }_B\end{array}\right.,$$

(45)

If the primal residual is much larger than the dual residual, the penalty factor will be multiplied by a factor ${\tau }_A$ greater than 1. If the primal residual is much smaller than the dual residual, the penalty factor will be divided by a factor ${\tau }_A$. In other cases, the penalty factor will remain unchanged. This method enables the penalty factor to be adaptively adjusted according to the progress of the algorithm, which helps to accelerate the convergence speed and reduce the number of iterations.

4.3. Model Solution Process

After establishing the distributed algorithm for the subproblem of maximizing the benefits of the multi-agent cooperation alliance of the VPPC, the specific solution process is shown in Figure 3.

5. Case Analysis

5.1. Basic Data

To validate the effectiveness of the proposed model and methodology, this study examines a VPPC comprising power-source-type, load-type, and hybrid VPPs through numerical case studies. The simulation adopts a 24 h scheduling period with 1 h time intervals. Key parameters are configured as follows: carbon emission allowance prices in the carbon market reference the EU Emissions Trading System [25], with upper and lower bounds set at CNY [0.1, 0.75] per ton, while the carbon dioxide sequestration cost is fixed at CNY 32.5 per ton. Load compensation prices are specified as 0.2 CNY/kWh for shiftable loads, 0.22 CNY/kWh for interruptible loads, and 0.25 CNY/kWh for loads possessing both characteristics. The power transmission fee is set to 0.07 CNY/kWh, with a maximum P2P exchange capacity of 120 kW between VPPs.

The detailed resource configurations and operational parameters of the three VPP systems are provided in

Table 1. Distributed resources in VPP1, VPP2, and VPP3.

VPP	WT	PV	GT	Electric Load/Electricity Demand Response	Heat Load/Thermal Demand Response	Waste Heat Recovery Device	Combined System of P2G and CCS	GB	EB	Energy Storage
VPP1	×	√	√	√	×	×	√	×	×	EES
VPP2	√	√	×	√	√	×	×	×	√	EES
VPP3	√	√	√	√	√	√	×	√	√	EES, TES

,

Table 2. Carbon emission parameters of each unit.

Equipment		Carbon Quota (kg/kWh)	Carbon Emission Intensity (kg/kWh)
CHP	GT	0.424	0.7 power/0.4 heat
	WHB
	ORC
GB		0.21	0.29
EB		/	/
Power purchase from the power grid		0.78	0.85
WT		0.078	/
PV			/

and

Table 3. Parameters of each VPP.

Equipment	Parameters	Value
		VPP1	VPP2	VPP3
GT	${\eta }_{GT}$	0.35	/	0.35
	$P_{i,GT}^{\min }/P_{i,GT}^{\max }$	0/170 kW	/	0/200 kW
GB	${\eta }_{EES}^{cha}/{\eta }_{EES}^{dis}$	0.9	/	/
	$H_{i,GB}^{\min }/H_{i,GB}^{\max }$	0/100 kW	/	/
EB	${\eta }_{EB}$	0.9	0.92	0.9
	$P_{i,EB}^{\min }/P_{i,EB}^{\max }$	0/200 kW	0/180 kW	0/200 kW
EES	${\eta }_{EES}^{cha}/{\eta }_{EES}^{dis}$	0.85/0.9	0.9/0.96	0.85/0.9
	$P_{i,EES}^{\min }/P_{i,EES}^{\max }$	60 kW	100 kW	80 kW
TES	${\eta }_{TES}^{cha}/{\eta }_{TES}^{dis}$	/	0.9/0.95	0.9/0.95
	$H_{i,TES}^{\min }/H_{i,TES}^{\max }$	/	60 kW	100 kW
CCS	${\eta }_{CCS}$		0.65	0.65
	${\eta }_{CCS}$	/	0/50 kW	0/50 kW
P2G	${\eta }_{P2G}$	/	0.7	/
	$P_{i,P2G}^{\min }/P_{i,P2G}^{\max }$	/	0/300 kW	/

and Figure 3. In Table 1, √ indicates that VPP has this item, while × indicates that it does not have this item.

The probability scenarios for WT, PV, and load in each VPP are derived using Latin hypercube sampling and synchronous back-reduction technology. The most probable typical scenarios are illustrated in Figure 4.

VPP1 is a load-type virtual power plant aggregating distributed PV resources only. To meet its electricity demand, VPP1 must purchase significant external power. Its internal users comprise industrial loads, which require not only daily electricity but also hydrogen production through P2G technology to manufacture industrial products. Accordingly, VPP1 features on-site P2G equipment for hydrogen generation. VPP2 operates as a power source-type VPP with substantial WT and PV output. Its electrical and thermal loads remain relatively low, resulting in surplus renewable energy during most time periods. VPP3 functions as a hybrid VPP integrating numerous distributed controllable loads. Despite possessing moderate WT and PV resources, it frequently fails to fulfill total load requirements and must procure external energy during most operational periods.

5.2. Result of Operation Optimization

5.2.1. Operation Results of the VPPC

Figure 5, Figure 6 and Figure 7 present the optimization results of the VPPC after the model proposed in this paper has been optimized.

• VPP1

Both hydrogen and electricity loads in VPP1 remain consistently high across all periods. Its PV generation is only available from 08:00 to 18:00, requiring GT power generation and external electricity purchases to compensate for the shortfall during remaining hours. As shown in Figure 5, VPP1 primarily satisfies its electricity and hydrogen loads through GT generation and electricity purchases from VPP2, supplemented by daytime PV. Between 10:00 and 16:00, when PV output peaks, GT generation decreases significantly while external electricity purchases remain minimal. Notably, VPP1 only procures marginal electricity from the main grid during 00:00–01:00, with the majority sourced from renewable-rich VPP2.

The system’s electricity storage charges during high-PV periods and discharges during high-electricity-price night hours. Since hydrogen production relies on water electrolysis, hydrogen storage functionally equates to electricity storage. Hydrogen storage is conducted during the hours 1:00, 4:00–5:00, and 11:00–15:00. This scheduling is economically advantageous as it leverages the lower electricity rates during 1:00 and 4:00–5:00, while also utilizing the higher photovoltaic output from VPP1 during 11:00–15:00. Regarding demand response, hydrogen load reduction and partial load shifting occur frequently from 00:00 to 09:00 and 16:00 to 24:00 due to insufficient internal energy supply. Conversely, during 10:00–15:00, increased PV absorption enables higher hydrogen loads.

• VPP2

As a power source-type VPP, VPP2 maintains substantial surplus renewable energy across all periods. Figure 6a indicates that beyond fully supplying its internal load, VPP2 sells most surplus electricity to VPP1 and VPP3.

• VPP3

Most of VPP3’s electrical load is supplied by its own renewable resources and GT. External electricity purchases occur during all periods except 19:00 and 21:00. The majority of externally sourced electricity comes from VPP2, with minor contributions from VPP1 and the main grid. Due to relatively high carbon emissions from GBs and waste heat boilers (WHBs), electrical and thermal loads remain elevated between 09:00 and 20:00. During this period, GT output increases significantly through CHP generation to supply the system. Concurrently, thermal loads utilize a portion of GT waste heat recovered by WHB. Between 03:00 and 05:00 when renewable surplus diminishes in both VPP2 and VPP3 while internal electrical/thermal loads remain relatively high, the system experiences energy shortages. During this scarcity window, the thermal load is supplied by GBs, whereas electric boilers (EBs) primarily serve thermal demand in other periods, thereby reducing overall system carbon emissions.

5.2.2. Power Interaction Situation

Figure 8 shows the electricity trading volume after negotiation obtained by each VPP through solving subproblem 1. It can be seen that VPP1 exports electricity in all time periods and is a power source-type VPP. At 19:00 and 21:00, VPP2 and VPP3 supply themselves.

The electricity transaction prices within the VPPC with and without the price constraint (Equation (20)) are shown in Figure 9 and Figure 10. Under the constraint mechanism, transaction prices for all VPPs remain between the grid’s electricity purchase price and selling price. This pricing structure reduces electricity procurement costs while increasing sales revenues for each participating VPP, enhancing their economic benefits. However, when omitting the constraint, VPP transaction prices periodically exceed these limits. Consequently, individual VPPs experience diminished alliance participation benefits, thereby weakening their cooperative willingness.

5.2.3. Interaction Situation of Carbon Emission Allowances

Figure 11 presents the total carbon allowance transactions of each VPP. VPP1 and VPP2 exhibit carbon quota deficits because their internal renewable energy cannot fully meet load demands, necessitating supplementary power/heat from GT and GB which generate carbon emissions. Conversely, VPP3’s abundant renewable resources create carbon reduction benefits resulting in quota surplus. Consequently, VPP1 and VPP2 purchase net carbon allowances of 191.03 kg and 240.25 kg, respectively, while VPP3 sells 431.28 kg net to other VPPs.

Table 4. P2P carbon trading volume and carbon trading price.

	Carbon Trading Volume, /kg	Carbon Trading Price/(yuan/kg)
VPP1–VPP2	−191.2	0.352
VPP1–VPP3	32.75	0.298
VPP2–VPP3	203.68	0.347

presents the P2P carbon trading volumes and prices within the VPP cluster framework. It is observed that all P2P carbon trading prices fall between the external carbon market’s purchase and sale unit prices for emission rights, indicating the VPPC’s capability to enhance revenue generation for each participating VPP.

5.2.4. Economic Analysis of VPPC

Table 5. Economics of each VPP (unit: CNY).

VPP	Independent Operation Cost	Cluster Operation Cost
		Total Cost (Including P2P)	P2P Cost
VPP1	1732.5	1683.23	440
VPP2	−1206.55	−1454	−802
VPP3	2298.4	2243.95	474

compares the operational costs of each VPP under independent and cluster operations. As a power source-type VPP, VPP2’s P2P transactions primarily involve providing electricity and carbon allowances to other VPPs, resulting in negative costs that indicate consistent profitability. Notably, cluster operation reduces both operational and carbon costs for all VPPs compared to independent operation, demonstrating the economic efficiency of collaborative VPP management.

5.2.5. Analysis of the Low Carbon Nature of the VPPC

Table 6. Comparison of the low carbon nature of VPPC operation.

VPP	Carbon Emission/kg		The Proportion of New Energy Consumption
	Independent Operation	Cluster Operation	Independent Operation	Cluster Operation
VPP1	457.57	478.04	70.92%	87.75%
VPP2	−759.68	−803.74
VPP3	500.3	527.65

compares the carbon emissions of each VPP under independent versus cluster operation modes. The data demonstrates that cluster operation reduces carbon emissions by 4.47%, 5.80%, and 5.47% respectively for each VPP, confirming the low-carbon advantage of collaborative VPP operation.

The renewable energy utilization rate—defined as the ratio of self-consumed or alliance-consumed renewable energy to total generation—quantifies system consumption capacity. Cluster operation achieves a 16.83 percentage-point higher utilization rate than independent operation. This metric not only measures VPPs’ renewable energy management capabilities but also reveals optimized resource allocation through multilateral bargaining within the alliance. Unlike centralized market transactions with the main grid that incur material and administrative costs, the VPPC enables point-to-point direct consumption via aggregated wind turbines (WT) and PV. This approach reduces both grid burdens and energy processing losses.

5.2.6. Performance Comparison: Original vs. Improved ADMM

Table 7. Improved performance comparison before and after ADMM.

	Iteration Count (Iterations)		Total Solve Time (s)
	Subproblem 1	Subproblem 2
Original ADMM	45	27	202.37
Improved ADMM	28	15	168.72

shows the performance before and after improved ADMM proposed in this paper: the improved ADMM converges after 28 iterations for Subproblem 1 and 15 iterations for Subproblem 2, which are 17 and 12 fewer than traditional ADMM respectively, achieving a solution time of 168.72 s and a 15.8% solving speed improvement.

6. Conclusions

This study establishes a multi-party bargaining framework for optimizing VPPC operations. We propose an asymmetric Nash bargaining model to coordinate cross-VPP resource allocation and implement a modified ADMM algorithm with dynamic penalty factors for privacy-preserving distributed computation. Empirical results demonstrate 20.37% reduction in total operating costs and 16.83% increase in renewable energy integration compared to independent VPP operation, while the enhanced ADMM algorithm accelerates convergence speed by 15.8% without compromising data privacy.

The findings of this study offer crucial insights for the practical application of VPPs. The traditional model confined to internal dispatch within a single VPP exhibits inherent limitations. Therefore, future practice should transcend the boundaries of individual VPPs, actively considering and facilitating P2P transactions among multiple VPPs. This is essential to promote the efficient allocation of energy resources across broader geographical areas and among diverse market entities. Concurrently, in organizing such multi-VPP P2P transactions, meticulous attention must be paid to privacy protection. It is imperative to proactively adopt distributed algorithms and methodologies, such as the one proposed in this work, to prevent the leakage of sensitive data during collaboration, thereby safeguarding the commercial confidentiality and operational security of all participating entities.

Moving forward, research must rigorously address the stark reality of increasingly frequent extreme weather events globally. Phenomena such as typhoons, blizzards, and persistent heatwaves typically exacerbate the inherent uncertainty in power output from weather-dependent volatile renewables—like wind and solar PV—integrated within VPPs. This heightened uncertainty substantially challenges the secure, stable operation of the overall power system, elevating operational risks. Furthermore, transmission security and integrity issues related to VPP communication infrastructure demand serious attention. Consequently, the adaptability and robustness of existing models under extreme weather conditions urgently require in-depth validation and enhancement through complex scenario simulations. An important future research direction involves investigating robust mechanisms for active coordination and mutual emergency support among multiple VPPs—such as optimized reserve sharing and flexible transaction responses—to bolster the resilience and robustness of the multi-VPP alliance as a holistic entity, improving its survivability and recovery capabilities following extreme disturbances. Simultaneously, robust communication security frameworks must be researched and implemented to bolster the security performance of communications during VPP operations.