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Abstract

With the rapid development of renewable energy and the urgent need for global carbon emission reduction, virtual power plants have become a high-profile energy management model that can integrate multiple energy resources. How to effectively integrate renewable energy to reduce carbon emissions, how to optimize the use of different energy resources, and how to fairly distribute economic benefits within virtual power plant clusters while encouraging the reduction of carbon emissions are issues that need to be addressed in research. The study first established a virtual power plant model and conducted in-depth optimization for its economic and environmental indicators. Subsequently, the study constructed a game model within the virtual power plant cluster, aiming to solve the problem of income distribution in this diversified energy system. The research results found that commercial users have the highest carbon emissions, followed by industrial users, while residential users have the lowest carbon emissions. In terms of optimized user electricity consumption behavior, the peak-to-valley difference rate of industrial users has been reduced by 17%, and the daily load rate has increased by 6%; the peak-to-valley difference rate of commercial users has been reduced by 12%, and the daily load rate has increased by 6%; The peak-to-trough difference rate for residential users decreased by 8%, and the daily load rate increased by 4%. In addition, the research also proposes a method of internal revenue distribution of virtual power plant clusters based on a carbon reward and punishment mechanism, which provides a new way for the synergy effects and economic benefit distribution of virtual power plants. Research is of positive significance in solving pressing issues in the field of energy management and provides strong support for the development of future sustainable energy systems.

Keywords

Virtual power plant carbon reward and punishment mechanism internal revenue sharing shapley value model IBDR

1. Introduction

With the increasing global concern about climate change and environmental protection, carbon incentive and penalty mechanisms have become one of the important means to promote low-carbon transition and reduce carbon emissions. Virtual Power Plant (VPP) clusters, as a new type of energy management model, integrate and optimize the utilization of distributed energy (DE) resources, which has the potential to improve energy use efficiency and reduce carbon emissions [1]. However, the problem of revenue sharing within VPP clusters has been a challenging topic [2]. Studying the revenue sharing issue within VPP (Virtual Power Plant) clusters is crucial as it relates to sustainable energy supply, cost-effectiveness, market incentives, reliability and environmental protection. VPP clusters contain diverse distributed energy resources and require effective coordination and management. Appropriate revenue sharing mechanisms can incentivize participants, reduce costs, reduce risks, promote the use of clean energy, help keep up with the development of technology and policies, and ensure the reliability and sustainability of the system. To address this issue, this study focuses on the revenue sharing methodology within VPP clusters considering carbon incentives and penalties, which is innovative and unique compared with the traditional revenue sharing methodology [3]. The innovation of the study is to incorporate the carbon incentive and penalty mechanism into the benefit sharing of VPP clusters, and to propose a VPP based on the Shapley value for addressing the problem of benefit sharing. By considering the carbon reduction benefits and the contribution of the participants, this study aims to establish a feasible and fair benefit sharing mechanism to incentivize the participants within the VPP cluster for participating in carbon reduction actions and promoting the advancement of sustainable energy. Through the innovative work of the study, it is expected to provide important theoretical and practical guidance for the construction of VPP clusters with carbon emission reduction awareness and fair distribution mechanisms, and to make positive contributions to the promotion of low-carbon energy transition and sustainable development.

The research is separated into four, the first part is the summary on the revenue distribution of VPP. The second part is the model construction and optimization of VPP on the ground of carbon reward and punishment mechanism. The third part is the analysis of the revenue sharing method of VPP clusters under the carbon reward and punishment mechanism. The fourth part is the summary of the whole paper.

VPP is a newly proposed carbon cycle concept in recent years. For addressing the flexibility assessment problem of VPP in managing a large amount of DE, Wang and other scholars proposed to adopt an opportunity constrained optimization model to formulate the flexibility assessment problem, represent the flexibility assessment as a combination of virtual generators and virtual batteries and decompose it by a robust optimization algorithm, and then introduce a boundary based on high-dimensional polyhedra contraction method is introduced to estimate the parameters of virtual generators and virtual batteries [4]. Zhang and Hredzak in order to aggregate DE storage systems into heterogeneous VPP, two kinds of VPP are constructed for supplying high volume power demand and high frequency power demand respectively, and a distributed secondary control system is introduced to regulate each of the storage systems in order to maintain a balanced charging state of all the energy storage systems within the VPP [5]. For addressing the issue of optimal bidding strategy for VPP, Vahedipour-Dahraie et al. constructed VPP including dispatchable energy, renewable energy (REN), energy storage systems and demand flexible customers, and determined bidding/offer strategies for VPP in day-ahead, real-time and rotating standby markets to maximize profits [6]. Gough et al. for exploring the potential of blockchain technology in the energy trading market, proposed a multilevel interactive energy optimization model to study the DE sources within a VPP, constructed a multilevel interactive energy optimization model, and introduced a relevant layer to ensure the automation and documentation of energy transactions [7]. To address the coordination problem in VPP operations to facilitate market and network integration of DE resources, Naughton et al. proposed a framework to jointly optimize multiple markets, systems and local network services provided by VPPs to maximize their revenues, decomposing the framework into three sequential coordination optimization problems. A robust scenario-based optimization approach is used for day-ahead resource scheduling and a second-order cone relaxation method is utilized for obtaining more accurate power flows [8]. These related studies provide strong connections and references for this study. In particular, they explore key issues in virtual power plant management, energy aggregation, optimal bidding strategies, blockchain technology applications, and VPP operations, which are closely related to the carbon reward and punishment mechanism and internal revenue sharing of virtual power plant clusters in this study Related. By drawing on the experience and methods of these studies, research can better explain the operation and management of virtual power plants, and how to effectively allocate internal benefits under the carbon reward and punishment mechanism.

The intra-cluster revenue sharing methodology has been studied by scholars in various fields. Ji et al. found that over-allocation of carbon credits by the government may be detrimental to manufacturers’ profitability under wholesale price and increase the difficulty of enforcing cap-and-trade regulation (CATR). The study investigates the production decision and contract setting under CATR in supply chains through a two-stage Stackelberg game model, and provides suggestions on optimal cap setting [9]. In order to understand the development trend of global carbon emissions research, Abeydeera et al. used scientometric analysis methods to review the literature related to global carbon emissions, spanning from 1981 to 2019, and examined the research literature on the assessment of greenhouse gas emissions and Carbon footprint content, and key topics related to climate change and the environmental impact of carbon emissions [10]. Liu et al. constructed a three-party evolutionary game model involving the relationship between transportation carbon deficit provinces, transportation carbon surplus provinces and the central government. The study discusses the evolutionary stability of the game in the various strategies. Finally, simulations using Matlab were conducted to validate the findings and provide strategic recommendations for the central government in cross-regional transportation emission reduction [11]. Wang et al. for addressing the issues of environmental pollution as well as multi-stakeholder conflict of interest in integrated energy systems. The study adopts an approach based on the carbon trading mechanism and Stackelberg game to realize the low-carbon economic co-optimization of the integrated energy system, proposes a multi-stakeholder low-carbon trading mechanism, establishes the mathematical model of each stakeholder, and solves the model by using a two-stage optimization algorithm [12]. Liu et al. explored the multi-stage low-carbon technology investment in the evolutionary model between the manufacturer and supplier strategy analysis, constructed an evolutionary model between manufacturers and suppliers using a bilateral matching and evolutionary theory-based approach, and established a green supply chain profit optimization model from the perspectives of centralized matching, decentralized matching and mismatching [13].

In summary, many experts have conducted research on VPP and cluster revenue sharing methods, but there is still room for optimizing the economic benefits shared by members under these methods, and the research is based on the carbon reward and punishment mechanism to study the revenue sharing methods of VPP clusters, with the expectation of enhancing the economic benefits shared by members.

2. Modeling of VPP based on carbon incentive and penalty mechanisms

Carbon incentives and disincentives possess an essential influence on combating climate change as well as achieving carbon reduction targets [14]. For meeting the challenge of carbon emissions and promote the advancement of clean energy, VPP modeling has become an effective solution. The VPP model integrates multiple decentralized REN sources and energy storage devices (ESD) into a unified energy system to improve energy reliability, economy and environmental protection.

2.1 VPP optimization model construction

A VPP is a generalization of a centralized virtual electric power plant by integrating and coordinating the energy and energy demand of DE resources and flexible loads (e.g., electric vehicles, electric water heaters, etc.) [15]. The VPP operation is showcased in Fig. 1.

Figure 1.

How the VPP works.

As shown in Fig. 1, upstream basic resources include adjustable loads, distributed power supplies and energy storage equipment. Controllable loads vary in different sectors, such as industry, commerce, public buildings and residents, each with different load management difficulties. Distributed power refers to small photovoltaic, wind power, thermal power and hydropower units. Energy storage technologies include mechanical energy storage and chemical energy storage. Midstream virtual power plant operators are mainly divided into resource aggregators and technical service providers. Resource aggregators use technologies such as the Internet of Things and big data to integrate data from various fields to realize the core coordination and control functions of virtual power plants. Technical service providers focus on the construction of virtual power plant software platforms and provide technical support to resource aggregators. Downstream power demanders include public utility enterprises (grid companies), energy retailers (power sales companies) and other market transaction participants, who conduct power trading, peak frequency regulation and demand side response to obtain economic benefits. These actors have an important impact on the reliability and economics of the power system. Four modules are usually considered for VPP modeling, which are dispatchable generating units, controllable loads, distributed power sources, and ESD. Among them, dispatchable generating units refer to power generation equipment that can be adjusted and controlled according to demand, including traditional coal-fired power plants as well as REN generation equipment like fuel cells and gas turbines (GTU). Controllable loads are consumer equipment that can be adjusted and controlled according to demand, and the modeling of controllable loads needs to take into account their power demand, adjustment response time, load optimization strategy, and other factors. Distributed power refers to small-scale energy generation devices dispersed in the power grid. By modeling distributed power, the VPP can achieve centralized management and coordinated control of distributed power to maximize the use of REN and enhance the reliability and stability of the power grid. ESD are devices used to store energy and release it when needed, and the modeling of ESD needs to take into account factors such as their capacity, efficiency, and charge/discharge rate. The VPP modeling process is showcased in Fig. 2.

Figure 2.

VPP modeling process.

The study is based on the GTU and energy storage equipment (ESE) of dispatchable generating units to start, the cost function of GTU (Gas Turbine) is usually based on its fuel cost, maintenance cost and operating cost composition, set the cost function as $C_{i}(E_{Gi})$ , $E_{Gi}^{\min}$ , $E_{Gi}^{\max}$ indicates the moment when the GTU produces the minimum power and the maximum power, specifically as shown in Eq. (1).

$\displaystyle\left\{{\begin{array}[]{l}E_{Gi}^{\min}=P_{Gi}^{\min}\times\tau\\ E_{Gi}^{\max}=P_{Gi}^{\max}\times\tau\\ \end{array}}\right.$ (1)

In Eq. (1), $P_{Gi}^{\min}$ denotes the minimum output power (OPO) of the GTU; $P_{Gi}^{\max}$ denotes the maximum OPO of the GTU, and $\tau$ denotes the time. The OPO constraint of the GTU is shown in Eq. (2).

$\displaystyle v_{i}(t)P_{Gi}^{\min}\leqslant P_{Gi}(t)\leqslant v_{i}(t)P_{Gi}% ^{\max}$ (2)

In Eq. (2), $v_{i}(t)$ denotes the state of the GTU, which is categorized into startup and shutdown states, The value range of $v_{i}(t)$ is usually 0 and 1. $v_{i}(t)=0$ means that the GTU is in down state, i.e. it is not generating or transmitting signals. $v_{i}(t)=1$ means that the GTU is on, i.e. it is generating or transmitting signals. The cost function of the GTU $C_{i}(E_{Gi})$ is shown in Eq. (3).

$\displaystyle C_{i}(E_{Gi})=\sum\limits_{j=1}^{n_{j}}{K_{ij}P_{Gi}+C^{sd}}v_{i% }(t)+C^{sm}v_{i}(t)$ (3)

In Eq. (3), $n_{j}$ denotes the number of segments of the nonlinear cost function approximated by segmental linearization, and $n_{j}=3$ denotes the division into three segments. $C^{sd}$ and $C^{sm}$ denote the cost required to shut down and turn on the GTU, and $K_{ij}$ is the slope of the linear number of three segments. The ESD part of the build consists of mathematical equations for the evolution of the dynamic system, which reflect how the state of the energy storage system evolves based on the current state, inputs and time. By solving the state transition equations, the state values of the system at different points in time can be obtained, and then the behavior and performance of the system can be analyzed and predicted. The specific expression is shown in Eq. (4).

$\displaystyle E_{q}^{s}(t)=E_{q}^{s}(t-1)+\eta^{SC}P_{q}^{SC}(t)\tau-\frac{1}{% \eta^{SD}}P_{q}^{SD}(t)\tau$ (4)

In Eq. (4), $E_{q}^{s}(t)$ denotes the residual electric energy of the energy storage device at the time of $t$ ; $P_{q}^{SC}(t)$ denotes the power input for the charging of the ESD; $P_{q}^{SD}(t)$ denotes the power output for the use of the ESD, and $\eta^{SC}$ and $\eta^{SD}$ denote the efficiency of the capacity conversion in the charging process, and the specific constraints are shown in Eq. (5).

$\displaystyle\left\{{\begin{array}[]{l}0\leqslant P_{q}^{SC}(t)\leqslant P_{q}% ^{SC.\max}\\ 0\leqslant P_{q}^{SD}(t)\leqslant P_{q}^{SD.\max}\\ \end{array}}\right.$ (5)

In Eq. (5), $P_{q}^{SC.\max}$ and $P_{q}^{SD.\max}$ denote the maximum input power and the maximum OPO of the ESD, respectively, and the constraint equation of the ESD is shown in Eq. (6).

$\displaystyle E_{q}^{S.\min}\leqslant E_{q}^{S}(t)\leqslant E_{q}^{S.\max}$ (6)

In Eq. (6), $E_{q}^{S.\min}$ denotes the upper limit (ULI) of the electric energy in the ESD, and $E_{q}^{S.\max}$ denotes the lower limit (LLI) of the electric energy in the ESD. For facilitating the understanding of the proposed model, it is assumed that the generation capacity of the VPP cluster is relatively small, and the VPP cluster is set as the price taker. Therefore, when participating in the bidding in the day-ahead market, the VPP cluster is just necessary for submitting a bid for electricity, but not a bid. It is assumed that the degree of volatility of the carbon market price is smaller than the degree of volatility of the electricity price in the spot market, consequently, the carbon price is assumed to be a constant value in the model. The day-ahead bidding strategy of the VPP cluster is built based on this assumption and described by a two-stage stochastic optimization model.

$\displaystyle\textit{Max}[(1-\beta)(R^{DA}+R^{RT}+R^{C}-C^{MT})+\beta X_{% \textit{CVaR}}]$ (7)

The study optimizes the VPP model by optimizing the ESE, where the objective function consists of two parts, which are the expected return and the conditional value-at-risk of the return of the VPP cluster. The operating cost of the VPP is shown in Eq. (8).

$\displaystyle C^{MT}=\sum\limits_{t}{n^{MT}C(P_{kt}^{MT})}$ (8)

In Eq. (8), $n^{MT}$ denotes the quantity of GTU and $C(P_{kt}^{MT})$ denotes the cost of GTU consumed over a period of time $t$ . The VPP revenue is shown in Eq. (9).

$\displaystyle R^{DA}=\sum\limits_{t}{\lambda_{t}^{DA}P_{t}^{DA}}$ (9)

In Eq. (9), $\lambda_{t}^{DA}$ serves as the final price of electricity traded in the market at time $t$ , and $P_{t}^{DA}$ serves as the quantity of electricity purchased by the VPP at a specific price at time $t$ . The final revenue of the VPP is shown in Eq. (10).

$\displaystyle R^{C}=\lambda_{C}\times({E_{\textit{VPP}}-E_{MT}})$ (10)

In Eq. (10), $\lambda_{C}$ is the price of the VPP at the time of carbon trading; $E_{MT}$ serves as the carbon emission of the GTU in a certain period of time, and $E_{\textit{VPP}}$ is the carbon emission credits allocated to the VPP. The optimized VPP model gives priority to low carbon emission generation sources when supplying electricity, and effectively manages and schedules the capacity of different generation sources to minimize the negative impact on the environment.

2.2 Research on VPP game modeling under carbon incentive and penalty mechanism

The two-stage Stackelberg (Stackelberg) game model for VPP is a model used to analyze the competitive strategies and distribution of benefits of VPP in the electricity market [16]. The model can be modeled and solved in two stages, in the first stage, the VPP cluster acts as a leader to develop its bidding strategy. The leader can decide its bidding volume and bidding price based on market demand, cost, generation capacity and other factors. In the second stage, other market participants as followers respond accordingly to the leader’s bidding strategy. Followers can choose to participate in the bidding, adjust their bidding volume or price, etc. Based on the results of the model, revenue sharing and benefit analysis can be performed [17]. The two-stage Stackelberg game model of VPP is showcased in Fig. 3.

Figure 3.

Two-stage Stackelberg game model of VPP.

The objective of the VPP operator in the upper level optimization problem is to guide the power consumption demand of the users in the system in the coming day by setting the internal power consumption price for each time period and encouraging the users to actively participate in incentive-based demand response with certain allowances. Such an objective aims to achieve the peaking role of the VPP and to maximize the benefits of the VPP itself while ensuring stable system operation. For ensuring that the real-time electricity consumption price set by the VPP operator for internal users remains within a reasonable range, it is necessary to set limits on the maximum and minimum values of the electricity consumption price, as well as the constraint expression is shown in Eq. (11).

$\displaystyle p_{\min,t}\leqslant p_{e,t}\leqslant p_{\max,t}$ (11)

In Eq. (11), $p_{e,t}$ represents the tariff-guided internal customer electricity price implemented by the virtual plant operator. Whereas $p_{\min,t}$ represents the reasonable LLI of the virtual plant operator’s electricity sales price to internal customers; $p_{\max,t}$ represents the reasonable ULI of the virtual plant operator’s electricity sales price to internal customers [18]. For protecting the rights and interests of the customers, the virtual plant operator utilizes the forecast information of time-of-day tariffs in the external market and adopts a price-based demand response strategy to regulate the real-time tariffs for internal customers. By utilizing the elasticity of demand for electricity prices by users, the virtual plant operator sets and publishes real-time electricity prices for each time period in the previous day, aiming to ensure that these prices are better than the time-of-day prices in the market, which is expressed as Eq. (12).

$\displaystyle 0\leqslant p_{e,t}\leqslant p_{\textit{TOU},t}$ (12)

In Eq. (12), $p_{\textit{TOU},t}$ represents the time-of-day tariff of the market. For the implemented Information-Based Demand Response (IBDR) strategy, the virtual plant operator signs a subsidy contract with the users, sends incentive signals to the demand-side users with subsidy measures, and takes direct load interruption actions to the users at appropriate time periods to ensure stable and reliable operation of the virtual plant internally and to meet the peaking demand of the external grid. grid’s peaking demand [19]. Therefore, the incentive price constraint can be expressed as Eq. (13).

$\displaystyle\rho_{\min}\leqslant\rho_{IB,t}+\zeta_{IB,t}\leqslant\rho_{\max}$ (13)

In Eq. (13), $\rho_{IB,t}+\zeta_{IB,t}$ is the initial price released by the VPP; $\rho_{\min}$ serves as the LLI of the initial price, as well as $\rho_{\max}$ represents the ULI of the initial price. The segmentation function is linearized as shown in Eq. (14).

$\displaystyle C=z1\ast(-cd(3+3w))+z2\ast(-cd(2+w))+z3\ast(-cd){}+z4\ast(cd)+z5% \ast(cd(2+w))+z6\ast(cd(3+3w))$ (14)

The objective function is approximated in the form of a convex function, thus realizing the proposed convex objective. This is shown in Eq. (15).

$\displaystyle C=\left\{{\begin{array}[]{l}z1+z2+z3+z4+z5+z6=1\\ v1+v1+v3+v4+v5=1\\ z1\leqslant v1\\ z2\leqslant v1+v2\\ z3\leqslant v2+v3\\ z4\leqslant v3+v4\\ z5\leqslant v4+v5\\ z6\leqslant v5\\ -3d\ast z1-2d\ast z2-d\ast z3+d\ast z4+2d\ast z5+3d\ast z6=evpp\_m\\ z,v\in[{0,1}]\\ \end{array}}\right.$ (15)

The game between the operator and the users of the VPP system can be expressed by a two-layer optimization model. By solving the two-layer optimization model, the Nash equilibrium solution of the optimization model of the VPP system could be gotten. The scheduling problem of the VPP system is formulated as a two-layer optimization issue and the mixed integer decision variables are used to describe the problem.

2.3 Revenue sharing methodology for VPP

VPPs can develop reasonable bidding strategies to optimize their returns in the carbon trading environment and ensure that participants receive fair returns in carbon trading through appropriate revenue sharing mechanisms. First, based on collected data and market forecasts, VPPs develop bidding strategies, including selecting markets to participate in, determining the amount of electricity to bid for and the bidding price. Second, VPP establishes a day-ahead bidding model, which takes into account market supply and demand, competitors’ behavior, technical constraints, and carbon rewards and penalties, and solves the day-ahead bidding model using appropriate optimization algorithms or numerical methods to obtain the optimal bidding strategy and results. Consider the impact of carbon rewards and penalties, and incorporate carbon emission reduction contributions into allocation considerations to encourage low-carbon emission power generation and energy consumption behaviors. The revenue allocation process for a specific VPP is showcased in Fig. 4.

Figure 4.

VPP day-ahead bidding model and revenue distribution flowchart considering carbon trading.

The last part of the revenue allocation is the VPP revenue allocation on the ground of Shapley value, and the study explores how to equitably allocate the revenue of each participant within the VPP cluster by combining the game model. Shapley value is a concept in game theory used to measure the degree of each participant’s contribution to the outcome of the game [20]. The allocation method of Shapley value is utilized for distributing the benefits of the VPP cluster, and the distribution of benefits of each VPP member is shown through Eq. (16).

$\displaystyle x_{i}=\sum\limits_{S\subseteq N/i}{\frac{s!(n-s-1)!}{n!}}(R(S% \cup\{i\}-R(S))$ (16)

In Eq. (16), $S$ represents the sub-coalition from the members in the VPP cluster; $s$ serves as the quantity of members in the coalition $S$ , and $n$ denotes the quantity of members in the VPP. $R(S\cup\{i\}$ denotes the gain from adding member $i$ to coalition $S$ , while $R(S)$ denotes the gain from coalition $S$ . The benefits of different coalitions are showcased in Table 1.

Table 1

Benefits of different alliances

Alliance	Income
{Gas turbine}	R1
{Energy storage equipment}	R2
{Wind turbine}	R3
{Photovoltaic unit}	R4
{Gas turbine, energy storage equipment}	R12
{Gas turbine, wind turbine}	R13
{Gas turbine, photovoltaic unit}	R14
{Energy storage equipment, wind turbines}	R23
{Energy storage equipment, photovoltaic unit}	R24
{Wind turbine unit, photovoltaic unit}	R34
{Gas turbine, energy storage equipment, wind turbine}	R123
{Gas turbine, energy storage equipment, photovoltaic unit}	R124
{Gas turbine, wind turbine, photovoltaic unit}	R134
{Energy storage equipment, wind turbines, photovoltaic units}	R234
{Gas turbine, energy storage equipment, wind turbine, photovoltaic unit}	R1234

According to Table 1, the benefit distribution model under the carbon reward and punishment mechanism can be derived as shown in Eq. (17).

$\displaystyle\left\{{\begin{array}[]{l}x_{1}=\frac{1}{12}(R_{12}+R_{13}+R_{14}% )+\frac{1}{12}(R_{123}+R_{124}+R_{134})+\frac{1}{12}R_{1234}-\frac{5}{8}R_{1}% \\ \\ x_{2}=\frac{1}{12}(R_{12}+R_{23}+R_{24})+\frac{1}{12}(R_{123}+R_{124}+R_{234})% +\frac{1}{12}R_{1234}-\frac{5}{8}R_{2}\\ \\ x_{3}=\frac{1}{12}(R_{13}+R_{23}+R_{34})+\frac{1}{12}(R_{132}+R_{134}+R_{234})% +\frac{1}{12}R_{1234}-\frac{5}{8}R_{3}\\ \\ x_{4}=\frac{1}{12}(R_{14}+R_{24}+R_{34})+\frac{1}{12}(R_{124}+R_{134}+R_{234})% +\frac{1}{12}R_{1234}-\frac{5}{8}R_{4}\\ \end{array}}\right.$ (17)

In Eq. (17), $x_{1}$ denotes the GTU; $x_{2}$ denotes the ESE; $x_{3}$ denotes the wind turbine; $x_{4}$ denotes the photovoltaic unit, and $R_{i}$ denotes the revenue divided among these four parts. Although the kernel method and core method are widely used in the revenue allocation problem, the Shapley value allocation method differs from the egalitarian idea of the core method as well as kernel method. The Shapley value method is more equitable and could accurately reflect the degree of contribution of each member to the VPP. It allocates benefits based on the marginal contribution rate and has a unique result that is easy to understand. Therefore, Shapley value method is one of the most commonly used methods to solve the problem of revenue allocation. In the study, the Shapley value method is used in the research for distributing the gains from the VPP’s participation in the electricity market and the carbon market among the internal members of the VPP.In real life, there are differences between industrial users, commercial users and residential users. Industrial users usually require large amounts of electricity and have high flexibility and risk appetite, while commercial users have moderate scale and responsiveness, while residential users have smaller needs and pay more attention to cost and stability. Different users require differentiated energy strategies, including price, energy supply flexibility and response options, to meet their respective needs.

3. Benefit analysis of VPP clusters under carbon incentive and penalty mechanisms

Under the carbon incentive mechanism, VPP clusters are able to provide electricity supply in a more environmentally friendly and sustainable manner and receive corresponding economic incentives. The study will analyze the benefits of VPP clusters based on carbon incentives and penalties, and explore the operation strategies and benefit distribution of VPP under the influence of the carbon market, through which targeted strategies and decision support can be provided for the operation of VPP clusters to achieve a win-win situation in terms of carbon emission reduction and economic benefits.

3.1 Analysis of VPP strategies under carbon incentive pricing

The study aims to investigate the operational strategies of VPP operators for different types of user scenarios. The VPP operator dispatches its internal equipment for satisfying the requirements of industrial, commercial and residential customers, and participates in the external energy market. Meanwhile, in order to respond to the “dual carbon target” policy, the virtual plant operator also obtains carbon allowances by participating in the traditional carbon trading market. The focus of the study is to analyze the behavioral characteristics of users and construct a VPP model to maximize the utility function of supply and demand for achieving the optimal equilibrium strategy of supply and demand. The optimization results of the game equilibrium between VPP and users are showcased in Table 2.

Table 2
Game equilibrium optimization results of VPP operators and industrial users

Scheduling model	Industrial users		Business user		Residential users
VPP operating income (yuan)	270965		351452		210708
VPP market revenue (yuan)	120220		144282		109821
VPP carbon trading revenue (yuan)	1197		1990		1446
VPP carbon emission (ton)	87	.48	89	.43	84	.72
User electricity cost (yuan)	203554		256363		166636
User peak DR compensation revenue (yuan)	54884		93503		72325

By analyzing the results of the 24-hour day-ahead scheduling, it is possible to observe differences in the performance of different types of users in terms of carbon emissions. Commercial users have the highest carbon emissions, followed by industrial users, while residential users have the lowest carbon emissions, which is due to the fact that commercial users have the best performance in terms of the total customer load and the amount of interruptible load during the peak hours, leading to their relatively high carbon emissions. Commercial users achieved the best performance, followed by industrial users, and residential users performed the worst in terms of operating revenues of the VPP operator and subsidized revenues of users during peak hours. The optimization results for the three user types are showcased in Table 3.

Table 3

Optimization results for three user types

Scheduling model	Industrial users	Business user	Residential users
Maximum daily load/MW	21.749	21.148	21.564
Minimum daily load/MW	10.909	10.112	10.337
Daily average load/MW	15.826	16.858	14.544
Peak-to-valley difference/%	10.839	11.035	11.227
Peak-to-valley difference rate/%	0.498	0.521	0.52

In accordance with the outcomes presented in Table 2, the price-based demand response (PBDR) strategy was adopted for different types of follower users to optimize their electricity consumption behavior. For industrial users, the implementation of PBDR resulted in a 17% reduction in peak-to-valley differentials and a 6% increase in daily load factor, indicating that industrial users benefited from system peak shaving and operational economics. Commercial customers experienced a 12% reduction in peak-to-valley differentials and a 6% increase in daily load factor, which is not as pronounced as industrial customers, but still shows that PBDR has a significant impact on commercial customers. However, the peak-to-valley differential for residential customers was reduced by only 8% and the daily load factor increased by 4%, indicating that residential customers are less responsive to PBDR, and especially weak in peak shaving and valley filling. The tariff strategies developed by the operators of the three types of users are shown in Fig. 5.

Figure 5.

The electricity price strategy formulated by the operators of the three types of users.

According to the observation results in Fig. 5, the following key points can be summarized. First, the electricity consumption tariffs of users show obvious differences in different time periods, and usually, the electricity consumption tariffs are the highest in the peak hours, the second in the normal hours, and the lowest in the valley hours, and this trend reflects the positive correlation between the increase in the demand of the users’ electricity loads and the market tariffs. Secondly, there are disparities in the characteristics of electricity tariffs for various types of users at various times of the day. Industrial users’ electricity load during peak hours, especially during 8–11 hours, is accompanied by an increase in wind power (WPO) and PV output, and the electricity output in the system is borne by clean energy sources; therefore, although the market electricity price continues to rise, the price of electricity consumption by internal users decreases instead, for improving the efficiency of electricity consumption as well as promoting the consumption of clean energy sources. Residential customers also show low values of electricity prices during the 7–13-time period, similar to the case of industrial customers. However, commercial customers’ electricity loads are consistently in the peak hours during the 10–21-time period, during which they have higher loads and clean energy has been sufficiently consumed, and thus higher electricity prices are needed to guide customers’ electricity consumption. Finally, except for the variability in specific time periods, consumer electricity prices gradually converge to the time-of-day tariffs in the external electricity market in other time periods, which coincides with the decrease in the output of clean energy sources, like WPO. The PBDR response power loading strategies for the three types of users are shown in Fig. 6.

Figure 6.

PBDR response power load strategy for three types of users.

The following key observations can be made from the analysis results in Fig. 6. First, by implementing the PBDR strategy and using price changes to guide the electricity consumption behavior of internal users, different types of users show obvious differences in electricity load changes, especially industrial users, whose electricity load curves show obvious cuts. Peak fill valley characteristics. During valley hours, the electricity load of industrial users increases significantly, while during peak hours, the electricity load decreases significantly. This shows that industrial users are highly sensitive to price and can flexibly adjust their electricity consumption behavior to adapt to price changes in different time periods. In contrast, the electricity load curve of commercial users presents a typical peak period that lasts for a long time. There are also certain fluctuations in the electricity load curve of residential users, but the changes are smaller. Because residential users have regular lives, stable electricity demand, simple equipment, and do not involve complex management, so the changes in electricity consumption are small. IBDR’s response contract compensation strategy for three types of users is shown in Fig. 7.

Figure 7.

IBDR response contract compensation strategy for three types of users.

By looking at Fig. 7, firstly, different types of users have different utility and willingness to participate due to their own electricity consumption, which leads to the VPP providing them with different peak subsidy prices. Specifically, the peak subsidy price is RMB 1.8/kWh for industrial users, RMB 1.7/kWh for commercial users, and RMB 2.15/kWh for residential users. This implies that the VPP provides targeted incentives to users according to their types of characteristics and needs to motivate them to take actions to conserve electricity during peak hours. IBDR The interruptible load strategy for the three types of user response is shown in Fig. 8.

Figure 8.

IBDR response interruptible load strategy for three types of users.

As can be seen from Fig. 8, residential customers show a positive attitude in IBDR, with a total interruptible load of 33.6 MW; commercial and industrial customers also have a high degree of demand response, with a total interruptible load of 30.1 MW and 55.0 MW, respectively. However, industrial customers have a relatively low degree of responsiveness, which is mainly limited by the peaking potential of their electricity-using process equipment. The commercial users performed well in terms of concentration of peak hours and smoothness of load profiles, making them suitable as interruptible users. To further promote demand-side management, the study should enhance the dissemination of smart electricity demand response policies to increase user participation and awareness of electricity saving.

3.2 Revenue analysis under optimal bidding strategy

The study proposes an optimal operation model of a VPP cluster considering carbon trading, which aims to achieve carbon emission reduction by optimizing the allocation of power resources, and involves the linear programming solution of a mixed integer linear programming problem and a Shapley-valued revenue sharing problem. For addressing these issues, the study used the YALMIP/CPLEX tool in MATLAB to solve the model in order to obtain the optimal operation strategy and revenue allocation scheme. Finally, a VPP containing 10 micro GTU units MT, a WPO producer WP, a photovoltaic producer PV, and an energy storage system is considered in the study, where these components work together to provide a reliable and low carbon emission electricity supply. The amount of bids and OPO at risk is shown in Fig. 9.

Figure 9.

Risk-neutral bidding volume and OPO.

By observing the OPO curves in Fig. 9a, it demonstrates that the battery performs charging and discharging operations at different times. During low demand and peak WPO output, the batteries are charged to store power, while during high demand and low WPO output, the batteries are discharged to release the stored power. This charging and discharging strategy helps to balance the power supply and demand in the system. Meanwhile, the bidding results in Fig. 9b can be used to observe the participation of VPPs in the carbon and electricity markets. In addition, when the risk appetite coefficient $\beta=0$ is applied, VPP shows a neutral risk attitude and realizes the maximum return. The risk preference coefficient $\beta$ is used to consider the different risk acceptance levels of each virtual power plant or energy resource provider. It can also be said to be a parameter used to describe the risk tolerance and preference of an individual or entity. This coefficient can be used in an allocation approach to weigh risks and rewards between different entities to ensure a fair distribution of benefits. The gain profiles and bidding strategies are shown in Fig. 10.

According to the results of the analysis, the returns of VPP are affected by the value of $\beta$ . It is observed in Fig. 10a that there is a positive correlation in the value of CVaR and the returns of VPP, i.e., the larger the value of $\beta$ is, the larger the value of CVaR is and the total return of VPP gradually decreases. This indicates that the higher the risk aversion of the VPP, the more significant is the decrease in its returns. For the battery and micro GTU units in the VPP, they have the ability to adjust their operational status for reducing the settlement risk resulting from the uncertainty of WPO and PV. When the $\beta$ value is greater than or equal to 0.4, the VPP is more sensitive to bidding risk, which leads to a significant reduction in the total return of the VPP even if the increase in the CVaR value is small. And when the $\beta$ value is less than 0.4, the VPP is less sensitive to the bidding risk, when the increase in the CVaR value has a slower decrease in the total VPP revenue. The operation of the battery in the VPP is affected by the risk appetite coefficient $\beta$ . According to the observation in Fig. 10b, the battery is in the charging state before 12:00 hours and in the discharging state after 12:00 hours. This change is closely related to the magnitude of the risk appetite coefficient $\beta$ . With the value of $\beta$ grows, the power curve of the battery shows a more conservative trend, i.e., during the battery charging process, $\beta$ is positively correlated with the power out of the VPP; while during the battery discharging process, $\beta$ is negatively correlated with the power out of the VPP. A comparison of the VPP yield outcomes is showcased in Table 4.

Table 4

Comparison of revenue outcomes of VPP

Alliance	Income/10 yuan³	Alliance	Income/10 yuan³	Alliance	Income/10 yuan³
{1}	12.57	{1, 3}	276.59	{1, 2, 3}	282.61
{2}	6.21	{1, 4}	232.44	{1, 2, 4}	238.23
{3}	251.06	{2, 3}	257.12	{1, 3, 4}	497.6
{4}	207.11	{2, 4}	212.76	{2, 3, 4}	477.92
{1, 2}	18.83	{3, 4}	472.08	{1, 2, 3, 4}	503.43

Figure 10.

Yield profile and bidding strategy.

Collaboration and carbon trading bring significant benefits to the VPP. First, the VPP consists of four main players: micro GTU units, storage batteries, wind turbine operators and photovoltaic generators, which are replaced by 1, 2, 3 and 4 in the table, with a total of 15 non-empty sub-consortia. When carbon trading is considered, the total revenue of the VPP increases by about 5.55% compared to when it operates alone, which means that through cooperation and carbon trading, synergies are realized among the members of the VPP and higher revenues are obtained. According to the results of the Shapley value, the micro GTU unit has a gain of 1.88 $\times$ 10³ yuan; the battery has a gain of 8.32 $\times$ 10³ yuan; the wind turbine producer has a gain of 2.60 $\times$ 10³ yuan; and the PV producer has a gain of 2.16 $\times$ 10³ yuan. This demonstrates that through collaboration and carbon trading, VPP members are able to share in the benefits and receive higher economic benefits than they would if they were operating alone.

4. Conclusion

For promoting the use of REN and carbon emission reduction, the study presented a VPP cluster revenue allocation method on the ground of the carbon reward and punishment mechanism, which first establishes a VPP model, then optimizes it so that the model can preferentially supply electric energy units with low carbon emissions, then constructs a game model within the cluster, and finally allocates the revenue of each VPP of the VPP cluster on the ground of the revenue contribution. The results show that there are differences between different types of users in terms of carbon emissions and economic benefits. Commercial users have the highest emissions, followed by industrial users, and residential users have the lowest emissions. In the optimized user behavior, the peak-to-valley ratio of industrial users is reduced by 17% and the daily load factor is increased by 6%. For commercial customers, the peak to valley differential is reduced by 12% and the daily load factor is increased by 6%. Peak to valley differentials for residential customers were reduced by 8% and daily load factor increased by 4%. Collaboration and carbon trading provide significant benefits to the VPP, with total VPP revenues increasing by approximately 5.55% compared to stand-alone operation. Micro-GTU units yielded 1.88 $\times$ 10³ yuan, storage batteries 8.32 $\times$ 10³ yuan, wind turbines 2.60 $\times$ 10³ yuan, and photovoltaic generators 2.16 $\times$ 10³ yuan. Collaboration and carbon trading realize synergies and increase economic benefits. The shortcoming of the study is that all relevant risk factors are not analyzed, which may have an influence on the economic returns of the VPP, and further research is necessary for overcoming the shortcomings in the future.

Footnotes

Funding

The work was financially supported by Science and Technology Projects from State Grid Corporation of China, (Research and Application of Key Technologies for Economic Operation of Virtual Power Plant Considering Real-time Carbon Flow, 5108-202218280A-2-383-XG).

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Internal revenue sharing methodology for virtual power plant clusters considering carbon incentive and penalty mechanisms

Abstract

Keywords

1. Introduction

2. Modeling of VPP based on carbon incentive and penalty mechanisms

2.1 VPP optimization model construction

3.1 Analysis of VPP strategies under carbon incentive pricing

Table 2 Game equilibrium optimization results of VPP operators and industrial users

Footnotes

Funding

References

Table 2
Game equilibrium optimization results of VPP operators and industrial users