P2P Optimization Operation Strategy for Photovoltaic Virtual Power Plant Based on Asymmetric Nash Negotiation

Abstract

Under the guidance of the “dual-carbon” target, the utilization of and demand for renewable energy have been growing rapidly. In order to achieve the complementary advantages of renewable energy in virtual power plants with different load characteristics and improve the rate of consumption, an interactive operation strategy for virtual power plants based on asymmetric Nash negotiation is proposed. Firstly, the photovoltaic virtual power plant is proposed to establish the optimal scheduling model for the operation of the virtual power plant, and then the asymmetric Nash negotiation method is adopted to achieve the fair distribution of benefits. Finally, the ADMM distribution is used to solve the proposed model in the solution algorithm. The simulation results show that the revenue enhancement rates are 28.27%, 1.09%, and 12.37%, respectively. The participating subjects’ revenues are effectively enhanced through P2P power sharing. Each subject can obtain a fair distribution of benefits according to the size of its power contribution, which effectively improves the enthusiasm of the PV virtual power plant to participate in P2P interactions and thus promotes the development and consumption of renewable energy.

1. Introduction

Vigorously developing renewable energy is a meaningful way to realize the goal of “dual-carbon”, based on which the Chinese government proposed the photovoltaic project to promote the healthy and green development of the energy industry [1]. Virtual power plants (VPPs) provide technical support for the coordinated scheduling of distributed energy systems [2]. With the help of advanced network communication technology, VPPs can efficiently integrate different ranges of distributed energy sources, carry out collaborative and optimized management among units, and achieve good operation economy and environmental protection [3].

As more and more virtual power plants are connected to the distribution network, multiple virtual power plants in the same region adjacent to each other can form a multi-virtual power plant alliance. Instead of the less efficient centralized scheduling, each virtual power plant uses a peer-to-peer (P2P) system for energy interaction. Realizing electric energy synergy and mutual aid among regional virtual power plant alliances can effectively reduce the operating costs of each virtual power plant while improving energy utilization and system stability, and can reduce the dependence on the enormous power grid [4,5,6].

Literature [7] constructed a three-level interactive energy management strategy for the optimal operation of multiple virtual power plants at multiple time scales to achieve low-carbon economic operation among virtual power plants. Literature [8] proposed a two-tier coordination mechanism market for a two-tier optimization model when multiple virtual power plants were involved in a multi-virtual power plant POW, and economic optimization was achieved through a two-level coordination mechanism of multiple VPPs and multi-scale rolling scheduling to maximize energy use. Literature [9] constructed a multi-virtual power plant model considering demand response and solved it using the gray wolf optimization algorithm to achieve low-carbon economic operation of the system.

However, the joint operation of multiple VPPs in the above literature only pursues the optimization of the overall interests, ignoring the existence of cooperative and competitive relationships among the VPPs. Thus, the fair distribution of benefits among the VPPs in the synergistic operation is not fully considered. It is challenging to balance the overall interests of the VPP alliance and the individual interests in the optimization results [10].

The energy trading mechanism based on game theory helped researchers study and analyze the operation optimization strategy among multiple virtual power plants in P2P energy trading [11]. Literature [12] utilized the Shapley value method based on cooperative game theory to distribute the benefits of each participating subject within the cooperative alliance. However, the model was complex to compute and could only guarantee the maximization of the internal benefits of the alliance. In literature [13], based on the Nash bargaining theory in cooperative games, the nonlinear optimization problem was converted into two subproblems that were easy to solve. ADMM was employed to provide sequential solutions to protect individual information privacy. Literature [14] proposed a stochastic bargaining game-based VPP-electricity transfer clearing scheduling strategy, which considered multiple uncertainties on both the source and load sides and used Nash negotiation to achieve a fair profit distribution. Literature [15] proposed a novel VPP two-tier competitive negotiation to improve profitability and utilized game theory based on leader and follower laws to improve pricing speed.

In the study mentioned above, the proposed strategy ignores the different degrees of contribution of each VPP to the coalition when the cooperation is running using the Nash bargaining method. That is to say, it is set so that each VPP has the same bargaining power, which obviously cannot fully mobilize the enthusiasm of each subject VPP to participate in the operation of alliance cooperation.

Aiming at the above problems, this paper proposes a P2P optimal operation strategy for a PV virtual power plant based on asymmetric Nash negotiation. Firstly, the new energy-generating devices, energy storage devices, gas turbines, etc., of the PV virtual power plant are modeled to establish the optimal scheduling model for the independent operation of the virtual power plant. Then, an asymmetric Nash negotiation method is used to achieve a fair distribution of the benefits. Finally, the ADMM algorithm is used to solve the proposed model in a distributed manner in the solution algorithm.

The potential contributions of this paper are as follows:

(1) An asymmetric Nash negotiation method is adopted, and the model is solved using the ADMM algorithm, which achieves a fair distribution of the benefits of the virtual power plants and ensures privacy among the virtual power plants.

(2) A P2P optimal operation strategy for PV virtual power plants considering demand response is proposed, and the virtual power plants improve their economic and low-carbon performance through P2P.

2. Photovoltaic Virtual Power Plant Architecture

With the gradual scale-up of all kinds of distributional energy resources, including distributed power supply, energy storage devices, electric vehicles, and adjustable loads connected to the power grid, the fluctuation and uncertainty of all kinds of distributional energy resources also put forward new requirements on the flexible operation of the system, while enhancing the system’s operation economy, flexibility, and environmental protection. The fluctuation and uncertainty of various distributional energy resources also put forward new requirements for the flexible operation of the system. In such a context, the emergence of the concept of the virtual power plant can realize the flexible control of a large number of distributional energy resources using regional multi-energy aggregation, thus maximizing the unique advantages of various types of distributional energy resources for the enhancement of the interaction between the source-grid-load-storage side of the system based on ensuring the safe and stable operation of the power grid.

A virtual power plant is called “virtual” because of its internal resources in the spatial distribution of a decentralized rather than a centralized physical entity; it is called a “power plant” because it has the overall synergistic consistency to achieve the same function as a power plant [16]. A virtual power plant is a virtual union formed by deeply integrating energy and information technology, utilizing advanced communication, measurement, control technology, and software systems. It entails assembling distributed new energy power stations, combined heat and power systems, controllable loads, energy storage devices, and other resources scattered all over the world and connected to power grids at different levels to participate in the operation and coordination of power grids and coordinate the conflicts between smart grids and distributed power sources. It serves to improve the reliability of power supply and fully exploit the value and benefits brought by distributed energy. The internal structure is shown in Figure 1 below.

The structure of the photovoltaic virtual power plant system constructed in this work is shown in Figure 1. Each virtual power plant contains a micro-gas turbine and an uncontrollable new energy generation unit: Virtual Power Plant 1 is a wind power unit, and Virtual Power Plants 2 and 3 are photovoltaic power generation units. The electrical load consists of regular load, reducible load (RL), and transferable load (TL). Each virtual power plant also contains an internal energy storage system. In the whole virtual power plant system, each is connected to the higher power grid through a shared connection node and can purchase or sell power to the power grid. In contrast, virtual power plants are connected through a contact line for power interaction. Each virtual power plant can purchase or sell power to other virtual power plants. In Figure 2, the dotted line is the wired bi-directional communication information flow network. The solid line is the power transmission line.

In order to promote the development of distributed power generation and better utilize the advantages of distributed power generation in terms of economy and security, on 31 October 2017, the China National Development and Reform Commission (NDRC) and the National Energy Administration (NEA) jointly issued the Circular on the Pilot of Distributed Power Generation Market-Based Transactions, emphasizing that eligible distributed power generation entities can carry out distributed P2P with neighboring power users under the supervision of the trading centers. Distributed P2P power trading is decentralized, transparent, and open, and it is conducive to realizing the balance between the supply and demand of energy in the vicinity. It is also highly efficient and low-carbon, which ensures the transaction’s fairness.

In order to promote local consumption of new energy generation and reduce transmission network losses, each virtual power plant interacts with electricity and information through the virtual power plant operator. When the power is not enough to support the operation of the virtual power plant, power is purchased from the higher grid. The PV virtual power plant P2P optimization operation strategy is shown in Figure 3, which determines the charging and discharging status of the energy storage in the virtual power plant, the regulation of the load, and the carbon emission of the system based on the PV virtual power plant P2P power trading volume, to realize the economic and low-carbon operation of the virtual power plant.

3. Mathematical Modeling of Photovoltaic Virtual Power Plant Considering Load-Side Demand Response

3.1. Demand Response Model

The introduction of fast-responding flexible resources on the load side can mobilize the enthusiasm of load-side response, reduce the economic burden brought by increasing the energy storage capacity, and further realize the consumption of wind and solar resources. The electrical loads within the virtual power plant are composed of rigid and flexible loads [17], and the flexible loads are, in turn, composed of transferable loads (TL) and reducible loads (RL) as follows:

$$P_i^{\mathrm{load}}(t)=P_i^{\mathrm{Rload}}(t)+P_i^{\mathrm{TL}}(t)+P_{i,in}^{\mathrm{RL}}(t)-P_{i,out}^{\mathrm{RL}}(t)$$

(1)

where $P_i^{\mathrm{load}}(t)$ is the predicted electric load power of virtual power plant i at time t.

3.1.1. Reducible Loads

Advanced energy storage and power curtailment of reducible loads can be equivalently regarded as virtual energy storage’s charging/discharging process. The reducible loads in this paper refer to a part of the electric load resources on the load side, and the mathematical model of reducible loads is as follows [18]:

$$0\le P_i^{\mathrm{RL}}(t)\le K_i^{\mathrm{RL}}{P}_i^{\mathrm{load}}(t)$$

(2)

where $P_i^{\mathrm{RL}}(t)$ is the curtailed power of the RL within the ITH virtual power plant at period t; $K_i^{\mathrm{RL}}$ is the proportion of load that can be curtailed as 0.1.

3.1.2. Transferable Loads

TL can shift the load usage period from one interval to another within a specific permissible range during the dispatch cycle and thus can realize the energy transfer in time, but its total load in a dispatch cycle is a certain amount; the TL mathematical model is as follows [19]:

$$\left\{\begin{array}{l}0\le P_{i,in}^{\mathrm{TL}}(t)\le u_{i,in}^{\mathrm{TL}}(t)(P_{i,\mathrm{in}-\max }^{\mathrm{TL}}(t-1)-P_{i,in}^{\mathrm{TL}}(t-1))\hfill \\ 0\le P_{i,\mathrm{out}}^{\mathrm{TL}}(t)\le u_{i,\mathrm{out}}^{\mathrm{TL}}(t)(P_{i,\mathrm{out}-\max }^{\mathrm{TL}}(t-1)-P_{i,\mathrm{out}}^{\mathrm{TL}}(t-1))\hfill \\ u_{i,\mathrm{in}}^{\mathrm{TL}}(t)u_{i,\mathrm{out}}^{\mathrm{TL}}(t)=0\hfill \\ {\displaystyle \sum _{i\in T_i}(u_{i,\mathrm{in}}^{\mathrm{TL}}(t)+u_{i,\mathrm{out}}^{\mathrm{TL}}(t))}=0\hfill \\ T_i=[T_{i,\mathrm{start}}^{\mathrm{TL}},T_{i,\mathrm{end}}^{\mathrm{TL}}]\hfill \\ {\displaystyle \sum _{i\in J}{\displaystyle \sum _{t=1}^T(u_{i,\mathrm{in}}^{\mathrm{TL}}(t)P_{i,\mathrm{in}}^{\mathrm{TL}}(t)-u_{i,\mathrm{out}}^{\mathrm{TL}}(t)P_{i,\mathrm{out}}^{\mathrm{TL}}(t))}}=0\hfill \end{array}\right.$$

(3)

where $u_{i,in}^{\mathrm{TL}}(t)$ and $u_{i,\mathrm{out}}^{\mathrm{TL}}(t)$ are the equivalent charging and discharging states of the ITH virtual power plant TL at period t, respectively. The charging/discharging state is taken as 1, and vice versa as 0. $P_{i,\mathrm{in}-\max }^{\mathrm{TL}}(t-1)$ and $P_{i,\mathrm{out}-\max }^{\mathrm{TL}}(t-1)$ are the equivalent maximum charging and discharging power of TL at period t − 1, respectively. $T_{i,\mathrm{start}}^{\mathrm{TL}}$ and $T_{i,\mathrm{end}}^{\mathrm{TL}}$ are the start and end periods, respectively, where the TL can be equivalently charged and discharged during the scheduling cycle.

3.2. Equipment Output Modeling

3.2.1. Gas Turbine Model

Micro-gas turbines generate electricity primarily by burning natural gas. The generation of electricity at moment t of the ITH virtual power plant $P_i^{\mathrm{GT}}(t)$ and the conversion relationship with natural gas consumption is as follows [20]:

$$P_i^{\mathrm{GT}}(t)=V_i^{\mathrm{GT}}(t){\eta }_{GT}{Q}_{{\mathrm{CH}}_4}$$

(4)

where $V_i^{\mathrm{GT}}(t)$ is the natural gas consumption; ${\eta }_{GT}$ is the power generation efficiency of the gas turbine; $Q_{{\mathrm{CH}}_4}$ is the calorific value of natural gas combustion.

3.2.2. Energy Storage Modeling

The state of charge of the energy storage system at moment t is as follows [21]:

$$\left\{\begin{array}{l}{S}_i(t)=(1-{\eta }^{\mathrm{loss}})S_i(t-1)+\eta P_i^{\mathrm{CHA}}(t)-{\displaystyle \frac{1}{\eta }}{P}_i^{\mathrm{DIS}}(t)\\ 0\le P_i^{\mathrm{CHA}}(t)\le u_i^{\mathrm{CHA}}(t)P_{\max }^{\mathrm{CHA}}\\ 0\le P_i^{\mathrm{DIS}}(t)\le u_i^{\mathrm{DIS}}(t)P_{\max }^{\mathrm{DIS}}\\ 0\le u_i^{\mathrm{DIS}}(t)+u_i^{\mathrm{CHA}}(t)\le 1\\ S_i^{\min }\le S_i(t)\le S_i^{\max }\end{array}\right.$$

(5)

where $S_i(t)$ is the capacity of the energy storage system of virtual power plant i at moment t; $P_i^{\mathrm{CHA}}(t)$ and $P_i^{\mathrm{DIS}}(t)$ are the charging and discharging power of the energy storage system of virtual power plant i at moment t; ${\eta }^{\mathrm{loss}}$ is the loss efficiency; $\eta$ is the charge/discharge efficiency; $P_{\max }^{\mathrm{CHA}}$ and $P_{\max }^{\mathrm{DIS}}$ are the maximum power for charging and discharging the energy storage system; $u_i^{\mathrm{CHA}}(t)$ and $u_i^{\mathrm{DIS}}(t)$ are charged and discharged states; $S_i^{\min }$ and $S_i^{\max }$ are minimum and maximum capacity limits.

4. Photovoltaic Virtual Power Plant P2P Optimization Operation Model

4.1. PV Virtual Power Plant P2P Optimization Operation Objective Function

The scheduling goal of the PV virtual power plant system is to reduce the operating cost and environmental pollution of the system while satisfying the electrical load as much as possible. To minimize the comprehensive cost of the virtual power plant itself, the optimal model of virtual power plant P2P is established. The consolidated cost of each virtual power plant $C_i^{\mathrm{VPP}}$ consists mainly of the following: transaction costs for higher-level energy networks $C_i^{\mathrm{BUY}}$, operating costs of battery energy storage systems inside virtual power plants $C_i^{\mathrm{BAT}}$, cost of carbon emissions $C_i^{{\mathrm{CO}}_2}$, virtual energy storage costs $C_i^{\mathrm{VS}}$, electricity sharing costs $C_i^{\mathrm{P}2\mathrm{P}}$.

$$\min C_i^{\mathrm{VPP}}=C_i^{\mathrm{BUY}}+C_i^{\mathrm{BAT}}+C_i^{{\mathrm{CO}}_2}+C_i^{\mathrm{VS}}+C_i^{\mathrm{P}2\mathrm{P}}$$

(6)

4.1.1. Transaction Costs of Higher-Level Energy Networks

The cost of purchasing energy for the ITH virtual power plant consists of the cost of purchasing and selling electricity to the external grid and the cost of purchasing natural gas as follows:

$$C_i^{\mathrm{BUY}}={\displaystyle \sum _{t=1}^T[({\lambda }_{\hspace{0.25em}}^{\mathrm{buy}}(t)P_i^{\mathrm{buy}}(t)-{\lambda }_{\hspace{0.25em}}^{\mathrm{sell}}(t)P_i^{\mathrm{sell}}(t))+{\lambda }_{{\mathrm{CH}}_4}(t)V_i^{\mathrm{buy}}(t)]}$$

(7)

where ${\lambda }_{\hspace{0.25em}}^{\mathrm{buy}}(t)$ and ${\lambda }_{\hspace{0.25em}}^{\mathrm{sell}}(t)$ are the tariffs for the purchase and sale of electricity for the VPP in period t, respectively; $P_i^{\mathrm{buy}}(t)$ and $P_i^{\mathrm{sell}}(t)$ are the power purchased and sold by VPP at time t, respectively; $V_i^{\mathrm{buy}}(t)$ and ${\lambda }_{{\mathrm{CH}}_4}(t)$ are the quantity of natural gas purchased and the price of natural gas purchased in period t, respectively.

4.1.2. Battery Energy Storage System Operating Costs

$$C_i^{\mathrm{BAT}}={\displaystyle \sum _{t=1}^T{\epsilon }^{\mathrm{BAT}}}(P_i^{\mathrm{CHA}}(t)+P_i^{\mathrm{DIS}}(t))$$

(8)

where ${\epsilon }^{\mathrm{BAT}}$ is the maintenance cost factor per unit of power.

4.1.3. Carbon Emission Costs

$$\left\{\begin{array}{l}{C}_i^{{\mathrm{CO}}_2}={\displaystyle \sum _{t=1}^T{e}_{{\mathrm{CO}}_2}}\left(E_i^{{\mathrm{CO}}_2}(t)-E_i^0(t)+E_i^{\mathrm{GRID}}(t)\right)\hfill \\ \begin{array}{l}{E}_i^{\mathrm{GRID}}(t)={\upsilon }_{{\mathrm{CO}}_2}{P}_i^{\mathrm{buy}}(t)\\ E_i^0(t)={\partial }_{{\mathrm{CO}}_2}{P}_i^{\mathrm{GT}}(t)\end{array}\hfill \\ E_i^{{\mathrm{CO}}_2}(t)={\alpha }_{{\mathrm{CO}}_2}{P}_i^{\mathrm{GT}}(t)\hfill \end{array}\right.$$

(9)

where $e_{{\mathrm{CO}}_2}$ is the cost of emissions per unit of CO₂; $E_i^{{\mathrm{CO}}_2}(t)$ is the carbon emission of the virtual power plant at moment t; $E_i^0(t)$ is the amount of carbon allowances of the virtual power plant at moment t; $E_i^{\mathrm{GRID}}(t)$ is the carbon emissions from grid power purchases at moment t; ${\upsilon }_{{\mathrm{CO}}_2}$ is the carbon emissions per unit of electricity; ${\partial }_{{\mathrm{CO}}_2}$ is the amount of carbon allowance per unit of gas turbine; ${\alpha }_{{\mathrm{CO}}_2}$ is the carbon emission per unit of gas turbine.

4.1.4. Demand Response Costs

$$C_i^{\mathrm{VS}}={\displaystyle \sum _{t=1}^T(s_i^{\mathrm{RL}}{P}_i^{\mathrm{RL}}(t)+s_i^{\mathrm{TL}}(}{P}_{i,\mathrm{in}}^{\mathrm{TL}}(t)+P_{i,\mathrm{out}}^{\mathrm{TL}}(t)))$$

(10)

where $s_i^{\mathrm{RL}}$ and $s_i^{\mathrm{TL}}$ are the costs of calling RL and TL, respectively.

4.1.5. Electricity Sharing Costs

$$C_i^{\mathrm{P}2\mathrm{P}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j\ne i}^{\varphi }{\lambda }_{i-j}^{\mathrm{P}2\mathrm{P}}(t)}}{P}_{i-j}^{\mathrm{P}2\mathrm{P}}(t)$$

(11)

where $\varphi$ is a collection of multi-virtual power plant alliances; $P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)$ is the interacting electric power of the ITH virtual power plant with the Jth virtual power plant at time t and $P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)>0$ denotes that the ITH VPP supplies electricity to the Jth VPP, on the other hand, obtaining power from the JTH VPP; ${\lambda }_{i-j}^{\mathrm{P}2\mathrm{P}}(t)$ is the price per unit of power corresponding to the interacted power $P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)$ at period t.

4.2. P2P Optimization Operation Constraints for Photovoltaic Virtual Power Plants

4.2.1. Energy Balance Constraints

The electric power balance constraint when each virtual power plant operates cooperatively, i.e., when power is interactively shared among virtual power plants, is

$$\left\{\begin{array}{l}{P}_i^{\mathrm{GT}}(t)+P_i^{\mathrm{DIS}}(t)+P_i^{\mathrm{NE}}(t)=P_i^{\mathrm{load}}(t)+P_i^{\mathrm{CHA}}(t)+P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)\\ V_i^{\mathrm{buy}}(t)=V_i^{\mathrm{GT}}(t)\end{array}\right.$$

(12)

where $P_i^{\mathrm{NE}}(t)$ is the new energy generation power of the ITH VPP; if i = 1, it is wind power, and the rest is PV.

4.2.2. Constraints on Energy Purchases from Higher-Level Energy Networks

$$\left\{\begin{array}{l}0\le P_i^{\mathrm{buy}}(t)\le P_i^{\mathrm{buy},\max }\hfill \\ \begin{array}{l}0\le P_i^{\mathrm{sell}}(t)\le P_i^{\mathrm{sell},\max }\\ 0\le V_i^{\mathrm{buy}}(t)\le V_i^{\mathrm{buy},\max }\end{array}\hfill \end{array}\right.$$

(13)

where $P_i^{\mathrm{buy},\max }$ and $P_i^{\mathrm{sell},\max }$ are the maximum value of the ITH VPP power purchase and sale, respectively; $V_i^{\mathrm{buy},\max }$ is the maximum value of gas purchased by the ITH VPP.

4.2.3. Power Sharing Interaction Constraints

$$\left\{\begin{array}{l}{\displaystyle \sum _{i\in \varphi }{P}_i^{\mathrm{P}2\mathrm{P}}(t)}=0\hfill \\ \left|P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)\right|\le P_{i-j}^{\max }\hfill \\ {\displaystyle \sum _{i\in \varphi }{C}_i^{\mathrm{P}2\mathrm{P}}(t)}=0\hfill \end{array}\right.$$

(14)

where $P_i^{\mathrm{P}2\mathrm{P}}(t)$ is the total power interactively shared by the ITH VPP in time period t.

4.2.4. Equipment Output Constraints

$$\left\{\begin{array}{l}{P}_i^{\mathrm{GT},\min }(t)\le P_i^{\mathrm{GT}}(t)\le P_i^{\mathrm{GT},\max }(t)\\ 0\le P_i^{\mathrm{NE}}(t)\le P_i^{\mathrm{NE},\max }(t)\end{array}\right.$$

(15)

where $P_i^{\mathrm{GT},\max }(t)$, $P_i^{\mathrm{GT},\min }(t)$, and $P_i^{\mathrm{NE},\max }(t)$ are the maximum value of gas turbine output, the minimum value of new energy generation output, and the maximum value of new energy generation output, respectively.

5. Based on the Asymmetric Nash Negotiation Solution Method

5.1. Asymmetric Nash Negotiation Models

When a coalition of virtual power plants is in operation, each virtual power plant belongs to a different body of interests, and its interests are different. Each virtual power plant is a typical “energy producer and seller” and often hopes to maximize its own interests through a fair and equitable competition method. Energy trading based on Nash bargaining can help incentivize win–win cooperation among virtual power plants to enhance their profit. The Nash bargaining game obtains a fair Pareto optimal solution and a Nash bargaining solution while satisfying the axioms of individual rationality, Pareto optimality, independence of linear transformations, and symmetry [22]. The standard Nash bargaining model is as follows:

$$\left\{\begin{array}{l}\max {\displaystyle \prod _{i\in \varphi }(R_i-R_i^0)}\hfill \\ \mathrm{s}.\mathrm{t}.R_i-R_i^0\ge 0\hfill \end{array}\right.$$

(16)

where $R_i$ and $R_i^0$ are the benefits of the ITH participant and the negotiation rupture point (when each participant operates independently), respectively; the constraint $R_i-R_i^0\ge 0$ ensures that the benefits to the subjects after participating in the cooperation are more significant than they would have been if they had operated independently.

From the above equation, it can be seen that the model is a multi-variable coupled, non-convex nonlinear model, which is challenging to solve directly, and the model can be transformed into two subproblems that are easy to solve: alliance benefits maximization subproblem 1 and benefit distribution subproblem 2.

(1)

Alliance Benefit Maximization Subproblem

$$\left\{\begin{array}{l}\min {\displaystyle \sum _{i=1}^N{C}_i^{\mathrm{VPP}}(P_i^{\mathrm{P}2\mathrm{P}}(t))}\\ \mathrm{s}.\mathrm{t}.\end{array}\right.$$

(17)

when solving subproblem 1, $C_i^{\mathrm{P}2\mathrm{P}}$ can be ignored, i.e., $C_i^{\mathrm{P}2\mathrm{P}}=0$. Since the energy sharing equilibrium constraint equation is multiply coupled among all virtual power plants, an auxiliary variable vector $P_{j-i}^{\mathrm{P}2\mathrm{P}}(t)$ is introduced for decoupling, transforming subproblem 1 into a doubly coupled model as shown in the following equation:

$$P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)+P_{j-i}^{\mathrm{P}2\mathrm{P}}(t)=0,\forall i$$

(18)

where $P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)$ denotes the amount of electricity that virtual power plant i expects to trade with virtual power plant j; $P_{j-i}^{\mathrm{P}2\mathrm{P}}(t)$ denotes the amount of electricity that virtual power plant j expects to trade with virtual power plant i. When $P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)=-P_{j-i}^{\mathrm{P}2\mathrm{P}}(t)$, it indicates that there is a power trading consensus between virtual power plant i and virtual power plant j.

This Lagrangian function is constructed by introducing the Lagrangian multiplier ${\lambda }_{ij}^1$ and the penalty factor ${\rho }_i^1$ by Equation (17).

(2)

Income distribution sub-issues

The standard Nash negotiation benefit distribution is generally the same, while the contribution made by the general subjects involved in the cooperation differs, which is unfair. The nonlinear function based on the natural logarithm measures the different contributions of each virtual power plant to the power-sharing process of the cooperative alliance, and each virtual power plant uses its different contributions as bargaining power to negotiate the revenue-sharing in the revenue-sharing subproblem [23]. The specific formulation is as follows.

First, the electrical energy $E_i^{\mathrm{sell}}$ supplied and the electrical energy $E_i^{\mathrm{recive}}$ received by each sub-VPP during the scheduling cycle while participating in the optimization process are calculated:

$$\left\{\begin{array}{l}{E}_i^{\mathrm{sell}}={\displaystyle \sum _{i\ne j}^{\varphi }{\displaystyle \sum _{t=1}^T\max }}(0,P_{i-j}^{\mathrm{P}2\mathrm{P}}(t))\\ E_i^{\mathrm{recive}}=-{\displaystyle \sum _{i\ne j}^{\varphi }{\displaystyle \sum _{t=1}^T\min }}(0,P_{i-j}^{\mathrm{P}2\mathrm{P}}(t))\end{array}\right.$$

(19)

The maximum amount of electricity to be provided $E_{\max }^{\mathrm{sell}}$ and the maximum amount of electricity to be received $E_{\max }^{\mathrm{recive}}$ for each VPP in the multi-virtual power plant consortium are as follows:

$$\left\{\begin{array}{l}{E}_{\max }^{\mathrm{sell}}=\max (E_i^{\mathrm{sell}})\hfill \\ E_{\max }^{\mathrm{recive}}=\max (E_i^{\mathrm{recive}})\hfill \end{array}\right.$$

(20)

The magnitude ${\omega }_i$ of the contribution of each VPP, measured using an exponential function with a natural constant e as the base, is as follows:

$${\omega }_i=e^{E_i^{\mathrm{sell}}/E_{\max }^{\mathrm{sell}}}-e^{-(E_i^{\mathrm{recive}}/E_{\max }^{\mathrm{recive}})}$$

(21)

This way, problem 2 can be converted:

$$\left\{\begin{array}{l}\min -{\omega }_i\ln {\displaystyle \sum _{i=1}^N(C_i^0-C_i^{\mathrm{VPP}}+C_i^{\mathrm{P}2\mathrm{P}})}\hfill \\ \begin{array}{l}\mathrm{s}.\mathrm{t}.\\ C_i^0-C_i^{\mathrm{VPP}}+C_i^{\mathrm{P}2\mathrm{P}}>0\end{array}\hfill \end{array}\right.$$

(22)

As in subproblem 1, auxiliary variables are introduced for decoupling as follows:

$$r_{i-j}^{\mathrm{P}2\mathrm{P}}(t)-r_{j-i}^{\mathrm{P}2\mathrm{P}}(t)=0,\forall i$$

(23)

where $r_{i-j}^{\mathrm{P}2\mathrm{P}}(t)$ denotes the optimal unit price of traded electricity that has been solved in subproblem 1 by virtual power plant i; $r_{j-i}^{\mathrm{P}2\mathrm{P}}(t)$ denotes the desired transaction unit price of virtual power plant j. When $r_{i-j}^{\mathrm{P}2\mathrm{P}}(t)=-r_{j-1}^{\mathrm{P}2\mathrm{P}}(t)$, it indicates that virtual power plant i and virtual power plant j have reached a consensus on the transaction price.

5.2. ADMM Algorithm Based Solution

When energy is traded between virtual power plants, each operator usually cannot know each other’s data information, and distributed solution methods can effectively solve the game interaction problem of energy exchange between multiple virtual power plants in this case. ADMM is widely used in distributed optimization problems due to its good convergence performance and fast computation speed [24].

In this paper, we construct a distributed optimization framework for the two subproblems sequentially and bring the optimal solution of energy interaction and equipment output computed in the former subproblem into the computational process of the latter subproblem. The steps are as follows, and the running process is shown in Figure 4.

Step 1: First, each virtual power plant’s data and load data are input to determine the maximum number of iterations and upper and lower limits.

Step 2: Then, subproblem 1 is solved, and power information interacts between virtual power plants; according to the model, the traded power and Lagrange multipliers are updated to determine the output of the equipment within each virtual power plant and the participation of load demand response, to output the results of the optimal inter-virtual power plants’ power trading, and save them.

Step 3: Immediately after that, subproblem 2 is solved to calculate the trading contribution value based on the electricity trading results between virtual power plants obtained in step 2 and to perform the information interaction of trading tariffs; the trading tariffs and Lagrange multipliers are updated to output the optimal trading results of the electricity tariffs between the optimal virtual power plants.

Step 4: According to the results obtained in steps 2 and 3, output the virtual power plant equipment output situation, the load demand response participation situation, and the power trading price.

This Lagrangian function is constructed by introducing the Lagrangian multiplier ${\lambda }_{ij}^1$ and the penalty factor ${\rho }_i^1$ by Equation (17).

The Lagrangian value-added function for subproblem 1 takes the following form:

$$\min f_i^1=C_i^{\mathrm{VPP}}+{\displaystyle \sum _t{\displaystyle \sum _j\left({\lambda }_{ij}^1\left(P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)+P_{j-i}^{\mathrm{P}2\mathrm{P}}(t)\right.\right)}}+{\displaystyle \frac{{\rho }_i^1}{2}}{‖P_{i-j}^{\mathrm{P}2\mathrm{P}}(t)+P_{j-i}^{\mathrm{P}2\mathrm{P}}(t)‖}_2^2$$

where ${\lambda }_{ij}^1$ is a Lagrange multiplier; ${\rho }_i^1$ is the penalty parameter.

The Lagrangian function for subproblem 2 is constructed by introducing the Lagrangian multiplier ${\lambda }_{ij}^2$ and penalty factor ${\rho }_i^2$ by Equation (22).

The Lagrangian value-added function form of subproblem 2 is as follows:

$$\min f_i^2=-{\omega }_i\ln (C_i^0-C_i^{\mathrm{VPP}}+C_i^{\mathrm{P}2\mathrm{P}})+{\displaystyle \sum _t{\displaystyle \sum _j\left({\lambda }_{ij}^2\left(r_{i-j}^{\mathrm{P}2\mathrm{P}}(t)+r_{j-i}^{\mathrm{P}2\mathrm{P}}(t)\right.\right)}}+{\displaystyle \frac{{\rho }_i^2}{2}}{‖r_{i-j}^{\mathrm{P}2\mathrm{P}}(t)+r_{j-i}^{\mathrm{P}2\mathrm{P}}(t)‖}_2^2$$

where ${\lambda }_{ij}^2$ is a Lagrange multiplier; ${\rho }_i^2$ is the penalty parameter.

The interaction quantities, Lagrange multiplier iterative forms, and convergence conditions for subproblems 1 and 2 can be found in the literature [25].

6. Example Analysis

6.1. Foundation Setup

In order to verify the effectiveness of the method proposed in this paper, day-ahead (00:00–24:00) optimal dispatch is carried out based on the forecast values of loads and renewable energy sources with an interval of 1 h. Matlab software version 2021 is used for simulation, taking three virtual power plants as an example, and the simulation parameters are shown in the following

Table 1. Model parameters.

Parameters	Numerical Value	Parameters	Numerical Value
$P_i^{\mathrm{CHA}}\left(t\right)$$,P_i^{\mathrm{DIS}}\left(t\right)$	500 kW	$P_{i-j}^{max}$ $P_i^{\mathrm{GT},\max }\left(t\right)$$,P_i^{\mathrm{GT},\min }\left(t\right)$ $P_i^{\mathrm{buy},max}$$,P_i^{\mathrm{sell},max}$ $s_i^{\mathrm{RL}}$$,s_i^{\mathrm{TL}}$ ${\eta }_{GT}$ $K_i^{\mathrm{RL}}$ ${\alpha }_{\mathrm{C}{\mathrm{O}}_2}$	2000 kW
$S_i^{min}$$,S_i^{max}$	100 kW, 1000 kW		500, 50 kW
${\eta }^{\mathrm{loss}}$	1%
$\eta$	0.95
${\lambda }_{\mathrm{C}{\mathrm{H}}_4}\left(t\right)$	3.2 yuan/m3		2000 kW
${\epsilon }^{\mathrm{BAT}}$	0.1 yuan/kW		0.05, 0.03 yuan/kW
$e_{\mathrm{C}{\mathrm{O}}_2}$	0.75 yuan/kg		0.45
${\upsilon }_{\mathrm{C}{\mathrm{O}}_2}$	1.072 kg/kWh		0.1
${\partial }_{\mathrm{C}{\mathrm{O}}_2}$	0.32 kg/kWh		0.613 kg/kWh

:

The renewable energy output forecast profile is shown in Figure 5, and the typical daily load profile of the virtual power plant is shown in Figure 6. Virtual Power Plant 1 relies mainly on wind power generation, which is not able to achieve local energy self-sufficiency because it is more stable during the daytime. So, Virtual Power Plant 1 takes an energy purchasing role. Virtual Power Plant 2 relies mainly on photovoltaic power generation, and its load characteristics show that the area is a residential area with a low demand for electricity during working hours. However, the morning and evening hours are the peak hours, so it acts as both an energy supplier and an energy receiver in the virtual power plant. Virtual Power Plant 3 relies mainly on photovoltaic power generation and acts as an energy supplier in the virtual power plant. The different settings of the supply side ensure the possibility of power interaction between the virtual power plants.

6.2. Analysis of Results

6.2.1. Analysis of Basic Scheduling Results

The output and demand response load optimization of each unit of the virtual power plant is shown in Figure 7, Figure 8 and Figure 9. Renewable energy sources, gas turbines, and storage batteries mainly provide the output of each virtual power plant. Virtual Power Plant 1 dramatically improves the utilization of renewable energy during the 1:00–5:00 and 21:00–24:00 time periods when renewable energy and gas turbine output are more significant than the load demand, and excess power is used for storage to meet self-generated load demand and traded to other virtual power plants that need power to earn a profit. At 10:00–20:00, peak shaving is executed by increasing the gas turbine power and demand response to meet the load demand. The renewable energy source of Virtual Power Plant 2 is PV, and the load characteristics are residential. There is a large electricity surplus during the daytime, so Virtual Power Plant 2 mainly trades electricity to the microgrids that have insufficient electricity during the daytime as a way of earning revenue, and the rest of it is stored to cope with the peak hours of electricity consumption in the evening. In the evening, Virtual Power Plant 2 firstly utilizes peak shaving to reduce the load demand and then utilizes energy storage discharge, combustion turbine generation, and purchasing electricity from other virtual power plants to satisfy its conformity demand. Virtual Power Plant 3, with its own lower load demand and its larger PV output during the daytime, sells the excess electricity to other virtual power plants to earn revenue through P2P from 7:00 to 17:00 and reduces the load demand in the evening using demand response.

The results of the P2P interactions between the virtual power plants are shown in Figure 10. During the 1:00–5:00 and 22:00–24:00 time slots, Virtual Power Plant 1 has a surplus of wind power generation and thus transmits power to Virtual Power Plants 2 and 3, which are not able to generate power at night and are in shortage of power, while Virtual Power Plant 1 has a shortage of its power supply due to a surge of electric load during the daytime. The photovoltaic power generation of Virtual Power Plants 2 and 3 is at its peak during this time and thus transmits power to Virtual Power Plant 1. In the 9:00–17:00 period, Virtual Power Plant 1 has a power shortage due to a surge in electrical load during the daytime, while the photovoltaic power generation of Virtual Power Plants 2 and 3 is at its peak and will therefore be transmitted to Virtual Power Plant 1.

The interactive operation of virtual power plants with different attributes can significantly improve the utilization rate of renewable energy, reduce the phenomenon of abandoned wind and light, and realize low-carbon operation. At the same time, it reduces the dependence on the superior power grid, effectively reduces the operating pressure of the entire power grid system, and improves the reliability of system operation. In addition to the trading of electricity, it can also reduce the transportation cost of electricity and the cost of electricity, enhance the income from the sale of electricity, and improve the economy of the entire virtual power plant alliance.

6.2.2. Algorithm Convergence Analysis

In this paper, the ADMM algorithm is used to iteratively solve the optimal scheduling scheme in the case of multiple virtual power plant interactions, and the convergence of the system cost of each virtual power plant is shown in Figure 11, Figure 12, Figure 13 and Figure 14. The system cost converges at the end of 53 iterations, with a convergence accuracy of 10⁻³.

As shown in Figure 11, the coalition cost minimization solution for Virtual Power Plant 1 significantly increases in the first 20 iterations. In comparison, after 20 iterations, it is iterated around 5878.32 yuan and finally converges at 5878.32. As seen in Figure 12, the coalition cost minimization solution for Virtual Power Plant 2 significantly increases in the first 20 iterations and reaches the minimizer at the third time; then, the cost starts to increase. The cost starts to increase due to the high cost of the remaining virtual power plants for the third time, and the total coalition cost is still at a high position. As can be seen from Figure 13, the coalition cost minimization solution for Virtual Power Plant 2 decreases in the first 20 iterations and finally converges to 2973.92 yuan.

It is shown that the distributed optimization algorithms all have good convergence performance and computational efficiency, considering each subject’s privacy protection and the need for optimal scheduling before the day.

6.2.3. Benefits and Costs Analysis

The P2P electricity trading price after asymmetric bargaining among the virtual power plants is shown in Figure 15, where the virtual power plants negotiate the P2P trading price among themselves based on the proposed asymmetric bargaining method. The trading price for each period is in the range of the selling and purchasing price of electricity with the upstream grid. As a result, P2P power trading can sell power at a price higher than the grid’s purchase price and buy new energy power at a price lower than the grid’s sale price, thus effectively increasing the revenue of each virtual power plant.

Table 2. Operating costs of virtual power plants before and after participation in the cooperative operation.

Virtual Power Plant Number	P2P Pre-Running Costs/yuan	P2P Post-Operational Costs/yuan	P2P Transaction Costs/yuan	Bargaining Final Costs/yuan	Revenue Enhancement/yuan
VPP1	10,053.21	5878.32	1332.21	7210.53	2842.68
VPP2	16,123.12	15,500.73	445.11	15,945.84	177.28
VPP3	1365.48	2973.92	−1777.32	1196.6	168.88
VPP Union	27,541.81	24,352.98	0	24,352.97	3188.84

gives the operating costs of each virtual power plant before and after participation in the cooperative operation. The virtual power plant alliance’s overall benefit was an improvement of CNY 3188.84 and a reduction in operating costs of approximately 11.58%. Using the asymmetric bargaining method proposed in this paper to allocate benefits asymmetrically according to the size of the energy contributed by each virtual power plant in the process of power-sharing, the operating cost of Virtual Power Plant 1 is reduced from CNY 10,053.21 to CNY 7210.53, that of Virtual Power Plant 2 is reduced from CNY 16,123.12 to CNY 15,945.84, and that of Virtual Power Plant 3 is reduced from CNY 1365.48 to CNY 1196.6. The revenues of Virtual Power Plants 1, 2, and 3 increased by CNY 2842.68, CNY 177.28, and CNY 168.88, with revenue enhancement ratios of 28.27%, 1.09%, and 12.37%, respectively. This indicates that through P2P power sharing, the interests of all participating subjects are effectively enhanced, and each subject can obtain a fair amount of benefit distribution according to the size of its power contribution.

7. Conclusions

In order to improve the rate of renewable energy consumption, reduce carbon emissions, and better achieve the “dual-carbon” goal, this paper proposes an optimal scheduling strategy for the interactive operation of photovoltaic multi-virtual power plants, which is combined with the analysis of examples to obtain the following conclusions:

(1)

The model of the microgrid and its infrastructure equipment is established, the operation strategy of virtual power plants with different load characteristics for power interaction and cooperation is proposed, and the interaction operation model is constructed so as to realize the efficient use of renewable energy and improve the utilization rate.

(2)

In the P2P optimal operation model of photovoltaic virtual power plants based on asymmetric Nash negotiation constructed in this paper, each virtual power plant can sell electricity to the rest of the virtual power plants at a price higher than the renewable feed-in tariffs, which improves their revenue.

(3)

The constructed asymmetric bargaining-based revenue-sharing model between virtual power plants can significantly increase the revenue of each virtual power plant in the process of power sharing and promote the enthusiasm of the park to participate in energy cooperation.

In the future, further research can be conducted on the gaming of electricity and heat to explore more accurate and fairer methods of distributing benefits. Carbon capture devices in virtual power plants can also be studied to minimize carbon emissions.