A Cooperative Operation Strategy for Multi-Energy Systems Based on the Power Dispatch Meta-Universe Platform

Abstract

To meet the challenges of renewable energy consumption and improve the efficiency of energy systems, we propose an intelligent distributed energy dispatch strategy for multi-energy systems based on Nash bargaining by utilizing the power dispatch meta-universe platform. First, the operational framework of the multi-energy system, including wind park (WP), photovoltaic power plant (PVPP), and energy storage (ES), is described. Using the power dispatch meta-universe platform, the models of WP, PVPP, and ES are constructed and analyzed. Then, a Nash bargaining model of the multi-energy system is built and transformed into a coalition profit maximization problem, which is solved using the alternating direction multiplier method (ADMM). Finally, the effectiveness of the proposed strategy is verified. The results show that the strategy greatly improves the consumption of renewable energy sources and the profit of the overall system.

1. Introduction

With the proposal of the “dual carbon” target, the traditional power supply system is gradually shifting towards a new type of power supply system with an increasing proportion of renewable energy [1]. Renewable energy capacity additions have risen rapidly in recent years [2]. However, renewable energy such as wind and photovoltaic (PV) power have shortcomings including randomness, intermittency, and volatility, resulting in low power quality. The large-scale grid integration of renewable energy can lead to voltage instability, further complicating grid control and dispatch operations. Thus, it has posed a huge challenge to the stable operation of the power system [3].

How to deal with uncertainty and increase penetration of renewable energy has become a research priority [4]. Reference [5] develops a stochastic optimization model for renewable energy sources to deal with the uncertainty of renewable energy sources. Reference [6] proposes a robust optimization model for microgrids, considering the uncertainty of renewable distributed energy sources (PV, wind, etc.), which improves the economics and robustness of microgrid operation. Reference [7] illustrates the ability of demand response to balance the volatility of renewable energy generation, thereby promoting higher penetration of renewable energy in the power system. However, stochastic optimization methods usually require accurate knowledge of the probability distribution of uncertainty, which may lead to unstable or imprecise optimization results if the probability distribution is inaccurate or difficult to obtain. Robust optimization tends to be more conservative, leading to situations where the system fails to maximize its potential profit or efficiency. Demand response may affect users’ living and working habits, reducing their comfort and convenience. Energy storage (ES) can cope with the uncertainty of renewable energy by using a medium to store electrical energy and releasing it for power generation when there is a demand for its utilization [8], which is one of the most important ways to increase the penetration of renewable energy sources [9]. Reference [10] overviews various energy storage technologies for handling fluctuations and uncertainties. Reference [11] puts forward the idea that the integration of ES emerges as a viable solution for supporting renewable energy sources integration. Reference [12] investigates the value of seasonal energy storage technologies for wind and PV power integration.

Although the above literature suggests that ES can cope with uncertainty and increase the penetration of renewable energy, it does not fully exploit the potential for synergistic operation of renewable energy and ES. Multi-energy systems can integrate a variety of energy resources and improve the diversity and stability of the energy supply [13]. It can optimize the efficiency of energy use by coordinating the complementarity and integration of different energy systems. Research on multi-energy systems is of great significance in addressing energy challenges and is one of the important strategic directions for promoting sustainable development in the energy sector [14]. Based on above, establishing a multi-energy system with renewable energy and ES can be an effective way to explore the potential for synergistic operation of renewable energy and ES. However, the traditional dispatching command space cannot break through the geospatial limitations. Relying on the traditional methods of communication, modelling, simulation, and analysis makes it difficult to adapt to the needs of power grid operation [15]. Thus, the strategy to balance the dispatch of multi-energy systems and improve overall operational profit is an urgent issue to be researched.

Regarding the dispatch strategy, meta-universe, as a new process of the digital revolution, is a highly interactive and ultra-temporal digital ecosystem that integrates multiple new technologies [16]. Through holographic construction, holographic simulation, and fusion of virtual world and real world, meta-universe technology is able to realize the complete mapping and real-time interactions of a physical power grid in virtual space. It can respond to the challenges of operational complexity and security risks brought by the construction of renewable power systems in an all-round way. The power dispatch meta-universe makes use of big data, modern communication, artificial intelligence, internet of things, and other technologies to mobilize widely distributed source network, load, and storage resources and realize overall coordinated control of the system. It is capable of solving the problem of grid stability control after the access of renewable energy sources with large random fluctuations and a high proportion of power electronic components. By constructing digital doppelgangers and avatars in the digital dispatch command space, it is able to break through the limitations of geographic space, strengthen the degree of synergy between all levels of dispatch, and greatly enhance the synergy of fault disposal and other aspects. Therefore, the distributed cooperative dispatch of energy sources in the system based on the power dispatch meta-universe platform can help to solve the problems faced by power dispatch in power systems with a high proportion of renewable energy sources.

Regarding improvement of overall operational profit, in recent years, many scholars have carried out research on game strategies for energy systems. In game theory, non-cooperative and cooperative games are effective methods for dealing with complex interest relationships among participants. Non-cooperative games emphasize autonomous decision-making among individuals, namely individual rationality. They mainly focus on the competitive relationships among different participants and cannot achieve social optimality. Reference [17] considers the user satisfaction based on the traditional game models and establishes a Stackelberg leader–follower game model with energy stations as the decision-maker and the user as responders. The model is solved using the distributed algorithm of the beetle antenna. Reference [18] constructs a multi-leader multi-follower Stackelberg game model and studies the interaction problem between multiple distributed energy stations and multiple energy users. Reference [19] establishes a real-time supply–demand interaction model for power systems based on the Stackelberg game. Reference [20] establishes a multi-agent game decision-making model based on evolutionary games, achieving collaborative optimization of multi-agent operations. However, the above research focuses on the competitive relationships among different participants, but the potential for cooperation among participants is insufficiently considered [21], which often leads to nonsocial optimality.

Cooperative games can balance the unity of individual rationality and overall rationality, and they typically achieve global or Pareto optimality. Participants can achieve better results by working together than by acting alone, as they can coordinate their actions with each other to optimize the results. Stable solutions can be reached through negotiation or agreement, which can be reliable long-term strategies because participants tend to stick to the agreements they reach. Commonly used methods of cooperative games for handling interest relationships include Shapley value [22], Nucleolus [23], and Nash bargaining theory [24]. The Shapley value and Nucleolus method have higher computational costs in situations with many participants, while the computational efficiency of Nash bargaining does not significantly change with the number of participants. To explore the potential for cooperation among participants with computational costs considered, this article considers using Nash bargaining, which has been widely used in the field of energy systems. Reference [25] proposes Nash bargaining-based collaborative energy management for regional integrated energy systems. Reference [26] constructs a Nash bargaining model for energy sharing between micro-energy grids and energy storage. Reference [27] proposes a general Nash bargaining-based framework to depict energy trading among autonomous prosumers. Reference [28] proposes a peer-to-peer energy trading model combining shared energy storage based on asymmetric Nash bargaining theory. Reference [29] proposes a distributed cooperative operation strategy for multi-agent energy systems based on Nash bargaining. Reference [30] proposes a cooperative operative model for the wind–solar–hydrogen multi-agent energy system based on Nash bargaining theory. Reference [31] uses Nash bargaining to construct a low-carbon cooperative game model for a multi-electricity–gas interconnection system. Reference [32] uses the Nash bargaining model to simulate the game behavior of various entities. Reference [33] also uses the Nash bargaining method to describe the economic interactions between community energy managers and PV consumers in order to improve individual and social benefits. The above literature indicates that Nash bargaining can effectively solve the profit improvement problem of multi-energy systems, and this method can protect the privacy of participants by applying the alternating direction multiplier method (ADMM) [34].

Based on the above analysis, this paper proposes a Nash bargaining-based intelligent distributed energy dispatch strategy for multi-energy systems using the power dispatch meta-universe platform. The main contributions are as follows:

(1)

Based on the power meta-universe platform, wind park (WP), PV power plant (PVPP), and ES models are constructed, and an operation model for multi-energy systems is established, where ES can effectively suppress the randomness and volatility of wind and PV power generation so that the consumption of wind and PV power can be promoted.

(2)

An innovative incentive energy dispatch strategy based on Nash bargaining is proposed for the multi-energy system with WP, PVPP, and ES. The mechanism can motivate WP, PVPP, and ES to cooperate for improving the alliance profit.

(3)

A distributed algorithm based on ADMM is designed to solve the problem of maximizing alliance profit, while the privacy of WP, PVPP, and ES is effectively preserved.

The remainder of this paper is organized as follows: Section 2 gives the problem description of the cooperative operation model of the multi-energy system based on the power dispatch meta-universe platform. Section 3 gives the mathematic formulation, including the models of WP, PVPP, and ES. Section 4 gives the Nash bargaining model and the distributed solving method based on ADMM. Section 5 performs case studies. Finally, Section 6 draws the conclusions.

2. Problem Description

A power dispatch meta-universe platform is built to address the new demands of power dispatch operations under the power system with a high proportion renewable energy, enhancing system reliability and stability. It has a virtual simulation function that can simulate different dispatching scenarios. Therefore, we built a typical multi-energy system with WP, PVPP, and ES based on this platform in order to achieve efficient energy dispatching, as shown in Figure 1. In the meta-universe platform, the WP, PVPP, and ES are all connected to the power grid and belong to different stakeholders. To promote the consumption of renewable energy, direct transactions of energy are allowed between the distributed generations and power consumers through the grid, while the grid will charge the network fee to recover the maintenance fee of the grid infrastructure [30].

In the cooperative operation model, WP, PVPP, and ES are considered as an alliance. ES can purchase power from WP and PVPP directly through negotiation, and WP and PVPP pay the network fees to the power grid. Through the power dispatch meta-universe platform, we can simulate the operation of WP, PVPP, and ES, which is conducive to enhancing the alliance profit.

3. Mathematic Formulation

3.1. Model of WP

WP generates profits $U_{\mathrm{W}\mathrm{P}}$ through transactions with ES and the power grid:

$$U_{\mathrm{W}\mathrm{P}}=U_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}+U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}$$

(1)

$$U_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}={\displaystyle \sum _{t=1}^T{p}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t}{P}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$$

(2)

$$U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}={\displaystyle \sum _{t=1}^T{p}_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}^t}{P}_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}^t$$

(3)

where $U_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}$ and $U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}$ are the profits made from the transaction with ES and the power grid, respectively; $p_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$ is the trading price with ES at time t; $p_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}^t$ is the wind power feed-in tariff at time t; and $P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$ and $P_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}^t$ are the electricity sold to ES and the power grid, respectively [30].

The costs associated with WP $C_{\mathrm{W}\mathrm{P}}$ include the maintenance fee, $C_{\mathrm{WPM}}$ and the network fee, $C_{\mathrm{WPN}}$:

$$C_{\mathrm{W}\mathrm{P}}=C_{\mathrm{WPM}}+C_{\mathrm{WPN}}$$

(4)

$$C_{\mathrm{WPM}}={\displaystyle \sum _{t=1}^T{\omega }_{\mathrm{W}\mathrm{P}}{P}_{\mathrm{W}\mathrm{P}}^t}$$

(5)

$$C_{\mathrm{WPN}}={\displaystyle \sum _{t=1}^T[{\alpha }_{\mathrm{W}\mathrm{P}}{(P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t)}^2+{\beta }_{\mathrm{W}\mathrm{P}}{P}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t]}$$

(6)

where ${\omega }_{\mathrm{W}\mathrm{P}}$ is the coefficient of the WP maintenance fee; $P_{\mathrm{W}\mathrm{P}}^t$ is the electricity produced by WP at time t; and ${\alpha }_{\mathrm{W}\mathrm{P}}$ and ${\beta }_{\mathrm{W}\mathrm{P}}$ are the network fee coefficients of WP.

The electricity produced by WP should satisfy the power balance constraint and should be less than the maximum electricity generation of WP, as follows:

$$P_{\mathrm{W}\mathrm{P}}^t=P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t+P_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}^t$$

(7)

$$0\le P_{\mathrm{W}\mathrm{P}}^t\le P_{\mathrm{W}\mathrm{P}}^{\max }$$

(8)

where $P_{\mathrm{W}\mathrm{P}}^{\max }$ is the maximum electricity generation of WP.

The objective function for WP, aimed at profit maximization, can be formulated as follows:

$$\max U_{\mathrm{W}\mathrm{P}}-C_{\mathrm{W}\mathrm{P}}$$

(9)

3.2. Model of PVPP

PVPP generates profits $U_{\mathrm{P}\mathrm{V}}$ through transactions with ES and the power grid:

$$U_{\mathrm{P}\mathrm{V}}=U_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}+U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}$$

(10)

$$U_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}={\displaystyle \sum _{t=1}^T{p}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t}{P}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$$

(11)

$$U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}={\displaystyle \sum _{t=1}^T{p}_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}^t}{P}_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}^t$$

(12)

where $U_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}$ and $U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}$ are the profits made from the transaction with ES and the power grid, respectively; $p_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$ is the trading price with ES at time t; $p_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}^t$ is the PV power feed-in tariff at time t; and $P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$ and $P_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}^t$ are the electricity sold to ES and the power grid, respectively [30].

The costs associated with PVPP $C_{\mathrm{P}\mathrm{V}}$ include the maintenance fee, $C_{\mathrm{PVM}}$ and the network fee, $C_{\mathrm{PVN}}$:

$$C_{\mathrm{P}\mathrm{V}}=C_{\mathrm{PVM}}+C_{\mathrm{PVN}}$$

(13)

$$C_{\mathrm{PVM}}={\displaystyle \sum _{t=1}^T{\omega }_{\mathrm{P}\mathrm{V}}{P}_{\mathrm{P}\mathrm{V}}^t}$$

(14)

$$C_{\mathrm{PVN}}={\displaystyle \sum _{t=1}^T[{\alpha }_{\mathrm{P}\mathrm{V}}{(P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t)}^2+{\beta }_{\mathrm{P}\mathrm{V}}{P}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t]}$$

(15)

where ${\omega }_{\mathrm{P}\mathrm{V}}$ is the coefficient of the PVPP maintenance fee; $P_{\mathrm{P}\mathrm{V}}^t$ is the electricity produced by PVPP at time t; and ${\alpha }_{\mathrm{P}\mathrm{V}}$ and ${\beta }_{\mathrm{P}\mathrm{V}}$ are the network fee coefficients of PVPP.

The electricity produced by PVPP should satisfy the power balance constraint and should be less than the maximum electricity generation of PVPP, as follows:

$$P_{\mathrm{P}\mathrm{V}}^t=P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t+P_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}^t$$

(16)

$$0\le P_{\mathrm{P}\mathrm{V}}^t\le P_{\mathrm{P}\mathrm{V}}^{\max }$$

(17)

where $P_{\mathrm{P}\mathrm{V}}^{\max }$ is the maximum electricity generation of PVPP.

The objective function for PVPP, aimed at profit maximization, can be formulated as follows:

$$\max U_{\mathrm{P}\mathrm{V}}-C_{\mathrm{P}\mathrm{V}}$$

(18)

3.3. Model of ES

The constraints that ES must adhere to include the state of the charge constraints, the charge/discharge power constraints, and the ES multiplying factor constraints.

(1) State of charge constraints

$$E_{\mathrm{E}\mathrm{S}}^t=(1-\tau )E_{\mathrm{E}\mathrm{S}}^{t-1}+[{\eta }_{\mathrm{a}\mathrm{b}\mathrm{s}}{P}_{\mathrm{E}\mathrm{S},\mathrm{a}\mathrm{b}\mathrm{s}}^t-{\displaystyle \frac{1}{{\eta }_{\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{a}}}}{P}_{\mathrm{E}\mathrm{S},\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{a}}^t]\mathsf{\Delta }t$$

(19)

$$P_{\mathrm{E}\mathrm{S},\mathrm{a}\mathrm{b}\mathrm{s}}^t=\mathrm{m}\mathrm{a}\mathrm{x}\{0,-P_{\mathrm{E}\mathrm{S}}^t\}$$

(20)

$$P_{\mathrm{E}\mathrm{S},\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{a}}^t=\mathrm{m}\mathrm{ax}\{0,P_{\mathrm{E}\mathrm{S}}^t\}$$

(21)

$$10\%E_{\mathrm{E}\mathrm{S},\mathrm{m}\mathrm{a}\mathrm{x}}\le E_{\mathrm{E}\mathrm{S}}^t\le 90\%E_{\mathrm{E}\mathrm{S},\mathrm{m}\mathrm{a}\mathrm{x}}$$

(22)

$$E_{\mathrm{E}\mathrm{S}}^0=20\%E_{\mathrm{E}\mathrm{S},\mathrm{m}\mathrm{a}\mathrm{x}}$$

(23)

$$E_{\mathrm{E}\mathrm{S}}^0=E_{\mathrm{E}\mathrm{S}}^T$$

(24)

Here, $\tau$ denotes the self-discharge efficiency of ES; $E_{\mathrm{E}\mathrm{S}}^t$ and $E_{\mathrm{E}\mathrm{S}}^{t-1}$ denote the energy storage level of ES at time t and time t − 1; ${\eta }_{\mathrm{a}\mathrm{b}\mathrm{s}}$ and ${\eta }_{\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{a}}$ denote the charging and discharging efficiencies of ES; $P_{\mathrm{E}\mathrm{S},\mathrm{a}\mathrm{b}\mathrm{s}}^t$ denotes the charging power of ES at time t; $P_{\mathrm{E}\mathrm{S},\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{a}}^t$ denotes the discharging power of ES at time t; $P_{\mathrm{E}\mathrm{S}}^t$ denotes the charging and discharging power of ES at time t; and $E_{\mathrm{E}\mathrm{S}}^0$ and $E_{\mathrm{E}\mathrm{S}}^T$ denote the energy levels at the beginning and end of the ES operational period.

(2)

Charge/discharge power constraint

$$-P_{\mathrm{E}\mathrm{S},\max }\le P_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}^t\le P_{\mathrm{E}\mathrm{S},\max }$$

(25)

(3)

ES multiplying factor constraints

The maximum capacity and maximum charge/discharge power of the ES are directly proportional. The specific are as follows:

$$E_{\mathrm{E}\mathrm{S},\mathrm{m}\mathrm{a}\mathrm{x}}=\beta P_{\mathrm{E}\mathrm{S},\mathrm{m}\mathrm{a}\mathrm{x}}$$

(26)

where β denotes the ES energy multiplication factor.

The costs associated with ES include the electricity cost and maintenance fee $C_{\mathrm{ESM}}$:

$$C_{\mathrm{E}\mathrm{S}}=U_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}+U_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}+U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}+C_{\mathrm{ESM}}$$

(27)

$$U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}={\displaystyle \sum _{t=1}^T{p}_{\mathrm{P}\mathrm{G}}^t}{P}_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}^t$$

(28)

$$C_{\mathrm{ESM}}={\displaystyle \sum _{t=1}^T({\omega }_{\mathrm{E}\mathrm{S}}{P}_{\mathrm{E}\mathrm{S}}^t+{\omega }_{\mathrm{LOAD}}{P}_{\mathrm{LOAD}}^t)}$$

(29)

where $U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}$ is the cost paid to the power grid; $p_{\mathrm{P}\mathrm{G}}^t$ is the day-ahead market price at time t; $P_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}^t$ is the electricity purchased from the power grid at time t; ${\omega }_{\mathrm{E}\mathrm{S}}$ and ${\omega }_{\mathrm{LOAD}}$ are the coefficients of the maintenance fee of the device and loads; and $P_{\mathrm{LOAD}}^t$ is the electricity demand of the load.

The operation of ES should satisfy the power balance constraint:

$$P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t+P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t+P_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}^t+P_{\mathrm{E}\mathrm{S}}^t=P_{\mathrm{LOAD}}^t$$

(30)

The objective function for ES, aimed at profit maximization, can be formulated as follows:

$$\max -C_{\mathrm{E}\mathrm{S}}$$

(31)

4. Nash Bargaining Theory

Nash bargaining theory is a fundamental concept in cooperative game theory that solves negotiation problems by determining the optimal and fair allocation of resources among multiple participants [35]. The theory is based on feasible sets, divergence points, and Nash bargaining solutions that aim to maximize the product of the participants’ utilities relative to their respective divergence points. Despite its advantages, the Nash bargaining theory has its limitations. For example, in practice, the theory must take into account the effects and interactions of multiple factors [36]. In the context of energy dispatch, especially in multi-energy systems involving WP, PVPP, and ES, Nash bargaining theory offers significant advantages by optimizing cooperative operations, protecting privacy, and enhancing decision-making capabilities. Combining Nash bargaining with the power dispatch meta-universe platform can enhance the decision-making capabilities of power grids using advanced simulation and optimization techniques, enabling better management of renewable energy sources and ES, optimizing system performance, and ensuring privacy.

4.1. Nash Bargaining Model

In the multi-energy system constructed on the power dispatch meta-universe platform, WP, PVPP, and ES act as rational participants aiming to maximize their profits. They are incentivized to engage in cooperation if it leads to increased profits or reduced costs. As self-interested rational participants, WP, PVPP, and ES prioritize determining an optimal energy dispatch strategy to achieve a Pareto optimal solution, thereby maintaining their cooperative relationship. The Nash bargaining theory, an important component of cooperative game theory, proves effective in achieving such a solution. The standard Nash bargaining model is formulated as follows [30]:

$$\left\{\begin{array}{l}\max {\displaystyle \prod _{n=1}^N(U_n-U_n^0)}\hfill \\ \mathrm{s}.\mathrm{t}. U_n\ge U_n^0 \hfill \end{array}\right..$$

(32)

where N is the number of participants; n is the index of participants; and $U_n$ is the utility of the participant n.

Based on the above, the Nash bargaining model of the multi-energy system with WP, PVPP, and ES can be written as follows:

$$\left\{\begin{array}{l}\max (U_{\mathrm{W}\mathrm{P}}-C_{\mathrm{W}\mathrm{P}}-U_{\mathrm{W}\mathrm{P}}^0)(U_{\mathrm{P}\mathrm{V}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{V}}^0)(-C_{\mathrm{E}\mathrm{S}}-U_{\mathrm{E}\mathrm{S}}^0)\hfill \\ \begin{array}{ll}\mathrm{s}.\mathrm{t}.& U_{\mathrm{W}\mathrm{P}}-C_{\mathrm{W}\mathrm{P}}\ge U_{\mathrm{W}\mathrm{P}}^0\hfill \\ & U_{\mathrm{P}\mathrm{V}}-C_{\mathrm{P}\mathrm{V}}\ge U_{\mathrm{P}\mathrm{V}}^0\hfill \\ & -C_{\mathrm{E}\mathrm{S}}\ge U_{\mathrm{E}\mathrm{S}}^0\hfill \end{array}\hfill \end{array}\right.$$

(33)

where $U_{\mathrm{W}\mathrm{P}}^0$, $U_{\mathrm{P}\mathrm{V}}^0$, and $U_{\mathrm{E}\mathrm{S}}^0$ are the rupture points of WP, PVPP, and ES.

4.2. Transformation of the Nash Bargaining Model

According to the basic inequality, the objective function of the Nash bargaining model (33) should satisfy the following:

$$\begin{array}{l} (U_{\mathrm{W}\mathrm{P}}-C_{\mathrm{W}\mathrm{P}}-U_{\mathrm{W}\mathrm{P}}^0)(U_{\mathrm{P}\mathrm{V}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{V}}^0)(-C_{\mathrm{E}\mathrm{S}}-U_{\mathrm{E}\mathrm{S}}^0)\\ \le {({\displaystyle \frac{U_{\mathrm{W}\mathrm{P}}-C_{\mathrm{W}\mathrm{P}}+U_{\mathrm{P}\mathrm{V}}-C_{\mathrm{P}\mathrm{V}}-C_{\mathrm{E}\mathrm{S}}-U_{\mathrm{W}\mathrm{P}}^0-U_{\mathrm{P}\mathrm{V}}^0-U_{\mathrm{E}\mathrm{S}}^0}{3}})}^3\\ ={({\displaystyle \frac{U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}-C_{\mathrm{W}\mathrm{P}}+U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}-C_{\mathrm{ESM}}-U_{\mathrm{W}\mathrm{P}}^0-U_{\mathrm{P}\mathrm{V}}^0-U_{\mathrm{E}\mathrm{S}}^0}{3}})}^3\end{array}$$

(34)

The equality holds if and only if

$$(U_{\mathrm{W}\mathrm{P}}-C_{\mathrm{W}\mathrm{P}}-U_{\mathrm{W}\mathrm{P}}^0)=(U_{\mathrm{P}\mathrm{V}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{V}}^0)=(-C_{\mathrm{E}\mathrm{S}}-U_{\mathrm{E}\mathrm{S}}^0)$$

(35)

Therefore, finding the solution of (33) is equivalent to find the solution of the following:

$$\max U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}-C_{\mathrm{W}\mathrm{P}}+U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}-C_{\mathrm{ESM}}-U_{\mathrm{W}\mathrm{P}}^0-U_{\mathrm{P}\mathrm{V}}^0-U_{\mathrm{E}\mathrm{S}}^0$$

(36)

Since $U_{\mathrm{W}\mathrm{P}}^0$, $U_{\mathrm{P}\mathrm{V}}^0$, and $U_{\mathrm{E}\mathrm{S}}^0$ are constants, the solution of (36) is equivalent to the solution of the problem of maximizing alliance profit:

$$\max U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}-C_{\mathrm{W}\mathrm{P}}+U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}-C_{\mathrm{ESM}}$$

(37)

By solving (37), the electricity that ES purchases from WP, PVPP, and the power grid can be obtained; i.e., the energy dispatch strategy can be obtained.

4.3. Distributed Solving Method Based on ADMM

Preserving the privacy of WP, PVPP, and the power grid in the multi-energy system is an important issue. The ADMM algorithm allows WP, PVPP, and ES to process data in a distributed manner without the need to centralize all the data to a single center for processing. On the one hand, the risk of data leakage that may be caused by centralized processing can be avoided. On the other hand, each participant can keep its private data and solve the problem locally with only intermediate data exchanged. Through that, the privacy of the participants can be preserved. Thus, ADMM is applied to solve (37).

New variables, ${\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$ and ${\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$, are introduced to denote the expected electricity purchased by ES from WP and PVPP, and $P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$ and $P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$ denote the expected electricity sold by WP and PVPP to ES [30]. When ${\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t=P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$ and ${\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t=P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$, WP and PVPP reach an agreement with ES on trading electricity.

The maximization problem is transferred to a minimization problem, and the augmented Lagrange function of (37) is formulated as follows:

$$\begin{array}{l}\min -(U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}-C_{\mathrm{W}\mathrm{P}}+U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}-C_{\mathrm{P}\mathrm{V}}-U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}-C_{\mathrm{ESM}})+ {\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t}({\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t)\\ +{\displaystyle \frac{{\rho }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}}{2}}{‖{\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t‖}_2^2+{\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t}({\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t)+{\displaystyle \frac{{\rho }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}}{2}}{‖{\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t‖}_2^2\end{array}$$

(38)

where ${\lambda }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t$ and ${\lambda }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t$ are Lagrange multipliers, and ${\rho }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}$ and ${\rho }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}$ are penalty factors.

Based on ADMM, the objective functions of WP, PVPP, and ES can be obtained by decomposing (38).

(1)

WP

$$\begin{array}{l}\min -(U_{\mathrm{W}\mathrm{P}2\mathrm{P}\mathrm{G}}-C_{\mathrm{W}\mathrm{P}})+ {\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t}({\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t)+{\displaystyle \frac{{\rho }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}}{2}}{‖{\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t‖}_2^2\\ \mathrm{s}.\mathrm{t}. \left(1\right)\text{–}\left(8\right)\end{array}$$

(39)

(2)

PVPP

$$\begin{array}{l}\min -(U_{\mathrm{P}\mathrm{V}2\mathrm{P}\mathrm{G}}-C_{\mathrm{P}\mathrm{V}})+{\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t}({\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t)+{\displaystyle \frac{{\rho }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}}{2}}{‖{\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t‖}_2^2\\ \mathrm{s}.\mathrm{t}. \left(10\right)\text{–}\left(17\right)\end{array}$$

(40)

(3)

ES

$$\begin{array}{l}\min (U_{\mathrm{P}\mathrm{G}2\mathrm{E}\mathrm{S}}+C_{\mathrm{ESM}})+ {\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t}({\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t) +{\displaystyle \frac{{\rho }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}}{2}}{‖{\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t‖}_2^2\\ +{\displaystyle \sum _{t=1}^T{\lambda }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t}({\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t)+{\displaystyle \frac{{\rho }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}}{2}}{‖{\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t‖}_2^2\\ \mathrm{s}.\mathrm{t}. \left(19\right)\text{–}\left(30\right)\end{array}$$

(41)

The steps to solve the Nash bargaining model are as follows:

(1) Initialization.

(2) ES: Based on $P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k+1)$ and $P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k+1)$, solve (41) to get ${\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k)$ and ${\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k)$.

(3) WP and PVPP: Based on ${\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k+1)$ and ${\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k+1)$, solve (39) and (40) to get $P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k+1)$ and $P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k+1)$.

(4) Update

$${\lambda }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k+1)={\lambda }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k)+{\rho }_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}\left({\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k+1)-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k+1)\right)$$

(42)

$${\lambda }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k+1)={\lambda }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k)+{\rho }_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}\left({\dot{P}}_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k+1)-P_{\mathrm{P}\mathrm{V}2\mathrm{E}\mathrm{S}}^t(k+1)\right)$$

(43)

(5) If

$$\max ({\displaystyle \sum _{t=1}^T{‖{\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k)-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k)‖}_2^2},{\displaystyle \sum _{t=1}^T{‖{\dot{P}}_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k)-P_{\mathrm{W}\mathrm{P}2\mathrm{E}\mathrm{S}}^t(k)‖}_2^2})<\delta \mathrm{or} k>k_{\max }$$

(44)

is satisfied, then (6). If not, $k=k+1$, then go back to (2).

(6) Stop

Through the above steps, the energy dispatch strategy can be obtained with privacy preserved.

5. Case Studies

5.1. Case Setting

In this section, the proposed energy dispatch strategy is verified. The objective functions are solved by GUROBI in MATLAB 2023a.

Table 1. Parameters of WP and PVPP [30].

Parameters	Values	Parameters	Values
ωWP	0.008	ωPV	0.0085
αWP	3 × 10−5	αPV	0.008
βWP	0.01	βPV	0.01
pWP2PG	0.34 (CNY/kWh)	pPV2PG	0.35 (CNY/kWh)
ωES	1.8 × 10−4	ωLOAD	0.022

shows the relevant parameters of WP, PVPP, and ES.

5.2. Process of Distributed Solution

Figure 2 shows the iterative solution process of the cooperative operation problem of the multi-energy system with WP, PVPP, and ES based on the ADMM method. The iterative process stops at the 54th time, and it takes 72.21 s. It does not only solve the cooperative operation problem of the multi-energy system with WP, PVPP, and ES, but it also effectively preserves the privacy of the participants in a distributed manner.

5.3. Results Analysis

Figure 3 and Figure 4 show the results of the ES’s power purchased from WP, PVPP, and the grid and the results of the ES’s operation in the power dispatch meta-universe platform, respectively. As can be seen from Figure 3, in order to reduce the cost of purchasing electricity, ES chooses to purchase 2303.67 kW from PVPP and 4421.30 kW from WP instead of the grid during the period of higher electricity price (8:00–22:00). While during the period of the lower electricity price (1:00–7:00) and (23:00–24:00), ES will choose to purchase 5317.25 kW of electricity from the grid instead of purchasing electricity from WP and PVPP. This allows the ES equipment to meet its own power demand, and the excess power is stored for later use during peak grid electricity prices, thus saving costs. The results show that ES purchases electricity from the grid during the grid electricity price valley periods, simultaneously meeting its own electricity demand and charging the ES device. The excess electricity is stored for later use during the grid electricity price peak periods, leading to cost savings. During periods of high grid electricity prices (8:00–22:00), ES chooses to purchase electricity from WP and PVPP. This can not only facilitate the consumption of renewable energy, but it also exhibits a notable peak-shaving effect. Additionally, ES further reduces the electricity cost paid the power grid by 4556.99 CNY. Additionally, the grid can yield an additional profit of 120.26 CNY by charging the network fees.

Figure 5 shows the sale of electricity from WP and PVPP to the power grid. On the one hand, WP and PVPP can sell the affluent power to the grid to promote the consumption of new energy and increase the profits of WP and PVPP; on the other hand, the grid can reduce the pressure of power generation by purchasing power from WP and PVPP on the premise of meeting the demand for electricity. Of this, WP sells 42,426.10 kW to the grid and PVPP sells 12,848.93 kW to the grid.

In summary, the proposed energy dispatch strategy based on the power dispatch meta-universe achieves cooperative dispatching among WP, PVPP, and ES, demonstrates effective peak-shaving, facilitates the consumption of renewable energy sources, and contributes to the cost savings of ES.

Table 2. Results of profits.

Cases	Alliance Profits (CNY)
Cooperation	25,873.01
Non-cooperation	14,111.28

shows the overall profits in the case that WP, PVPP, and ES cooperate or not. The profit in the non-cooperation case is 14,111.28 CNY, and the profit in the cooperation case is 25,873.01 CNY. The comparison shows that the profit after the cooperation has increased by 11,761.73 CNY compared to the profit before the cooperation, which is an improvement of about 83.35%. This result verifies the effectiveness of the energy dispatch strategy proposed in this paper. In summary, the overall profit of the multi-energy system in the cooperation case is significantly improved by the energy dispatch strategy proposed in this paper.

6. Conclusions

This paper presents an intelligent distributed energy dispatch strategy for a multi-energy system integrating WP, PVPP, and ES. Modeling WP, PVPP, and ES within the power dispatch meta-universe platform facilitates a comprehensive depiction of their interrelationships and interactions. This framework enables distributed cooperative dispatching of power systems with a significant share of renewable energy, aiming to achieve optimal energy efficiency and economic benefits while ensuring privacy preservation. The main conclusions are as follows:

(1)

The distributed optimization algorithm based on ADMM does not only realize the distributed and efficient solution of the cooperative operation problem of the multi-energy system, but it also effectively protects the privacy of WP, PVPP, and ES.

(2)

The cooperative operation model established on Nash bargaining coordinates the dispatch of the multi-energy system through the power dispatch meta-universe platform, which promotes the consumption of renewable energy and has a certain peak-shaving effect for the grid.

(3)

The validation of the energy dispatch strategy proposed in this paper through Nash bargaining based on the power dispatch meta-universe platform shows that the overall profit of the multi-energy system in the cooperation case is about 83.35% higher than that of the non-cooperation case.

(4)

This method is helpful to realize the deduction of renewable energy dispatch strategies, and it further enhances the power grid intelligent decision-making ability of the power dispatching metaverse integrating multi-source spatiotemporal data.

Although the ADMM method effectively solves the dispatch problem of the multi-energy system with WP, PVPP, and ES in a distributed manner, the time to solve the problem is not satisfactory. Thus, the solving efficiency needs to be improved. In the future, we will improve the ADMM method to enhance the solving efficiency.