With increased severity in energy and environmental issues, decarbonization has emerged as an unavoidable trend in the future energy industry (Li et al., 2023). A virtual power plant (VPP) is a system that uses information technology to aggregate and coordinate resources such as distributed generators, energy storage, and interruptible load to enhance the stability and security of the power grid. The global energy system is accelerating its transition to renewable energy (Zhong et al., 2023a; Sarantakos et al., 2023; Wang et al., 2023). As a crucial energy structure for the future, multi-energy flow systems have the capacity to interconnect different types of energy (electricity, heat, gas, etc.); unify the planning, operation, and dispatch of various energy devices; and achieve efficient energy utilization (Chen et al., 2020; Wang et al., 2020). However, with the large-scale integration of renewable energy, encompassing distributed power sources, energy storage, and dispatchable loads, the volatility of multi-energy flow systems is also on the rise (Zhou et al., 2017; Zhong et al., 2023b). A multi-energy flow VPP, as an integrated energy network that connects electricity–gas–thermal energy sources, can coordinate and dispatch various internal units including renewable energy, gas resources, and thermal resources, which can not only provide more economic benefits but also help achieve the goal of energy-saving and emission reduction. At present, the multi-energy flow VPP faces difficulties such as high actual carbon emissions, complex multi-energy flow optimization variables, and multi-optimization objectives. It is urgent to explore how to improve the renewable energy consumption capacity of the multi-energy-flow VPP while reducing carbon emissions. The interconnection of diverse energy devices within multi-energy flow virtual power plants enables coordinated dispatch of electricity, gas, and heat, facilitating complementary utilization of multiple energy flows (Zhang et al., 2019; Gao et al., 2023; Wu et al., 2023). This not only effectively mitigates the fluctuations in multi-energy flow systems, reduces distribution grid losses, and enhances energy utilization efficiency but also promotes supply–demand balance, bringing about significant economic benefits.

Currently, when various types of energy are interconnected and complementarily integrated within a VPP, the involvement of diverse entities with different interests and complex energy and information exchange relationships among these entities pose a series of challenges in multi-energy flow VPP energy dispatch (Yang et al., 2023). A multi-energy flow VPP faces difficulties such as high actual carbon emissions, complex multi-energy-flow optimization variables, and multi-optimization objectives. It is urgent to explore how to improve the renewable energy consumption capacity of multi-energy flow VPPs. Many scholars have undertaken initial investigations into the challenges of energy dispatch in VPPs, with ant colony algorithms and consensus algorithms finding widespread application in the realm of energy dispatch. Ant colony algorithms are suitable for centralized energy dispatch. These algorithms possess global search capabilities and simulate the process of ants searching for food, thus helping in finding the global optimal solution for complex energy dispatch problems. Consensus algorithms, on the other hand, are applicable to distributed energy dispatch. They use real-time status information from neighboring substations and continually update their status to maintain consistency among all substations, thus ensuring the stable operation of the overall energy system.

However, there are still many challenges facing the energy dispatch process in multi-energy flow VPPs:

The energy interaction among electricity, gas, and heat within the VPP, coupled with the interdependence between the VPP, substations, and distribution grids, makes the energy dispatch of multi-energy flow VPPs an extremely complex problem. Complex energy and information exchange relationships exist among multiple entities (Li et al., 2022; Huang et al., 2023). Due to the conflicts of ownership, optimization objectives, and interests among different entities, the increase in the multi-energy flow coupling degree will inevitably make the mutual influence among various energy subsystems more obvious. Traditional single-layer energy dispatch methods usually only consider the optimization of a single energy source when solving the multi-energy flow dispatch model, ignoring the coordination of multi-energy flow. Moreover, the local fluctuations of the system affect the solution of the whole system, resulting in high dispatch costs and high network losses, which are unsuitable for the complex energy dispatch for multi-energy flow VPPs.

In traditional ant colony algorithms, the concentration of pheromones and the heuristic function typically remain static. As the number of iterations increases, there is a gradual rise in the concentration of pheromones, potentially elevating the risk of converging toward local optima. Simultaneously, the value of the heuristic function decreases, possibly resulting in excessive dependence on pheromones. In the context of energy dispatch for multi-energy-flow VPPs, the adaptability of traditional ant colony algorithms decreases. This results in a slow convergence rate when solving the energy dispatch problem for multi-energy flow VPPs, making it challenging to meet the real-time requirements of such dispatch.

Consensus algorithms achieve consistency for all substation states through the transmission of state information among neighboring substations. However, during the consensus iteration process, there is a delay in the transmission of state information among neighboring substations. This leads to traditional consensus algorithms being unable to promptly and accurately obtain state information from neighboring substations, affecting the convergence speed of the consensus iteration, increasing the fluctuation of multi-energy flow within the VPP, and resulting in high dispatch costs and distribution grid losses in the energy dispatch for multi-energy flow VPPs.

During the consensus iteration process, factors such as channel conditions and geographical locations cause a delay in the transmission of state information between neighboring substations. Traditional consensus algorithms overlook the time delay in the transmission of state information, making it challenging to promptly and accurately acquire the state information of neighboring substations. This, in turn, affects the convergence speed of the consensus iteration, increases the fluctuations in multi-energy flow within the VPP, and results in excessively high dispatch costs and distribution grid losses in the energy dispatch for the multi-energy-flow VPPs.

Presently, extensive research is being conducted on the energy dispatch for VPPs. One approach involves conceptualizing VPPs as coalitions of wind generators and electric vehicles, establishing an operational model based on linear programming. This model, as discussed in Vasirani et al. (2013), demonstrates how scheduling the supply to the grid and storage in electric vehicle batteries can enhance the VPP’s profitability. Another highlighted in Yang et al. (2013), Yang et al. proposed a distributed optimal dispatch method using the distributed primal-dual sub-gradient algorithm. This method involves coordinating the individual decision-making of distributed energy resources within the VPP through limited communication, ultimately maximizing the VPP’s profit. In the context of multiple distributed generators within a VPP, a distributed control strategy is introduced in Xin et al. (2013). This strategy aims to guide the VPP to converge and operate at an optimal output power determined by the costs of distributed generations and the required services assigned by the distribution grid. Mohy-ud din et al. (2020) adopts the linearization method to solve the energy transaction management problem of integrated energy systems based on VPPs. The linearization-based optimization method is well-suited for addressing linear optimization objectives of a relatively straightforward nature. However, it encounters challenges when attempting to tackle complex nonlinear optimization targets, such as those related to distribution power grid loss. There is currently much research on the use of intelligent algorithms in the field of VPP energy dispatch. Abdolrasol et al. (2018); Hannan et al. (2021) applied optimization research to solve the application problems of current technologies, adding value by enhancing them in the direction of optimal solutions. Zhang et al. (2023a) focuses on the interaction between electricity and heat, demonstrating the influence of multiple factors on the safe operation of electricity. Yan et al. (2020) focuses on the efficiency and convergence accuracy of the method in solving the electricity and gas system model. However, the above-mentioned literature has not taken into account the coupling of multi-energy flow within VPPs nor has it considered energy dispatch strategies with multiple layers of interaction.

Various studies have explored the multi-energy flow complementation of VPPs. Cui et al. (2016) integrated electric boilers and heat storage equipment into wind power plants, using thermoelectric conversion for consume wind power consumption. Yuan et al., as highlighted in Guili et al. (2017), achieved “thermoelectric decoupling” through use of electric heating equipment, enabling coordinated dispatch of thermoelectric power in the system. Li et al. (2019) analyzed the operation strategy of a multi-energy flow complementary system with the goal of enhancing the system economy. Additionally, there have been advancements in the application of ant colony algorithms. Niknam et al. proposed a novel approach based on the ant colony algorithm for the distribution management system in the context of dispersed generation (Niknam et al., 2005). Trivedi et al. (2015) used the ant colony optimization technique to address multiple environment dispatch problems in microgrids, solving the generation dispatch problem. Hou et al. introduced a versatile optimization algorithm named the generalized ant colony optimization algorithm to tackle discontinuous, nonconvex, nonlinear constrained optimization problems (Hou et al., 2002). Blockchain technology has also been incorporated into VPP systems, as presented by Wang et al. in Jing et al. (2022), where a VPP system architecture based on blockchain was proposed, accompanied by a blockchain partition consensus algorithm for VPP dispatch. Furthermore, consensus-based algorithms have been introduced. Naina and Swarup (2022) proposed a robust, fully distributed consensus-based algorithm utilizing a monotonic decreasing consensus gain function to mitigate the effects of communication delays and noise, allowing the VPP to optimize electricity output and intake based on grid demand. For addressing trust issues in real-time VPP dispatch, Qi et al. designed a hybrid consensus mechanism combining multiple algorithms and proposed a mixed consensus algorithm based on convex optimization problems in Yu et al. (2022), optimizing computational resources and improving VPP dispatch efficiency. Xu et al. (2019) proposed a two-layer distributed coordinated control method for managing VPPs in an active distribution power grid, with the first layer dispatching the total output power of multiple VPPs and the second layer handling the output power of each intelligent agent within the VPPs. Despite these advancements, challenges persist: 1) one notable issue is real-time adjustment of pheromone concentration and heuristic functions. With the increase in the number of iterations, the adaptability of traditional ant colony algorithms diminishes, leading to slow convergence speeds when addressing the energy dispatch problem of multi-energy-flow VPPs. 2) There is a delay in the transmission of state information among neighboring substations, causing traditional consensus algorithms to be unable to promptly and accurately obtain state information from neighboring substations. This affects the convergence speed of the consensus iteration, increases the fluctuation of multi-energy flow within the VPP, and leads to high dispatch costs and distribution grid losses in the energy dispatch for multi-energy flow VPPs.

In response to the aforementioned issues, we propose a two-layer iterative energy dispatch strategy for a multi-energy flow VPP in the distribution power grid. First, we establish an energy dispatch framework for a multi-energy flow VPP in the distribution power grid. Second, we decompose the energy dispatch optimization problem of a multi-energy flow VPP into an upper-layer multi-energy flow VPP energy dispatch sub-problem and a lower-layer distributed substation energy dispatch sub-problem. The upper-layer optimization is designed to minimize distribution grid loss and compensatory electricity price cost, adhering to the constraints of VPP output and power flow balance. Moreover, the lower-layer optimization focuses on minimizing dispatch costs within the constraints of the natural gas pipeline network, thermal network, and inequality. Finally, we propose a two-layer iterative energy dispatch algorithm that incorporates an improved ant colony algorithm and a delay-aware consensus algorithm. This approach reduces the dispatch costs and distribution grid losses of multi-energy flow VPP energy dispatch, enhancing the real-time performance of the energy dispatch process.

The innovation points are given as follows:

A two-layer iterative energy dispatch strategy for a multi-energy flow VPP: the transmission of substation dispatch power occurs from the upper layer to the lower layer, while the lower layer transmits load dispatch ability information to the upper layer. This process enables the realization of a two-layer optimal dispatch method for the multi-energy flow VPP. This strategy achieves coordinated dispatch of electricity, gas, and heat flows, addressing the challenges posed by complex energy and information exchange relationships and conflicting interests among different entities. The two-layer energy dispatch strategy for multi-energy flow in the distribution power grid couples the electric–gas energy sources through gas turbines at the upper layer and couples the electric–thermal energy sources through electric boilers at the upper layer, achieving the complementarity of multi-energy flow. At the lower layer, the two-layer energy dispatch of multi-energy flow only optimizes the output of electric power energy. It improves the flexibility of the VPP, effectively alleviates the fluctuation of the multi-energy flow system, reduces the loss of the distribution power grid, and achieves the coordination and balance of the multi-energy-flow VPP internally.

Multi-energy flow VPP energy dispatch based on the improved ant colony algorithm: in light of real-time operational cost deviations, this paper adjusts the computation of pheromone concentration and heuristic functions dynamically to consider the evolving conditions. This adjustment enhances the algorithm’s adaptability, improves convergence speed, and ensures the real-time performance of multi-energy flow VPP energy dispatch.

Distributed substation energy dispatch based on the delay-aware consensus algorithm: considering the impact of communication delays on consensus convergence. The introduction of a proportional–derivative (PD) controller enables a rapid response to changes in the state information of each substation. Additionally, a time-dependent feedback term is incorporated into the PD controller to adjust dispatch signal updates, improving convergence speed, suppressing fluctuations in multi-energy-flow within the VPP, and reducing the dispatch costs and distribution grid losses of multi-energy flow VPP energy dispatch.

Figure 1 shows the energy dispatch framework for a multi-energy flow VPP in the distribution power grid, which consists of a cloud layer, an edge layer, and a device layer. The cloud layer is composed of a regional multi-energy-flow dispatch center, a grid dispatch center, and a power trading center. The edge layer is composed of multiple VPPs, where each VPP is responsible for communicating and interacting with various substations within its jurisdiction. It undertakes substation dispatch, monitoring, and other edge analytics functions. The set of VPPs is represented as K = { 1,2 , … , k , … , K } . The device layer consists of multiple substations, and the k-th VPP has N _k substations. Each substation includes a distributed power generator, energy storage, interruptible load, a gas turbine, and an electric heating boiler.

The VPPs are connected to the distribution power grid, and there is a coupling relationship between them. The set of distribution grid nodes is denoted as I = { 1,2 , … , i , … , I } . In the natural gas network, there are natural gas nodes supplied by gas sources, and gas turbines can achieve gas-to-electricity conversion. Therefore, there is a node coupling relationship between the distribution power grid and the natural gas network. The set of nodes in the natural gas network is denoted as Z = { 1,2 , … , z , … , Z } , and the set of gas sources is denoted as O = { 1,2 , … , o , … , O } . The thermal network consists of thermal load nodes and electric heating boilers. Electric heating boilers are responsible for providing heat, which achieve electricity-to-heat conversion to supply the thermal load. Therefore, a node coupling relationship exists between the distribution power grid and the thermal network. The set of thermal load nodes is denoted as M = { 1,2 , … , m , … , M } .

We use a time-slotted model in which the overall optimization period is segmented into T time slots, each with an equal duration of τ. The set of time slots is denoted as T = { 1 , … , t , … , T } . In the cloud layer, the integrated regional energy dispatch center collaborates with the grid dispatch center and the power trading center. It receives the information on real-time power grid status from the grid dispatch center, that on real-time market price from the power trading center, and that of load dispatch capacity from the edge layer. Subsequently, the integrated regional energy dispatch center engages in optimization to minimize compensatory electricity price cost and distribution power grid loss, determining optimal power dispatch values for each VPP. The resulting VPP energy dispatch strategies are then disseminated to the edge layer. In the edge layer, VPPs dispatch power to the substation groups within their jurisdiction. At the device layer, the substations optimize the dispatch cost of their internal resources and dispatch power to their internal resources accordingly. The summary of the main notations in this paper is shown in Table 1.

The two-layer iterative energy dispatch problem for a multi-energy flow VPP in the distribution power grid can be decomposed into two optimization sub-problems: the upper-layer multi-energy flow VPP energy dispatch sub-problem and the lower-layer distributed substation energy dispatch sub-problem.

The principle of the proposed algorithm is illustrated in Figure 2. The two-layer iterative energy dispatch strategy incorporates an improved ant colony algorithm in the upper layer and a delay-aware consensus algorithm in the lower layer. First, a combined pheromone update strategy and improved pheromone factor and heuristic factor were adopted to improve the ant colony algorithm for solving the sub-problem of multi-energy flow VPP energy dispatch. This involves adjusting the dispatch power of each VPP according to diverse service requirements. The calculated dispatch power was distributed to each substation for lower-layer optimization. Second, communication interaction was carried out among the substations, with the micro-increment rate of substation dispatch cost serving as the consensus variable for the consensus iteration. To solve the substation energy dispatch sub-problem, the PD controller was introduced into the traditional consensus algorithm. Information exchange occurs between the two layers: the upper layer issues dispatch power to the lower layer for substation scheduling, and the lower layer uploads information on the load dispatch capability.

To validate the effectiveness of the proposed algorithm, we use a simulation model based on a modified IEEE 33-node distribution grid system. Figure 4 illustrates the specific topological relations of each VPP. There are three VPPs in the model, each containing multiple substations. Each substation contains different quantities of distributed generators, energy storage, interruptible loads, gas turbines, and electric heating boilers.

We compare the proposed algorithm with three baselines, with baseline 1 using the DDPG algorithm in the upper layer and the traditional consensus algorithm in the lower layer, baseline 2 using the traditional ant colony algorithm in the upper layer and the traditional consensus algorithm in the lower layer, and baseline 3 using the particle swarm optimization algorithm in the upper layer and the traditional consensus algorithm in the lower layer. Compared with similar deep learning algorithms, the DDPG algorithm has higher training efficiency (Zhang et al., 2023c). Although the desired dispatching value is almost the same as the theoretical optimal value, the real-time requirement of power dispatching is ignored. Table 2 shows the simulation parameters (Pasetti et al., 2018; Gough et al., 2022; Liang and Ma, 2022). The power constraints of various resources in each substation are shown in Tables 3–5. We simulate a 24-hour operation, optimizing dispatch every hour, with a consensus iteration period of 0.1 s.

In Figure 5A, the distribution power grid loss versus time is depicted for the mentioned algorithms. The figure reveals that the proposed algorithm consistently produces lower losses in comparison to the other three algorithms. Taking 4:00 as an example, compared to baseline 1, baseline 2, and baseline 3, the proposed algorithm reduces grid loss by 11.27%, 8.03%, and 3.96%, respectively. The proposed algorithm can adjust the convergence speed according to the delay, thereby reducing the dispatch delay and leading to a decrease in distribution power grid loss.

Figure 5B shows the optimized dispatch process of the mentioned algorithms at 16:00. At the beginning of the mentioned algorithms, the total cost is rapidly decreasing. In the end, baseline 1 fluctuates within a certain range and can only achieve dynamic convergence. Baseline 2, baseline 3, and the proposed algorithm reach convergence after 88, 74, and 60 iterations, and their total dispatch costs are $12,000, $9,700, and $7,000, respectively. Compared with baseline 1, baseline 2, and baseline 3, the proposed algorithm reduces the total dispatch cost by 94.38%, 71.42%, and 38.57%, respectively. The proposed algorithm exhibits the fastest convergence speed due to the introduction of changing factors in the ant colony algorithm and PD correction in the consensus algorithm. The change factor and PD correction in the proposed algorithm significantly accelerate the convergence speed.

Figure 6A shows the dispatch power of each substation within VPP I at 16:00. At the beginning of the iteration, the power of substation 1 and substation 3 increases rapidly and the power of substation 2 decreases rapidly, and finally the resources of each substation converge to a stable value. After the PD correction, the convergence of the substations is significantly accelerated. Taking substation 2 as an example, convergence was reached through 38 iterations in 3.8 s before PD correction, and convergence was reached through 23 iterations in 2.3 s after PD correction.

Figure 6B shows the cost increment rate versus time for each substation within VPP 1 at 16:00. The initial value of the cost increment rate is different for each substation, with a higher initial value for substation 2 and lower initial values for substations 1 and 3. At the beginning of the iteration, the cost increment rate of each substation area changes rapidly. The traditional consensus algorithm reaches convergence for all substations after 55 iterations in 5.5 s. The convergence speed is accelerated after the PD correction, reaching convergence for 45 iterations in 4.5 s with a result of 21.42.

Figure 7A shows the simulation time to reach convergence versus β when σ = 0.1 kW and Ω = 0.02$/kW. In the beginning, increasing β will strengthen PD correction. The algorithm converges with larger fluctuations during each iteration, leading to a decrease in convergence time. The minimum time required for the simulation to reach convergence is 276 ms. Continuously increasing the β will lead to over-correction of PD, making it difficult for the algorithm to converge due to continuous fluctuations, resulting in an extension of convergence time. β has the shortest convergence time at a value of 1.18.

Figure 7B shows the simulation time to reach convergence versus σ and Ω when β = 1. To achieve convergence, two constraints need to be satisfied simultaneously, so a small value for either constraint will result in an extremely long convergence time. The convergence time will only decrease when both σ and Ω are large. When both parameter settings are large, the simulation time required to achieve convergence is 276 ms.

Figure 7C shows the dispatch cost of the proposed algorithm and traditional consensus algorithm at the lower layer under different communication delays. When the communication delay is low, the dispatch cost difference between the two algorithms is not significant. When the delay is large, the proposed algorithm has lower dispatch costs compared to the traditional consensus algorithm. This is because the proposed algorithm introduces PD correction, which can adjust the convergence speed according to the communication delay. In the case of high communication delay, the convergence speed of the proposed algorithm is faster, so the dispatch cost is lower.

Figure 8 shows the dispatch power of each substation in different VPPs. It can be observed that the power fluctuation of each substation is not large in the time range of 0–24 h. In VPP1, the power of substations 1, 2, and 3 fluctuates around 130, 280, and 190, respectively. In VPP2, the power of substations 4 and 5 fluctuates around 80 and 170, respectively. In VPP3, the power of substations 6, 7, and 8 fluctuates around 230, 170, and 230, respectively.

This paper proposes a novel two-layer iterative energy dispatch strategy for multi-energy flow VPPs in distribution power grids. The upper layer sub-problem of multi-energy flow VPP energy dispatch is tackled using an improved ant colony algorithm, while the lower layer substation energy dispatch is addressed through a delay-aware consensus algorithm. To enhance the convergence speed of the delay-aware consensus algorithm and enable real-time energy dispatch of the multi-energy flow VPP, a PD control mechanism is integrated. Simulation results demonstrate that the proposed algorithm significantly reduces the total dispatch cost by 61.11% and 45.45% compared to the two baseline algorithms. Moreover, the convergence speed is increased by 18.18% compared to the traditional consensus algorithm after incorporating the PD control mechanism. In the future, we plan to explore energy cooperative dispatch between electric vehicles and multi-energy flow VPPs.