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For the regional multi-energy system, the use of a centralized optimization scheduling method may result in increased energy consumption, scheduling costs, and network latency due to the centralized transmission, processing, computation, and distribution of distributed new energy power supply operation information and load demand information. To mitigate these issues, alternative scheduling methods should be considered. Edge computing technology makes use of various data sensors, data routing and other devices configured in the regional multi-energy system to analyze and process the collected operation information data on the side of each distributed power generation equipment. The calculation results are then transmitted to the cloud service data computing center for centralized coordination and scheduling. Based on this, this paper establishes a cloud-side coordinated scheduling framework of multi-node energy data information interaction for regional multi-energy systems, as shown in Figure 1.

The scheduling framework shown in Figure 1 is mainly composed of five scheduling service layers: equipment entity layer, state data perception layer, edge computing layer, data network communication layer, and cloud service application layer (Ilic et al., 2010; Si et al., 2020). Computing servers are configured in the corresponding service layers to facilitate data processing, analysis, and storage.

(1) The equipment entity layer is composed of various energy equipment and equipment operation control module. The main task is to use each energy equipment to generate electricity, heat, gas and other energy supply to the consumer. Through the equipment operation control module, it controls and adjusts the operation status of energy equipment.

As shown in Figure 1, the construction of the physical entity model of each energy supply equipment within the system is the basis for the optimal scheduling of the regional multi-energy system. To carry out this study, the network topology of the regional multi-energy system is established, as shown in Figure 2. The system is composed of photovoltaic cells, wind turbines, gas turbines, gas boilers, PtG equipment, and energy storage equipment. It provides electricity and heat energy to the system energy users by purchasing natural gas from the superior gas network. Part of the natural gas is directly supplied to the users through the gas network. The gas turbine and gas boiler are used to provide electricity and heat energy to the system energy users, respectively. The wind turbine and photovoltaic are used to provide electricity to users. The system is connected to the main power grid to compensate for any electricity shortages. The PtG equipment is used to output the gas energy to the energy users. The energy storage equipment is mainly used to regulate the input and output of various energy sources of the regional multi-energy system by charging and discharging energy.

Assuming that the regional multi-energy system being studied includes m edge computing layer base stations (which handle the main tasks of the edge computing layer and the data network communication layer) and n energy-consuming users. These can be denoted as edge computing layer base station set M = { 1 , 2 , … , m } and energy-consuming user set N _user = { 1 , 2 , … , n }, respectively. At this time, all energy-consuming users in the regional multi-energy system must satisfy the constraints of Eq. 14. N user = ∪ k N user , k ∈ M (14)

The edge computing layer base station provides data support and scheduling calculation services to energy consumption users and the cloud service layer. This is achieved according to the edge computing module, data storage and communication module, data routing and other equipment deployed in the system. At the same time, the base station can transmit the calculated data and collected data to the neighboring base station. Then, by allocating the computation tasks to be completed by its own base station, it realizes the cooperative computation of multiple edge computing base stations to better complete the edge node scheduling optimization in the regional multi-energy system. If the edge computing layer base station is responsible for a small amount of computation tasks, the current base station can be used to complete the scheduling tasks.

If all energy equipment and energy consumption users in the scheduling process of the regional multi-energy system perform system scheduling optimization at the same time, all the computation tasks of the edge computing layer base station are allocated according to Eq. 15. X = x n , i , m x n , i , m = 1 , the computational task  i  of the energy consumption user  n  are assigned to the base station  m 0 , else (15) where X is the system scheduling task allocation decision set; x _n,i,m is the corresponding values taken in the set.

Meanwhile, at least one base station in the edge computing layer must perform all computational tasks while satisfying the constraint of Eq. 16. ∑ m ∈ M x n , i , m = 1 , ∀ n ∈ N , i ∈ Y n E X , m cul = ∑ n ∈ N ∑ i ∈ Y n c n , i x n , i , m ≤ E ⁡ max m cul ⁡ , m ∈ M E X , m sto = ∑ n ∈ N ∑ i ∈ Y n e n , i x n , i , m ≤ E ⁡ max m sto ⁡ , m ∈ M (16) where the first term is the constraint on the computational tasks to be completed by the edge computing layer base station; the second and third terms are the constraints on the response of the computational and data storage capacity of the edge computing layer base station m; E ^cul _X,m and E ^sto _X,m are the amount of the response of the computational and data storage capacity of the edge computing layer base station m, and Emax^cul _m and E ⁡ max m sto are their corresponding upper limits; c _n,i is the scheduling task computation demand; e _n,i is the scheduling task data storage demand; Y _n is the optimized scheduling computation task n in the system.

When performing optimized scheduling computation tasks for the regional multi-energy system, each task requires energy for computation and data communication, as well as incurs transmission delays. Therefore, the cost and transmission delay consumed by the edge computing layer and the cloud service application layer can be expressed by Eq. 17: C coop , t = N u m M C cul , m T ¯ coop = 1 N u m N ∑ n ∈ N T coop , i T coop , i = max i ∈ Y n T n , i send + T n , i cul + T n , i merge + T n , i return (17) where C _coop,t is the consumption cost of the optimized scheduling computation task performed by the regional multi-energy system; Num _M is the number of edge computing layer base stations executing the computation task at time t; C _cul,m is the operation cost of the mth edge computing layer base station; T _coop,i is the transmission delay of the optimized scheduling computation task performed by the regional multi-energy system at time t, and T ¯ coop is the average of its delay value; Num _N is the number of energy consuming users; T n , i send , T n , i cul , T n , i merge , and T n , i return are the optimization scheduling task transmission delay, computation delay, computation result convergence delay, and computation result return delay, respectively.

In the actual optimization scheduling process, the computing process of multi-node cloud-edge cooperative scheduling in the regional multi-energy system is shown in Figure 3.

The state data sensing layer collects the operating state data and ledger data of each energy equipment in the equipment entity layer and stores them in the databases of the edge computing layer and the cloud service application layer. Then, the optimization scheduling task begins at each energy equipment and energy consumption user. It is then uploaded to the edge computing layer, where the computing task is allocated based on Eq. 15. The corresponding optimization computation is executed, and the operation scheduling commands are sent to the equipment entity layer based on the computational results to regulate the operation state of the energy equipment. At the same time, the computation results are summarized, merged, and sent to the cloud service application layer. Finally, the cloud service application layer performs the scheduling of region multi-energy systems covered by the edge computing layer base stations based on the received scheduling optimization data and the energy equipment operation data. The scheduling optimization calculation is unified and coordinated for the whole multi-energy system. The calculation results are also sent to the edge computing layer through the data network communication layer.

To fully utilize the multi-node cloud-edge collaborative scheduling capability in the optimization and scheduling process of the regional multi-energy system, the double-layer optimization scheduling model of the regional multi-energy system is established as shown in Figure 4. The upper-layer optimization model in the cloud service application layer adopts an intelligent optimization algorithm to minimize the overall operation and scheduling cost of the regional multi-energy system. It completes the scheduling optimization of the systems in the coverage area of the different regional edge computing layer base stations in the regional multi-energy system and obtains the optimal energy supply scheduling scheme, based on the received scheduling optimization data and energy equipment operation data. The lower-layer optimization model is that the edge computing layer calculates the optimal energy supply scheduling scheme based on the optimal energy supply scheduling scheme and control commands calculated by the cloud service application layer.

The objective function of the upper-layer scheduling optimization model for the cloud service application layer can be described by Eq. 18: min ⁡ F 1 = ∑ t = 1 24 ∑ i = 1 N u m M C e P i , t + ∑ i = 1 N u m M ∑ j = 1 N u m M C exchange e P i , j , t e + C exchange g P i , j , t g + C exchange h P i , j , t h + ∑ i = 1 N u m M α i F 2 + ∑ t = 1 24 C coop , t (18) where F ₁ is the overall operation and scheduling cost of the regional multi-energy system; C _e is the unit electric energy interaction price between the regional multi-energy system covered by different regional edge computing layer base stations and the large power grid; P _i,t is the interactive electric power between the regional multi-energy system covered by different regional edge computing layer base stations and the large power grid; C ^e _exchange, C ^g _exchange, and C ^h _exchange are the unit exchange cost of electricity, natural gas, and heat energy in the area covered by the ith and jth regional edge computing layer base stations, respectively; P i , j , t e , P i , j , t g , and P i , j , t h are the exchange power of electricity, natural gas, and heat energy in the area covered by the ith and jth regional edge computing layer base stations, respectively; When the regional system covered by the ith regional edge computing layer base station exchanges electricity, natural gas and heat energy to the region covered by the jth regional edge computing layer base station, P i , j , t e , P i , j , t g , and P i , j , t h are taken as a positive value, and the opposite are taken as a negative value; α _i is the scheduling optimization priority of the different regional edge computing layer base station, the larger the value of the priority level is, the higher the priority level of the computation order is in the calculation of the optimized scheduling task in this region; F ₂ is the scheduling and operating cost of the regional multi-energy system covered by the regional edge computing layer base stations obtained by the edge computing layer calculation.

The objective function of the lower-layer scheduling optimization model for the edge computing layer can be described by Eq. 19: min ⁡ F 2 = ∑ t = 1 24 ∑ i = 1 N u m M ∑ I C i , I , t P i , I , t (19) where C _i,I,t is the operating cost of the Ith energy equipment in the area covered by the ith regional edge computing layer base station at time t; P _i,I,t is the electricity, heat energy or gas energy supply of the Ith energy equipment at time t.

In addition to the consideration of system operating costs, the regional multi-energy system to perform scheduling calculations is also required to consider the scheduling task transmission delay under the multi-node cloud-edge collaborative scheduling strategy, and minimize the data transmission delay of the scheduling optimization calculation process, which can be expressed by Eq. 20: min ⁡ F 3 = T ¯ coop (20)

The supply balance constraints for electricity, gas, and heat in the regional multi-energy system can be described by Eq. 21 ∑ I 1 P i , I 1 , t − P i , e , t c + P i , e , t d + P i , t + P i , j , t e = P i , Le , t ∑ I 2 P i , I 2 , t − P i , g , t in + P i , g , t out + P i , j , t g = P i , Lg , t P i , GB , t − P i , h , t in + P i , h , t out + P i , j , t h = P i , Lh , t (21) where P _i,Le,t , P _i,Lg,t , and P _i,Lh,t are the electricity, heat and gas loads in the area covered by the ith regional edge computing layer base station, respectively; I ₁ is the set of electricity energy equipment in the area covered by the ith regional edge computing layer base station, and I ₁ = {wind turbine, photovoltaic, and PtG equipment}; I ₂ is the set of natural gas energy equipment in the area covered by the ith regional edge computing layer base station, and I ₂ = {gas turbine, PtG equipment, and gas boiler}; P ^e _i,j,t , P ^g _i,j,t , and P ^h _i,j,t are the exchange power of electricity, natural gas, and heat energy between the areas covered by the ith and jth edge computing layer base station, respectively; P ^c _i,e,t and P ^d _i,e,t , P ⁱⁿ _i,g,t and P ^out _i,g,t , P ⁱⁿ _i,h,t and P ^out _i,h,t are the charging and discharging power of the battery storage equipment, gas storage equipment and heat storage equipment at time t, respectively.

The operation constraints of multiple energy equipment in the regional multi-energy system can be described by Eq. 22 P i , w , t min ≤ P i , w , t ≤ P i , w , t max P i , PV , t min ≤ P i , PV , t ≤ P i , PV , t max P i , PtG , t e , ⁡ min ≤ P i , PtG , t e ≤ P i , PtG , t e , ⁡ max P i , GT , t min ≤ P i , GT , t ≤ P i , GT , t max P i , GB , t min ≤ P i , GB , t ≤ P i , GB , t max P i , PtG , t g , ⁡ min ≤ P i , PtG , t g ≤ P i , PtG , t g , ⁡ min P i , e , t c , ⁡ min ≤ P i , e , t c ≤ P i , e , t c , ⁡ max P i , e , t d , ⁡ min ≤ P i , e , t d ≤ P i , e , t d , ⁡ max P i , g , t in , ⁡ min ≤ P i , g , t in ≤ P i , g , t in , ⁡ max P i , g , t out , ⁡ min ≤ P i , g , t out ≤ P i , g , t out , ⁡ max P i , h , t in , ⁡ min ≤ P i , h , t in ≤ P i , h , t in , ⁡ max P i , h , t out , ⁡ min ≤ P i , h , t out ≤ P i , h , t out , ⁡ max (22) where P i , w , t min and P i , w , t max , P i , PV , t min and P i , PV , t max , P i , PtG , t e , ⁡ min and P i , PtG , t e , ⁡ max are the minimum and maximum output power of the wind turbine, photovoltaic and electricity power consumed by PtG equipment in the area covered by the ith regional edge computing layer base station, respectively; P i , GT , t min and P i , GT , t max , P i , GB , t min and P i , GB , t max , P i , PtG , t g , ⁡ min and P i , PtG , t g , ⁡ min are the minimum and maximum values of the gas power consumed by gas turbine, gas boiler, and gas output power of PtG equipment in the area covered by the ith regional edge computing layer base station, respectively; P i , e , t c , ⁡ min and P i , e , t c , ⁡ max , P i , e , t d , ⁡ min and P i , e , t d , ⁡ max are the minimum and maximum values of the charging power and discharging power of the battery storage equipment at the time t, respectively; P i , g , t in , ⁡ min and P i , g , t in , ⁡ max , P i , g , t out , ⁡ min and P i , g , t out , ⁡ max are the minimum and maximum values of the charging power and discharging power of the gas storage equipment at time t; P i , h , t in , ⁡ min and P i , h , t in , ⁡ max , P i , h , t out , ⁡ min and P i , h , t out , ⁡ max are the minimum and maximum values of the charging power and discharging power of the heat storage equipment at time t, respectively.

Data transmission constraints in the multi-node cloud-edge cooperative scheduling framework. The relevant equations can be found in Eqs 15–17.

The regional grid operations flow constraints can be described by Eq. 23 P i , w , t + P i , PV , t − P i , PtG , t e − P i , e , t c + P i , e , t d + P i , t + P i , j , t e − P i , Le , t = U i , x ∑ y = 1 U i , y G x y ⁡ cos ⁡ θ x y + B x y ⁡ sin ⁡ θ x y Q i , w , t + Q i , PV , t + Q i , t + Q i , j , t e − Q i , Le , t = U i , x ∑ y = 1 U i , y G x y ⁡ sin ⁡ θ x y − B x y ⁡ cos ⁡ θ x y (23) where U i , x and U i , y are the voltage at the node x and node y in the regional grid covered by the ith regional edge computing layer base station; Q i , w , t , Q i , PV , t , Q i , t , and Q i , j , t e are the output reactive power of wind turbine, output reactive power of photovoltaic, interaction reactive power with the larger grid, and reactive power exchange between regional grids, respectively; Q i , Le , t is the reactive power of loads within the regional grid; G x y and B x y are the conductance and conductivity between the node x and node y in the regional grid, respectively.

The whale optimization algorithm is a heuristic, single-objective optimization algorithm that simulates the feeding behavior of whale groups (Mirjalili and Lewis, 2016). It has the advantages of a simple algorithm structure, easy implementation, and high convergence speed and optimization accuracy. proposes a multi-objective whale optimization algorithm for solving regional multi-energy system scheduling schemes, based on a multi-objective algorithm framework with non-dominated as well as congestion ranking. The algorithm is divided into three phases: encircling prey, bubble net attack, and searching prey.

In a multi-objective optimization problem with n objective functions F _i (x), i = 1, 2, … , n, a decision variable Y _a is said to dominate Y _b if Eq. 30 is satisfied. If there is no other decision variable that can dominate a decision variable, it is considered a non-dominated solution. F i Y a ≥ F i Y b , ∀ i ∈ 1 , 2 , 3 , ⋯ , n F i Y a > F i Y b , ∃ i ∈ 1 , 2 , 3 , ⋯ , n (30)

This paper proposes the idea of multi-objective particle swarm algorithm, which takes the global optimal solution as the target of bubble net attack, and the local optimal solution as the target of prey search. To achieve a local optimal solution, select the individual that dominates the current local optimal solution after moving positions. If the individual after moving position and the current local optimal solution do not dominate each other, randomly select both as the local optimal solution to ensure solution distribution and non-domination. The process of whale moving position fully uses the information obtained in the process of whale moving position, and the global optimal solution is selected according to the hierarchical analysis method, which ensures the effectiveness and objectivity of the global optimal solution selection process.

The distribution of the solution set of the algorithm uses the results of the crowding degree ranking in this paper as the standard for updating the solution set in the iterative process. The crowding degree is calculated using Eq. 31. Y d = Y d + F i + 1 − F i − 1 F max − F min (31) where F _max and F _min are the maximum and minimum values of the objective function, respectively; F _i-1 and F _i+1 are the values of the objective function of the previous individual and the next individual after the descending order ranking, respectively.

The algorithm uses the crowding degree, which can visualize the distribution of solutions. A larger crowding degree indicates a better distribution of solutions, while a smaller crowding degree indicates a worse distribution. Therefore, during the iteration process of updating the solution set, larger solutions can be filtered based on the size of the crowding degree, and smaller solutions can be eliminated to maintain diversity and distribution of solutions.

Figure 5 shows the solution process, and the specific steps are as follows:

(1) Initialize parameters, such as the output population size and iteration number, for each equipment in the regional multi-energy system. Randomly initializing the position of each individual in the output population, and initializing the local optimal value of each equipment in the regional multi-energy system.