In the proposed ADNs, the energy trading between the power supplier and the user provides sufficient energy at a low rate without dependence on other power suppliers [16]. Therefore, the extra energy provided by the transaction nodes could be used for reliable power transactions via blockchain, which meets the economic demand of the power grid. Assuming that each group of transaction nodes could store the dispensable extra energy and have its energy storage capacity with the limitations set, and the transaction nodes could have different energy requests over a period of time, the ADN system architecture can be shown as Fig. 1.

In which the decentralized blockchain architecture of ADN power transactions is designed. The transaction information is stored in blocks and each node is related to renewable energy sources like solar energy, hydropower, and wind power to meet the energy demand of corresponding areas [14]. The storage perception and storage perception processing requests are proposed to handle the energy requests of the nodes. Meanwhile, considering the costs and storage capacity, the multi-objective particle swarm algorithm is used to search for an economic and safe power transaction plan, which minimizes the purchase cost of the user and maximizes the sales of the power supplier.

The processing of the trading requests submitted by the users in the centralized trading system will bring up the heavy cost of data processing and computation [17]. Therefore, a decision variable DNid∈(0,1) is defined to map the transaction node id in the blockchain network to power generation (0) or request (1) within t∈T, which can be expressed as follows:

(1)DNid=random(0,1)

Whereas the variation of the dispensable energy storage in a generation cycle is:

(2)Es={Es+Gr,DNid=0&Es+Gr≤ElEl,DNid=0&Es+Gr>ElEs,DNid=1

In the equations, DNid=0 indicates that the amount of energy equal to the power generation rate Gr can be generated. If the additional energy (Es+Gr) does not exceed the storage limit El, it will be added to the energy storage unit Es. If the storage limit El is exceeded, the storage unit will be filled directly to reach the upper limit El. DNid=1 indicates a request for transaction. Since the request is randomly generated, the change of Es is also random [18].

If the internal storage unit El cannot satisfy the random request of the storage unit W, the request of the remaining storage units will be sent through the network, which is expressed as follows:

(3)InNode={W,El≥WEl,El<W,Request={0,El≥WW−El,El<WW={random(0,200),DNid=10,DNid=0

The distance matrix Dis[·][·] is assumed to describe the distance between the storage unit and the transaction node, and it is used to obtain the cost of the request. Based on the distance between transaction nodes, the relatively smaller transmission cost per unit distance Ct will be added to the basic fee and thus request the cost of n energy unit C from transaction node e to f is:

(4)C=Cb(n)+Ct(Dis[e][f])where Cb is the basic fee. This cost function requires a fair distribution of requests between users and power suppliers. The cost-benefit analysis also needs to be performed to analyze the economic feasibility of energy trading [19].

In the transaction process, the energy request is randomly made by the transaction node. If the transaction node can meet its requirements, it can be regarded as self-sufficient [22]. If the current energy of the node cannot meet the demand, the transaction node will request additional energy from the ADN. The energy request mechanism includes cost perception request and storage perception request, the flow of which is shown in Fig. 3.

The blockchain technology solves the security problem of power transactions, shortens the time of authentication of the original trading platform, and improves the transaction efficiency [24]. Based on the blockchain technology, the power trading scheme uses the particle swarm algorithm for multi-objective optimization to optimize the power transaction, and introduces the power price formulation mode and power purchase strategy to the intelligent contract [25].

For the power supplier in the trading chain, under the constraints of price and transaction priority, multiple options for selling electricity in intelligent contracts are used to achieve the best benefit, and guarantee the transaction security at the same time. Because the spot trading is still in its infancy, big users’ direct power purchase is the main concern. The power supply focuses on making attractive power sales schemes to increase the power purchase of big users, thus improve the market competitiveness [26].

Specific to the two energy request mechanisms of cost-perception request and storage perception request, particle swarm optimization algorithm is selected for the optimal power transaction scheme search [15]. By using particle swarm optimization mathematical modeling, process optimization, and generation of particle non-inferior solution set, it is applied to the power trading market, and generates the optimal real-time power trading scheme under the constraints of all parties to meet the minimum cost. Particle swarm optimization is the whole step of generating a non-inferior solution, which includes the initial screening of the non-inferior solution and updating of the non-inferior solution set. When the particle swarm is not updated, a random particle from the non-inferior solution set is selected as the optimal solution of the swarm. The particle update process is shown as:(5)vk+1=ωvk+c1ζ1(Pidk−xk)+c2ζ2(Pgdk−xk)xk+1=xk+vk+1

In the equation, v is the particle velocity; k is the current number of iterations; ω is the inertial weight; c1,c2 is a constant value; ζ1,ζ2 is a random number with the value of 0 and 1; Pidk and Pgdk is the individual or global optimal particle position, respectively; x is the particle position.

Through the particle swarm multi-objective search algorithm, the power transaction scheme is optimized in the real-time power price transaction process of the power transaction node. Five types of power suppliers (thermal, photovoltaic, hydropower, wind, nuclear) are assumed to participate in transaction competition for the user power purchase, and their power transaction volume, on-grid price, and transmission costs are different. We use particle swarm optimization to model this transaction process and carry out the multi-objective search. Among them, the on-grid price of the power stations is ψ; the power transaction volume is E; the power transmission and power distribution mean value is ψ¯. Then the optimization objective function is:

(6){minψe=∑i=15ψimminEm=∑i=15Eim

In the equation, ψe and Em is the on-grid price and the power transaction volume of the final transacted power plant; m is the selected power plant.

The associated constraint is:

(7)∑i=15(ψi+ψ¯i)Ei∑i=15Ei≤0.5∑i=15(ψi+ψ¯i)Ei∑i=15Ei≤0.5

In the inequality, ψ¯i is the total cost of power transmission and distribution.

To simulate the randomness of the power trading market to the greatest extent, the particle swarm algorithm is modified. Specifically, the lowest cost is not to select the scheme with the lowest power for each purchaser, but to select the optimal power volume and power price combination scheme based on the overall transaction, so as to increase the power utilization rate of renewable energy source power plants and reduce the reliability of fossil fuel power plants. In the market constraint, the optimized particle swarm optimization algorithm is integrated into the intelligent contract and operated by the criteria of user purchase demand and low power price, so as to ensure the openness, transparency, and intelligence of the optimal power transaction scheme.

Taking the power supply and demand of ADN within 24 h as an example, this paper analyzes the power transaction status based on block-chain. According to the experimental scenario, the power quantity of the traditional fossil fuel power plant is set to 250 MW. The new energy power plants which have great randomness and volatility due to the influence of the natural environment, are used as a supplement to the power supply. Between 0:00 and 6:00 a.m., photovoltaic and wind power plants are affected by the environment and generate limited electricity. Therefore, there are fewer new energy suppliers involved in the power transaction. After 7:00 a.m., users’ power consumption gradually rises and the demand for power increases, but the increase in new energy generation lags behind the user demand. Therefore, the power transaction market is in the seller’s market, and the power price is high; new energy power providers can sell electricity at a relatively high price through block-chain announcements. The daily changes of power generation and transaction price are shown in Fig. 6.

As can be seen from Fig. 6, the output of the new energy supply is relatively random. About 9:00 a.m., its output is more and the power generation reaches a short-term peak. And the power supply and demand state is constantly displayed in the ADN power transaction based on block-chain. In this way, the new energy supplier can adjust its power sale price in real-time, improve the transaction rate, and reduce the amount of abandoned wind and light. With the normalization of new energy generation, the price of power transactions tends to stabilize. In addition, around 1:00 and 5:00 p.m., the power generated by new energies increases, and through the block-chain transaction process, the new energy power price reduces, resulting in the power transactions. Because the block-chain-based power transactions can be completed in a very short, new energy suppliers and users almost close the deal at the same time.

Although the impact of balance constraints on power transactions in ADN is secondary, it is critical from the user’s point of view. Both cost and storage are the key factors should be considered. The purchasing capacity cannot exceed the maximum storage capacity except the real-time supply load. Therefore, cost and storage need to achieve a balanced state to maximize the benefits of users. The energy balance change of transaction nodes in which cost perception and storage perception algorithms participate are shown in Fig. 7.

As can be seen from Fig. 7a, the available storage and income of transaction nodes in the network do not depend on the initial storage of transaction nodes. In addition, the cost perception algorithm allows the transaction node to buy electricity fairly for the user. Therefore, during any exchange period, transaction nodes will not incur high costs due to transmission. As can be seen in Fig. 7b, significant equilibrium differences can be observed for transaction node 3. Because node 3 has a certain amount of energy storage, it has advantages in network transactions, which leads to differences in the distribution of income among transaction nodes.