A-RESS new dynamic and smart system for renewable energy sharing problem

Description of the problem

Depending on the geographical location of the regions, renewable energy sources may change, e.g., some of the countries are sunny allover the year, while for others the sun comes out for only few days. Hence, a country with a continuous and important opportunity of renewable energy production is known as a producing country, while a country which cannot meet its proper needs is known as a consuming country. Since, the production and storage of renewable energy are expensive and in order to optimise these costs while ensuring a clean environment, a system with a local and global regulator for energy sharing can optimise the life cost of the renewable energy powers and reduce their loss for a green environment.

Our aim is to build an undirected and dynamic graph connecting the different N hybrid power plants (of different involved countries). The graph is dynamic, since a power plant can be added/deleted at any time and it is undirected because any power plant can switch from an energy supplier to an energy consumer and vice versa. The graph is incomplete because it is useless to connect power plants which are at large distances. Each hybrid power plant X_i, i ∈ {1,…, N} in a region R_i, maintains important information as:

• The estimated quantity of renewable energy that can be produced Prod(X_i) per day,

• The remaining quantity of renewable energy in batteries Stock(X_i) per day,

• The estimated quantity of needed energy Needs(X_i) for the region under several conditions, i.e., current season, temperature, etc.

• The quantity of energy to keep in reserve Reserve(X_i) for any risk.

For predicting these data, i.e., Prod(X_i) and Needs(X_i), and for a high performance and accuracy for the proposed A-RESS system, several existing models can be adopted for estimating energy production and consumption. Most of them are based on Artificial Intelligent and machine learning techniques, amongst, artificial neural network (ANN) based model that have provided good results for real-time prediction of energy production (Bermejo et al., 2019; Shapi, Ramli & Awalin, 2021); Multiple Linear Regression (Solyali, 2020); Support Vector Machine (Kaytez, 2020; Walker et al., 2020); Random Forest (Walker et al., 2020); K-Nearest Neighbour (Shapi, Ramli & Awalin, 2021); Multilayer Perceptron (Chammas, Makhoul & Demerjian, 2019); etc. The prediction of the required quantities of energy is based mainly on daily meteorological data and production/consumption histories for a given period. The latter is divided into two types of features: Historical features, i.e., energy previous consumption, and weather features, i.e., temperature, humidity, solar radiation, wind speed, wind direction, pressure, rainfall amount, degree of cloudiness, type of day (weekday/weekend/holiday), type of hour (daytime/night-time), season, etc. Most studies cited above showed the effectiveness of Artificial Neural Network (ANN) and Support Vector Machine (SVM) based models. The integration of an ANN or an SVM model in our system for the required daily data will be considered in the future work.

Once the daily quantity of energy to provide by each supplier X_i to its consumer X_j neighbors is determined (using Eq. 3). The transfer of renewable energy can be done at a local level means between plants of the same country; in this case the energy will be offered. The energy can also be sold when the transfer involves plants of different countries. In this work, we will focus on the international scale. For simplifying the proposed system, we assume that each country contains one single power plant X_i. A transfer cable is provided between two power plants X_i and X_j only if the distance between these two plants is not large. Hence X_i and X_j are considered as neighbors ,i.e., Ng(X_i). Our goal is to optimise the shared quantity of renewable energy while minimizing the cost of transportation and maintaining a high level of transportation reliability. The possessing of the transmission line depends on the quantity of energy to be transported and the distance between the two power plants to interconnect. Note that each transfer process will obviously lead to some loss of energy.

The decision of any power plant for whether acquiring some quantity of renewable energy or producing the same needed quantity of non-renewable energy is based on the basic price of the plant’s installation, the amortization period, the transfer cable installation, etc. In addition, any X_i can deliver or store energy if and only if its both needs and risk reserve are satisfied. For reducing the loss of energy, the quantity received by X_i must not exceed its needs/risk reserve.

New formalization for renewable energy sharing problem

A renewable energy distribution problem can be formalised as a Constraint Optimisation Problem (COP). A COP is a Tuple(X, D, C, F) as follows:

• X = {X₁, X₂,…, X_n} with X_i = (X_i.io₁, X_i.io₂,…, X_i.io_k), where X_i represents a power plant and X_i.io_j, j ∈ {1,…, ||Ng(X_i)||}, is the quantity of energy to provide/get to/from X_j, j ≠ i. Note that X_j ∈ Ng(X_i) only if these two plants are linked together, i.e., Ng(X_i) is the set of all neighbors of X_i,

• D = {D₁, D₂,…, D_n} where D_i = (val₁, val₂,…, val_k) with val_j ∈ N, are the possible quantities of renewable energy to provide/get to/from each X_j ∈ Ng(X_i). If X_i is a power plant provider then ∀ X_j∈ Ng (X_i), X_i.io_j ≥ 0.

• C = {C_Prof, C_Share, C_Rec} where

• – Profitability Constraint C_Prof: the cost of requesting some quantities of renewable energy from neighbors should be better than producing the same quantity of non-renewable energy (see Eq. 1). These costs involve: the cost of the transfer, the cost of the cable installation, the cost of air pollution, etc.

(1) $$\sum _{j\in \mathrm{N}\mathrm{g}(X_i)}({\beta }_{ij}\ast X_i.i{o}_j)-({\gamma }_i\ast \sum _{j\in \mathrm{N}\mathrm{g}((X_i)}(1-{\alpha }_{ij})\ast X_i.i{o}_j)<0$$

where

α_ij is the proportion of lost energy, determined according to the link type between X_i and X_j, its length, the weather condition, etc. γ_i is the cost of producing 1 KW of non-renewable energy by the plant X_i, and β_ij is the cost of exchanging 1 KW of renewable energy between two plants X_i and X_j.

• – Shared Quantity Constraint C_Share: the total shared quantity per plant should not exceed the available quantity of energy to be given as in Eq. (2).

(2) $$\sum _{X_j\in \mathrm{N}\mathrm{g}(X_i)}{X}_i.i{o}_j\le Avail(X_i)$$

where

(3) $$Avail(X_i)=Prod(X_i)+Stock(X_i)-Needs(X_i)-Reserve(X_i)$$

• – Received Quantity Constraint C_Rec: the total received quantity of renewable energy per a plant should not exceed the needed energy as in Eq. (4).

(4) $$\sum _{X_i\in \mathrm{N}\mathrm{g}(X_j)}(1-{\alpha }_{ij})X_j.i{o}_i+Avail(X_j)\simeq 0$$

Solving this COP consists in finding the optimal (according to the objective function F) instantiation of all variables X with values of their domains D that satisfies all the constraints C. An optimal solution X * = {X*₁, X*₂, …, X*_n} for this problem is a solution that maximizes the satisfaction of all neighbors requests, F(X *). Each power plant tries to compensate the spent cost of its installation by serving the maximum in needy regions with possible quantities. In addition, this system tries to maximize the benefit from distributing energy. The cost of purchasing/selling energy differs from one plant to another according to the price of the link installation, the distance between the regions, etc.

Each plant X_i will try to find values X *_i = (X*_i.io₁,X*_i.io₂,…, X*_i.io_k) with k = ||Ng(X_i)||, that optimizes F(X), as shown in Eq. (5).

(5) $$F(X^{\ast })=\underset{X}{min}F(X)$$

(6) $$F(X)=g(X)-h(X)$$

where, g(X), is the function that measures the degree of non-satisfaction of all the plants X_i ∈ X (as given in Eq. 7). An energy plant supplier X_i is satisfied only if the maximum of its extra produced energy is shared with neighbors, while an energy plant consumer X_j is satisfied only if it gets the maximum of the energy it needs. As for h(X), it computes the global cost of all the energy exchanged between all the plants (as given in Eq. 8). If h(X) > 0 then most plants are suppliers; otherwise most plants are consumers.

(7) $$g(X)=\sum _{X_i\in X}{(\sum _{X_j\in Ng(X_i)}{X}_i.i{o}_j-Avail(X_i))}^2$$

(8) $$h(X)=\sum _{X_i\in X}\sum _{X_j\in \mathrm{N}\mathrm{g}(X_i)}{\beta }_{ij}\ast X_i.i{o}_j$$

Recall that β_ij is the cost of exchanging 1 KW of energy between two plants X_i and X_j. This cost is not the same for all plants, it is subject to type and length of the used cable, the installation cost of the plant, etc. Both quantities, h(X) and g(X) should be normalized.

System architecture

In the multi-agent proposed system, each agent will be assigned to a power plant. Three types of agent are used, a Supplier, a Consumer and a Neutral Agents. Supplier agents are those who have an excess of renewable energy and subsequently can provide some of it to the neighbors who are indigent. These latter agents are the Consumer. A neutral agent is an agent that is able to satisfy its needs and does not have any extra energy.

Each agent X_i maintains five static knowledge (i) Estimated quantity of renewable energy that its power plant can produce by per day, (ii) Available quantity of renewable energy in its power plant batteries per day, (iii) Estimated quantity of needed energy for its power plant, (iv) Quantity of energy to keep in reserve for any risk and (v) Number of all its neighbors ||Ng(X_i)||. Agents also have dynamic knowledge, this knowledge differs according to the type of agent. A supplier might be mapped into a consumer if it faces a lack of energy at any day, same for a Consumer. Agents can be mapped according to their daily needs. All these types of agents have to cooperate together in order to maximize their own satisfaction.

Global dynamic system

The proposed multi-agent global dynamic is divided into two phases:

• An initialization phase

• A negotiation phase

During the initialization phase, each agent will use its trained ANN model to estimate the production and the needs of the day. As we mentioned before this process will be discussed in another research work. According to the obtained estimations, decides the quantity of available renewable energy to share with neighbors. If the Avail(X_i) is a positive value then X_i will be a Supplier; otherwise it will be a Consumer. Agents can then start the second phase.

During the negotiation phase, each Consumer agent, will check first whether is it profitable to get the needed quantity or to use non-renewable energy according to Eq. (1). If yes, then it will send a request to all its neighboring Supplier, with the needed quantity i.e., the agent will divide the needed quantity |Avail(X_i)| on the number of Suppliers. Each Supplier X_j that receives demands from related Consumers, proceeds first by checking whether it is possible to grant them all, i.e., Avail(X_j) is equal or greater than the summation of all requested quantities. If so, each Consumer will receive what it needs and the extra-quantity will be kept for further requests. Otherwise, the agent X_j will determine the proportion p_ij of each request according to the total needs (summation of all asked quantities from all X_i ∈ Ng(X_i)). X_i will reply to all its requesters with possible quantities (see Eq. 9).

(9) $$X_i.i{o}_j=p_{ij}\ast Avail(X_i)$$

(10) $$p_{ij}={\displaystyle \frac{X_i.i{o}_j}{\sum _{X_j\in \mathrm{N}\mathrm{g}(X_i)}{X}_i.i{o}_j}}$$

Each Consumer agent X_i will check the total amount of energy that it is willing to get from all Suppliers. If the whole quantity is equal to its need (satisfying constraint of the Eq. 4) and optimise its objective function F(X_i), it replies with an acceptance. Otherwise, if it is less than its needs (due to some energy loss or non availability of enough energy on the Supplier side), then it will resend to other Suppliers, that are willing to provide more, asking them for the missing quantity. The same negotiation proceeds until all available quantities are distributed and all Consumers get the maximum of what they can get. Once the negotiation process is over, the power plant may start exchanging their agreed quantities.

System architecture description

In this section, we will describe our multi-agent system using the ODD (Overview, Design, and Details) protocol proposed by Grimm et al. (2006).

System complexity

In order to evaluate the computational efficiency of the proposed system and decide whether it can be used in practical applications or not, we computed the time complexity of the underlying multi-agent system. Since a multi-agent system is defined as a set of interacting agents in an environment, we need to determine the complexity at two levels, the agent level (as an atomic unit) and the system level (including the interactions). In the following, we assumed N the total number of agents, each agent is connected at most to N/2 other agents as neighbors.

• At the agent level: According to its behavior, each agent has to predict the quantities of renewable energy to be produced and to be consumed in order to estimate the quantity to be offered. The complexity of this process depends on the trained regression model that will be used. Note that most of the existing models are polynomial. Then the agent has to process m(N/2) values to/from neighbors, with m the total number of iterations to attend consumers’ satisfaction. In the worst case, only one Consumer will be satisfied at each communication, so the total number of iterations for a Supplier will be N/2. Hence, each consumer will process O(N²) instructions.

• At the system level: According to the designed interactions, a first communication is required between agents to exchange their states (Consumer or Supplier). This first step requires O(N²) messages at most. Then, Consumer agents will negotiate with their Suppliers to get what they can get. These communications sending/receiving requests/answers between agents resumes until all consumers are satisfied (no more available quantities to be shared). Assume that at each communication one neighbor is satisfied, so the total communications will be equal to the number of neighbors for each agent, means O(N²). All agents will process O(N³) messages.

Illustration example

To illustrate the global dynamic of our proposed system, let’s consider the following example: assume we have five regions {X₁, X₂,…, X₅} described in the Table 1.

To represent the distance graph, we assume that the two regions X_i and X_j are linked if the distance d_ij is less than the maximum distance D. In our example, we assume that d₁₅, d₁₃, d₂₃, d₂₄, d₄₅ ≥ D as shown in the following graph:

The Table 2 gives an example of the estimated energy per region.

During the initial phase, agents will first estimate their energy available quantity and decide about their current status, i.e., whether a Consumer, a Supplier or a Neutral agent. Then they will exchange their status as given in the following graph:

During negotiation phase, the Consumer agents will send a message to all neighboring Suppliers to ask for the needed quantities. X₁ will ask for 2,000 KW from X₅ and X₄ will ask for 750 KW from X₂ and X₅. Then X₅ will compute p₅₁ = 0.72 and p₅₄ = 0.28, and inform X₁ and X₄ about the quantities they are willing to receive, i.e., 1,080 KW for X₁ and 420 KW for X₄. As for X₂, it will inform X₄ that it is able to get only 500 KW. The Consumer agent will accept the offer given by Suppliers, since no additional affordable energies as given in Table 3.

Experimental evaluation

For an effective performance evaluation of our A-RESS system, we need to show that: (i) All produced quantities of renewable energy will be shared among involved power plants, and (ii) None of the power plants that lack energy, gets more than its demand. This system can be adopted by one large country, e.g., Saudi-Arabia or by several neighboring countries. The aim is to guarantee both, the maximum use of produced renewable energy for a less environment damage and the minimum loss of energy. We implemented a prototype of our system using JADE environment, a Java programming language on an Intel (R) Pentium (R) Dual CPU T3200 processor with a Microsoft Windows 7 operating system.

Several experiments were performed under the following assumptions:

• The number of countries is 10, {X₁, X₂,…, X₁₀} described in the Table 4.

• For each country only one power plant is installed. We will have one agent per country.

• A link exists between two countries if the distance between them is less than some threshold, for our experiments is 2,500 km.

• A country X_i can be Neutral, Supplier or Consumer according to its maintained data. These data, i.e., Prod(X_i), Needs(X_i), Stock(X_i) and Reserve(X_i), are generated randomly.

The performance of our A-RESS system is evaluated in terms of three metrics: (i) the CPU time for scalability testing, (ii) the energy availability per region before/after sharing and (iii) the difference between afforded/received for sensibility testing. The obtained results are represented in the following Figures.

To determine the selling price of 1 KW of renewable energy, we needed to consider the initial renewable energy power plant and link installation cost β⁰_i, the amortization period t_i and the discount rate σ_i. The selling price of a 1 KW of non-renewable energy is represented by a geometric suite (as given in Eq. 11).

(11) $${\beta }_{ij}={\sigma }_i^n{\beta }_{ij}^0+a$$

with n ∈ [0..t_i] and a is a fixed fees.

In our experiments, 30 samples were generated. These samples differ in terms of the estimated quantities of energy consumption, production, remaining quantity in batteries and the quantity to keep in reserve. So, the numbers of Neutral, Supplier and Consumer agents vary from one sample to another.

In Fig. 1, the blue curve shows the total quantities of available energy, while the red curve shows the total quantities of shared energy for all Supplier agents per sample. Note that for most samples both curves superimposed. Only for few cases the available quantity is slightly greater the shared one. This means that most produced energy by suppliers will be used by consumers and consequently the loss of energy is very few.

In Fig. 2, the blue curve describes the total quantities of requested energy and total quantities of received energy for all consumer agents per sample. Notice that the two curves overlap for many samples. This means that for these samples the consumers are well satisfied and they got what they requested. For sample 21, the consumers received only 25% of their requested quantities. This gap between requested/received quantity can be justified but the results given in Fig. 3 where it is shown that for Sample 21, the number of Consumers are far greater than the number of suppliers. In addition, it is worthy to notice that none of the consumers received more than what it requested.

To approve the consistency of the obtained results, Fig. 4 matches the total quantities of energy shared by all the Supplier agents with the total quantities of energy received by all Consumers agents, per sample. Note that the two curves are almost fully superimposed. We infer that all shared quantities have been well received by the Consumer agents.

From all above obtained results, we believe that despite the variation of the random inputs (Prod(X_i), Needs(X_i), Stock(X_i) and Reserve(X_i)), the proposed multi-agent dynamic is accurate. In all cases, a Supplier agent cannot offer more than what it is available for it, a Consumer agent cannot receive more than it needs and mainly most of the produced quantity of renewable energy is well distributed.

To test the scalability of our approach, we varied the number of plants from 10 to 200 and we measured the required CPU time. Figure 5 shows that the CPU time increases, with polynomial growth, according the number of plants. This is due to the number of messages that are exchanged in order to attend a compromise between all agents. This number is a polynomial function of the number of plants. For 10 power plants we needed 80 s while for 200 power plants, we had 620 s.