Abstract
This paper presents a risk-based competitive bi-level framework for optimal decision-making in energy sales by a distribution company (DISCO) in an active distribution network (ADN). At the upper level of this framework, the DISCO and a rival retailer compete for selling energy. The DISCO intends to maximize its profit in the competitive market. Therefore, it is very important for the DISCO to make a decision and offer an optimal price for attracting customers and winning the competition. Networked microgrids (MGs) at the lower level, as the costumers, intend to purchase energy from less expensive sources in order to minimize costs. There is a bi-level framework with two different targets. The genetic algorithm is used to solve this problem. The DISCO needs to be cautious, so it uses the conditional value at risk (CVaR) to reduce the risk and increase the probability of making the desired profit. The effect of this index on the trade between the two levels is studied. The simulation results show that the proposed method can reduce the cost of MGs as the costumers, and can enable the DISCO as the seller to win the competition with its rivals.
IN active distribution networks (ADNs), energy retailers purchase energy from the wholesale electricity market and sell it to their customers. Therefore, they deal with wholesale prices and loads of unknown customers. In addition, in this retail environment, the principle of competition must be considered so that each customer has the right to choose. In the case of no competition among retailers, they are not cautious and offer prices to the customers with the only intention of increasing their profit. The profit of retailers has an unsustainable nature due to unknown market prices, load demand, and the prices of competitors.
In the past, various strategies were available to reduce the risks of retailers’ decisions in the retail electricity market. In [
The technical, economic and environmental effects of microgrids (MGs) in ADNs have been investigated in previous studies. Three types of demand response programs are considered for the optimal scheduling of electrical and thermal energy consumptions by the customers in [
Additionally, the operation of MGs and DISCO is studied in [
In [
In [
The competitive environment in the bi-level framework of power exchange in the presence of DISCO and MGs as the two different levels of trade is ignored in most literature. The presence of a competitor forces the sellers to improve the quality and balance the offered prices. Moreover, customers will have more options. In this paper, MGs are in the networked mode under a unique beneficiary as costumers, and seek to minimize their costs. Additionally, the DISCO and a rival retailer compete with each other for selling energy. Therefore, the DISCO seeks to maximize its profits in competition with the retailer. There are two levels of trade with two different targets. These two different targets depend on the decision-making by the DISCO to offer optimal prices to MGs.
This paper focuses on the important subject of modeling a bi-level framework, in which, despite the inconsistency between the targets of the levels, the trade between them is fully modeled in a competitive space. Technically, it is very important for the DISCO to make a decision and present an optimal price to costumers in the presence of the rival retailer. Moreover, the objective of the networked MGs as costumers is to minimize the costs. Therefore, the genetic algorithm is used for this problem. The principle of competition in the energy market forces the DISCO to be cautious for winning the competition and sell energy as much as possible. Therefore, by using the genetic algorithm, the DISCO offers the optimal prices to the customers to achieve its goal. In the competition with the retailer, the DISCO employs the CVaR index to include cautiousness in its objective function. The proper selection of a higher weight of cautiousness helps the DISCO make a certain profit with higher probability and less risk. The presented model enables the DISCO to win every competition with rivals. In addition, this case has a considerable impact on reducing the cost of MGs.
The rest of the paper is organized as follows. Section II presents the networked MGs with single management. Section III presents the problem formulation for a competitive bi-level framework for the operation of ADNs. Simulation results are thoroughly discussed in Section IV. Finally, Section V concludes the paper.
The operation of networked MGs means that MGs can interact and access the resources of each other [

Fig. 1 Networked MGs with single management.
ADNs consist of several DGs and interruptible loads (ILs). These resources are utilized in the form of several MGs so that the management of ADNs is facilitated. The nature of the used resources is the same for all MGs. The components considered in each MG are shown in

Fig. 2 Components in each MG.
The operation problem of DISCO and BNMG in the presence of a rival retailer is formulated as a bi-level optimization problem as follows. At the upper level, the DISCO and the rival retailer are introduced as [
(1) |
(2) |
(3) |
(4) |
In the proposed model, the DISCO considers the scenarios of prices offered by the retailer and purchases energy from the wholesale market and sells it to the BNMG. The profit of this trade can be calculated using (1). Accordingly, if , the DISCO has sold power to the BNMG; if , the DISCO has purchased power from the BNMG; and if , no power has been exchanged between the DISCO and BNMG.
(5) |
(6) |
(7) |
(8) |
The objective function of the problem, which is the profit function of the DISCO considering the risk, can be written as:
(9) |
In (9), defines the weight of caution for the DISCO and is conventionally between 0 and 1. We consider its minimum, maximum, and middle values for the CVaR index. The risk-averse operators prefer larger values of to achieve a certain expected profit and win the competition, while risk-lover (seeker) operators prefer smaller values of expecting higher average profit. If the DISCO considers a larger , it has in fact more bias towards CVaR in its objective function, and can achieve the minimum profit with high probability. The lower-level problem in the bi-level framework deals with networked MGs with a single management as described in (10). This problem includes the total cost of MGs , i.e., the cost of the power exchanged with the DISCO, the cost of the power exchanged with the retailer, the cost of generating power by the DG units, and the cost of the IL. The parameters in (10) are defined in (11)-(17) [
(10) |
(11) |
(12) |
(13) |
(14) |
(15) |
(16) |
(17) |

Fig. 3 Competitive bi-level framework of energy trade between wholesale and retail markets.

Fig. 4 Bi-level decision-making leader-follower structure in problem of transactions (bids and offers) among DISCO, retailer, and networked MG.

Fig. 5 Flowchart of DISCO profit problem in a competitive market.
The assumptions of the problem are presented as follows.
1) The model presented in this paper is intended for one hour and will be solved for this period.
2) Power losses in the problem are ignored.
3) DG and IL are considered as the sources of each MG.
In the presented bi-level framework, four MGs are studied as shown in
In this section, the transactions among DISCO, retailer, and BNMG are simulated. The results of the simulations are presented in
Since we intend to solve the problem with more details, three different values are considered for . equal to unity indicates a fully risk-averse DISCO; equal to zero indicates a full risk-seeking behavior; and equal to 0.5 indicates 50% risk-seeking behavior. This coefficient is another input of the optimization problem in this paper. The third column gives the value of the decision-making variable of the DISCO. In fact, the purpose of solving the problem is to obtain the optimal value of this variable. The decision-making variable, which is the optimal price agreed upon by the DISCO and BNMG, is given in the tables for every wholesale price and . For this optimal price, the amount of power purchased by the BNMG from the DISCO, the amount of power purchased from the retailer, the power generated by DGs, and the power from IL resources of the networked MGs are calculated. Moreover, the value of the objective function of the DISCO, profit of the operator, CVaR index, profit of retailer, and MG costs are calculated and presented in these tables.
The simulation results in

Fig. 6 Generated power of MG resources with different prices in wholesale market for .

Fig. 7 Generated power of MG resources with different prices in wholesale market for .
The DISCO intends to maximize the average expected profit, so it trades with MGs at lower prices to compete with the retailer and achieve the guaranteed minimum profit. Based on the results of

Fig. 8 Generated power of MG resources with different prices in wholesale market for .

Fig. 9 Effect of increasing β on retail market prices and overall cost of MGs. (a) Retail market prices presented by DISCO to BNMG. (b) Overall cost of MGs.

Fig. 10 Effect of increasing β on average power sold by retailer and DISCO. (a) Sold by retailer. (b) Sold by DISCO.

Fig. 11 Effect of increasing on average profits. (a) Average profit of retailer. (b) Average profit of DISCO.
Accordingly, the probability of making the minimum expected profit for the DISCO increases, as shown in

Fig. 12 Effect of increasing β on CVaR and objective function. (a) CVaR. (b) Objective function.
It is important to note that if the DISCO takes a risk and does not increase (not being risk-averse), its profit may be reduced considerably and it may not be able to compete with the retailer. Based on (9), an increase in makes the minimum expected profit of DISCO (CVaR) more important than the average expected profit in the objective function. In (9), the objective function of the problem is equal to the weighted sum of the minimum and average profits expected by the DISCO. The risk-averse operators tend to increase and make a minimum profit with less risk, while the risk-seeker operators prefer to decrease and make a higher profit.
In this paper, a risk-based competitive bi-level framework has been modeled for the optimal decision-making in energy sales by the DISCO in an ADN. The ADN including four MGs is considered as the case study. The decision of the DISCO to sell energy in a competitive environment is very important and needs to be taken with caution. As the competitive nature of the energy market urges, the DISCO has to offer the optimal price to the customers to win the competition.
Accordingly, the optimal prices are determined by a genetic algorithm, and the DISCO offer them to the MGs. The existence of competition in selling power in market causes risk for sellers, so the CVaR index is used to reduce the risk in the objective function of the DISCO. This index in the objective function of the problem corresponds to the weighted cautiousness of the DISCO.
Simulation results show that by increasing the weight of CVaR, the power sold by the DISCO increases, while the power sold by the retailer decreases. Therefore, the DISCO is satisfied with a certain amount of profit (rather than with high profit) and keeps offering lower prices to the customers to compete with the retailer. However, the profit of the retailer as the rival of the DISCO falls sharply, and the DISCO wins the competition. Another achievement is the reduction of the overall cost of MGs by increasing the weight of CVaR in the objective function. Consequently, the impacts of market price and CVaR on the decision-making at both levels of the proposed model are clearly investigated. The results reveal that the proposed bi-level optimization enables the DISCO to win the competition with rivals and achieve its expected profit in any situation.
NOMENCLATURE
Symbol | —— | Definition |
---|---|---|
A. | —— | Indices |
j | —— | Index of microgrids (MGs) |
Meanw | —— | Average value in each scenario |
N | —— | Number of scenarios |
w | —— | Scenario of price offered by distribution company (DISCO) |
B. | —— | Parameters |
—— | Probability of a certain profit | |
—— | The maximum price of exchange between DISCO and MGs |
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