Elsevier

Applied Energy

Volume 236, 15 February 2019, Pages 985-996
Applied Energy

Credit rating based real-time energy trading in microgrids

https://doi.org/10.1016/j.apenergy.2018.12.013Get rights and content

Highlights

  • A credit rating based multi-leader multi-follower game is proposed.

  • A best response algorithm is designed to obtain the unique equilibrium strategy.

  • The impact level of transmission losses on trading behaviors is discussed.

Abstract

In this paper, we investigate the problem of credit rating management in energy trading among microgrids subject to transmission losses and wheeling cost. The main concern is how to constrain the default behaviors of retailers to enable all the consumers and retailers to be actively involved in the energy trading. By endowing retailers as leaders and consumers as followers, we establish a multi-leader multi-follower dynamic game model and propose a scorecard model based on logistic regression to evaluate retailers’ credit ratings. The concept of trust degree is then introduced for all the retailers as a punitive measure to relate their credit ratings with the reduction in the profit. With such a strategy, we can theoretically show that a unique equilibrium exists for the dynamic game model. Moreover, a best response algorithm is proposed to make the consumers and retailers achieve the equilibrium iteratively. Numerical simulations are provided to demonstrate the effectiveness and efficiency of the proposed method. It is found that default behaviors of selfish retailers can be greatly constrained with only a slight degradation of the interests of other participants, thereby promoting the establishment of a trustworthy trading market. We also discuss the influence level of transmission losses on trading behaviors of retailers and consumers.

Introduction

As an emerging platform for energy supply-demand coordination, energy-cyber-physical systems (e-CPSs) have appeared [1]. Such systems face many challenges, especially insufficient supply or oversupply due to the intermittent nature and highly variable supply of renewable energy generations [2]. As an essential component of e-CPSs, microgrids can be used to solve the above problem by establishing energy trading markets [3]. To be specific, the microgrids with rich production capacity act as retailers while those with insufficient production capacity act as consumers. Through energy trading, retailers and consumers can fulfill their own needs, simultaneously achieving energy complementation across microgrids in the distribution network without further stressing the macrogrid [4].

Recently, many efforts have been devoted to designing efficient and economical market-based energy trading mechanisms [5]. For instance, Ref. [6] proposed a distributed energy management mechanism between generators and energy users to maximize the social welfare, which, however, suffered from certain fairness issues. Considering this, Lee et al. in [7] presented a power pricing scheme based on coalitional game, which could realize a fair distribution of revenue between electricity suppliers and energy users. As an extension, Wang and Huang [8] studied an incentive mechanism for forming coalitions based on the Nash bargaining theory to achieve proactive energy trading. Note that in energy trading markets, different retailers generally have different retail prices. Motivated by this observation, Ref. [9] investigated a discriminate pricing scheme to ensure an envy-free market trading atmosphere. Different from the above works, the energy users’ dishonesty was taken into account in [10]. The authors designed a Vickrey-Clarke-Groves mechanism to motivate energy users to provide true information when bidding for energy. This mechanism can maximize the social benefits of all participants instead of individual interests.

Since market participants are selfish in general, both retailers and consumers will pursue their own interests instead of the social benefits, leading to a non-cooperative market. To characterize such trading behaviors of both energy supply and demand, Stackelberg game is widely exploited to model and analyze trading problems in the market [11]. It has a hierarchical structure for sequential decision making by dividing all participants into leaders and followers [12]. For example, Stackelberg game was used to investigate the impact of coal-electricity price linkage policies on the enterprises [13]. Likewise, Yu et al. formulated the interactions between a utility company and energy users, presenting a single-leader multi-follower (SLMF) game model [14]. In the presence of unknown utilities of energy users, Ratliff et al. in [15] proposed to estimate the utilities first based on first-order necessary conditions for Nash equilibria, and then established a reversed Stackelberg game model between a building manager and energy users. However, the SLMF model fails to characterize an energy market with multiple energy sellers and multiple buyers efficiently. Another thread then prevails, where a framework of multi-leader multi-follower (MLMF) is presented. In this regard, Ref. [16] investigated the multiple energies trading for an integrated energy system. Ref. [17] combined the SLMF and MLMF to propose a two-loop leader-follower game model to capture the interactions among different types of market participants spanning from generators, the grid operator, service providers to energy users. One main characteristic of energy trading is the energy transmission cost, e.g., transmission losses [18] and the wheeling cost [19]. It is of note that most of the above works assume that there is no transmission cost for both the retailers and consumers to simplify the theoretical analysis. However, such practical issues probably affect the trading behaviors and interests of both supply and demand sides. This topic is still largely unexplored.

Another pressing issue is the credit of the participants in an energy trading market. Note that the market participants are selfish in general. They are prone to default for better profit. Such a behavior is clearly harmful to the interests of others, sapping participants’ enthusiasm, even leading to market collapse. In this manner, how to establish an effective credit management to constrain the default behaviors of retailers, guaranteeing active participation of both retailers and consumers, is urgent.

At present, there are several related works about credit assessment in the banking industry [20], peer-to-peer lending [21], life insurance [22], etc. The first stream of works adopt artificial intelligence techniques, e.g., Support Vector Machines [23], in risk assessment problems. Ref. [24] further improved the performance by taking individual transaction history data into account. A dynamic modeling framework with the ability of sensing themselves and learning adaptively was investigated in [25]. However, these artificial intelligence techniques still lack clear interpretability, from which it is hard to get an intuitive explanation about the obtained results. The second stream of works focus on statistic methods and optimization models. Ref. [26] utilized the logistic regression analysis to evaluate the risk assessment of China’s peer-to-peer network platform. A multinomial logit approach was proposed in [27] to improve the predictive performance of binomial logit models. Different from the above works which is only devoted to credit assessment, Ref. [28] further estimated the expected loss based on the default probability obtained by a logistic regression model. As for the energy trading field, we find that few of the existing works have investigated the credit rating management. It is promising but challenging to constrain retailers’ default behaviors while simultaneously maximizing the benefits of both retailers and consumers and ensuring fairness.

In this paper, we aim to solve the above practical issues and focus on investigating the credit rating management in energy trading. Specifically, we propose a scorecard model based on logistic regression to constrain the default behaviors of retailers by punishing those with low credit ratings. Taking transmission losses and wheeling cost into account, a credit rating based multi-leader multi-follower dynamic game model is established to maximize the welfare of retailers and minimize the purchasing cost of consumers. Theoretically, it is shown that the proposed credit rating management enables the existence of a unique pure equilibrium strategy. A best response algorithm is then proposed to obtain the unique equilibrium strategy, which guarantees the objective of each market participant. It is found that default behaviors of selfish retailers can be greatly constrained with only a slight degradation of the interests of other participants, thereby promoting their active participation and the establishment of a trustworthy trading market.

The remainder of this paper is organized as follows. Section 2 presents the system model across the network. Section 3 introduces the credit rating management to assess each retailer’s default behaviors. The MLMF dynamic game model based on the credit rating management is elaborated on in Section 4. The existence and uniqueness of the equilibrium strategy have been proved and a best response algorithm is also described. Numerical results are shown in Section 5, while Section 6 concludes this paper.

Section snippets

System model

We consider a realistic scenario of the distribution network, where a number of microgrids equipped with renewable energy generators, e.g., wind and solar power generators, and battery energy storage systems (BESSs) trade energy with each other. A schematic diagram is shown in Fig. 1 for illustration (see also Table 1, Table 2 for the description of the used symbols). In this paper, we focus on a real-time energy trading, where one day is divided into T time periods, T={1,,T}, with a fixed

Credit rating management

In this section, a scorecard model based on logistic regression is proposed to estimate default probabilities of retailers, built on which punitive measures are taken to constrain default behaviors of those retailers with low credit ratings. The credit rating management is periodically assessed by a credit rating company as shown in Fig. 1.

Pricing and energy scheduling

In this section, we formulate the pricing and energy scheduling problem as a MLMF game based on the credit rating management. In period tT, each retailer jNrt as a leader determines its retail price Pjt and the sales iNctEi,jt to maximize its payoff Zjt. Each consumer i as a follower chooses its purchases Di,0t,Di,jt (jNrt) to minimize its purchasing cost zit. The model is formally defined asΩt=NrtNct,{Sjt}jNrt,{sit}iNct,{Zjt}jNrt,{zit}iNct,where Sjt={iNctEi,jt,Pjt} and sit={Di,0t,D

Simulation evaluations

In this section, we shall provide extensive simulation results to validate the effectiveness of the proposed method. We consider a distribution network consisting of 10 microgrids shown in Fig. 4(a). We use the data set collecting the hourly solar and wind power productions at several different locations in Hong Kong [32] as the power generations of microgrids for the following simulations studies. Fig. 4 (b) depicts the power generations (power output per kW capacity) of five microgrids, i.e.,

Conclusion and future work

In this paper, we investigate the problem of credit rating management for real-time pricing and energy scheduling among microgrids, which is the pressing issue faced by the energy-cyber-physical systems. A multi-leader multi-follower game model is formulated and the equilibrium strategy is proved to uniquely exist. The equilibrium strategy guarantees that all market participants achieve their own optimal objectives and keeps fairness among consumers. A best response algorithm is proposed to

References (36)

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This work is supported by National Key Research and Development Program of China (Grant No. 2016YFB0901900), National Natural Science Foundation of China (Grant Nos. 61603215, 61521063), and Natural Science Foundation of Shanghai (Grant No. 18ZR1419900).

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