Multi-agent electricity markets: Retailer portfolio optimization using Markowitz theory

https://doi.org/10.1016/j.epsr.2017.02.031Get rights and content

Highlights

  • A new optimization model to solve the retailers’ portfolio of end-use electricity consumers optimization problem, using a risk–return optimization to compute the portfolio and Markowitz theory to establish the efficient frontier.

  • The model evaluates the risk (Value-at-Risk (VaR)) and return of mixing different shares of end-use customers in a retailer's portfolio.

  • The retailer's risk attitude is a crucial parameter used to establish a difference between the importance given to risk and expected return in the optimization problem.

  • We adapt the Markowitz theory to establish the efficient frontier for the portfolio, in order to only obtain a share of customers that result in a point (axis: VaR, expected return) inside the efficient frontier.

  • Development of case-studies to define the optimal portfolio of clients for retailers in specific markets. We performed three case-studies using real data of the Iberian market. Considering better tariffs to consumers, we obtained portfolios that lead to reasonable returns and smaller risk to retailers. We also concluded that by being more restricted and efficient in relation to the share of consumers in the portfolios, retailers can offer more competitive tariffs.

Abstract

The major electricity market models include: pools, bilateral contracts and hybrid models. Pool prices tend to change quickly and variations are usually highly unpredictable. In this way, market participants can enter into bilateral contracts to hedge against pool price volatility. In bilateral contracts, market participants can set the terms and conditions of agreements independent of the market operator. The hybrid model combines features of both pools and bilateral contracts.

This paper is devoted to risk management and the optimization of the portfolios of retailers operating in liberalized electricity markets. It introduces a model for optimizing portfolios composed by end-use consumers using the Markowitz theory. It also presents an overview of a multi-agent system for electricity markets. The system simulates the behavior of various markets entities, including generating companies, retailers and consumers. The final part of the paper presents three case studies on portfolio optimization involving risk management: a retailer (a software agent) optimizes its portfolio by taking into account the attitude towards risk and the offer of a 3-rate tariff to five different types of consumers: industrial, large and small commercial, residential and street lightning. The results show that the retailer, by being more realistic in choosing consumers to its portfolio, can offer more competitive tariffs to key consumers and keep the portfolio optimal and stable in relation to the risk–return ratio.

Introduction

Hunt and Shuttleworth [1] propose four models to chart the evolution of the electricity supply industry towards full competition: regulated monopoly, purchasing agency, wholesale competition, and retail competition (see also [2]). Three major market models have been considered to achieve the key objectives of ensuring a secure system and facilitating an economical operation [2], [3]: electricity pools (day-ahead and intraday markets), bilateral transactions (forwards, futures, options and contracts for difference) and hybrid markets. The negotiation of bilateral contracts will only converge to agreement if both sides can find a pool/bilateral mix that provides an acceptable compromise between risk and benefit [4], [5], [6]. This is one of the problems that retailers face when defining their portfolios of consumers.

Typically, electricity retailers buy energy in spot markets and sign bilateral contracts (e.g., forwards) with producers in order to satisfy customers. Retailers often follow a business as usual strategy with the objective of maximizing revenue, i.e., they give small discounts to consumers to attract them. The discounts depend on the consumption profile of each customer (residential, commercial, industrial, etc.), but normally are similar for customers with similar consumption profiles. Hence, there is no “discrimination” between consumers with a particular consumption profile. However, the discounts are mainly made in promotional campaigns to obtain new customers, i.e., old customers do not normally have additional benefits with new campaigns. This business as usual strategy may lead to some problems regarding the loyalty of customers, specially customers that care more about the electricity cost than with the energy provider or the relation between the two. Other problem is the customers’ risk, namely retailers do not usually differentiate between customers with similar consumption profiles, and by pursuing the objective of increasing the number of clients to increase the revenue (absolute values), they use a strategy that maximizes the revenue, instead of maximizing the return and minimizing the risk associated with the customers in the portfolio (relative values). Accordingly, retailers consider large portfolios that can potentially lead to high revenues, but may involve high risks, and frequently require large investments (due to their dimension). Simply put, retailers consider large portfolios that bring a significant volatility to their revenues.

In this paper, we focus on the dual objective of maximizing the return and minimizing the risk associated with portfolios composed of end-use customers. This can be done by differentiating between similar customers and selecting specific customers. In particular, differentiating between customers by proposing different tariffs to consumers of a specific type, but with different consumption patterns. Selecting customers by proposing better tariffs to customers that can benefit retailers (and rejecting or proposing worse tariffs to customers that can impair the portfolio, instead of accepting all customers). Proposing better tariffs to key customers, in relation to other competitive retailers, and having a special care to update these tariffs by taking into account market prices, consumption patterns and promotional campaigns, can be important to increase key customers’ loyalty, keeping the portfolio more stable in terms of risk–return.

Thus, this paper is devoted to both risk management (in bilateral contracting) and optimization of retailers’ portfolios. It presents several key features of software agents able to compute an optimized portfolio composed by end-used customers, paying special attention to risk management, notably pricing strategies, a dual-objective optimization model for dealing with risk and return (maximizing the return and minimizing the risk), and also the influence of the risk attitude in the composition of the portfolio. The risk attitude (also known as risk preference or risk appetite) of agents plays an important role in their negotiation behavior, imposing limits to the trading margin and thus influencing the negotiation offers. The risk attitude can be classified as risk-averse, risk-neutral and risk-seeking. As expected, higher risk attitudes influence more the negotiation behavior of the agents.

There are several approaches to deal with portfolio management [7], [8], but they mainly refer to the optimization of assets, especially in the stock exchange, which was the initial purpose of the Markowitz theory [9]. In relation to electricity markets (EMs), the most important pieces of work about portfolio optimization focus on strategic bidding [10], [11], where the authors try to obtain the optimal quantity of electricity to buy or sell in different market types. In Ponsich et al. [12], the authors provide a survey of algorithms to solve the portfolio optimization problem for other real-world applications (i.e., applications different of the EM). In Rockafellar et al. [13], the authors consider a new approach for simultaneous calculation of the value-at-risk (VaR) and the optimization of the conditional VaR (CVaR) for a broad class of problems.

The electricity market has several players with the objective of trading electricity. The aggregators [14], [15] and the traders [16], [17] are the players that play a role similar to that of the retailers [19]. However, their inherent market behavior is different, so these two types of agents will not receive our preponderance in this work. Now, there are other approaches related to the electricity sector similar to ours [16], [17], [18], [19], [20]. Teive et al. [16] proposed an approach for solving the contract portfolio optimization problem by using a multi objective genetic algorithm. In [17], the authors proposed a decision support system for solving the problem of contract portfolio optimization — choose the best set of market options to sell or buy electricity — by using linear programming, and also to perform a risk analysis of the portfolio performance, using VaR and CVaR metrics. In this piece of work, traders act as speculators, so they do not have fixed end-use consumers in the demand-side neither fixed generators in the supply-side. Basically, they aim at optimizing the revenue by trying to buy electricity at low prices and selling it at higher prices. The authors developed a case-study where a trader have: (i) to buy 1000 MWh of energy both in the spot market (500 MWh), and by signing forward contracts (500 MWh) and then (ii) sell this energy quantity by considering forward and option (call or put) contracts. The optimization problem consists in choosing the quantity of electricity to sell trough these types of contracts. Our major objectives are different from that of the previous two publications [16], [17]. In particular, we have the goal of obtaining an optimized portfolio of end-use consumers by introducing a multi-agent system (MAS), pricing strategies for defining tariffs, and a decision making process taking into account the Markowitz theory.

Suksonghong et al. [18] studied the application of several genetic algorithms to the portfolio optimization problem of a generating company (GenCo). The optimization of the GenCo's portfolio consists in choosing the best allocation of the produced electricity to the spot market and forward bilateral contracts. The authors aim at analyzing the performance of different genetic algorithms to solve this problem. Hatami et al. [19] developed a decision support framework for electricity retailers that need to purchase electricity to satisfy their clients. The objective is to optimize the electricity purchasing options between the spot market, forward contracts, call options, interrupted contracts and self-generating facilities. This approach is different from ours, because the authors consider a fixed number of clients and optimize the portfolio of markets options to purchase electricity. Here, we take into account the spot market prices to choose the best group of clients (portfolio optimization) with whom each retailer wants to sign forward contracts.

Kazagic et al. [20] aimed at defining the best power generators in order to achieve specific targets related to renewable energy sources penetration and decarbonization. They try to solve the problem of designing a power system with several generators (the portfolio). They optimize the share of each generator in the electricity production in order to achieve specific environmental targets.

After performing an analysis of the bibliography related to retailers and portfolios optimization, we concluded that there is a small number of pieces of work that address the problem of defining optimized portfolios of end-use customers. The majority of studies consider the supply-side point of view, consisting in defining the best markets for power producers selling their electricity. From the demand-side point of view, the existing studies consist mainly in optimizing the quantity of electricity (a fixed number of contracts with consumers) that must be bought in different markets (day-ahead, forward, etc.) in order to satisfy the electricity required by consumers. Teive et al. [16] performed some work similar to ours, but as explained before, they only consider the optimized electricity quantity (fixed) that a trader wants to sell in a bilateral transaction, i.e., they do not characterize consumers neither take into account their load profiles (variable consumption).

In this work we pursue a different objective, since we try to define efficient groups of consumers with different load profiles by optimizing the risk–return output. Basically, we consider that retailers sign forward contracts with several end-use consumers (industrial, commercial, residential and street lightning) and buy electricity from the day-ahead market. Then, we compute the Markowitz frontier by both using several pricing strategies (i.e., strategies for offering tariffs to consumers) and taking into account the retailers risk attitude. Following this, we define efficient portfolios by considering the Markowitz frontier (see Section 3 for more details).

The work presented here refines and extends our previous work on the day-ahead electricity market [21], [22], and mainly in the area of automated negotiation between different parties based on a generic negotiation model [23], [24], which was adapted to the negotiation of bilateral contracts between sellers and buyers of electricity [25], and extended with strategies to hedge against spot prices volatility [26], [27]. In [28], we present a deterministic approach to the trader problem, i.e., we introduce a model for optimizing a retailer's portfolio of consumers. The work described in this article is the most similar to the work presented here. Both pieces of work try to obtain an optimized portfolio of consumers, but the approach adopted in [28] is limited, by considering the past only, i.e., we know the past market prices and the consumers’ consumptions and by using a deterministic algorithm we obtain the optimized portfolio for a specific period of time (e.g., one week). In this paper, we aim at obtaining the optimized portfolio of consumers for the future, by taking into account the market price volatility and the consumption variability of end-use consumers along time.

Specifically, the purpose of this article is threefold:

  • 1.

    To develop a model for optimizing the portfolios of retailer agents (composed by end-use customers), using risk management and the Markowitz theory;

  • 2.

    To extend a multi-agent system to simulate EMs, by modeling retailer agents (equipped with the above model) and different consumer agents, namely residential, commercial, industrial and street lightning (see [28] for more details about the different types of consumers).

  • 3.

    To develop three case-studies to illustrate (and test) the model. The case studies involve a retailer (software agent) that wants to optimize its portfolio of clients using real data from the Iberian Market (MIBEL). The retailer is a moderate risk-averse agent.

In the three aforementioned case-studies, we perform three simulations, using the following pricing strategies:

  • Simulation 1 – “Equal tariff” strategy;

  • Simulation 2 – “Equal tariff” and “Minimize the VaR of a tariff at a minimum return” strategies;

  • Simulation 3 – “Equal tariff” and “Minimize the VaR of a tariff at a minimum return” strategies, with a market price forecast.

The main results of the article are summarized in Table 1. For moderate risk-averse retailers, we can conclude that they will only want consumers of the following types: small commercial (SCom), street lightning (SL) and industrial (Ind). This occurs because SCom consumers lead to higher returns (relative values), SL consumers mitigate risk (lower VaR) and Ind consumers lead to higher absolute returns (they are favorable when retailers desire a portfolio with high revenues). Large commercial (LCom) consumers have a consumption pattern similar to SCom consumers, but give a lower relative return. So, when both types of consumers (SCom and LCom) are considered, they increase the risk of the portfolio. Thus, for risk-averse retailers, LCom consumers are not favorable in portfolios with a substantial share of SCom consumers. Residential (Res) consumers have a consumption pattern with high volatility, so they increase the risk of the portfolio. Res consumers are only favorable in cases where they give high returns to retailers (risk seeking agents). For risk-averse retailers, they can be favorable when risk mitigation measures are applied, such as risk sharing [27].

The remainder of the paper is structured as follows. Section 2 describes some aspects of bilateral contracting and risk management. Section 3 introduces a model for the optimization of a retailer's portfolio of clients. Section 4 presents an overview of the multi-agent system (MAS) and illustrates graphically the main steps of the simulations performed. Section 5 presents three case studies on portfolio optimization and risk management. Finally, concluding remarks are presented in Section 6.

Section snippets

Bilateral contracting and risk management

Either physical or financial, a bilateral contract is typically negotiated weeks or months prior to its delivery and can include the following specifications [2]: (1) starting date and time, (2) ending date and time, (3) price per hour (€/MWh) over the length of the contract, (4) variable power (MW) amount over the length of the contract, and (5) range of hours when the contract is to be delivered. In a more general form, the MW amount, contract length and price could be time-varying. This

The problem

Consider a retailer operating in an electricity market constituted by several consumers with different load profiles. The retailer wants to sign a forward contract with a set of consumers, and then to satisfy their energy needs, submits bids to buy energy at the pool market (day-ahead market). Taking into account the aforementioned phases of the risk management process, the following risk factors can be considered: day-ahead market price volatility, variability of electricity consumption of

Multi-agent system

The principal components of the multi-agent system under development include a graphical user interface (GUI), a simulation mechanism, and a number of domain-specific agents. The graphical user interface allows users to set agent-specific parameters, specify and monitor trading simulations, and perform a variety of administrative tasks such as saving simulations (see Fig. 5). The simulation mechanism does not depend on any domain-specific knowledge and controls all trading simulations. The

Case studies on portfolio optimization

The following three case studies illustrate how retailers can choose optimal portfolios of clients depending on their risk attitude and pricing strategies (i.e., the tariffs offered to consumers). Each case-study involves a specific retailer agent, namely James Owen (a software agent), CEO of Retail Energy Service, an experienced electricity retailer in Europe that is studying the Portuguese electricity market in order to start operating on it. James Owen buys energy in the electricity pool,

Conclusion

This article has presented a formal description of a model for optimizing the retailers’ portfolio of clients. Also, this article has presented an overview of a multi-agent system to simulate energy markets, placing emphasis on the interaction between retailers and end-use customers. In addition, the article has presented three case-studies to test the optimization model using real data from the Iberian electricity market (MIBEL). The model was tested by considering a moderate risk-averse

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    This work was performed under the project MAN-REM (FCOMP-01-0124-FEDER-020397) and PD/BD/105863/2014 (H. Algarvio), supported by FEDER Funds through the program “COMPETE-Programa Operacional Temático Factores de Competividade” and National Funds through “FCT-Fundação para a Ciência e a Tecnologia”.

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