Energy exchange among heterogeneous prosumers under price uncertainty

Highlights

• We study the impact of P2P energy exchange on the value of a joint PV investment.

• We determine the optimal size of each prosumer PV plant with P2P exchange of energy.

• Prosumers are characterized by different self-consumption profiles.

• The price of exchanged energy is uncertain and depends on purchase and sale prices.

• The feasibility depends on the shape of the individual demand and supply curves.

Abstract

In this paper, we provide a real options model framing prosumers’ investment in photovoltaic plants. This is presented in a Smart Grid context where the exchange of energy among prosumers is possible. We determine the optimal size of the photovoltaic installations based on the influence the self-consumption profiles on the exchange of energy among prosumers. We calibrate the model using figures relative to the Northern Italy energy market and investigate the investment decision allowing for different prosumer profiles and consider several combinations of their individual energy demand and supply. Our findings show that the shape of individual energy demand and supply curves is crucial to the exchange of energy among prosumers, and that there could be circumstances under which no exchange occurs.

Introduction

The last decade has witnessed the increasing use of renewable energy sources as alternative to fossil fuels. Policymakers have widely encouraged such processes to achieve decarbonization targets. In this context, even though much effort is still required to achieve a sustainable energy production, a number of distributed power plants have been installed in Italy and in other EU countries.¹

Compared to fossil fuels, renewable energy sources are known to be beneficial, but in load curves comparisons are often characterized by inflexible production which makes management of the electricity grid challenging (for instance, in terms of inefficiency, congestion rents, power outages, etc.). In particular, photovoltaic (PV) production shows a certain variability depending on daily and seasonal solar irradiation, which constraints (i) covering night-time demand and (ii) handling peak demand since energy production is concentrated only in certain daily time slots. Therefore, innovation in the energy system should see it benefit from the introduction of digitalization in the development of so-called smart grids (SG)² which can be defined as “robust, self-healing networks that allow bidirectional propagation of energy and information within the utility grid”.³

Such a technological transformation is exemplified by three fundamental elements: (i) the continuous integration of Distributed Energy Resources (DER), (Sousa et al., 2019, Bussar et al., 2016, Zhang et al., 2018),⁴; (ii) the massive introduction of Information and Communication Technology (ICT) devices (Saad al-sumaiti et al., 2014); and (iii) the central role of prosumers’⁵ production and consumption choices (Luo et al., 2014, Sommerfeldt and Madani, 2017, Espe et al., 2018, Zafar et al., 2018).

The SG context allows energy market players to adopt new behaviors. This is particularly relevant to traditional consumers who, characteristically passive in buying and receiving energy from the centralized grid, gain the opportunity to proactively manage their consumption and production (Zafar et al., 2018), reducing their energy consumption costs by self-consuming the energy produced by their PV plants (Luthander et al., 2015, Masson et al., 2016) as well as integrating effectively and efficiently into the electricity markets (Parag and Sovacool, 2016).⁶

Indeed, the EU’s Clean energy for all Europeans package ⁷ establishes a new legal framework for the internal energy market and devotes particular attention to the potential economics and environmental benefits for consumers. The EU Directive 2018/2001⁸ formally introduces the renewables consumers and sets out the elements necessary to ensure the promotion and widespread uptake of this status.

As is widely acknowledged by researchers in this field, SG deployment, as well as its development, is also strictly related to the peer-to-peer (P2P) energy trading concept.⁹

Exchange P2P represents “direct energy trading between peers, where energy from small-scale DERs in dwellings, offices, factories, etc, is traded among local energy prosumers and consumers”(Alam et al., 2017, Zhang et al., 2018).¹⁰ Households and firms, as well as public authorities, can participate directly in the energy transition by co-investing in, producing, selling and distributing renewable energy. For these new players, the benefits arising in the energy markets range from their positive contribution in helping utilities to solve energy management issues (Zafar et al., 2018) as well to boosting investments in renewable energy plants, thanks to the potential savings gained from cooperative investment decisions and the new flexibility in energy sourcing options. It is nonetheless important to note that these positive impacts strictly depend on the costs of adopting the technology and the shape of the demand curve of the agents involved.

The effects of direct exchange of energy among prosumers on SG deployment, have been analyzed and developed by researchers offering different perspectives and exploiting various approaches.¹¹ A wide strand of this literature focuses on the study of the microgrids, as communities of prosumers, paying particular attention to their relationship with the electricity network, as well as to the behavioral characteristics of prosumers. Researchers have also recognized the significant need for a proper market design for the prosumer era (Parag and Sovacool, 2016, Morstyn et al., 2018). Several optimization techniques have been used to investigate prosumers’ behaviors in self-consumption, exchange and investment choices (Zafar et al., 2018, Angelidakis and Chalkiadakis, 2015, Razzaq et al., 2016), with most focusing on cost minimization (Liu et al., 2018). Alternative approaches are provided instead by Gonzalez-Romera et al. (2019), in which the benefit to prosumers is determined by minimizing the exchange of energy, rather than its cost and by Ghosh et al. (2018), where the price of P2P exchanged energy is defined with the aim of minimizing the consumption of conventional energy, notwithstanding the prosumers’ aim is of minimizing their own payoffs.

Yet, there remain still several interesting themes related to this topic that require further development, such as whether the additional flexibility provided by exchange P2P has value, how it might affect investment decisions, and whether it can be supported by data. Some of the literature has attempted to answer these questions by studying the possible combinations of agents in a microgird context (Mishra et al., 2019), or focusing on decentralized energy systems under different supply scenarios (Ecker et al., 2017, Talavera et al., 2019), investigate the PV plant sizing problem from the perspective of cost competitiveness and self-consumption maximization whereas Jiménez-Castillo et al. (2019) exploit the net present value (NPV) technique with a similar purpose but also focus on economic profitability. To the best of our knowledge, problems entailed in the possibility of matching load and supply curves in an uncertain environment, as well as in an exchange P2P framework, are yet to be investigated under this perspective.

This paper contributes to the real options literature studying investment in infrastructure for the production and exchange of energy.¹²

Among contributions to these field, those closest to ours are:  Bertolini et al. (2018) and Castellini et al. (2021), on the optimal plant sizing and investment decisions under uncertainty; Luo et al. (2014), focusing on the impact of cooperative energy trading on renewable energy utilization in a microgrid context; Zhang et al. (2018), who investigate the feasibility of P2P energy trading with flexible demand; Gonzalez-Romera et al. (2019), which develops a minimization problem with the aim of minimizing the energy exchange in a framework of two prosumer households; and Bellekom et al. (2016), whose agent-based model was developed in a residential community context under different prosumption scenarios.

Our paper provides a theoretical framework for modeling the decision of two agents¹³ to invest in a PV plant, assuming they are integrated into an intelligent network (i.e. in a SG context), where exchange P2P is possible. Each agent can produce energy, self-consume it, and close any gap between their production and consumption needs by trading with both the national grid (N) and the other agent. Thanks to the technical structure of the SG, they can also sell energy directly to the energy market for a stochastic price.¹⁴ Finally, each agent can buy energy from an energy provider that operates on the national energy market under a long-term contract at a fixed constant price, while the price for the exchange of energy P2P (between the two prosumers) is modeled as a weighted average of the two prices for buying and selling energy from and to the energy market. The investment decision is irreversible and taken cooperatively to allow prosumers to exchange energy P2P. Due to the high uncertainty over demand evolution and market prices, technological advances, and ever-changing regulatory environment (Schachter and Mancarella, 2015, Schachter and Mancarella, 2016, Cambini et al., 2016), we build a real options (RO) model to capture the value of managerial flexibility associated with the operation of the plant. In a two-agents context, our purpose is to understand the characteristics of their supply–demand profiles that favor the exchange of energy and whether they are compatible with the existence of an exchange P2P framework. Secondly, we identify the size of the PV plant that maximizes the joint benefit of the two agents and, finally, focus on the quantity of energy exchange P2P and the self-consumption profiles which allow prosumers to attain the highest economic savings.

While the value of self-consumption and exchange (Bertolini et al., 2018, Castellini et al., 2021) are two topics already studied in the literature, inquiry into the conditions for the initiation of an exchange P2P structure in a two-agent RO framework and the calculation of exchange energy rates is, to the best of our knowledge, novel.

To address this, we study the investment decision under different prosumers’ behaviors, taking into account all possible combinations of energy demand and supply for the two agents in exchange P2P. These are summarized in four scenarios we consider. Scenario 1 refers to the case of an excess of supply from both prosumers. Scenario 2 conversely focuses on an excess of demand. Scenario 3 describes the case where prosumer 1 needs no more than the amount the prosumer 2 could provide, while prosumer 2 needs more than what prosumer 1 can provide. Scenario 4 instead analyzes the case whereby prosumer 2 needs no more than what prosumer 1 could provide, while prosumer 1 needs more than the amount prosumer 2 can provide. Each scenario is therefore characterized by constraints in terms of energy exchange between the prosumers, leading to specific conditions with which the prosumers’ self-consumption behaviors must comply to assure the feasibility of the scenario. To calculate the feasibility of our scenarios, we calibrate our model by using Italian energy market data. Model calibration is performed on a dataset built using Italian Zonal Electricity Prices to obtain the parameters of the stochastic price paid to the prosumers for the energy sold to N. The cost of the investment is determined using the methodology of Bertolini et al. (2018) and the other parameters refer to data provided by EUROSTAT, the International Renewable Energy Agency (IRENA) and International Energy Agency (IEA).

The main findings of our paper are here briefly listed.

• All four scenarios show some feasible conditions for energy exchange and only a few have economic significance and are feasible in reality.

• Among these, the profiles assuring the maximum benefit (NPV of the generated savings), are characterized by perfectly asymmetric and mutually complementary demand functions: agents produce, consume and exchange energy in such a way as to cover each other’s opposite daytime demand functions. If they have an excess supply (as in the case of scenario 1) they also sell some of their production to $N$ in order to maximize the benefit. If they have excess demand (as in the case of scenario 2), they sell nothing to $N$ but cover all their daytime demand with their own energy production.

• The scenarios showing the lowest savings are the two asymmetric scenarios (3 and 4) characterized by excess demand for one agent and excess supply for the other, and vice versa. The combination which guarantees the existence of the exchange P2P framework is that whereby one agent produces to self-consume and sell, and the other agent buys the surplus of the other agent and sells all of its production to the grid. The maximum savings are guaranteed by the two agents cooperating in such a way that one of them allows the other to maximize their own earnings. Under a cooperative perspective, the gain is shared between the agents. In this context, it is observed that one agent invests in an over-sized PV plant, while the other chooses a plant size similar to those identified in scenarios 1 and 2.

• In all scenarios, although the prosumers are characterized by different supply–demand profiles, very similar total savings are achieved. This depends on the possible combinations of production, self-consumption and energy exchange. In some cases, this involves making the most of mutual exchange, in other cases producing and exchanging with N, so as to reduce energy costs. The best case (i.e. having the highest NPV), however, is that where the prosumers are characterized by excess supply and asymmetric and complementary load curves.

By comparing of the feasible solutions and the daily 24-hour load curves we are able to identify, for each scenario, the optimal combinations to maximize prosumers’ savings.

The paper now proceeds as follows: in Section 2, we present the basic set-up of our model. In Section 3, we identify the expected net energy cost to be borne by each prosumer once the PV project is activated. In Section 4, we set the optimization problem aiming to identify the optimal capacities of the prosumers’ PV system and describe our four exchange P2P scenarios. For each of the latter, we find analytically the respective prosumers’ optimal capacities (detailed in Appendix A.4). In Section 5, we present the model calibration. Section 6 presents and discuss our main results. Appendix concludes.