The Economics of Demand-side Flexibility in Distribution Grids.

• Author: Nouicer, Athir

1. INTRODUCTION

   The Clean Energy Package (CEP) Directive (EU) 2019/944 calls on the Member States to develop regulatory frameworks that incentivize distribution system operators (DSOs) to consider the use of flexibility as an alternative to grid expansion. DSOs will have to develop and publish network development plans that make a trade-off between the use of flexible resources and system expansion. How this will be implemented is one of the main open issues in the evolution of electricity markets in Europe (Meeus, 2020).

   There are only a few studies that focus on this trade-off. BMWi (2014), a study for the German energy ministry, finds that allowing DSOs to curtail up to 3% of Distributed Generation (DG) would save about 40% of the network expansion cost. ENEDIS (2017) considers the costs and benefits of six flexibility options, both on the demand and supply sides, and finds that they may provide critical net gains by 2030. At the EU level, CE and VVA Europe (2016) developed an impact assessment report for the European Commission that estimates up to [euro]5 billion annual savings in the EU by avoiding distribution investments towards 2030 from both demand and supply sides flexibility. More recently there were several local flexibility projects implemented in EU Member States and the UK, led by DSOs, TSOs, both or independent operators such as Piclo Flex in the UK (Frontier Economics and ENTSO-E, 2021). For DSOs, many use cases are identified in Jarry and Servant (2021), from which the most advanced are for grid planning: investment deferral and permanent embedded solution, and for grid operation: demand congestion, high-voltage injection congestion and outage management. In the UK, Germany, Sweden, the Netherlands and France, 2 GW of flexibility were contracted in 2020. A large part of it is in the UK, with 1463 MW and in Germany with 400 MW (Jarry and Servant, 2021). Some flexibility projects, e.g. the German DSO Mitnetz Strom test case with Nodes marketplace, have already shown the important savings in grid operation that could be realized when procuring flexibility (Anaya and Pollitt, 2020). The regulatory framework governing these flexibility projects is under continuous development following the CEP provisions, and a network code for demand-side flexibility is expected to be developed starting from 2022 to target the regulatory barriers to unlock further benefits (European Commission, 2021).

   In the academic literature, Spiliotis et al. (2016) propose a model that assesses the trade-off between grid expansion and demand and DG curtailment. They find that for a congested 24-node radial distribution network, all physical expansions could be avoided with 12% flexible demand. Klyapovskiy et al. (2019) consider flexibility from the demand side and in terms of technical solutions using grid assets and compare them to traditional reinforcement over a period of four years. Asensio et al. (2017) develop a bi-level model for the distribution network and renewable energy expansion planning under a Demand Response (DR) framework. They use a nodal network where the upper-level minimizes generation and network investment cost and the lower-level minimizes the overall payment faced by the consumers. They show how DR can contribute to adequately accommodating renewable generation in joint expansion planning. Additionally, the potential of DR for deferring investments has been successfully demonstrated.

   The first contribution of this paper is to assess the interaction between implicit and explicit demand-side flexibility. Implicit demand-side flexibility is when prosumers react to price signals triggered by electricity market prices and network tariffs. Explicit demand-side flexibility is when the DSO curtails consumers' loads for a certain amount of compensation. Two streams of literature can be identified. First, the state-of-the-art papers on network tariff design, such as Abdelmotteleb et al. (2018), Burger et al. (2020), De Villena et al. (2021), and Schittekatte and Meeus (2020), do not consider the interaction with explicit demand-side flexibility. Second, the state-of-the-art papers on explicit demand-side flexibility (also referred to as active grid management in engineering literature), such as Sarker et al. (2015), Spiliotis et al. (2016) and Asensio et al. (2017), do not consider the interaction with network tariffs. To the best of our knowledge, no prior work has been developed to analyze this relationship. In this paper, we model both to study this interaction in order to fill this gap in the literature.

   The second contribution of this paper is on the level of compensation for explicit demand-side flexibility. Many studies focus on the level of compensation for supply-side flexibility, but we are not aware of a similar study on demand-side flexibility. CEER (2020) highlights the importance of investigating administrative approaches for DSO's access to flexibility, especially in case of inefficiency or market failure of market-based approaches.

   The third contribution of this paper is through modelling. We develop a long-term bi-level equilibrium model. The upper level (UL) is a regulated DSO optimizes the social welfare deciding on the network investment and/or curtailing consumers as well as setting the network charge level to recover network and flexibility costs. The lower level (LL) consists of consumers, which can be prosumers or passive consumers, that maximize their own welfare. Prosumers can invest in solar PV and battery systems. They react to the network tariffs and to the compensation provided by the DSO for curtailing them. The regulated DSO anticipates the reaction of the consumers when investing in the network and when setting the level of curtailment of passive consumers and prosumers.

   The paper is structured in five sections. In section 2, we introduce the modelling approach. In section 3, we detail the results of a numerical example. Then in section 4, we present the limitation of our approach. Finally, in conclusion, we summarize our main findings and their policy implications.

2. METHODOLOGY

   In this section, we first introduce our modelling approach, picturing the game-theoretical model and summarizing the relevant academic literature. We then present the mathematical formulation with the different players' optimization problems and the underlying assumptions.

   2.1 Modelling Approach

   To model electricity systems, game theory and agent-based economics are rigorous opponents. In game theory (non-cooperative), there are two generally used solution techniques: dominance arguments and equilibrium analysis (Kreps, 2003). Dominance strategy is when the best strategy will be the same regardless of how other agents act. Nash equilibrium is settled when each agent understands and assumes the other player's optimal strategies when optimizing his own strategy.

   Weidlich and Veit (2008) provide a critical survey on the use of agent-based wholesale electricity market models. They conclude that most agent-based models of the electricity market represent the demand-side as a fixed and price-insensitive load. Nevertheless, this approach could allow introducing different assumptions on consumers other than fully rational and active or completely passive (Schittekatte, 2019).

   Saguan et al. (2006) provide a discussion between equilibrium and agent-based modelling to study imperfect competition in electricity markets. They show that game theory, which has been widely used to analyze such strategic interactions, allows to easily study very large systems, relying on a set of assumptions. Game theory is convenient for electricity systems as it enables to investigate the strategic behavior of agents with different interests influencing the outcome of other agents. The benefits of game-theoretic models can be categorized into two directions: First, they characterize the incentives for specific market participants to act strategically. Second, they inform market design (Bose and Low, 2019).

   In game theory, the Nash Equilibrium solution is found by solving complementarity models that represent the simultaneous optimization problems of one or several agents being all decision-makers. Complementarity formulations can have several variations. We find, for instance, Mixed Complementarity Problems (MCPs) whose conditions include equalities and complementarity conditions. In the case of a situation that encompasses a leader and a follower setting, the formulation is developed as a Mathematical Program with Equilibrium Constraints (MPEC). These problems contain complementarity conditions in the constraint set. When there are several leaders, the problems are formulated as Equilibrium Problems with Equilibrium Constraints (EPECs).

   MCPs are typically used for the modelling of market power in the case of an oligopoly. Nevertheless, these models can lead to myopic and contradictory behaviour (Devine and Siddiqui, 2020). MPECs are closely related to Stackelberg (Kaldor and von Stackelberg, 1936). The leader anticipates the reaction of one or several followers.

   Over the past two decades, the use of bi-level programming has received growing attention among academics. It can address many real-world problems, as they can be formulated as MPECs. Many academic papers and books have focused on this kind of programming problem (e.g. Luo et al. (1996) and Dempe (2002)). In the electricity sector, in particular, it has also been increasingly applied. The model used in this paper is an extended version of that used in Schittekatte and Meeus (2020), which in turn builds on Schittekatte et al. (2018). It has the same game-theoretical set-up. Schittekatte and Meeus (2020) apply a cost minimization formulation that only looks at distribution tariffs as an implicit demand-side flexibility solution. In this paper, we include explicit demand-side flexibility in a welfare maximization context.

   Our stylized model has a so-called...