Risk aversion in multilevel electricity market models with different congestion pricing regimes
Introduction
Most electricity systems will require significant investments in new generation capacity and transmission infrastructure to meet targets set out in the Paris agreement, as well as in national and international legislation. These investments are made under significant uncertainty (e.g., about future levels and locations of electricity demand, renewable policies, investment and operational costs), which is especially relevant as projects have long lead times and assets have long lifespans. However, investors in general do not like exposure to uncertainty and related risks for their investments, i.e., they have a risk-averse attitude with regard to their investment decisions. In response to this challenge, a wide range of stochastic transmission and generation expansion planning frameworks have been developed to analyze optimal investment levels and subsequent market operation given these uncertainties.
However, these frameworks generally assume that markets guide decisions almost perfectly. In particular, they usually assume that locational price signals exist, and therefore, that transmission constraints are perfectly internalized, e.g., through the use of nodal pricing in wholesale markets. They also often assume a single central planner. In sharp contrast to those assumptions, most electricity markets, most notably in Europe, feature imperfect locational price signals, using much larger price zones that generally correspond to national borders. Even in US-style nodal pricing markets, trading between markets is not perfect. Moreover, investment decisions are made by sequentially multiple decision makers who do not always correctly anticipate risk aversion of decision makers at subsequent markets.
To date we therefore lack methods to investigate the effect of uncertainty and risk aversion in markets that have imperfect locational price signals, and that are characterized by sequential decision making by a number of separate market participants. In those environments the different decision makers may have different attitudes towards risk and different anticipations of each other’s level of risk aversion. This paper is a first attempt to remedy this gap. We generalize the literature on risk-averse transmission and generation planning to settings where locational price signals are imperfect and decisions are made at multiple levels by risk-averse agents. We formulate a multi-level modeling framework which considers electricity transmission planning, followed by generation investment planning, market operation, and finally by redispatch. The model can be applied to both nodal and zonal pricing configurations. This allows us to compare the effects of uncertainty and risk aversion in both nodal and zonal pricing markets. Moreover, since transmission companies often claim to be risk-neutral and modeling risk aversion is not yet standard practice in industry, our framework also allows for analysis of a setting in which a risk-neutral transmission company is ignorant about risk aversion of generation companies in a setup with nodal as well as zonal pricing. This allows for comparison of a risk-neutral transmission company which correctly anticipates risk-averse generation investment with a risk-neutral transmission company which incorrectly models generation investment as risk-neutral. In doing so, we quantify the expected cost of ignoring risk aversion, similar to how previous studies have quantified the expected cost of ignoring uncertainty (van der Weijde and Hobbs, 2012).
We use investment in electricity systems as an example since considering multi-level decision making and imperfect locational price signals are particularly important there. However, multi-level stochastic optimization problems that include risk aversion are used in a large number of other applications. This includes modeling of other types of infrastructure investment (e.g., gas, as in Egging et al., 2017, disaster resilience modeling (e.g., Aldarajee et al., 2020), energy storage (e.g., Brijs et al., 2017, portfolio optimization (e.g., Nazari et al., 2015) and others. Although these applications often assume that all decisions are made by a single planner, and that price signals are not distorted, the real-world settings they examine usually have multiple decision makers and market imperfections. Our key results highlight the fact that these issues are important, and should therefore also inform further research beyond electricity markets.
We find that uncertainty and risk aversion have a fundamentally different effect in markets that do not have perfect locational price signals as compared to markets with nodal pricing. In a zonal pricing market, locational differences in costs are the only spatial driver of investment within zones, while in a nodal pricing market, locational demand uncertainties also have an effect. Moreover, zonal pricing markets have fewer opportunities to adjust investment levels to lower risk exposure. Both transmission investment and the spatial distribution of generation investment are therefore more substantially affected by risk aversion in a nodal pricing market. In addition, nodal markets have a stronger link between transmission and generation investment, as transmission investment changes nodal price differences. In a setup where transmission investment is decided before generation investment, this gives transmission investors more control over generation investment than in zonal markets; uncertainty therefore also affects transmission planners in a different way. This also means that transmission planners in a nodal pricing market should be particularly aware of the degree of risk aversion among generation investors to be able to make optimal transmission expansion decisions. In a zonal market, transmission planners face a risk of investing too little (and therefore end up with high redispatch costs) or too much (and ending up with stranded assets), but in a nodal pricing markets this additionally decreases the efficiency of the generation capacity investment outcome.
Naturally, our quantitative results are derived using a number of restrictive assumptions, including perfect competition and perfect risk trading. They are also contingent on the specific uncertainties and network parameters we consider. Nevertheless, our results show the importance of considering market imperfections when analyzing risk in energy markets. Our results might also, for example, explain the relative lack of emphasis on energy-related financial products in markets with fewer locational price signals. They underline the importance of correctly identifying the level of risk aversion among generation investors when planning transmission. More accurate representations of attitudes to risk in the generation investment sector are therefore a logical next step in the development of transmission planning methods, now that stochastic methods have been widely adopted.
The remainder of the paper is organized as follows. The next Section 2 introduces the methodology and Section 3 describes the model and solution approach. Section 4 describes a stylized two-node example and Section 5 provides results. Section 6 discusses the main results and Section 7 concludes.
Section snippets
Stochastic and risk-averse modeling: state of art
Our methods build on the existing stochastic power systems expansion planning literature, which has a long history. Initial applications of stochastic modeling focused on single-level expansion problems (e.g., De La Torre et al., 1999, Awad et al., 2010). Because, in liberalized electricity markets, infrastructure and generation assets are generally planned by different entities, subsequent models explicitly represent the multi-level nature of decision making, and in particular the need for
The trilevel market model with risk aversion
The sequence of decisions described in Section 2.2 can be translated into a stochastic trilevel market model according to Grimm et al. (2016). In the following, we first introduce all relevant variables and parameters, before explaining each level of the model in detail. For reasons of simplification we assume a greenfield approach but it would be straightforward to extend the model to account for existing transmission and generation capacity and possible disinvestment.
Test case
The model presented in Section 3 is suitable to be applied to networks of various sizes and markets with different congestion pricing schemes. Our goal in Sections 4 Test case, 5 Results is to quantify and to disentangle the different effects that occur due to risk aversion. In the following, we therefore apply our model to a stylized two-node example, which allows us to explicitly analyze market outcomes and their main drivers. We consider two cases in which either
- (i)
the market consists of a
Results
In this section, we discuss results of the two-node test case for different degrees of risk aversion and uniform as well as nodal pricing. Section 5.1 states investments in generation and transmission capacity, Section 5.2 presents results for welfare and prices on an aggregated level, Section 5.3 analyzes more detailed results for individual scenarios and on the composition of the tail scenarios that determine the CVaR, and Section 5.4 discusses implications of a risk-neutral transmission
Discussion
The previous section has shown how imperfect price signals and multi-level decision making can be incorporated in transmission and generation expansion planning models. Our numerical results further illustrate how risk aversion affects market outcomes under different pricing regimes. Consistent with the previous literature (e.g., Munoz et al., 2017, Diaz et al., 2019), we find that risk-averse generation companies invest more in renewable generation capacity. Although renewable generation
Conclusions
In this paper, we have proposed new methods to extend the existing literature on risk-averse planning to include imperfect locational price signals, as well as multi-level decision making with different attitudes towards risk and different expectations about the level of risk aversion of lower-level decision makers. All of these features are typically present in electricity markets, and our methods therefore enable a much richer analysis of risk aversion.
We have applied these methods to analyze
CRediT authorship contribution statement
Mirjam Ambrosius: Conceptualization, Methology, Data curation, Software, Formal analysis, Validation, Visualization, Writing. Jonas Egerer: Conceptualization, Methology, Data curation, Software, Formal analysis, Validation, Visualization, Writing. Veronika Grimm: Conceptualization, Methology, Formal analysis, Validation, Writing. Adriaan H. van der Weijde: Conceptualization, Methology, Formal analysis, Validation, Writing.
Acknowledgments
This research has been performed as part of the Energie Campus Nürnberg (EnCN) and is supported by funding of the Bavarian State Government, Germany and the Emerging Field Initiative (EFI) of the Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany through the project “Sustainable Business Models in Energy Markets” and by the Emerging Talents Initiative (ETI) of the Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany for Jonas Egerer. We also thank the Deutsche
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