TY - INPR A1 - Egerer, Jonas A1 - Grimm, Veronika A1 - Grübel, Julia A1 - Zöttl, Gregor T1 - Long-run market equilibria in coupled energy sectors: A study of uniqueness N2 - We propose an equilibrium model for coupled markets of multiple energy sectors. The agents in our model are operators of sector-specific production and sector-coupling technologies, as well as price-sensitive consumers with varying demand. We analyze long-run investment in production capacity in each sector and investment in coupling capacity between sectors, as well as production decisions determined at repeated spot markets. We show that in our multi-sector model, multiplicity of equilibria may occur, even if all assumptions hold that would be sufficient for uniqueness in a single-sector model. We then contribute to the literature by deriving sufficient conditions for the uniqueness of short- and long-run market equilibrium in coupled markets of multiple energy sectors. We illustrate via simple examples that these conditions are indeed required to guarantee uniqueness in general. The uniqueness result is an important step to be able to incorporate the proposed market equilibrium problem in more complex computational multilevel equilibrium models, in which uniqueness of lower levels is a prerequisite for obtaining meaningful solutions. Our analysis also paves the way to understand and analyze more complex sector coupling models in the future. KW - Energy Markets KW - Sector Coupling KW - Regional Pricing KW - Uniqueness KW - Short- and Long-Run Market Equilibrium Y1 - 2021 ER - TY - JOUR A1 - Böttger, Tom A1 - Grimm, Veronika A1 - Kleinert, Thomas A1 - Schmidt, Martin T1 - The Cost of Decoupling Trade and Transport in the European Entry-Exit Gas Market with Linear Physics Modeling JF - European Journal of Operational Research N2 - Liberalized gas markets in Europe are organized as entry-exit regimes so that gas trade and transport are decoupled. The decoupling is achieved via the announcement of technical capacities by the transmission system operator (TSO) at all entry and exit points of the network. These capacities can be booked by gas suppliers and customers in long-term contracts. Only traders who have booked capacities up-front can "nominate" quantities for injection or withdrawal of gas via a day-ahead market. To ensure feasibility of the nominations for the physical network, the TSO must only announce technical capacities for which all possibly nominated quantities are transportable. In this paper, we use a four-level model of the entry-exit gas market to analyze possible welfare losses associated with the decoupling of gas trade and transport. In addition to the multilevel structure, the model contains robust aspects to cover the conservative nature of the European entry-exit system. We provide several reformulations to obtain a single-level mixed-integer quadratic problem. The overall model of the considered market regime is extremely challenging and we thus have to make the main assumption that gas flows are modeled as potential-based linear flows. Using the derived single-level reformulation of the problem, we show that the feasibility requirements for technical capacities imply significant welfare losses due to unused network capacity. Furthermore, we find that the specific structure of the network has a considerable influence on the optimal choice of technical capacities. Our results thus show that trade and transport are not decoupled in the long term. As a further source of welfare losses and discrimination against individual actors, we identify the minimum prices for booking capacity at the individual nodes. KW - Entry-Exit Gas Market KW - Gas Market Design KW - Multilevel Optimization KW - Robust Optimization Y1 - 2020 ER - TY - INPR A1 - Grimm, Veronika A1 - Nowak, Daniel A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schwartz, Alexandra A1 - Zöttl, Gregor T1 - A Tractable Multi-Leader Multi-Follower Peak-Load-Pricing Model with Strategic Interaction N2 - While single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower games that can be applied, e.g., to model strategic booking decisions in the European entry-exit gas market. For this nontrivial class of games, we develop a solution algorithm that is able to compute the complete set of Nash equilibria instead of just individual solutions or a bigger set of stationary points. Additionally, we prove that for this class of games, the solution set is finite and provide examples for instances without any Nash equilibria in pure strategies. We apply the algorithm to a case study in which we compute strategic booking and nomination decisions in a model of the European entry-exit gas market system. Finally, we use our algorithm to provide a publicly available test library for the considered class of multi-leader multi-follower games. This library contains problem instances with different economic and mathematical properties so that other researchers in the field can test and benchmark newly developed methods for this challenging class of problems. KW - Game theory KW - Nash-Cournot equilibria KW - Multi-leader multi-follower game KW - Peak-load pricing Y1 - 2020 U6 - https://doi.org/10.1007/s10107-021-01708-0 ER - TY - INPR A1 - Runge, Philipp A1 - Sölch, Christian A1 - Albert, Jakob A1 - Wasserscheid, Peter A1 - Zöttl, Gregor A1 - Grimm, Veronika T1 - Economic comparison of electric fuels produced at excellent locations for renewable energies: A Scenario for 2035 N2 - The use of electric fuels (e-fuels) enables CO2-neutral mobility and opens therefore an alternative to fossil-fuel-fired engines or battery-powered electric motors. This paper compares the cost-effectiveness of Fischer-Tropsch diesel, methanol, and hydrogen stored as cryogenic liquid (LH2) or in form of liquid organic hydrogen carriers (LOHCs). The production cost of those fuels are to a large extent driven by the energy-intensive electrolytic water splitting. The option of producing e-fuels in Germany competes with international locations with excellent conditions for renewable energy harvesting and thus very low levelized cost of electricity. We developed a mathematical model that covers the entire process chain. Starting with the production of the required resources such as fresh water, hydrogen, carbon dioxide, carbon monoxide, electrical and thermal energy, the subsequent chemical synthesis, the transport to filling stations in Germany and finally the energetic utilization of the fuels in the vehicle. We found that the choice of production site can have a major impact on the mobility cost using the respective fuels. Especially in case of diesel production, the levelized cost of electricity driven by the full load hours of the applied renewable energy source have a huge impact. An LOHC-based system is shown to be less dependent on the kind of electricity source compared to other technologies due to its comparatively low electricity consumption and the low cost for the hydrogenation units. The length of the transportation route and the price of the filling station infrastructure, on the other hand, clearly increase mobility cost for LOHC and LH2. KW - Electric fuels, Hydrogen Utilization, Hydrogen Import, LOHC, Mobility Y1 - 2020 ER - TY - JOUR A1 - Grimm, Veronika A1 - Rückel, Bastian A1 - Sölch, Christian A1 - Zöttl, Gregor T1 - Regionally differentiated network fees to affect incentives for generation investment JF - Energy N2 - In this paper we propose an equilibrium model that allows to analyze subsidization schemes to affect locational choices for generation investment in electricity markets. Our framework takes into account generation investment decided by private investors and redispatch as well as network expansion decided by a regulated transmission system operator. In order to take into account the different objectives and decision variables of those agents, our approach uses a bi-level structure. We focus on the case of regionally differentiated network fees which have to be paid by generators (a so called g-component). The resulting investment and production decisions are compared to the outcome of an equilibrium model in the absence of such regionally differentiated investment incentives and to an overall optimal (first-best) benchmark. To illustrate possible economic effects, we calibrate our framework with data from the German electricity market. Our results reveal that while regionally differentiated network fees do have a significant impact on locational choice of generation capacities, we do not find significant effects on either welfare or network expansion. KW - Electricity Markets, Network Expansion, Generation Expansion, Investment Incentives, Computational Equilibrium Models Y1 - 2019 U6 - https://doi.org/10.1016/j.energy.2019.04.035 IS - 177 SP - 487 EP - 502 ER - TY - JOUR A1 - Grimm, Veronika A1 - Grübel, Julia A1 - Rückel, Bastian A1 - Sölch, Christian A1 - Zöttl, Gregor T1 - Storage investment and network expansion in distribution networks: The impact of regulatory frameworks JF - Applied Energy N2 - In this paper we propose a bi-level equilibrium model that allows to analyze the impact of different regulatory frameworks on storage and network investment in distribution networks. In our model, a regulated distribution system operator decides on network investment and operation while he anticipates the decisions of private agents on storage investment and operation. Since, especially in distribution networks, voltage stability and network losses have a decisive influence on network expansion and operation, we use a linearized AC power flow formulation to adequately account for these aspects. As adjustments of the current regulatory framework, we consider curtailment of renewable production, the introduction of a network fee based on the maximum renewable feed-in, and a subsidy scheme for storage investment. The performance of the different alternative frameworks is compared to the performance under rules that are commonly applied in various countries today, as well as to a system-optimal (first-best) benchmark. To illustrate the economic effects, we calibrate our model with data from the field project Smart Grid Solar. Our results reveal that curtailment and a redesign of network fees both have the potential to significantly reduce total system costs. On the contrary, investment subsidization of storage capacity has only a limited impact as long as the distribution system operator is not allowed to intervene in storage operation. KW - Computational Equilibrium Models; Electricity Markets; Investment Incentives; Distribution Network Expansion Planning; Storage Investment and Operation; Renewable Energy Production; (Self-) Consumption Y1 - 2019 U6 - https://doi.org/10.1016/j.apenergy.2019.114017 IS - 262 ER - TY - JOUR A1 - Runge, Philipp A1 - Sölch, Christian A1 - Albert, Jakob A1 - Wasserscheid, Peter A1 - Zöttl, Gregor A1 - Grimm, Veronika T1 - Economic comparison of different electric fuels for energy scenarios in 2035 JF - Applied Energy N2 - Electric fuels (e-fuels) enable CO2-neutral mobility and are therefore an alternative to battery-powered electric vehicles. This paper compares the cost-effectiveness of Fischer-Tropsch diesel, methanol and Liquid Organic Hydrogen Carriers. The production costs of those fuels are to a large part driven by the energy-intensive electrolytic hydrogen production. In this paper, we apply a multi-level electricity market model to calculate future hourly electricity prices for various electricity market designs in Germany for the year 2035. We then assess the economic efficiency of the different fuels under various future market conditions. In particular, we use the electricity price vectors derived from an electricity market model calibrated for 2035 as an input for a mathematical model of the entire process chain from hydrogen production and chemical bonding to the energetic utilization of the fuels in a vehicle. Within this model, we perform a sensitivity analysis, which quantifies the impact of various parameters on the fuel production cost. Most importantly, we consider prices resulting from own model calculations for different energy market designs, the investment cost for the electrolysis systems and the carbon dioxide purchase price. The results suggest that the use of hydrogen, which is temporarily bound to Liquid Organic Hydrogen Carriers, is a favorable alternative to the more widely discussed synthetic diesel and methanol. KW - Sector Coupling, Eletricity Markets, Electric fuels, Hydrogen Utilization, LOHC, Mobility Y1 - 2019 U6 - https://doi.org/10.1016/j.apenergy.2018.10.023 IS - 233-234 SP - 1078 EP - 1093 ER - TY - INPR A1 - Grimm, Veronika A1 - Martin, Alexander A1 - Sölch, Christian A1 - Weibelzahl, Martin A1 - Zöttl, Gregor T1 - Market-Based Redispatch May Result in Inefficient Dispatch N2 - In this paper we analyze a uniform price electricity spot market that is followed by redispatch in the case of network congestion. We assume that the transmission system operator is incentivized to minimize redispatch cost and compare a cost-based redispatch (CBR) to a market-based redispatch (MBR) mechanism. For networks with at least three nodes we show that in contrast to CBR, in the case of MBR the redispatch cost minimizing allocation may not be short-run efficient. As we demonstrate, in case of MBR the possibility of the transmission system operator to reduce redispatch cost at the expense of a reduced welfare may be driven by the electricity supply side or the electricity demand side. If, however, the transmission system operator is obliged to implement the welfare maximizing (instead of the redispatch cost minimizing) dispatch by regulation, this will result in an efficient dispatch also in case of MBR. KW - Electricity Markets, Redispatch, Congestion Management, Computational Equilibrium Models Y1 - 2019 ER - TY - JOUR A1 - Ambrosius, Mirjam A1 - Egerer, Jonas A1 - Grimm, Veronika A1 - van der Weijde, Adriaan H. T1 - Uncertain bidding zone configurations: The role of expectations for transmission and generation capacity expansion JF - European Journal of Operational Research N2 - Ongoing policy discussions on the reconfiguration of bidding zones in European electricity markets induce uncertainty about the future market design. This paper deals with the question of how this uncertainty affects market participants and their long-run investment decisions in generation and transmission capacity. Generalizing the literature on pro-active network expansion planning, we propose a stochastic multilevel model which incorporates generation capacity investment, network expansion, and market operation, taking into account uncertainty about the future bidding zone configuration. Using a stylized two-node network, we disentangle different effects that uncertainty has on market outcomes. If there is a possibility that future bidding zone configurations provide improved regional price signals, welfare gains materialize even if the change does not actually take place. As a consequence, welfare gains of an actual change of the bidding zone configuration are substantially lower due to those anticipatory effects. Additionally, we show substantial distributional effects in terms of both expected gains and risks, between producers and consumers and between different generation technologies. Y1 - 2019 U6 - https://doi.org/10.1016/j.ejor.2020.01.024 IS - 285 (1) SP - 343 EP - 359 ER - TY - JOUR A1 - Bichler, Martin A1 - Grimm, Veronika A1 - Kretschmer, Sandra A1 - Sutterer, Paul T1 - Market Design for Renewable Energy Auctions: An Analysis of Alternative Auction Formats JF - Energy Economics N2 - Auctions are widely used to determine the remuneration for renewable energies. They typically induce a high concentration of renewable energy plants at very productive sites far-off the main load centres, leading to an inefficient allocation as transmission line capacities are restricted but not considered in the allocation, resulting in an inefficient system configuration in the long run. To counteract these tendencies effectively, we propose a combinatorial auction design that allows to implement regional target capacities, provides a simple pricing rule and maintains a high level of competition between bidders by permitting package bids. By means of extensive numerical experiments we evaluate the combinatorial auction as compared to three further RES auction designs, the current German nationwide auction design, a simple nationwide auction, and regional auctions. We find that if bidders benefit from high enough economies of scale, the combinatorial auction design implements system-optimal target capacities without increasing the average remuneration per kWh as compared to the current German auction design. The prices resulting from the combinatorial auction are linear and anonymous for each region whenever possible, while minimal personalised markups on the linear prices are applied only when necessary. We show that realistic problem sizes can be solved in seconds, even though the problem is computationally hard. KW - renewable energy auction, combinatorial auction, market design Y1 - 2019 U6 - https://doi.org/10.1016/j.eneco.2020.104904 IS - 92 ER - TY - JOUR A1 - Grimm, Veronika A1 - Kretschmer, Sandra A1 - Mehl, Simon T1 - Green innovations: The organizational setup of pilot projects and its influence on consumer perceptions JF - Energy Policy N2 - Pilot-, test- and demonstration-projects (PTDs) are a prominent policy tool to promote the adoption of smart, green technologies. However, as technology adoption is heavily dependent on the individual attributes and beliefs of potential adopters, it is important to understand the influence of a PTD’s organizational setup on technology perception. By varying the information about a PTD’s organizational setup in a survey experiment among a selected sample of potential PTD-participants, we gather first experimental evidence for the effect of different setups on the perception of green technologies. We show that the organizational setup has a significant impact on a product’s perceived contribution to the energy transition, its establishment in the market, cost-reduction potential, innovativeness and environmental friendliness. In particular, full organizational cooperation between government, university and industry consistently improves perceptions compared to a partial setup. Regarding the willingness to participate in a PTD, we find that communication and support are the most imperative aspects and even more important than economic benefits. Our findings provide policy-makers with a more ample foundation on how PTDs should be designed to successfully transfer technologies to the market. KW - Pilot projects, Organizational setup, Adoption decision, Quadruple Helix, Innovation diffusion Y1 - 2019 U6 - https://doi.org/10.1016/j.enpol.2020.111474 IS - 142 ER - TY - INPR A1 - Veronika, Grimm A1 - Kretschmer, Sandra A1 - Mehl, Simon T1 - Home energy storage: A characterization of potential adopters in Germany N2 - Home energy storage (HES) poses a promising option to foster flexible electricity demand and grid-stabilising self-supply. Understanding the characteristics of potential storage adopters and their motives for adopting is essential to enable targeted measures to promote diffusion. This paper presents an in-depth analysis of motivational and psychological factors as well as product characteristics that affect the willingness to adopt domestic energy storage. Based on a selective sample of solar panel owners as the main energy storage target group, we find that potential adopters differ systematically in their evaluation of economic and non-economic characteristics of home energy storage. Using correlation-based average linkage clustering, we identify four distinct types of storage adopters: finance-oriented, independence-oriented, idealistic and multilaterally oriented households. Our findings emphasise that segment-specific policy strategies and support mechanisms are needed to stimulate HES adoption to pave the way for a sustainable energy system. KW - Energy storage, Consumer segmentation, Adoption decision, Innovation diffusion Y1 - 2019 ER - TY - JOUR A1 - Kleinert, Thomas A1 - Grimm, Veronika A1 - Schmidt, Martin T1 - Outer Approximation for Global Optimization of Mixed-Integer Quadratic Bilevel Problems JF - Mathematical Programming (Series B) N2 - Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel problems and the most recent algorithms use branch-and-cut techniques from mixed-integer programming that are especially tailored for the bilevel context. In this paper, we consider MIQP-QP bilevel problems, i.e., models with a mixed-integer convex-quadratic upper level and a continuous convex-quadratic lower level. This setting allows for a strong-duality-based transformation of the lower level which yields, in general, an equivalent nonconvex single-level reformulation of the original bilevel problem. Under reasonable assumptions, we can derive both a multi- and a single-tree outer-approximation-based cutting-plane algorithm. We show finite termination and correctness of both methods and present extensive numerical results that illustrate the applicability of the approaches. It turns out that the proposed methods are capable of solving bilevel instances with several thousand variables and constraints and significantly outperform classical solution approaches. KW - Bilevel optimization KW - Outer approximation KW - Quadratic programming KW - Convex mixed-integer nonlinear optimization Y1 - 2019 ER - TY - JOUR A1 - Grimm, Veronika A1 - Kleinert, Thomas A1 - Liers, Frauke A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Optimal Price Zones of Electricity Markets: A Mixed-Integer Multilevel Model and Global Solution Approaches JF - Optimization Methods and Software N2 - Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modeling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended KKT transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformation. KW - Multilevel Optimization KW - Mixed-Integer Nonlinear Optimization KW - Graph Partitioning KW - Generalized Benders Decomposition KW - Electricity Market Design} Y1 - 2017 IS - 34(2) SP - 406 EP - 436 ER - TY - JOUR A1 - Grimm, Veronika A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - A Multilevel Model of the European Entry-Exit Gas Market JF - Mathematical Methods of Operations Research N2 - In entry-exit gas markets as they are currently implemented in Europe, network constraints do not affect market interaction beyond the technical capacities determined by the TSO that restrict the quantities individual firms can trade at the market. It is an up to now unanswered question to what extent existing network capacity remains unused in an entry-exit design and to what extent feasible adjustments of the market design could alleviate inefficiencies. In this paper, we offer a four-level modeling framework that is capable of analyzing these issues and provide some first results on the model structure. In order to decouple gas trading from network congestion management, the TSO is required to determine technical capacities and corresponding booking fees at every entry and exit node up front. Firms book those capacities, which gives them the right to charge or discharge an amount of gas at a certain node up to this capacity in every scenario. Beyond these technical capacities and the resulting bookings, gas trade is unaffected by network constraints. The technical capacities have to ensure that transportation of traded quantities is always feasible. We assume that the TSO is regulated and determines technical capacities, fees, and transportation costs under a welfare objective. As a first step we moreover assume perfect competition among gas traders and show that the booking and nomination decisions can be analyzed in a single level. We prove that this aggregated model has a unique solution. We also show that the TSO's decisions can be subsumed in one level as well. If so, the model boils down to a mixed-integer nonlinear bilevel problem with robust aspects. In addition, we provide a first-best benchmark that allows to assess welfare losses that occur in an entry-exit system. Our approach provides a generic framework to analyze various aspects in the context of semi-liberalized gas markets. Therefore, we finally discuss and provide guidance on how to include several important aspects into the approach, such as network and production capacity investment, uncertain data, market power, and intra-day trading. KW - Entry-Exit System KW - Gas Market KW - Multilevel Modeling Y1 - 2017 IS - 89(2) SP - 223 EP - 255 ER - TY - JOUR A1 - Ambrosius, Mirjam A1 - Grimm, Veronika A1 - Kleinert, Thomas A1 - Liers, Frauke A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning JF - Energy Economics N2 - In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the optimal configuration of price zones and available transfer capacities on a network in order to optimally govern investment and production decisions in the long run. In a multilevel mixed-integer nonlinear model that contains a graph partitioning problem on the first level, we determine welfare-maximizing price zones and available transfer capacities for a given electricity market and analyze their impact on market outcomes. Using a generalized Benders decomposition approach developed in Grimm et al. (2019) and a problem-tailored scenario clustering for reducing the input data size, we are able to solve the model to global optimality even for large instances. We apply the approach to the German electricity market as an example to examine the impact of optimal zoning on key performance indicators such as welfare, generation mix and locations, or electricity prices. It turns out that even for a small number of price zones, an optimal configuration of zones induces a welfare level that almost approaches the first best. KW - Electricity Markets KW - Price Zones KW - Investment Incentives KW - Multilevel Optimization KW - Graph Partitioning Y1 - 2018 IS - 92 ER - TY - JOUR A1 - Egerer, Jonas A1 - Grimm, Veronika A1 - Kleinert, Thomas A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - The Impact of Neighboring Markets on Renewable Locations, Transmission Expansion, and Generation Investment JF - European Journal of Operational Research N2 - Many long-term investment planning models for liberalized electricity markets either optimize for the entire electricity system or focus on confined jurisdictions, abstracting from adjacent markets. In this paper, we provide models for analyzing the impact of the interdependencies between a core electricity market and its neighboring markets on key long-run decisions. This we do both for zonal and nodal pricing schemes. The identification of welfare optimal investments in transmission lines and renewable capacity within a core electricity market requires a spatially restricted objective function, which also accounts for benefits from cross-border electricity trading. This leads to mixed-integer nonlinear multilevel optimization problems with bilinear nonconvexities for which we adapt a Benders-like decomposition approach from the literature. In a case study, we use a stylized six-node network to disentangle different effects of optimal regional (as compared to supra-regional) investment planning. Regional planning alters investment in transmission and renewable capacity in the core region, which affects private investment in generation capacity also in adjacent regions and increases welfare in the core region at the cost of system welfare. Depending on the congestion-pricing scheme, the regulator of the core region follows different strategies to increase welfare causing distributional effects among stakeholders. KW - Neighboring Markets KW - Renewables KW - Network Expansion KW - Multilevel Optimization KW - Benders Decomposition Y1 - 2019 ER - TY - JOUR A1 - Grimm, Veronika A1 - Rückel, Bastian A1 - Sölch, Christian A1 - Zöttl, Gregor T1 - The impact of market design on transmission and generation investment in electricity markets JF - Energy Economics N2 - In this paper we propose an equilibrium model in order to analyze the impact of electricity market design on generation and transmission expansion in liberalized electricity markets. In a multi-level structure, our framework takes into account that generation investment and operation is decided by private investors, while network expansion and redispatch is decided by a regulated transmission system operator — as well as the different objectives of firms (profit maximization) and the regulator (welfare maximization). In order to illustrate the possibilities to quantify long term economic effects with our framework, we calibrate our model for the German electricity market. We consider various moderate adjustments of the market design: (i) the division of the market area into two price zones, (ii) the efficient curtailment of renewable production and (iii) a cost-benefit-driven balance between network expansion and network management measures. We then analyze the impact of these market designs on generation and transmission investment in case those design elements are anticipated upon network development planning. The resulting investment and production decisions are compared to a benchmark that reflects the current German electricity market design and to an overall optimal first-best benchmark. Our results reveal that price zones do have a significant impact on locational choice of generators and result in a reduced need for network expansion, but lead to only moderate annual welfare gains of approximately 0.9% of annual total system costs. Anticipation of optimal curtailment of renewables and a cost-benefit-driven use of redispatch operations upon network expansion planning, however, implies a welfare gain of over 4.9% of annual total system costs per year as compared to the existing market design, which equals 85% of the maximum possible welfare gain of the first-best benchmark. KW - Electricity Markets, Network Expansion, Generation Expansion, Investment Incentives, Market Design, Congestion Management, Computational Equilibrium Models Y1 - 2019 U6 - https://doi.org/10.1016/j.eneco.2020.104934 IS - 93 ER - TY - JOUR A1 - Grimm, Veronika A1 - Grübel, Julia A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Nonconvex Equilibrium Models for Gas Market Analysis: Failure of Standard Techniques and Alternative Modeling Approaches JF - European Journal on Operational Research N2 - This paper provides a first approach to assess gas market interaction on a network with nonconvex flow models. In the simplest possible setup that adequately reflects gas transport and market interaction, we elaborate on the relation of the solution of a simultaneous competitive gas market game, its corresponding mixed nonlinear complementarity problem (MNCP), and a first-best benchmark. We provide conditions under which the solution of the simultaneous game is also the solution of the corresponding MNCP. However, equilibria cannot be determined by the MNCP as the transmission system operator's (TSO’s) first-order conditions are insufficient, which goes back to nonconvexities of the gas flow model. This also implies that the welfare maximization problem may have multiple solutions that sometimes do not even coincide with any of the market equilibria. Our analysis shows that, even in the absence of strategic firms, market interaction fails to implement desirable outcomes from a welfare perspective due to the TSO’s incentive structure. We conclude that the technical environment calls for a market design that commits the TSO to a welfare objective through regulation and propose a design where the market solution corresponds to a welfare maximum and vice versa. KW - Natural Gas Markets KW - Nonconvex Equilibrium Models KW - Uniqueness KW - Multiplicity KW - Fundamental Welfare Theorems Y1 - 2017 IS - 273(3) SP - 1097 EP - 1108 ER - TY - JOUR A1 - Grimm, Veronika A1 - Orlinskaya, Galina A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Optimal Design of Retailer-Prosumer Electricity Tariffs Using Bilevel Optimization JF - Computers & Operations Research N2 - We compare various flexible tariffs that have been proposed to cost-effectively govern a prosumer's electricity management - in particular time-of-use (TOU), critical-peak-pricing (CPP), and a real-time-pricing tariff (RTP). As the outside option, we consider a fixed-price tariff (FP) that restricts the specific characteristics of TOU, CPP, and RTP, so that the flexible tariffs are at least as profitable for the prosumer as the fixed-price tariff. We propose bilevel models to determine the optimal interplay between the retailer's tariff design and the prosumer's decisions on using the storage, on consumption, and on electricity purchases from as well as electricity sales to the grid. The single-level reformulations of the considered bilevel models are computationally highly challenging optimization problems since they, e.g., combine bilinearities and mixed-integer aspects for modeling certain tariff structures. Based on a computational study using real-world data, we find that RTP increases retailer profits, however, leads to the largest price volatility for the prosumer. TOU and CPP only yield mild additional retailer profits and, due to the multiplicity of optimal plans on the part of the prosumer, imply uncertain revenues for the retailer. KW - Electricity tariffs KW - Pricing KW - Bilevel optimization KW - Mixed-integer optimization KW - Tariff design Y1 - 2019 IS - 114 ER - TY - JOUR A1 - Grimm, Veronika A1 - Martin, Alexander A1 - Schmidt, Martin A1 - Weibelzahl, Martin A1 - Zöttl, Gregor T1 - Transmission and generation investment in electricity markets: The effects of market splitting and network fee regimes JF - European Journal of Operational Research N2 - We propose an equilibrium model that allows to analyze the long-run impact of the electricity market design on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission system operator and private firms in expectation of an energy-only market and cost-based redispatch. In different specifications we consider the cases of one vs. multiple price zones (market splitting) and analyze different approaches to recover network cost—in particular lump sum, generation capacity based, and energy based fees. In order to compare the outcomes of our multilevel market model with a first best benchmark, we also solve the corresponding integrated planner problem. Using two test networks we illustrate that energy-only markets can lead to suboptimal locational decisions for generation capacity and thus imply excessive network expansion. Market splitting heals these problems only partially. These results are valid for all considered types of network tariffs, although investment slightly differs across those regimes. KW - Electricity market modeling KW - Mixed-integer nonlinear optimization KW - Multilevel programming KW - Network expansion KW - Transmission management Y1 - 2016 U6 - https://doi.org/10.1016/j.ejor.2016.03.044 VL - 254 IS - 2 SP - 493 EP - 509 ER - TY - JOUR A1 - Grimm, Veronika A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - Uniqueness of Market Equilibrium on a Network: A Peak-Load Pricing Approach JF - European Journal of Operational Research N2 - In this paper we analyze peak-load pricing in the presence of network constraints. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested capacities, taking into account that market prices reflect scarce transmission capacities. We state general conditions for existence and uniqueness of the market equilibrium and provide a characterization of equilibrium investment and production. The presented analysis covers the cases of perfect competition and monopoly - the case of strategic firms is approximated by a conjectural variations approach. Our result is a prerequisite for analyzing regulatory policy options with computational multilevel equilibrium models, since uniqueness of the equilibrium at lower levels is of key importance when solving these models. Thus, our paper contributes to an evolving strand of literature that analyzes regulatory policy based on computational multilevel equilibrium models and aims at taking into account individual objectives of various agents, among them not only generators and customers but also, e.g., the regulator deciding on network expansion. KW - Pricing KW - Peak-Load Pricing KW - Networks KW - Uniqueness Y1 - 2017 U6 - https://doi.org/10.1016/j.ejor.2017.03.036 VL - 261 IS - 3 SP - 971 EP - 983 ER - TY - INPR A1 - Grimm, Veronika A1 - Grübel, Julia A1 - Schmidt, Martin A1 - Schwartz, Alexandra A1 - Wiertz, Ann-Kathrin A1 - Zöttl, Gregor T1 - On a Tractable Single-Level Reformulation of a Multilevel Model of the European Entry-Exit Gas Market with Market Power N2 - We propose a framework that allows to quantitatively analyze the interplay of the different agents involved in gas trade and transport in the context of the European entry-exit system. Previous contributions have focused on the case of perfectly competitive buyers and sellers of gas, which allows to replace the respective market equilibrium problem by a single welfare maximization problem. Our novel framework considers the mathematically more challenging case of a monopolistic and thus strategic gas seller. In this framework, the objective functions of the gas sellers and buyers cannot be aggregated into a common objective function, which is why a multilevel formulation is necessary to accurately capture the sequential nature of the decisions taken. For this setup, we derive sufficient conditions that allow for reformulating the challenging four-level model as a computationally tractable single-level reformulation. We prove the correctness of this reformulation and use it for solving several test instances to illustrate the applicability of our approach. KW - Multilevel optimization KW - Reformulations KW - Gas markets KW - Market power Y1 - 2023 ER - TY - INPR A1 - Grimm, Veronika A1 - Hintermüller, Michael A1 - Huber, Olivier A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Zöttl, Gregor T1 - A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport N2 - We investigate a class of generalized Nash equilibrium problems (GNEPs) in which the objectives of the individuals are interdependent and the shared constraint consists of a system of partial differential equations. This setup is motivated by the modeling of strategic interactions of competing firms, which explicitly take into account the dynamics of transporting a commodity, such as natural gas, through a network. We establish the existence of a variational equilibrium of the GNEP. In the case of symmetric firms, we identify an equivalent optimization problem. We use this model to numerically explore the impact of linepacking, that is the use of the network as a temporary storage device. In particular, we study the firms' decisions under various linepacking abilities and analyze which market participants benefit from it. Y1 - ER - TY - JOUR A1 - Egerer, Jonas A1 - Grimm, Veronika A1 - Niazmand, Kiana A1 - Runge, Philipp T1 - The economics of global green ammonia trade – "Shipping Australian wind and sunshine to Germany" JF - Applied Energy N2 - This paper contributes to understanding the transformation of global energy trade to green energy carriers, focusing on green ammonia as the foreseeable first green hydrogen carrier. We provide a comprehensive overview of today's ammonia trade and assess scaling options for the trade of green ammonia. To that aim, we develop an optimization model for the integrated assessment of the green ammonia value chain that covers all steps from green ammonia production in an exporting country, up to delivery to a harbor in an importing country. The model endogenously chooses among different technology options and determines cost minimal operation. In a case study, we apply the model to the large-scale import of ammonia from Australia to Germany in a scenario for 2030. The results show that green ammonia can reach cost parity with gray ammonia even for moderate gas prices (but not necessarily with blue ammonia) if CO2 prices are high enough. We also provide a sensitivity analysis with respect to the interest rate and other key technical and economic parameters and show that cracking ammonia to provide pure hydrogen comes at a 45 % cost markup per MWh at the destination. KW - green ammonia KW - ammonia trade KW - optimization model KW - case study Australia to Germany Y1 - 2023 U6 - https://doi.org/https://doi.org/10.1016/j.apenergy.2023.120662 VL - 334 ER -