Refine
Language
- English (23)
Keywords
- Multilevel Optimization (3)
- Uniqueness (3)
- Graph Partitioning (2)
- Pricing (2)
- Adjustable Robustness (1)
- Benders Decomposition (1)
- Bilevel optimization (1)
- Computational Equilibrium Models; Electricity Markets; Investment Incentives; Distribution Network Expansion Planning; Storage Investment and Operation; Renewable Energy Production; (Self-) Consumption (1)
- Continuous Optimization (1)
- Demand side flexibility Load management Multi market bidding Stochastic programming Production planning Demand response (1)
Document Type
- Article (12)
- Preprint (10)
- Working Paper (1)
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.
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.
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.
Dynamic Pricing and Strategic Retailers in the Energy Sector: A
Multi-Leader-Follower Approach
(2023)
We consider strategic retail pricing in markets, where retail companies buy commodities at fluctuating wholesale prices and resell them to final consumers by applying dynamic retail tariffs. This is of especially large relevance in the context of energy markets where substantial wholesale price fluctuations are observed. Policy makers currently foster the introduction of such dynamic tariff schemes. From a modelling point of view, we propose a multi-leader-follower problem to investigate the implications of strategic retail pricing and we compare the impacts of implementing dynamic tariffs on retailers and final consumers. Our analysis tackles different aspects: first, we formulate the model and provide theoretical results. Second, we develop algorithms, which solve the multi-leader-follower problem and allow us to characterize the resulting market equilibria. Third, we calibrate and solve our framework based on data of the German retail electricity market for the years 2020 and 2021. This allows us to quantitatively assess the impact of introducing real time prices on retailers’ profits and customers’ benefits. As our results show, dynamic real-time pricing on the one hand typically increases market efficiency, which confirms previous results obtained without the explicit consideration of strategic behavior. On the other hand, however, as a novel aspect, dynamic real-time pricing turns out to significantly reduce equilibrium profits in case of strategic firms. This effect is especially large in environments with strongly fluctuating wholesale prices.
A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport
(2021)
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.
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.
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.
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.
Multi-modal distributed energy system planning is applied in the context of smart grids, industrial energy supply,and in the building energy sector. In real-world applications, these systems are commonly characterized by existing system structures of different age where monitoring and investment are conducted in a closed-loop, with the iterative possibility to invest. The literature contains two main approaches to approximate this computationally intensive multiperiod
investment problem. The first approach simplifies the temporal decision-making process collapsing the multistage decision to a two-stage decision, considering uncertainty in the second stage decision variables. The second approach considers multi-period investments under the assumption of perfect foresight. In this work, we propose a
multi-stage stochastic optimization problem that captures multi-period investment decisions under uncertainty and solves the problem to global optimality, serving as a first-best benchmark to the problem. To evaluate the performance of conventional approaches applied in a multi-year setup and to solve the multi-period problem at lower computational effort, we propose a rolling horizon heuristic that on the one hand reveals the performance of conventional approaches
applied in a multi-period set-up and on the other hand enables planners to identify approximate solutions to the original
multi-stage stochastic problem. Additionally, we consider an open-loop version of the rolling horizon algorithm to evaluate how single-period investments perform with respect to the entire scenario tree and compared to multi-period investments.
We conduct a real-world case study and investigate solution quality as well as the computational performance of the proposed approaches. Our findings indicate that the approximation of multi-period investments by two-stage stochastic approaches yield the best results regarding constraint satisfaction, while deterministic multi-period approximations yield
better economic and computational performance.
We consider equilibrium problems under uncertainty where firms
maximize their profits in a robust way when selling their output. Robust
optimization plays an increasingly important role when best guaranteed objective
values are to be determined, independently of the specific distributional
assumptions regarding uncertainty. In particular, solutions are to be determined
that are feasible regardless of how the uncertainty manifests itself within
some predefined uncertainty set. Our analysis adopts the robust optimization
perspective in the context of equilibrium problems. First, we consider a singlestage,
nonadjustable robust setting. We then go one step further and study the
more complex two-stage or adjustable case where a part of the variables can
adjust to the realization of the uncertainty. We compare equilibrium outcomes
with the corresponding centralized robust optimization problem where the
sum of all profits are maximized. As we find, the market equilibrium for
the perfectly competitive firms differs from the solution of the robust central
planner, which is in stark contrast to classical results regarding the efficiency of
market equilibria with perfectly competitive firms. For the different scenarios
considered, we furthermore are able to determine the resulting price of anarchy.
In the case of non-adjustable robustness, for fixed demand in every time step
the price of anarchy is bounded whereas it is unbounded if the buyers are
modeled by elastic demand functions. For the two-stage adjustable setting,
we show how to compute subsidies for the firms that lead to robust welfare
optimal equilibria.