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Abstract Purpose of ReviewThe share of asynchronous inverter-based resources is increasing in many electricity systems, displacing synchronous generators. This leads to a decreasing level of system inertia, which threatens electricity-system stability. This dynamic raises the question of how to secure sufficient levels of inertia. One possibility is taking a market-based approach to incentivize the installation of inertia-providing equipment. To this end, this paper reviews market designs to reimburse inertia provision that are discussed in the literature. Recent FindingsWe find five distinct market designs to remunerate inertia that are discussed in the literature—bilateral negotiation, tendering, auctions, bonus systems, and integrating inertia-related constraints into energy-market models. In addition, there are other approaches that are not based on a market mechanism—penalties, regulatory obligations, self-provision by electricity-system operators, and redispatch. We examine current approaches that are employed by Ireland, Great Britain, Australia, and Germany, which demonstrate the real-world use of these theoretical designs. We assess the five market designs based on their advantages and disadvantages. SummaryWe find that there is not a single market design that outperforms the othersvis-à-visall market-performance indicators. Which market design is suited best for a specific use case depends upon the particular circumstances. A solely market-based solution may not be sufficient to secure electricity-system stability and should be enriched with regulatory guidelines to mitigate the risk of market failure. 

Abstract Nested Benders’s decomposition is an efficient means to solve large-scale optimization problems with a natural time sequence of decisions. This paper examines the use of the technique to decompose and solve efficiently capacity-expansion problems for electricity systems with hydroelectric and renewable generators. To this end we develop an archetypal planning model that captures key features of hydroelectric and renewable generators and apply it to a case study that is based on the Columbia River system in the northwestern United States of America. We apply standard network and within-year temporal simplifications to reduce the problem’s size. Nevertheless, the remaining problem is large-scale and we demonstrate the use of nested Benders’s decomposition to solve it. We explore refinements of the decomposition method which yield further performance improvements. Overall, we show that nested Benders’s decomposition yields good computational performance with minimal loss of model fidelity. 

Purpose of Review We survey operational models of water-distribution systems. Although such modeling is important in its own right, our focus is motivated by the growing desire to examine and manage the nexus between water-distribution and electricity systems. As such, our survey discusses computational challenges in modeling water-distribution systems, co-ordination dynamics between water-distribution and electricity systems, and gaps in the literature. Recent Findings Modeling water-distribution systems is made difficult by their highly non-linear and non-convex physical properties. Co-ordinating water-distribution and electricity systems, especially with the growing supply and demand uncertainties of the latter, requires fast optimization techniques for real-time system management. Although many works suggest means of co-ordinating the two systems, practical applications are limited, due to the systems having separate and autonomous management and ownership. Nonetheless, recent works are navigating this challenge, by seeking methods to foster improved co-ordination of the two systems while respecting their autonomy. Additionally, with the backdrop of increased security threats, there is a growing need to bolster infrastructure protection, which is complicated by the intertwined nature of the two systems. Summary By providing a steady supply of potable water to satisfy residential, commercial, agricultural, and industrial demands, water-distribution systems are pivotal components of modern society and infrastructure. The extant literature presents many models and optimization strategies that are tailored for operating water-distribution systems. Yet, there remain unexplored problems, particularly related to simplifying model computation, capturing the flexibility of water-distribution systems, and capturing interdependencies between water-distribution and other systems and infrastructures. Future research that addresses these gaps will allow greater operational efficiency and resilience. 

Electricity systems in many parts of the world are becoming more dependent upon natural gas as an electricity-generation fuel. As such, electricity and natural-gas markets are becoming more interconnected. Contemporaneously, some electricity and natural-gas markets are integrating vertically, through the merger of electricity and natural-gas suppliers. The market-efficiency impacts of such vertical integration are unclear. On one hand, vertical integration could exacerbate market power, whereas on another it could mitigate double marginalization. To study this question, this paper develops a Nash–Cournot model of the two interconnected markets. The model is converted into a linear complementarity problem, which allows deriving Nash equilibria readily. Some theoretical results are derived for the case of a merger involving symmetric firms. In addition, the model is applied to a stylized example with a range of parameter values. We find that integration is social-welfare enhancing—which implies that mitigating double marginalization outweighs the exercise of market power. In most cases, the effects of merger can give rise to a prisoner’s-dilemma-type outcome. Merger is beneficial to the merging firms. However, profits of non-merging firms and total supplier profits decrease following a merger. Overall, our results suggest that vertical integration in energy markets may be socially beneficial. JEL Classification:C61, C72, D43, L1, L94, L95, Q4