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This book presents an overview of the risks involved in modern electricity production, delivery and trading, including technical risk in production, transportation and delivery, operational risk for the system operators, market risks for traders, and political and other long term risks in strategic management. Using decision making under uncertainty as a methodological background, the book is divided into four parts, with Part I focusing on energy markets, particularly electricity markets. Topics include a nontechnical overview of energy markets and their main properties, basic price models for energy commodity prices, and modeling approaches for electricity price processes.

Part II looks at optimal decisions in managing energy systems, including hydropower dispatch models, cutting plane algorithms and approximative dynamic programming; hydro-thermal production; renewable; stochastic investments and operational optimization models for natural gas transport; decision making in operating electricity networks; and investment in extending energy production systems.

Part III explores pricing, including electricity swing options and the pricing of derivatives with volume control. Part IV looks at long-term and political risks, including energy systems under aspects of climate change, and catastrophic operational risks, particularly risks from terrorist attacks.



Energy Markets


Chapter 1. Energy Markets

Most of the risks in energy production and trading are related to market prices. As a consequence, this first chapter provides a short introduction to energy markets. Products (or more precisely contracts) which are traded in energy markets can concern either the physical delivery of energy (physical settlement) or only the payment of the financial value of such a delivery (financial settlement). In the case of a physical settlement, the traded quantities directly influence the whole system; if the settlement is financial, trades are basically bets on prices. Motivated by this distinction, we separate this chapter into two major parts: The first part considers the physical side of markets, focusing on the physical spot markets for natural gas and electric power. The second part serves as an introduction to the financial aspects of the markets, describing derivatives on physical spot contracts. In both sections our geographical focus will be on European markets. Due to the inhomogeneities of market designs, we will focus on stylized market characteristics rather than details. We mainly consider natural gas and electricity due to their distinctively different behavior to financial markets.
Peter Gross, Raimund M. Kovacevic, Georg Ch. Pflug

Chapter 2. Introduction to Price Models for Energy

The goal of this chapter is to present models which describe the dynamics of energy commodity spot prices and their forward curves. Recent developments in energy markets together with the use of new technologies caused changes in the dynamics of spot prices and there is a growing need to understand it. Given the spot price of an exchange-traded commodity we assume the forward curve, with a large set of liquid maturities is available. The forward curve provides information about the market perception of future spot prices and can be easily used to describe energy price behavior. In this chapter specific models which show to be suitable to capture the properties of energy prices are described.
Rita L. D’Ecclesia

Chapter 3. Price Dynamics in Electricity Markets

With the liberalization of global power markets, modeling of exchange-traded electricity contracts has attracted significantly the attention of both academic and industry. In this paper we offer an overview of the most common deseasonalization techniques and modeling approaches in the literature. We extract the deterministic component of EEX Phelix hourly electricity prices and we discuss different financial and time-series models for their stochastic component. Additionally we apply extreme value theory (EVT) to investigate the tails of the price changes distribution. Generally our results suggest EVT to be of interest to both risk managers and portfolio managers in the highly volatile electricity markets.
Florentina Paraschiv

Optimal Decisions in Managing Energy Systems


Chapter 4. Price-Driven Hydropower Dispatch Under Uncertainty

After a review of hydropower optimization models, we focus on price-driven hydropower dispatch models under uncertainty of the electricity price. We present two modeling approaches for pumped-storage plants. In the first model, the water level is constrained in expectation. We discuss the marginal price of water, which is obtained analytically, and influences of price variances. The second model is a multistage stochastic linear program on a scenario tree. Financial risk is constrained by a time-consistent extension of CVaR (conditional-value-at-risk). The model has two time scales: The short-term dispatch decision is separated from the long-term planning by aggregating electricity prices into occupation times at price levels. The risk constraint is tested in a case study.
Martin Densing

Chapter 5. On Cutting Plane Algorithms and Dynamic Programming for Hydroelectricity Generation

We consider dynamic programming (DP) approximations to hydro-electric reservoir scheduling problems. The first class of approximate DP methods uses decomposition and multi-modeling heuristics to produce policies that can be expressed as the sum of one-dimensional Bellman functions. This heuristic allows us to take into account non-convexities (appearing in models with head effect) by solving a MIP at each time stage. The second class of methods uses cutting planes and sampling. It is able to provide multidimensional policies. We show that the cutting plane methods will produce better policies than the first DP approximation on two convex problem formulations of different types. Modifying the cutting plane method to approximate the effect of reservoir head level on generation also yields better results on problems including these effects. The results are illustrated using tests on two river valley systems.
Andy Philpott, Anes Dallagi, Emmanuel Gallet

Chapter 6. Medium-Term Operational Planning for Hydrothermal Systems

The planning of operations of hydrothermal systems is, in general, divided into coordinated steps which focus on distinct modeling details of the system for different planning horizons. The medium-term operation planning (MTOP) problem, one of the operation planning steps and the focus of this chapter, aims at defining weekly generation for each power plant with the minimum expected operational cost over a specific planning horizon, with regard especially to the uncertainties related to reservoir inflows. Consequently, it is modeled as a stochastic problem and solving it requires the use of multistage stochastic optimization algorithms. In this sense, the objective of this chapter is to discuss the problem features, its particularities, and its importance in the overall operational planning. The stochastic methods usually used to solve this problem and some applications are also presented.
Raphael E. C. Gonçalves, Michel Gendreau, Erlon Cristian Finardi

Chapter 7. Stochastic Optimization of Power Generation and Storage Management in a Market Environment

This chapter provides an overview of practically applying mathematical optimization techniques to short-term and medium-term planning of a power generation system in a market environment. The considered power generating system may contain thermal plants (gas or coal fired), hydro power plants, new renewables, as well as dedicated energy storages (e.g., gas storages, hydro reservoirs). We argue that stochastic optimization is an appropriate modeling framework in order to take into account the uncertainty of input data (such as natural hydrologic inflows and energy market prices), market decision structures, as well as the optional character of power generating units and energy storages.
Andreas Eichhorn

Chapter 8. Risk Measures in Multi-Horizon Scenario Trees

Production assurance requirements are used to ensure that the operation of natural gas transportation networks is robust with respect to flow and production disruptions. They also affect strategies for optimal infrastructure investments. Motivated by a combined investment and operational optimization model for natural gas transport, we describe how to address such requirements through risk measure formulations such as Average Value-at-Risk. The large number of operational scenarios required for a meaningful analysis of the risk measures creates a computational challenge. A new scenario tree structure, multi-horizon scenario trees, can improve computational tractability. We investigate properties of the risk measures such as time consistency for such scenario trees and illustrate this discussion with a stylized example.
Adrian S. Werner, Alois Pichler, Kjetil T. Midthun, Lars Hellemo, Asgeir Tomasgard

Chapter 9. Controlled Islanding as Robust Operator Response Under Uncertainty

In the past decade there have been multiple high-profile cases of cascading blackouts, often resulting in the disconnection of tens of millions of consumers in large areas. It appears that in hindsight many of these disturbances could have been prevented by timely interventive action. In the actual cases, however, lack of complete knowledge about the state of the system undergoing a blackout event has prevented such action. This chapter reviews approaches to the problem of finding optimal interventions for a power system in the early stages of a cascading blackout. Conceptually the problem is one of optimization under uncertainty or robust optimization: the goal is to find a set of corrective actions that will guarantee power supply to as many customers as possible, in all, or at least most, of the possible states that the system may be in. To tackle the problem directly as a stochastic or robust optimization problem is intractable due to the complexities involved, foremost the number of possible states that would have to be considered. We argue, guided by example, that a robust response is to disconnect lines in such a manner as to create an island containing the affected part of the network. We give an overview of such approaches, notably those involving mixed-integer programming to directly design islands that admit a stable steady-state operating point.
A. Grothey, W. Bukhsh, K. I. M. McKinnon, P. A. Trodden

Chapter 10. Complementarity and Game-Theoretical Models for Equilibria in Energy Markets: Deterministic and Risk-Averse Formulations

Electricity and natural gas transmission and distribution networks are subject to regulation in price, service quality, and emission limits. The interaction of competing agents in an energy market subject to various regulatory interventions is usually modeled through equilibrium problems that ensure profit maximization for all the agents. These types of models can be written in different manners, for example, by means of mixed complementarity problems, variational inequalities, and game-theoretical formulations. More generally, we consider energy markets both in deterministic and stochastic settings and explore theoretical relations between the various formulations found in the literature and in practice. Our analysis shows that the profit-maximization complementarity model is equivalent to a game with agents minimizing costs if the setting is deterministic or risk neutral. On the other hand, when the agents exhibit risk aversion which is natural in this type of markets, the equivalence no longer holds. This gives rise to an interesting economical interpretation. As a complement to our theoretical study, and for the European natural gas market with deterministic data, we present some numerical results showing the impact of market power on equilibrium prices.
Juan Pablo Luna, Claudia Sagastizábal, Mikhail Solodov

Chapter 11. Optimal Planning and Economic Evaluation of Trigeneration Districts

Trigeneration, or combined cooling, heat and power (CCHP), is the process by which electricity, heating and cooling are simultaneously generated from the combustion of a fuel. Trigeneration systems for serving the electricity, thermal and cooling loads in residential districts are a possible solution to enhance energy efficiency, reduce fossil fuel consumption and increase the use of renewable energy sources in the residential sector. Technical, economical and financial issues have to be taken into account when planning a trigeneration system or when expanding an existing generation system. In this chapter a two-step decision support procedure is presented for analysing alternative system configurations. The first step is based on a mixed integer linear programming model that allows to describe the system components in great detail and computes the annual optimal dispatch of the distributed generation system with a hourly discretization, taking into account load profiles, fuel costs and technical constraints. The optimal dispatch is then used for the economic evaluation of the investment, taking into account prices of commodities, taxation, incentives and financial aspects. The procedure allows to compare alternative plant configurations and can be used as a simulation tool, for assessing the system sensitivity to variations of model parameters (e.g. incentives and ratio debt/equity).
Maria Teresa Vespucci, Stefano Zigrino, Francesca Bazzocchi, Alberto Gelmini

Chapter 12. Renewable Energy and Its Impact on Power Markets

The widespread introduction of renewable energy production is transforming electricity markets all around the globe. The changes are often hard to anticipate for market participants and the resulting uncertainty about future market conditions, policy regimes, technologies, and prices makes participation in these markets risky. In this article, we focus on changes induced by the growing capacities of wind power and photovoltaic electricity production. We highlight some aspects of power markets that are currently changing fundamentally due to increased capacities in these technologies. In particular, we discuss technological development, predictability and stochastic modeling of wind and solar output, policy issues pertaining to subsidies for renewable energies, and effects on the electricity prices on spot markets. We illustrate our findings using data from Germany and the Californian electricity market.
David Wozabal, Christoph Graf, David Hirschmann

Chapter 13. Copula-Based Hedge Ratios for Renewable Power Generation

The electricity price and production volume determine the revenue of a renewable electricity producer. Feed-in variations to power plants and high price volatility result in significant cash flow uncertainty. A copula-based Monte Carlo model is used to relate price and production volume and to find optimal hedge ratios through minimization of risk measures such as variance, hedge effectiveness, cash flow at risk, and conditional cash flow at risk. In our case study, all risk measures argue for an optimal hedge ratio between 35 and 60% of expected production. The highest risk reduction is achieved by the use of forward contracts with long time to maturity but at the expense of a low risk premium. Conversely, short-term futures and forwards only provide marginal risk reduction, but can yield attractive positive risk premiums. These findings underline the importance of distinguishing the use of derivative contracts for speculation and hedging purposes, through positions in short-term and long-term contracts, respectively.
Audun Nordtveit, Kim T. Watle, Stein-Erik Fleten

Chapter 14. Investment in Stochastic Electricity-Production Facilities

This chapter considers a profit-oriented private investor interested in building stochastic electricity-production facilities, such as solar and wind power plants. This investor sells its production in a competitive pool-based electricity market and faces uncertainties related to demand growth, its production level, and its investment cost. Adopting a multistage approach, a stochastic complementarity model is formulated to determine the optimal capacity to be built by the investor to maximize its expected profit while minimizing its profit volatility. An example considering a wind power investor is presented to illustrate the working of the proposed model.
Luis Baringo, Antonio J. Conejo



Chapter 15. Pricing of Energy Contracts: From Replication Pricing to Swing Options

The principle of replication or superhedging is widely used for valuating financial contracts, in particular, derivatives. In the special situation of energy markets, this principle is not quite appropriate and might lead to unrealistic high prices, when complete hedging is not possible, or to unrealistic low prices, when own production is involved. Therefore we compare it to further valuation strategies: acceptability pricing weakens the requirement of almost sure replication and indifference pricing accounts for the opportunity costs of producing for a considered contract. Finally, we describe a game-theoretic approach for valuating flexible contracts (swing options), which is based on bi-level optimization.
Raimund M. Kovacevic, Georg Ch. Pflug

Chapter 16. Energy Derivatives with Volume Controls

We analyse two classes of power derivatives with volume control, tolling agreements and flexible load contracts. Under certain assumptions, we can price a tolling agreement by resorting to theory of flexible load contracts, when using the fuel cost as numeraire in the power price. Tolling agreements can be priced as a strip of spread options under simple set of controls. Finally, we prove a general theory based on dynamic programming for these two classes of derivatives. We base our theory on price dynamics driven by Brownian motion.
Fred Espen Benth, Marcus Eriksson

Long Term and Political Risks


Chapter 17. Risk Hedging Strategies Under Energy System and Climate Policy Uncertainties

The future development of the energy sector is rife with uncertainties. They concern virtually the entire energy chain, from resource extraction to conversion technologies, energy demand, and the stringency of future environmental policies. Investment decisions today need thus not only to be cost-effective from the present perspective, but have to take into account also the imputed future risks of above uncertainties. This chapter introduces a newly developed modeling decision framework with endogenous representation of above uncertainties. We employ modeling techniques from finance and in particular modern portfolio theory to a systems engineering model of the global energy system and implement several alternative representations of risk. We aim to identify salient characteristics of least-cost risk hedging strategies that are adapted to considerably reduce future risks and are hence robust against a wide range of future uncertainties. These lead to significant changes in response to energy system and carbon price uncertainties, in particular (i) higher short- to medium-term investments into advanced technologies, (ii) pronounced emissions reductions, and (iii) diversification of the technology portfolio. From a methodological perspective, we find that there are strong interactions and synergies between different types of uncertainties. Cost-effective risk hedging strategies thus need to take a holistic view and comprehensively account for all uncertainties jointly. With respect to costs, relatively modest risk premiums (or hedging investments) can significantly reduce the vulnerability of the energy system against the associated uncertainties. The extent of early investments, diversification, and emissions reductions, however, depends on the risk premium that decision makers are willing to pay to respond to prevailing uncertainties and remains thus one of the key policy variables.
Volker Krey, Keywan Riahi

Chapter 18. Comparative Assessment of Accident Risks in the Energy Sector

This chapter is structured in five parts. The introduction discusses the relevance of accidents in the energy sector and puts them into the broader perspective of sustainability, energy security, and critical infrastructure protection. Furthermore, an overview of various risk assessment concepts is given. The second part provides a detailed overview of the comprehensive framework for comparative risk assessment developed by the Paul Scherrer Institut (PSI), at the core of which is the energy-related severe accident database (ENSAD). Third, a broad range of risk indicators and other measures are described and calculated allow for an objective, fair, and quantitative comparison of accident risks across a broad range of fossil, nuclear, and renewable technologies. This evaluation is complemented by a compilation of additional risk factors that can play a key role in decision processes and stakeholder interaction. However, for the time being they are often not amenable to full quantification because they cannot be described and analyzed by traditional risk metrics mainly focusing on consequences or because only limited historical experience is available. The chapter ends with a summary of the main findings and conclusions that can be drawn from comparative risk assessment as well as their potential implications for policy making.
Peter Burgherr, Stefan Hirschberg, Matteo Spada


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