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Table of Contents


Challenges and Perspectives of Optimization in the Energy Industry


1. Current and Future Challenges for Production Planning Systems

This article elaborates on the coming challenges production planning departments in utilities are facing in the near and remote future. Firstly, we will motivate the complexity of production planning, followed by a general solution approach to this task. The development of a new generation of energy management tools seems necessary to fulfill the need to handle uncertainty and eventually cover stochastic processes in energy planning. These new energy management systems have to include complex workflows and different methods and tools into the planning process.
Torben Franch, Max Scheidt, Günter Stock

2. The Earth Warming Problem: Practical Modeling in Industrial Enterprises

The earth warming problem will be one of the most difficult problems for industrial enterprises in the world. Heavily energy consuming industries, i.e., steel, power, refinery and chemical, have to establish a powerful management system to deal with the Earth warming problem. The core of this management system is the planning function. The planner should take more complicated criteria into consideration than before. Some of the criteria conflict with each other. At the same time, surroundings of the planning work will be continuously unstable because of political and economical changes in the world. We have to make an effort to implement a planning tool to help planners facing uncertain problems under multi criteria. The idea of modeling is the first step to accomplish a practical planning tool for ordinary planning persons for daily decision making work processes. Mathematical programming approaches are very promising to develop this kind of planning tool.
Susumu Ikenouye

Deterministic Methods


3. Trading Hubs Construction for Electricity Markets

In this chapter, we consider a problem of constructing trading hubs in the structure of the electricity wholesale markets. The nodes of a trading hub are used to calculate a reference price that can be employed by the market participants for different types of hedging. The need for such a reference price is due to considerable variability of energy prices at different nodes of the electricity grid at different periods of time. The hubs construction is viewed as a mathematical programming problem here. We discuss its connections with clustering problems, consider the heuristic algorithms of solution and indicate some complexity issues. The performance of algorithms is illustrated on the real-life data.
Pavel A. Borisovsky, Anton V. Eremeev, Egor B. Grinkevich, Sergey A. Klokov, c V. Vinnikov

4. A Decision Support System to Analyze the Influence of Distributed Generation in Energy Distribution Networks

Recent changes in electric network infrastructure and government policies have created opportunities for the employment of distributed generation to achieve a variety of benefits. In this paper we propose a decisions support system to assess some of the technical benefits, namely: (1) voltage profile improvement; (2) power losses reduction; and (3) network capacity investment deferral, brought through branches congestion reduction. The simulation platform incorporates the classical Newton—Raphson algorithm to solve the power flow equations. Simulation results are given for a real Semiurban medium voltage network, considering different load scenarios (Summer, Winter, Valley, Peak and In Between Hours), different levels of microgeneration penetration, and different location distributions for the microgeneration units.
J. N. Fidalgo, Dalila B. M. M. Fontes, Susana Silva

5. New Effective Methods of Mathematical Programming and Their Applications to Energy Problems

Convex programming algorithms, which have polynomial-time complexity on the class of linear problems are considered. The paper addresses the Chebyshev points of bounded convex sets, algorithms of their search as well as their different applications in convex programming, for elementary approximations of attainability sets, optimal control, global optimization of additive functions on convex polyhedrons and in the integer programming.
New formulations of energy problems made possible by the following methods are discovered: minimal shutdown during power shortages in a power supply system, search for optimal states in thermodynamic systems, optimal allocation of water resources. The applicability of polynomial-time algorithms to such problems is demonstrated. Consideration is given to the problem of search for the Chebyshev points in multi-criteria models of electric power system expansion and operation.
Valerian P. Bulatov

6. Improving Combustion Performance by Online Learning

In this chapter, combustion process is improved by computing control settings with clustering algorithms. The framework involves learning from a high-dimensional data stream generated by the combustion process. Thus the system's dynamics is captured. The concepts of virtual age of the boiler and the control settings are introduced. The confidence of applying a control setting to improve boiler performance is quantified. The framework is easy to implement and it handles a large number of process variables. The ideas introduced in this paper have been implemented at a 20 MW boiler controlled with a standard control system. That system makes run-time recommendations to the standard control system.
Andrew Kusiak, Zhe Song

7. Critical States of Nuclear Power Plant Reactors and Bilinear Modeling

We present a new system methodology for modeling of nonlinear processes in nuclear power plant cores. This methodology makes use of a variety of different approaches from different mathematical fields. The problem of modeling critical states is reduced to a bilinear subproblem. A scheme which provides stable parameter identification and adaptive control for the nuclear nuclear power plant described by the bilinear differential equation is presented. Abnormal events are found via a system-theoretical approach. Transitions to critical states can be detected by bilinear analysis of observed characteristics and by optimization of sensory measurements. Latent conditions and critical parameters in the reactor core are estimated trough a bilinear modeling.
Vitaliy A. Yatsenko, Panos M. Pardalos, Steffen Rebennack

8. Mixed-Integer Optimization for Polygeneration Energy Systems Design

In this chapter we introduce polygeneration energy systems in the context of future energy systems, and modeling and optimization issues involved in planning and configuration design of polygeneration processes. A mixed-integer nonlinear programming (MINLP) model is developed for the design optimization of polygeneration energy systems. A suitable superstructure is introduced, based on partitioning a general polygeneration energy system into four major blocks, for each of which alternative available technologies and types of equipment are considered. A detailed case study, involving a coal-based polygeneration plant producing electricity and methanol, is presented to demonstrate the key features and applicability of the proposed approach.
Pei Liu, Efstratios N. Pistikopoulos

9. Optimization of the Design and Partial-Load Operation of Power Plants Using Mixed-Integer Nonlinear Programming

This paper focuses on the optimization of the design and operation of combined heat and power plants (cogeneration plants). Due to the complexity of such an optimization task, conventional optimization methods consider only one operation point that is usually the full-load case. However, the frequent changes in demand lead to operation in several partial-load conditions. To guarantee a technically feasible and economically sound operation, we present a mathematical programming formulation of a model that considers the partial-load operation already in the design phase of the plant. This leads to a nonconvex mixed-integer nonlinear program (MINLP) due to discrete decisions in the design phase and discrete variables and nonlinear equations describing the thermodynamic status and behavior of the plant. The model is solved using an extended Branch and Cut algorithm that is implemented in the solver LaGO. We describe conventional optimization approaches and show that without consideration of different operation points, a flexible operation of the plant may be impossible. Further, we address the problem associated with the uncertain cost functions for plant components.
Marc Jüdes, Stefan Vigerske, George Tsatsaronis

10. Optimally Running a Biomass-Based Energy Production Process

A multiplant biomass-based energy production process is able to extract the chemical energy from various agricultural products. Such a process consists of several plants that are able to deal with biomasses of different types. Each type of plant has distinct mass-to-energy yields for each particular product type. Since the scale of the process may be geographically wide, transportation costs also have an impact on the overall profitability. Biomasses have different unit costs, and end-products (electrical energy, refined bioethanol, but also several other cross-products of the biomasses that are not necessarily energy-related) have different selling prices; hence, deciding the amount of each different biomass to process in order to maximize revenues and minimize costs is a nontrivial task. In this paper we propose a mathematical programming formulation of this problem and discuss its application to a real-world example.
Maurizio Bruglieri, Leo Liberti

11. Mathematical Modeling of Batch, Single Stage, Leach Bed Anaerobic Digestion of Organic Fraction of Municipal Solid Waste

Energy recovery can play an important role in municipal solid waste (MSW) management strategies by providing a saleable by-product and mitigating the environmental effects of the residue that requires disposal. Incineration, in-vessel anaerobic digestion processes and bioreactor landfills can all produce energy and can be used for pretreatment of MSW prior to eventual disposal. Organic fraction of municipal solid waste (OFMSW) is biochemically converted to methane and carbon dioxide in anaerobic digesters and bioreactor landfills. A lumped parameter mathematical model that describes this conversion process in a batch, single-stage, leach bed anaerobic digester under flooded conditions is developed and validated in this chapter. The model uses information such as mass of organic matter loaded in the vessel, amount of water used to flood the waste bed, headspace volume, alkalinity, pH and initial microbial concentrations to predict methane (or biogas) production rate, composition of biogas, residual concentration of organic matter, intermediate metabolites and alkalinity, and pH variations when the digester is operated at mesophilic (38°C) temperature. Most parameters of the model were obtained from literature and a sensitivity analysis used to identify those that required further refinement for improving model predictions. To improve numerical stability and rapid convergence of simulations, a novel solution procedure was developed to solve the charge balance equations in the differential algebraic equations set. Parameter estimation and model validation was carried out using data obtained from three pilot scale experiments conducted in 200 l vessels with 30 kg of OFMSW. Whereas parameter estimation was carried out using the results of one experiment, the model was validated using the results of the other two. The model was found to satisfactorily predict the experimental results and revealed that sufficient concentrations of microbial populations are present naturally in OFMSW and these can be activated rapidly by providing adequate alkalinity to prevent acidification. Such a start up procedure guarantees sustained and stable operation of the digester. Additional simulations determined that alkalinity and pH buffering capabilities provided by an initial concentration of ͌11 g l−1 of sodium bicarbonate (NaHCO3) was sufficient to accomplish this.
Takwai E. Lai, Abhay K. Koppar, Pratap C. Pullammanappallil, William P. Clarke

12. Spatially Differentiated Trade of Permits for Multipollutant Electric Power Supply Chains

In this paper, we consider electric power supply chain networks in which the power generators have distinct power plants and associated technologies and we develop a model of tradable pollution permits in the case of multiple pollutants and spatially distinct receptor points. We formulate the governing equilibrium conditions as a finite-dimensional variational inequality and demonstrate that, under the proposed multipollutant permit trading scheme, the environmental standards are achieved. Finally, we describe a computational procedure that exploits the structure of the problem. We also present numerical examples.
Trisha Woolley, Anna Nagurney, John Stranlund

13. Applications of TRUST-TECH Methodology in Optimal Power Flow of Power Systems

The main objective of the optimal power flow (OPF) problem is to determine the optimal steady-state operation of an electric power system while sat- isfying engineering and economic constraints. With the structural deregulation of electric power systems, OPF is becoming a basic tool in the power market. In this paper, a two-stage solution algorithm developed for solving OPF problems has several distinguished features: it numerically detects the existence of feasible solutions and quickly locates them. The theoretical basis of stage I is that the set of stable equilibrium manifolds of the quotient gradient system (QGS) is a set of feasible components of the original OPF problem. The first stage of this algorithm is a fast, globally convergent method for obtaining feasible solutions to the OPF problem. Starting from the feasible initial point obtained by stage I, an interior point method (IPM) at stage II is used to solve the original OPF problem to quickly locate a local optimal solution. This two-stage solution algorithm can quickly obtain a feasible solution and robustly solve OPF problems. Numerical test systems include a 2,383-bus power system.
Hsiao-Dong Chiang, Bin Wang, Quan-Yuan Jiang

Stochastic Programming: Methods and Applications


14. Scenario Tree Approximation and Risk Aversion Strategies for Stochastic Optimization of Electricity Production and Trading

Dynamic stochastic optimization techniques are highly relevant for applications in electricity production and trading since there are uncertainty factors at different time stages (e.g., demand, spot prices) that can be described reasonably by statistical models. In this paper, two aspects of this approach are highlighted: scenario tree approximation and risk aversion. The former is a procedure to replace a general statistical model (probability distribution), which makes the optimization problem intractable, suitably by a finite discrete distribution. Our methods rest upon suitable stability results for stochastic optimization problems. With regard to risk aversion we present the approach of polyhedral risk measures. For stochastic optimization problems minimizing risk measures from this class it has been shown that numerical tractability as well as stability results known for classical (nonrisk-averse) stochastic programs remain valid. In particular, the same scenario approximation methods can be used. Finally, we present illustrative numerical results from an electricity portfolio optimization model for a municipal power utility.
Andreas Eichhorn, Holger Heitsch, Werner Römisch

15. Optimization of Dispersed Energy Supply —Stochastic Programming with Recombining Scenario Trees

The steadily increasing share of wind energy within many power generating systems leads to strong and unpredictable fluctuations of the electricity supply and is thus a challenge with regard to power generation and transmission. We investigate the potential of energy storages to contribute to a cost optimal electricity supply by decoupling the supply and the demand. For this purpose we study a stochastic programming model of a regional power generating system consisting of thermal power units, wind energy, different energy storage systems, and the possibility for energy import. The identification of a cost optimal operation plan allows to evaluate the economical possibilities of the considered storage technologies.
On the one hand the optimization of energy storages requires the consideration of long-term planning horizons. On the other hand the highly fluctuating wind energy input requires a detailed temporal resolution. Consequently, the resulting optimization problem can, due to its dimension, not be tackled by standard solution approaches. We thus reduce the complexity by employing recombining scenario trees and apply a decomposition technique that exploits the special structure of those trees.
Alexa Epe, Christian Küchler, Werner Römisch, Stefan Vigerske, Hermann-Josef Wagner, Christoph Weber, Oliver Woll

16. Stochastic Model of the German Electricity System

We present a model of the German electricity system which is able to describe the system in arbitrary spatial and temporal resolution. Due to the high temporal resolution the model generator is particularly suitable to analyse the influence of uncertain and fluctuant parameters like the wind supply to the existing electricity system. Germany is represented by 29 knots within Germany and 13 knots of neighbouring countries. Major transmission lines between these knots are modelled in a stylized manner. The model calculates the optimal capacities as well as the energy flows. We will discuss stochastic programming options as latest extension of the model generator. The stochastic parameters are the fuel costs respectively the CO2 prices. It is also attempted to handle the supply of wind energy in a stochastic way.
Nina Heitmann, Thomas Hamacher

17. Optimization of Risk Management Problems in Generation and Trading Planning

Due to increased cost pressure on power generation and trading companies, caused by operation under market conditions, a cost efficient management of the risks becomes more important. As a result of the liberalization of the markets for electrical energy companies are exposed to higher uncertainties in power generation and trading planning, e.g., the volatility of the prices for electrical energy and for primary energies, especially natural gas. Additionally, bankruptcies of companies in the energy sector, e.g., ENRON or TXU Europe, have demonstrated that the loss of trading partners may cause a major disprofit, if not hedged appropriately. Together with risk management regulations, the need for risk management in generation and trading planning is increasing.
The objective of this work is the development of adequate methods for generation and trading planning, i.e., maximization of the contribution margin, taking the risks into account. The risk management process comprises identification and analysis of both risks and their impacts as well as the control of the occurring risks.
In this work two approaches, a separate expost and an integrated risk management method, have been developed using appropriate algorithms [2]. The expost approach uses the schedule of the power plants from the generation planning as given input data and optimizes the trading decisions by means of risk management concepts. The integrated approach yields the optimal generation and trading decision in terms of maximal contribution margin as well as minimal risk in one step.
The multicriterial optimization of the maximal contribution margin as well as the minimal risk is implemented either by risk constraints which limit the risk to a maximum or by utility functions which map the combination of contribution margin and risk to a single criterion.
The investigations of different systems demonstrate the results of the different risk management methods, whereas in this paper the results of a thermal dominated typical German generation and trading company are discussed.
Investigation of the effectiveness of the risk management methods using different power markets show improvement of the risk control participating in these markets compared to the negligence of these opportunities. Entering markets for weather and primary energy derivatives can reduce the risk of the portfolio.
The investigations show the tradeoff between contribution margin and risk. Depending on the risk aversion of the company the risk can be reduced for the tradeoff of a lower contribution margin. Comparing the results of the expost and the integrated risk management, it can be summarized that the integrated approach is more effective. This is due to the advantage of the integrated risk management method using both redispatch of the power plants for risk management purposes and even more important for adaptation to changed trading decisions.
Boris Blaesig, Hans-Jürgen Haubrich

18. Optimization Methods Application to Optimal Power Flow in Electric Power Systems

Optimal power flow is an optimizing tool for power system operation analysis, scheduling and energy management. Use of the optimal power flow is becoming more important because of its capabilities to deal with various situations. This problem involves the optimization of an objective functions that can take various forms while satisfying a set of operational and physical constraints. The OPF formulation is presented and various objectives and constraints are discussed. This paper is mainly focussed on review of the stochastic optimization methods which have been used in literature to solve the optimal power flow problem. Three real applications are presented as well.
Virginijus Radziukynas, Ingrida Radziukyniene

19. WILMAR: A Stochastic Programming Tool to Analyze the Large-Scale Integration of Wind Energy

Wind power is highly variable and partly unpredictable and therefore energy systems of the future have to cope with increased variability and stochasticity. The paper describes the use of a novel stochastic programming model to assess the impact of increased wind power generation on electricity systems. This WILMAR model takes explicitly the stochastic behavior of wind generation and the forecast errors into account. Also a detailed modeling of power plant, grid and market characteristics is performed. WILMAR thus allows to assess the impact of increased wind generation on reserve needs and usage, power plant operation and system cost.
Christoph Weber, Peter Meibom, Rüdiger Barth, Heike Brand

Stochastic Programming in Pricing


20. Clean Valuation with Regard to EU Emission Trading

In the electric power industry the observed increases of electricity price dynamics combined with the characteristic periodicity of related decision processes have motivated the use of multistage stochastic programming in recent years to provide flexible models for practical applications in the sector. Specifically in power generation and trading the planning process must obey highly complex interrelations between manifold influences. They range from short term price fluctuations as observed in spot markets to long term changes of fundamental influences. Not only changes in the electric supply system itself must be considered, but also the related availability and costs of required fuels. For example, the prices and usability of natural gas in power generation also depend on the existence of respective deployment and distribution systems. Furthermore the electric power sector is exposed to manifold regulatory uncertainties related to the rules imposed by the responsible authorities. Recently environmental issues have become very popular due to the ongoing discussion on climate change. In January 2005 the European Emissions Trading Scheme (EU ETS) has been launched which by many is considered a new key element in efficient electricity market operations. In this paper we will introduce a modeling framework that considers the influence of emission trading on portfolio problems in the electric power sector by applying clean valuation schemes that particularly take fuel costs, emission efficiency in combination with investment possibilities and generation flexibility into account. Sensitivity analysis is performed with respect to changes in technology, volatilities and price scenarios.
Karl Frauendorfer, Jens Güssow

21. Efficient Stochastic Programming Techniques for Electricity Swing Options

We consider the valuation of contracts of electrical energy supply with optionalities. After discussing appropriate stochastic programming models and presenting especially suited solution algorithms, a set of price scenarios is simulated based on a probabilistic model of the electricity spot market price at the EEX. We determine empirically upper and lower bounds for the stochastic optimization over any scenario tree obtained by reduction techniques. Furthermore, we introduce constraints restricting all scenarios to have identical contract exercise amounts cumulated over various fixed subperiods. Calculation of the losses of the optimal value of the objective function caused by these constraints shows that, for subperiods of 1 month, no substantial loss is encountered. This suggests a temporal decoupling heuristic where the depth of scenario trees is reduced to a suitable subperiod, yielding a good approximation to the valuation problem with substantially reduced complexity.
Marc C. Steinbach, Hans-Joachim Vollbrecht

22. Delta-Hedging a Hydropower Plant Using Stochastic Programming

An important challenge for hydropower producers is to optimize reservoir discharges, which is subject to uncertainty in inflow and electricity prices. Furthermore, the producers want to hedge the risk in the operating profit. This article demonstrates how stochastic programming can be used to solve a multireser-voir hydro scheduling case for a price-taking producer, and how such a model can be employed in subsequent delta-hedging of the electricity portfolio.
Stein-Erik Fleten, Stein W. Wallace


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