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About this book

Energy is one of the world`s most challenging problems, and power systems are an important aspect of energy related issues. This handbook contains state-of-the-art contributions on power systems modeling and optimization. The book is separated into two volumes with six sections, which cover the most important areas of energy systems. The first volume covers the topics operations planning and expansion planning while the second volume focuses on transmission and distribution modeling, forecasting in energy, energy auctions and markets, as well as risk management. The contributions are authored by recognized specialists in their fields and consist in either state-of-the-art reviews or examinations of state-of-the-art developments. The articles are not purely theoretical, but instead also discuss specific applications in power systems.

Table of Contents


Operation Planning


Constructive Dual DP for Reservoir Optimization

Dynamic programming (DP) is a well established technique for optimization of reservoir management strategies in hydro generation systems, and elsewhere. Computational efficiency has always been a major issue, though, at least for multireservoir problems. Although the dual of the DP problem has received little attention in the literature, it yields insights that can be used to reduce computational requirements significantly. The stochastic dual DP algorithm (SDDP) is one well known optimization model that combines insights from DP and mathematical programming to deal with problems of much higher dimension that could be addressed by DP alone. Here, though, we describe an alternative “constructive” dual DP technique, which has proved to be both efficient and flexible when applied to both optimization and simulation for reservoir problems of modest dimension. The approach is illustrated by models from New Zealand and the Nordic region.
E. Grant Read, Magnus Hindsberger

Long- and Medium-term Operations Planning and Stochastic Modelling in Hydro-dominated Power Systems Based on Stochastic Dual Dynamic Programming

This chapter reviews how stochastic dual dynamic programming (SDDP) has been applied to hydropower scheduling in the Nordic countries. The SDDP method, developed in Brazil, makes it possible to optimize multi-reservoir hydro systems with a detailed representation. Two applications are described: (1) A model intended for the system of a single power company, with the power price as an exogenous stochastic variable. In this case the standard SDDP algorithm has been extended; it is combined with ordinary stochastic dynamic programming. (2) A global model for a large system (possibly many countries) where the power price is an internal (endogenous) variable. The main focus is on (1). The modelling of the stochastic variables is discussed. Setting up proper stochastic models for inflow and price is quite a challenge, especially in the case of (2) above. This is an area where further work would be useful. Long computing time may in some cases be a consideration. In particular, the local model has been used by utilities with good results.
Anders Gjelsvik, Birger Mo, Arne Haugstad

Dynamic Management of Hydropower-Irrigation Systems

This chapter compares the performance of static and dynamic management strategies for a water resources system characterized by important hydropower and agricultural sectors. In the dynamic approach, water for crop irrigation is no longer considered as a static asset but is rather allocated so as to maximize the overall benefits taking into account the latest hydrologic conditions and the productivities of other users throughout the basin. The complexity of the decision-making process, which requires the continuous evaluation of numerous trade-offs, calls for the use of integrated hydrologic-economic models. The two water resources allocation problems discussed in this paper are solved using stochastic dual dynamic programming formulations.
A. Tilmant, Q. Goor

Latest Improvements of EDF Mid-term Power Generation Management

To optimize mid-term power generation management, Electricité de France (EDF) has developed a set of computer tools, which provide an order of magnitude of the supply and demand balance for the few following years. They also compute hydraulic reservoir management strategies for short-term unit commitment to correctly handle hydraulic reservoirs. This set of tools must be used every day with 500 scenarios and must give results in less than half an hour. Calculation durations are really critical. That is the reason why we had to study in depth the modeling and the optimization methods to reduce calculation durations as much as possible.In this set of tools, a new simulator has been developed with numerous improvements. Those improvements consist in a more precise generation unit modeling and a better generation unit commitment optimization. Those allow, for instance, to take into account piecewise linear Bellman function to optimize hydraulic reservoir commitment and to use either exact methods of resolution or several heuristics to optimize generation unit commitment. The first kind of heuristics begins with a choice of thermal power stations that are in use at a specific time, then allocates a part of the total production to each power plant. The second type is based on a branch and bound algorithm to solve a mixed integer program (MIP). Moreover, this article compares the performances of several linear solvers on an industrial problem.
Guillaume Dereu, Vincent Grellier

Large Scale Integration of Wind Power Generation

In a scenario of large scale penetration of renewable production from wind and other intermittent resources, it is fundamental that the electric systems have appropriate means to compensate the effects of the variability and randomness of the wind power availability. This concern was traditionally met by the promotion of the wind resource studies and in the identification of solutions based on reversible hydropower dams. However, in the electric system planning, other options deserve to be evaluated. This chapter evaluates the methods and technologies that can be used to minimize the intermittence, such as grid integration, technical distribution of the generators, geographic distribution of the generators, improved forecasting techniques, power plants providing operational and capacity reserve, interconnection with other grid systems, curtailment of intermittent technology, distributed generation, complementarily between renewable sources, energy storage, demand-side management, and demand-side response.
Pedro S. Moura, Aníbal T. de Almeida

Optimization Models in the Natural Gas Industry

With the surge of the global energy demand, natural gas plays an increasingly important role in the global energy market. To meet the demand, optimization techniques have been widely used in the natural gas industry, and has yielded a lot of promising results. In this chapter, we give a detailed discussion of optimization models in the natural gas industry, with the focus on the natural gas production, transportation, and market.
Qipeng P. Zheng, Steffen Rebennack, Niko A. Iliadis, Panos M. Pardalos

Integrated Electricity–Gas Operations Planning in Long-term Hydroscheduling Based on Stochastic Models

The integration of natural gas and electricity sectors has increased sharply in the last decade as a consequence of combined cycle natural gas thermal power plants. In some countries such as Brazil, gas-fired generation has been a major factor in the overall growth of natural gas consumption. When related to the operations planning, in some hydrothermal systems, a national system operator dispatches these gas-fired plants (along with other thermal sources such as coal, oil, and nuclear) in conjunction with the country’s hydroelectric plants by using a production-costing model based on stochastic programming. The algorithm determines the optimal hydro-to-thermal energy production ratio on the basis of the expected benefit of reducing thermal plant generation over a large number of hydrological scenarios, along a planning horizon of some years. This means that the optimal scheduling decision today depends on the assumptions about future load growth and future entrance of new generation capacity. Stochastic dynamic programming models are extensively used. However, the hydrothermal scheduling models usually do not take into account the possibility of future fuel supply constraints, either in production or in transportation. The assumption of fuel supply adequacy is felt to be reasonable for the more mature markets such as coal and oil. However, because of the fast growth of the natural gas market, it is possible that demand outpaces supply or transportation investments. Indications that gas-related constraints could be relevant were observed in New England, in the US, and in Brazil in 2004, where several megawatt of combined-cycle generation could not be dispatched when needed due to constraints in pipeline capacity. The objective of this work is to present a methodology for representing the natural gas supply, demand, and transportation network in the stochastic hydrothermal power scheduling model. Application of the integrated electricity–gas scheduling model is illustrated in case studies, with realistic configurations of the 90GW Brazilian system.
B. Bezerra, L. A. Barroso, R. Kelman, B. Flach, M. L. Latorre, N. Campodonico, M. Pereira

Recent Progress in Two-stage Mixed-integer Stochastic Programming with Applications to Power Production Planning

We present recent developments in two-stage mixed-integer stochastic programming with regard to application in power production planning. In particular, we review structural properties, stability issues, scenario reduction, and decomposition algorithms for two-stage models. Furthermore, we describe an application to stochastic thermal unit commitment.
Werner Römisch, Stefan Vigerske

Dealing With Load and Generation Cost Uncertainties in Power System Operation Studies: A Fuzzy Approach

Power systems are currently facing a change of the paradigm that determined their operation and planning while being surrounded by multiple uncertainties sources. As a consequence, dealing with uncertainty is becoming a crucial issue in the sense that all agents should be able to internalize them in their models to guarantee that activities are profitable and that operation and investment strategies are selected according to an adequate level of risk. Taking into account the introduction of market mechanisms and the volatility of fuel prices, this paper presents the models and the algorithms developed to address load and generation cost uncertainties. These models correspond to an enhanced approach regarding the original fuzzy optimal power flow model developed by the end of the 1990s, which considered only load uncertainties. The paper also describes the algorithms developed to integrate an estimate of active transmission losses and to compute nodal marginal prices reflecting such uncertainties. The developed algorithms use multiparametric optimization techniques and are illustrated using a case study based on the IEEE 24 bus test system.
Bruno André Gomes, João Tomé Saraiva

OBDD-Based Load Shedding Algorithm for Power Systems

Load shedding has been extensively studied for years. It has been used as an important measure for emergency control. This paper shows that the problem is NP-hard and introduce a way to obtain load shedding strategies based on ordered binary decision diagram (OBDD). The advantages of our method include that priority relationships among different loads are explicitly characterized and all solutions that violate static constrains including power balance, priority, and real power flow safety are excluded. This will make search for load shedding schemes that satisfy transient stability much more efficient.
Qianchuan Zhao, Xiao Li, Da-Zhong Zheng

Solution to Short-term Unit Commitment Problem

The Lagrangian relaxation approach to solve the unit commitment problem for a large system comprising both thermal and hydro generating units is presented. Commitment states of thermal units are obtained by solving thermal subproblems of Lagrangian dual problem. To get the output levels of hydro units, the hydrothermal scheduling is performed with a thermal unit commitment schedule obtained by solving thermal subproblems. Extensive constraints are considered. Nonlinear functions are used for thermal generation cost, water discharge rate and sulfur oxide emission. A general transmission loss formula is utilized for incorporating transmission loss. The variable metric method is used for updating the Lagrangian multipliers during maximization of the dual function. The Lagrangian multipliers are adjusted by the linear interpolation method during searching for a feasible suboptimal solution near the dual optimal point. A refinement algorithm is used to fine tune the schedule. A unit commitment expert system is employed for checking the feasibility of the solution and for handling constraints, which are difficult or impractical to be implemented in commitment algorithm. Results of the implementation on a utility are shown.
Md. Sayeed Salam

A Systems Approach for the Optimal Retrofitting of Utility Networks Under Demand and Market Uncertainties

This paper presents a systematic optimization approach to the retrofitting of utility systems whose operation faces uncertainties in the steam demand and the fuel and power prices. The optimization determines retrofit configurations to minimize an (expected) annualised total cost, using a stochastic programming approach deployed at two levels. The upper level optimizes structural modifications, while the second level optimizes the operation of the network. Uncertainties, modelled by distribution functions, link the two stages as the lower layer produces statistical information used, in aggregate form, by the upper level. The approach uses a case study to demonstrate its potential and value, producing evidence that uncertainties are important to consider early and that the two-level optimization effectively screens networks capable to afford unexpected changes in the parameters.
O. Adarijo-Akindele, A. Yang, F. Cecelja, A. C. Kokossis

Co-Optimization of Energy and Ancillary Service Markets

Many electricity markets now co-optimize production and pricing of ancillary services such as contingency reserve and regulation with that of energy. This approach has proved successful in reducing ancillary service costs and in providing consistent pricing incentives for potential providers of both energy and ancillary services Here we discuss the basic concepts involved, the optimization formulations employed to clear such co-optimized markets, and some of the practical issues that arise.
E. Grant Read

Expansion Planning


Investment Decisions Under Uncertainty Using Stochastic Dynamic Programming: A Case Study of Wind Power

The present paper adopts a real options approach to value wind power investments under uncertainty. Flexibility arises from the possibility to defer the construction of a wind farm until more information is available, the alternative to abandon the investment, and the options to select the scale of the project and up-scale the project. Taking into account uncertainties in future electricity prices, subsides, and investment costs, the problem is solved by dynamic stochastic programming. The motivation rests on a real business case of the major Norwegian power producer Agder Energi and experience from the Nordic power market at Nord Pool.
Klaus Vogstad, Trine Krogh Kristoffersen

The Integration of Social Concerns into Electricity Power Planning: A Combined Delphi and AHP Approach

The increasing acceptance of the principle of sustainable development has been a major driving force towards new approaches to energy planning. This is a complex process involving multiple and conflicting objectives, in which many agents were able to influence decisions. The integration of environmental, social and economic issues in decision making, although fundamental, is not an easy task, and tradeoffs must be made. The increasing importance of social aspects adds additional complexity to the traditional models that must now deal with variables recognizably difficult to measure in a quantitative scale. This study explores the issue of the social impact, as a fundamental aspect of the electricity planning process, aiming to give a measurable interpretation of the expected social impact of future electricity scenarios. A structured methodology, based on a combination of the Analytic Hierarchy Process and Delphi process, is proposed. The methodology is applied for the social evaluation of future electricity scenarios in Portugal, resulting in the elicitation and assignment of average social impact values for these scenarios. The proposed tool offers guidance to decision makers and presents a clear path to explicitly recognise and integrate the social preferences into electricity planning models.
P. Ferreira, M. Araújo, M. E. J. O’Kelly

Transmission Network Expansion Planning Under Deliberate Outages

This chapter sets forth a new approach for transmission network expansion planning that accounts for increasingly plausible deliberate outages. Malicious attacks expose the network planner, a centralized entity responsible for expansion decisions of the entire transmission network, to a new challenge: how to expand and reinforce the transmission network so that the vulnerability against intentional attacks is mitigated while meeting budgetary limits. Two vulnerability-constrained transmission expansion models are presented in this chapter. The first model allows the network planner to analyze the tradeoff between economic- and vulnerability-related issues and its impact on the expansion plans. The uncertainty associated with intentional outages is modeled through scenarios. Vulnerability is measured in terms of the system load shed. In the second model, the risk associated with the nonrandom uncertainty of deliberate outages is incorporated through the minimax weighted regret criterion. The proposed models are formulated as mixed-integer linear programs for which efficient solvers are available. Illustrative examples show the performance of both models.
Natalia Alguacil, José M. Arroyo, Miguel Carrión

Long-term and Expansion Planning for Electrical Networks Considering Uncertainties

The impending regulation of European electricity markets has led to an increasing cost pressure for network system operators. This applies in equal measure to transmission and distribution network operators. At the same time, boundary conditions of network planning are becoming more and more uncertain as a consequence of unbundling formerly integrated generation, transmission and distribution companies. To reduce network costs without worsening security and quality of supply, planning of transmission and distribution networks needs to be improved. For this, several computer-based optimization methods have been developed over the last years. In this chapter, boundary conditions and degrees of freedom that need to be taken into account during network optimization are discussed at first. Following that, the most commonly used optimization algorithms are presented, and the practical application of those methods is summarized.
T. Paulun, H.-J. Haubrich

Differential Evolution Solution to Transmission Expansion Planning Problem

Restructuring and deregulation have exposed the transmission planner to new objectives and uncertainties. As a result, new criteria and approaches are needed for transmission expansion planning (TEP) in deregulated electricity markets. This chapter proposes a new market-based approach for TEP. An improved differential evolution (IDE) model is proposed for the solution of this new market-based TEP problem. The modifications of IDE in comparison to the simple differential evolution method are the following: (1) the scaling factor F is varied randomly within some range, (2) an auxiliary set is employed to enhance the diversity of the population, (3) the newly generated trial vector is compared with the nearest parent, and (4) the simple feasibility rule is used to treat the constraints. Results from the application of the proposed method on the IEEE 30-bus, 57-bus, and 118-bus test systems demonstrate the feasibility and practicality of the proposed IDE for the solution of TEP problem.
Pavlos S. Georgilakis

Agent-based Global Energy Management Systems for the Process Industry

Energy utility systems are typically responsible for satisfying internal customers (e.g., the various process plants in the industrial complex). The increasing independence of business units in the complex matches an emerging trend in the utility systems to operate for own economic viability and for the encouragement to trade with both internal and external customers. The paper presents a dynamic management system supporting autonomy and the optimal operation of the utility system. The management system comprises three functional components, which support negotiation, short-term (tactical) and long-term (strategic) optimisation. The negotiation component involves an agent-based system exploiting the knowledge base established with real-time and historical data, whereas the optimisation provides a primal front (operational changes) and background front (structural changes) to account for the tactical and strategic decisions.
Y. Gao, Z. Shang, F. Cecelja, A. Yang, A. C. Kokossis

Optimal Planning of Distributed Generation via Nonlinear Optimization and Genetic Algorithms

The paper proposes a comparison between a nonlinear optimization tool and genetic algorithms (GAs) for optimal location and sizing of distributed generation (DG) in a distribution network. The objective function comprises of both power losses and investment costs, and the methods are tested on the IEEE 69-bus system. The study covers a comparison between the proposed approaches, the influence of GAs parameters on their performance in the DG allocation problem and the importance of installing the right amount of DG in the best suited location.
Ioana Pisică, Petru Postolache, Marcus M. Edvall


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