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A spatial mean-variance MIP model for energy market risk analysis
Abstract
The paper presents a short-term market risk model based on the Markowitz mean-variance method for spatial electricity markets. The spatial nature is captured using the correlation of geographically separated markets and the consideration of wheeling administration. The model also includes transaction costs and other practical constraints, resulting in a mixed integer programming (MIP) model. The incorporation of those practical constraints makes the model more attractive than the traditional Markowitz portfolio model with continuity. A case study is used to illustrate the practical application of the model. The results show that the MIP portfolio efficient frontier is neither smooth nor concave. The paper also considers the possible extension of the model to other energy markets, including natural gas and oil markets.
... 2007;Muñoz i in. 2009;Rockafellar, Uryasev 2000;Yu 2002). ...
... Coraz częściej pojawiają się opinie, że historyczne dane nie mogą stanowić wystarczającej podstawy dla prognozy przyszłych wartości analizowanych zmiennych, ponieważ niepewności, które będą w przyszłości wpływać na wartości zmiennych są prawie niemożliwe do oszacowania, co sprawia, że przyszłe wartości zmiennych są trudne do przewidzenia (Kienzle, Andersson 2008;Zhu, Fan 2010). A ponadto, w przyszłości mogą mieć miejsce poważne zmiany warunków, przez co prognozowanie wartości na podstawie danych historycznych nie jest właściwą metodą (Yu 2002). Duża dynamika rynków energii sprawia, że założenie, iż przeszłość odzwierciedla przyszłość na rynkach energii jest założeniem bardzo trudnym do zaakceptowania (Blanco 1998). ...
... W godzinach szczytu ceny spot energii elektrycznej są często determinowane cenami gazu ziemnego (Yu 2002). Wynika to z tego, że źródła energii opalane gazem są często źródłami, o krańcowych kosztach produkcji energii, kształtującymi ceny na rynku energii elektrycznej, co prowadzi do silnej korelacji pomiędzy cenami energii elektrycznej i gazu (Roques i in. ...
Przedsiębiorstwo energetyczne chcąc zwiększyć swój potencjał produkcyjny staje przed koniecznością doboru technologii wytwarzania energii do istniejącego portfela technologii.
Właściwy wybór technologii ma kluczowe znaczenie dla powodzenia przedsięwzięcia inwestycyjnego i rozwoju przedsiębiorstwa. W pracy zaproponowano sposób, w jaki przedsiębiorstwo energetyczne powinno, na podstawie predefiniowanych kryteriów, dokonywać doboru technologii poprzez wybór projektu inwestycyjnego z pewnej liczby dostępnych do realizacji projektów wykorzystujących różne technologie, uwzględniając przy tym wpływ wybranego projektu na istniejący portfel wytwórczy przedsiębiorstwa, dostępną elastyczność decyzyjną oraz wartość przedsiębiorstwa i analizę ryzyka. Zaprezentowano algorytm postępowania, który pozwala prowadzić modelowanie symulacyjne w zakresie wyboru projektu do realizacji. Skuteczność tego algorytmu sprawdzono na przykładzie hipotetycznego problemu decyzyjnego z zakresu wyboru technologii wytwarzania energii elektrycznej, który potwierdził hipotezę mówiącą, że technologie energetyczne bazujące na gazie ziemnym mogą być rozpatrywane przez przedsiębiorstwo energetyczne jako te, których wdrożenie buduje wartość przedsiębiorstwa i ogranicza ryzyko jego funkcjonowania. Uzyskane wyniki
zostały porównane z wynikami tradycyjnej metody oceny ekonomicznej projektów wykorzystującej klasyczny rachunek dyskonta.
... Quadratic programming is used to solve the problem. The mean-variance model was extended to power portfolio optimization problems in [4], [16], and [17]. A power portfolio optimization problem considering forward contracts and generation units was presented in [17]. ...
... The mean-variance model was extended to power portfolio optimization problems in [4], [16], and [17]. A power portfolio optimization problem considering forward contracts and generation units was presented in [17]. It is to minimize the cost variance of the portfolio subject to transaction cost limits, generation unit constraints, and financial constraints. ...
... By collecting terms related to Option i from L in (14), the option subproblem is given as (17) where is calculated based on (10) by dropping the term and using latest expected values for other variables. The subproblem is subject to discrete values of in (4). ...
In a deregulated electric power system, multiple markets of different time scales exist with various power supply instruments. A load serving entity (LSE) has multiple choices from these instruments to meet its load obligations. In view of the large amount of power involved, the complex market structure, the risks in such volatile markets, the stringent constraints to be satisfied, and the long time horizon, a power portfolio optimization problem is of critical importance for an LSE to serve its load, maximize its profit, and manage its risks. In this paper, a midterm power portfolio optimization problem with risk management is presented. Key instruments are considered, risk terms based on semi-variances of spot market transactions are introduced, and penalties on load obligation violations are added to the objective function to improve algorithm convergence and constraint satisfaction. To overcome the inseparability of the resulting problem, a surrogate optimization framework is developed, enabling a decomposition and coordination approach. Numerical testing results show that our method effectively provides decisions for various instruments to maximize profit and manage risks, and it is computationally efficient
... Such a mix can be determined by applying mean-variance portfolio theory (see e.g. Kienzle and Andersson, 2008, Krey, 2008, Awerbuch, 2006, Yu, 2003, Humphreys and McClain, 1998, and Bar-Lev and Katz, 1976. Here, a social planner (e.g. ...
This dissertation discusses four topics where government interventions could cause incentive for market inefficiencies. Chapter 2 estimates the efficiency of public good provision and deals with the question of whether fiscal equalization among Swiss cantons reduces the incentive for efficiency. Despite the aspiration for equity gains, fiscal equalization can even increase disparities if cantons on the receiving end lack incentives for efficiency, commonly known as the “flypaper effect” (Inman, 2008). The efficiency of contributing cantons may be undermined as well, giving rise to an equity-efficiency trade-off (Stiglitz, 1988). Chapter 3 and 4 provide an empirical analysis of the efficiency of Swiss hospitals. As in many other developed countries, increasing health care expenditures have highlighted the importance of health care reforms that pursue efficiency gains. One such reform includes transitioning to a prospective payment system. The assumption is that a change to predetermined and fixed payments places hospitals at operating risk and increases their cost efficiency (e.g. Newhouse, 1996). However, the challenge for policy makers is how to reward efficiency, which involves identifying the differences caused by inefficiency instead of by heterogeneity due to exogenous influences. Chapter 3 and 4 deal with the importance of heterogeneity in the measurement of hospital performance and investigate whether heterogeneity has an influence on the effectiveness of performance based payment systems. An analysis of the relevance of efficiency measurement in the provision of electricity is presented in Chapter 5. Stochastic frontier analysis and data envelopment analysis are the two most prevalent approaches for the measurement of efficiency. However, they are only suitable when productive units are homogenous with regard to technology (relaxed in Chapter 3 and 4) and have little uncertainty in input prices. In the provision of electricity, both of these assumptions are not satisfied. In these circumstances a risk-adjusted efficiency measurement that involves the optimal mix of technology provides a more reliable measurement. This is the case in Chapter 5, where portfolio theory is applied to estimate the efficiency of electricity provision in the United States and Switzerland. Die vorliegende Doktorarbeit umfasst vier Aufsätze, die den effizienten Einsatz öffentlicher Ressourcen untersuchen. Kapitel 2 untersucht, wie effizient die Schweizer Kantone ihre öffentlichen Güter im besten Fall bereitstellen können und welchen Einfluss dabei der interkantonale Finanzausgleich auf die tatsächlich erzielte Effizienz hat. Obwohl der Finanzausgleich zum Ziel hat, Disparitäten zwischen den Kantonen zu minimieren, können diese grösser werden, wenn Bezügerkantone keine Anreize haben, die erhaltenen Ressourcen effizient einzusetzen. In der Literatur ist dieser Effekt als «flypaper effect» bekannt (Inman, 2008). Die Effizienz der Geberkantone kann ebenfalls negativ beeinflusst werden, was in einem «equity-efficiency» trade-off enden kann (Stiglitz, 1988). Die Ergebnisse der Untersuchung bestätigen beide Effekte auf die Effizienz. Kapitel 3 und 4 untersuchen die Effizienz der Schweizer Spitäler. Die seit Jahrzehnten ansteigenden Gesundheitsausgaben steigern zunehmend das Interesse für Reformen, die einen effizienteren Einsatz öffentlicher Ressourcen in Spitälern anstreben. Eine Möglichkeit bietet der Wechsel von einem retrospektiven zu einem prospektiven Finanzierungssystem. Die Theorie geht davon aus, dass die Spitäler mit dem Systemwechsel einem erhöhten operativen Risiko ausgesetzt sind und dadurch mehr Anreize zur Effizienz haben (Newhouse 1996). Die Herausforderung bleibt jedoch, die Spitäler nur nach ihren effizienten Leistungen zu bezahlen. Dies bedingt die Identifikation von Kostenunterschieden, die aufgrund der Ineffizienz und nicht aufgrund der Heterogenität bei den verwendeten Technologien entstehen. Die beiden Kapitel befassen sich im Detail mit diesem Identifikationsproblem und untersuchen empirisch, ob die Heterogenität einen Einfluss auf die Effektivität der prospektiven Finanzierung hat. Der letzte Artikel befasst sich in Kapitel 5 mit der Relevanz der Effizienzmessung bei der Stromproduktion. Die zwei bekannten Verfahren der Effizienzmessung sind die Stochastic Frontier Analysis (SFA) und die Data Envelopment Analysis (DEA). Beide setzen für eine aussagekräftige Untersuchung voraus, dass die untersuchten Unternehmen vergleichbare Produktionstechnologien anwenden (in Kapitel 3 und 4 vernachlässigt) und keine Unsicherheiten bezüglich der Inputpreise bestehen. Bei der Stromproduktion sind diese Annahmen jedoch verletzt, was eine Anwendung der klassischen Effizienzmethoden verunmöglicht. Notwendig wird eine risikoadjustierte Effizienzmessung, die den optimalen Mix der verfügbaren Technologien berücksichtigt. Kapitel 5 bestimmt die effiziente Stromproduktion in der Schweiz und den USA anhand einer Portfolioanalyse.
... The application of the portfolio optimization model in the electric sector has, however, been a rather absent subject of research. Among the few exceptions are a model of risk management in the short term, by applying the Markowitz model to optimize the portfolio and minimize risk in energy markets [13]. ...
Meta-heuristic search methods are used to find near optimal global solutions for difficult optimization problems. These meta-heuristic processes usually require some kind of knowledge to overcome the local optimum locations. One way to achieve diversification is to start the search procedure from a solution already obtained through another method. Since this solution is already validated the algorithm will converge easily to a greater global solution. In this work, several well-known meta-heuristics are used to solve the problem of electricity markets participation portfolio optimization. Their search performance is compared to the performance of a proposed hybrid method (ad-hoc heuristic to generate the initial solution, which is combined with the search method). The addressed problem is the portfolio optimization for energy markets participation, where there are different markets where it is possible to negotiate. In this way the result will be the optimal allocation of electricity in the different markets in order to obtain the maximum return quantified through the objective function.
... Several papers have also applied mean/variance portfolio theory across geographic locations. Yu (2003) considers the question of choosing efficient portfolios of energy and ancillary services sales by a generation owners able to sell in spatially distributed wholesale electricity markets. Roques, Hiroux, and Saguan (2010) consider the optimal country-level deployment of wind generation units for France, Denmark, Austria, Germany and Spain, using a sample of countrylevel hourly wind output in these five countries. ...
Hourly plant-level wind and solar generation output and real-time price data for one year from the California ISO control area is used to estimate the vector of means and the contemporaneous covariance matrix of hourly output and revenues across all wind and solar locations in the state. Annual hourly output and annual hourly revenues mean/standard deviation efficient frontiers for wind and solar resource locations are computed from this information. For both efficient frontiers, economically meaningful differences between portfolios on the efficient frontier and the actual wind and solar generation capacity mix are found. The relative difference is significantly larger for aggregate hourly output relative to aggregate hourly revenues, consistent with expected profit-maximizing unilateral entry decisions by renewable resource owners. Most of the hourly output and hourly revenue risk-reducing benefits from the optimal choice of locational generation capacities is captured by a small number of wind resource locations, with the addition of a small number of solar resource locations only slightly increasing the set of feasible portfolio mean and standard deviation combinations. Measures of non-diversifiable wind and solar energy output and revenue risk are computed using the actual market portfolio and the risk-adjusted expected hourly output or hourly revenue maximizing portfolios.
... Such a mix can be determined by applying mean-variance portfolio theory (see e.g. Kienzle and Andersson, 2008;Krey, 2008;Awerbuch, 2006;Yu, 2003;Berger et al., 2003;Humphreys and McClain, 1998;Bar-Lev and Katz, 1976). Here, a social planner (e.g. ...
This study applies financial portfolio theory to determine efficient frontiers in the provision of electricity for the United States and Switzerland. Expected returns are defined by the rate of productivity increase of power generation (adjusted for external costs), volatility, by its standard deviation. Since unobserved productivity shocks are found to be correlated, Seemingly Unrelated Regression Estimation (SURE) is used to filter out the systematic component of the covariance matrix of the productivity changes. Results suggest that as of 2003, the feasible maximum expected return (MER) electricity portfolio for the United States contains more Coal, Nuclear, and Wind than actual but markedly less Gas and Oil. The minimum variance (MV) portfolio contains markedly more Oil, again more Coal, Nuclear, and Wind but almost no Gas. Regardless of the choice between MER and MV, U.S. utilities are found to lie substantially inside the efficient frontier. This is even more true of their Swiss counterparts, likely due to continuing regulation of electricity markets.
... El modelo de media-varianza ha sido extendido a la optimización de Portafolios de Energía en distintos estudios (Jun et al., 2006). El problema de optimizar un Portafolio de Energía considerando contratos a plazo y unidades de generación fue presentado en Yu (2002). El problema consistió en minimizar la varianza del costo del Portafolio de Energía, sujeto a los límites de los costos de las transacciones, a las restricciones de las unidades de generación y a limitaciones nancieras. ...
Los Sistemas Eléctricos de Potencia (SEP) son constantemente modificados por la incorporación de nuevos proyectos que tienen como fin aumentar la capacidad de generación o de transmisión de energía eléctrica, así como mejorar el desempeño del SEP. Un Portafolio de Proyectos de Inversión en un Sistema Eléctrico de Potencia (PPISEP) es considerado en este trabajo como un conjunto de proyectos de ampliación de la capacidad instalada de un SEP. Estos proyectos de ampliación pueden consistir en incrementos de las capacidades de las plantas generadoras o de las líneas de transmisión del SEP. El presente trabajo desarrolla una metodología que permite mejorar los PPISEP. Esta mejora consiste en determinar el momento de inicio en el cual los proyectos de inversión se deben comenzar a construir y la cantidad de energía activa promedio que cada proyecto de inversión debe introducir al SEP, de tal forma que se incremente el balance económico de la empresa poseedora del SEP y se disminuya el consumo pronosticado no cubierto de energía activa promedio. Para ello, el SEP es considerado como un modelo de repartición de energía activa
promedio, por periodos de tiempo, desde los generadores hasta las cargas mediante líneas de transmisión. Debido a que la mejora del PPISEP entra dentro de un problema de optimización, el presente trabajo hace uso de la técnica de optimización Algoritmo Simplex Entero Mixto (ASEM) para plantear la resolución de este problema. La metodología desarrollada en este trabajo utiliza la simulación por Monte Carlo para modelar las aleatoriedades del SEP y se basa en diversos aspectos teóricos de la optimización mediante la
simulación, la planificación de la expansión de los SEP y la teoría de grafos. Dicha metodología es presentada en forma de pseudocódigo y la misma es implementada en un ejemplo numérico, cuyos resultados son analizados mediante herramientas estadísticas.
... None of the papers addressed above involves more than one locational electricity price process. [25,26,47] address the planning of contracts taking into account various locational electricity prices, but based on a Markowitz mean-variance scheme, not on stochastic programming. Many authors have used conditional value at risk (CVaR) for risk measuring (e.g. ...
This paper presents a medium term power portfolio optimization model for a power producer in a competitive electricity market, considering locational electricity prices and risk management. The methodology developed includes modeling the multivariate stochastic evolution of locational electricity prices, the construction of a scenario tree that represents this evolution, and the formulation and solution of a stochastic optimization model. Using this methodology a power producer holding thermal generating units in more than one location may maximize expected profit while keeping a limited risk exposure. The model considers the possibility of trading electricity forward contracts in different locations and contracts for difference. In addition, its output includes amounts of electricity transactions in locational spot markets and power production in generating units. The computational experiments performed indicate that the correlation between locational electricity prices is very relevant for power producers holding generating units in those locations, since it significantly affects the relation between expected profit and risk.
... The basic principle is akin to an index dealing with multiple types of risks of diversified sources. Yu (2003) presents a short-term market risk model based on the Markowitz mean-variance method for spatial electricity markets. Lesbirel (2004) explores the relationship between energy security and the diversification of sources by using MPT to calculate the systematic risks and specific risks to energy security faced by Japan from 1970to 1999. ...
... Applications of this concept to energy investment where risks are considered can be seen in[16][17][18][19]. Yu[20]presents a model to assess risks in a multi-pool setting. A comprehensive review of the state-of-the-art in energy portfolio can be found in Kienzle et al.[21]. ...
The rapid development of technologies, their increasing complexity and variety, long lead times of R&D and market dynamics have made the task of technology selection difficult. Considering high level of competitiveness, organizations need to strategically allocate their limited resources to the best subset of possible projects. Today, the increased consumption of energy in modern industrial societies, in addition to the risk of quick exhaustion of fossil resources, has brought about irreversible and threatening environmental changes faced by the world. Dealing with these challenges, decision makers focus on the development of renewable energy technology viewed both as a process of diversification of energy sources and as a creation of an alternative energy option that will help curb down global climate change. To successfully tackle investment projects in renewable energy, it is essential to use models facilitating decision making process and guarantying the greatest possible value for organizations. Technology portfolio managers have traditionally used consensus-based tools, such as Analytical Hierarchy Process (AHP), Delphi but these tools are limited in their ability to fully quantify the impact of technology portfolio selection on the overall aspects of the system. This paper presents the results of developing a mathematical model for renewable technology portfolio selection at an oil industry R&D center maximizing support of the organization's strategy and values. The model balances the cost and benefit of the entire portfolio. It is also flexible and changes can be applied very easily. (c) 2012 Elsevier Ltd. All rights reserved.
... Yu [7] presents a short-term market risk model based on the Markowitz mean-variance portfolio theory. The model is suitable for assessing the risk of profit making competitive power producers in a multi-pool setting. ...
In this paper the efficiency of the electricity generation portfolio of BKW, a major Swiss utility, is analyzed. By applying mean-variance portfolio theory to the current and to possible future generation mixes, efficient frontiers are derived. The analysis based on relative changes in generation costs is complemented by an actual costs analysis. More-over, a method that takes into account physical boundaries using the so-called capacity factor is presented in order to translate the obtained portfolio allocations into physical quantities, i.e. into required installed capacities. It is shown that the method gives useful insight regarding future investment plans and provides valuable support for investment decision makers.
... hanges are characterized by skewness and excess kurtosis, implying that conditional densities likely are not normal. However, under these conditions GARCH does not provide useful inferences and should be replaced by an alternative approach (Rabemananjara, 1993). In addition, possible correlations between price shocks are not speci…cally considered. Yu (2003) presents a short-term market risk model again based on the Markowitz mean-variance approach, where the covariance matrix re ‡ects di¤erent developments of fuel prices across regional electricity markets. Yu includes transaction costs and other constraints such as minimum contracting quantities that limit the amount of wheeling, resultin ...
Using …nancial portfolio theory, this study determines e¢ cient Swiss electricity gener-ating energy mixes. These e¢ cient allocations in fact satisfy at least two constitutional objectives of energy policy, viz. "secure provision" and "low cost to the economy". Expected returns are given by the (negative of the) future rate of increase of Swiss power generation costs. Volatility relates to the standard deviation of the portfolio composed of nuclear, run-of-river, hydro-storage, and solar tech-nologies. Since shocks in generation costs are correlated, we use the seemingly unrelated regression estimation (SURE) method for …ltering out the systematic component of the covariance matrix of the cost changes. When introducing constraints and taking account of external costs such as global warming and health losses, the results suggest that at observed generation costs 2003, the maximum expected return (MER) portfolio would call for a shift towards nuclear power and solar. By way of contrast, the minimum variance (MV) portfolio mainly contains nuclear power, hydro-storage, and solar. For 2035, the MER portfolio would nearly exclusively be based on nuclear, while the MV alternative would combine nuclear, run-of-river, solar, and gas. as well the participants in the Infrastructure Day (D-Berlin, 8 Oct 2005) for many helpful comments.
... In addition, possible correlations between price shocks are not specifically considered. Yu (2003) presents a short-term market risk model again based on the Markowitz meanvariance approach, where the covariance matrix reflects different developments of fuel prices across regional electricity markets. Yu includes transaction costs and other constraints such as minimum contracting quantities that limit wheeling, resulting in a mixed integer programming problem. ...
This study applies financial portfolio theory to determine efficient electricity-generating technology mixes for Switzerland and the United States. Expected returns are given by the (negative of the) rate of increase of power generation cost. Volatility of returns relates to the standard deviation of the cost increase associated with the portfolio, which contains Nuclear, Run of river, Storage hydro and Solar in the case of Switzerland, and Coal, Nuclear, Gas, Oil, and Wind in the case of the United States. Since shocks in generation costs are found to be correlated, the seemingly unrelated regression estimation (SURE) method is applied for filtering out the systematic component of the covariance matrix of the cost changes. Results suggest that at observed generation costs in 2003, the maximum expected return (MER) portfolio for Switzerland would call for a shift towards Nuclear and Solar, and therefore away from Run of river and Storage hydro. By way of contrast, the minimum variance (MV) portfolio mainly contains Nuclear power and Storage hydro. The 2003 MER portfolio for the United States contains Coal generated electricity and Wind, while the MV alternative combines Coal, Nuclear, Oil and Wind. Interestingly, Gas does not play any role in the determination of efficient electricity portfolios in the United States.
... Mean-variance portfolio analysis, an established part of modern finance theory, is based on the pioneering work of Markowitz (1952), Varian (1993) and Fabozzi et al. (2002). In addition to its widespread use for financial portfolio optimization, mean-variance portfolio analysis has been applied to valuing offshore oil leases [Helfat (1988)], real asset portfolios in electricity generation [among others, Lev and Katz (1976), Adegbulugbe et al. (1989), Humphreys and McClain (1998), Awerbuch (2000, Awerbuch and Berger (2003), Berger (2003), Yu (2003), Awerbuch et al. (2004), Wenk and Madlener (2007, and Krey and Zweifel (2009)], and quantifying climate change mitigation risks [Springer (2003)]. This section outlines in more detail the theory of Markowitz mean-variance portfolio theory, and explains its use in this contribution. ...
This study uses Markowitz mean-variance portfolio theory with forecasted data for the years 2005 to 2035 to determine efficient electricity generating technology mixes for Switzerland. The SURE procedure has been applied to filter out the systematic components of the covariance matrix. Results indicate that risk-averse electricity users in 2035 gain in terms of higher expected return, less risk, more security of supply and a higher return-to-risk ratio compared to 2000 by adopting a feasible minimum variance (MV) technology mix containing 28 percent Gas, 20 percent Run of river, 13 percent Storage hydro, 9 percent Nuclear, and 5 percent each of Solar, Smallhydro, Wind, Biomass, Incineration, and Biogas respectively. However, this mix comes at the cost of higher CO2 emissions.
... ting that the price changes are characterized by skewness and excess kurtosis, implying that conditional densities likely are not normal. However, under these conditions GARCH does not provide useful inferences and should be replaced by an alternative approach. In addition, possible correlations between price shocks are not specifically considered. Yu (2003) presents a short-term market risk model again based on the Markowitz mean-variance approach, where the covariance matrix reflects different developments of fuel prices across regional electricity markets. Yu includes transaction costs and other constraints such as minimum contracting quantities that limit wheeling, resulting in a mixed ...
This study applies financial portfolio theory to determine efficient electricity-generating technology portfolios for the United States and Switzerland, adopting an investor point of view. Expected returns are defined by the rate of decrease of power generation cost (with external costs included), their volatility, by its standard deviation. The 2003 portfolio contains Coal, Nuclear, Gas, Oil, and Wind in the case of the United States, and Nuclear, Storage hydro, Run of river, and Solar in the case of Switzerland, a country without domestic supplies of fossil fuels. Since shocks in generation costs are found to be correlated, Seemingly Unrelated Regression Estimation (SURE) is used to filter out the systematic component of the covariance matrix of the cost changes. Results suggest that as of 2003, the feasible maximum expected return (MER) electricity portfolio for the United States contains more Coal, Nuclear, and Wind than actual but markedly less Gas and Oil. By way of contrast, the minimum variance (MV) portfolio combines markedly more Oil, Coal, Nuclear, and Wind but almost no Gas. Therefore, regardless of the choice between MER and MV, U.S. utilities as investors are substantially inside the efficient frontier. This is even more true of their Swiss counterparts, likely due to continuing regulation of electricity markets.
بخش خصوصی نقش مهمی را در گسترش و بهرهبرداری از تولید برق در اکثر کشورها، به خصوص
کشورهایی که بازار آزاد برق دارند، ایفا میکند. سیاستگذاران وظیفه دارند تا از طریق
سیاستگذاریهای خود، بخش خصوصی را در جهت سرمایهگذاری هرچه بیشتر در این بخش ترغیب
کنند تا موجب رفاه بیشتر جامعه شود. متقابلا، وظیفه کارگزاران خصوصی این است که خود را در
برابر ریسکهای موجود در این بخش از جمله ریسک نظارتی 1، عدم اطمینان از قیمت سوخت، در
دسترس بودن منابع طبیعی، عدم اطمینان تقاضای برق، قیمت گرفتن و ذخیره کربندیاکسید و
غیره محافظت کنند . به جای توجه صرف به هزینههای پروژه بهتر است که بر معیار ریسک تمرکز
نمود. همچنین سرمایهگذاران خصوصی میتوانند از تنوع به عنوان یک استراتژی برای کاهش ریسک
استفاده کنند . در این مقاله مروری بر کاربردهای اصلی و چالشهای بهینهسازی پرتفوی برای دو
عامل اصلی بخش خصوصی، یعنی سرمایهگذاران و مدیران ارائه شده است . با مرور مقالات و ادبیات
پیشین نتیجهگیری شد که اولا، اطمینان بیش از حد به دادههای تاریخی و تحلیلهای آماری برای
پیشبینی رفتار آینده قیمتها و تغییرات آتی آن، به ضرر تحلیلهای ساختاری است. دوم،
تکنولوژیهای تجدیدپذیر که جزء جداییناپذیر تکنولوژیهای تولید انرژی برق هستند و نقش مهمی
در کاهش ریسک پرتفوی تولید برق دارند و این مسئله به دلیل دادههای ناکافی و پیچیدگی
محاسباتی تا حد زیادی در محاسبات پرتفوی نادیده گرفته شده است.
The private sector plays a major role in the expansion and operation of power systems in most countries, especially those running liberalized electricity markets. Policymakers have the task of inducing private agents, through their regulatory designs, to make decisions that point toward social welfare maximization. Conversely, it is a task of private agents to protect themselves against the risks of the sector, including regulatory risks, international fuel price uncertainty, climate change policies, natural resource availability, electricity demand uncertainty, CO2 clearance prices, etc. Instead of hiding all of these risks within the total project costs and losing competitiveness, private agents can use diversification as a strategy to deal with them. This paper presents a review of the main applications, voids and challenges of portfolio optimization for two key agents of the private sector: investors and managers. The problem of the investor is to design a technology portfolio to invest in that maximizes its expected returns and limits risks, while the manager has to design a portfolio of financial/physical instruments (long-term contracts, futures, etc.) to sell/buy electricity and hedge against price risks. We have found two fundamental issues in the literature; the first and most important is excessive confidence in historical data and statistical analysis for predicting future price behavior for a changing future in detriment of more structural analysis. Structural analysis can include particularities of modern power systems such as future transmission changes, congestion, operational constraints (ramps), new entrants, new technologies, and new demand grow patterns that cannot be taken into account by simply analyzing price historical values. The second is the omission of renewable complementarities, which is a proven characteristic of dispersed renewable plants that may have important risk-mitigation effects, although it has largely been ignored in portfolio analysis due to insufficient data, modeling limitations, and computational complexity.
With the development of electricity markets, trading scheduling with risk management becomes more and more important for Generation Companies (Gencos) to protect themselves from the risk of extreme price volatility in the spot market. This paper investigates the effect of two financial instruments (ie, futures contracts and financial transmission rights) in trading scheduling based on the principles of the Modern Portfolio Theory and hedging. Historical data of the PJM electricity market are used to demonstrate the proposed approach to energy allocation. Simulation results indicate that futures contracts and financial transmission rights can reduce the risk of spot and bilateral transaction, respectively, and therefore affect physical trading in these two markets to some extent.
In a deregulated electricity market with transmission constraints and limited number of producers, bidding strategy has become a major issue. In this market, each GenCo may increase its own profit through a favorable bidding strategy. This paper proposes a new method to obtain the Nash equilibrium points for optimal bidding strategy of GenCo's without the use of game theory. For this purpose, the first optimal bidding problem is modeled with two optimization sub-problem. In the first sub-problem, each GenCo maximizes its payoff, and in the second subproblem, a system dispatch will be accomplished. Then, particle swarm optimization (PSO) algorithm is used to find optimal bidding strategy of each GenCo in this method. finally, each GenCo update its optimal bidding strategy in terms of optimal bidding strategy of other GenCo's until Nash equilibrium points are obtained. The Western System Coordinating Council (WSCC) nine bus test system is used to illustrate the implementation of the proposed method for a typical power system.
This chapter addresses the problem of optimal investment in generation based on mean-variance portfolio analysis. It is assumed the investor can freely create a portfolio of shares in generation located on buses of the electrical network. Investors are risk averse, and seek to minimize the variance of the weighted average locational marginal price (LMP) in their portfolio, and to maximize its expected value. Simulations are conducted using a standard IEEE 68-bus network that resembles the New York-New England system, and LMPs are calculated in accordance with the PJM methodology for a fully optimal AC power flow solution. Results indicate that the network topology is a crucial determinant of the investment decision as line congestion makes it difficult to deliver power to certain nodes at system peak load. Determining those nodes is an important task for an investor in generation as well as the transmission system operator. Mean-variance analysis can be used by the system operator and investors to calculate the risk and returns from investments at various nodes in the system with stochastic load fluctuations. This approach takes into consideration both nodal price variance and covariance with the prices on the other nodes. The analysis becomes more complex when dynamic effects of the new investment on LMPs are taken into consideration, but these considerations may be important to the profitability of the new investment.
In the proposed approach, financial data are collected automatically and are input to a GM(1,1) prediction model to forecast the future trends of the collected data. The forecast data are then reduced using a GM(1,N) model, classified using a K-Means clustering algorithm, and processed by a Rough Set (RS) classification module which selects appropriate investment stocks. Finally, a Minimum Variance At Risk (MVAR) scheme comprising five Grey Relational Analysis (GRA) models and the Markowitz means-variance (MV) model is employed to identify the efficient frontier which achieves the optimal tradeoff between the minimum risk and the maximum rate of return.
This paper examines different types of optimization techniques and provides a spatial analysis of energy prices. The last decade has seen an increasing interest in deregulated energy markets. There are few papers, to the author's knowledge, that have considered portfolio optimization, however not in the Italian zonal energy market since deregulation. In deregulated energy markets with zonal pricing the market is partitioned into a number of zones, each of which is assigned a market price to which market participants react to at any given point in time. The paper investigates with emphasis on portfolio theory accounting for the initial capital requirement for the various zones in the Italian energy market and computes the optimal allocation weights needed in the various zones to mitigate the risk inherent in the market. The market risk subsequently affects the zonal prices since these prices combine to bring about the single national electricity price (prezzo unico d'acquisto, PUN). Implementing a modified version of the Mean–Variance portfolio theory, we draw policy implications based on the empirical evidence providing good risk management strategy for market participants.
Power system planning is a capital intensive investment-decision problem. The majority of the conventional planning conducted since the last half a century has been based on the least cost approach, keeping in view the optimization of cost and reliability of power supply. Recently, renewable energy sources have found a niche in power system planning owing to concerns arising from fast depletion of fossil fuels, fuel price volatility as well as global climatic changes. Thus, power system planning is under-going a paradigm shift to incorporate such recent technologies. This paper assesses the impact of renewable sources using the portfolio theory to incorporate the effects of fuel price volatility as well as CO2 emissions. An optimization framework using a robust multi-objective evolutionary algorithm, namely NSGA-II, is developed to obtain Pareto optimal solutions. The performance of the proposed approach is assessed and illustrated using the Indian power system considering real-time design practices. The case study for Indian power system validates the efficacy of the proposed methodology as developing countries are also increasing the investment in green energy to increase awareness about clean energy technologies.
Covers all major issues of CO₂ in Power Systems
Gives readers state of the art information on all aspects of power systems modeling and optimization
Provides even non-experts with an overview of the fields
The Handbook of CO₂in Power Systems' objective is to include the state-of-the-art developments that occurred in power systems taking CO₂emission into account. The book includes power systems operation modeling with CO₂emissions considerations, CO₂market mechanism modeling, CO₂regulation policy modeling, carbon price forecasting, and carbon capture modeling. For each of the subjects, at least one article authored by a world specialist on the specific domain is included.
In a competitive electricity market with highly fluctuated electricity price, local distribution companies (LDCs) need to purchase electric power from several energy markets, such as spot markets, long-term tolling agreements and forward contracts. This is to maximize profits and minimize risks. Conditional Value-at-Risk(CVaR) can measure risk efficiently, but only one kind of price distribution rule could be considered. In fact, the spot electricity price usually does not limited to normal distribution, and it might be shown as logarithmic normal distribution if there was no enough supply at peak load situation. In such case, the novel WCVaR method - Weighted Conditional Value-at-Risk - is proposed to measure the purchasing risk of LDC with multiple purchase options, especially when the electricity price has more than one distribution rules. The Mean-WCVaR model is built as a mathematical programming problem to derive the efficient frontier that indicates the optimal tradeoffs available to LDC between expected revenue and purchasing risk in several energy markets. Simulation results show the efficiency of the proposed model. The proposed model paves a new way for LDC to determine the optimal purchasing strategies considering the risk.
In a competitive electricity market with highly fluctuated electricity price, local distribution companies (LDCs) need to purchase electric power from several energy markets, such as spot markets, long-term tolling agreements and forward contracts, to maximize profits and minimize risks. Conditional Value-at-Risk (CVaR) can measure risk efficiently, but only one kind of price distribution rule may be considered. In fact, the spot electricity price usually does not follow the normal distribution, and it might be shown as logarithmic normal distribution if there was no enough supply at peak load situation. In this paper, a novel WCVaR method—Weighted Conditional Value-at-Risk—is proposed to measure the purchasing risk of LDC with multiple purchase options, especially when the electricity price follows more than one distribution rules. The Mean–WCVaR model is built as a mathematical programing problem to derive the efficient frontier that indicates the optimal tradeoffs available to LDC between expected revenue and purchasing risk in several energy markets. The existence of optimal solution of proposed WCVaR model is proved mathematically. Simulation results show the efficiency of the proposed model. The proposed model provides a new method for LDC to determine the optimal purchasing strategies considering the risk. Copyright © 2011 John Wiley & Sons, Ltd.
Using …nancial portfolio theory, this paper investigates energy mixes of Switzerland that e¢ ciently satisfy two constitutional objectives, viz. secure provision and low cost to the economy. The e¢ cient frontier in terms of …nal consumption is constructed esti-mating time-varying variances and covariances in energy prices us-ing GARCH (Generalized Autoregressive Conditional Heteroscedas-tic) models. Additionally, the TGARCH variant serves to control for excess kurtosis. The results suggest that at observed market prices, a shift towards nuclear power and away from natural gas and gasoline would reduce both expected increase in the Swiss energy bill and its price volatility.
In this study, Markowitz mean-variance portfolio theory is applied to electricity-generating technologies of the United States
and Switzerland. Both an investor (focused on changes in return) and a current user (focused on return in levels) view are
adopted to determine efficient frontiers of electricity generation technologies in terms of expected return and risk as of
2003. Since shocks in generation costs per kWh (the inverse of returns) are correlated, Seemingly Unrelated Regression Estimation
(SURE) is used to filter out the systematic components of the covariance matrix. Results suggest that risk-averse investors
and risk-neutral current users in the United States are considerably closer to their efficiency frontier than their Swiss
counterparts. This may be due to earlier and more thorough deregulation of electricity markets in the United States.
In dieser Studie werden effiziente Portfolien nach Markowitz für die USA und der Schweiz berechnet. Dabei wird die Sicht eines
Investors (für den die Rendite der Veränderung der gewonnen kWh/USD entspricht) der Sicht des laufenden Benutzers (für den
die Rendite den kWh/USD selbst entspricht) gegenübergestellt. De zwischen den Schocks, die auf die Stromerzeugungskosten einwirken,
Korrelationen bestehen, wird das SURE (Seemingly Unrelated Regression Estimation) Verfahren angewendet, um eine über die Zeit
stabile Kovarianzmatrix zu erhalten. Das tatsächliche Technologieportfolio der USA liegt dichter an der Effizienzgrenze als
dasjenige der Schweiz. Ein möglicher Grund hierfür ist die Energiemarktliberalisierung, die in den USA deutlich weiter vorangeschritten
ist als in der Schweiz.
This paper provides an analysis on renewable energy development in China, and discusses the impact of the recently enacted national renewable energy law and related government policy and provisions. The paper centers on analyzing wind power development since wind power has almost reached the stage of commercialization. It shows that China has a huge wind resource which can be more evenly harvested to relive the country from devastating pollution problems. However, in order to better use its wind resources in the country, a few management and technical issues will have to be streamlined.
A power supplier in deregulated environment needs to allocate its generation capacities to participate in contract and spot markets. The well-known mean-variance method is inappropriate to deal with assets whose price distribution is non-normal. In order to model the electricity assets with different distributions into portfolio optimization, this paper proposes a stochastic programming approach based on genetic algorithm and Monte-Carlo simulation. In the real market data based numerical study, the performances of the proposed method and the standard mean-variance method are compared. It was found that the proposed method can obtain significantly better portfolios in the situation that non-normally distributed assets exist for trading. The modeling capacity, flexibility and robustness will make the proposed method potentially useful in application.
This paper presents a new generation expansion model that considers the fluctuation of fuel prices and effects of CO2 trading. This model is applied to Viet Nam power sector during 2013-2030. This model finds out the efficient curve containing all feasible technology mixes. Each feasible mix represented by a value of risk-aversion factor has different value of risk, revenue from CO2 trading and present value of total cost (PVTC). The result shows that the higher the PVTC, the lower the volatility of fuel cost and the higher the revenue from CO2 trading. In the case of Viet Nam, if the investor selects high value of risk-aversion factor, renewables, such as solar and win, will become attractive. Furthermore, coal will be the dominant technology that replaces gas and oil.
An electric power supplier in the deregulated environment needs to allocate its generation capacities to participate in contract and spot markets. Different trading portfolios will provide suppliers with different future revenue streams of various distributions. The classical mean-variance (MV) method is inappropriate to deal with the trading portfolios whose return distribution is non-normal. In order to consider the non-normal characteristics in electricity trading, this study proposes a new model based on expected utility theory (EUT) and employs a hybrid genetic algorithm (GA) - Monte-Carlo simulation technique as solution approach. In the real market data-based numerical studies, the performances of the proposed method and the standard MV method are compared. It was found that the proposed method is able to obtain better portfolios than MV method when non-normal asset exists for trading. The simulation results also reveal the accumulation effect along trading period, which will improve the normality of the supplier trading portfolios. The authors believe the proposed method is a useful complement for the MV method and conditional value at risk (CVaR)-based methods in the supplier trading portfolio decision and evaluation.
In the competitive electricity market environment, generation dispatching is bid-based, and individual generation companies (Gencos) are required to compete with rivals through bidding to the market. Competition implies the opportunities for Gencos to get more profit and, in the meantime, the risk of not being dispatched. As a result, it has become a major concern for Gencos to build optimal bidding strategies so as to maximize profits while minimizing risks associated. In this paper, a new approach is developed for building optimal bidding strategies with risks taken into account for Gencos participating in a pool-based single-buyer electricity market. It is assumed that each Genco bids a linear supply function and that the system is dispatched to minimize the total purchasing cost of the single-buyer. Each Genco chooses the coefficients in the linear supply function for making tradeoff between two conflicting objectives: profit maximization and risk minimization. A stochastic optimization model is established for the purpose and a novel method for solving this problem is presented. Numerical test results for a simulated electricity market with six Gencos show clearly the essential features of the developed model and method.
The paper concentrates on the analysis of semivariance (SV) as a market risk measure for market risk analysis of mean–semivariance (MSV) portfolios. The advantage of MSV over variance as a risk measure is that MSV provides a more logical measure of risk than the MV method. In addition, the relationship of the SV with the lower partial movements is discussed. A spatial risk model is proposed as a basis of risk assessment for short-term energy markets. Transaction costs and other practical constraints are also included. A case study is provided to show the successful application of the model.
This article presents a model for investing in renewable energies in the framework of the Spanish electricity market in a way that risk is minimized for the investor while returns are maximized. The model outlined here is based on an economic model for calculating cash flows intended to obtain the internal rate of return (IRR) of the different energies being studied: wind, photovoltaic, mini hydro and thermo electrical. The IRRs obtained are considered the returns on investment, while their standard deviations are considered associated risks. In order to minimize risk, a comprehensive portfolio of investments is created that includes all off the available energies by means of a system of linear equations. The solution of the linear system is graphically checked using the efficient frontier method for the different financing options. Several case studies within the Renewable Energies Plan (PER is its Spanish abbreviation) that is in force in Spain in the period 2005-2010 are analysed in order to illustrate the method, as are other case studies using different types of financing, helping us to reach the pertinent conclusions.
In principle, portfolio optimization in electricity markets can make use of the standard mean-variance model going back to Markowitz. Yet a key restriction in most electricity markets is the limited liquidity. Therefore the standard model has to be adapted to cope with limited liquidity. An application of this model shows that the optimal hedging strategy for generation portfolios is strongly dependent on the size of the portfolio considered as well as on the variance-covariancematrix used and the liquidity function assumed.
In most electricity markets, a key restriction for portfolio optimization is the limited liquidity. Hence, standard models for decision problems have to be adapted to cope with this situation. This paper shows an approach dealing with this situation by including a liquidity function into the standard mean-variance model going back to Markowitz. This leads to a quadratic optimization problem which is solved by using the Lagrange method. The main purpose of this paper is to analyse the optimal hedging strategies for power generators. For this, three different case studies are regarded to recognize several effects like dependency on the planning horizon or the interdependencies of electricity markets and the markets for fossil-fuels or CO2 certificates. Therefore, the case of base electricity on the German power exchange EEX, the case of coal at the API and the CO2 certificates are considered.
J. F. Benders devised a clever approach for exploiting the structure of mathematical programming problems withcomplicating variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more tractable). For the class of problems specifically considered by Benders, fixing the values of the complicating variables reduces the given problem to an ordinary linear program, parameterized, of course, by the value of the complicating variables vector. The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for building up adequate representations of (i) the extremal value of the linear program as a function of the parameterizing vector and (ii) the set of values of the parameterizing vector for which the linear program is feasible. Linear programming duality theory was employed to derive the natural families ofcuts characterizing these representations, and the parameterized linear program itself is used to generate what are usuallydeepest cuts for building up the representations.In this paper, Benders'' approach is generalized to a broader class of programs in which the parametrized subproblem need no longer be a linear program. Nonlinear convex duality theory is employed to derive the natural families of cuts corresponding to those in Benders'' case. The conditions under which such a generalization is possible and appropriate are examined in detail. An illustrative specialization is made to the variable factor programming problem introduced by R. Wilson, where it offers an especially attractive approach. Preliminary computational experience is given.
The paper disputes the negative conclusion of prof. Mandler on the thesis by Garegnani, Schefold, Parrinello that intertemporal general equilibrium theory too is undermined by reswitching and reverse capital deepening. The paper argues that Mandler’s conclusion rests upon highly criticisable assumptions that render the equations of intertemporal general equilibrium identical to those of general equilibria without capital goods. The Walrasian treatment of the capital endowment is criticized in Part I on the basis of its insufficient persistence, and of other ‘methodological’ criticisms that are systematically surveyed. In Part II it is shown through a numerical example that Mandler’s claim, that the assumption of a single consumer guarantees uniqueness of intertemporal equilibrium independently of reswitching or reverse capital deepening, rests on the absence of production of capital goods in the last period of the equilibrium; this assumption is thus revealed to be one of the tricks that prevents the existence of capital goods from changing the properties of the equilibrium relative to those of equilibria without capital
This paper outlines a decision analysis procedure to guide
dispatchers in applying corporate policy for economic decisions when
risk is involved. These techniques enable dispatchers to implement
corporate policies without waiting for an answer from another group or
groups within accepted guidelines. The intent of the procedure is to
reduce the guidelines to expert system rules, which may be applied
without extensive analysis. Such a set of tools is often used in other
industries by administrative staff instead of engineering staff. Tools
such as the one reported here are needed for the new business
environment for profit opportunities to be achieved while maintaining
security. The tool described within this paper was designed for a
mid-western generation company to handle reserve or contingent contract
requests
Portfolio management in the finance literature has typically used optimization algorithms to determine security allocations within a portfolio in order to obtain the best tradeoff between risk and return. These algorithms, despite some improvements, are restrictive in terms of an investor's risk aversion (utility function). Since individual investors have different levels of risk aversion, this paper proposes two portfolio optimization algorithms that can be tailored to the specific level of risk aversion of the individual investor and performs ex-post evaluation tests of the algorithm performance. I.
This paper introduces a convex and normally constrained hydrothermal scheduling method. Convexity is achieved by using a hydro water loss term and a piece-wise linear representation of the relationship between water head and volume. A basic technique is developed for obtaining normal constraints, developed for the first time in this paper, by converting the conditional constraints into unconditional constraints. An example of the conditional constraints is the hydrothermal unit on/off status being expressed as a function of the unit minimum up/down times. Unit start-up and shut-down variables are summed over the minimum-up time and the minimum-down time and the summations are being limited to one. In each case this is to prevent immature unit start-up or shut-down. This allows the hydrothermal scheduling problem to become an ordinary mixed integer problem that can be solved by using standard commercial mixed integer programming solvers. These solvers can be purchased on the market for a few thousand dollars, far below the prices of the specially designed hydrothermal scheduling software products from consulting firms. The algorithm developed in this paper is tested for different cases with good results, especially for small hydrothermal systems.
Grantham, Mayo, Van Otterloo and Company LLC (GMO)uses mixed-integer-programming (MIP) methods to construct portfolios that are close (in terms of sector and security exposure) to target portfolios, have the same liquidity, turnover, and expected return as the target portfolios, control frictional costs, and do so with fewer dist inct stocks and with fewer transactions. It also applies MIP methods to portfolios consisting of several subportfolios. It uses the MIP approach to construct 11 quantitatively managed portfolios representing over 4 million by reducing the number of trading tickets written by 75 to 85 percent; (5) improving the trading process; and (6) improving performance in simulation in a US fund consisting of growth stocks with small market capitalization.
A great many people provided comments on early versions of this paper which led to major improvements in the exposition. In addition to the referees, who were most helpful, the author wishes to express his appreciation to Dr. Harry Markowitz of the RAND Corporation, Professor Jack Hirshleifer of the University of California at Los Angeles, and to Professors Yoram Barzel, George Brabb, Bruce Johnson, Walter Oi and R. Haney Scott of the University of Washington.
When transmission constraints limit the flow of power in an electric network, there are likely to be strong interaction effects across different parts of the system. A model of imperfect competition with strategic interactions in an electricity transmission network illustrates a possible exercise of market power that differs from the usual analysis of imperfect competition in more familiar product markets. Large firms could exercise horizontal market power by increasing their own production, lowering some prices, and exploiting the necessary feasibility constraints in the network to foreclose competition from others. This behavior depends on the special properties of electric networks, and reinforces the need for market analysis with more realistic network models.
The original Markowitz model of portfolio selection has received a widespread theoretical acceptance and it has been the basis for various portfolio selection techniques. Nevertheless, this normative model has found relatively little application in practice when some additional features, such as fixed costs and minimum transaction lots, are relevant in the portfolio selection problem. In this paper different mixed-integer linear programming models dealing with fixed costs and possibly minimum lots are introduced. Due to the high computational complexity of the models, heuristic procedures, based on the construction and optimal solution of mixed integer subproblems, are proposed. Computational results obtained using data from the Milan Stock Exchange show how the proposed heuristics yield very good solutions in a short computational time and make possible some interesting financial conclusions on the impact of fixed costs and minimum lots on portfolio composition.
The general mean-semivariance portfolio optimization problem seeks to determine the efficient frontier by solving a parametric non-quadratic programming problem. In this paper it is shown how to transform this problem into a general mean-variance optimization problem, hence the Critical Line Algorithm is applicable. This paper also discusses how to implement the critical line algorithm to save storage and reduce execution time.
Economics plays a major role in the application of reliability concepts and the attainment of an acceptable level of reliability. Inadequate reliability of electric power supply ultimately costs the customers much more than good reliability. It is therefore important to determine the optimal reliability level at which the reliability investment achieves the best results in reducing the customer damage costs due to power supply interruptions. This paper presents a technique to calculate cost related reliability indices of a composite system at the load points and for the overall system. These cost related reliability indices are calculated in the form of both annualized and annual values. System studies conducted on two reliability test systems are presented, which provide insight into the variation of the indices with different system factors.
Sumario: I. Illustrative portfolio analyses -- II. Relationships between securities and portfolios -- III. Efficient portfolios -- IV. Rational choice under uncertainty. Bibliografía : P. 305-314
Examines the arbitrage model of capital asset pricing as an alternative to the mean variance capital asset pricing model introduced by Sharpe, Lintner and Treynor. Overview of the arbitrage theory; Role of the arbitrage model in explaining phenomena observed in capital markets for risky assets; Influence of the presence of noise on the pricing relation. (Из Ebsco)
Transactions costs invalidate the Black‐Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. Discrete revision using Black‐Scholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. This paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision. The technique permits calculation of the transactions costs of option replication and provides bounds on option prices.
The Environmental Stewardship Scheme provides payments to farmers for the provision of environmental services based on agricultural foregone income. This creates a potential incentive compatibility problem which, combined with an information asymmetry on farm land heterogeneity, could lead to adverse selection of farmers into the scheme. However, the Higher Level Scheme (HLS) design includes some features that potentially reduce adverse selection. This paper studies the adverse selection problem of the HLS using a principal agent framework at the regional level. It is found that, at the regional level, the enrolment of more land from lower payment regions for a given budget constraint has led to a greater overall contracted area (and thus potential environmental benefit) which has had the effect of reducing the adverse selection problem. In addition, for landscape regions with the same payment rate (i.e. of the same agricultural value), differential weighting of the public demand for environmental goods and services provided by agriculture (measured by weighting an environmental benefit function by the distance to main cities) appears to be reflected into the regulator’s allocation of contracts, thereby also reducing the adverse selection problem.
Investor owned generation is being encouraged all over the world
by the de-regulatory climate and the need to defray the heavy capital
demands of plant. Contracts between the investor and the host utility
determine the price of electricity and include penalties for nondelivery
and compensation for failure to accept contracted energy. While it is
widely appreciated that uncertainty of future conditions has an
important bearing on the terms of the contract, especially in developing
countries, a theoretical framework for examining these factors has not
been developed. A theoretical model for linking the degree of future
uncertainty, the expected production costs of the investor and the
expected production cost of the host utility, with the electricity
prices and penalty charges, is developed in this paper. The insight
gained from these mathematical models will be useful in contractual
decision making. The financial strategy employed is known as Build
Operate and Transfer (BOT)
Deregulation in the US electric utility industry has lead to the
entry of many new market participants, particularly power marketers,
which in turn has lead to a much more active and fluid electricity
market. With the advent of new market instruments that can be used to
hedge one's exposure to market risks, power portfolio management takes
on new meaning and new tools and techniques can be used to manage risk.
This paper concentrates on long-term project valuation and power
portfolio management issues in a competitive environment. It describes a
method of valuing risky projects based on options pricing theory and
decision analysis and its implementation to long-term power portfolio
management or integrated resource planning for an electric utility in
Texas. The author believes that the methodology described in this paper
has wide application in the deregulated competitive electricity market
from integrated resource planning for utilities facing competition and
valuing a power plant investment by an independent power producer to
pricing electricity options
This paper proposes solutions for electricity producers in the
field of financial risk management for electric energy contract
evaluation. The efficient frontier is used as a tool to identify the
preferred portfolio of contracts. Each portfolio has a probability
density function for the profit. For important scheduling policies,
closed form solutions are found for the amount of futures contracts that
correspond to the efficient frontier. Production scheduling must
consider resource constraints. It is found that, without resource
constraints, the portfolio with the highest expected profit can be
preferred-even for a risk-averse decision-maker. When resource
constraints are present, portfolios not corresponding to the maximum
expected profit criteria will more frequently be preferred
Series FACTS such as series capacitors or phase shifters, by
controlling the power flows in a network, can help reduce the flows in
heavily loaded lines, resulting in an increased loadability of the
network and a reduced cost of production. The influence of multiple
phase shifters on the network flows is complex, because they interact on
one another, and the problem of the optimal location is essential. This
paper proposes an index for measuring the benefit of a given set of
phase shifters. The best location for a set of phase shifters is found
by a genetic algorithm for a 36 line test case and for the French
network
This paper presents a methodology to analyze the risk of short
term power system operational planning in the presence of electrical
load forecast uncertainty. As the authors' methodology requires an
estimate of the load forecast variance, a Bayesian load forecaster is
used in the practical implementation. They express their results as a
function of forecast lead time from one to five days into the future, in
terms of $/MWH. The risk due to load forecast uncertainty is based on
the forecast variance, and found by determining the expected cost of
perfect information. They illustrate their risk evaluation method in a
case study with utility-derived power system data and temperature
forecast data from the US National Weather Service
The purpose of this paper is to report the extension of an
analytical method of comparing natural diversity with controlled
diversity, and to show the results of comparing the peak load resulting
from natural diversity in a set of nonidentical air conditioning units
to the peak load of the same set of air conditioners under DSM control.
The central limit theorem for nonidentical distributions is used as the
theoretical background for the extension. Several case studies are
illustrated and the results show that the peak load reduction by direct
load control is almost linearly proportional to the increases of the
on-time ratios of the air conditioners under control
The purpose of this paper is to report an analytical method of
comparing natural diversity with controlled diversity, and to show the
results of comparing the peak load resulting from natural diversity in a
set of air conditioning units to the peak load that can be achieved with
DSM control of the same set of air conditioners. In this study it is
assumed that the energy use by the air conditioners is the same in both
cases. Under this assumption, an analytical model for finding the
probabilities of all the possible peak loads is developed and
illustrated in case studies
This paper presents a genetic algorithm (GA) solution to the unit
commitment problem. GAs are general purpose optimization techniques
based on principles inspired from the biological evolution using
metaphors of mechanisms such as natural selection, genetic recombination
and survival of the fittest. A simple GA algorithm implementation using
the standard crossover and mutation operators could locate near optimal
solutions but in most cases failed to converge to the optimal solution.
However, using the varying quality function technique and adding problem
specific operators, satisfactory solutions to the unit commitment
problem were obtained. Test results for power systems of up to 100 units
and comparisons with results obtained using Lagrangian relaxation and
dynamic programming are also reported
This paper discusses the evaluation of risk management strategies
as a part of integrated resource planning. Value- and scope-related
uncertainties can be addressed during the process of planning, but
uncertainties in the operating environment require technical analysis
within planning models. Flexibility and robustness are two key classes
of strategies for managing the risk posed by these uncertainties. This
paper reviews standard capacity expansion planning models and shows that
they are poorly equipped to compare risk management strategies. Those
that acknowledge uncertainty are better at evaluating robustness than
flexibility, which implies a bias against flexible options. Techniques
are available to overcome this bias
Load uncertainty contributes to system operational risk; thus the
study of system operating reserve or unit commitment risk requires a
load model that includes the uncertainty in load as well as the
variation with time. The authors propose a Gauss-Markov load model. This
random process model includes both the time variation and the
uncertainty in load. This load model is used to predict, conditional on
what is known at a previous hour, the mean and the variance of the
system hourly load. This mean and variance are required for a system
operating reserve study and a broad spectrum of production simulations.
The proposed load model is described, the model is justified, and the
model is illustrated via an example