There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

1 Introduction 2 Electromagnetic Transients 3 Synchronous Machine Modeling 4 Synchronous Machine Control Models 5 Single-Machine Dynamic Models 6 Multimachine Dynamic Models 7 Multimachine Simulation 8 Small-Signal Stability 9 Energy Function Methods Appendix A: Integral Manifolds for Model Bibliography Index

Power System Dynamics and Stability

https://www.lef.wiwi.uni-due.de/fileadmin/fileupload/BWL-LEF/Seminarreihe/RWeron14_Essen.pdf

Electricity price forecasting: A review of the state-of-the-art with a look into the future

A variety of methods and ideas have been tried for electricity price forecasting (EPF) over the last 15 years, with varying degrees of success. This review article aims at explaining the complexity of available solutions, their strengths and weaknesses, and the opportunities and treats that the forecasting tools offer or that may be encountered. The paper also looks ahead and speculates on the directions EPF will or should take in the next decade or so. In particular, it postulates the need for objective comparative EPF studies involving (i) the same datasets, (ii) the same robust error evaluation procedures and (iii) statistical testing of the significance of the outperformance of one model by another.

Preface. Acknowledgments. 1 Complex Electricity Markets. 1.1 Liberalization. 1.2 The Marketplace. 1.2.1 Power Pools and Power Exchanges. 1.2.2 Nodal and Zonal Pricing. 1.2.3 Market Structure. 1.2.4 Traded Products. 1.3 Europe. 1.3.1 The England and Wales Electricity Market. 1.3.2 The Nordic Market. 1.3.3 Price Setting at Nord Pool. 1.3.4 Continental Europe 13. 1.4 North America. 1.4.1 PJM Interconnection. 1.4.2 California and the Electricity Crisis. 1.4.3 Alberta and Ontario. 1.5 Australia and New Zealand. 1.6 Summary. 1.7 Further Reading. 2 Stylized Facts of Electricity Loads and Prices. 2.1 Introduction. 2.2 Price Spikes. 2.2.1 Case Study: The June 1998 Cinergy Price Spike. 2.2.2 When Supply Meets Demand. 2.2.3 What is Causing the Spikes?. 2.2.4 The Definition. 2.3 Seasonality. 2.3.1 Measuring Serial Correlation. 2.3.2 Spectral Analysis and the Periodogram. 2.3.3 Case Study: Seasonal Behavior of Electricity Prices and Loads. 2.4 Seasonal Decomposition. 2.4.1 Differencing. 2.4.2 Mean or Median Week. 2.4.3 Moving Average Technique. 2.4.4 Annual Seasonality and Spectral Decomposition. 2.4.5 Rolling Volatility Technique. 2.4.6 Case Study: Rolling Volatility in Practice. 2.4.7 Wavelet Decomposition. 2.4.8 Case Study: Wavelet Filtering of Nord Pool Hourly System Prices. 2.5 Mean Reversion. 2.5.1 R/S Analysis. 2.5.2 Detrended Fluctuation Analysis. 2.5.3 Periodogram Regression. 2.5.4 Average Wavelet Coefficient. 2.5.5 Case Study: Anti-persistence of Electricity Prices. 2.6 Distributions of Electricity Prices. 2.6.1 Stable Distributions. 2.6.2 Hyperbolic Distributions. 2.6.3 Case Study: Distribution of EEX Spot Prices. 2.6.4 Further Empirical Evidence and Possible Applications. 2.7 Summary. 2.8 Further Reading. 3 Modeling and Forecasting Electricity Loads. 3.1 Introduction. 3.2 Factors Affecting Load Patterns. 3.2.1 Case Study: Dealing with Missing Values and Outliers. 3.2.2 Time Factors. 3.2.3 Weather Conditions. 3.2.4 Case Study: California Weather vs Load. 3.2.5 Other Factors. 3.3 Overview of Artificial Intelligence-Based Methods. 3.4 Statistical Methods. 3.4.1 Similar-Day Method. 3.4.2 Exponential Smoothing. 3.4.3 Regression Methods. 3.4.4 Autoregressive Model. 3.4.5 Autoregressive Moving Average Model. 3.4.6 ARMA Model Identification. 3.4.7 Case Study: Modeling Daily Loads in California. 3.4.8 Autoregressive Integrated Moving Average Model. 3.4.9 Time Series Models with Exogenous Variables. 3.4.10 Case Study: Modeling Daily Loads in California with Exogenous Variables. 3.5 Summary. 3.6 Further Reading. 4 Modeling and Forecasting Electricity Prices. 4.1 Introduction. 4.2 Overview of Modeling Approaches. 4.3 Statistical Methods and Price Forecasting. 4.3.1 Exogenous Factors. 4.3.2 Spike Preprocessing. 4.3.3 How to Assess the Quality of Price Forecasts. 4.3.4 ARMA-type Models. 4.3.5 Time Series Models with Exogenous Variables. 4.3.6 Autoregressive GARCH Models. 4.3.7 Case Study: Forecasting Hourly CalPX Spot Prices with Linear Models. 4.3.8 Case Study: Is Spike Preprocessing Advantageous?. 4.3.9 Regime-Switching Models. 4.3.10 Calibration of Regime-Switching Models. 4.3.11 Case Study: Forecasting Hourly CalPX Spot Prices with Regime-Switching Models. 4.3.12 Interval Forecasts. 4.4 Quantitative Models and Derivatives Valuation. 4.4.1 Jump-Diffusion Models. 4.4.2 Calibration of Jump-Diffusion Models. 4.4.3 Case Study: A Mean-Reverting Jump-Diffusion Model for Nord Pool Spot Prices. 4.4.4 Hybrid Models. 4.4.5 Case Study: Regime-Switching Models for Nord Pool Spot Prices. 4.4.6 Hedging and the Use of Derivatives. 4.4.7 Derivatives Pricing and the Market Price of Risk. 4.4.8 Case Study: Asian-Style Electricity Options. 4.5 Summary. 4.6 Further Reading. Bibliography. Index.

Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach

In this paper, the most frequently used power system maintenance strategies are reviewed. Distinction is made between strategies where maintenance consists of replacement by a new (or "good as new") component and where it is represented by a less costly activity resulting in a limited improvement of the component's condition. Methods are also divided into categories where maintenance is performed at fixed intervals and where it is carried out as needed. A further distinction is made between heuristic methods and those based on mathematical models; the models themselves can be deterministic or probabilistic. From a review of present maintenance policies in electric utilities, it is concluded that maintenance at fixed intervals is the most frequently used approach, often augmented by additional corrections. Newer "as needed"-type methods, such as reliability-centered maintenance (RCM), are increasingly considered for application in North America, but methods based on mathematical models are hardly ever used or even considered. Yet only mathematical approaches where component deterioration and condition improvement by maintenance are quantitatively linked can determine the effect of maintenance on reliability. Although more complex, probabilistic models have advantages over deterministic ones: they are capable of describing actual processes more realistically, and also facilitate optimization for maximal reliability or minimal costs.

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The Present Status of Maintenance Strategies and the Impact of Maintenance on Reliability

Role of probability models in power system engineering concepts and theorems of probability random variables functions of random variables stochastic processes decision analysis reliability probabilistic structural design and analysis of transmission systems preventive maintenance, inspection and replacement probabilistic load flow probabilistic short circuit analysis probabilistic power system stability Monte Carlo simulation elements of acceptance sampling.

Probability Concepts in Electric Power Systems

This paper introduces a method for forecasting energy prices using artificial intelligence methods, such as neural networks and fuzzy logic, and a combination of the two. The new approach is compared with some of the exiting methods. Various factors affecting the market clearing price are investigated. Results for the Ontario electricity market are presented.

Energy price forecasting in the Ontario competitive power system market

The purpose of maintenance is to extend equipment lifetime, or at least the mean time to the next failure. While too little maintenance may have very costly consequences, maintenance, too, incurs expenditures and it may not be economical to perform it too frequently. Therefore, the two costs must be balanced. In the past, attempts to approximate this balance have often been based on trial and error. In this paper, a probabilistic model is proposed for the purpose, and a computer program based on this model is described. The model provides a quantitative connection between reliability and maintenance, a link missing in the heuristic approaches. The component ageing process is modelled, and the mean and distribution of the remaining life to failure are predicted for any stage of ageing. The method is applied to a practical example.

George J. Anders

Papers

The Present Status of Maintenance Strategies and the Impact of Maintenance on Reliability

Probability Concepts in Electric Power Systems

Energy price forecasting in the Ontario competitive power system market

Probabilistic evaluation of the effect of maintenance on reliability. An application [to power systems]

Rating of Electric Power Cables: Ampacity Computations for Transmission, Distribution, and Industrial Applications