Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of testing the hypothesis that p = 1.

https://www.jstor.org/stable/info/2286348

Distribution of the Estimators for Autoregressive Time Series with a Unit Root

/pdf/economics-of-natural-resources-and-the-environment-43k62iyyte.pdf

Economics of natural resources and the environment

Hawaii International Conference on System Sciences

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.

Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters

This paper proposes a methodology for choosing the best transmission expansion plan considering various types of security (operating reliability) criteria. The proposed method minimizes the total cost that includes the investment cost of transmission as well as the operating cost and standby cost of generators. The purpose of the study is development of new methodology for solving transmission system expansion planning problem subject to contingency criteria which are essentially extensions of the (N-1) contingency criterion. The transmission expansion problem uses an integer programming framework, and the optimal strategy is determined using a branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. The characteristics of the proposed method are illustrated by applying it to a five-bus system and a 21-bus system. The results of these case studies demonstrate that the proposed method provides a practical way to find an optimal plan for power system expansion planning.

Transmission Expansion Planning Using Contingency Criteria

The restructured market for electricity in the UK has experienced a systematic pattern of price spikes associated with the use of market power by the two dominant generators. Partly in response to this problem, the share of capacity owned by any individual generator after restructuring was limited in Victoria, Australia. As a result, a much more competitive market resulted with prices substantially lower than they were under regulation. Nevertheless, an erratic pattern of price spikes exists and the price volatility is a potential problem for customers. This paper argues that the use of a uniform price auction (UPA) for electricity markets exacerbates price volatility. A discriminatory price auction (DPA) is proposed as a better alternative that would reduce the responsiveness of price to errors in forecasting total load.

Market power and price volatility in restructured markets for electricity

Probabilistic reliability criteria, such as LOLP, LOLE, EENS etc., have been used extensively for generation expansion planning throughout the world. Typically, only deterministic reliability criteria, such as (N-1) or (N-2) contingencies, have been used for grid expansion planning until now. The main reason is the difficulty in determining the optimum design of a grid expansion plan using probabilistic reliability criteria and in developing the appropriate mathematical model that incorporates the chosen reliability criterion for the transmission system. Optimum design in grid expansion planning is still an important element of overall electric power system planning in deregulated electricity markets. One of the potential improvements in generation and grid expansion planning comes from the use of a more realistic reliability level as a criterion to constrain the form of the optimum expansion problem. A methodology is proposed that uses a probabilistic reliability criterion to determine an optimum plan for transmission system expansion using a criterion that minimises the expected cost, which includes both construction and outage costs, using a probabilistic reliability criterion loss of load expectation R
LOLE. The optimum value of the reliability criterion R
LOLE
 *
 is determined at the minimum value of the combined total of the cost of constructing new transmission and the customer outage cost associated with supply interruptions. The characteristics and effectiveness of this methodology are illustrated by a case study using a 21-busbar test system

Probabilistic reliability criterion for planning transmission system expansions

It is well known that given a network that can become constrained on voltage or real power flows, reserves must also be spatially located in order to handle all credible contingencies. However, to date, there is no credible science-based method for assigning and pricing reserves in this way. Presented in this paper is a new scheduling algorithm incorporating constraints imposed by grid security considerations, which include one base case (intact system) and a list of possible contingencies (line-out, unit-lost, and load-growth) of the system. By following a cost-minimizing co-optimization procedure, both power and reserve are allocated spatially for the combined energy and reserve markets. With the Lagrange multipliers (dual variables) obtained, the scheduling algorithm also reveals the locational shadow prices for the reserve and energy requirements. Unlike other pricing and scheduling methods in use, which are usually ad-hoc and are based on engineering judgment and experience, this proposed formulation is likely to perform better in restructured markets when market power is a potential problem. An illustrative example of a modified IEEE 30-bus system is used to introduce concepts and present results.

/pdf/locational-pricing-and-scheduling-for-an-integrated-energy-1khqekvv1v.pdf

Timothy D. Mount

Papers

Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters

Transmission Expansion Planning Using Contingency Criteria

Market power and price volatility in restructured markets for electricity

Probabilistic reliability criterion for planning transmission system expansions

Locational pricing and scheduling for an integrated energy-reserve market