George Papaefthymiou

MCMC for Wind Power Simulation

This paper contributes a Markov chain Monte Carlo (MCMC) method for the direct generation of synthetic time series of wind power output. It is shown that obtaining a stochastic model directly in the wind power domain leads to reduced number of states and to lower order of the Markov chain at equal power data resolution. The estimation quality of the stochastic model is positively influenced since in the power domain, a lower number of independent parameters is estimated from a given amount of recorded data. The simulation results prove that this method offers excellent fit for both the probability density function and the autocorrelation function of the generated wind power time series. The method is a first step toward simple stochastic black-box models for wind generation.

Using Copulas for Modeling Stochastic Dependence in Power System Uncertainty Analysis

The increasing penetration of renewable generation in power systems necessitates the modeling of this stochastic system infeed in operation and planning studies. The system analysis leads to multivariate uncertainty analysis problems, involving non-Normal correlated random variables. In this context, the modeling of stochastic dependence is paramount for obtaining accurate results; it corresponds to the concurrent behavior of the random variables, having a major impact to the aggregate uncertainty (in problems where the random variables correspond to spatially spread stochastic infeeds) or their evolution in time (in problems where the random variables correspond to infeeds over specific time-periods). In order to investigate, measure and model stochastic dependence, one should transform all different random variables to a common domain, the rank/uniform domain, by applying the cumulative distribution function transformation. In this domain, special functions, copulae, can be used for modeling dependence. In this contribution the basic theory concerning the use of these functions for dependence modeling is presented and focus is given on a basic function, the Normal copula. The case study shows the application of the technique for the study of the large-scale integration of wind power in the Netherlands.

Dynamic sizing of energy storage for hedging wind power forecast uncertainty

In market conditions where program responsible parties are penalized for deviations from proposed bids, energy storage can be used for compensating the energy imbalances induced by limited predictability of wind power. The energy storage capacity necessary for performing this task will differ between delivery periods, according to the magnitude and the evolution of forecast errors in each delivery period. A methodology is presented for the assessment of the necessary storage capacity for each delivery period, based on the degree of risk that the power producer accepts to be exposed to. This approach leads to a dynamic assessment of the energy storage capacity for different delivery periods. In such a context, energy storage is used as a means of risk hedging against penalties from the regulation market. The application of the algorithm on real data (both measurements and forecasts) of the yearly output of a wind farm shows that the application of a dynamic daily sizing of the necessary storage leads to a significant reduction of the storage capacity used, without affecting the producers profit significantly. The method proposed here may provide the basis for the introduction of storage as an independent market entity, where each producer may rent the necessary daily storage capacity for hedging the risk of the wind power limited predictability.

Generation of Statistical Scenarios of Short-term Wind Power Production

Short-term (up to 2-3 days ahead) probabilistic forecasts of wind power provide forecast users with a paramount information on the uncertainty of expected wind generation. Whatever the type of these probabilistic forecasts, they are produced on a per horizon basis, and hence do not inform on the development of the forecast uncertainty through forecast series. This issue is addressed here by describing a method that permits to generate statistical scenarios of wind generation that accounts for the interdependence structure of prediction errors, in plus of respecting predictive distributions of wind generation. The approach is evaluated on the test case of a multi-MW wind farm over a period of more than two years. Its interest for a large range of applications is discussed.

Estimation of Power System Variability due to Wind Power

The incorporation of wind power generation to the power system leads to an increase in the variability of the system power flows. The assessment of this variability is necessary for the planning of the necessary system reinforcements. For the assessment of this variability, the uncertainty in the system inputs should be modeled, comprising of the time-dependent stochasticity of the system loads and the correlated wind resources. In this contribution, a unified Monte-Carlo simulation methodology is presented that addresses both issues. The application of the method for the analysis of the wind power integration in the New England test system is presented.

An approach to the real-time power balancing for enhancing the security of electrical networks

This paper presents the concept of real-time Centre Of Angle (COA) for a multi-area power system. The core idea is to generate some on-line information about the remedial actions which should be taken to enhance the security of an electrical power network subjected to a sever disturbance. Also, by applying mathematical concepts, the paper improves the real-time concept of COA for being used in the electrical networks by considering the characteristics of the Electrical Energy Market (EEM). The suggested real-time COA makes it possible to maintain the synchronism between the participating generators in one area and other generators located in other areas. The paper, based on the real-time COA, introduces an alarm signal which can warn that the trend of area isolation (islanding) is proceeding, before the area gets fully isolated.

Using copulas for modeling stochastic dependence in power system uncertainty analysis

The increasing penetration of renewable generation in power systems necessitates the modeling of this stochastic system infeed in operation and planning studies. The system analysis leads to multivariate uncertainty analysis problems, involving non-Normal correlated random variables. In this context, the modeling of stochastic dependence is paramount for obtaining accurate results; it corresponds to the concurrent behavior of the random variables, having a major impact to the aggregate uncertainty (in problems where the random variables correspond to spatially spread stochastic infeeds) or their evolution in time (in problems where the random variables correspond to infeeds over specific time-periods). In order to investigate, measure and model stochastic dependence, one should transform all different random variables to a common domain, the rank/uniform domain, by applying the cumulative distribution function transformation. In this domain, special functions, copulae, can be used for modeling dependence. In this contribution the basic theory concerning the use of these functions for dependence modeling is presented and focus is given on a basic function, the Normal copula. The case study shows the application of the technique for the study of the large-scale integration of wind power in the Netherlands.

Small disturbance angle stability indication in the electrical networks with variable speed wind turbines

The fast growing application of sustainable energy sources imposes major structural changes on the current electric power systems. One of these structural changes is to make use of large variable speed wind turbines within the conventional electrical power networks. The installation of these wind turbines has, indeed, indispensable impacts on the dynamic behavior of the existing electric power systems. Thus, it is important to gain a rather generalized overview on how these wind turbines, which mostly use Doubly Fed Induction Generators (DFIGs), affect the system stability. This paper performs an analytical analysis for the indication of small disturbance rotor angle stability in the power systems equipped with variable speed wind turbines using DFIGs. Also, in order to consider the stochastic characteristic of the sustainable energy sources, the paper applies an iterative-stochastic method to analyze the small disturbance angle stability. The suggested iterative-stochastic methodology is numerically verified, within this paper, by getting applied to an electric power test system.