Ellipsoidal Prediction Regions for Multivariate Uncertainty Characterization

While substantial advances are observed in probabilistic forecasting for power system operation and electricity market applications, most approaches are still developed in a univariate framework. This prevents from informing about the interdependence structure among locations, lead times and variables of interest. Such dependencies are key in a large share of operational problems involving renewable power generation, load and electricity prices for instance. The few methods that account for dependencies translate to sampling scenarios based on given marginals and dependence structures. However, for classes of decision-making problems based on robust, interval chance-constrained optimization, necessary inputs take the form of polyhedra or ellipsoids. Consequently, we propose a systematic framework to readily generate and evaluate ellipsoidal prediction regions, with predefined probability and minimum volume. A skill score is proposed for quantitative assessment of the quality of prediction ellipsoids. A set of experiments is used to illustrate the discrimination ability of the proposed scoring rule for misspecification of ellipsoidal prediction regions. Application results based on three datasets with wind, PV power and electricity prices, allow us to assess the skill of the resulting ellipsoidal prediction regions, in terms of calibration, sharpness and overall skill.Comment: 8 pages, 7 Figures, Submitted to IEEE Transactions on Power System

Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System

An Integrated Multi-Time-Scale Modeling for Solar Irradiance Forecasting Using Deep Learning

For short-term solar irradiance forecasting, the traditional point forecasting methods are rendered less useful due to the non-stationary characteristic of solar power. The amount of operating reserves required to maintain reliable operation of the electric grid rises due to the variability of solar energy. The higher the uncertainty in the generation, the greater the operating-reserve requirements, which translates to an increased cost of operation. In this research work, we propose a unified architecture for multi-time-scale predictions for intra-day solar irradiance forecasting using recurrent neural networks (RNN) and long-short-term memory networks (LSTMs). This paper also lays out a framework for extending this modeling approach to intra-hour forecasting horizons thus, making it a multi-time-horizon forecasting approach, capable of predicting intra-hour as well as intra-day solar irradiance. We develop an end-to-end pipeline to effectuate the proposed architecture. The performance of the prediction model is tested and validated by the methodical implementation. The robustness of the approach is demonstrated with case studies conducted for geographically scattered sites across the United States. The predictions demonstrate that our proposed unified architecture-based approach is effective for multi-time-scale solar forecasts and achieves a lower root-mean-square prediction error when benchmarked against the best-performing methods documented in the literature that use separate models for each time-scale during the day. Our proposed method results in a 71.5% reduction in the mean RMSE averaged across all the test sites compared to the ML-based best-performing method reported in the literature. Additionally, the proposed method enables multi-time-horizon forecasts with real-time inputs, which have a significant potential for practical industry applications in the evolving grid.Comment: 19 pages, 12 figures, 3 tables, under review for journal submissio

Stochastic Model for Power Grid Dynamics

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy...Comment: framework for a system-level analysis of the power grid from the viewpoint of complex network

Incorporating life cycle external cost in optimization of the electricity generation mix

The present work aims to examine the strategic decision of future electricity generation mix considering, together with all other factors, the effect of the external cost associated with the available power generation technology options, not only during their operation but also during their whole life cycle. The analysis has been performed by integrating the Life Cycle Assessment concept into a linear programming model for the yearly decisions on which option should be used to minimize the electricity generation cost. The model has been applied for the case of Greece for the years 2012-2050 and has led to several interesting results. Firstly, most of the new generating capacity should be renewable (mostly biomass and wind), while natural gas is usually the only conventional fuel technology chosen. If externalities are considered, wind energy increases its share and hydro-power replaces significant amounts of biomass-generated energy. Furthermore, a sensitivity analysis has been performed. One of the most important findings is that natural gas increases its contribution when externalities are increased. Summing-up, external cost has been found to be a significant percentage of the total electricity generation cost for some energy sources, therefore significantly changing the ranking order of cost-competitiveness for the energy sources examined