The costs of electricity systems with a high share of fluctuating renewables - a stochastic investment and dispatch optimization model for Europe

Renewable energies are meant to produce a large share of the future electricity demand. However, the availability of wind and solar power depends on local weather conditions and therefore weather characteristics must be considered when optimizing the future electricity mix. In this article we analyze the impact of the stochastic availability of wind and solar energy on the cost-minimal power plant mix and the related total system costs. To determine optimal conventional, renewable and storage capacities for different shares of renewables, we apply a stochastic investment and dispatch optimization model to the European electricity market. The model considers stochastic feed-in structures and full load hours of wind and solar technologies and different correlations between regions and technologies. Key findings include the overestimation of fluctuating renewables and underestimation of total system costs compared to deterministic investment and dispatch models. Furthermore, solar technologies are - relative to wind turbines - underestimated when neglecting negative correlations between wind speeds and solar radiation.Stochastic programming; electricity; renewable energy

Stochastic Models for Solar Power

International audienceIn this work we develop a stochastic model for the solar power at the surface of the earth. We combine a deterministic model of the clear sky irradiance with a stochastic model for the so-called clear sky index to obtain a stochastic model for the actual irradiance hitting the surface of the earth. Our clear sky index model is a 4-state semi-Markov process where state durations and clear sky index values in each state have phase-type distributions. We use per-minute solar irradiance data to tune the model, hence we are able to capture small time scales fluctuations. We compare our model with the on-off power source model developed by Miozzo et al. (2014) for the power generated by photovoltaic panels, and to a modified version that we propose. In our on-off model the output current is frequently resampled instead of being a constant during the duration of the " on " state. Computing the autocorrelation functions for all proposed models, we find that the irradiance model surpasses the on-off models and it is able to capture the multiscale correlations that are inherently present in the solar irradiance. The power spectrum density of generated trajectories matches closely that of measurements. We believe our irradiance model can be used not only in the mathematical analysis of energy harvesting systems but also in their simulation

A Guide to Solar Power Forecasting using ARMA Models

We describe a simple and succinct methodology to develop hourly auto-regressive moving average (ARMA) models to forecast power output from a photovoltaic solar generator. We illustrate how to build an ARMA model, to use statistical tests to validate it, and construct hourly samples. The resulting model inherits nice properties for embedding it into more sophisticated operation and planning models, while at the same time showing relatively good accuracy. Additionally, it represents a good forecasting tool for sample generation for stochastic energy optimization models

Bayesian parameter inference with stochastic solar dynamo models

Time-series of cosmogenic radionuclides stored in natural archives such as ice cores and tree rings are a proxy for solar magnetic activity on multi-millennial time-scales. Radionuclides data exhibit a number of interesting features such as intermittent stable cycles of high periods and Grand Minima. Although a lot of effort has gone into the development of sound physically based stochastic solar dynamo models, it is still largely unclear what are the underlying mechanisms that lead to the observed phenomena. Answering these questions requires quantitatively calibrating the models to the data and comparing performances of different models with the associated uncertainties in model parameters and predictions. Bayesian statistics is a consistent framework for parameter inference where knowledge about model parameters is expressed through probability distributions and updated using measured data. However, Bayesian inference with non-linear stochastic models can become computationally extremely expensive and it is therefore hardly ever applied. In recent years, sophisticated and scalable algorithms have emerged, which have the potential of making Bayesian inference for complex stochastic models feasible. We intend to investigate the power of Approximate Bayesian Computation (ABC) and Hamiltonian Monte Carlo (HMC) algorithms. We present our first inference results with stochastic solar dynamo models

The spectral evolution of impulsive solar X-ray flares. II.Comparison of observations with models

We study the evolution of the spectral index and the normalization (flux) of the non-thermal component of the electron spectra observed by RHESSI during 24 solar hard X-ray flares. The quantitative evolution is confronted with the predictions of simple electron acceleration models featuring the soft-hard-soft behaviour. The comparison is general in scope and can be applied to different acceleration models, provided that they make predictions for the behavior of the spectral index as a function of the normalization. A simple stochastic acceleration model yields plausible best-fit model parameters for about 77% of the 141 events consisting of rise and decay phases of individual hard X-ray peaks. However, it implies unphysically high electron acceleration rates and total energies for the others. Other simple acceleration models such as constant rate of accelerated electrons or constant input power have a similar failure rate. The peaks inconsistent with the simple acceleration models have smaller variations in the spectral index. The cases compatible with a simple stochastic model require typically a few times 10^36 electrons accelerated per second at a threshold energy of 18 keV in the rise phases and 24 keV in the decay phases of the flare peaks.Comment: 9 pages, 4 figures, accepted for publication by A&

Daily Solar Energy Estimation for Minimizing Energy Storage Requirements in PV Power Plants

This paper proposes an optimized energy management strategy (EMS) for photovoltaic (PV) power plants with energy storage (ES) based on the estimation of the daily solar energy production. This EMS produces a constant-by-hours power reference which mitigates the stochastic nature of PV production typically associated to the solar resource, and enables PV power plants to take part in the day and intraday electricity markets. The possibility of using the intraday market sessions to refine the plant's power reference paves the way to minimizing the energy capacity ratings of the ES system required to operate the PV power plant without incurring excessive production deviations. This proposal is analyzed on an annual basis using actual irradiance data and theoretical irradiance models extracted from official databases