A Multiperiod OPF Model Under Renewable Generation Uncertainty and Demand Side Flexibility

Renewable energy sources such as wind and solar have received much attention in recent years and large amount of renewable generation is being integrated to the electricity networks. A fundamental challenge in power system operation is to handle the intermittent nature of the renewable generation. In this paper we present a stochastic programming approach to solve a multiperiod optimal power flow problem under renewable generation uncertainty. The proposed approach consists of two stages. In the first stage operating points for conventional power plants are determined. Second stage realizes the generation from renewable resources and optimally accommodates it by relying on demand-side flexibility. The benefits from its application are demonstrated and discussed on a 4-bus and a 39-bus systems. Numerical results show that with limited flexibility on the demand-side substantial benefits in terms of potential additional re-dispatch costs can be achieved. The scaling properties of the approach are finally analysed based on standard IEEE test cases upto 300 buses, allowing to underlined its computational efficiency.Comment: 8 pages, 10 figure

What\u27s Love Got to Do with It? An Exploration of the Symposium and Plato\u27s Love

To many people love is special, sacred even. Love plays a countless number of roles for a countless number of people. Contemporary ideas about love, however, are more in alignment with the philosophies of Aristotle, and not of Plato. Aristotle held that love could exist as many people see it today – wishing well for others purely for their own sake. But Plato disagreed. Plato claimed that love was a way by which one could better themselves and become wiser. In this thesis, I explain Plato’s theory of love put forth in the Symposium. I also explore the textual evidence for the selfish nature of Plato’s love

Using conditional kernel density estimation for wind power density forecasting

Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this paper, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate VARMA-GARCH (vector autoregressive moving average-generalized autoregressive conditional heteroscedastic) model, with a Student t distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms

Skill forecasting from ensemble predictions of wind power

International audienceOptimal management and trading of wind generation calls for the providing of uncertainty estimates along with the commonly provided short-term wind power point predictions. Alternative approaches for the use of probabilistic forecasting are introduced. More precisely, focus is given to prediction risk indices aiming to give a comprehensive signal on the expected level of forecast uncertainty. Ensemble predictions of wind generation are used as input. A proposal for the definition of prediction risk indices is given. Such skill forecasts are based on the spread of ensemble forecasts (i.e. a set of alternative scenarios for the coming period) for a single prediction horizon or over a look-ahead period. It is shown on the test case of a Danish offshore wind farm how these prediction risk indices may be related to several levels of forecast uncertainty (and potential energy imbalances). Wind power ensemble predictions are derived from the conversion of ECMWF and NCEP ensemble forecasts of meteorological variables to wind power ensemble forecasts, as well as by a lagged average approach alternative. The ability of prediction risk indices calculated from the various types of ensembles forecasts to resolve among situations with different levels of uncertainty is discussed

A robust optimisation approach using CVaR for unit commitment in a market with probabilistic offers

The large scale integration of renewable energy sources (RES) challenges power system planners and operators alike as it can potentially introduce the need for costly investments in infrastructure. Furthermore, traditional market clearing mechanisms are no longer optimal due to the stochastic nature of RES. This paper presents a risk-aware market clearing strategy for a network with significant shares of RES.We propose an electricity market that embeds the uncertainty brought by wind power and other stochastic renewable sources by accepting probabilistic offers and use a risk measure defined by conditional value-at-risk (CVaR) to evaluate the risk of high re-dispatching cost due to the mis-estimation of renewable energy. The proposed model is simulated on a 39-bus network, whereby it is shown that significant reductions can be achieved by properly managing the risks of mis-estimation of stochastic generation

Chance-constrained generic energy storage operations under decision-dependent uncertainty

Compared with large-scale physical batteries, aggregated and coordinated generic energy storage (GES) resources provide low-cost, but uncertain, flexibility for power grid operations. While GES can be characterized by different types of uncertainty, the literature mostly focuses on decision-independent uncertainties (DIUs), such as exogenous stochastic disturbances caused by weather conditions. Instead, this manuscript focuses on newly-introduced decision-dependent uncertainties (DDUs) and considers an optimal GES dispatch that accounts for uncertain available state-of-charge (SoC) bounds that are affected by incentive signals and discomfort levels. To incorporate DDUs, we present a novel chance-constrained optimization (CCO) approach for the day-ahead economic dispatch of GES units. Two tractable methods are presented to solve the proposed CCO problem with DDUs: (i) a robust reformulation for general but incomplete distributions of DDUs, and (ii) an iterative algorithm for specific and known distributions of DDUs. Furthermore, reliability indices are introduced to verify the applicability of the proposed approach with respect to the reliability of the response of GES units. Simulation-based analysis shows that the proposed methods yield conservative, but credible, GES dispatch strategies and reduced penalty cost by incorporating DDUs in the constraints and leveraging data-driven parameter identification. This results in improved availability and performance of coordinated GES units