This paper describes a new approach to online forecasting of power production from PV systems. The method is suited to online forecasting in many applications and in this paper it is used to predict hourly values of solar power for horizons of up to 36 h. The data used is 15-min observations of solar power from 21 PV systems located on rooftops in a small village in Denmark. The suggested method is a two-stage method where first a statistical normalization of the solar power is obtained using a clear sky model. The clear sky model is found using statistical smoothing techniques. Then forecasts of the normalized solar power are calculated using adaptive linear time series models. Both autoregressive (AR) and AR with exogenous input (ARX) models are evaluated, where the latter takes numerical weather predictions (NWPs) as input. The results indicate that for forecasts up to 2 h ahead the most important input is the available observations of solar power, while for longer horizons NWPs are the most important input. A root mean square error improvement of around 35% is achieved by the ARX model compared to a proposed reference model.

/pdf/online-short-term-solar-power-forecasting-1ljgpbshkb.pdf

Online Short-term Solar Power Forecasting

The derivative-free global optimization algorithms developed in Part I of this study, for linearly constrained problems, are extended to nonconvex n-dimensional problems with convex constraints. The initial $$n+1$$n+1 feasible datapoints are chosen in such a way that the volume of the simplex generated by these datapoints is maximized; as the algorithm proceeds, additional feasible datapoints are added in such a way that the convex hull of the available datapoints efficiently increases towards the boundaries of the feasible domain. Similar to the algorithms developed in Part I of this study, at each step of the algorithm, a search function is defined based on an interpolating function which passes through all available datapoints and a synthetic uncertainty function which characterizes the distance to the nearest datapoints. This uncertainty function, in turn, is built on the framework of a Delaunay triangulation, which is itself based on all available datapoints together with the (infeasible) vertices of an exterior simplex which completely contains the feasible domain. The search function is minimized within those simplices of this Delaunay triangulation that do not include the vertices of the exterior simplex. If the outcome of this minimization is contained within the circumsphere of a simplex which includes a vertex of the exterior simplex, this new point is projected out to the boundary of the feasible domain. For problems in which the feasible domain includes edges (due to the intersection of multiple twice-differentiable constraints), a modified search function is considered in the vicinity of these edges to assure convergence.

Delaunay-based derivative-free optimization via global surrogates, part II: convex constraints

Comparing various solar irradiance categorization methods – A critique on robustness

The intermittent and stochastic nature of Renewable Energy Sources (RESs) necessitates accurate power production prediction for effective scheduling and grid management. This paper presents a comprehensive review conducted with reference to a pioneering, comprehensive, and data-driven framework proposed for solar Photovoltaic (PV) power generation prediction. The systematic and integrating framework comprises three main phases carried out by seven main comprehensive modules for addressing numerous practical difficulties of the prediction task: phase I handles the aspects related to data acquisition (module 1) and manipulation (module 2) in preparation for the development of the prediction scheme; phase II tackles the aspects associated with the development of the prediction model (module 3) and the assessment of its accuracy (module 4), including the quantification of the uncertainty (module 5); and phase III evolves towards enhancing the prediction accuracy by incorporating aspects of context change detection (module 6) and incremental learning when new data become available (module 7). This framework adeptly addresses all facets of solar PV power production prediction, bridging existing gaps and offering a comprehensive solution to inherent challenges. By seamlessly integrating these elements, our approach stands as a robust and versatile tool for enhancing the precision of solar PV power prediction in real-world applications. 

Forecasting Solar Photovoltaic Power Production: A Comprehensive Review and Innovative Data-Driven Modeling Framework

Delaunay-based derivative-free optimization leveraging global surrogates (∆-DOGS) is a recentlydeveloped optimization algorithm designed for nonsmooth functions in a handful of adjustable parameters. The first implementation of the original ∆-DOGS algorithm used polyharmonic splines to develop an inexpensive interpolating “surrogate” of the (expensive) function of interest. The behavior of this surrogate was found to be irregular in cases for which the function of interest turned out to be much more strongly dependent on some of the adjustable parameters than others. This irregularity of the surrogate led to the optimization algorithm requiring many more function evaluations than might have otherwise been necessary. In the present work, a modified interpolation strategy, dubbed multivariate adaptive polyharmonic splines (MAPS), is proposed to mitigate this irregular behavior, thereby accelerating the convergence of ∆-DOGS. The MAPS approach modifies the natural polyharmonic spline (NPS) approach by rescaling the parameters according to their significance in the optimization problem based on the data available at each iteration. This regularization of the NPS approach ultimately reduces the number of function evaluations required by ∆-DOGS to achieve a specified level of convergence in optimization problems characterized by parameters of varying degrees of significance. The importance of this rescaling of the parameters during the interpolation step is problem specific. To quantify its beneficial impact on a practical problem, we compare ∆-DOGS with MAPS to ∆-DOGS with NPS on an application related to hydrofoil shape optimization in seven parameters; results indicate a notable acceleration of convergence leveraging the MAPS approach.

Delaunay-based optimization in CFD leveraging multivariate adaptive polyharmonic splines (MAPS)

A new uncertainty quantification (UQ) algorithm for the error analysis of solar power forecasting is introduced. In solar power forecasting, there is a strong need for lenders, operators, traders, and Virtual Power Plant (VPP) to evaluate the forecasting results provided by different forecast providers. The algorithm potentially evaluates the third party's forecast to increase the performance of VPP. This algorithm includes four stages: First stage generates the clear sky model and the normalized solar power irradiance. In the second stage, the measured solar energy data are classified into different categories based on the Gaussian Mixture Models (GMMs). In the third stage, the new data are classified into one of the pre-defined categories based on Numerical Weather Prediction (NWP) features using the k nearest neighbor combined with the General Pattern Search (kNN-GPS) algorithm. Finally, a well conditioned Kriging model is applied to each class and quantifies the prediction intervals for the third party's forecasts using the idea behind analog ensemble forecasting method.

Multi-stage algorithm for uncertainty analysis of solar power forecasting

According to some embodiments, the present disclosure may include a method of analyzing solar power forecasts that may include obtaining a test dataset of historical irradiance at a location of a solar power generating system, and normalizing the test dataset based on a clear sky model at the location. The method may also include clustering the test dataset into multiple weather classes that each include a set of characteristics, obtaining a forecast of irradiance at the solar power generating system, and classifying the forecast into one of the weather classes, and determining confidence intervals of the forecast based on the set of characteristics of the one of the plurality of weather classes. The method may additionally include, based on the confidence intervals of the forecast, performing one of increasing output or decreasing output of a source of energy alternative to solar energy.

Operating a solar power generating system

PROBLEM TO BE SOLVED: To provide a method etc., for analyzing prediction of photovoltaic power generation.SOLUTION: The method may include obtaining the test data set of historical radiant quantity at the position of a photovoltaic power generation system, and normalizing the test data set on the basis of a radiant quantity fine weather model at the position. The method may further include clustering the test data set into a plurality of weather classes each including a set of characteristics, obtaining the prediction of radiant quantity with regard to a given future point of time in the photovoltaic power generation system, classifying the prediction into one of the plurality of weather classes, and determining the confidence interval of prediction on the basis of a set of characteristics of one of the plurality of weather classes. The method may further include carrying out, on the basis of the confidence interval of prediction, one of the increased output and the decreased output of an energy generation source that takes the place of solar energy.SELECTED DRAWING: Figure 3

Method for operating photovoltaic power generation system

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Multi-stage algorithm for uncertainty analysis of solar power forecasting

Operating a solar power generating system

Method for operating photovoltaic power generation system