Scientific

A Principal-Agent model for optimal Incentives in renewable investments

Speaker: 
René Aïd
Date: 
Thu, Jul 27, 2023
Location: 
PIMS, University of British Columbia
Online
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

We analyze the optimal regulatory incentives to foster the development of non-emissive electricity generation when the demand for power is served either by a one firm (monopoly) or by two interacting firms (competition). The regulator wishes to encourage green investments to limit carbon emissions, while simultaneously reducing intermittency of the total energy production. We find that the regulation of competing interacting firms is more efficient than the regulation of the monopoly situation as measured with the certainty equivalent of the principal’s value function. This higher efficiency is achieved thanks to a higher degree of freedom of the incentive mechanisms which involves cross-subsidies between firms. Joint work with Annika Kemper (Bielefeld University) and Nizar Touzi (Ecole Polytechnique).

Class: 

Renewable Energy Supply, Electricity Storage, and the Economics of Forecasting

Speaker: 
Werner Antweiler
Date: 
Wed, Jul 26, 2023
Location: 
PIMS, University of British Columbia
Online
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

Electricity markets balance an increasingly intermittent supply with price-inelastic demand, while climate change and electrification of mobility are contributing to transforming diurnal and seasonal demand patterns. Electricity systems face an increasing level of stochasticity, and market participants need to inform their dispatch decisions based on 24-hour price forecasts for participation in Day-Ahead Markets, which in turn depend on supply and demand forecasts. The arrival of grid-scale electricity storage is also creating new scope for prices forecasts, while smaller scale storage systems act as price takers. In the long term, large-scale deployment of grid-scale electricity storage has the potential of significantly reducing price variation through arbitrage, which could shift the “value added” of forecasting from short-term (intra-day) to long-term predictions, and from supporting operational (dispatch) decisions to supporting capacity (investment) decisions.

Class: 

Short-term wind forecasting using spatio-temporal covariance models

Speaker: 
Tianxia (Tylar) Jia
Date: 
Wed, Jul 26, 2023
Location: 
PIMS, University of British Columbia
Online
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

This talk introduces a methodology for improving short-term wind speed forecasting in Alberta. Regime-switching spatio-temporal covariance models are applied using two datasets: (1) large-scale reanalysis dataset containing large scale atmospheric information for atmospheric clustering using k-means and hidden Markov models; (2) wind speed data from 131 weather stations across Alberta are used to train and test the covariance models. The predictive performance is assessed for different models and clustering methods.

Class: 

Offshore wind forecasting and operations for the offshore wind energy areas in the U.S. Mid Atlantic

Speaker: 
Aziz Ezzat Ahmed
Date: 
Wed, Jul 26, 2023
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

The rising U.S. offshore wind sector holds great promise, both environmentally and economically, to unlock vast supplies of clean, domestic, and renewable energy. To harness this valuable resource, Gigawatt (GW)-scale offshore wind projects are already under way at several locations off of the U.S. coastline. This promising future, however, is still clouded with uncertainties on how to optimally manage those ultra-scale offshore wind assets, which would be operating under harsh environmental and operational conditions, in relatively under-explored territories, and at unprecedented scales. I will present some of our progress in formulating tailored forecasting and optimization models aimed at minimizing some of those uncertainties. Our models and analyses are largely tailored and tested using data from the U.S. Mid-Atlantic—where several GW-scale wind projects are currently under development.

Class: 

A Tribute to Bill Aiello

Speaker: 
Brian Marcus
Date: 
Wed, Jul 26, 2023
Location: 
PIMS, University of British Columbia
Zoom
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

A tribute to Bill Aiello

Class: 
Subject: 

The role of wind speed variability in very long-term wind power forecasts

Speaker: 
Nina Effenberger
Date: 
Wed, Jul 26, 2023
Location: 
PIMS, University of British Columbia
Online
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

How much wind power will a turbine generate over its lifetime? To answer such questions, we can consider climate model output to generate very long-term wind power forecasts on the scale of years to decades. One major limitation of the data projected by climate models is their coarse temporal resolution that is usually not finer than three hours and can be as coarse as one month. However, wind speed distributions of low temporal resolution might not be able to account for high frequency variability which can lead to distributional shifts in the projected wind speeds. Even if these changes are small this can have a huge impact due to the highly non-linear relationship between wind and wind power and the long forecast horizons we consider. In my talk, I will discuss how the resolution of wind speed data from climate projections affects wind power forecasts.

Class: 

Multivariate forecasting in energy systems with a large share of renewables

Speaker: 
Jethro Browell
Date: 
Wed, Jul 26, 2023
Location: 
PIMS, University of British Columbia
Online
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

Forecasts of renewable power production and electricity demand for multiple time periods and/or spatial expanses are required to operate modern power systems. Furthermore, probabilistic forecasts are necessary to facilitate economic decision-making and risk management. This gives rise to the challenge of producing forecasts that capture dependency between variables, over time, and between multiple locations. The Gaussian Copula has been widely used for multivariate energy forecasting, including for wind power, and is readily scalable given that the entire dependency structure is described by a single covariance matrix; however, estimating this covariance matrix in high dimensional problems remains a research challenge. Furthermore, it has been found empirically that this covariance matrix is often non-stationary and evolves over time. Two methods are presented for parameterising covariance matrices to enable conditioning on explanatory variables and as a step towards more robust estimation.

We consider two approaches, one based on modelling the parameters of covariance functions using additive models, and the second modelling individual elements of the modified Cholesky decomposition, again using additive models. We show how this gives rise to a wide range of possible parametric structures and discuss model selection and estimation strategies. Finally, we demonstrate though two case studies the improvement in forecast quality that these methods yield, and the importance and value of capturing the dynamics of dependency structures in wind power forecasting and net-load forecasting in the presence of embedded renewables.

Class: 

A Concise Overview on State-of-the-Art Solar Resources and Forecasting

Speaker: 
Jan Kleissl
Date: 
Wed, Jul 26, 2023 to Thu, Jul 27, 2023
Location: 
PIMS, University of British Columbia
Online
Conference: 
PIMS-FACTS Workshop on Forecasting and Mathematical modeling for Renewable Energy
Abstract: 

The ability to forecast solar irradiance plays an indispensable role in solar power forecasting, which constitutes an essential step in planning and operating power systems under high penetration of solar power generation. Since solar radiation is an atmospheric process, solar irradiance forecasting, and thus solar power forecasting, can benefit from the participation of atmospheric scientists. In this talk, the two fields, namely, atmospheric science and power system engineering are jointly discussed with respect to how solar forecasting plays a part. Firstly, the state of affairs in solar forecasting is elaborated; some common misconceptions are clarified; and salient features of solar irradiance are explained. Next, five technical aspects of solar forecasting: (1) base forecasting methods, (2) post-processing, (3) irradiance-to-power conversion, (4) verification, and (5) grid-side implications, are reviewed. Following that, ten research topics moving into the future are enumerated; they are related to (1) data and tools, (2) numerical weather prediction, (3) forecast downscaling, (4) large eddy simulation, (5) dimming and brightening, (6) aerosols, (7) spatial forecast verification, (8) multivariate probabilistic forecast verification, (9) predictability, and (10) extreme weather events. Last but not least, a pathway towards ultra-high PV penetration is laid out, based on a recently proposed concept of firm generation and forecasting.

Class: 

Free boundary problems in optimal transportation

Speaker: 
Jiakun Liu
Date: 
Tue, Aug 8, 2023
Location: 
PIMS, University of British Columbia
Zoom
Conference: 
Kantorovich Initiative Seminar
Abstract: 

In this talk, we introduce some recent regularity results of free boundary in
optimal transportation. Particularly for higher order regularity, when
densities are Hölder continuous and domains are $C^2$, uniformly convex, we obtain the free boundary is $C^{2,\alpha}$ smooth. We also consider another mode
case that the target consists of two disjoint convex sets, in which
singularities of optimal transport mapping arise. Under similar assumptions,
we show that the singular set of the optimal mapping is an $(n-1)$-dimensional
$C^{2,\alpha}$ regular sub-manifold of $\mathbb{R}^n$. These are based on a
series of joint work with Shibing Chen and Xu-Jia Wang.

Class: 
Subject: 

A Nonsmooth Approach to Einstein's Theory of Gravity

Speaker: 
Robert McCann
Date: 
Tue, Aug 1, 2023
Location: 
PIMS, University of British Columbia
Abstract: 

While Einstein’s theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. In positive-definite signature, there is a highly successful theory of metric and metric-measure geometry which includes Riemannian manifolds as a special case, but permits the extraction of nonsmooth limits under curvature and dimension bounds analogous to the energy conditions in relativity: here sectional curvature is reformulated through triangle comparison, while Ricci curvature is reformulated using entropic convexity along geodesics of probability measures.

This lecture explores recent progress in the development of an analogous theory in Lorentzian signature, whose ultimate goal is to provide a nonsmooth theory of gravity. We highlight how the null energy condition of Penrose admits a nonsmooth formulation as a variable lower bound on timelike Ricci curvature.

Class: 
Subject: 

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