Day-Ahead Probabilistic Forecast of Solar Irradiance: A Stochastic Differential Equation Approach

Badosa, Jordi; Gobet, Emmanuel; Grangereau, Maxime; Kim, Dae-Young

doi:10.1007/978-3-319-99052-1_4

Cited by 19 publications

(25 citation statements)

References 23 publications

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“…By solving it numerically, we find val(LP ) = 1.7023, which shows that for p sol,tot ≤ a ≥ 0, α, β ≥ 0.5, this SDE has a unique strong solution with values in [0, 1] almost surely, see [26].…”

Section: Other Voltage Regulation Devicesmentioning

confidence: 91%

“…Its value is 0 when the sky is completely cloudy (i.e., even at day, there would be no light) and 1 for a completely clear sky. The deterministic time-dependent envelop x sol,norm models the time evolution of the normalized solar power we would observe if the sky were clear.We suppose it is given by x To build a scenario tree, we use the stochastic model in [26] for the clear-sky index I sol , based on a Fisher-Wright-type Stochastic Differential Equation (SDE), given by:…”

Section: Time Grid Consideredmentioning

confidence: 99%

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Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

Grangereau

Ackooij

Gaubert

2022

Electric Power Systems Research

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We propose a generic multistage stochastic model for the Alternating Current Optimal Power Flow (AC OPF) problem for radial distribution networks, to account for the random electricity production of renewable energy sources and dynamic constraints of storage systems. We consider single-phase radial networks. Radial three-phase balanced networks (medium-voltage distribution networks typically have this structure) reduce to the former case. This induces a large scale optimization problem, which, given the non-convex nature of the AC OPF, is generally challenging to solve to global optimality.We derive a priori conditions guaranteeing a vanishing relaxation gap for the multi-stage AC OPF problem, which can thus be solved using convex optimization algorithms. We also give an a posteriori upper bound on the relaxation gap. In particular, we show that a null or low relaxation gap may be expected for applications with light reverse power flows or if sufficient storage capacities with low cost are available. Then, we discuss the validity of our results when incorporating voltage regulation devices. Finally, we illustrate our results on problems of planning of a realistic distribution feeder with distributed solar production and storage systems. Scenario trees for solar production

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Section: Other Voltage Regulation Devicesmentioning

confidence: 91%

Section: Time Grid Consideredmentioning

confidence: 99%

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

Grangereau

Ackooij

Gaubert

2022

Electric Power Systems Research

Self Cite

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show abstract

“…Clear sky index (CSI) is also required for the AnEn, and it is computed as a ratio between the current GHI (forecasted or measured) and the clear-sky GHI value. Clear-sky GHI estimations are computed using the empirical model proposed by [22].…”

Section: Methodsmentioning

confidence: 99%

A Two-Step Energy Management Method Guided by Day-Ahead Quantile Solar Forecasts: Cross-Impacts on Four Services for Smart-Buildings

Calderon-Obaldia¹,

Badosa²,

Migan‐Dubois³

et al. 2020

Preprint

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The research work hereby presented, emerges from the urge to answer the well-known question of how the uncertainty of intermittent renewable sources affects the performance of a microgrid and how could we deal with it. More specifically, we want to evaluate what could be the impact in performance of a microgrid intended to serve a smart-building (powered by photovoltaic panels and with battery energy storage), when the uncertainty of the photovoltaic-production forecasts is considered in the energy management process. For this, several objectives (or services) are targeted based in a two-step (double-objective) energy management framework, that combines optimization-based and rule-based algorithms. The performance is evaluated based on some particular services proposed as performance indicators. Simulations are performed using data of a study-case microgrid (Drahi-Xnovation center, Ecole Polytechnique, France). The use of quantile forecasts (obtained with an analog-ensemble method) is tested as a mean to deal with (i.e. decrease) the uncertainty of the solar PV production. The proposed energy management framework is compared with basic reference strategies and the results show the superior performance of the former in almost all the services and forecasting scenarios proposed. The contrasting nature among some of the target services is one of the main conclusions of this work, as well as the different requirements in terms of forecasts when optimizing for different services and seasons of the year. This fact highlights the usefulness of the quantile forecasting approach, as a tool to deal with the intrinsic uncertainty of PV power production

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“…This variable is simply the ratio of the clouded area on the celestial sphere. Dynamics of the cloud cover as a macroscopic meteorological variable can be considered as a stochastic process having the bounded range 76,77 . The generated power per unit area of a solar panel is proportional to the solar irradiance, 78 and the irradiance decreases as the cloud cover increases.…”

Section: Applicationsmentioning

confidence: 99%

Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations

Yoshioka

Yaegashi

Tsujimura

et al. 2020

Appl Stoch Models Bus & Ind

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Planning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other.

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Day-Ahead Probabilistic Forecast of Solar Irradiance: A Stochastic Differential Equation Approach

Cited by 19 publications

References 23 publications

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

A Two-Step Energy Management Method Guided by Day-Ahead Quantile Solar Forecasts: Cross-Impacts on Four Services for Smart-Buildings

Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations

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