![Modeling of extraterrestrial solar radiation
• The Sun emits radiant energy in an amount that is a function of its
temperature. Blackbody model can be used to describe how much
radiation the sun emits. A blackbody is defined to be a perfect emitter as
well as a perfect absorber
• The wavelengths emitted by a blackbody depend on its temperature as
described by Planck’s law:
𝐸𝜆 =
3.74×1010
λ5[𝑒
14.4
𝜆𝑇
−1
]
Where,
Eλ is the emissive power per area (W/m2 μm),
T is the absolute temperature of the body (K),
λ is the wavelength (μm).](https://image.slidesharecdn.com/elmenreich-khatib-machinelearningtechniquesforthesmartgridmodelingofsolarenergyusingai-140522012456-phpapp02/85/Machine-Learning-Techniques-for-the-Smart-Grid-Modeling-of-Solar-Energy-using-AI-23-320.jpg)
![Modeling of extraterrestrial solar radiation
• To calculate the daily extraterrestrial solar radiation on the top of the
atmosphere, the path that the earth rotates around the sun must be
considered.
• The eccentricity of the ellipse is small and the orbit is, in fact, quite nearly
circular. Therefore, the extraterrestrial solar radiation in W/m2 can be
described as,
𝐼 𝑜 = 1367 ×
𝑅 𝑎𝑣
𝑅
2
where
Rav is the mean sun-earth distance
R is the actual sun-earth distance depending on the day of the year
• After all, the daily extraterrestrial solar radiation can be given as follows,
𝐼 𝑜 = 1367[1 + 0.034 cos
360𝑛
365
]](https://image.slidesharecdn.com/elmenreich-khatib-machinelearningtechniquesforthesmartgridmodelingofsolarenergyusingai-140522012456-phpapp02/85/Machine-Learning-Techniques-for-the-Smart-Grid-Modeling-of-Solar-Energy-using-AI-24-320.jpg)
Machine Learning Techniques for the Smart Grid – Modeling of Solar Energy using AI
- 1. Machine Learning Techniques for the Smart Grid – Modeling of Solar Energy using AI Networked and Embedded Systems Professor Dr. Wilfried Elmenreich Dr. Tamer Khatib
- 2. Overview • Scope of this tutorial • Meta-heuristic search algorithms • Artificial neural networks • Modeling of solar radiation Modeling extraterrestrial and terrestrial solar radiation Clear sky model Satellite based models Sky transmittance-based models Ground meteorological measurement based model ANN-based modeling of solar radiation
- 3. • Automated planning and scheduling • Machine learning • Natural language processing • Perception • Robotics • Social intelligence • Creativity • Artificial general intelligence Artificial Intelligence Areas Image soruce: Creative Commons, Wikipedia
- 4. • Automated planning and scheduling • Machine learning • Natural language processing • Perception • Robotics • Social intelligence • Creativity • Artificial general intelligence Artificial Intelligence Techniques Image soruce: Creative Commons, Wikipedia
- 5. • Metaheuristic search algorithms PART I
- 6. • For optimization problems • Etymology: – Meta – upper level – Heuristic – to find – Heuristic = deterministic – Meta-heuristic = utilizing randomization in search • So it is “only” for search problems ? Every engineering or design challenges can be formulated into a search problem over a solution space • Solution space can be particular large and multi-dimensional – Standard optimization algorithms don’t finish in acceptable time – Need for meta-heuristic Meta-heuristic search algorithms
- 7. Overview on Search Techniques • Metaheuristics = Guided random search techniques
- 8. • Metaheuristics are strategies that guide the search process • Goal is to efficiently explore the search space to find (near-)optimal solutions • No single technique • Metaheuristic algorithms are approximate and typically non-deterministic • Metaheuristic algorithms might fail by getting trapped in confined and deceptive areas of the search space • Metaheuristics are typically not problem-specific Properties of Meta-heuristic Search Algorithms
- 9. • Trajectory methods – Basic Idea: Iterative improvement – Simulated annealing (Scott Kirkpatrick, C. Daniel Gelatt and Mario P. Vecchi, 1983) – Tabu search (Fred Glover, 1986) – Variable neighborhood search (Mladenovic, Hansen, 1997) Meta-heuristic Search Algorithms (1) x1 x2 x3 X4 X5
- 10. • Population-based methods – Genetic algorithm (John Holland 1975) – Evolutionary algorithms – Genetic programming (Fogel 1964) – Swarm Algorithms Meta-heuristic Search Algorithms (2)
- 12. Searching for Rules • Simulation of target system as playground • Evolvable model of local behavior (e.g., fuzzy rules, ANN) • Define goal via fitness function (e.g., maximize throughput in a network) • Run evolutionary algorithm to derive local rules that fulfill the given goal System model Goals (fitness function) Simulation Explore solutions Evaluate & Iterate Analyze results
- 13. System architecture Building Self-Organizing Systems 13 Wilfried Elmenreich 6 major components: task description, simulation setup, interaction interface, evolvable decision unit, objective function, search algorithm
- 14. Agent behavior to be evolved • Controls the agents of the SOS • Processes inputs (from sensors) and produces output (to actuators) • Must be evolvable – Mutation – Recombination • We cannot easily do this with an algorithm represented in C code… Agent Control System „Agent‘s Brain“
- 15. Artificial Neural Networks • Each neuron sums up the weighted outputs of the other connected neurons • The output of the neuron is the result of an activation function (e.g. step, sigmoid function) applied to this sum • Neural networks are distinguished by their connection structure – Feed forward connections (layered) – Recursive (Ouput neurons feed back to input layer) – Fully meshed
- 16. Evolving Neural Networks 3.2 -1.2 3.2 3.2 -0.1 -4.2 0.2 0.0 3.5 -1.2 3.2 3.2 -0.1 -4.2 0.2 0.0 Mutation 0.0 -1.2 1.2 3.2 -0.1 1.2 1.2 0.0 3.5 2.2 3.2 3.2 -0.1 -4.2 0.2 0.5 Recomb ination 3.2 -1.2 3.2 3.2 -0.1 -4.2 0.2 0.0
- 17. Framework for Evolutionary Design • FREVO (Framework for Evolutionary Design) • Modular Java tool allowing fast simulation and evolution • FREVO defines flexible components for – Controller representation – Problem specification – Optimizer
- 18. Giving FREVO a Problem • Basically, we need a simulation of the problem • Interface for input/output connections to the agents – E.g. for the public goods game: – Your input last round – Your revenue • Feedback from a simulation run -> fitness value • FREVO source code and simple tutorial for a new problem at http://frevo.sourceforge.net
- 19. PART II • Modeling of solar radiation
- 20. Application example • Modeling of solar radiation Modeling extraterrestrial and terrestrial solar radiation Clear sky model Satellite based models Sky transmittance-based models Ground meteorological measurement based model ANN Based modeling of solar radiation
- 21. • Solar energy is part of the sun’s energy which falls at the earth’s surface. It can be harnessed, to heat water or to move electrons in a solar cell. • Solar radiation data provide information on sun’s potential in a specific location. These data are very important for designing solar energy systems. • Due to the high cost and installation difficulties in measuring devices, these data aren't always available. thus, alternative prediction ways are needed. Preface: Solar energy
- 22. How big is solar energy ? Source: Boyle, G. 2004. Renewable Energy. OXFORD..
- 23. Modeling of extraterrestrial solar radiation • The Sun emits radiant energy in an amount that is a function of its temperature. Blackbody model can be used to describe how much radiation the sun emits. A blackbody is defined to be a perfect emitter as well as a perfect absorber • The wavelengths emitted by a blackbody depend on its temperature as described by Planck’s law: 𝐸𝜆 = 3.74×1010 λ5[𝑒 14.4 𝜆𝑇 −1 ] Where, Eλ is the emissive power per area (W/m2 μm), T is the absolute temperature of the body (K), λ is the wavelength (μm).
- 24. Modeling of extraterrestrial solar radiation • To calculate the daily extraterrestrial solar radiation on the top of the atmosphere, the path that the earth rotates around the sun must be considered. • The eccentricity of the ellipse is small and the orbit is, in fact, quite nearly circular. Therefore, the extraterrestrial solar radiation in W/m2 can be described as, 𝐼 𝑜 = 1367 × 𝑅 𝑎𝑣 𝑅 2 where Rav is the mean sun-earth distance R is the actual sun-earth distance depending on the day of the year • After all, the daily extraterrestrial solar radiation can be given as follows, 𝐼 𝑜 = 1367[1 + 0.034 cos 360𝑛 365 ]
- 25. Modeling of terrestrial solar radiation • Attenuation of incoming radiation is a function of the distance that the beam has to travel through the atmosphere, which is easily calculable, as well as factors such as dust, air pollution, atmospheric water vapor, clouds, and turbidity
- 26. Modeling of terrestrial solar radiation • There are many theories for modeling terrestrial solar radiation, Clear sky model Satellite based model Environmental measurement based model Ground meteorological measurement based model
- 27. Clear sky model • Beam radiation at the surface can exceed 70% of the extraterrestrial flux • Constant and uniform attenuation factor is assumed • Isotropic model is assumed
- 28. Clear sky model
- 31. Ground meteorological measurement based model
- 32. Ground meteorological measurement based model
- 33. Ground meteorological measurement based model
- 34. Sensitivity of data 34 0 100 200 300 400 500 600 700 800 900 0 10000 20000 30000 40000 50000 0 100 200 300 400 500 600 700 800 900 1000 0 10000 20000 30000 40000 50000 60000 0 100 200 300 400 500 600 700 800 900 0 10000 20000 30000 40000 50000
- 35. Model type and configuration and inputs
- 36. Number of neurons in the hidden layer • If a low number of hidden neurons are used, under fitting may occur and this will cause high training and generalization error while over fitting and high variance may occur when the hidden layer consist of a large number of hidden neurons. • Usually the number of hidden nodes can be obtained by using some rules of thumb. For example, • the hidden layer’s neurons have to be somewhere between the input layer size and the output layer size. • the hidden layer will never require more than twice the number of the inputs. • the number of hidden nodes are 2/3 or (70%-90%) of the number of input nodes. • In addition, it has been recommended that by adding the number of the input to the number of the output and multiply the result by (2/3), the number of the hidden nodes can be achieved.
- 37. Modeling results using GRNN
- 38. Summary • Artificial Intelligence algorithms are complex algorithms to handle complex problems • Simple, deconstructable problems (given network, linear composable power flows) -> standard algorithms • Complex problems (many variables, open questions such as network structure) -> complex algorithms • We covered: – Evolutionary algorithms – Artificial neural networks – Neural network application for modeling of solar radiation
- 39. Thank you Welcome any question Einführung in Smart Grids 39 Wilfried Elmenreich
- 40. Further Links • Video: 6 minute introduction to FREVO: http://youtu.be/1wTyozYGG4I • Download FREVO (open source): http://frevo.sourceforge.net • A. Sobe, I. Fehérvári, and W. Elmenreich. FREVO: A tool for evolving and evaluating self-organizing systems. In Proceedings of the 1st International Workshop on Evaluation for Self-Adaptive and Self-Organizing Systems, Lyon, France, September 2012. • I. Fehervari and W. Elmenreich. Evolution as a tool to design self- organizing systems. In Self-Organizing Systems, volume LNCS 8221, pages 139–144. Springer Verlag, 2014. • T. Khatib, A Mohamed, K Sopian. A review of solar energy modeling techniques. J. of Renewable & Sustainable Energy Reviews. 2012.16(5): 2864-2869. • T. Khatib, A. Mohamed, K. Sopian, M. Mahmoud. Assessment of Artificial Neural Networks for Hourly Solar Radiation Prediction. J. of Photoenergy. 2012. 2012(ID 946890):1-7.