Photo-voltaic power daily predictions using expanding PDE sum models of polynomial networks based on Operational Calculus

Zjavka, Ladislav

doi:10.1016/j.engappai.2019.103409

Cited by 15 publications

(12 citation statements)

References 25 publications

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“…Overall energy consumption is computed as the sum of the individual load of each component at each time state. A combination algorithm is necessary to schedule load sequences in switching times of the selected equipment in several possible consumption plans according to the initial prediction of PVP production 24 to balance it with the SoC. The feasible load schemes are verified using the presented PQ models in the second stage to select the optimal ones that can be re‐combined according to user specifications or changed conditions.…”

Section: Discussionmentioning

confidence: 99%

“…D-PNN is able to model high nonlinear uncertain systems as the polynomial degree, which corresponds to the converted PDE order, doubles in each next PNN layer. 24 A…”

Section: Differential Machine Learningmentioning

confidence: 99%

“…Each PNN node searches for the best‐fit two‐inputs from the previous layer to compose and solve its specific sub‐PDE components using operation calculus (OC). D‐PNN is able to model high nonlinear uncertain systems as the polynomial degree, which corresponds to the converted PDE order, doubles in each next PNN layer 24

A \frac{\partial^{2} u}{\partial x_{1}^{2}} goodbreak+ B \frac{\partial^{2} u}{\partial x_{1} x_{2}} goodbreak+ C \frac{\partial^{2} u}{\partial x_{2}^{2}} goodbreak+ D \frac{\partial u}{\partial x_{1}} goodbreak+ E \frac{\partial u}{\partial x_{2}} goodbreak+ italicFu goodbreak+ G goodbreak= 0

…”

Section: Differential Deep and Stochastic Machine Learning With Regre...mentioning

confidence: 99%

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Power quality statistical predictions based on differential, deep and probabilistic learning using off‐grid and meteo data in 24‐hour horizon

Zjavka

2021

Intl J of Energy Research

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Off-grid systems using renewable energy (RE) are dependent on the stochastic power supply, which results in a high level of uncertainty, noise, and variability in the operational conditions. Power quality (PQ) norms specify allowable variations in relevant parameters of grid systems, necessary to maintain certain limits to guarantee their fault-tolerant states. 24-hour PQ prediction is vital in planning power consumption and utilization in smart off-grid houses based on RE. PQ data for all possible combinations of grid-attached household appliances and variable outside conditions cannot be measured completely or described exactly by physical equations. PQ predictions on daily bases using artificial intelligence (AI) models are requisite because atmospheric fluctuations and anomalies in local weather primarily influence the induced power and potential operation mode in real off-grids. Load specifics and possible collisions of the switched-on power consumers together with alterations in RE production can lead to additional disturbances in PQ and the consequent instability of the autonomous system. An automatic selection algorithm can give preliminary suggestion or correct several eventual energy consumption variants based on load time-shifting to allow efficient utilization of the predicted photovoltaic power (PVP). PQ models can after examine feasible daily load scenarios, offered by the system or re-defined by the users, scheduling selected equipment in the optimal switch intervals to ensure the system stability primarily. Users will have several practical options to choose from or combine the best ones to meet their demand in the optimal PQ and load planning strategy. This 2-step self-determination and verification procedure can help in effective operation of smart-grids in consolidation of their future state, balancing its power demands with local RE potential. The AI statistical models were evolved with the pre-assessed lengths of daily data periods. After that, they are applied to the last unseen data series, used in testing, to predict one-step sequences of the target PQ parameters in the trained all-day horizon.Parametric C++ application software with applied PQ and weather data is available for free to allow reproducibility of the results.

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Section: Discussionmentioning

confidence: 99%

“…D-PNN is able to model high nonlinear uncertain systems as the polynomial degree, which corresponds to the converted PDE order, doubles in each next PNN layer. 24 A…”

Section: Differential Machine Learningmentioning

confidence: 99%

A \frac{\partial^{2} u}{\partial x_{1}^{2}} goodbreak+ B \frac{\partial^{2} u}{\partial x_{1} x_{2}} goodbreak+ C \frac{\partial^{2} u}{\partial x_{2}^{2}} goodbreak+ D \frac{\partial u}{\partial x_{1}} goodbreak+ E \frac{\partial u}{\partial x_{2}} goodbreak+ italicFu goodbreak+ G goodbreak= 0

…”

Section: Differential Deep and Stochastic Machine Learning With Regre...mentioning

confidence: 99%

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Power quality statistical predictions based on differential, deep and probabilistic learning using off‐grid and meteo data in 24‐hour horizon

Zjavka

2021

Intl J of Energy Research

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“…Gradual modular extension and error minimization can lead, according to Goeddel’s theorem of incompleteness, to optimal pattern model in adaptation to input–output data samples. As D-PNN applies the L transformation to PDE derivatives and a self-selection of 2-input nodes, no signal pre-processing or feature extraction is needed 27 . D-PNN gradually forms a binary PNN tree structure.…”

Section: Ai Methods Used In Equipment Load Pq Predictionmentioning

confidence: 99%

Power quality approximation for household equipment load combinations using a stepwise growth in input parameters of AI models

Zjavka

2022

Sci Rep

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Detached off-grids, subject to the generated renewable energy (RE), need to balance and compensate the unstable power supply dependent on local source potential. Power quality (PQ) is a set of EU standards that state acceptable deviations in the parameters of electrical power systems to guarantee their operability without dropout. Optimization of the estimated PQ parameters in a day-horizon is essential in the operational planning of autonomous smart grids, which accommodate the norms for the specific equipment and user demands to avoid malfunctions. PQ data for all system states are not available for dozens of connected / switched on household appliances, defined by their binary load series only, as the number of combinations grows exponentially. The load characteristics and eventual RE contingent supply can result in system instability and unacceptable PQ events. Models, evolved by Artificial Intelligence (AI) methods using self-optimization algorithms, can estimate unknown cases and states in autonomous systems contingent on self-supply of RE power related to chaotic and intermitted local weather sources. A new multilevel extension procedure designed to incrementally improve the applicability and adaptability to training data. The initial AI model starts with binary load series only, which are insufficient to represent complex data patterns. The input vector is progressively extended with correlated PQ parameters at the next estimation level to better represent the active demand of the power consumer. Historical data sets comprise training samples for all PQ parameters, but only the load sequences of the switch-on appliances are available in the next estimation states. The most valuable PQ parameters are selected and estimated in the previous algorithm stages to be used as supplementary series in the next more precise computing. More complex models, using the previous PQ-data approximates, are formed at the secondary processing levels to estimate the target PQ-output in better quality. The new added input parameters allow us to evolve a more convenient model form. The proposed multilevel refinement algorithm can be generally applied in modelling of unknown sequence states of dynamical systems, initially described by binary series or other insufficient limited-data variables, which are inadequate in a problem representation. Most AI computing techniques can adapt this strategy to improve their adaptive learning and model performance.

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“…The literature [6] combined the concept of fractional order to improve a model of anisotropic diffusion, which also led to the research on the application of fractional order in the field of image edge detection. The literature [7] proposed an improved image edge detection model with anisotropic diffusion by different diffusion coefficient functions. The literature [8] gives an image diffusion model, which reflects the complexity of image texture with the help of local variance of the image, and also introduces fractional order in the model.…”

Section: Related Studiesmentioning

confidence: 99%

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Chen

2021

Advances in Mathematical Physics

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In recent years, with the rapid development of image processing research, the study of nonstandard images has gradually become a research hotspot, for example, fabric images, remote sensing images, and gear images. Some of the remote sensing images have a complex background and low illumination compared with standard images and are easy to be mixed with noise during acquisition; some of the fabric images have rich texture information, which adds difficulty to the related processing, and are also easy to be mixed with noise during acquisition. In this paper, we propose a fractional-order adaptive P -Laplace equation image edge detection algorithm for the problem of image edge detection in which the edge and texture information of the image is lost. The algorithm can apply for the order adaptively to filter the noise according to the noise distribution of the image, and the adaptive diffusion factor is determined by both the fractional-order curvature and fractional-order gradient of the iso-illumination line and combined with the iterative approach to realize the fine-tuning of the noisy image. The experimental results demonstrate that the algorithm can remove the noise while preserving the texture and details of the image. A fractional-order partial differential equation image edge detection model with a fractional-order fidelity term is proposed for Gaussian noise. The model incorporates a fractional-order fidelity term because this fidelity term smoothes out the rougher parts of the image while preserving the texture in the original image in greater detail and eliminating the step effect produced by other models such as the Perona-Malik (PM) and Rudin-Osher-Fatemi (ROF) models. By comparing with other algorithms, the image edge detection effect is measured with the help of evaluation metrics such as peak signal-to-noise ratio and structural similarity, and the optimal value is selected iteratively so that the image with the best edge detection result is retained. A convolutional mask image edge detection model based on adaptive fractional-order calculus is proposed for the scattered noise in medical images. The adaption is mainly reflected in the model algorithm by constructing an exponential parameter relation that is closely related to the image, which can dynamically adjust the parameter values, thus making the model algorithm more practical. The model achieves the scattering noise removal in four steps.

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Photo-voltaic power daily predictions using expanding PDE sum models of polynomial networks based on Operational Calculus

Cited by 15 publications

References 25 publications

Power quality statistical predictions based on differential, deep and probabilistic learning using off‐grid and meteo data in 24‐hour horizon

Power quality statistical predictions based on differential, deep and probabilistic learning using off‐grid and meteo data in 24‐hour horizon

Power quality approximation for household equipment load combinations using a stepwise growth in input parameters of AI models

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

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Photo-voltaic power daily predictions using expanding PDE sum models of polynomial networks based on Operational Calculus

Cited by 15 publications

References 25 publications

Power quality statistical predictions based on differential, deep and probabilistic learning using off‐grid and meteo data in 24‐hour horizon

Power quality statistical predictions based on differential, deep and probabilistic learning using off‐grid and meteo data in 24‐hour horizon

Power quality approximation for household equipment load combinations using a stepwise growth in input parameters of AI models

Fractional-Order Adaptive P -Laplace Equation-Based Art Image Edge Detection

Contact Info

Product

Resources

About

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection