Prediction of Solar Concentration Flux Distribution for a Heliostat Based on Lunar Concentration Image and Generative Adversarial Networks

ABSTRACT

The predictive analysis of solar flux distribution on the receiver surface is critical in optimizing the concentration processes of concentrating solar power (CSP) plants. Due to the difficulties of directly measuring the solar flux distribution of the heliostat field, tracking the Moon and measuring the lunar concentration ratio distribution become a promising option. However, many factors affect the flux distribution of a heliostat field. To obtain an accurate predictive model for the solar flux distribution, we propose a deep-learning method using conditional generative adversarial networks (cGAN) and lunar concentration images. The method can take account of tracking errors of individual heliostats, defects of reflecting surfaces, as well as atmospheric attenuation effects, and has the potential to give a reliable prediction of solar flux distribution. Mathematical relations between the solar flux distribution and the solar concentration ratio distribution are discussed in the paper. Experiments have been designed and carried out with an ordinary heliostat at the Beijing Badaling solar concentrating power station. Experimental results show that the AI-generated solar concentration ratio distributions are very close to the actual solar concentration ratio distributions, demonstrating the feasibility of AI models for the prediction of solar flux distribution.

Nomenclature

Abbreviation	=	Description
CSP	=	Concentrating solar power
PV	=	Photovoltaic
CCD	=	Charge-Coupled Device
CRD	=	Concentration Ratio Distribution
CGAN	=	Conditional Generative Adversarial Networks
DNI	=	Direct Normal Irradiance
FFT	=	Fast Fourier Transform
GAN	=	Generative Adversarial Networks
SSIM	=	Structural Similarity Index Measure
Symbol	=	Description
$\mathit{CR}{\left(\mathit{x},\mathit{y}\right)}_{\mathit{moon}}$	=	Lunar concentration ratio distribution on the target surface
$I_{\mathit{moon}}$	=	Illuminance distribution of lunar spots on the target surface
$\mathit{DN}{I}_{\mathit{moon}}$	=	Direct normal irradiance of the Moon
$\mathit{CR}{\left(\mathit{x},\mathit{y}\right)}_{\mathit{sun}}$	=	Solar concentration ratio distribution on the target surface
$\mathit{F}\left(\mathit{x},\mathit{y}\right)$	=	Solar flux distribution on the target surface
$\mathit{DN}{I}_{\mathit{sun}}$	=	Direct normal irradiance of the Sun
$\mathit{G}$	=	Generator
$\mathit{D}$	=	Discriminator
$L_{\mathit{GAN}}\left(\mathit{G},D_y,\mathit{X},\mathit{Y}\right)$	=	The GAN loss function between generator $\mathbf{G}$ and discriminator ${\mathbf{D}}_{\mathbf{y}}$
$L_{\mathit{cyc}}\left(\mathit{G},\mathit{F}\right)$	=	Cycle Consistency Loss
${\mathbb{E}}_{\mathit{y}\text{~}{\mathit{p}}_{\mathit{data}}\left(\mathit{y}\right)}$	=	Expectation of y with the distribution ${\mathbf{p}}_{\mathbf{data}}\left(\mathbf{y}\right)$
${\mathbb{E}}_{\mathit{x}\text{~}{\mathit{p}}_{\mathit{data}}\left(\mathit{x}\right)}$	=	Expectation of x with the distribution ${\mathbf{p}}_{\mathbf{data}}\left(\mathbf{x}\right)$
${\mu }_x$	=	The average gray value of image $\mathbf{x}$
${\mu }_y$	=	The average gray value of image $\mathbf{y}$
$\mathit{C}$	=	constant
${\mathit{\sigma }}_{\mathit{x}}$	=	variance of image $\mathbf{x}$
${\mathit{\sigma }}_{\mathit{y}}$	=	variance of image $\mathbf{y}$
${\mathit{\sigma }}_{\mathit{xy}}$	=	covariance between image $\mathbf{x}$ and $\mathbf{y}$

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by National Natural Science Foundation of China (No. 61671429).