Geographic smoothing of solar PV: results from Gujarat

Klima, Kelly; Apt, Jay

doi:10.1088/1748-9326/10/10/104001

Cited by 43 publications

(32 citation statements)

References 36 publications

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“…It was also suggested that the frequency at which the steeper decay starts may be a function of the plant size. An analysis of the power spectra of several PV power plants in India showed different power-law exponents in the range −3.12 to −2.46 and that connecting several plants in the same area together resulted in a steeper decay limited by the decay of the largest power plant [25]. Our analysis shows that the solar radiation spectrum already exhibits a robust power-law decay at intermediate and high frequencies even in the absence of extraneous factors such as turbidity and cloud occlusion.…”

Section: Discussionmentioning

confidence: 99%

Geographic Dependence of the Solar Irradiance Spectrum at Intermediate to High Frequencies

Bel

Bandi

2019

Phys. Rev. Applied

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The solar radiation spectrum is important for renewable energy harvesting, as well as climate and ecological systems analysis. In addition to seasonal/annual and diurnal oscillations, the signal is composed of different frequencies (f ) that modulate each other. This results in a continuous spectrum with a power-law dependence over the entire frequency range from 1/year up to at least 1/min. Geographical location plays an important role in determining the temporal variability of solar radiation and naturally affects its spectral power-law decay, primarily due to the latitudinal dependence of daylight duration and its seasonal variation,. Employing a model to calculate the clear sky solar radiation intensity at various global locations, we show that significant spatial variability exists, particularly versus the latitude, which we quantify via the exponent of the spectral power-law. At most locations, the spectral power-law dependence of the intermediate (1/day < f < 1/hour) frequencies is different from that of the high (f > 1/hour) frequencies. We demonstrate the origin of this power-law dependence from simple arguments, explain its geographic dependence and discuss the implications for photovoltaic power generation and solar-driven systems, and hence the impact on grid stability. INTRODUCTIONSolar radiation is directly or indirectly responsible for almost all life and energy processes on the earth. It plays an important role in the analysis and modeling of climate [1,2] and ecological systems [3][4][5]. Usually only slow variation in solar radiation is deemed important, and fluctuations at sub-daily timescales are averaged out, although cases to the contrary do exist [6][7][8][9]. In solar energy harvesting and, in particular, for solar photovoltaic power production, the fast fluctuations at frequencies f > 1/day are of greater importance [10] because they fall in the range bounded between grid response and consumer load variation timescales. Since solar radiation intensity varies with location on the earth, particularly due to changes in the angle of incidence and diurnal duration dependence on the earth's latitude due to its obliquity (axial tilt relative to the orbital plane), it impacts all the abovementioned processes. Therefore, the importance of understanding the geographic dependence of solar radiation spectral characteristics cannot be overemphasized.In this letter, we study the geographic dependence of the solar radiation spectrum at various locations on the earth using data generated from an open source Ineichen-Perez Clear Sky Model (CSM) [11,12], which we first compare against a measured spectrum for a specific location (Sede Boqer, Israel, coordinates: 30.852310, 34.780586, altitude: 490 m above sea level). Analysis of spectra from real measurements is complicated by particularities such as local topographic features, strong fluctuations from cloud passage that act as multiplicative noise, etc. Calculated CSM spectra help separate these dependencies and allow one to focus on spectral features th...

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Section: Discussionmentioning

confidence: 99%

Geographic Dependence of the Solar Irradiance Spectrum at Intermediate to High Frequencies

Bel

Bandi

2019

Phys. Rev. Applied

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“…Recent studies of PV-related variability have analyzed power spectra of PV systems and solar irradiance (Calif et al, 2013;Curtright and Apt, 2008;Klima and Apt, 2015;Lave and Kleissl, 2010;Marcos et al, 2011a;Tabar et al, 2014;Yordanov et al, 2013b), compared power fluctuations from specific PV plants with corresponding irradiance measurements Marcos et al, 2011a;van Haaren et al, 2014), and characterized power variability as a function of PV plant…”

Section: Introductionmentioning

confidence: 99%

Local short-term variability in solar irradiance

2016

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Abstract. Characterizing spatiotemporal irradiance variability is important for the successful grid integration of increasing numbers of photovoltaic (PV) power systems. Using 1 Hz data recorded by as many as 99 pyranometers during the HD(CP) 2 Observational Prototype Experiment (HOPE), we analyze field variability of clear-sky index k * (i.e., irradiance normalized to clear-sky conditions) and sub-minute k * increments (i.e., changes over specified intervals of time) for distances between tens of meters and about 10 km. By means of a simple classification scheme based on k * statistics, we identify overcast, clear, and mixed sky conditions, and demonstrate that the last of these is the most potentially problematic in terms of short-term PV power fluctuations. Under mixed conditions, the probability of relatively strong k * increments of ±0.5 is approximately twice as high compared to increment statistics computed without conditioning by sky type. Additionally, spatial autocorrelation structures of k * increment fields differ considerably between sky types. While the profiles for overcast and clear skies mostly resemble the predictions of a simple model published by Hoff and Perez (2012), this is not the case for mixed conditions. As a proxy for the smoothing effects of distributed PV, we finally show that spatial averaging mitigates variability in k * less effectively than variability in k * increments, for a spatial sensor density of 2 km −2 .

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“…All renewables fluctuate with the natural variability in their energy sources [1,2]. Wind [3] and solar photovoltaics [4], in particular, exhibit fluctuations over a range of magnitudes and time scales (from milliseconds up to a day). Such fluctuations threaten electrical grid stability [5,6] when their magnitudes form a large fraction of power carried by the grid over time scales comparable to the grid response time.…”

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confidence: 99%

Spectrum of Wind Power Fluctuations

Bandi

2017

Phys. Rev. Lett.

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Wind power fluctuations for an individual turbine and plant have been widely reported to follow the Kolmogorov spectrum of atmospheric turbulence; both vary with a fluctuation time scale τ as τ^{2/3}. Yet, this scaling has not been explained through turbulence theory. Using turbines as probes of turbulence, we show the τ^{2/3} scaling results from a large scale influence of atmospheric turbulence. Owing to this long-range influence spanning 100s of kilometers, when power from geographically distributed wind plants is summed into aggregate power at the grid, fluctuations average (geographic smoothing) and their scaling steepens from τ^{2/3}→τ^{4/3}, beyond which further smoothing is not possible. Our analysis demonstrates grids have already reached this τ^{4/3} spectral limit to geographic smoothing.

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Geographic smoothing of solar PV: results from Gujarat

Cited by 43 publications

References 36 publications

Geographic Dependence of the Solar Irradiance Spectrum at Intermediate to High Frequencies

Geographic Dependence of the Solar Irradiance Spectrum at Intermediate to High Frequencies

Local short-term variability in solar irradiance

Spectrum of Wind Power Fluctuations

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