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On-grid and off-grid photovoltaic systems forecasting using a hybrid meta-learning method

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Abstract

In this paper, we investigate two types of photovoltaic (PV) systems (on-grid and off-grid) of different sizes and propose a reliable PV forecasting method. The novelty of our research consists in a weather data-driven feature engineering considering the operation of the PV systems in similar conditions and merging the results of deterministic and stochastic models, namely Machine Learning algorithms (Random Forest—RF, eXtreme Gradient Boost—XGB) and Deep Learning algorithms (Deep Neural Networks—DNN, Gated Recurrent Unit—GRU) into a Hybrid Meta-learning Forecasting method. It combines the estimations of the above-mentioned algorithms with relevant features to predict the PV output using a Long Short-Term Memory model. To design the PV forecast for off-grid systems, that are equally important for prosumers, and approximate the potential power of these systems, the level of load and charging state of the batteries are considered. In this context, feature engineering using the weather and PV output data, including PV characteristics, is relevant to obtaining a performant and robust PV forecast for various use cases taking into account the size and connectivity of the PV systems. On average, the Mean Absolute Error and Mean Absolute Percentage Error have halved compared to values obtained with deterministic methods and are 25% lower than the stochastic models.

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Notes

  1. https://www.homerenergy.com/products/pro/docs/3.10/how_homer_calculates_the_pv_array_power_output.html.

  2. https://www.iso.org/obp/ui/#iso:std:iso:9847:ed-1:v1:en.

  3. https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.savgol_filter.html.

  4. https://pvlib-python.readthedocs.io/en/stable/.

  5. https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html.

  6. https://developer.accuweather.com/.

  7. https://openweathermap.org/api.

  8. https://docs.stormglass.io.

Abbreviations

\(t, h\) :

Time interval of the records and the corresponding hour

\(\Delta t\) :

Interval between two time steps

\(T\) :

Number of records corresponding to the training interval

\(S,s\) :

Total number of sources for the weather web API, index of the API source

\(n,i\) :

Number of inverters and corresponding index

\({XW}^{t}\) :

Input set built from weather variables

\({P}_{i}^{t}\), \(\widehat{{P}_{i}^{t}}\) :

Generated and predicted power of inverter i at time t (W)

\({X}_{i}^{t}\) :

Input of the ML&DL models for inverter i (array)

\({y}_{i}^{t}\) :

Target variable of the output power of the inverter i (W)

\(k\) :

Index of the stochastic models (RF, XGB, DNN, GRU) used in predictions

\(\widehat{{y}_{i,k}^{t}}\) :

Predicted values of the ML&DL models for the inverter i (W)

\({{\text{Wind}}}_{s}^{t}\) :

Wind speed at time t provided by the API source s (m/s)

\({{\text{Cloud}}}_{s}^{t}\) :

Cloud cover at time t provided by the API source s (%)

\({{\text{Temp}}}_{s}^{t}\) :

Temperature at time t provided by the API source s (°C)

\({{\text{Hum}}}_{s}^{t}\) :

Humidity at time t provided by the API source s (%)

\({{\text{Pressure}}}_{s}^{t}\) :

Pressure at time t provided by the API source s (Pa)

\({{\text{UV}}}_{s}^{t}\) :

UV index at time t provided by the API source s \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{Precip}}}_{s}^{t}\) :

Precipitation at time t provided by the API source s (mm/h)

\({{\text{Sol}}}_{i}^{t}\) :

Effective solar irradiance at time t calculated based on pyranometer measurements for inverter i \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{POA}}}_{i}^{t}\) :

Plane of Array irradiance at time t measured by the pyranometer for inverter i \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{Sol}}}_{{\text{STC}}}\) :

Reference irradiance or solar irradiance under STC \(\left( {1000\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({\text{SF}}\) :

Soiling factor of the modules (approx. 0.97)

\({n}_{m}, m\) :

Number of the installed modules and index of the module

\({{\text{PD}}}_{m}^{t}, {{\text{PD}}}_{i}^{t}\) :

PV module, respectively, PV output of the inverter i calculated using deterministic model based on the measurements of pyranometer (W)

\({{\text{Sol}}}_{i,s}^{t}\) :

Effective solar irradiance at time t determined for the source s of the weather API for the inverter i \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{Sol}}}_{i,0}^{t}\) :

Effective solar irradiance at time t determined for the clear sky model for the inverter i \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{P}_{{\text{STC}}}}_{m}\) :

Rated capacity of the module m under Standard Test Conditions (STC)

\({{f}_{p}}_{m}\) :

Derating factor of the module m

\({{\alpha }_{p}}_{m}\) :

Temperature coefficient power of the module m(%/°C)

\({T}_{{\text{cell}} m}^{tf}\) :

Cell temperature of the module m (°C)

\({{T}_{{\text{STC}}}}_{m}\) :

Cell temperature under STC (25 °C)

\({{\eta }_{{\text{Pc}}}}_{m}\) :

Power conditioning efficiency of the module m

\({A}_{m}\) :

Area of the module m (m2)

\({{\eta }_{{\text{STC}}}}_{m}\) :

Module efficiency under STC (%)

\({\eta }_{m}^{t}\) :

Module efficiency at time t (%)

\({{\text{Type}}}_{i}\) :

Inverter type on-grid, off-grid, \({{\text{Type}}}_{i}\in \left\{{\text{onG}},\mathrm{ offG}\right\}\)

\({c}_{j},{n}_{c}\) :

Convolution coefficients applied in Savitzky–Golay filter, total number of coefficients

\({{\text{PLoad}}}_{i}^{t}\) :

Load power measured by the inverter i at time t (W)

\({{\text{PBat}}}_{i}^{t}, {{\text{SOC}}}_{i}^{t}\) :

Battery power and SOC measured by the inverter i at time t (%)

\({{\text{DNIextra}}}^{t}\) :

Direct normal extraterrestrial solar irradiance \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{DNI}}}_{s}^{t},{{\text{DHI}}}_{s}^{t},{{\text{GHI}}}_{s}^{t}\) :

Direct normal irradiance, diffuse horizontal irradiance and global horizontal irradiance determined for source s \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{AirT}}}_{s}^{t}\) :

Atmospheric transmittance at time t calculated based on \({{\text{CC}}}_{s}^{t}\) provided by the API source s (%)

\({Z}^{t}\) :

Apparent zenith angle (°)

\({{\text{AZ}}}^{t}\) :

Solar azimuth angle (°)

\({\beta }_{i}\) :

Tilt angle of the PV arrays connected to inverter i (°)

\({\Phi }_{i}\) :

Azimuth angle of the PV arrays connected to inverter i (°)

\(\rho \) :

Albedo or ground reflectance

\({{\text{Aoi}}}_{i}^{t}\) :

Angle of incidence on the PV arrays connected to inverter i at time t (°)

\({{\text{POA}}}_{i,s}^{t}, {{\text{POAd}}}_{i,s}^{t},{{\text{POAsky}}}_{i,s}^{t}, {{\text{POAg}}}_{i,s}^{t}\) :

Plane of Array total (global) irradiance, direct (beam), sky diffuse and ground diffuse irradiance for source s \(\left( {\frac{{\text{W}}}{{{\text{m}}^{2} }}} \right)\)

\({{\text{CSol}}}_{i,s}^{t}\) :

Weather data-driven variable of the cloud cover and effective solar irradiance

\({{\text{hSol}}}_{i,s}^{t}\) :

Weather data-driven variable of the time interval and effective solar irradiance

\({{\text{Pmin}}}_{i,s}^{t},{{\text{Pstd}}}_{i,s}^{t}, {{\text{Pmax}}}_{i,s}^{t}, {{\text{Pmean}}}_{i,s}^{t}\) :

The analytical values of the generated power for each value of \({{\text{hSol}}}_{i,s}^{t}\) of the inverter i

\({\text{RMSE}}, {R}^{2}, {\text{MAPE}}, {\text{MAE}}\) :

Evaluation metrics of the forecast performance

\(\widehat{{{\text{PD}}}_{m,s}^{t}}, \widehat{{{\text{PD}}}_{i,s}^{t}}\) :

PV module, respectively, PV output of the inverter i estimated for source s using deterministic model (W)

\({XM}_{i}^{t}\) :

Input of the HMF model

\(p\) :

Number of variables (features) of the input \({XM}_{i}^{t}\)

\({\omega }_{i}\),\({a}^{t}\) :

Variables of the LSTM model

\(d\) :

Daily time sequences used in LSTM (\(d=96\))

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Acknowledgements

This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS-UEFISCDI, project number PN-III-P4-PCE-2021-0334, within PNCDI III.

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  1. Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, No. 6 Piaţa Romană, Bucharest, Romania

    Simona-Vasilica Oprea & Adela Bâra

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Contributions

A.B. and S.V.O. wrote the main manuscript text and A.B. prepared all figures and the concept idea, including the revision of the manuscript. S.V.O. created all table and performed the checking of the manuscript.

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Correspondence to Simona-Vasilica Oprea.

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Oprea, SV., Bâra, A. On-grid and off-grid photovoltaic systems forecasting using a hybrid meta-learning method. Knowl Inf Syst 66, 2575–2606 (2024). https://doi.org/10.1007/s10115-023-02037-8

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