Solar, Wind, and Battery Storage Modeling with Machine Learning

Module: Sustainable Tech | Difficulty: Premium

Energy Output Modeling

Solar irradiance follows the clear-sky model:

where is the extraterrestrial irradiance, is the beam transmittance, and is the air mass. For wind power, the kinetic energy flux is:

where is air density, is rotor swept area, and is wind speed.

Battery Degradation Modeling

The capacity fade follows a power-law model:

where is initial capacity and is the degradation exponent.

Comparison

| Model | Input Features | Output | Accuracy | |-------|---------------|--------|----------| | ARIMA | Time series | Generation forecast | 85-90% | | LSTM | Weather + historical | Hourly generation | 92-96% | | XGBoost | Multi-feature | Power curve | 94-97% | | Physics-ML hybrid | Physical + data | System output | 96-99% |

Python Implementation

import numpy as np
from sklearn.ensemble import GradientBoostingRegressor

class SolarIrradianceModel:
    def __init__(self, latitude, longitude):
        self.lat = latitude
        self.lon = longitude
        self.declination = 23.45 * np.sin(np.radians(360/365 * (284 + np.arange(365))))

    def clear_sky_beam(self, hour_angle, air_mass_coeff=0.7):
        zenith = np.arccos(
            np.sin(np.radians(self.lat)) * np.sin(np.radians(self.declination)) +
            np.cos(np.radians(self.lat)) * np.cos(np.radians(self.declination)) * np.cos(np.radians(hour_angle))
        )
        G0 = 1361 * (1 + 0.033 * np.cos(np.radians(360 * np.arange(365) / 365)))
        tau_b = np.exp(-air_mass_coeff / np.cos(zenith))
        return G0 * tau_b

    def wind_power_density(self, wind_speed, air_density=1.225, rotor_area=1000):
        return 0.5 * air_density * rotor_area * wind_speed**3

    def predict_generation(self, weather_data, panel_area=50, efficiency=0.20):
        beam = self.clear_sky_beam(weather_data['hour_angle'])
        diffuse = beam * 0.15
        total_irradiance = beam + diffuse
        power = total_irradiance * panel_area * efficiency
        return np.maximum(power, 0)

Research Insight: Hybrid physics-ML models achieve 96-99% accuracy by embedding physical constraints into neural network architectures. The key challenge remains modeling rare weather events and extreme conditions where training data is sparse.