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Learning Long-Term Temporal Dependencies in Photovoltaic Power Output Prediction Through Multi-Horizon Forecasting

This paper proposes an architecture-independent multi-horizon forecasting framework that leverages joint optimization of sequential sky imagery and historical PV data to capture long-term temporal dependencies, thereby significantly improving the accuracy and robustness of photovoltaic power output predictions compared to traditional single-horizon models.

Original authors: Sumit Laha, Ankit Sharma, Hassan Foroosh

Published 2026-05-20

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Sumit Laha, Ankit Sharma, Hassan Foroosh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to guess how much electricity a solar farm will produce in the next hour. The sun is great, but it's fickle. Clouds roll in, the light dims, and the power output drops. To keep the power grid stable, we need to predict these changes accurately.

This paper introduces a new way to make those predictions, moving from a "one-step-at-a-time" approach to a "look-ahead" approach. Here is the breakdown using simple analogies:

The Old Way: The "Stop-and-Go" Driver

Traditionally, solar forecasting models act like a driver who only looks at the road one second at a time.

The Task: The model looks at the current sky and the last 15 minutes of power data, then tries to guess only what the power output will be exactly 15 minutes from now.
The Problem: By focusing only on that single future moment, the model gets "lazy." It learns to take a shortcut to get the answer right for that one specific second, but it misses the bigger picture of how the clouds are actually moving and changing over time. It's like trying to guess the ending of a movie by only looking at the final frame; you might get the result, but you don't understand the story.

The New Way: The "Marathon Runner"

The authors propose a Multi-Horizon approach. Instead of guessing just one point in the future, the model is asked to guess the power output for every single minute leading up to that future point (e.g., minute 1, minute 2, all the way to minute 15).

The Analogy: Imagine a runner training for a marathon.
- Single-Horizon: The runner only practices sprinting the last 100 meters of the race. They might be fast at the end, but they don't know how to pace themselves or handle the hills in the middle.
- Multi-Horizon: The runner practices the entire race distance. To get the last 100 meters right, they must understand how to run the first 10 miles, how the wind feels at mile 5, and how their legs feel at mile 12.
The Result: Because the model has to predict the whole sequence at once, it is forced to learn the "story" of the weather. It understands the relationship between the clouds moving now and how they will affect the sun later. This forces the model to learn deeper, more complex patterns (called "temporal dependencies") that the old method missed.

The "Magic" Ingredient: Joint Optimization

The paper calls this Joint Optimization.

The Metaphor: Think of a choir.
- In the old method, you ask each singer to hit one specific note perfectly, but you don't care if they sound good together.
- In the new method, you ask the choir to sing a whole melody. To get the melody right, every singer has to listen to the others and adjust their timing. They can't just rush to the end; they have to stay in sync.
Why it works: This "group effort" prevents the computer model from getting stuck in a "local trap" (a quick, easy solution that isn't actually the best). It forces the model to keep learning and adjusting its internal "muscles" (weights and filters) for longer, leading to a smarter, more robust prediction.

The Results: Better Accuracy, Same Effort

The researchers tested this new method on two different types of computer brains (architectures called SUNSET and MobileNet).

The Outcome: The "Marathon Runner" (Multi-Horizon) consistently predicted the power output more accurately than the "Stop-and-Go" driver (Single-Horizon), especially on cloudy days when the weather is tricky.
The Cost: The best part? It didn't require a supercomputer. The new method only added a tiny, almost invisible amount of extra work (less than 0.4% more computer memory) to get these much better results.

Summary

This paper doesn't invent a new type of solar panel or a new camera. Instead, it changes how we teach the computer to think. By asking the computer to predict a whole sequence of future events rather than just one single moment, we force it to understand the "flow" of the weather. This leads to smarter, more reliable predictions for our power grid, ensuring that even when the clouds roll in, we know exactly how much power we'll have.

Technical Summary: Learning Long-Term Temporal Dependencies in Photovoltaic Power Output Prediction Through Multi-Horizon Forecasting

Problem Statement
The rapid expansion of solar photovoltaic (PV) capacity introduces significant challenges to grid stability due to the intermittent nature of solar irradiance, driven by seasonal variations and sudden weather changes. While deep learning-based direct forecasting using ground-based sky images (GSI) has become a dominant approach, existing literature is constrained by two primary limitations:

Single-Horizon Focus: Most models are trained to predict a single future value (point prediction) at a specific time $T$ , failing to exploit the rich temporal dependencies inherent in the evolution of solar conditions.
Architecture-Specific Evaluations: Research often relies on a single network architecture (e.g., a specific CNN variant) and small datasets, limiting the generalizability of conclusions regarding model performance.

The central research question addressed is whether a deep learning model trained to forecast multiple future time points simultaneously can more effectively capture the intricate temporal dependencies governing solar conditions compared to traditional single-point estimation.

Methodology
The authors propose a multi-horizon forecasting framework that shifts the paradigm from single-step estimation to joint optimization over a sequence of future values.

Problem Formulation: The task is defined as a mapping function $\psi$ $ψ$ that takes historical sky images ( $I$ $I$ ) and historical PV power outputs ( $P$ $P$ ) over a window $H$ $H$ with interval $\delta$ $δ$ to predict future outputs.
- Single-Point: Predicts PV output at a specific future time $t + T$ .
- Multi-Horizon: Predicts PV outputs for the entire sequence from $t + 1$ to $t + T$ simultaneously.
Architecture Independence: The approach is designed to be architecture-agnostic. The authors validate this using two distinct baseline models:
1. SUNSET: A specialized CNN architecture designed for direct image-based PV power nowcasting.
2. MobileNet (v3 large): A lightweight, pre-trained convolutional network modified to accept sequential image inputs and historical PV data.
Input Processing: The models ingest sequential RGB sky images (historical 15 minutes at 1-minute intervals) and historical PV power data. For MobileNet, the input layer is modified to handle multiple image frames, and fully connected layers are frozen or adapted to fuse image and time-series features.
Objective Function: The networks are trained using Mean Squared Error (MSE) loss across all predicted time steps in the horizon.

Key Contributions

Demonstration of Long-Term Dependency Learning: The paper provides experimental evidence that joint optimization over a sequence of future values enables deep neural networks to better capture latent inter-step temporal dependencies.
Architecture-Independent Improvement: The multi-horizon approach is shown to improve accuracy across different network designs (SUNSET and MobileNet), positioning it as a general enhancement strategy rather than a replacement for specific architectures.
Computational Parsimony: The method achieves superior accuracy with negligible computational overhead. The increase in trainable parameters is minimal (e.g., ~0.15% for SUNSET and ~0.4% for MobileNet) compared to single-output models.

Experimental Results
The methodology was evaluated using the SKIPP'D dataset (Sky Images and Photovoltaic Power Generation Dataset), comprising aligned sky images and PV logs from 2017–2019 under varying weather conditions (sunny, partly cloudy, overcast).

Performance Metrics: The multi-horizon approach consistently outperformed single-point prediction in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE).
- On the SUNSET model with 64×64 inputs, RMSE improvements were 9.01% (15-min horizon), 5.6% (30-min horizon), and 3.4% (60-min horizon).
- Improvements were observed across both sunny and cloudy days, with particularly significant gains on sunny days (e.g., 56.13% RMSE improvement on a specific sunny test day).
Statistical Analysis: The multi-horizon models demonstrated higher $R^2$ scores and regression lines closer to the identity line (45-degree line), indicating better goodness-of-fit and generalization.
Internal Mechanism Analysis:
- Weight Gradients: Analysis of gradient magnitudes revealed that multi-horizon models exhibit a slower convergence rate compared to single-point models. This suggests the network avoids "precocious convergence" (getting stuck in local minima) and continues to learn complex features for a longer duration.
- Filter Diversity: Cosine similarity analysis of filters showed that multi-horizon training maintains higher filter diversity, preventing the network from collapsing into redundant feature representations.

Significance and Claims
The paper claims that this work provides a scalable and efficient solution to improve the resilience of modern power grids. By transitioning from single-point estimation to a holistic multi-horizon framework, the authors demonstrate that:

Deep learning models can better model the evolution of solar conditions by avoiding premature convergence.
This improvement is achieved without significant computational cost, making it highly suitable for real-time grid integration.
The approach serves as a robust, architecture-independent upgrade to existing forecasting models, enhancing predictive accuracy across the entire forecast horizon.

The authors remain modest regarding future implications, noting that current experiments are limited to the SKIPP'D dataset (California climate) and small-scale residential PV systems. They suggest that future work could explore diverse global weather conditions, utility-scale spatial variability, and the integration of meteorological variables (humidity, wind) or transformer-based architectures.

The Old Way: The "Stop-and-Go" Driver

The New Way: The "Marathon Runner"

The "Magic" Ingredient: Joint Optimization

The Results: Better Accuracy, Same Effort

Summary

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