Improving Day-Ahead Grid Carbon Intensity Forecasting by Joint Modeling of Local-Temporal and Cross-Variable Dependencies Across Different Frequencies

AI summary

Authors: Bowen Zhang, Hongda Tian (corresponding author), Adam Berry, A. Craig Roussac Affiliations: Data Science Institute, University of Technology Sydney; Human Technology Institute, University of Technology Sydney; Buildings Alive Pty Ltd. arXiv: 2601.06530v1 [cs.LG], 10 Jan 2026

Overview

Research area: Multivariate time series forecasting applied to electricity systems — specifically, short-term forecasting of the grid carbon intensity factor (CIF) using deep learning.

Technical level: Advanced. The paper builds on convolutional networks, continuous wavelet transforms, wavelet local multiple correlation, and prior multivariate forecasting architectures (PatchTST, iTransformer, TimeMixer, and others). Readers unfamiliar with time-frequency analysis will need to consult references.

One-sentence scope: The paper proposes a two-module deep learning model that captures local-temporal patterns and dynamic cross-variable relationships at multiple wavelet frequencies, and evaluates it against ten existing forecasting models across four Australian electricity markets.

What This Paper Is About

The carbon intensity of electricity — how many grams of CO2-equivalent are emitted per kilowatt-hour — changes hour by hour as the mix of generation sources shifts. Buildings, batteries, and electric vehicles can shift their consumption to cleaner periods, but only if they know in advance when those periods will occur. The goal of this paper is to forecast the grid carbon intensity factor one day ahead more accurately than existing methods, particularly in grids with high and volatile renewable penetration.

Key Contributions

1. A Local-Temporal Multi-Wavelet Kernel Convolution (LT-MWKC) module that divides the input series into overlapping patches of varying lengths and applies multiple wavelet-based convolutional kernels (for example, Morlet and Mexican Hat) in parallel, extracting localized temporal patterns across several frequencies.

2. A Cross-Variable Dynamic-Wavelet Correlation Convolution (CV-DWCC) module that systematically encodes all possible combinations of input variables using wavelet local multiple correlation (WLMC), selects the dominant variable within each combination, and learns from these structured correlation tensors with 2D convolution.

3. State-of-the-art accuracy on a four-region benchmark: combining the two modules produces the best RMSE, MAE, and SMAPE across the four Australian markets studied (NSW, SA, QLD, VIC), outperforming LSTM, SVR, LSTNet, Crossformer, Informer, TimesNet, DLinear, NonStaFormer, PatchTST, iTransformer, TimeMixer, and WPMixer.

4. Built-in interpretability: the paper uses Grad-CAM to show how the model reallocates attention across input variables and time steps during a real grid disruption, alongside an ablation study confirming that the two modules contribute complementary benefits.

Main Findings

• Best performance in all four markets. On the proposed model, RMSE/MAE/SMAPE were 47.09 / 36.56 / 5.25 in NSW, 99.27 / 70.29 / 32.21 in SA, 31.17 / 19.46 / 2.96 in QLD, and 79.36 / 57.93 / 7.13 in VIC (RMSE and MAE in g CO2-e/kWh, SMAPE in percent). The proposed model achieved the lowest value on every one of the twelve metric-region combinations reported.

• Largest advantage in the most volatile market. In South Australia — described as renewable-dominated, with wind and solar as the main sources — the paper reports the proposed model achieves an MAE 26.9% lower than the best-performing comparative model examined. Among the comparison models in Table 1, SA MAE values ranged from 76.72 (LSTNet) to 116.42 (SVR).

• Volatile and steady conditions both handled. In case studies of the days with the largest and smallest CIF variation in NSW and SA, the model tracked rapid changes and turning points more closely than alternatives such as NonStaFormer and TimesNet, which the authors describe as tending to smooth out peaks or lag sharp transitions; on flatter trajectories the model also maintained lower error.

• Ablation — removing LT-MWKC hurts. Excluding the LT-MWKC module increased MAE by 22.0% in NSW, 42.8% in SA, 31.8% in QLD, and 30.3% in VIC.

• Ablation — removing CV-DWCC hurts more. Excluding the CV-DWCC module increased MAE by 52.5% in NSW, 48.8% in SA, 61.4% in QLD, and 46.6% in VIC, a larger degradation than removing LT-MWKC in every region.

• Interpretability during a real outage. In a case study of the 12 November 2022 South Australia separation event — triggered around 4:00 PM by a double-circuit transmission tower failure that tripped the South East–Tailem Bend 275 kV lines and the Keith–Tailem Bend 132 kV line, isolating SA from the NEM — Grad-CAM showed a clear rise in feature saliency after the event at time step 16. The model prioritized non-renewable energy generation during the initial curtailment period, then shifted focus to renewable energy generation as output stabilized, and still predicted the following day (13 November 2022) well.

• Data and setup. The study uses four Australian states — New South Wales, South Australia, Queensland, and Victoria — over hourly intervals from January 1, 2020 to December 31, 2023, with five input variables (CIF, grid load demand, renewable energy generation, non-renewable energy generation, and temperature) sourced from AEMO and OpenNEM. Each sample uses 24 hours of input to predict the next 24 hours of CIF, generated with a 1-hour sliding window, giving 35,017 samples per state; results are averaged over 5-fold cross-validation.

Methodology in Plain English

The researchers treat carbon intensity forecasting as a multivariate time series problem: several related hourly signals go in, and the next 24 hours of carbon intensity come out. Their model runs two processing streams in parallel and then blends the results with a softmax-weighted fusion mechanism, followed by fully connected layers.

The first stream targets patterns that unfold over short stretches of time. Rather than cutting the history into fixed, non-overlapping blocks, it cuts it into overlapping patches of different lengths, so the model can see both brief fluctuations and longer local trends without abrupt boundaries between segments. Each patch is passed through convolutional filters shaped like wavelets — mathematical functions that are sensitive to different rhythms in a signal — with several wavelet types used at once, and the outputs are combined through learnable weights.

The second stream targets relationships between variables. It computes wavelet local multiple correlation, a method that measures how strongly variables move together at a particular time and a particular frequency, and does this for every possible combination of the input variables. For each combination it also identifies which variable is "dominant" — the one that best explains the others at that moment. The resulting correlation maps and dominant-variable maps are stacked and processed with 2D convolutions, letting the model learn how relationships such as "renewable generation rises, so carbon intensity falls" change depending on grid conditions and timescale.

Both streams are trained end-to-end against the same forecasting objective, and each region's model is tuned with grid search to keep the comparison with baselines fair. Interpretability is examined post hoc with Grad-CAM, which highlights which parts of the input the convolutional layers found most influential.

Why This Matters

Impact on research. The paper argues that prior work on CIF forecasting and on general multivariate forecasting handles three things incompletely: fine-grained local-temporal dependencies, dynamic (rather than static or linear) cross-variable dependencies, and multi-frequency structure. Its specific claim of novelty is that no existing research models cross-variable dependencies under multi-frequency, and that most wavelet-based methods use only a single wavelet basis. The ablation results quantify how much each gap costs.

Real-world applications:

• Pre-cooling buildings during low-carbon-intensity periods, so demand is reduced during the high-intensity afternoon — the scenario illustrated in Figure 1 with an example from October 15, 2022.
• Optimizing battery storage charging and discharging to align with cleaner generation availability.
• Scheduling electric vehicle charging into low-emission windows.
• Day-ahead load scheduling and operational planning, which the paper notes is where errors from smoothed or lagged forecasts matter most.

Industry relevance. The work was funded by the RACE for 2030 Cooperative Research Centre with support from Buildings Alive Pty Ltd. and the University of Technology Sydney, indicating direct interest from the building energy management sector. The four-region evaluation deliberately spans grids from coal- and gas-dominated (NSW, QLD, VIC) to renewable-dominated (SA), which is the range of conditions an operator or aggregator would encounter. Because higher renewable penetration makes carbon intensity less predictable — a point the paper raises in the introduction — forecasting methods that hold up in volatile conditions have commercial value as grids decarbonize.

Future Directions

1. Broader geographic generalization. The authors state that their findings are preliminary and that further evaluation on a broader test set is needed to confirm generalizability; future work will explore global electricity markets beyond the four Australian states.

2. Load optimization using the forecast. The paper proposes developing load optimization methods that actively consume real-time CIF forecast signals, moving from prediction to control.

3. Wider interpretability validation. The outage case study is described as an initial investigation; the authors intend to extend Grad-CAM analysis to a broader range of scenarios and regions.

4. Input variable expansion. The study deliberately uses a limited set of five input variables rather than an exhaustive dataset; whether additional variables improve performance is left open.

Target Audience

This paper is most useful to machine learning researchers working on multivariate time series forecasting and time-frequency methods, and to energy systems researchers and practitioners — grid operators, demand-response and building energy management companies, battery and EV charging operators — who need reliable day-ahead carbon intensity signals. Data scientists at organizations implementing carbon-aware scheduling will find the architectural ideas and the interpretability case study directly applicable, while readers new to the area will need background in wavelet analysis and deep forecasting architectures to follow the method in full.

Not reported in the paper: specific software frameworks, hardware used for training, the exact values of the wavelet kernel lengths, the number of CWT scales J, and code or data availability statements.

Authors’ abstract

Accurate forecasting of the grid carbon intensity factor (CIF) is critical for enabling demand-side management and reducing emissions in modern electricity systems. Leveraging multiple interrelated time series, CIF prediction is typically formulated as a multivariate time series forecasting problem. Despite advances in deep learning-based methods, it remains challenging to capture the fine-grained local-temporal dependencies, dynamic higher-order cross-variable dependencies, and complex multi-frequency patterns for CIF forecasting. To address these issues, we propose a novel model that integrates two parallel modules: 1) one enhances the extraction of local-temporal dependencies under multi-frequency by applying multiple wavelet-based convolutional kernels to overlapping patches of varying lengths; 2) the other captures dynamic cross-variable dependencies under multi-frequency to model how inter-variable relationships evolve across the time-frequency domain. Evaluations on four representative electricity markets from Australia, featuring varying levels of renewable penetration, demonstrate that the proposed method outperforms the state-of-the-art models. An ablation study further validates the complementary benefits of the two proposed modules. Designed with built-in interpretability, the proposed model also enables better understanding of its predictive behavior, as shown in a case study where it adaptively shifts attention to relevant variables and time intervals during a disruptive event.