Multi-Region Electric Load Forecasting

• MRELF is a forecasting approach for disaggregated electric loads that jointly models multiple regional series along with weather and spatial factors.
• It leverages methods such as forecast combination, adaptive probabilistic updating, and joint multivariate sequence modeling to capture regional dependencies.
• Practical case studies from Italy, ISO New England, Great Britain, and Europe demonstrate its impact on operational balancing and planning.

Searching arXiv for papers on multi-region electric load forecasting and closely related formulations. I’ll look up arXiv entries that match multi-region, multivariate, and weather-aware load forecasting so the article can be grounded in current papers. Multi-Region Electric Load Forecasting (MRELF) denotes forecasting settings in which load targets are regionally disaggregated, multiple geographically distinct load series are predicted jointly, or cross-regional dependence is introduced explicitly or implicitly. In recent arXiv work, this label covers very short-term/day-ahead forecasting for Italy at 15-minute resolution over seven bidding zones plus the national aggregate (Girolimetto et al., 17 Feb 2025), short-to-mid-term daily peak forecasting for the 8 ISO New England zones through joint multivariate sequence modeling (Fu et al., 2023), adaptive probabilistic forecasting across 14 Great Britain regions and 7 U.S. cities with separate regional models (Vilmarest et al., 2023), and dependence-aware probabilistic mid-term forecasting of hourly load across 24 European countries (Zimmermann et al., 2024). The field therefore comprises not a single architecture but a family of formulations spanning hierarchy, multivariate coupling, adaptive online updating, and weather-aware regional representation.

1. Scope and conceptual boundaries

A central distinction in MRELF is between true joint multi-region forecasting and adjacent but weaker formulations. The most direct multi-region setting appears when multiple regional loads are forecast jointly as a multivariate output. In the ISO New England study, the target vector contains the demands for all 8 zones, and the model forecasts these outputs jointly rather than training one independent model per region in the main formulation (Fu et al., 2023). By contrast, the Italian Terna study is multi-region because the targets are regionally disaggregated by bidding zone and because the preferred method performs a global multi-task combination using all zones together, even though the method is framed as a post-processing layer on top of existing forecasts rather than a new primary spatiotemporal load model (Girolimetto et al., 17 Feb 2025).

A second boundary concerns cross-sectional repeated single-region forecasting. The adaptive probabilistic forecasting framework for Great Britain and U.S. cities is highly relevant to MRELF, but the models are built independently for each region or city; there is no shared parameterization across zones, no pooled multi-task model, and no joint multivariate forecast (Vilmarest et al., 2023). The adaptive online HMM work similarly evaluates a shared methodology across seven regional datasets of different sizes and time-varying consumption patterns, but does not explicitly model cross-region dependence or shared latent dynamics across regions (Álvarez et al., 2020).

A third boundary concerns spatial inputs versus spatial outputs. The geo-distributed meteorological-factor framework uses multiple weather locations within one city or region, treats weather locations as graph nodes, and predicts one regional aggregate load. It therefore addresses an important regional weather-encoding subproblem, but it does not jointly forecast multiple regional loads and does not model interactions among multiple load zones (Zhou et al., 4 Jan 2025). This distinction is important because MRELF is often conflated with any load-forecasting problem involving spatially distributed covariates.

These distinctions suggest that MRELF should be understood as a spectrum. At one end are models with explicit multi-output regional targets; at the other are methods that remain region-wise but are operationally relevant because they scale across heterogeneous regions or encode intra-regional spatial structure.

2. Regional structures, temporal scales, and data regimes

The literature spans sharply different regional units, temporal resolutions, and forecast horizons. The following configurations are explicitly documented.

Setting	Regional units	Resolution and horizon
Terna public-data refinement (Girolimetto et al., 17 Feb 2025)	7 bidding zones + Italy total	15-minute; $h=1,\ldots,96$
MMMPF on ISO New England (Fu et al., 2023)	8 zones	Daily peak; 1 to 60 days ahead
Adaptive forecasting in Great Britain / U.S. (Vilmarest et al., 2023)	14 regions / 7 cities	Half-hourly with one-day latency / daily next day
Pan-European probabilistic forecasting (Zimmermann et al., 2024)	24 countries	Hourly; 52 weeks
Feeder long-term forecasting (Dong et al., 2019)	403 feeders	Annual seasonal peak; 3-year test window

These settings correspond to materially different operational problems. The Terna setting is explicitly “immediately after Terna publishes” the measured load for the previous day and the forecast load for the current day; each forecast day contains 96 quarter-hourly values, and the national load is disaggregated into seven zone-level components (Girolimetto et al., 17 Feb 2025). The ISO New England setting downsamples hourly data to daily peak demand and uses the most recent 30 days of demand history to forecast 1 to 60 future daily peaks for 8 zones (Fu et al., 2023). The pan-European model instead forecasts hourly country-level load over a horizon of $H = 168 \times 52$ hours, using 4 years of in-sample data in a rolling-window design with 50 forecasting experiments and 200 simulated trajectories per forecast (Zimmermann et al., 2024).

Regional organization also varies structurally. In Italy, the system contains 8 time series total: 7 zonal loads plus the national total, and the paper explicitly notes the hierarchical structure that the national load is disaggregated into the seven zone-level components (Girolimetto et al., 17 Feb 2025). In the feeder long-term study, the hierarchy is between a planning area and 403 distribution feeders, with area-level exogenous features and feeder-level drivers combined in a hybrid top-down/bottom-up design (Dong et al., 2019). At the opposite extreme, the single scalable LSTM study uses 3891 smart meters and treats the forecasting problem as one shared model across many disaggregated electricity time series rather than a power-system regional hierarchy (Alonso et al., 2019).

The temporal scale also changes what “multi-region” means. Sub-hourly and hourly forecasting emphasize operational balancing, daily and weekly horizons emphasize scheduling and planning under known future covariates, and annual feeder forecasting emphasizes capacity expansion and distribution planning. MRELF is therefore unified less by horizon than by the coexistence of multiple regional series, regional heterogeneity, and some form of information sharing or dependence modeling.

3. Methodological families

One major family consists of forecast combination and post-processing methods. The Terna paper does not build a new load model from scratch for each zone; instead, it proposes a post-processing or forecast combination layer on top of existing forecasts. The base forecasts are Terna’s zonal forecasts and a zonal daily-random-walk naive forecast, while the preferred method is a stacked-regression multi-task combination approach that combines them jointly across all regions (Girolimetto et al., 17 Feb 2025). In this formulation, multi-region structure enters through joint error exploitation rather than through an explicit spatial dynamical model.

A second family consists of joint multivariate sequence models. The MMMPF framework is a training framework rather than a single architecture. It forecasts a sequence of future multivariate outputs by masking future target values, keeping known future predictor variables visible, and training the model to reconstruct the masked target sequence. The framework is demonstrated with LSTM, TCN, and Transformer backbones and is explicitly multivariate, with 8 zonal demands per future day in the electricity application (Fu et al., 2023). This is one of the clearest instances of direct joint MRELF in the surveyed material.

A third family comprises adaptive probabilistic region-wise forecasters. In the Great Britain and U.S. city study, the methodology is two-stage: an adaptive point forecast using a Kalman-filtered state-space version of a GAM, followed by probabilistic forecasting via quantile regression on residuals adapted online by online gradient descent and Bernstein Online Aggregation over multiple learning rates (Vilmarest et al., 2023). The online HMM approach likewise emphasizes adaptive online learning techniques that update model parameters recursively and sequential prediction techniques that obtain probabilistic forecasts using the most recent parameters (Álvarez et al., 2020). These methods are region-wise rather than jointly multivariate, but they address nonstationarity and uncertainty in ways that are directly relevant to multi-region operations.

A fourth family consists of global cross-entity models with indirect relevance to MRELF. The feeder long-term forecasting paper converts multi-year feeder LTLF into multi-timestep sequence prediction, groups feeders by load composition using K-means, and uses a GRU-based selective sequence learning mechanism to choose among Single-year Recursive, Single-year with Interval, and Multi-year Ahead configurations for each individual feeder (Dong et al., 2019). The single scalable LSTM paper trains one shared recurrent model per group of household entities, showing that a global model can learn common temporal structure and generalize to unseen entities at low marginal cost (Alonso et al., 2019). This suggests a broader design pattern in which many related series are pooled into one model even when explicit inter-region dependence is absent.

Taken together, these families indicate two dominant design logics. One logic seeks direct coupling of regional outputs within a common model; the other seeks scalability, adaptation, or representation sharing across many regional or subregional series without enforcing a fully coupled multivariate state.

4. Weather, spatial covariates, and representation learning

Weather modeling is a recurring driver of MRELF architecture. The geo-distributed meteorological-factor study argues that selecting MF from one representative location or from averaged MF is inadequate because meteorological conditions vary substantially within a city or region due to urban heat island effects, atmospheric dynamics, topography or terrain differences, and heterogeneous land use and economic activity (Zhou et al., 4 Jan 2025). The proposed integrated learning objective is

$$\arg \min_{g,f} \sum_{t \in T_{\text{train}}} L\big(f(g(X_t, A), X_{O,t}), y_t\big),$$

where $g$ is a representation generator for geo-distributed meteorology, $f$ is the forecasting model, $A \in \mathbb{R}^{n \times n}$ is the spatial relationship matrix among weather locations, and $X_O$ contains other features such as calendar variables and historical loads. In the reported framework, meteorology is organized as a graph $G(X,A)$, with $A_{ij}=1$ if locations $i$ and $H = 168 \times 52$0 are adjacent and $H = 168 \times 52$1 otherwise (Zhou et al., 4 Jan 2025).

For MRELF, the significance of this work is modular rather than direct. The paper itself states that a natural extension would be to use load regions or subregions as one graph, weather locations as another graph or bipartite structure, or one local weather graph per region whose learned embedding feeds a joint multi-region forecasting model (Zhou et al., 4 Jan 2025). In other words, the study provides a regional weather encoding module that can be embedded in a larger multi-region architecture.

The pan-European probabilistic model takes a different route. It uses hourly average temperatures in the 5 most populous cities in each country, smooths temperature into two series using VETS with $H = 168 \times 52$2 and $H = 168 \times 52$3, fits country-specific temperature GAMs, and introduces cross-country dependence through residual covariance among temperature forecast errors (Zimmermann et al., 2024). Spatial weather dependence is therefore handled not by neighboring-country weather regressors or a spatial field model, but by country-level temperature trajectories whose innovations are correlated across countries.

A further adjacent direction is automated spatio-temporal weather modeling. The French national-load study states that, in current state-of-the-art load forecasting models, the spatio-temporal modeling of the weather is fixed, and proposes a deep-learning-based methodology intended to improve spatio-temporal weather modeling for load forecasting; the methodology is also described as fully adaptable to forecasting renewable energy production (Keisler et al., 2024). Although the provided material does not specify its full architecture, it reinforces the broader tendency to treat weather encoding as a central bottleneck.

A common limitation across these strands is that the exact graph construction procedure, normalization strategy, and weather forecast versus reanalysis alignment are often underspecified. This suggests that weather representation remains one of the least standardized but most consequential components of MRELF pipelines.

5. Probabilistic forecasting, adaptation, and dependence structures

Probabilistic MRELF can be framed at several levels: marginal quantiles per region, adaptive probabilistic updating over time, or cross-region dependent scenario generation. The MMMPF framework adopts a quantile-forecasting view. It trains on the pinball loss for selected quantiles $H = 168 \times 52$4, enabling lower, median, and upper forecasts for each future horizon and region (Fu et al., 2023). Its probabilistic output is therefore a set of quantile forecasts rather than a parametric joint density.

The adaptive GAM-based framework formulates forecasting as estimating $H = 168 \times 52$5 in the online setting. Its point forecast is adapted by a Kalman filter on a linear Gaussian state-space version of a GAM, while probabilistic forecasts are obtained by adaptive quantile regressions on residuals using online gradient descent and BOA (Vilmarest et al., 2023). The same paper is explicit about a key limitation: there is no multivariate predictive distribution across regions, and the conclusion identifies adaptive multivariate probabilistic forecasts as a natural extension (Vilmarest et al., 2023).

The online HMM approach addresses uncertainty and nonstationarity by learning HMM parameters recursively and generating sequential probabilistic forecasts with the most recent parameters, with experimental evaluation across large, medium, and small regional datasets (Álvarez et al., 2020). Its relevance to MRELF lies in robustness across heterogeneous regional settings rather than in direct modeling of inter-region dependence.

The pan-European model is the clearest dependence-aware probabilistic system. It combines country-specific GAMs with stochastic submodels for temperature, socio-economic and political state, and autoregressive residuals, and it simulates these components iteratively with Gaussian innovations using covariance matrices estimated in-sample (Zimmermann et al., 2024). Cross-country dependence is therefore introduced within stochastic blocks through residual covariance, and in the state model additionally through VAR or VECM structures. In the VECM specification, the rank is set to $H = 168 \times 52$6, implying one common underlying unit root across the $H = 168 \times 52$7 country state series (Zimmermann et al., 2024). At the same time, the paper explicitly states that joint dependence across the three stochastic blocks was not modeled because in-sample correlations between blocks were judged too small.

A recurrent controversy in MRELF is whether marginal probabilistic forecasts for many regions are sufficient. The surveyed literature indicates that they are often operationally useful, but they are not equivalent to a coherent multivariate predictive distribution across regions. That gap is especially salient when reserve procurement, stochastic dispatch, or simultaneous regional risk constraints depend on cross-sectional dependence rather than on separate marginal intervals.

6. Evaluation, misconceptions, and open problems

Empirical evaluation remains heterogeneous across MRELF settings. In ISO New England daily peak forecasting, Table 1 reports average MAPE averaged over all 8 zones and all horizons from 1 to 60 days. For the same backbone, MMMPF beats both RSF and DMF: LSTM 4.99 versus 8.63 versus 19.22, TCN 6.00 versus 9.62 versus 18.67, and Transformer 5.56 versus 7.92 versus 17.72 (Fu et al., 2023). In feeder-scale long-term forecasting, SSL performs best against the three individual sequential configurations. In summer, SSL records AMAPE 7.45%, RMSE 30.5, and $H = 168 \times 52$8; in winter, AMAPE 6.76%, RMSE 29.5, and $H = 168 \times 52$9 (Dong et al., 2019). In the scalable household LSTM setting, the shared LSTM improves benchmark performance by more than 20% on average and generalizes to unseen entities, but that evidence is indirect for region-level MRELF because the study does not include explicit spatial or hierarchical structure (Alonso et al., 2019).

Several misconceptions recur. First, multi-location weather input is not equivalent to multi-region load forecasting: the geo-distributed MF framework forecasts one regional aggregate load while treating weather locations, not load regions, as graph nodes (Zhou et al., 4 Jan 2025). Second, repeated separate regional forecasting is not the same as a coupled multi-region model: the adaptive Great Britain/U.S. framework and the online HMM method are relevant to MRELF but do not explicitly model cross-region dependence or shared latent dynamics across regions (Vilmarest et al., 2023). Third, a global model across many series does not by itself solve hierarchy or topology: the scalable LSTM and feeder-sequence models share information across entities, yet they do not impose hierarchical reconciliation or explicit network-aware coupling (Alonso et al., 2019).

Hierarchy and coherence remain open issues. The Terna system has an explicit hierarchical structure because the national load is disaggregated into seven zone-level components, but the paper is centered on multi-region forecast combination rather than on explicit reconciliation constraints (Girolimetto et al., 17 Feb 2025). The feeder long-term study explicitly states that there is no area-to-feeder aggregation or disaggregation consistency constraint such as “sum of feeder forecasts must equal area forecast,” and the adaptive regional probabilistic framework lists hierarchical aggregation constraints and probabilistic coherence across regions among the elements it does not model (Dong et al., 2019). These omissions do not invalidate the methods, but they delimit what kind of MRELF problem is actually being solved.

The literature also exposes persistent implementation gaps. Some papers do not report normalization or standardization, missing-value imputation, outlier treatment, weather forecast versus reanalysis alignment, or detailed graph construction rules (Zhou et al., 4 Jan 2025). In the MMMPF study, uncertainty is represented through quantiles, but standard probabilistic evaluation metrics such as CRPS, interval coverage, Winkler score, or calibration curves are not reported (Fu et al., 2023). A plausible implication is that future MRELF work will need to integrate explicit spatial or network structure, coherent multivariate probabilistic outputs, and more fully specified preprocessing pipelines if cross-regional dependence, hierarchy, and operational reproducibility are all to be addressed simultaneously.