SolarBoost: Forecasting Distributed PV Output

• SolarBoost is a forecasting method for distributed photovoltaic systems that decomposes regional output into grid-level contributions using a shared per-unit function multiplied by time-varying latent capacities.
• It employs an alternating optimization approach that combines gradient boosting with Kalman filtering to update both the per-unit weather-to-output mapping and grid-specific capacity estimates.
• The method has demonstrated improved efficiency and accuracy in DPV forecasting, yielding significant RMSE reductions and operational benefits in real-world deployments.

SolarBoost is a forecasting method for distributed photovoltaic (DPV) systems that predicts a region’s aggregated gross PV power output by decomposing it into grid-level contributions, each expressed as a shared per-unit output function multiplied by a time-varying generalized-capacity term. In the strict sense, the name refers to the framework introduced in “SolarBoost: Distributed Photovoltaic Power Forecasting Amid Time-varying Grid Capacity” (Geng et al., 24 Oct 2025). In broader solar-energy literature, related usage sometimes denotes boosting-based forecasting pipelines more generally, but those are adjacent methodologies rather than the specific latent-capacity formulation that defines SolarBoost proper (Ahmed et al., 29 Jun 2025).

1. Distributed-photovoltaic forecasting context

SolarBoost was developed for distributed photovoltaic forecasting rather than centralized photovoltaic forecasting. The distinction is foundational. Centralized photovoltaic systems are relatively uniform and easier to model as single sites or small collections of homogeneous plants, whereas distributed photovoltaic systems aggregate many geographically dispersed and heterogeneous rooftop or community installations. SolarBoost targets the future aggregated gross PV output $Y_t$ of a region, such as a city, using weather forecasts and auxiliary features defined on spatial grids. The inputs are represented as a tensor of shape $T \times K \times D$, where $T$ is the number of time steps, $K$ is the number of spatial grids, and $D$ is the feature dimension (Geng et al., 24 Oct 2025).

The method is motivated by several sources of nonstationarity that are acute in DPV. The utility typically observes only the regional aggregate rather than per-rooftop or per-grid generation. Installed capacity changes over time as more systems are added, so identical weather can correspond to different aggregate output at different dates. Geographic variability means that city-level averaging can erase informative local structure, and equipment diversity introduces additional variation from panel orientation, type, maintenance status, and degradation. SolarBoost is designed around the proposition that aggregate DPV output is not merely a function of aggregated weather variables; it is a weighted sum of grid-level weather responses, with weights that themselves vary over time (Geng et al., 24 Oct 2025).

This framing distinguishes SolarBoost from common baselines that either average weather features across grids or flatten grid-level features into one long vector. It also places SolarBoost within a broader forecasting landscape in which many solar models still operate at site level or on pooled weather data. Short-term PV forecasting with NGBoost on two PV parks in Southern Germany, for example, addresses probabilistic forecasting and interpretability for utility-scale parks rather than latent grid-level aggregation, while comparative irradiance studies with XGBoost, LightGBM, and CatBoost typically treat irradiance regression from hourly meteorological covariates without an explicit time-varying capacity layer (Mitrentsis et al., 2021, Soleymani et al., 2023).

2. Latent generalized-capacity formulation

The core SolarBoost model represents total output as a sum over spatial grids: $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$ where $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$ is the feature vector for grid $i$ at time $t$, $f(\cdot;\boldsymbol{\theta})$ is a shared per-unit-capacity output function, and $T \times K \times D$0 is the grid’s generalized-capacity (Geng et al., 24 Oct 2025).

Generalized-capacity is broader than installed nameplate capacity. It is defined to absorb actual capacity, efficiency decay, panel-type differences, panel orientation, maintenance effects, and missing grid-level information. This separation is central to the method. The shared function $T \times K \times D$1 captures the relatively stable weather-to-per-unit-output mapping, while $T \times K \times D$2 captures the time-varying effective contribution of each grid. A direct implication is that SolarBoost treats DPV nonstationarity primarily as a capacity-allocation problem superimposed on a more stable per-unit production law (Geng et al., 24 Oct 2025).

Learning is posed as a constrained optimization problem: $T \times K \times D$3 with

$T \times K \times D$4

Here $T \times K \times D$5 is the known total city-level capacity, nonnegativity constrains grid contributions, and $T \times K \times D$6 enforces gradual temporal evolution (Geng et al., 24 Oct 2025).

This formulation encodes SolarBoost’s basic modeling claim: city-scale DPV forecasting is improved by explicitly reconstructing the latent spatial allocation of effective capacity rather than by learning a single aggregate regressor over pooled inputs. The paper also introduces the conceptual relation $T \times K \times D$7 to emphasize that capacity drift induces a multiplicative shift in the weather-to-output mapping, and that simply scaling an aggregate model by total-capacity ratio is generally insufficient because the distribution of capacity across grids also changes (Geng et al., 24 Oct 2025).

3. Optimization procedure and boosting architecture

The original loss couples all grids inside a squared error term and jointly depends on both $T \times K \times D$8 and $T \times K \times D$9, so SolarBoost introduces a surrogate upper bound and solves the problem by alternating minimization. The forecasting function is updated through residual-style boosting, while the generalized-capacity sequence is updated through a state-space procedure (Geng et al., 24 Oct 2025).

For the function update, the paper defines an incremental learner

$T$0

and writes the updated predictor additively as

$T$1

with learning rate $T$2. The surrogate yields per-instance gradient and Hessian terms for tree boosting: $T$3

$T$4

These expressions make higher-capacity grids more influential during tree fitting. In implementation, SolarBoost uses Gradient Boosted Decision Trees, specifically LightGBM and XGBoost, as the function-learning backbone (Geng et al., 24 Oct 2025).

For the generalized-capacity update, SolarBoost rewrites the surrogate in matrix form and then casts capacity estimation as a linear dynamical system. The state transition is

$T$5

and the observation model is

$T$6

This Kalman-filter formulation reduces the update cost from $T$7 for direct joint optimization to $T$8, which is one of the main algorithmic arguments for the method. In practice, $T$9 is initialized uniformly, $K$0, and the generalized-capacity sequence is divided into subsequences of length $K$1, keeping capacity constant within each subsequence. For forecasting horizon $K$2, SolarBoost uses future features $K$3 and the latest estimated capacity $K$4 (Geng et al., 24 Oct 2025).

4. Theory, data, and empirical behavior

SolarBoost is supported by both theoretical analysis and experiments on synthetic and real-world datasets. The first theoretical result states that, under bounded capacity changes and sufficient sample size, grid-level modeling has a tighter upper bound than aggregate modeling. The theorem is given as

$K$5

and is interpreted as showing that aggregate models trade lower variance for bias under capacity drift, whereas grid-level models are unbiased and eventually preferable as sample size grows. The second theorem states that $K$6, implying that rough generalized-capacity estimates may still suffice when grid-level inputs are highly correlated (Geng et al., 24 Oct 2025).

The synthetic evaluation uses datasets with $K$7 grids and $K$8 features, with

$K$9

Two capacity regimes are used: an AR dataset and a Kalman dataset. On normalized generalized-capacity RMSE, SolarBoost achieved $D$0 on the Kalman dataset and $D$1 on the AR dataset, versus $D$2 and $D$3 for AverageGrid. On the first grid of the AR dataset, unit-output RMSE was $D$4 for SolarBoost, compared with $D$5 for IdealFit and $D$6 for AverageGrid. On aggregate prediction RMSE $D$7, SolarBoost achieved $D$8 on the Kalman dataset and $D$9 on the AR dataset, versus $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$0 and $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$1 for AverageGrid and $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$2 and $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$3 for FlattenGrid (Geng et al., 24 Oct 2025).

The real-world experiments use five cities in eastern China from January 30, 2020 to September 30, 2024, with power data at 15-minute resolution and weather data from numerical weather prediction at 0.1-degree resolution. The features are irradiation, temperature, cloud cover, and sine/cosine transforms of time-of-day and seasonality. Training spans January 30, 2020 to August 31, 2024; testing spans September 1, 2024 to September 30, 2024, with test size $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$4 for each city. SolarBoost obtains the best RMSE $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$5 in all five cities: $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$6, $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$7, $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$8, $$\hat Y_t = \sum_{i=1}^{K} c_{t,i} f(\boldsymbol{x}_{t,i};\boldsymbol{\theta}),$$9, and $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$0, compared with AverageGrid at $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$1, $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$2, $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$3, $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$4, and $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$5; FlattenGrid at $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$6, $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$7, $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$8, $\boldsymbol{x}_{t,i} \in \mathbb{R}^D$9, and $i$0; CNN-LSTM at $i$1, $i$2, $i$3, $i$4, and $i$5; Ave-SARIMAX at $i$6, $i$7, $i$8, $i$9, and $t$0; and Flat-SARIMAX at $t$1, $t$2, $t$3, $t$4, and $t$5. For City A specifically, the reported RMSE reductions are $t$6 versus AverageGrid, $t$7 versus FlattenGrid, $t$8 versus CNN-LSTM, $t$9 versus Ave-SARIMAX, and $f(\cdot;\boldsymbol{\theta})$0 versus Flat-SARIMAX. The appendix reports 1000 boosting iterations, learning rate $f(\cdot;\boldsymbol{\theta})$1, max tree depth $f(\cdot;\boldsymbol{\theta})$2, and $f(\cdot;\boldsymbol{\theta})$3 on toy data and $f(\cdot;\boldsymbol{\theta})$4 on real data. Ablation shows a U-shaped RMSE curve as the number of grids $f(\cdot;\boldsymbol{\theta})$5 varies, and regularization performs best around $f(\cdot;\boldsymbol{\theta})$6, with stable performance for $f(\cdot;\boldsymbol{\theta})$7 between roughly $f(\cdot;\boldsymbol{\theta})$8 and $f(\cdot;\boldsymbol{\theta})$9. The least-squares joint capacity update without Kalman filtering took $T \times K \times D$00 s for $T \times K \times D$01, whereas the Kalman update took under $T \times K \times D$02 s; convergence times were $T \times K \times D$03 s for SolarBoost, $T \times K \times D$04 s for CNN-LSTM, $T \times K \times D$05 s for Flat-SARIMEX, and $T \times K \times D$06 s for Ave-SARIMEX (Geng et al., 24 Oct 2025).

5. Deployment and operational significance

SolarBoost was deployed in a province in eastern China starting in October 2024. The operational scale reported for that deployment is substantial: 158,000 square kilometers, 100 million people, 37 million kilowatts of installed DPV capacity, and approximately 10% of China’s total distributed PV capacity in 2024. Prior to deployment, forecasting was manual and based on operator experience, weather information, and hand-crafted rules. SolarBoost was integrated through the eForecaster platform, which collects updated DPV output and NWP data, preprocesses data, trains models online, stores models in a distributed file system, and generates day-ahead forecasts every morning at 9 AM. Retraining is done weekly (Geng et al., 24 Oct 2025).

The deployment section reports business-facing performance in terms of

$T \times K \times D$07

Under that measure, average accuracy improved from 95.7% to 96.3%. Over a 90-day period from Oct. 8, 2024 to Jan. 5, 2025, the improved forecasts reportedly reduced curtailment by 63.89 million kWh and generated \$0.41 million in revenue. The paper also states that the inferred capacity estimates provide useful signals for distribution network planning and DPV capacity planning, which suggests that SolarBoost is not only a forecasting model but also a latent-state estimator with planning relevance (Geng et al., 24 Oct 2025).

A broader implication is that SolarBoost belongs to a class of operational solar-forecasting systems where the forecasting target is not a single plant’s output but an evolving, partially observed portfolio of small installations. This differs materially from site-level probabilistic PV forecasting with methods such as NGBoost, where the main emphasis is calibrated uncertainty and SHAP-based interpretability for individual utility-scale parks, and from tabular irradiance regression studies in which Random Forest, LightGBM, and XGBoost are compared under common hyperparameter tuning on NSRDB-style datasets (Mitrentsis et al., 2021, Soleymani et al., 2023).

6. Relation to adjacent usages, limitations, and outlook

The term “SolarBoost” can be misunderstood if it is detached from the specific DPV context of the 2025 forecasting paper. It does not denote the microgrid-sizing framework BOOST, whose acronym expands to Battery-solar Ordinal Optimization Sizing Technique and addresses PV-battery sizing and dispatch rather than DPV forecasting (Chehade et al., 18 Jan 2025). Nor does it simply mean “any boosting-based solar model.” The wider literature does contain boosting-centered solar forecasting studies—for example, a U.S. smart-energy-management study using Random Forest and XGBoost on multi-site solar-production categories, and a probabilistic short-term PV forecasting framework based on NGBoost plus SHAP—but those should be read as related methodological neighbors rather than as SolarBoost itself (Ahmed et al., 29 Jun 2025, Mitrentsis et al., 2021).

Several limitations are explicit in the SolarBoost paper. The method currently relies solely on DPV data; the authors suggest that incorporating CPV information and transferring useful characteristics from centralized to distributed settings may improve accuracy. The framework depends on known total capacity $T \times K \times D$08, temporal smoothness assumptions, and the idea that latent heterogeneity can be represented through multiplicative generalized-capacity weights. The shared per-unit function $T \times K \times D$09 across grids may be restrictive if different areas truly follow different weather-to-output mappings that cannot be reduced to scalar reweighting. Capacity is also assumed to change gradually and is often treated as constant within subsequences or daily windows, which may be strained by abrupt topology changes, outages, or maintenance shocks. Future work is stated in terms of more effective optimization algorithms, more complex capacity modeling, and extension to other renewable energy systems (Geng et al., 24 Oct 2025).

Read against adjacent solar-forecasting research, SolarBoost’s specific contribution is therefore not merely the use of gradient boosting. Its defining innovation is the combination of grid-level modeling, latent generalized-capacity estimation, and alternating boosted-function plus Kalman-filter optimization for DPV systems under time-varying installed capacity. That focus distinguishes it from ensemble studies where boosting is simply one regressor among several, and from solar-energy-management studies where XGBoost performs well but does not clearly dominate other tree ensembles (Soleymani et al., 2023, Ahmed et al., 29 Jun 2025).