Solar forecasting explained · 20 October 2026 · Full English version

Direct PV power forecasting: why reduce dimensionality?

A day of measurements contains many values, but not necessarily as many independent pieces of information. Dimensionality reduction seeks a compact representation, then checks whether it remains useful for forecasting.

Why forecast PV power directly?

Battery scheduling and grid injection decisions often need the electrical power actually delivered by a plant. One route forecasts solar irradiance, transposes it to the module plane, then models electrical conversion. Another forecasts future power directly from the plant’s past production.

The direct route avoids reconstructing the entire conversion chain for this task. The measurements already reflect the recent response of the modules and inverter. This does not make weather information irrelevant: sky observations, satellites and numerical weather predictions can provide information that the plant’s own history does not contain.

Why compress the history?

Imagine feeding a model every half-hourly measurement from the previous day. Neighboring values often move together. Treating each as a completely separate input may increase the input size without adding proportionate information. Dimensionality reduction constructs a smaller set of coordinates representing that trajectory.

Several nearly identical photographs do not necessarily provide several new views of an object. Yet removing one may also discard an important detail. Compression must be evaluated, rather than assumed beneficial.

Two questions, two diagnostics

• Is the geometry preserved? A model-free filter assesses local neighborhoods and global distances.
• Is the representation useful for forecasting? A wrapper evaluates it with a forecasting model, here an Extreme Learning Machine (ELM).

Geometric fidelity does not automatically imply predictive usefulness. The repository compares PCA, manifold methods and an autoencoder using these complementary perspectives.

Worked example: from 48 inputs to 4 coordinates

A day sampled every 30 minutes gives 48 power values. Reducing them to 4 coordinates means 12 times fewer inputs. This is a dimensionality ratio, not a measured speedup.

For a 100-neuron hidden layer, the input weights number 4,800 before reduction and 400 afterward, excluding biases, output weights and any calendar inputs. But a linear 48-to-4 projection itself stores 192 coefficients, potentially plus centering and scaling information. A nonlinear transformation may cost more.

Suppose test RMSE is 100 W without reduction and 102 W with reduction: error rises by 2% in exchange for a more compact representation. Whether that is acceptable depends on the application. These are illustrative values, not manuscript results.

What makes the comparison credible?

Fit the transformation only on past training data. Reserve future dates for testing and use identical horizons and evaluation samples. Include the unreduced model and simple baselines. Count the transformation’s cost: a smaller input does not guarantee a cheaper complete pipeline.

The choice depends on site, horizon and data quality. Compression does not solve missing history at a new plant or undocumented changes in plant operation.

Explore the collaborative work

The MATLAB repository includes a Palaiseau example and a quick smoke-test mode. Its seven-method comparison separates geometric preservation from forecasting utility. The associated manuscript remains unsubmitted; this page reports no unpublished numerical findings.

The project code uses the MIT license. The bundled drtoolbox retains its own non-commercial terms; check them before reuse.

MATLAB code and protocolNext: why deploy frugal models?