A Nonlinear Time Series Analysis of Electrical Load, Frequency, and Area Control Error (ACE)

Abstract: Over the past decade, there has been a rapid increase in the adoption of privately owned rooftop solar photovoltaic (PV) systems and electric vehicles (EVs). Grid operators, however, have limited access to these distributed resources. Consequently, rooftop PVs and EVs act as hidden loads, creating significant discrepancies between the predicted and actual electricity demand. These discrepancies lead to large fluctuations in system frequency and area control error (ACE). Both ACE and frequency exhibit very short correlation times — approximately 10 - 20 minutes, respectively. We propose a model-free prediction approach based on Takens’ theorem and state-space reconstruction, commonly referred to as Empirical Dynamic Modeling (EDM), to perform short-term forecasting of ACE and frequency time series in the steady state. Within the EDM framework, we use the simplex prediction implementation for attractor reconstruction with an embedding dimension E to describe the complexity and a single delay magnitude τ to establish the characteristic timescale for prediction, and further extend the model using Manifold Dimensional Expansion (MDE), which allows for modeling of processes with multiple timescales. We apply four different prediction methods within this framework and compare their short-predictionhorizon (5 minutes) forecasting performance using simple ARIMA and persistence forecasts as baseline reference models.