Abstract
This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.
Highlights
Due to the aggressive deployment of Wide Area Monitoring Systems (WAMS), a deluge of time series data streams are emerging from modernizing smart grids
In order to address the aforementioned limitations of canonical Time-Domain Vector Fitting (TDVF), this paper introduces a generalized vector fitting extension, known as Real-Time Vector Fitting (RTVF)
While the RTVF algorithm can be applied across a broad range of dynamical engineering systems, it was developed to perform real-time predictive modeling of power system dynamics in the presence of ambient perturbations
Summary
We denote a generic scalar as x, a generic vector as x or X0 , and a generic matrix as. X. The identity matrix is denoted as I, with size inferred from the context. We use the symbol s for the complex frequency (Laplace) variable; R and C represent the sets of real and complex numbers, respectively. We consider a possibly nonlinear dynamic system S with input and output signals denoted as u(t) ∈ RP and y(t) ∈ RP , respectively. We denote with x(t) ∈ R Nsome unknown system state vector, we assume no information on the internal system representation. Acquired at sampling rate Fs. Without loss of generality, we set t1 = 0 throughout this paper. All derivations will hold true for t1 6= 0, provided the time variable is redefined as t ← t − t1
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