Data-driven Symbolic Regression for Identification of Nonlinear Dynamics in Power Systems

Stanković, A.M.; Saric, Aleksandar A.; Sarić, Andrija T.; Transtrum, Mark K.

doi:10.1109/pesgm41954.2020.9281935

Cited by 11 publications

(4 citation statements)

References 11 publications

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“…In power system, the library of candidate dynamics is selected that contains a mix of nonlinear (trigonometric) multiplication of variables (e.g.

Vsin(\delta -\theta )

and

Vcos(\delta -\theta )

) [30, 31]. Each row in Equation (14) represents the row in Equation (1c), and the sparse coefficients

\zeta _k

corresponding to the

k\text{-}th

row of the Ξ is identified from the initial values

\widehat{\zeta _k}

using a sparse regression algorithm, such as least absolute shrinkage and selection operator (LASSO) [19]:

\begin{align} \zeta _k = argmin_{\zeta _k}\parallel \dot{X_k} - \widehat{\zeta _k}\Theta ^{Tr}(X) \parallel _2 + \alpha \parallel \widehat{\zeta _k}\parallel _1, \end{align}

where

\dot{X_k}

represents the

k\text{-}th

row of

\dot{X}

.…”

Section: Methodsmentioning

confidence: 99%

“…In power system, the library of candidate dynamics is selected that contains a mix of nonlinear (trigonometric) multiplication of variables (e.g. Vsin(𝛿 − 𝜃) and Vcos(𝛿 − 𝜃)) [30,31]. Each row in Equation ( 14) represents the row in Equation (1c), and the sparse coefficients 𝜁 k corresponding to the k-th row of the Ξ is identified from the initial values ζk using a sparse regression algorithm, such as least absolute shrinkage and selection operator (LASSO) [19]:…”

Section: Sparse Identification Of Nonlinear Dynamicsmentioning

confidence: 99%

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Sparse identification for model predictive control to support long‐term voltage stability

Tran

Nguyen

et al. 2022

IET Generation Trans & Dist

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Along with the increased installation of distributed energy resources (DER), long-term voltage stability can be improved if proper coordination is developed between DERs and grid controllers, for example, Load Tap Changer (LTC). In most of the proposed methods, the steady-state voltage-sensitivity analysis has been implemented to predict the voltage state, which is the state's dynamic evolution in abnormal operations of the grid with high shares of DERs. This paper presents a system identification-based model predictive control (MPC), which can coordinate DERs and LTC to restore the voltage to the pre-fault condition after emergencies. First, the online voltage evolution is predicted based on the sparse identification of the nonlinear dynamics (SINDY) technique. Then, the SINDYbased voltage prediction is combined with an adaptive MPC in the centralized controller. In addition, the nonlinear of DERs have been modeled to avoid the MPC-based coordination jeopardizing the local constraints of DERs. The proposed method has been tested in a modified CIGRE benchmark network. Simulation results show that the dynamic voltage is effectively estimated by the SINDY method. Furthermore, the developed MPC model smoothly supports faster voltage recovering time with the least number of control actions of LTCs.

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“…In power system, the library of candidate dynamics is selected that contains a mix of nonlinear (trigonometric) multiplication of variables (e.g.

Vsin(\delta -\theta )

and

Vcos(\delta -\theta )

) [30, 31]. Each row in Equation (14) represents the row in Equation (1c), and the sparse coefficients

\zeta _k

corresponding to the

k\text{-}th

row of the Ξ is identified from the initial values

\widehat{\zeta _k}

using a sparse regression algorithm, such as least absolute shrinkage and selection operator (LASSO) [19]:

\begin{align} \zeta _k = argmin_{\zeta _k}\parallel \dot{X_k} - \widehat{\zeta _k}\Theta ^{Tr}(X) \parallel _2 + \alpha \parallel \widehat{\zeta _k}\parallel _1, \end{align}

where

\dot{X_k}

represents the

k\text{-}th

row of

\dot{X}

.…”

Section: Methodsmentioning

confidence: 99%

Section: Sparse Identification Of Nonlinear Dynamicsmentioning

confidence: 99%

Sparse identification for model predictive control to support long‐term voltage stability

Tran

Nguyen

et al. 2022

IET Generation Trans & Dist

View full text Add to dashboard Cite

show abstract

“…For example, for chemical reactors, the temperature-dependence of the reaction kinetics is based on the Arrhenius law, which suggests using exponential terms in the reactor temperature dynamic equation in the SINDy library (Abdullah and Christofides, 2023). Conversely, trigonometric functions form an appropriate basis for power systems (Stanković et al, 2020). In the ALE process studied, since quadratic polynomials were sufficient to accurately capture the system dynamics when used in conjunction with the proposed data reconstruction scheme, no other basis functions were considered.…”

Section: Dynamic Model Developmentmentioning

confidence: 99%

Sparse identification modeling and predictive control of wafer temperature in an atomic layer etching reactor

Ou,

Abdullah,

Wang

et al. 2024

Chemical Engineering Research and Design

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“…While the SINDy algorithm has found applications in various disciplines, its utilization in power system analysis has been limited, with only a handful of studies exploring its potential in this domain [20][21][22][23]. Notably, these investigations have predominantly focused on analyzing the broader power system and have primarily relied on first-order system models, as exemplified in a 2020 paper on power system applications [20].…”

mentioning

confidence: 99%

On SINDy Approach to Measure-Based Detection of Nonlinear Energy Flows in Power Grids with High Penetration Inverter-Based Renewables

Saeed Kandezy,

Jiang,

2024

Energies

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The complexity of modern power grids, caused by integrating renewable energy sources, especially inverter-based resources, presents a significant challenge to grid operation and planning, since linear models are unable to capture the complex nonlinear dynamics of power systems with coupled muti-scale dynamics, and it necessitate an alternative approach utilizing more advanced and data-driven algorithms to improve modeling accuracy and system optimization. This study employs the sparse identification of nonlinear dynamics method by leveraging compressed sensing and sparse modeling principles, offering robustness and the potential for generalization, allowing for identifying key dynamical features with relatively few measurements, and providing deeper theoretical understanding in the field of power system analysis. Taking advantage of the this method in recognizing the active terms (first and high order) in the system’s governing equation, this paper also introduces the novel Volterra-based nonlinearity index to characterize system-level nonlinearity. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise is adopted to clearly show the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to inverter-based resources, revealing system-level (second-order) nonlinearity compared to module-level (first order) nonlinearity in conventional synchronous generators. The proposed index quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the profile of the proposed index.

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Data-driven Symbolic Regression for Identification of Nonlinear Dynamics in Power Systems

Cited by 11 publications

References 11 publications

Sparse identification for model predictive control to support long‐term voltage stability

Sparse identification for model predictive control to support long‐term voltage stability

Sparse identification modeling and predictive control of wafer temperature in an atomic layer etching reactor

On SINDy Approach to Measure-Based Detection of Nonlinear Energy Flows in Power Grids with High Penetration Inverter-Based Renewables

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