Optimal Steady-State Voltage Control Using Gaussian Process Learning

Pareek, Parikshit; Weng, Yu; Nguyen, Hung D.

doi:10.1109/tii.2020.3047844

Cited by 29 publications

(10 citation statements)

References 34 publications

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“…It is important to note that measuring the distance between two known PDFs is different than minimizing distance between two distributions in parametric form[15].In this work, the idea is to perform functional operations of distance or difference minimization, on constraint PDFs, in a feature space. The Kernel-based method has shown great promise in solving power system problems via working over functions such as Gaussian process being regression over functions[16],[17]. We choose to use Kernel Mean Embedding (KME) for mapping constraint PDF to deterministic elements in RKHS[13],[18].…”

mentioning

confidence: 99%

Non-parametric Joint Chance-Constrained OPF via Maximum Mean Discrepancy Penalization

Pareek

Nguyen

2022

Electric Power Systems Research

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mentioning

confidence: 99%

Non-parametric Joint Chance-Constrained OPF via Maximum Mean Discrepancy Penalization

Pareek

Nguyen

2022

Electric Power Systems Research

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“…The GP is a non-parametric modeling method allowing modeling of prior information and performing regression for a subspace of input [20][21][22]. The non-parametric behavior means that we can employ the model with different distributions, once it is trained for an uncertain load subspace, without retraining.…”

Section: Affine Policy For Rt Operationmentioning

confidence: 99%

State-Aware Stochastic Optimal Power Flow

Pareek¹,

Nguyen²

2021

Sustainability

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The increase in distributed generation (DG) and variable load mandates system operators to perform decision-making considering uncertainties. This paper introduces a novel state-aware stochastic optimal power flow (SA-SOPF) problem formulation. The proposed SA-SOPF has objective to find a day-ahead base-solution that minimizes the generation cost and expectation of deviations in generation and node voltage set-points during real-time operation. We formulate SA-SOPF for a given affine policy and employ Gaussian process learning to obtain a distributionally robust (DR) affine policy for generation and voltage set-point change in real-time. In simulations, the GP-based affine policy has shown distributional robustness over three different uncertainty distributions for IEEE 14-bus system. The results also depict that the proposed SA-OPF formulation can reduce the expectation in voltage and generation deviation more than 60% in real-time operation with an additional day-ahead scheduling cost of 4.68% only for 14-bus system. For, in a 30-bus system, the reduction in generation and voltage deviation, the expectation is achieved to be greater than 90% for 1.195% extra generation cost. These results are strong indicators of possibility of achieving the day-ahead solution which lead to lower real-time deviation with minimal cost increase.

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“…The data-driven linearization methods has also been developed [17,18]. Although the model-based linear approximations are easy to solve, they loose accuracy and are only valid near the operating point where they are linearized [19]. Also, majority of the model-based approximations focus on linear form via decoupling the voltage-power relationship under resistance to reactance ratio assumptions [20][21][22].…”

Section: Closed-form Power Flow Approximationmentioning

confidence: 99%

“…The GP is a non-parametric modeling method allowing modeling of prior information and performing regression for a subspace of input [39,203,204]. The nonparametric behaviour means that we can employ the model with di↵erent distributions, once it is trained for an uncertain load subspace, without retraining.…”

Section: A Ne Policy For Rt Operationmentioning

confidence: 99%

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Analytical approximations and decision-making techniques for power systems under uncertainty

Pareek¹

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The integration of distributed energy resources and increasing adoption of electric vehicles continue to drive uncertainty in power systems to an unprecedented level.In view of reduced applicability of traditional analysis and decision-making methods, this dissertation aims to address the need for new approaches, by attempting to solve three di↵erent sets of problems.This dissertation first proposes an analytical power flow approximation and develops a closed-form power flow framework. The thesis proposes a novel framework using Gaussian process regression to learn node voltage as a closed-form function of e↵ective bus load or injection vector. The proposed approximation is valid over a subspace of load, where the 'subspace' is used to describe a hypercube within which uncertain loads/injections lie. The approximation framework explains the system's behavior under uncertainty via Gaussian process hyper-parameter based interpretability. The proposed method achieves low mean absolute error of order 10 5 (per unit) in voltage magnitude and 10 4 (rad.) in angle when tested on 33-Bus and 56-Bus systems. Also, the proposed framework is used to develop an optimal steady-state voltage control framework using a linear voltage-power relationship. Simulation results on the 69-Bus system have shown the independence of approximation error with system loading and uncertainty levels. Therefore, control mechanisms developed based on the proposed analytical approximation are suitable under uncertainty. The framework also addresses the challenges posed by independent entity integration (e.g., peer-to-peer energy trading), as independent operational decisions of prosumers a↵ect the entire network. The proposed probabilistic feasibility set construction method-for privacy-preserving feasibility assessment-is tractable and handles non-parametric injection uncertainties by applying the worst-case performance analysis theorem over the proposed closed-form power flow approximation. The developed method's ability to capture the variations in probabilistic feasibility set for storage connected at a node in a 33-Bus network is shown via numerical simulations under di↵erent levels of total renewable penetration and uncertainty.xviiContents Statement of Originality iii

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Optimal Steady-State Voltage Control Using Gaussian Process Learning

Abstract: Optimal steady-state voltage control using Gaussian process learning

Cited by 29 publications

References 34 publications

Non-parametric Joint Chance-Constrained OPF via Maximum Mean Discrepancy Penalization

Non-parametric Joint Chance-Constrained OPF via Maximum Mean Discrepancy Penalization

State-Aware Stochastic Optimal Power Flow

Analytical approximations and decision-making techniques for power systems under uncertainty

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