Data-Driven Probabilistic Optimal Power Flow With Nonparametric Bayesian Modeling and Inference

Sun, Weigao; Zamani, Mohsen; Hesamzadeh, Mohammad Reza; Zhang, Haitao

doi:10.1109/tsg.2019.2931160

Cited by 51 publications

(27 citation statements)

References 45 publications

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“…On the other hand, in (5), the signal uncertainties are on the LHS and do not follow the Gaussian distribution. Therefore, not only the Gaussian-assumptionbased models used in [15]- [17] but also the GMM-based methods proposed in [25]- [27] can not be directly applied.…”

Section: Problem Formulationmentioning

confidence: 99%

“…GMM is a universal approximator of probability densities, and any non-Gaussian distribution can be approximately fitted with a finite number of Gaussian components [24]. In [25], [26], GMM was used to fit the non-Gaussian renewable energy uncertainties. Then, the chance constraints were directly reformulated into tractable forms based on the quantile of uncertainties.…”

Section: Introductionmentioning

confidence: 99%

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Chance-constrained regulation capacity offering for HVAC systems under non-Gaussian uncertainties with mixture-model-based convexification

Chen¹,

Zhang²,

Hui³

et al. 2022

Preprint

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Heating, ventilation, and air-conditioning (HVAC) systems are ideal demand-side flexible resources to provide regulation services. However, finding the best hourly regulation capacity offers for HVAC systems in a power market ahead of time is challenging because they are affected by non-Gaussian uncertainties from regulation signals. Moreover, since HVAC systems need to frequently regulate their power according to regulation signals, numerous thermodynamic constraints are introduced, leading to a huge computational burden. This paper proposes a tractable chance-constrained model to address these challenges. It first develops a temporal compression approach, in which the extreme indoor temperatures in the operating hour are estimated and restricted in the comfortable range so that the numerous thermodynamic constraints can be compressed into only a few ones. Then, a novel convexification method is proposed to handle the non-Gaussian uncertainties. This method leverages the Gaussian mixture model to reformulate the chance constraints with non-Gaussian uncertainties on the left-hand side into deterministic non-convex forms. We further prove that these non-convex forms can be approximately convexified by secondorder cone constraints with marginal optimality loss. Therefore, the proposed model can be efficiently solved with guaranteed optimality. Numerical experiments are conducted to validate the superiority of the proposed method.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chance-constrained regulation capacity offering for HVAC systems under non-Gaussian uncertainties with mixture-model-based convexification

Chen¹,

Zhang²,

Hui³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…T HE upsurge in the renewable penetration and dynamic loads has made Probabilistic Optimal Power Flow (POPF) a necessary tool providing necessary uncertainty description in the decision and state variables [1]. Existing POPF methods fall under analytical, approximate, and Monte-Carlo Simulation (MCS) based categories [1], [2]. These methods have various limitations, like dependencies on approximate power flow formulations, complicated implementation, or lacking data-based guarantees and substantial sample set requirements.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Process Learning-Based Probabilistic Optimal Power Flow

Pareek

Nguyen

2021

IEEE Trans. Power Syst.

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In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a nonparametric Bayesian inference-based uncertainty propagation approach, called Gaussian Process (GP). We also suggest a new type of sensitivity called Subspace-wise Sensitivity, using observations on the interpretability of GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems show that the proposed method provides reasonably accurate solutions when compared with Monte-Carlo Simulations (MCS) solutions at different levels of uncertain renewable penetration and load uncertainties. The proposed method requires a lesser number of samples and elapsed time. The non-parametric nature of the proposed method is manifested by testing uncertain injections that follow various distributions in the 118-bus system. The low error value results verify the proposed method's capability of working with different types of input uncertainty distributions.

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“…Another approach is to use Sobol sequence [6,7] or Latin hypercube sampling (LHS) [8] to generate samples of POPF inputs. In [9,10], Markov chain Monte Carlo method is applied to draw samples from Sobol sequence for POPF computation, which demonstrate a higher efficiency than MCS. In [8], a rank correlation based LHS method is suggested for POPF computation, which requires a smaller sample size than MCS.…”

mentioning

confidence: 99%

Analyzing Probabilistic Optimal Power Flow Problem by Cubature Rules

2021

Turk J Elec Eng & Comp Sci

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This paper is devoted to reveal some properties of the probabilistic optimal power flow (POPF) problem.In conjunction with Hermite polynomial model, Nataf transformation is introduced to map POPF problem to the independent standard normal space. Firstly, a multivariate polynomial model is employed to represent the function relationship between POPF inputs and outputs. Then, moment matching equations are derived to characterize the uncertainty effects of POPF inputs on outputs; three cubature rules are derived to calculate statistical moments of POPF outputs. Finally, along with Monte Carlo simulation method, the proposed methods are tested on IEEE 57-bus system and IEEE 118-bus system, whereby it reveals some characteristics of the function relation between POPF inputs and outputs.

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Data-Driven Probabilistic Optimal Power Flow With Nonparametric Bayesian Modeling and Inference

Cited by 51 publications

References 45 publications

Chance-constrained regulation capacity offering for HVAC systems under non-Gaussian uncertainties with mixture-model-based convexification

Chance-constrained regulation capacity offering for HVAC systems under non-Gaussian uncertainties with mixture-model-based convexification

Gaussian Process Learning-Based Probabilistic Optimal Power Flow

Analyzing Probabilistic Optimal Power Flow Problem by Cubature Rules

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