On solving probabilistic load flow for radial grids using polynomial chaos

Appino, Riccardo Remo; Mühlpfordt, Tillmann; Faulwasser, Timm; Hagenmeyer, Veit

doi:10.1109/ptc.2017.7981264

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…One possibility to render the problem finite-dimensional is to use polynomial chaos expansion (PCE), a Hilbert space technique for random variables of finite variance. Polynomial chaos has been applied to (optimal) power flow problems before [3,[5][6][7][8]. The advantages of PCE for Problem (2) are threefold: i) we are not restricted to a specific family of random variables such as Gaussians, ii) we can compute moments of random variables from the PCE coefficients alone, and iii) we can propagate uncertainties through the full power flow equations.…”

Section: Problem Formulationmentioning

confidence: 99%

Uncertainty Quantification for Optimal Power Flow Problems

Mühlpfordt

Hagenmeyer

Faulwasser

2019

Proc Appl Math and Mech

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The need to de‐carbonize the current energy infrastructure, and the increasing integration of renewables pose a number of difficult control and optimization problems. Among those, the optimal power flow (OPF) problem—i.e., the task to minimize power system operation costs while maintaining technical and network limitations—is key for operational planning of power systems. The influx of inherently volatile renewable energy sources calls for methods that allow to consider stochasticity directly in the OPF problem. Here, we present recent results on uncertainty quantification for OPF problems. Modeling uncertainties as second‐order continuous random variables, we will show that the OPF problem subject to stochastic uncertainties can be posed as an infinite‐dimensional L2‐problem. A tractable reformulation thereof can be obtained using polynomial chaos expansion (PCE), under mild assumptions. We will show advantageous features of PCE for OPF subject to stochastic uncertainties. For example, multivariate non‐Gaussian uncertainties can be considered easily. Finally, we comment on recent progress on a Julia package for PCE.

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Section: Problem Formulationmentioning

confidence: 99%

Uncertainty Quantification for Optimal Power Flow Problems

Mühlpfordt

Hagenmeyer

Faulwasser

2019

Proc Appl Math and Mech

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“…The space limitations prohibit a thorough introduction of PCE; we refer to [19,25] for further details. For applications of PCE in the power systems context we refer to [8,10,[26][27][28][29].…”

Section: Equivalence Of Hopf and Ccopfmentioning

confidence: 99%

The Price of Uncertainty: Chance-Constrained OPF vs. in-Hindsight OPF

Muhlpfordt

Hagenmeyer

Faulwasser

2018

2018 Power Systems Computation Conference (PSCC)

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The operation of power systems has become more challenging due to feed-in of volatile renewable energy sources. Chance-constrained optimal power flow (ccOPF) is one possibility to explicitly consider volatility via probabilistic uncertainties resulting in mean-optimal feedback policies. These policies are computed before knowledge of the realization of the uncertainty is available. On the other hand, the hypothetical case of computing the power injections knowing every realization beforehandcalled in-hindsight OPF (hOPF)-cannot be outperformed w.r.t. costs and constraint satisfaction. In this paper, we investigate how ccOPF feedback relates to the full-information hOPF. To this end, we introduce different dimensions of the price of uncertainty. Using mild assumptions on the uncertainty we present sufficient conditions when ccOPF is identical to hOPF. We suggest using the total variational distance of probability densities to quantify the performance gap of hOPF and ccOPF. Finally, we draw upon a tutorial example to illustrate our results.

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“…Recently, analytical methods such as the general polynomial chaos (gPC) expansion are gathering interest in power system applications due to their high accuracy with low computational time [9][10][11][12][13][14][15][16]. It has been shown in the literature that the gPC outweighs other analytical methods used for probabilistic power flow as this method preserves the nonlinearity of the power flow.…”

Section: Introduction 1background and Motivationmentioning

confidence: 99%