Maximum likelihood estimation of distribution grid topology and parameters from smart meter data 1stLisa Laurent

2025-05-02 0 0 1.27MB 5 页 10玖币

侵权投诉

Maximum likelihood estimation of distribution grid

topology and parameters from smart meter data

1st Lisa Laurent

Institute of Electrical Engineering

EPFL

Lausanne, Switzerland

lisa.laurent@epﬂ.ch

2nd Jean-S´

ebastien Brouillon

Institute of Mechanical Engineering

EPFL

Lausanne, Switzerland

jean-sebastien.brouillon@epﬂ.ch

3rd Giancarlo Ferrari-Trecate

Institute of Mechanical Engineering

EPFL

Lausanne, Switzerland

giancarlo.ferraritrecate@epﬂ.ch

Abstract—This paper deﬁnes a Maximum Likelihood Estima-

tor (MLE) for the admittance matrix estimation of distribution

grids, utilising voltage magnitude and power measurements

collected only from common, unsychronised measuring devices

(Smart Meters). First, we present a model of the grid, as well

as the existing MLE based on voltage and current phasor

measurements. Then, this problem formulation is adjusted for

phase-less measurements using common assumptions. The effect

of these assumptions is compared to the initial problem in various

scenarios. Finally, numerical experiments on a popular IEEE

benchmark network indicate promising results. Missing data can

greatly disrupt estimation methods. Not measuring the voltage

phase only adds 30% of error to the admittance matrix estimate

in realistic conditions. Moreover, the sensitivity to measurement

noise is similar with and without the phase.

I. INTRODUCTION

New intermittent energy agents in distribution network

e.g. wind, solar, storage and controllable loads, bring major

changes into the grid operations and planning. In the past,

power generation used to be centralised which implies unidi-

rectional electrical power ﬂows from higher to lower voltage

levels. Today, grids are evolving towards decentralised energy

generation and bi-directional ﬂows. Although it offers the

possibility of better optimising the power ﬂows in the network,

it requires a better knowledge of the grid topology and line

parameters, which are contained in the admittance matrix.

However, obtaining an exact estimation of this matrix remains

difﬁcult since the admittances can either be unavailable or

deviate from their exact values due to topology changes or

external factors, such as faults.

The recent installation of numerous sensors in distribu-

tion grids has developed interest for automatic, data-driven

approaches to identify the admittance matrix. Most of the

recent contributions require measurements from micro Phasor

Measurement Units (µPMUs) [1, 2, 3, 4, 5]. However, today’s

grid measurements mainly come from Smart Meters, which

measure the nodal active and reactive power injection as

well as the nodal voltage magnitude without requiring time

synchronisation. Micro-PMUs, in contrast, use a GPS signal

to measure the phase angles between each nodes precisely. The

aforementioned studies show that parameters identiﬁcation,

Research supported by the Swiss National Science Foundation under the

NCCR Automation (grant agreement 51NF40 180545).

even with synchronised data, is a very challenging task.

Moreover, an accurate measurement of voltages is crucial as

their variations are very small compared to the rated value,

which means that any erroneous or missing measurement can

quickly make the identiﬁcation problem ill-posed.

Only few papers address the grid parameters estimation

problem using Smart Meters, and they are all based on

Ordinary Least-Squares (OLS) regressions [6, 7, 8]. In order

to reﬁne the parameters identiﬁed with OLS, the works [7]

and [8] use a Newton-Raphson method, which relies heavily

on tuned constants and initial point, often leading to case-

dependent results. Moreover, the authors of [6] and [7] use a

noise on voltage measurements that may be highly correlated

to the signal, and [8] does not specify how this noise is

generated. Finally, [8] uses a mix of µPMUs and Smart Meters

which is realistic at medium-high voltages but not at low

voltages.

The aim of this paper is to provide a frequentist approach to

the identiﬁcation problem with Smart Meter data, independent

from tuning parameters requiring knowledge of the system.

To do so, we will adapt the Maximum Likelihood Estimator

(MLE) from [4] because it is a statistically efﬁcient and

unbiased estimator. In addition, it allows the use of prior

knowledge, if present, in a mathematically supported way

through a Bayesian framework. The main contribution of this

paper is the reformulation of the MLE when the phase is

unknown using the linearised power-ﬂow equations.

The paper is organised as follows. First, a grid model is

presented to formally deﬁne the admittance matrix, then the

Maximum Likelihood Estimator problem is stated. The latter is

then transformed to adapt to Smart Meter measurements. Then,

the necessary approximations are discussed by comparing

them theoretically with the power ﬂow equations. Finally,

a case study is conducted on the IEEE 33 bus benchmark

network to verify the theoretical results and to study the effect

of various noise levels.

A. Preliminaries and notations

Let j=√−1denote the imaginary unit. For x∈C,x∗is its

complex conjugate. x∈Rndenotes a vector, X∈Rm×nde-

notes a matrix of size m-by-nand XTis its transpose. Im×n

is the m-by-nidentity matrix. For a (m, n)matrix X, ||X||Fis

arXiv:2210.02217v1 [eess.SY] 5 Oct 2022

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Maximumlikelihoodestimationofdistributiongridtopologyandparametersfromsmartmeterdata1stLisaLaurentInstituteofElectricalEngineeringEPFLLausanne,Switzerlandlisa.laurent@ep.ch2ndJean-S´ebastienBrouillonInstituteofMechanicalEngineeringEPFLLausanne,Switzerlandjean-sebastien.brouillon@ep.ch3rdGiancarloF...

展开>> 收起<<

Maximum likelihood estimation of distribution grid topology and parameters from smart meter data 1stLisa Laurent.pdf

共5页,预览1页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Maximum likelihood estimation of distribution grid topology and parameters from smart meter data 1stLisa Laurent

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: