【鲁棒电力系统状态估计】基于投影统计的电力系统状态估计的鲁棒GM估计器（Matlab代码实现）

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📋📋📋++本文目录如下：++🎁🎁🎁

目录

[💥1 概述](#💥1 概述)

[📚2 运行结果](#📚2 运行结果)

[🎉3 参考文献](#🎉3 参考文献)

[🌈4 Matlab代码实现](#🌈4 Matlab代码实现)

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💥1 概述

稳健的电力系统状态估计器对于监测和控制应用至关重要。根据我们的经验，我们发现使用投影统计的鲁棒广义最大似然（GM）估计器是文献中最好的方法之一。它对多个交互和符合不良数据、不良杠杆点、不良零注入以及某些类型的网络攻击具有鲁棒性。此外，它的计算效率很高，使其适用于在线应用程序。除了GM估计器良好的击穿点外，它在高斯或其他厚尾非高斯测量噪声下具有很高的统计效率。使用SCADA测量的GM估计器的原始版本是由Mili和他的同事在1996年提出的[1]。通过在 [R2] 中使用吉文斯旋转，其数值稳定性得到了增强。在[R3]中，GM估计器被扩展为同时估计变压器抽头位置和系统状态。不良的零点注入也得到了解决。在[R4]中，提出了GM估计器来处理创新和观测异常值以及动态状态估计中的测量损失。测试系统包括 IEEE 14 总线、30 总线和 118 总线系统。仅包括 SCADA 测量值。

由于结果图比较多，本文仅展现IEEE118节点运行结果图。

📚 2 运行结果

部分代码：

zdata = zconv(nbus); % Get Conventional Measurement data..

[bsh g b] = line_mat_func(nbus); % Get conductance and susceptance matrix

type = zdata(:,2);

% Type of measurement,

% type =1 voltage magnitude p.u

% type =2 Voltage phase angle in degree

% type =3 Real power injections

% type =4 Reactive power injection

% type =5 Real power flow

% type =6 Reactive power flow

z = zdata(:,3); % Measurement values

Z=z;% for ploting figures

fbus = zdata(:,4); % From bus

tbus = zdata(:,5); % To bus

Ri = diag(zdata(:,6)); % Measurement Error Covariance matrix

e = ones(nbus,1); % Initialize the real part of bus voltages

f = zeros(nbus,1);% Initialize the imaginary part of bus voltages

E = [f;e]; % State Vector comprising of imaginary and real part of voltage

G = real(ybus);

B = imag(ybus);

ei = find(type == 1); % Index of voltage magnitude measurements..

fi = find(type == 2); % Index of voltage angle measurements..

ppi = find(type == 3); % Index of real power injection measurements..

qi = find(type == 4); % Index of reactive power injection measurements..

pf = find(type == 5); % Index of real power flow measurements..

qf = find(type == 6); % Index of reactive power flow measurements..

Vm=z(ei);

Thm=z(fi);

z(ei)=Vm.*cosd(Thm); % converting voltage from polar to Cartesian

z(fi)=Vm.*sind(Thm);

nei = length(ei); % Number of Voltage measurements(real)

nfi = length(fi); % Number of Voltage measurements(imaginary)

npi = length(ppi); % Number of Real Power Injection measurements..

nqi = length(qi); % Number of Reactive Power Injection measurements..

npf = length(pf); % Number of Real Power Flow measurements..

nqf = length(qf); % Number of Reactive Power Flow measurements..

nm=nei+nfi+npi+nqi+npf+nqf; % total number of measurements

% robust parameters

tol=1;

maxiter=30;% maximal iteration for iteratively reweighted least squares (IRLS) algorithm

c=1.5; % for Huber-estimator

bm=mad_factor(nm); % correction factor to achieve unbiasness under Gaussian measurement noise

%%%%%%% GM-estimator%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% flat initialization

iter=1;

s=1;

%% For the GM-estimator to be able to handle two conforming outliers located on the same bus

%% the local redundancy must be large enough

%% add outliers %%

🎉3 参考文献

文章中一些内容引自网络，会注明出处或引用为参考文献，难免有未尽之处，如有不妥，请随时联系删除。

[R1] L. Mili, M. Cheniae, N. Vichare, and P. Rousseeuw, ``Robust state estimation based on projection statistics," IEEE Trans. Power Syst, vol. 11, no. 2, pp. 1118--1127, 1996.

[R2] R. C. Pires, A. S. Costa, L. Mili, "Iteratively reweighted least-squares state estimation through givens rotation," IEEE Trans. Power Syst., Vol. 14, no. 4, pp. 1499--1507, 1999.

[R3] R. C. Pires, L. Mili, F. A. Becon Lemos, ``Constrained robust estimation of power system state variables and transformer tap positions under erroneous zero-injections," IEEE Trans. Power Syst., vol. 29, no. 3, pp. 1144--1152, May 2014.

[R4] J. B. Zhao, M. Netto, L. Mili, "A robust iterated extended Kalman filter for power system dynamic state estimation", IEEE Trans. Power Syst., DOI:10.1109/TPWRS.2016.2628344, in press.

🌈4 Matlab代码实现