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目录
电力系统状态估计正面临不同类型的 异常。这些可能包括由严重测量误差或 通信系统故障。负载或发电的突然变化可能是 根据实现的状态估计方法被视为异常。 此外，将电网视为一个信息物理系统，状态 估计容易受到错误数据注入攻击。现有的 异常分类的方法无法准确分类（区分 之间）上述三种类型的异常，尤其是当它来的时候 区分突然的负载变化和错误的数据注入攻击。 该文提出一种检测异常存在的新算法，对 异常类型和识别异常的来源，即测量 在数据错误的情况下包含严重错误，或与负载相关的总线 经历突然变化，或错误数据针对的状态变量 注入攻击。该算法结合了分析和机器学习 （ML） 方法。第一阶段利用分析方法来检测异常 通过组合 $\chi^2$-测试和异常检测指数来呈现。第二个 阶段利用 ML 对异常类型进行分类并识别其 原产地，特别是对突然负载变化的区分 和虚假数据注入攻击。所提出的基于ML的方法被训练成 独立于网络配置，无需重新训练 网络拓扑更改后的算法。通过实施获得的结果 所提算法在IEEE 14总线测试系统上验证了算法的准确性和 所提算法的有效性。
详细文章见第三部分。
部分代码：
% Used to calculate H matrix, the state variables should be the forcasted
function H = H_matrix(num,V,del)
%num = 14;
ybus = ybusppg(num); % Get YBus..
zdata = zdatas(num); % Get Measurement data..
bpq = bbusppg(num); % Get B data..
nbus = max(max(zdata(:,4)),max(zdata(:,5))); % Get number of buses..
type = zdata(:,2); % Type of measurement, Vi - 1, Pi - 2, Qi - 3, Pij - 4, Qij - 5, Iij - 6..
% z = zdata(:,3); % Measuement values..
fbus = zdata(:,4); % From bus..
tbus = zdata(:,5); % To bus..
% Ri = diag(sig); % Measurement Error..
% V = ones(nbus,1); % Initialize the bus voltages..
% del = zeros(nbus,1); % Initialize the bus angles..
% E = [del(2:end); V]; % State Vector..
G = real(ybus);
B = imag(ybus);
vi = find(type == 1); % Index of measurements..
ppi = find(type == 2);
qi = find(type == 3);
pf = find(type == 4);
qf = find(type == 5);
nvi = length(vi); % Number of Voltage measurements..
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..
% iter = 1;
% tol = 5;
% Jacobian..
% H11 - Derivative of V with respect to angles.. All Zeros
H11 = zeros(nvi,nbus-1);
% H12 - Derivative of V with respect to V..
H12 = zeros(nvi,nbus);
for k = 1:nvi
for n = 1:nbus
if n == k
H12(k,n) = 1;
end
end
end
% H21 - Derivative of Real Power Injections with Angles..
H21 = zeros(npi,nbus-1);
for i = 1:npi
m = fbus(ppi(i));
for k = 1:(nbus-1)
if k+1 == m
for n = 1:nbus
H21(i,k) = H21(i,k) + V(m)* V(n)*(-G(m,n)*sin(del(m)-del(n)) + B(m,n)*cos(del(m)-del(n)));
end
H21(i,k) = H21(i,k) - V(m)^2*B(m,m);
else
H21(i,k) = V(m)* V(k+1)*(G(m,k+1)*sin(del(m)-del(k+1)) - B(m,k+1)*cos(del(m)-del(k+1)));
end
end
end
% H22 - Derivative of Real Power Injections with V..
H22 = zeros(npi,nbus);
for i = 1:npi
m = fbus(ppi(i));
for k = 1:(nbus)
if k == m
for n = 1:nbus
H22(i,k) = H22(i,k) + V(n)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));
end
H22(i,k) = H22(i,k) + V(m)*G(m,m);
else
H22(i,k) = V(m)*(G(m,k)*cos(del(m)-del(k)) + B(m,k)*sin(del(m)-del(k)));
end
end
end
% H31 - Derivative of Reactive Power Injections with Angles..
H31 = zeros(nqi,nbus-1);
for i = 1:nqi
m = fbus(qi(i));
for k = 1:(nbus-1)
if k+1 == m
for n = 1:nbus
H31(i,k) = H31(i,k) + V(m)* V(n)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));
end
H31(i,k) = H31(i,k) - V(m)^2*G(m,m);
else
H31(i,k) = V(m)* V(k+1)*(-G(m,k+1)*cos(del(m)-del(k+1)) - B(m,k+1)*sin(del(m)-del(k+1)));
end
end
end
% H32 - Derivative of Reactive Power Injections with V..
H32 = zeros(nqi,nbus);
for i = 1:nqi
m = fbus(qi(i));
for k = 1:(nbus)
if k == m
for n = 1:nbus
H32(i,k) = H32(i,k) + V(n)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-del(n)));
end
H32(i,k) = H32(i,k) - V(m)*B(m,m);
else
H32(i,k) = V(m)*(G(m,k)*sin(del(m)-del(k)) - B(m,k)*cos(del(m)-del(k)));
end
end
end
% H41 - Derivative of Real Power Flows with Angles..
H41 = zeros(npf,nbus-1);
for i = 1:npf
m = fbus(pf(i));
n = tbus(pf(i));
for k = 1:(nbus-1)
if k+1 == m
H41(i,k) = V(m)* V(n)*(-G(m,n)*sin(del(m)-del(n)) + B(m,n)*cos(del(m)-del(n)));
else if k+1 == n
H41(i,k) = -V(m)* V(n)*(-G(m,n)*sin(del(m)-del(n)) + B(m,n)*cos(del(m)-del(n)));
else
H41(i,k) = 0;
end
end
end
end
% H42 - Derivative of Real Power Flows with V..
H42 = zeros(npf,nbus);
for i = 1:npf
m = fbus(pf(i));
n = tbus(pf(i));
for k = 1:nbus
if k == m
H42(i,k) = -V(n)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-del(n))) - 2*G(m,n)*V(m);
else if k == n
H42(i,k) = -V(m)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-del(n)));
else
H42(i,k) = 0;
end
end
end
end
% H51 - Derivative of Reactive Power Flows with Angles..
H51 = zeros(nqf,nbus-1);
for i = 1:nqf
m = fbus(qf(i));
n = tbus(qf(i));
for k = 1:(nbus-1)
if k+1 == m
H51(i,k) = -V(m)* V(n)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-del(n)));
else if k+1 == n
H51(i,k) = V(m)* V(n)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-del(n)));
else
H51(i,k) = 0;
end
end
end
end
% H52 - Derivative of Reactive Power Flows with V..
H52 = zeros(nqf,nbus);
for i = 1:nqf
m = fbus(qf(i));
n = tbus(qf(i));
for k = 1:nbus
if k == m
H52(i,k) = -V(n)*(-G(m,n)*sin(del(m)-del(n)) + B(m,n)*cos(del(m)-del(n))) - 2*V(m)*(-B(m,n)+ bpq(m,n));
else if k == n
H52(i,k) = -V(m)*(-G(m,n)*sin(del(m)-del(n)) + B(m,n)*cos(del(m)-del(n)));
else
H52(i,k) = 0;
end
end
end
end
% Measurement Jacobian, H..
H = [H11 H12; H21 H22; H31 H32; H41 H42; H51 H52];
部分理论来源于网络，如有侵权请联系删除。
