The Grey Forecasting Model

Features

The grey forecasting model needs to consider less external factors and does not rely too much on historical data, which is in line with the characteristics of “poor data” and “easy to fluctuate” of power system load.

Data generation

The accumulation generation

$x^{(1)}(k)=\sum_{m=1}^k x^{(0)}(m)$

Described as 1-AGO.

The subtraction generation

$a^{(i)}(x^{(r)}(k))=a^{(0)}(x^{(r)}(k))-a^{(0)}(x^{(r)}(k-1))$

Described as i-IAGO.

The mean generation

The adjacent mean generation value

$z(k)=0.5x(k)+0.5x(k)$

The non-adjacent mean generation value

$z(k)=0.5x(k-1)+0.5x(k+1)$

hole:$x(k)$.

Grey prediction model modelling

Grey system modelling is to reduce the uncertainty of information by mining and collating the initial data, and then carry out mathematical modelling on this basis.

Modeling mechanism of grey prediction model

Marking the $x^{(0)}$ as the modelling sequence of GM(1,1):

$x^{(0)}=\{x^{(0)}(1),x^{(0)}(2),\cdots,x^{(0)}(n)\}$

Marking the $x^{(1)}$ as the first-order accumulation of $x^{(0)}$.

Marking the $z^{(1)}$ as the mean sequence of $x^{(1)}$.

The grey differential equation:

$x^{(0)}(k)+az^{(1)}(k)=u$

Differential equation for albinism:

$\frac{\mathrm d x^{(1)}}{\mathrm d t}+ax^{(1)}=u$

$P=[a,u]^T=(B^TB)^{-1} B^Ty_n$

$B=\begin{bmatrix} -z^{(1)}(2) & 1\\ -z^{(1)}(3) & 1\\ \vdots & \vdots\\ -z^{(1)}(n) & 1\\ \end{bmatrix}$

$y_n=[x^{(0)}(2),x^{(0)}(3),\cdots,x^{(0)}(n)]^ T$