Incremental segmented slope residential load pattern clustering based on three-stage curve profiles

ABSTRACT

This paper tackles high computational complexity in using Euclidean distance for residential load profiles (RLPs) similarity by proposing a three-stage incremental segmented slope clustering framework. The first two stages involve static clustering, where we obtain typical residential load profiles through piecewise slope clustering. In the third stage, dynamic clustering is performed based on the slope similarity of RLPs. This method enhances clustering performance and reduces computation cost, outperforming various benchmarks, with simulation results confirming the framework's effectiveness.

KEYWORDS:

• Residential load profiles
• three-stage segmented slope clustering
• incremental pattern clustering
• slope similarity

Nomenclature

$\mathit{\sigma }(d_i^a,d_i^b)$	=	a metric that evaluates if the slope aspect of $x_i^t$ on day $\mathit{a}$ and day $\mathit{b}$ at time $\mathit{j}$ is identical or not
$\mathit{ad}{v}_d$	=	the average deviation of $U_d$ from the minimum value of each column
$\mathit{ad}{v}_s$	=	the average deviation of $U_s$ from the minimum value of each column
$c_i^r$	=	the $\mathit{r}$-th clustering centre obtained after clustering user $\mathit{i}$ in the first stage
$\mathit{c}{c}_i$	=	the final TRLPs of all customers in the static data set
$d_{ij}^t$	=	the slope direction of the $\mathit{j}$-th segment of $x_i^t$
$\mathit{d}{x}_j$	=	the deviation between $G_j$ and its maximum value $max(G_j)$
$f_{\mathit{d},\mathit{j}}$	=	the deviation of an element in $U_j^d$ from its minimum value $min(U_j^d)$
$f_{\mathit{s},\mathit{j}}$	=	the deviation of an element in $U_j^s$ from its minimum value $min(U_j^s)$
$\mathit{G}$	=	segmented slope co-directional matrix
$\mathit{g}(d_i^a,d_i^b)$	=	the number of slope segments with the same direction on day $\mathit{a}$ and day $\mathit{b}$ of $x_i^t$
$g_{\mathit{ij}}$	=	the number of segmented slopes in the same direction on the $\mathit{i}$-th and $\mathit{j}$-th days of the user
$k_i$	=	the number of categories after the first stage clustering
$p_{ij}^t$	=	the slope steepness of the $\mathit{j}$-th segment of $x_i^t$
$u_{aq}^d$	=	the average slope difference between the RLP $\mathit{a}$ and the clustering centre $\mathit{q}$ in different slope direction section
$u_{aq}^s$	=	the average slope difference between the RLP $\mathit{a}$ and the clustering centre $\mathit{q}$ in the same slope direction section
$U_j^d$	=	the average slope dissimilarity between other $\mathit{t}$ curves and $\mathit{j}$
$U_j^s$	=	the average slope similarity between other $\mathit{t}$ curves and $\mathit{j}$
$x_i^t$	=	the RLPs of user $\mathit{i}$ on the $\mathit{t}$-th day
$\mathit{z}$	=	the number of current TRLPs
DBI	=	Davidson-Boding Index
ISSC	=	Incremental Segmented Slope Clustering
RLP	=	Residential Load Profile
SOM	=	Self-Organizing Map
SSC	=	Segmented Slope Clustering
TRLP	=	Typical Residential Load Profile
WSOM	=	Weighted Self-Organizing Map

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the China Southern Power Grid Company Limited under the Grant No. 036000KK52222009 (GDKJXM20222125).