Fuzzy Clustering-Based Deep Learning for Short-Term Load Forecasting in Power Grid Systems Using Time-Varying and Time-Invariant Features

. 2024 Feb 21;24(5):1391. doi: 10.3390/s24051391

Algorithm 1 Fuzzy C-Means (FCM) Algorithm

Input: All time-invariant vectors ${\bar{y}}_{I}^{(i)}$ , with $i = 1, 2, \dots, M$ .
Output: The centres of the clusters, $\bar{V} = {{\bar{v}}_{1}, {\bar{v}}_{2}, \dots, {\bar{v}}_{N_{c}}}$ ; the fuzzy partition coefficient, $V_{p c}$
Step 1: Set the algorithmic parameters, $N_{c}$ , m, $\bar{A}$ , and the threshold, $ϵ$ .
Step 2: Randomly initialize a membership matrix, ${\hat{U}}^{i t e r} = [{\hat{u}}_{i k}^{i t e r}]$ , with
the iteration $i t e r = 1$ .
Step 3: Compute the cluster centres $\bar{V} = {{\bar{v}}_{1}, {\bar{v}}_{2}, \dots, {\bar{v}}_{N_{c}}}$ using (12).
Step 4: Set $i t e r = i t e r + 1$ .
Step 5: Compute an updated membership matrix, ${\hat{U}}^{i t e r} = [{\hat{u}}_{i k}^{i t e r}]$ ,
with ${\hat{u}}_{i k}^{i t e r} = {\hat{u}}_{k} ({\bar{y}}_{I}^{(i)})$ using (10).
Step 6: Compare whether ${\hat{U}}^{i t e r}$ is higher than ${\hat{U}}^{i t e r - 1}$ :
If $| | {\hat{U}}^{i t e r} - {\hat{U}}^{i t e r - 1} | |$ is smaller than $ϵ$ ,
then compute the fuzzy partition coefficient, $V_{p c}$ ,
$V_{p c} = \frac{1}{M} \sum_{i = 1}^{N_{c}} \sum_{j = 1}^{M} {(\hat{u_{i j}^{i t e r}})}^{2}$
goto Step 7.
Else Set ${\hat{U}}^{i t e r - 1}$ as ${\hat{U}}^{i t e r}$ and goto Step 3.
Step 7: Return The cluster centres, $\hat{V}$