What is the name for this metric? I have been using the metric shown below for a while, in a power forecasting context. We call it WAPE (Weighted Average Percentege Error, but I have never seen any references in papers, just some questionable like blogs:
$WAPE = 100 \cdot \frac{\sum_i |y_i - \hat{y_i}|}{\sum_i y_i}$
where $y_I$ defines de observed value and $\hat{y_i}$ the predicted one.
Is there any name for it? Exist any reliable publication or reference?
EDIT
Found an entry on Wikipedia with this metric, named Weighted Mean Absolute Percentage Error (wMAPE):
$$
wMAPE = \frac{\sum_i |y_i - \hat{y_i}|}{\sum_i y_i}
$$

Perhaps you are not finding much because this statistic is not very interesting in general. First, what happens when $y_i$ are not all positive? The denominator can become very small (for normal $y_i$) or even zero (for discrete $y_i$). Even if $y_i$ are positive by the law of large numbers the denominator will be close to $n \mu$ where $\mu$ is the mean of $y_i$, so basically the metric will be approximately mean absolute deviation divided by $\mu$.
