Electrical Consumption Outlier Detection Suppose you have several years of monthly consumption (kWh) data for 500,000 electrical meters and your job is to look for outlier behavior of various types. How would you approach modeling the meters with an ideal goal of giving each meter an outlier score? If for each meter you had other data (factor and/or numeric) in addition to consumption, how would this change your approach?
 A: I would use Intervention Detection as discussed here http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html . There are 4 types of interventions ; Pulse , step/level , seasonal pulse and local time trend  (I) . This approach can be used with or without user-suggested factors (X). The General Model is a SARMAX model https://autobox.com/pdfs/SARMAX.pdf . Note that the X's can impact The Y both contemporaneously and in a lag fashion. The historical effect of previous Y values is called the arima structure.
Model building would be used using available automatic software that simultaneously identified the structure following iterative self-validating heuristics described here https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf and elsewhere. 
One could then rank the meters by the frequency of the different kinds of "outliers" .
EDITED after OP asked for some more details about incorporating the effects of user-suggested causals the X's . https://autobox.com/pdfs/A.pdf lays out the flow whle How to use Dynamic Regression models in R to forecast future sales might also be of help and Tsay's intro to Transfer Function (SARMAX) identification here http://www.math.cts.nthu.edu.tw/download.php?filename=569_fe0ff1a2.pdf&dir=publish&title=Ruey+S.+Tsay-Lec1 . As a broad overview of causal modelling I wrote this piece to contrast regression with Transfer Function (SARIMAX) modelling https://autobox.com/pdfs/regvsbox-old.pdf.
Another reference that I had presented at a conference is also educational as to the whys and wherefores of causal model identification http://www.autobox.com/pdfs/WHY-WE-FILTER.ppt 
