Multivariate Time-Series Clustering
Aleksandr Blekh's answer in this older question provides a lot of interesting reading material for time-series clustering methods and examples. Also, I include below some interesting reading material for calculating similarity among multivariate time-series (the latest 2 are quite old but I think they are very interesting):


An approach on the use of DTW with multivariate time-series (the paper actual refers to classification but you might want to use the idea and adjust it for clustering)
A paper on clustering of time-series
A PCA-based similarity measure for multivariate time-series
A review on feature extraction and pattern recognition methods in time-series data 


Before proceeding with any method, I believe it is important to spend some time to think of the following:


Try to select the right step for your input data (e.g. if the time-steps are per second, the time-series might be too long and unnecessarily detailed for this job, while hourly data might catch the patterns better). 
Seasonality might be interesting to take under consideration: e.g. if the time-series are hourly and last for several days/months, there might be some daily/monthly seasonality. In this case, you might want to calculate and compare the average day/month from each time-series (if so, you will also need to decide whether weekdays and weekends should be averaged all together or treated in a different way).
Depending on what you are trying to find out, you need to decide
whether Dynamic time warping (DTW) is useful for you. For example, if
2 time-series have the exact same pattern but one of the 2 has a
time-delay, should they still belong in the same cluster? (and how
small/big time-delay is acceptable to put them in the same cluster?)