Yes. Although Apple does not reveal each code's exact meaning, I have learned from observation that Previous shutdown cause: 0 will always appear if a desktop Mac's power is suddenly interrupted. I have never seen it associated with anything other than that. From those observations it is reasonable to infer the reason for the shutdowns is a power interruption, and not something that can be fixed with software.
The reason for the power interruption can be external to the Mac, such as a defective power cord, wall socket, or poor power quality in your home or electric utility. You can eliminate those potential causes by substituting a different power cord and / or a quality UPS.
Possible internal causes could be an intermittent connection or similar fault anywhere in its power supply circuit, which includes the path from the iMac power receptacle, to the power supply itself, to low voltage paths throughout its logic board and all the connections within. Those causes become much more difficult to troubleshoot.
If you are not successful using a different power cord and UPS then schedule an appointment to have Apple evaluate your iMac. The nature of intermittent problems is such that the likelihood of a prompt and accurate diagnosis is slim. Describe the problem in as much detail as you can, but be prepared for them to immediately conclude there is nothing wrong with it. If they do, insist they keep it for a while longer.
I hate to give you bad news, but your concerns bear a striking resemblance to this Discussion: Re: Re: Re: iMac shuts down randomly for no apparent reason. It involves an iMac model nearly identical to yours. Whether that problem was ultimately resolved or not is unknown, but please read my reply dated Nov 29, 2015 replying to mikestan56. It is on the last page, and might point to a possible solution for you. If you decide to read the entire Discussion beware that it contains lot of irrelevant and distracting crosstalk.
Please follow up with your determinations.