PSUs can cause any various symptoms, and this would be no exception. If you believe your PSU might be too low for your hardware, then it probably is. Best way to look for a PSU is go for one that's 100W above what you anticipate it'll need. This is especially considering that any PSU running at 80% load or higher for any amount of time will start wearing out its parts quickly, so you want to avoid it as much as possible by going for higher. Also brand names and model series are actually very important in determining reliability of PSUs, since when you purchase a PSU you aren't paying for "performance" but rather reliability.
As for the crashdumps, I do notice in the syslog that while the BSODs did start at April 11, unexpected system shutdowns do occur frequently all the way back to even the first day of Windows installation on March 31. Have you been manually turning off the system for whatever reason? If not, then the system has been restarting forcefully, which could be caused by a heat sensor detecting an overheating CPU, a motherboard failure, or a PSU failure (PSU being most common).