Unfortunately, I don't think there is any way that this can be achieved or worked around. The PI Graphic Webpart doesn't seem to be able to use the configured time range in ProcessBook, or to have the trends in the svg not to be using the time range defined in the webpart or from the PI Timerange webpart.
Is this still the case Han, as I have a report that shows the previous days data which is controlled by the Time Range webpart, however the trends are for the last 30 days in the Graphic webpart. I also note that there are no plans in the roadmap to enhance the PI WebParts. I have placed an idea Control ProcessBook and Coresight trend and bar parameters with AF attibutes , as I do think that it is sometimes useful to be able to show different items for different time ranges.
My use case is for when I want to calculate a daily compliance state but it is based on either fixed or variable operational periods, so in the wastewater sludge world the countdown clock for retention and the tank filling over the last 30 days.