Do I need to buy SketchUpPro for use with OpenStudio?

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It's more of a legal issue as to whether or not you need to purchase SketchUp Pro. The license agreement for SketchUp Make says...

Trimble Navigation Limited and/or its affiliates ("Trimble") gives you a personal, worldwide, royalty-free, non-assignable and non-exclusive license to use the executable version of the Software for non-commercial use only. Non-commercial use means: you may not sell, rent, lease or lend the output of the Software or the Services. If you are a for-profit organization of any kind, or an employee of a for-profit organization using the Software or Services in that capacity, you are engaged in commercial activity; therefore, in order to use the Software and Services, you must purchase a SketchUp Pro license.

So if you're creating energy models in OpenStudio with the aid of SketchUp in any capacity for-profit, you need to purchase SketchUp Pro to not be in violation of the SketchUp Make license agreement. At least that's how I read it.

You do not need to buy it, the default download is SketchUp Pro and as you said it gets downgraded to SketchUp after 1-month wich is enough to use with OpenStudio, for non-profit purposes.

Importing DWGs is a feature that is only available in SketchUp Pro. This can be a differentiator depending on your workflow to create geometry.

No you do not need SketchUpPro to use with OpenStudio. The free version of SketchUp works with it just fine.