This is a fantastic question, thank you for asking!
Your question alluded to process and methodology, but I'd argue the first word to start with is "strategy".
Effective innovation teams have a clear innovation strategy that's tied to the company strategy. For instance, at Duquesne Light we have a performance framework that emphasizes five areas - safety, excellent customer service, affordability, reliability, and sustainability. Our innovation strategy is to contribute to each performance "pillar" in measurable ways.
Before considering the process, the first screen therefore is to consider whether and how the idea in question contributes to the company/innovation strategy. For us, if we can't envision significant impact against more than one of our performance framework pillars, then we discard the idea and/or execute it at a business unit level.
Takeaways: Establish an innovation strategy that complements the overall strategy, consider each idea in light of that strategy, and use that for a "first screen" down-selection
One very overlooked - but extremely important - component of innovating effectively is governance. Governance is essentially about decision making rights: Who gets to decide, on what criteria, and when? The key is to establish governance as early as possible.
Good governance bodies are generally "one stop shops" making decisions in one place as quickly as possible. However, to do that effectively it needs to be cross-functional (so all relevant company orgs are represented), the decision making criteria need to be clear up front, people need to act in the company's best interest and not just their organization, and critically you need to have executive buy-in, support, and participation in this governance body.
Example: At Duquesne Light, we've established the "Innovation Council". Think of this as a quasi shark tank composed of every major department. We went to our CEO to have him nominate the members and we made it clear that this is the group that decides on which innovation projects to pursue. We meet roughly bi-weekly to hear "pitches" of new innovation ideas. Decisions are made on those innovation ideas in no more than 48 hours from the pitch.
Takeaways: Governance is everything! Establish clear organizational decision making rights with executive support. Make sure all major groups at the utility are represented in that governance body. Then set the expectation that those bodies - and those bodies alone - decide so you can move quicker than the rest of the org (frankly)
Again, this was a great question and hope this answer helps...good luck moving the industry forward!