In this case, government grants to individual homeowners looking to connect to the public utility makes the most sense. It's also easy to quantify since you can see how many people are interested in connecting to the grid who aren't currently. Governments can find multiple ways to source funds for those grants. Homeowners would apply for those grants and get funds for the connection. If funds aren't provided directly they are often provided as credits against property tax. The gov pays the utility directly.

I've seen it done this way for many different projects.