Sometimes live music pops up to remind you that it truly is an in-the-moment experience.

Take the Roaming Roots Revue at Celtic Connections in 2013. Singer-songwriter Peter Kelly, who performs under the name Beerjacket, had just settled down in the solo spotlight on the Glasgow Royal Concert Hall main stage when the guitar he was using (borrowed from the show's curator, Roddy Hart, as his own had been misbehaving at the soundcheck) went on the blink.

Kelly persevered, overcame the technical difficulties, won the audience over purely on the strength of his performance. With the crowd on his side, and now joined by the Revue's musical ensemble, he went on to pretty much steal the show with a rendition of Bruce Springsteen's Atlantic City.

"How do I put it?" Kelly asks philosophically when looking back on that particular turning point. "It was so surreal to me to be in the largest venue that I'd ever played, with the largest band I've ever played with, doing one of the largest songs I've ever heard - I mean, you can't hold back on Atlantic City. It was such an impassioned moment, a fantastic moment in my life. I've bumped into people who say 'I know you'. And that's the moment they know me from."

Perhaps the triumph-of-the-underdog element wouldn't have been quite the same if this had happened in front of a different crowed, in a different city, at a different festival. Perhaps it was something uniquely special to Celtic Connections.

"It was totally in keeping with the spirit of that festival and the idea behind it," Kelly agrees. "I suppose the Celtic part of it has mutated into lots of different things over time but one of the things that has remained is that sense of honesty, 100%-proof real music in whatever shape that is."

Kelly returns to Celtic Connections on the final day of its 2015 programme as part of the Hazy Recollections strand. The Sunday afternoon residency at the O2 ABC, which aims to blur the lines between the festival's diverse musical roots, provides a platform for a number of artists each week (as well as Beerjacket, the session on February 1 features Inge Thomson, Alice Bentley, Three Blind Wolves and a mystery guest).

Much of Kelly's set will be drawn from his most recent album, Darling Darkness, which was placed at No 8 on the Sunday Herald's Top 50 Scottish Albums of 2014. But he hints that he might unveil some new material too in stripped-back solo format.

"I think new songs will probably feature," he admits, "but I don't like to hatch them too early because I don't really write in the way that a lot of people do. I don't write songs, I write albums. The songs tend to complete each other, so I might have a lot of songs appear at once but not have written for a year, and it's because they've all got a supportive role.

"At Celtic Connections, it's a bit like setting out your stall. You have to approach it with a kind of seriousness because you have musicians travelling thousands of miles across the world to play to an audience that has gathered on the reputation of the festival. I want to show the best reflection of the basic version of what I do - a basic, honest reflection of where I am now."

The other, equally important, part of Kelly's career is his full-time day job as a teacher in Hamilton. So, given that his Hazy Recollections gig falls on the festival's final day - a school night, after all - will he extend his visit to Celtic Connections for an into-the-small-hours session and face his pupils next morning with the coolest excuse?

"I don't know if I'll go out after," he says. "Maybe that's not a very rock'n'roll thing to say, but I'm not very rock'n'roll. That might be a disappointment if you thought I'd paint the town in a devil-may-care manner but I am, after all, quite a responsible adult.

"Are excuses ever cool?" he muses. "'The dog ate my responsibility...' I love responsibility. That's one of my great vices: to take on as much as possible and never let anyone down."

Beerjacket plays Hazy Recollections at O2 ABC, Glasgow on February 1 at 2.30pm.