MIF15: Björk @ Castlefield Arena, Manchester, 5 July

Nothing can quite prepare you for the almost uncomfortable normality of her entrance. Rather than, as you'd hope, beam herself down from her home planet or, inspired by the app-spawning tech adventures of 2011's Biophilia, simply send along in her place a giant floating hologram of herself, Björk pulls the rug and employs the everyday: she simply walks on stage and starts to sing. If that's just a little too normal, fear not. For a start, she's dressed as a moth, modelling the LBD re-cut for the season with must-have added wings and face mask-cum-helmet.

For this European premiere of her most recent album Vulnicura, Manchester International Festival gives locals their second Björk exclusive in just four years, following the world debut of Biophilia over six nights at Campfield Market Hall in 2011. The step up to Castlefield Arena's gaping amphitheatre might swap her previous show's intimate performance art for the unruly demands of stadium season but Bjork appears to neither notice nor care. As punters squeeze into the bowl in their thousands and a column of bars, questionable outside catering options and portaloos add workaday grime to a venture so grandiose, the (excellent) Heritage Orchestra set in motion a night of wonders.

That voice: it still, after all these years, heats the air around it. She might still sound like a teenage girl channelling Dick Van Dyke when she speaks ("Thank yooww, Manchestahhh!"), but Björk doesn't so much sing as simply exhale. Stonemilker, Vulnicura's desperately tender opening, sets an initially mournful tone. Lionsong, Black Lake and Family follow, and they form an opening suite that scoffs at the event's bustling scale. Fleshing out her live set-up is co producer The Haxan Cloak and percussionist Manu Delago but beats are in short supply early on. Around the edges of the crowd, there are pockets detached and oblivious: booze and chatter threatens to impact. But then, as the sun sets, the atmosphere builds. The clatter and rasp of Notget gives way to a brace of tracks (Hunter and Bachelorette) from Homogenic. Smoke bombs fire from above the stage, covering the venue in an unearthly pink mist. The masses on the floor start to move. Possibly Maybe muscles its way in and suddenly everything starts to feel reassuringly weird.

That's not to say that there's not this edge that remains, that once we're fully engaged you worry that she might take it up only to bring it right back down. Even in the storming second half, the tone is rhapsodic rather than rampant. A cheap shot now (Human Behaviour? Violently Happy?) and they'll hear us in Iceland, but Björk's singular aesthetic has little room for compromise. In an era that demands the ribbons and bows of crowd-pleasing commerce, there's more chance of a Sugarcubes reunion than Björk: The Greatest Hits Tour.

Hence, in the closing straight, there's a thrilling but undeniably nervy trade-off between big beats (Wanderlust, an electrifying encore of Hyperballad) and scratchy chamber electro (Mutual Core.) Still, would you have it any other way? Vulnicura is an album that asks a lot of the listener but here it blooms in wholly unexpected ways and delivers a shared experience that navigates the awkwardness of tonight's setting with overwhelming heart and soul. "I wish to synchronize our feelings," Björk sings within moments of appearing tonight. Manchester is in no mood to argue.