NEW YORK — Frenzied “Frozen” fans: chill. Your prayers for a faithfully well-executed Broadway rendition of your favorite animated movie musical have been answered.

The altogether respectable production devised by the creative team — director Michael Grandage, designer Christopher Oram, songwriters Kristen Anderson-Lopez and Robert Lopez and book writer Jennifer Lee — seizes capably on the solemn Nordic grandeur of Disney’s 2013 movie version. And we cannot underestimate the import of a musical arriving at this moment that deals with young women coming to terms with their own power: not with its limits, but with its awesome range.

These attributes — which also include the most endearing life-size puppet to be herded onto Broadway since “War Horse” (I speak of Sven, the noble reindeer) — ensure that a warm reception awaits “Frozen” from its devoted base. 

Winning over the uninitiated, though, may be a tougher task for the eagerly anticipated musical that had its official opening Thursday night at the St. James Theatre. What may prevent “Frozen” from appealing to more sophisticated theater crowds is the unfulfilled promise of the plot. We’re teased in this venture with the idea of an animated story wrought in three dimensions with more psychological subtlety than is the custom in Disney musicals. Because “Frozen” attempts to traverse the tender and intimate terrain of trauma and loss of love. But it never achieves that necessary climax — paradoxical in a show of this title — when a spectator’s heart is able to melt.

Based loosely on a fairy tale by Hans Christian Andersen, Lee’s script recounts the travails of orphaned royal sisters, Elsa (Caissie Levy), the Scandinavian kingdom’s new queen, and Anna (Patti Murin), who are separated because of the dangerous magic that emanates from Elsa’s hands: her anger or passion can literally freeze people and objects. (Elsa controls her secret by wearing gloves; when the power is catastrophically revealed after one of her gloves is taken from her, you are left to wonder why she doesn’t simply carry an extra pair.)

The power should be a compelling metaphor, but instead it just feels like an expository device, allowing set designer Oram, lighting designer Natasha Katz and special-effects wizard Jeremy Chernick to create some nifty visuals. A moment when Elsa touches the proscenium arch, seemingly transforming it from wood to solid ice, has the desired wow factor, as does a quicksilver costume change by Elsa in her remote mountain ice fortress, during the evening’s marquee (and Oscar-winning) song, “Let It Go,” which Levy delivers with the requisite supercharged vocal brio.

Several of the Lopezes’ numbers from the movie — “Do You Want to Build a Snowman?” “For the First Time in Forever,” “Love Is an Open Door” — are buoyantly summoned to life again. Murin, as bubbly Anna, proves to be a winning touchstone, and the actresses at my performance who played the sisters as children, Ayla Schwartz and especially the naturally funny Mattea Conforti, were exceptionally well cast. Still, many of the numbers added for the stage version, particularly a long and unfortunate comedy number, “Hygge” (pronounced “Hoo-ga”), are not the entertaining enhancements they’re intended to be.

Olaf the snowman, cheerily voiced and operated by Greg Hildreth, is a mechanical homage to director Julie Taymor’s evocation of Timon the meerkat in Disney’s artistically triumphant stage version of “The Lion King.” Even better is puppetmaker Michael Curry’s Sven, who lopes comically onto the stage behind mountain man/Anna love interest Kristoff (a pleasing Jelani Alladin). Andrew Pirozzi is the heroic puppeteer who, completely camouflaged, gives Sven his mournful majesty. Although there are a whole slew of other actors playing enchanted mountain trolls called the Hidden Folk, Pirozzi is the show’s best Hidden Folk by far.

So even if “Frozen” is afflicted with some narrative lumps, and might not convert you if the film didn’t make you want to sing, the fans in your family will thank you for taking them. On evenings such as this, I defer to the member of my family who grew up on Disney videos: my now adult daughter Lizzie, who pronounced the stagecraft of “Frozen” sufficiently cool.

Frozen , music and lyrics by Kristen Anderson-Lopez and Robert Lopez, book by Jennifer Lee. Sets and costumes, Christopher Oram; choreography, Rob Ashford; music supervision, Stephen Oremus; lighting, Natasha Katz; special effects, Jeremy Chernick; sound, Peter Hylenski; video, Finn Ross; puppets, Michael Curry. With John Riddle, Robert Creighton, Kevin Del Aguila, Timothy Hughes, Olivia Phillip, Audrey Bennett, Brooklyn Nelson. About 2 hours 20 minutes. $99.50-$200. At St. James Theatre, 246 W. 44th St., New York. Visit or call 866-870-2717.