She's soundchecking the only song she'll perform later and, for now, it's appropriately named: 'Dancing On My Own'. Forever professional, she's singing with an intense seriousness, at volume, but few of the children and parents already gathered in this outdoor concert venue are paying her much attention. There is a teenage fan-girl perched on the edge of a bright green bench in row one, eyes locked on Robyn, mouthing every lyric and imitating moves learned from studying the song's video, but she strolls away aimlessly when the band departs, checks her phone for messages, and you wonder why no one seems to be bothering a Swedish pop superstar when they have a chance to do so. Here's a 30-year-old woman who has been famous in her country for 15 years. People are intrinsically tied into her story and she has their respect - not least for wrestling her way out of a major label deal five years ago and going it alone with her Robyn album, which won her more critical and commercial success than she'd ever enjoyed before.

1 Don't think that you are special.
2 Don't think that you are of the same standing as others.

I turn and witness a most bizarre setting for a live TV show, Sommar Krysste, due to be beamed across Sweden in less than two hours. The venue is called Stora Scenen and it's part of Gröna Lund, an amusement park on a small island in central Stockholm - a real, functioning amusement park with a drop tower, roller coaster, giant octopus ride and house of ghosts that wild kids are riding now and will continue to ride throughout the broadcast.

However, this is not the shining superpower of a Disneyland-type park. Neon paint is slapped coarsely on any and every wooden wall and surface and if you look to corners you'll see chips and wilts caused by harsh winters when Gröna Lund is closed to visitors and must be spooked by the absence of screams; or perhaps because they somehow linger in the silence. There's history here, too. A sombre-looking set of dwellings still remain on the island and it was around them that a fairground was originally built in 1883.

On stage, it's becoming more Europop than you could ever imagine. Cookies n Beans, a trio of brassy, busty and orange girls who made their name doing Dolly Parton covers, have finished their quick run-through and made way for some kind of soul choir who do 'Olé Olé' to little or no bemusement from the growing crowd. Then a crew member walks past in a t-shirt emblazoned with: 'BORN TO BE BAD'.

Robyn is backstage in a small, cabin-like dressing room eating Thai food off a foam plate with a plastic picnic spoon. She's almost-dressed for later in a burgundy velvet dress and oddly thick tights that have what seem to be rags stitched onto them. Her shock of blonde hair is styled to a quiff, and although she's short, she's broad-shouldered and commanding to witness. It's a work day and she has her work face on.

'I was in England a couple of weeks ago and I did this music show that they decided to record on the set of Hollyoaks,' she explains. 'This is kind of like that - super commercial but very, very ironic at the same time. This is our… this is Stockholm's amusement park - the one and only - but it's run down and trashy and just like, you know, a classic Stockholm feature. I think that's why we're here and they [the TV producers] are making a thing out of it being that way.'

Yet, as a venue for summer concerts, Stora Scenen has a distinguished past. A series of photographs framed on the wall outside Robyn's dressing room show that Hendrix played here in 1970, Little Richard in 1975, Marc Bolan soon after and Miles Davis in 1987. Bob Marley, whose three Stora Scenen performances have gone down in local legend, holds the attendance record. He attracted 32,000 people to the island in 1980 and one of his sons, Damian 'Jr Gong' Marley, is listed as playing here with Nas in a month's time.

There's much to talk about with Robyn. There's her long history in music that most people in Britain only found out about after she had a UK number 1 in 2007 with the Kleerup-produced 'With Every Heartbeat'; there's the sense that, with Lykke Li, Fever Ray and Mapei, Swedish pop is enjoying another golden era; and then there's Robyn's plan to release three albums in 2010, the first of which, Body Talk Part 1, came out in June and finds her heading on from American hip-hop/R&B-inspired pop and deeper into dance music. Two of the eight new tracks are ballads, but with Diplo and Röyksopp helping out elsewhere, as well as her long-time producer/collaborator Klas Åhlund, the overarching feel is of being club-bound and responding to the senses and emotions that are heightened in that environment.

We do talk about these things and she speaks with clarity, and measure, and the kind of confidence you'd expect of a woman who has proved equally adept at being the CEO of her own affairs as she is at delivering diamond hook after diamond hook. She says the three-album plan is an attempt to find a solution to not being able to write as much as she'd like to, especially when touring, and it's also a response to the way people have come to consume music, which she thinks of as a challenge and not something to moan about. And about the new wave of Swedish pop she says, 'There's no rivalry, but there's definitely not this 'one big happy family' thing going on that everyone thinks. Everyone is very friendly and easy to work with, but we don't see each other as often as everyone imagines. We do hook up, though, and when we do it's awesome. I mean, me and Lykke, we've got to know each other well and we're friends. We're at the same places sometimes and it's the same thing with Karin [Fever Ray] and [singer-songwriter and Robyn/The Knife collaborator] Jenny Wilson. But it's not like I hang out with them often.'

There's a problem with this interview, however. Circumstance dictates that Robyn must have her make-up done while we talk, forcing her speech to become peppered with such asides as, 'Um… Sorry, I'm just trying to keep still.' To help, others (her stylist, manager…) are joining in, giving their opinions on whether Body Talk Part 1 is an aggressive record ('Some parts!') and filling in details that Robyn needn't provide herself. It makes for a fun but frustrating situation inevitably destined to produce stock answers when in fact something unforeseen is beginning to emerge from Robyn - insecurity, maybe, or certainly some kind of… mood.

'I think I'm making music for grown-ups who remember what it's like to be a teenager,' she says. 'The state of mind you're in when you're a teenager is something, I feel, that affects you for the rest of your life, even if you're not an outsider anymore, or even if you're happy and married, or happily still rebelling. If you're where you want to be, what got you there is still a big part of you, and that's that feeling of not fitting in. The feeling of wanting to be understood and wanting to find a connection with other people is a big driving force, and that idea is interesting to me.'

3 Don't think that you are smarter than others.
4 Don't fancy yourself as being better than others.

I tell her I read an interview she did with Popjustice where she claimed she was the perpetual outsider, and that seems surprising.

'I can totally see how that might sound weird, because I'm white and I'm from a rich country and I'm [sarcastically] a popstar,' she responds. 'But for me that perspective is from not feeling like I fitted in and growing up in a different way [her parents ran a travelling theatre company], touring all over the place, coming back home and having different kinds of experiences. But I don't think I experienced anything different from other people - I think all people feel like that when they're young. They feel like they're not understood.'

5 Don't think that you know more than others.
6 Don't think that you are more important than others.

There's a disturbance and Robyn says, 'I have to go onstage in 10 minutes, so I have to go and get ready. Or rather, we're supposed to be ready in 10 minutes. But you can hang out.'

She talks in Swedish to her associates.

'Actually, if you could just leave, I'm going to change…'

I step outside, look at my watch (7.50pm — 10 minutes before cameras roll) and slip into an immediate grump. I doubt I'll be given more of Robyn's time, even though it's promised for after the show. I wanted to ask her about her parents getting divorced (she wrote her first song soon after, aged 11) and whether that might have something to do with her fascination with a teenage state of mind. But I know I've blown my chance. Already, I've asked, 'was there a sense when you put the Robyn album out that you had to separate yourself from the teeny-bopper image you had?' Sternly, she replied: 'I've never felt like I had to separate myself from what I did before, but I felt like it was very important to me to be very clear to people here about what it was that I was doing. I didn't want to talk about anything other than the music and I wanted to be very focused on the album. Even though people are really cool here in Sweden, maybe before it became more about my private life, or the feeling that I had to talk about that more than my music.'

Robyn, changed, ducks behind a wall to smoke a cigarette. She saw me on her way out, ignored me and now even her manager is giving me the thousand-yard stare. I feel dirty, dumb, crabby… Long way to come for a 20-minute interview conducted with an audience, but, hold up… IT'S SHOWTIME!!!

Giant blue gates open and a man and a woman, both 12-foot high and theatrically dressed as a bride and groom enter the arena. They're followed by two clowns, also on stilts, and a third pair sporting mock 19th century costumes and wigs, one of whom, a black woman, is smothered in white make-up like some kind of grotesque reverse black face. These bizarre specimens have been employed to hover around the sides of the venue, beam fake smiles and dance (with their arms) at any hint of music. They begin by tensely looking like they're really enjoying the nauseating theme tune to the show, which is brashly being piped throughout this corner of the park (and throughout the TV speakers of the nation). It finishes, a robotic presenter does her introductory piece to camera, and then the entertainment begins - with a surprisingly hardcore rap group.

Every bench is now occupied. The group's lead MC is snaking his way among them, high-fiving 10-year-old children and barking at others being violently slung about on rides in the near distance. Few manage to wave an arm or pump a fist in the air.

Song finished, attention focuses on two giant screens erected on either side of the stage where a tape of comedy skits and TV bloopers is being rolled. Everyone is laughing, except the production crew who are frantically ensuring sound equipment is in position for the next performer. He's introduced as the current Swedish pop idol Erik Grönwall and he does a song appropriately called 'Crash And Burn'.

Behind me, on a balcony, Robyn is being mic'd up for a short live interview during which she will have to suffer the indignity of being shown, for the hundredth time no doubt, footage of her singing when she was 16. I understand only four words of the interview - 'body', 'talk', 'part' and 'one' - before cameras swing back to centre stage to catch Cookies n Beans belting out their number.

I'm suddenly gasping for alcohol, and this being Sweden, I'm correct in assuming that an amusement park will have a bar. I order two beers and a Sambuca - all for myself - park myself on a chair with a rug slung over it to keep drinkers warm and notice Robyn weaving her way back through the punters from where she was being interviewed. Once again, no one bothers her - not for an autograph, not for a picture hastily taken on a mobile phone. In fact, most people turn to one side and look embarrassed if they do catch her eye by accident. And Robyn herself certainly isn't courting attention. She's moves gracefully through the crowd - regally, almost - tapping a shoulder if she has to, but without creating fuss.

7 Don't think that you are good at anything.
8 Don't laugh at others.

The screens cut to an ad break, providing time for the presenter to check her make-up again and the giant soul choir to take their positions on stage. But the booze is kicking in now and things are becoming a blur. Next time I look up, the lottery numbers are being read out to camera, just as the sun is setting over this crazy scene.

I saunter away from the bar presuming Robyn, the headliner as such, is next up. She is. Expertly, she launches into 'Dancing On My Own' with a band that has two drummers, one on either side of her, but neither of which can steal any attention from their singer. She's so much more of a star than anyone else who has performed this evening and the sudden change in atmosphere across the park reflects it. Families who may not have even known this show was due to be shot today flock towards the venue, which is barely separated from the roller coasters and drop towers that surround it.

And yet Robyn cuts something of a lonely figure on stage singing this almost excruciatingly teeny minor-key track with a chorus that goes, "I'm in the corner watching you kiss her / I'm right over here, why can't you see me / I'm giving it my all, but I'm not the girl you're taking home / I keep dancing on my own."

The show finishes with a group ensemble that Robyn is noticeably absent from. I nip over to the bar for another quick shot and consider following the masses towards the ferry back to the mainland when I get a text from Robyn's manager that reads, simply: 'Robyn is waiting for you.'

The extra 10 minutes I got with Robyn were a disgrace of bad questioning fired across in panic and borne of drunkenness, yes, but mostly of being bemused by this strange day's adventure in Europop, which, in fact, had left me feeling in awe of the composure of the Swedish people. But I didn't want the cool head of Robyn any more. I wanted some of that passion she puts into her performances and songs. Did I get it? Not really, but when asked if she ever looked at YouTube interviews of herself from when she was 16 and whether she recognised the astonishingly focused and intelligent person in them, she did come back with this astonishingly focused and intelligent answer…

'I grew up with parents who really liked what they did and that was inspiring to me. They always made me feel like I was in the right place. I wasn't sure back then what it was I wanted to do, but I was figuring it out. That was the drive. It still is, and I think you can spend your whole life trying to figure that out. But for me, it was never about the fame, and it was never about the money; it was about really loving pop music. Because it's a commercial music, people always associate it with money and success, but what I felt when I first heard Neneh Cherry, or Michael Jackson, or Madonna, and even Kate Bush and Prince… those were big moments for me and that's what I want to communicate back. That's why I did this show today. It's not like I think I'm blessing people with my music, but I love trying to make a connection. It's my tradition. It's what I grew up in and it's what I know.'

9 Don't think that any one of us cares about you.
10 Don't think that you can teach others anything.

I didn't know about Jante's Law — defined as 'a pattern of group behaviour towards individuals within Scandinavian communities, which negatively portrays and criticises success and achievement as unworthy and inappropriate' — until I got back to the UK and asked Swedish friends about Robyn and how she fits into the national consciousness. It seemed unusual that she could walk freely among fans and not be bothered, and her perception of her ordinariness - of her being trapped in a state of mind that's identical to anyone else's - seemed extraordinary for a woman who has been famous for all of her adult life.

'Nobody really becomes a huge star in Sweden,' one friend told me. 'I think it's the Swedish mentality. Everything is a bit even and sometimes bland. No one is super rich, no one is super poor, and it's quite equal between women and men.

'Famous people don't have to worry about having 200 people waiting with cameras at the airport, because no one ever gets as famous in Sweden as they can abroad. I think she is the biggest star in Sweden right now, but it's kind of no big deal here. Like ABBA, for example. Swedes would be like: "Have you ever heard about ABBA?" And really mean it.'

The 10 rules of Jante's Law, reproduced throughout this piece, were identified by a Norwegian/Danish author called Aksel Sandemose in his 1933 novel En flyktning krysser sitt spor (A Fugitive Crosses His Tracks). Recite them to a Scandinavian and witness a solemn nodding of the head, regardless of whether they're familiar with Sandemose. But in that book, there is an unofficial rule that is loosely recognised as number 11. It states: 'Don't think that there is anything we don't know about you.'