The excitement on Fulda's University Square hinted at the imminent arrival of an A-list celebrity. Crowds jostled impatiently to pass through a security check, a total of 5,000 gathering in front of two big screens, some on picnic benches, others standing, while hundreds more watched from the roofs and windows of offices and apartment blocks.

When Angela Merkel appeared, waving and smiling amid a sea of orange balloons and "Angie" placards, camera phones shot into the air and a rousing cheer went up.

After five hard weeks of campaigning ahead of Sunday's election, it might have been expected that the German chancellor would look exhausted at one of her final rallies in the western state of Hesse last week. But she was in fighting mood. "I was back in my constituency today and tanked up a bit of the Baltic sea breeze," she told the crowds. "After that I feel ready for anything."

If, as widely expected, the 59-year old German leader is re-elected for a third term, she will be on course to become Europe's longest-serving female leader, outstripping Margaret Thatcher's claim to the title.

Since first coming to power in 2005, Merkel has rejected the comparisons between herself and Britain's "Iron Lady". Indeed, apart from a few biographical details, the similarities between the conservative social democrat and the free marketeer are few and far between. Germans, at least, have long stopped making the comparison.

But comparisons there are. Both female and scientists, able to survive on little sleep, the two women suffered from image problems at the start of their leaderships. Advisers to Thatcher suggested she carry a handbag and soften her voice, while Merkel got highlights, a more relaxed hairstyle and learned to deal with the issue of how to look in control by holding her hands in a rhombus shape in front of her stomach, now her trademark gesture. But the differences between them, not least politically, are far bigger than the similarities. One revealing example is that, while Thatcher sold off council houses, Merkel is in favour of rent controls.

Fascination with the Protestant pastor's daughter is on a par with that of the grocer's daughter. Merkel's has been the extraordinary rise of a girl who grew up in small-town communist East Germany to become arguably the most powerful woman in the world. Among Germans, her appeal lies as much in her misfit status on the political scene, including the questions as to how a childless, female Protestant managed to make it to the helm of a political party dominated by Catholic west German males, and from there to become a towering figure on the international stage.

Summing up the anomaly, Berthold Kohler, one of the publishers of the conservative Frankfurter Allgemeine (FAZ), says: "Twelve years ago, when she was elected as the head of the Christian Democrats, no one imagined she'd still be in the driver's seat in 2013, let alone that she would be looking back having spent seven years in the chancellery."

The former German chancellor Helmut Kohl was the first to discover Merkel, recognising her potential when she was 35, and the press officer of the GDR's Democratic Awakening party. He awarded her her first ministerial role in 1990. Just nine years later she effectively turned against him, using a comment piece in the FAZ to tell the rest of the Christian Democratic Union (CDU) they should distance themselves from him, after a funding scandal that nearly sank the party.

He was the first of the many males whose political corpses have strewn her career path. Though they have almost all fallen on their own swords (for taking backhanders, plagiarising PhDs), their demise under her leadership has earned her one of her many nicknames, Männermörderin (men murderer). She has often forged better relationships with women. Indeed, her office manager and closest adviser is Beate Baumann, who is said to know her almost as well as her husband, shy chemistry professor Joachim Sauer. She has also forged lasting friendships with Hillary Clinton, Condoleezza Rice and Christine Lagarde.

And while having learned to work with her male counterparts, including George W Bush, Nicolas Sarkozy, Silvio Berlusconi, and to a lesser extent Vladimir Putin, she has let it be known that she despises their displays of overblown machismo. It has been she – the first to admit she dislikes conflict – who has stood up and literally rearranged the chairs at conferences in a last-ditch, and arguably maternal, intervention to forge better communication.

But still she remains a mystery to many Germans. "You know me," has been her frequent mantra at election rallies, accompanied by remarks about how well the German economy is doing – by which she means "a vote for me is a vote for the continuity of these good times".

But, says Stefan Kornelius, foreign editor of the Süddeutsche Zeitung, whose biography of Merkel, The Chancellor and Her World, was published on Saturday, to many Germans "this politician who rose almost unnoticed to lead the leaders of Europe" still remains a conundrum. "The Germans have been pondering the mystery of Merkel for many years, trying to interpret her character and the inner workings of her mind," he says.

In interviews over the years, and in the runup to this election, there has been a drip feed of stories, largely from Merkel herself, accompanied by the release of 22 pictures from her childhood to the present, that have helped to build up something of a picture. Almost every German knows that her favourite foods, which she enjoys making herself, are plum cake and potato soup. We recently learned that she first got drunk on cherry wine and that a Soviet soldier once stole her bicycle.

Applying pragmatism to her desire to learn English under communism, she devoured technical manuals and copies of the Morning Star. A favourite anecdote is how she was in a sauna, a weekly date she kept with a girlfriend, when she heard that the Berlin Wall had come down in 1989. Rather than rush out on to the streets of the divided city, the two stayed until the end of their session, only later heading out into the November night to join the crowds crossing into the west before heading home to bed.

She also let it be known in the last couple of weeks, how, when she separated from her first husband, Ulrich Merkel, after just five years of marriage, she took refuge in a Berlin squat recommended by friends. (We also know from previous tellings of their separation, that, ever the pragmatist, she took the washing machine with her when she left.)

Asked at a citizens' forum earlier this month just how much the chancellorship had changed her, Merkel readily admitted that she had lost her confidence to drive a car, "except on small country roads", having enjoyed the luxury over the past few years of being chauffeur-driven everywhere. Opponents might seize on that to say she is detached from ordinary people. Except there is plenty of evidence to the contrary. After a recent Brussels summit that went through the night, she was seen in her local supermarket, buying a leek, a bottle of wine and some olive oil, dressed in the same suit in which she had negotiated a major deal some few hours previously.

While those close to her will cite her mental rigour and her pragmatism as being at the heart of her winning formula, her secret, say an increasing number, lies in her ability to "send voters to sleep": of maintaining her support base through what political scientists have described as "asymmetric demobilisation" – a deliberate dulling of the issues and defusing conflicts with her opponents by absorbing their positions, so that, according to one expert, "they have no oxygen to breathe". To make the point, the general secretary of the Social Democrats, Andrea Nahles, went so far as to sing a song from her favourite children's book character, Pippi Longstocking, to argue that Merkel was grossly simplifying the issues. "I'll shape my world … just the way I like it," she intoned, slightly off-key, in front of a stunned Bundestag audience.

The CDU's response was to thank Nahles in a letter for her "perhaps unintended compliment", saying it appreciated the comparison between Merkel and Pippi who, like the chancellor, "has lots of fans in Germany … lives independently and is very courageous … a girl who broke loose from the gender role prescribed for her by society".