The biggest prize will be rich, heavily industrialised Baden-Württemberg, Germany's third-most-populous state with close to 11 million inhabitants.

The state is somewhat of an anomaly. In 2011 elections, just weeks after the Fukushima nuclear disaster, the Green Party swept to power there in a political earthquake mainly caused by nuclear Angst, bringing Germany its first Green premier, Winfried Kretschmann.

But what looked like a one-off could firmly establish the strongly pro-renewables Greens as the dominant force in the southwestern state that for decades had been a stronghold of Chancellor Angela Merkel's Christian Democrats (CDU).

Thanks to the immense popularity of Kretschmann, the Greens have been leading in all opinion polls this month, with 32-33.5% of voter preferences, while the formerly much bigger CDU can expect to get 28-30%. It would be the first time the Greens have become the strongest party in a state election.

The Social Democrats (SPD) - which five years ago had only slightly fewer votes than the Greens and are their junior coalition partner in the state - are now looking at a disastrous 13-16% of the vote, while the anti-refugee Alternative for Germany (AfD) party is expected to enter the state parliament for the first time with 11-13%.

The Free Democrats (FDP), which still haven't shaken off their pro-nuclear stand entirely, but which count former Fraunhofer ISE head Eicke Weber as a candidate, can also hope to enter parliament.

If opinion polls are right, Kretschmann can either continue his coalition with the Social Democrats or try a coalition with the CDU, to which he has warmed up in recent years.

During his term in office, the premier has pushed for a pro-renewables overhaul in policy at utility EnBW, which is owned by the state and some of its municipalities.

EnBW, despite struggling from the burden of having to pay for the nuclear exit and declining profit margins at its fossil generation, has advanced faster than other utilities in embracing green power and making a profit from it. The utility, despite being headquartered in the inland state, has become a major investor in offshore wind, and today it handed a consortium led by Engie unit Cofely Fabricom a contract for the substation at its 497MW Hohe See project in the North Sea.

Onshore, moderate-wind Baden-Württemberg, with 144MW added last year, is still a laggard among the states, but wind expansion at least is picking up after a dismal 21MW was added in 2014. The government says it first had to reform zoning rules that had previously impeded the build-up of onshore wind, and it expects expansion to gain pace now.

In any case, Baden-Württemberg's policy is in stark contrast to that of neighbouring Bavaria, another southern industrial powerhouse, where the conservative government has gone out of its way to put stones in the way of the energy transition, with, among other things, a distance rule for onshore wind that has killed off almost all new projects.

In the Bundesrat, Germany's upper house that represents the states, Kretschmann has been vociferous in defending renewables and trying to stop the CDU-SPD federal government from slashing support for renewables too much.

Elections will also be held on Sunday in Rhineland-Palatinate (four million people) and Sachsen-Anhalt (2.2 million people). In those states the Green party is expecting losses, as it lacks a popular leader like Kretschmann.

In Rhineland-Palatinate the CDU is in a tight race with the SPD, which has run the state with the Greens as its junior partner. In the eastern state of Sachsen-Anhalt, the CDU is in the lead, but the right-wing populist AfD may come in second.

If the AfD performs strongly in all three states, pressure for Merkel to change her pro-immigrant stand will grow; some in the CDU may even call for her to step down.

The importance of these state elections goes way beyond the regional level and may show a dramatic shake-up of Germany's party system.