Whether it be a thermal power station or nuclear power station or a hydroelectric damn its impossible to keep all the dynamos running at a fixed speed.
As such how do power companies regulate the voltage from wildly varying ones to near perfect 110/220 v for household use?
I'm also interested to know how was this done in older times like early 1900s and before.
How does some god knows what voltage and frequency generated at a dam ends up as steady 50 hz sine wave household voltage
It's 50Hz when generated - the generators are built with a number of phases and run at a constant speed.
Whether it be a thermal power station or nuclear power station or a hydroelectric damn its impossible to keep all the dynamos running at a fixed speed.
Other way round: before connecting a generator to the grid, it is absolutely essential that it is running at almost the right speed, and in phase with the grid. Once it's locked into the grid, there is a feedback process. Trying to run "ahead" will increase the resistance torque along the shaft, running "behind" will decrease it. This keeps the corresponding turbines running at the right speed.
So when powering up the system, the generator would be spun up with manual control of turbine power levels, then carefully brought into phase, and then a huge switch would be thrown to connect it to the grid.
The 19th-century system for doing this involving lamps is described in https://en.wikipedia.org/wiki/Synchronization_(alternating_current)
See also How to synchronize a generator on the electrical grid?
(Big exceptions: wind turbines and solar PV panels. But that warrants a whole other question and answer essay. As does "what happens when you don't have the grid to sync to", known as black start.)
Also see
The electricity grid: what keeps small power generators from being 'driven' by large ones?
I think it helps you understand when you think of an electrical machine as both a motor and a generator. They are both at the same time, and when they are running on a power grid, they support each other.
Synchronous AC machines running on a grid indeed all run at fixed speed. And they all have a fixed voltage too, which is both set by the grid.
As the machines are mechanically coupled to the turbine, the turbines run at a fixed speed, too. When you put mechanical power on the generator through the turbine, it doesn't run faster but instead the angular displacement between the mechanical rotation angle and the electrical phasor angle increases. Second, the generated voltage increases a little bit over that of the grid offers at the place so the current flow direction is into the grid. That way the generator can transform mechanical power into electrical power and push it into the grid.
As a result, all machines on the grid as a whole are running a little bit faster. The more machines the grid has, the smaller the effect from one single machine. So controlling the power available to the grid can be achieved by regulating the frequency.
A simple dynamo is a synchronous machine, too, but doesn't run on a grid. In that case, the frequency and voltage are variable. It's no-one there who can help out.
In the beginning of AC electrification, grids were weak, only a few machines on them, and frequency and voltage had been fluctuating a lot. But at all times, the frequency and voltage was shared by all machines on the grid. Inherently. That's how synchronous AC machines works.
Before, with DC electrification, there was no frequency for regulation, in was all done by regulating the voltage, which is a bit more tricky, as it heavily depends on the load distribution on the grid.
Before you attach the generator on the grid it has to be synchronized by means of regultating the water flow from a dam. Then the generator is switched on the grid. At this time it still doesn't produce any elecricity, becuase it is unloaded and switching the mode of operation from motor to genrator. For example if the water flow is reduced, then it will work as motor and force the flow. If the flow is increased then it turns into a generator, in both situations the speed is equal, only the phase lag is different.
The exact frequency is dictated by the joint of large power plants that are regulating the frequency, the others, smaller power plants just follow.
Without automated phase frequency control and global frequency clocks with an error of < 0.0001 ppm for reference, the grid would slow down in frequency with loading effects on generators and rise in frequency with lower demand. Every generator has some means to control Voltage and Frequency independently with parameters monitored locally but references from the remote interconnect site. Also phase as well, is critical, which is the time integration of frequency error.
The simple way to understand this is the output impedance of the grid is much lower than the demand load impedance such that load changes do not affect the grid voltage too much. This impedance ratio is the same as the regional step load voltage regulation error. Parameters are often measured in "per unit" or p.u. of the nominal values.
Unfortunately in some countries with a loose grid, consumers try to do their own regulation with voltage auto tap changers which then causes more load current to boost voltage and in effect causes a positive feedback loop to the generator making their grid unstable. This can only be improved slowly with bigger transformers and more supply sources to shunt and lower the grid impedance while not exceeding thenratio for short circuit current in any one transformer. The bigger xxx MV transformers must also have a higher Zo of 8 to 10% due to the extreme internal forces limitations, so it is not a simple solution but a steady infrastructure growth to improve power quality.
Thus since the grid is intelligently controlled , every minute an algorithm is computed at an interconnect point and new parameters for each generator are fed back to ensure supply meets demand at the lowest cost with phase/frequency/voltage feedback to each source at connection points.
This in turn affects the power stored on the grid to meet surge demands. It affects RMS voltage, frequency and phase at the end user by many complex interconnected control systems with a regional centralized reference managed by a government regulators group that dictates to all roviders and delivers to all customers, the measureable power standards established in the Industry for each region.
A loose grid in one region might vary 5% in frequency with insufficient redundancy, while a very tight grid might be < 0.0001 PPM, some of the time but vary much more then have a low mean frequency error over a daily cycle. The cost of stability is greater and its tolerance allows more short term cost reduced flexibility but may cost more in maintenance from surges, so changes are made very slowly. Each source may have different rate structures and capacity.
You can read about "some" of the simpler algorithms here.
Where I live in Ontario, Canada , Hydro One owns and operates around 30,000 circuit km of high voltage lines: 115kV, 230kV & 500kV within 5% ( with <1% due to source variation and 4% from load variation) and 123,000 circuit km of low voltage <=50kV within another 5% ( which includes load variations and line drop ) and thus the subscriber enjoys a voltage tolerance of 10% max but is typically within 2% in many residential areas.
Power glitches are very infrequent as well as fault shutdowns are normally very brief annually perhaps a few times a year in one given area. This high quality service level is due to high redundancy and good condition based maintenance (CBM) rather than just time based maintenance or fault fixing. But then we still complain about rising prices and plans to privatize it short short term political financial gain and long term cost increases to users.
This is accomplished through a complex network of load-balance , rate-structures contract pricing for 27 interconnections with 2 other Provinces and 3 States in the US. The regulation of source and balance supply and demand for the best price. Since Nuclear loads must be 100% as it is not an adjustable source, guaranteed pricing and delivery.
Generation is controlled by voltage and phase to the grid and by automated tap changes for each transformer station with communication between the stations to anticipate changes.
