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I experienced similar grid problems in various parts of Africa. There are several approaches, but none are particularly cheap or local:
1) Provide localised back-up using engine generators, probably diesel. may be possible to convert these to run on old vegetable oil - need to strain it and keep it warm, and increase injector pressure a bit. More basic engines, and especially ones with chunky injectors e.g. Mercedes; work best.
2) Any microgeneration scheme needs to guard against back feeding into the grid, which is a potentially life threatening risk to anyone working on the distribution system. Clever inverters e.g. Trace SW range, can take account of this and disconnect the grid and only feed locally when the grid fails. It can also be done using a contactor between grid and local distribution that is held in by the grid. Grid fails, connection is broken. However, this needs a manual reset because if it automatically reconnects when the grid returns, you inverter or generator is unlikely to be synchronised and the result will be fried electronics, most likely at your end.
3) Simplest system is an enlarged uninterruptible power supply (UPS). Use an inverter-charger to keep a bank of batteries full. Grid fails > charger becomes inverter and generates mains supply from the energy stored in the batteries. Safety measures in (2) apply to prevent back-feed and synching issues.
4) Photovoltaics, with batteries and inverters can provide long term off-grid power but will be expensive if you want to run heavy loads like conventional fridges and air-con. Forget any form of electric heat - cooking, kettles, etc. I work for a company that has been supplying PV systems for medical applications, particularly in Africa, for 20 years: www.dulas.org.uk
5) If it's very windy, small wind turbines could be an option and can be made locally. They don't produce much though, and it really does need to be windy a lot of the time. Larger turbines can be linked with diesel generators to form wind-diesel hybrids that can run localised grids of tens or hundreds of kilowatts. Specialised kit and needs the wind, but quite a robust system.
6) Hydro is best where the water falls some distance - at least 10 metres is good. Low head is also possible but needs high flows so turbines and civils are bigger and more expensive. Power = flow x head (height of water fall)
Hope that provides a few ideas. Happy to add more detail if they want to take it further.