Here is how to estimate the electric power produced by solar cell arrays, wind turbines, hydroelectric turbines, and biomass-combustion powered steam plants. All you need to to is to look at the power generator, make some size estimates, and then do some simple mathematics. Your power estimates should be between a half and double the actual power.

Solar Cells

The sun shines about 1000 watts per meter square of electromagnetic energy on the surface of the earth. This is called the solar constant, C.
All affordable solar cells convert this sunlight into electric power with 10% efficiency, e.

So all you need to do to estimate the electric power, P, in watts, produced by a solar array is to estimate the area of sunlight it collects, A, in square meters.

Then just multiply this area by the Solar Constant and the 10% efficiency of the cells.

P = ACe

This means that a 1 meter square array of solar cells will produce about
P = ACe
P = 1 x 1000 x 0.1 = 100 watts.

You could use it to power one bright lightbulb, only while the sun is shining, unless you have a battery to store the energy.

Wind Turbines

Once again it starts with area, A, the area swept out by the blades of the wind turbine.

Let's say we have a wind turbine with propeller blades that reach out 10 m from the central hub. the area they sweep out is then A = pr² = 300 m²

The power of the wind that blows through this area is P.

Power is energy per time P = E/t in this case it is kinetic energy of the wind

E = 1/2 mv² but we want the energy per second so we'll need the mass that blows through the blades in a second m = dvt

where d is the density of the air = 1 kg/m³

and v is the windspeed, say 10 m/s

and t is 1 s

Then the power would be P = A 1/2 d t v³ watts

P = 300 x 1/2 x 1 x 1 x 10³ = 100,000 watts

It is a 100 kilowatt wind turbine.
It would power 1000 bright light bulbs.

Hydroelectric

The power of falling water, P, is the energy of falling water per second, P = E/t.
The energy here is the potential energy, E = mgh.

where m is the mass in kilograms of water that falls per second.

g is the acceleration of gravity 10 m/s²

and h is how high the water falls.

Let's say you estimate that the height of water falling is h = 10 m
and the rate of flow is m/t = 100 kg/s

Then the power is

P = m g h /t = 100 x 10 x 10 / 1 = 10,000 watts.

It is a 10 kilowatt hydroelectric plant.

Biomass

The key thing to remember is the dieter's law:
every bit of dry carbohydrate contains E = 100 Calories per ounce
in metric units this is about E = 15 Joules per gram or 15,000 J/kg.
(This is easier for coal fired plants because coal is dry weight, but its harder for plants powered by water hyacinths because they are mostly water so here you'll have to estimate how much mass remains when it is dry.)

To estimate the power of biomass you have to estimate the dry mass, m, burned per second, t.
Let's say you estimate that about one ton, 1000 kg is burned per hour or m/t = 0.3 kg/s.

The power is P = m/t x E

Then P = 0.3 * 15,000 = 5 kW.

This power is then converted into steam which turns a turbine to produce electric energy this conversion is done with less than 50% efficiency.

So we'll say it produces about 2 kW per dry ton of biomass burned per hour.

By the way a ton is approximately the mass of a cubic meter of stuff.

Paul Doherty