Hydropower is a type of renewable energy where the flow of water is converted to electrical energy. Although it does come with some difficulties and cost to build, it is much more reliable than wind power.


  • Predictable & reliable energy source.

    • Water flow is not as much intermittent as sunshine or wind.
  • Low cost operation.
  • Dams double as flood control units.

Hydropower Operation Principal

Similarly to wind turbines, the basic hydropower generator consist of 2 main parts:

  • Turbine
  • Electric Generator

The water rotates the turbine blades (propeller) that are attached to a shaft. As a result, the rotating shaft rotates the rotor in the 3-phase synchronous machine. Thus, generating electricity.

Based on where the hydro generator is situated, there are 2 main types:

  • Barrage based generator
    • uses in dams
  • Underwater Hydro Turbines
    • Built into the floor of rivers
    • Same equation applies as for wind turbines
Figure: Barrage based Generator used in dams

Fig 1: Barrage (dam) based generator

Figure: Underwater Hydropower Turbine

Fig 2: Underwater hydro turbines

Types of Hydroelectricity generation

  • Run of River
  • Pumped Hydro Electric Storage

The idea behind Pumped Hydro Electric Storage is to raise water to high levels. The flow of water is controlled while generating electricity. Next, the water is pumped back.

Usually, there are overproduction of electricity from nuclear or coal sources. That is to say, these sources can’t just be stopped for the time of day when people use less energy. This extra energy is thus used to pump water up.

Run of River turbines capture the natural down flow of the river. The water has kinetic energy which is transformed into electric energy. In some cases, a stream is separated from the main river flow that is used for power generation.

Run of River Hydropower Dams

Based on the height of water reservoir we distinguish between 3 types of dams:

  • Lowe Head
  • Medium Head
  • High Head

Certainly, the high head will deliver the highest pressure on the turbine. Mostly the reservoir is situated on mountains and as a result, the penstock runs through them.

Hydroelectric Dam operation principle

Fig 3: Operation of Hdropower Dams. Source: Wikimedia Commons

Pumped Hydroelectric Storage

The operation is very similar to Run of River dams. The difference that the water is pumped back uphill to the reservoir at night.

Fossil power plants can’t just be turned off. If they are on full power, they can’t be easily slowed down. Although, at nights, the energy demand is significantly lower than during the days. That is to say, this surplus energy is used to pump water back to the reservoir at night time.

The overall efficiency is 80%!

At Pumped Hydroelectric storages the water is stored up in a reservoir. It can be used when there is a sudden higher demand on electricity. Pumped Hydroelectric Storages are the best large-scale approach for energy storage. Note, they essentially do the same a batteries but at a much larger scale.

Working principle for Pumped Hydroelectric Power Plants at Day

Fig 4: Night time operation of Pumped Hydroelectric power plants. The surplus energy generated by the power plants is used to pump water back up to the reservoire.

Working principle for Pumped Hydroelectric Power Plants at Night

Fig 4: Day operation of Pumped Hydroelectric power plants. The down flow of water generates electricity by driving the turbine. 

Hydropower Dam Potential Energy Calculation

Note, this is the case for the barrage based generators, not for the underwater hydro turbines. They use the same formula for the wind turbines.

Picture this as a vertical cylinder. There isa pipe filled with water coming down from the reservoir – the penstock.

First things first. Here are some relationships we have to understand:

Equations: basic equations related to hydropower
  • F: force (N)
  • m: mass (kg)
  • g: gravitational acceleration (9.8 m/s^2)
  • h: height of head (m)
  • P: power (N-m/s)
  • p: pressure (Pa) or (N/m^2)
  • E: energy (J) or (N-m)
  • t: time (s)
  • V: volume (m^3)
  • Q: flowrate (m^3 /s)

So, there is a pipe and there is water in it.

This water has some mass. Mass is essentially the area of the pipe x height x the density of water.

If the water has mass and g is the gravitational acceleration, we can easily calculate the Force. It is the force the water has on the generator. F = m *g


Using the Force and Area, let’s derive an equation for the pressure. The pressure is essentially force that is applied on a certain area.

Equation: Deriving an equation for pressure


Using the pressure equation, we can find an equation on the power:

Equation: Deriving an equation for Power

Potential Energy:

Knowing that Power is Energy over time we can easily derive a formula for the Potential Energy:

Equation: Deriving an equation for Potential Energy


How much coal is required to generate 1kWh energy if coal has an energy of 24 MJ/kg?


  • Power = Energy transferred per unit time: P = E/t.
  • P(W)*t(s) = E(J)
  • 1 kWh = 1000 W x 3600s = 3.6 MJ

3600 as there are 3600 seconds in an hour. So:

1kWh = 3.6MJ

The coal has 24 MJ/kg energy. So, 3.6/24 = 0.15 kg coal is required to generate 1kWh energy.

Exercise 2:

We have 1 tonnes of water. How high should it be raised to generate 1kWh energy? Assume the round trip efficiency is 80%.

g = 9.81 m/s^-2

Round trip efficiency: it is the actual energy we can get out from something. Let’s take the example of batteries, we charge them with a certain energy, but can only get 80% out of them.


Calculation: finding the height of from Energy, gravitational acceleration, mass and effciency

The energy that is stored in 150 g of coal is equal to having 1 tonnes of water 459 m high up.