Hydroelectric dams: the main source of renewable energy

Hydroelectric dams are a traditional (and virtually exclusive) method of generatingpower from water, and the world’s leading source ofrenewable energy. They work by holding water in a reservoir at a higher altitude, then releasing it to flow through turbines. The kinetic energy of the moving water is converted into electricity by these turbines.

How hydroelectric dams work

Hydroelectric dams vary in size and generating capacity. Some large dams, such as the Three Gorges Dam in China, have a generating capacity of over 22,000 megawatts (MW), while smaller dams can produce just a few megawatts. The water storage capacity of these reservoirs also varies considerably. The reservoir of the Three Gorges Dam has a storage capacity of 39.3 billion cubic meters of water.

The efficiency of hydroelectric dams is generally high, often reaching 85-90%. This means that a large proportion of the stored water’s potential energy is converted into electricity. However, it’s important to note that hydroelectric dams don’t always operate at maximum capacity. Electricity production depends on factors such as the amount of water available and the need for electricity.

How do you calculate the potential energy contained in a dam?

To calculate the potential energy contained by a dam, we need to take into account the mass of water retained, the head of the water and the acceleration due to gravity. Here’s the formula for gravitational potential energy (E_p): E_p = m × g × h_mean, where :

  • E_p is gravitational potential energy in joules (J)
  • m is the mass of the retained water in kilograms (kg)
  • g is the acceleration due to gravity, which is approximately 9.81 meters per square second (m/s²) on Earth
  • h_average is the average head of water in meters (m)

To find the mass of water retained, you need to know the volume of water in the tank (V) and the density of the water (ρ). The density of pure water at room temperature is around 1,000 kg/m³. The mass of the water is obtained by multiplying the volume by the density: m = V × ρ. Combining the two formulas, you get the following equation for calculating the potential energy contained by a dam:

E_p = V × ρ × g × h

It’s important to note that this equation gives the maximum potential energy contained by the dam. In practice, not all of this energy will be converted into electrical energy, due to various losses and turbine efficiency.

Example: how much energy does the Hoover Dam store?

Let’s take the example of the Hoover Dam in the USA, located on the border between Arizona and Nevada, which has long been the world’s largest dam. It is 221.4 m high and its reservoir, Lake Mead, is around 35.2 billion cubic meters (3.52 × 10^10 m³). To calculate the maximum potential energy contained by Hoover Dam, we can use the previously mentioned equation (E_p = V × ρ × g × h_mean) using the specific values for Hoover Dam:

  • Volume (V): 3.52 × 10^10 m³
  • Water density (ρ): 1,000 kg/m³
  • Gravity acceleration (g): 9.81 m/s² Average head (h_m³): 1,000 mm
  • Average head (h_average): 110.7 m

E_p = (3.52 × 10^10 m³) × (1,000 kg/m³) × (9.81 m/s²) × (110.7 m)

E_p ≈ 3.83 × 10^16 joules

This value represents the maximum potential energy stored in the Hoover Dam reservoir. However, it should be noted that the actual efficiency of converting potential energy into electrical energy depends on several factors, such as the efficiency of turbines and generators, as well as transmission and distribution losses. In practice, the overall conversion efficiency for a hydroelectric dam is generally in the range of 80% to 90%. Hoover Dam has a generating capacity of around 2,080 megawatts (MW), and produces an average of around 4.2 billion kilowatt-hours (kWh) of electricity per year.

The price of dams

In terms of cost, hydroelectric dams often require substantial investment to build. However, once built, they have a relatively long lifespan (several decades) and relatively low operating costs. The average cost of electricity generated by hydroelectric dams is estimated at between 0.03 and 0.12 USD per kilowatt-hour (kWh), although this may vary according to local conditions and the size of the project.

Dams around the world

Hydropower is a major source of renewable energy, and hydroelectric dams are found all over the world. Here are a few countries with significant hydropower capacity and some of the world’s largest dams:

  1. China is the world leader in terms of hydropower capacity, with around 356 GW installed by 2020. The Three Gorges Dam, the world’s largest dam, has an installed capacity of 22,500 MW and contains around 39.3 billion cubic meters, with a height of around 200m, representing a storage capacity of around 8.48 TWh.
  2. Brazil has significant hydroelectric capacity, estimated at around 104 GW in 2020. The Itaipu dam, located on the border between Brazil and Paraguay, has an installed capacity of 14 GW and a reservoir of 29 billion cubic meters of water, with a height of 236m, corresponding to around 4.67 TWh of storage.
  3. The United States has an installed hydroelectric capacity of around 103 GW in 2020. The Hoover Dam, located on the Arizona-Nevada border, has an installed capacity of 2.08 GW and a reservoir of 35 billion cubic meters of water, with a height of 221.4m, which would correspond to around 10.6 TWh of storage.
  4. Canada has an installed hydroelectric capacity of around 82 GW in 2020. The James Bay complex, comprising several dams and hydroelectric power stations, has a total installed capacity of around 16.5 GW and a reservoir of 137 billion cubic meters of water, with a height of 100m, which would correspond to around 11.67 TWh of storage.
  5. Russia has an installed hydroelectric capacity of around 51 GW in 2020. The Saiano-Shushensk dam has an installed capacity of 6.4 GW and a reservoir of 31.3 billion cubic meters of water, with a height of 210m, which would correspond to around 1.57 TWh of storage.

It is important to note that these figures may change over time as new dams are built. The installed capacities mentioned above are based on data available in 2020.

  2. Hoover Dam (USA):
    • Reservoir volume: approx. 35 billion cubic meters (Lake Mead) [3].
    • Potential energy: ~ 0.88 TWh (assuming an average head of 180 m and an efficiency of 90%).
  3. James Bay complex (Canada) :
    • Reservoir volume: approx. 137 billion cubic meters for all reservoirs in the complex [4].
    • Potential energy: ~ 11.67 TWh (assuming an average water head of 50 m and 90% efficiency).
  4. Saiano-Shushensk dam (Russia) :
    • Reservoir volume: approx. 31.3 billion cubic meters [5].
    • Potential energy: ~ 1.57 TWh (assuming an average head of 105 m and 90% efficiency).