Question

A hydroelectric facility is built to deliver a peak power of \(1 \mathrm{GW}\), which it manages to do for three months of the year during the spring snow- melt. But for three months in summer, it drops to \(700 \mathrm{MW}\), then \(500 \mathrm{MW}\) for three months in fall. In winter, it drops way down to \(200 \mathrm{MW}\) for three months. Using the concept of the capacity factor (Definition 11.2.1), what is the annual average capacity factor for this facility?

Short answer

Answer: The annual average capacity factor for the hydroelectric facility is 60%.

Step-by-step solution

Calculate the maximum possible energy output for each season

To calculate the maximum possible energy output for each season, we will multiply the peak power of the facility (\(1 \mathrm{GW}\)) by the time duration (in hours) of each season. Maximum possible energy output in spring = \(1 \mathrm{GW} \times 3 \times 30 \times 24 \mathrm{hours} = 2160 \mathrm{GWh}\) Do the same for other seasons, considering that the peak power remains 1GW: Maximum possible energy output in summer = 2160 GWh Maximum possible energy output in fall = 2160 GWh Maximum possible energy output in winter = 2160 GWh

Calculate the actual energy output for each season

To calculate the actual energy output for each season, we will multiply the given power output by the time duration (in hours) of each season. Actual energy output in spring = \(1 \mathrm{GW} \times 3 \times 30 \times 24 \mathrm{hours} = 2160 \mathrm{GWh}\) Actual energy output in summer = \(0.7 \mathrm{GW} \times 3 \times 30 \times 24 \mathrm{hours} = 1512 \mathrm{GWh}\) Actual energy output in fall = \(0.5 \mathrm{GW} \times 3 \times 30 \times 24 \mathrm{hours} = 1080 \mathrm{GWh}\) Actual energy output in winter = \(0.2 \mathrm{GW} \times 3 \times 30 \times 24 \mathrm{hours} = 432 \mathrm{GWh}\)

Calculate the total maximum and actual energy output for the year

Total maximum energy output for the year = Maximum possible energy output in spring+ Maximum possible energy output in summer + Maximum possible energy output in fall + Maximum possible energy output in winter. Total maximum energy output for the year = \(2160 + 2160 + 2160 + 2160 = 8640 \mathrm{GWh}\) Total actual energy output for the_year = Actual energy output in spring + Actual energy output in summer + Actual energy output in fall + Actual energy output in winter. Total actual_energy output for the_year = \(2160 + 1512 + 1080 + 432 = 5184 \mathrm{GWh}\)

Calculate the annual average capacity factor

Lastly, we will calculate the capacity factor using the following formula: Capacity factor = \(\frac{\text{Total actual energy output}}{\text{Total maximum energy output}}\) Capacity factor = \(\frac{5184 \mathrm{GWh}}{8640 \mathrm{GWh}}\) Capacity factor = \(0.6\) or \(60\%\) The annual average capacity factor for this hydroelectric facility is \(60\%\).

Key concepts

Capacity Factor

The capacity factor of a power plant is a crucial measurement that indicates its efficiency and performance over time. It's defined as the ratio of actual energy produced to the maximum possible energy that could be produced if the plant operated at full capacity all the time. This tells us how much of the plant's potential output is being utilized.
For example, if a hydroelectric plant has a capacity factor of 60%, it means that the facility is producing 60% of its potential maximum energy output throughout the year. In practical terms, it helps to understand how actual conditions, such as water availability or demand cycles, affect the plant’s performance.
Low capacity factors indicate that a plant is not operating at full potential, which could be due to environmental factors or maintenance issues. However, it's essential to compare capacity factors across similar types of power plants since technology types, like solar, wind, and hydroelectric, have inherently different capacity factors due to the nature of their energy sources.

Energy Output Calculation

Calculating the energy output of a hydroelectric facility involves determining both the maximum potential and the actual energy produced over a given period. The energy output is typically measured in gigawatt-hours (GWh).
To find the energy output, you first determine how long the facility operates at different power levels. For instance, if a plant operates at 1 GW for three months, you calculate the energy output for that period as \[ \text{Energy output in spring} = 1 \text{ gigawatt} \times (3 \times 30 \times 24) \text{ hours} = 2160 \text{ GWh} \]
The same calculation process applies to other time periods with adjusted power levels due to factors like seasonal water flow variations. Understanding these calculations is vital for predicting operational efficiency and for economic analysis, ensuring that energy production is optimized throughout the year.

Renewable Energy Sources

Hydroelectric energy is a significant type of renewable energy, derived from the natural flow of water in rivers and dams. It stands out due to its relatively high capacity factor compared to other renewables like solar or wind.
Hydroelectric plants harness the energy from water flowing from higher to lower elevation, converting this kinetic energy into electricity without the emission of greenhouse gases during operation. This makes it a crucial player in the global effort to produce clean energy and combat climate change.
Renewable energy sources like hydroelectricity are key to reducing dependency on fossil fuels, helping reduce environmental impact. However, it's important to manage these resources sustainably to ensure they continue to provide clean energy for future generations. Building a balance between energy production and environmental conservation is essential for the continued success of hydroelectric power.