Question

While the Chief Joseph Dam on the Columbia River can generate as much as \(2.62 \mathrm{GW}\left(2.62 \times 10^{9} \mathrm{~W}\right)\) of power at full flow, the river does not always run at full flow. The average annual production is 10.7 TWh per year \(\left(10.7 \times 10^{12} \mathrm{Wh} / \mathrm{yr}\right)\). What is the capacity factor of the dam: the amount delivered vs. the amount if running at \(100 \%\) capacity the whole year?

Short answer

Answer: The capacity factor of the dam is approximately 46.8%.

Step-by-step solution

Find the maximum possible annual production

First, let's find the maximum possible annual production by multiplying the maximum power generation (2.62 x 10^9 W) by the total number of hours in a year (8760 hours). Maximum possible annual production = Maximum power generation x Total hours per year \(= (2.62 \times 10^{9} \mathrm{W})(8760 \mathrm{~h/yr})\)

Convert the maximum possible annual production to Wh

To find the maximum annual production in watt-hours, we need to multiply the result from Step 1 by 1 hour. Maximum possible annual production in Wh = Result from Step 1 x 1 hour \(= (2.62 \times 10^{9} \mathrm{W})(8760 \mathrm{~h/yr})(1 \mathrm{~h})\)

Calculate the capacity factor

Now we can find the capacity factor by dividing the average annual production by the maximum possible annual production. Capacity factor = \(\frac{10.7 \times 10^{12} \mathrm{Wh} / \mathrm{yr}}{(2.62 \times 10^{9} \mathrm{W})(8760 \mathrm{~h/yr})(1 \mathrm{~h})}\)

Simplify and find the capacity factor

By simplifying the expression in Step 3, we can find the capacity factor. Capacity factor = \(\frac{10.7 \times 10^{12} \mathrm{Wh} / \mathrm{yr}}{ (2.62 \times 10^{9} \mathrm{W})(8760 \mathrm{~h/yr})(1 \mathrm{~h})}\) \(= \frac{10.7 \times 10^{12}}{2.62 \times 10^9 \times 8760}\) Now, from calculations, Capacity factor \(\approx 0.468\) Thus, the capacity factor of the dam is approximately 46.8%. This means that the dam is producing 46.8% of its maximum possible production on average over the year.

Key concepts

Renewable Energy Production

Renewable energy sources are paramount to a sustainable future, harnessing the power of natural processes like solar radiation, wind flow, and water cycle. Dams, like the Chief Joseph Dam on the Columbia River, contribute significantly to renewable energy production by converting the kinetic energy of flowing water into electricity through hydroelectric power generation. This transformation happens when the flowing water turns turbines, which then power generators to produce electricity. The energy production from renewable resources like hydroelectric dams is vital because it offers a way to reduce greenhouse gas emissions and dependence on fossil fuels.

The amount of electricity a renewable source can produce varies significantly due to factors like river flow rates for hydropower or sunlight for solar panels. These variations affect the overall annual energy output, making the assessment of capacity factor crucial to understand the actual performance versus the theoretical maximum output. By understanding this, stakeholders can make informed decisions about investments, maintenance, and the role of these renewable sources in the wider energy mix.

Energy Conversion Efficiency

Energy conversion efficiency is a measure of how well a power generation system can convert a given source of energy, like the kinetic energy of water in a dam, into useful electrical energy. It's represented as a percentage, indicating the proportion of input energy that is successfully transformed into electrical power. For example, even though the Chief Joseph Dam could potentially generate 2.62 GW of power, the actual energy conversion can be less due to energy losses inherent in the conversion process.

In the context of hydropower, these losses might result from factors such as friction in turbines, electrical resistance, or water flow that isn't captured by the dam. High energy conversion efficiency is desired as it implies more energy is harnessed with less waste. While capacity factor measures the ratio of actual output to potential output over time, energy conversion efficiency examines the instantaneous ability of a power plant to convert energy from its immediate source into electricity.

Annual Energy Output

The annual energy output of a power generation facility like the Chief Joseph Dam is the total amount of electricity it produces over a year. It's important to note that this is different from the maximum potential output, which assumes full capacity operation all year round. The actual output is usually less than the maximum due to variations in natural energy sources and other operational factors.

Using the provided example, the average annual output of the dam is 10.7 TWh. To understand this in context, we must note that natural factors such as river flow levels play a significant role in the dam's output. Lower river levels will lead to a reduced ability to produce electricity. This output is a crucial gauge of the dam's contribution to energy supply and helps in planning for energy needs and assessing renewable energy targets. With the calculated capacity factor of approximately 46.8%, we learn that the dam operates under half its maximum capacity on average across the year, potentially due to environmental variations and facility limitations.