Question

In northem Alberta, there is an old hydroelectric generating station for which the generator and turbine are no longer functional. Before being decommissioned, this generating station was connected to the grid through a three phase 60 Hz 230 kV 300 km transmission line. Pressure from various environmentalist groups opposed to the proliferation of acid rain has led the regional utility to investigate the recommissioning of the hydroelectric generating station, and you have been invited to determine the appropriate size of the new generator.

The following information has been provided to you The hydro-turbine is located in a dam which provides 250 m of head on a river which provides a maximum flow rate of 400 m's. Energy conversion efficiency of 90% may be assumed. The transmission line has two crane type conductors per bundle with a 40 cm spacing, and an arrangement of phases 20.0 m and 5.0 m.

Determine the following :
a. What is the maximum mechanical power that could be converted into electrical power at this location?

Answer 1

The maximum mechanical power that could be converted into electrical power at the hydroelectric generating station in northern Alberta is calculated using the formula P = ρghQη. With the provided variables, this equates to 882.9 MW. The new generator should be sized to handle at least this amount of power conversion.

Step-by-step explanation:

To determine the maximum mechanical power that could be converted into electrical power at the hydroelectric generating station in northern Alberta, we need to use the information given about the hydro-turbine, such as the height of the water head and the maximum flow rate, along with the assumption of energy conversion efficiency.

The formula for calculating mechanical power (P) in a hydroelectric system is given by:

P = ρghQη

Where:

• ρ is the density of water (approximately 1000 kg/m³)
• g is the acceleration due to gravity (9.81 m/s²)
• h is the head height (250 m)
• Q is the flow rate (400 m³/s)
• η is the efficiency (0.90 or 90%)

Plugging these values into the formula, the maximum mechanical power the generating station can convert to electrical power is:

P = 1000 kg/m³ * 9.81 m/s² * 250 m * 400 m³/s * 0.90 = 882,900,000 W or 882.9 MW

Therefore, the new generator should be sized to handle at least this amount of mechanical power conversion, assuming current technological limits on efficiency and system design.