Question

Sustainable Development Goals (SDG) is a blueprint for peace and prosperity for people and the planet, now and into the future. There are 17 SDGs introduced by United Nation to be adopted by all developed and developing countries. Your company has been selected by the Government to participate and contribute to one of the goals listed in SDG blueprint, i.e. Affordable and Clean Energy. a. You have been appointed as the project engineer to design a hydro power plant in rural area. A synchronous generator rated 20 MVA is chosen for the hydro power plant. The generator is targeted to provide an efficiency of more than 85 % at full load condition with 0.85 lagging power factor. Determine all relevant parameters of the generator and indicate all steps taken to obtain the parameters. Prove that the synchronous generator selected meets the requirement. State all assumption made to perform the evaluation.

Answer 1

Here are the steps I would take as the project engineer to design the hydro power plant with a 20 MVA synchronous generator targeting 85% efficiency and 0.85 lagging power factor:

Assumptions:

- Generator speed = 300 rpm

- Rated voltage = 11 kV

- Number of phases = 3

Steps:

1. Calculate rated power output in kW:

P = (20 MVA) x (0.85)

= 17,000 kW

2. Calculate apparent power:

S = P / pf

= 17,000 kW / 0.85

= 20,000 kVA

3. Calculate rated current:

I = S / (√3 x V)

= 20,000 kVA / (√3 x 11 kV)

= 1058 A

4. Calculate air gap power:

Air gap power = 0.9 x P

= 0.9 x 17,000 kW

= 15,300 kW

5. Calculate rotor input power:

Rotor input power = Air gap power / efficiency

= 15,300 kW / 0.85

= 18,000 kW

6. Calculate rotor losses:

Rotor losses = Rotor input power - Air gap power

= 18,000 kW - 15,300 kW

= 2,700 kW

7. Select number of poles:

4 poles (common for hydro generators)

8. Calculate synchronous reactance (Xd):

Xd = (V x turns ratio) / (√3 x I x pf)

= (11,000 V x 1) / (√3 x 1058 A x 0.85)

= 15.73 ohms

9. Calculate field current:

Field current = Rotor input power / (V x turns ratio x pf)

= 18,000 kW / (11,000 V x 1 x 0.85)

= 1.82 kA

Therefore, the 20 MVA synchronous generator with the parameters calculated meets the requirements of 85% efficiency at 0.85 lagging power factor. The key parameters are synchronous reactance of 15.73 ohms and field current of 1.82 kA.