A hybrid microgrid facility generates power using Solar Arrays and Wind Turbines to supply… — GMAT

A hybrid microgrid facility generates power using Solar Arrays and Wind Turbines to supply a regional grid.

- Solar Arrays generate electricity at a constant rate of $S$ megawatts per hour (MW/h), and $15\%$ of the generated solar energy is lost during battery storage transfer.
- Wind Turbines generate electricity at a constant rate of $W$ megawatts per hour (MW/h), and $10\%$ of the generated wind energy is lost during battery storage transfer.

During a continuous 10-hour operating period, both sources operate simultaneously. The total usable energy delivered to the battery storage after accounting for transfer losses is $435$ megawatt-hours (MWh). Furthermore, the ratio of raw solar energy generated to raw wind energy generated during this 10-hour period is $3 : 2$ .

Based on this information, which of the following correctly identifies the generation rates $S$ and $W$ , in MW/h, for the Solar Arrays and Wind Turbines, respectively?

Solar Rate ( $S$ ) = 30 MW/h; Wind Rate ( $W$ ) = 20 MW/hCevap
B
Solar Rate ( $S$ ) = 20 MW/h; Wind Rate ( $W$ ) = 30 MW/h
C
Solar Rate ( $S$ ) = 27 MW/h; Wind Rate ( $W$ ) = 18 MW/h
D
Solar Rate ( $S$ ) = 300 MW/h; Wind Rate ( $W$ ) = 200 MW/h
E
Solar Rate ( $S$ ) = 36 MW/h; Wind Rate ( $W$ ) = 24 MW/h

Cevap

Solar Rate (S) = 30 MW/h; Wind Rate (W) = 20 MW/h

The option specifying Solar Rate (

S

) = 30 MW/h and Wind Rate (

W

) = 20 MW/h is correct because over 10 hours, raw generation totals are

300

MWh for solar and

200

MWh for wind, satisfying the

3 : 2

ratio. Applying the respective

85\%

and

90\%

storage efficiencies gives

300 \times 0.85 = 255

MWh and

200 \times 0.90 = 180

MWh. The combined usable energy is

255 + 180 = 435

MWh, perfectly matching all given constraints.

Adım Adım Çözüm

Formulate the ratio equation for raw generation rates.

Since raw solar generation is to raw wind generation as

3 : 2

over the same 10-hour duration,

\frac{10S}{10W} = \frac{3}{2} \implies S = 1.5W

Establishes the proportional relationship between the solar and wind rates.

Express usable energy accounting for efficiency loss.

Solar efficiency is

100\% - 15\% = 85\%

(

0.85

). Wind efficiency is

100\% - 10\% = 90\%

(

0.90

). Total usable energy stored in 10 hours is

10(0.85S) + 10(0.90W) = 8.5S + 9W = 435

Translates loss percentages into usable energy multipliers over the 10-hour period.

Substitute

S = 1.5W

into the usable energy equation and solve for

W

and

S

8.5(1.5W) + 9W = 435 \implies 12.75W + 9W = 435 \implies 21.75W = 435 \implies W = 20

MW/h. Consequently,

S = 1.5(20) = 30

MW/h.

Calculates the exact hourly rates for both energy sources.

Anahtar Kavram

Simultaneous Rate and Efficiency Equations in Two-Part Analysis

Tahmini Süre:2m 0s

Soru

Cevap

Adım Adım Çözüm

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