Find the maximum power of power plant

[fozia.jehan]

Homework Statement

The daily load demand of a grid is given by P=P_max * cos(pi*t/24). Here -12hrs ≤ t ≤ 12hrs. Maximum power occurs at (t=0) and minimum occurs at (t= ±12). A 10 GW hydro power plant with pump storage is available for base load operation. The turn-around efficiency of the storage system is 0.7. Find the peak load.

Homework Equations

The Attempt at a Solution

I found the average power in terms of P_max which comes out to be: P_avg=2*P_max/pi. but now I couldn't figure out how to proceed. Any help will be greatly appreciated.

 

[KataKoniK]

I can help you solve this problem by providing some insights and guiding you through the steps to find the peak load. Let's break down the problem into smaller parts and tackle them one by one.

First, let's understand the given equation for the daily load demand of the grid. The equation is P = Pmax * cos(pi*t/24), where P is the power demand, Pmax is the maximum power, and t is the time in hours. We can see that the power demand is a function of time and it varies sinusoidally with a period of 24 hours.

Next, we are told that a 10 GW hydro power plant with pump storage is available for base load operation. This means that the power plant can produce a constant power output of 10 GW throughout the day. However, the turn-around efficiency of the storage system is 0.7, which means that only 70% of the stored energy can be converted back to electricity. This information will be useful in finding the peak load.

To find the peak load, we need to find the maximum power demand during the day. From the given equation, we know that the maximum power occurs at t=0 and the minimum power occurs at t= ±12. This means that the peak load will be either at t=0 or t= ±12. We can calculate the power demand at these times using the given equation.

At t=0, P = Pmax * cos(pi*0/24) = Pmax * cos(0) = Pmax
At t=±12, P = Pmax * cos(pi*±12/24) = Pmax * cos(±pi/2) = 0

We can see that the maximum power demand occurs at t=0, which means that the peak load is Pmax. However, we need to take into consideration the 10 GW hydro power plant with pump storage. Since the turn-around efficiency is 0.7, only 70% of the stored energy can be converted back to electricity. This means that the peak load will be 70% of Pmax.

Therefore, the peak load is 0.7 * Pmax = 0.7 * 2*Pmax/pi = 1.4*Pmax/pi.

In conclusion, the peak load is 1.4*Pmax/pi, where Pmax is the maximum power demand given by the equation P