Two generating stations are operating in parallel at 11KV and are interconnected as shown in figure 3b. They are generating of 10mw. The loads connected to the respective generating stations are 15MW and 25MW at upf’s. Calculate the phase angle between the bus bar when the generating stations are equally loaded.

To determine the phase angle between the bus bar when two generating stations are equally loaded, we need to analyze the power distribution and the relationship between the loads and the generation capacity. Let's break this down step by step.

Understanding the System

We have two generating stations operating in parallel, each at a voltage of 11 kV, and they are generating a total of 10 MW. The loads connected to these stations are 15 MW and 25 MW, respectively. Since the total generation (10 MW) is less than the total load (40 MW), we need to find out how the loads can be balanced and what the phase angle will be when the stations are equally loaded.

Power Distribution

When two generators operate in parallel, they share the load based on their capacity and the impedance of the lines connecting them to the load. The phase angle between the bus bars can be calculated using the formula:

• P = V * I * cos(θ)

Where:

• P = Power (in watts)
• V = Voltage (in volts)
• I = Current (in amperes)
• θ = Phase angle (in degrees)

Calculating the Current

First, we need to calculate the current for each generator. The total power generated is 10 MW, and since they are operating at 11 kV, we can find the current:

• Power (P) = Voltage (V) * Current (I) * Power Factor (cos(θ))
• 10 MW = 11 kV * I * 1 (assuming unity power factor for simplicity)

Rearranging gives:

• I = 10,000 kW / 11 kV = 909.09 A

Load Sharing

Now, we need to determine how the loads are shared between the two generators. If they are equally loaded, each generator will take half of the total load. However, since the total load is 40 MW, and the total generation is only 10 MW, we need to find the effective load each generator will handle.

Let’s denote:

• Load on Generator 1 = L1
• Load on Generator 2 = L2

Given that:

• L1 + L2 = 10 MW

Assuming equal loading, we can say:

• L1 = L2 = 10 MW / 2 = 5 MW

Calculating the Phase Angle

Now, we can calculate the phase angle using the power formula again. For each generator, we can rearrange the formula:

• cos(θ) = P / (V * I)

For Generator 1:

• cos(θ1) = 5 MW / (11 kV * 909.09 A)

Calculating this gives:

• cos(θ1) = 5,000 kW / 10,000 kW = 0.5

Thus, θ1 = cos^-1(0.5) = 60 degrees.

For Generator 2, the calculation is the same since they are equally loaded:

• cos(θ2) = 5 MW / (11 kV * 909.09 A) = 0.5

Thus, θ2 = 60 degrees as well.

Final Thoughts

The phase angle between the bus bars when the generating stations are equally loaded is 60 degrees. This indicates that both generators are synchronized and sharing the load effectively, even though the total generation is less than the total load. In practical scenarios, adjustments would be necessary to ensure stability and efficiency in the power system.