Question

Frequency Modeling Assume a system with the following parameters: Pmax = 90 GW, H = 6 sec, D = 0.3, fnom. = 60 Hz, fsp 60 Hz, Droop = 0.04, and G = 0.3. This system is producing 70 GW of power when load is suddenly increased to 73 GW. = a) Plot PR, PGov. and f vs. time for 50 seconds after the change.

Answer 1

After a sudden increase in load from 70 GW to 73 GW, the plot of power reference (PR), governor power (PGov), and frequency (f) versus time for the 50 seconds following the change indicates a transient response.

Step-by-step explanation:

In a power system, the frequency deviation is a critical parameter reflecting the balance between generation and load. The frequency response can be modeled using the swing equation, which is expressed as ΔP = ΔPR - ΔPGov, where ΔP is the change in mechanical power, ΔPR is the change in power reference, and ΔPGov is the change in governor power. The governor equation relates ΔPGov to the frequency deviation, and the system parameters provided help characterize this response.

Given the sudden load increase, the governor responds by adjusting the power output to maintain system stability. The plot of PR, PGov, and f over time illustrates the dynamic nature of these adjustments. The droop parameter (Droop) and system gain (G) play crucial roles in determining how quickly and effectively the system responds to changes in load. The transient response, characterized by deviations in frequency and power outputs, gradually stabilizes over the 50-second period, demonstrating the system's ability to regulate power generation and maintain nominal frequency in the face of disturbances.

In summary, the graphical representation of PR, PGov, and f over the 50 seconds following the load change provides insights into the transient behavior of the power system. The interplay of parameters such as Pmax, H, D, fnom., fsp, Droop, and G influences the dynamic response, showcasing the system's resilience in adapting to sudden changes in load demand.

Answer 2

To plot PR, PGov, and f vs. time after the load change, we can use the given parameters. The system has a maximum power, governor time constant, droop coefficient, nominal frequency, steady-state frequency, and gain. The equations for PR, PGov, and f can be used to plot the values over time.

Step-by-step explanation:

To plot PR, PGov, and f vs. time after the load change, we can use the given parameters. The system has a maximum power of 90 GW (Pmax), a governor time constant of 6 sec (H), a droop coefficient of 0.04 (D), a nominal frequency of 60 Hz (fnom), a steady-state frequency of 60 Hz (fsp), and a gain of 0.3 (G).

To plot PR, we need to calculate the power difference between the system's power output and the power consumed by the load. PR = Pmax - PGov, where PGov is the power output regulated by the governor. To plot PGov, we can use the droop equation: PGov = Pmax - D * (fnom - f), where f is the instantaneous frequency.

To plot f, we can use the frequency deviation equation: f = fsp + (G/H) * (PR - Pmax). Substituting the values into the equations, we can plot PR, PGov, and f vs. time for 50 seconds after the load change.