An Interconnected 50 Hz Power System Consists Of One Area

An Interconnected 50 Hz Power System Consists Of One Area With Three T

An interconnected 50 Hz power system consists of one area with three turbine-generator units rated 1000 MVA, 750 MVA, and 500 MVA, respectively. The droop of each unit is 5% based on its own rating. Initially, each unit operates at half its own rating. The system load suddenly increases by 200 MW. Determine (a) the per unit area frequency response characteristic on a 1000 MVA system base, (b) the steady state drop in area frequency, and (c) the increase in turbine mechanical power output of each unit. Assume that the reference power setting of each turbine-generator remains constant. Neglect losses and the dependence of load on frequency.

Paper For Above instruction

The stability and response characteristics of interconnected power systems are critical for ensuring reliable operation amid fluctuations in load demand. This paper analyzes a simplified scenario involving a single area interconnected power system with three turbine-generator units. The units are rated at 1000 MVA, 750 MVA, and 500 MVA, with all units initially operating at half their respective ratings. A sudden increase in system load of 200 MW challenges the frequency stability, necessitating a detailed examination of the frequency response characteristics, steady-state frequency decline, and the subsequent increase in turbine mechanical power output for each generator.

System Configuration and Initial Conditions

The system comprises three turbine-generators with ratings of 1000 MVA, 750 MVA, and 500 MVA. The droop characteristic for each unit is 5%, based on its own rating. Operating initially at half capacity, the initial power output for each unit can be established as follows:

  • Unit 1: 500 MW
  • Unit 2: 375 MW
  • Unit 3: 250 MW

The total initial power is 1125 MW, with the area operating at nominal frequency 50 Hz. When an influx load of 200 MW occurs suddenly, the power balance is disturbed, and frequency responses are triggered to restore equilibrium.

Frequency Response Characteristic (a)

The frequency response of the power system can be described using the droop characteristic. The droop coefficient (R) relates the change in power output of each generator to the change in frequency:

R = (percentage droop) / (system base power) = 0.05 / 1000 MVA = 0.00005 per unit Hz

This indicates that for a 1 Hz change, each generator's power output adjusts by 0.00005 times its rated power in per unit. Since initially, each is operating at half, the initial power in MW for each based on rating is:

  • Unit 1: 500 MW
  • Unit 2: 375 MW
  • Unit 3: 250 MW

A total of 1125 MW initially. Upon the load increase of 200 MW, the total load becomes 1325 MW. Assuming the reference power remains constant and neglecting losses, the change in power output for each generator to accommodate this load increase is proportionate to their droop characteristics.

The per unit change in frequency (Δf) is derived from the aggregate droop effect. Since the power increase is shared among the generators according to their droop sensitivities, the total system frequency change is:

Δf = ΔP / (Sum of all droops in MW per Hz)

Where ΔP = 200 MW, and the total droop sensitivity (in MW/Hz) is computed as the sum of individual droops:

Total droop = For each unit, droop coefficient in MW/Hz can be calculated as:

  • Unit 1: R1 = 0.05 × 1000 = 50 MW/Hz
  • Unit 2: R2 = 0.05 × 750 = 37.5 MW/Hz
  • Unit 3: R3 = 0.05 × 500 = 25 MW/Hz

Total droop sensitivity:

R_total = 50 + 37.5 + 25 = 112.5 MW/Hz

Thus, the initial frequency change due to the load increase is:

Δf = 200 MW / 112.5 MW/Hz ≈ 1.7778 Hz

However, since the initial frequency is 50 Hz, the new steady-state frequency becomes:

f_ss = 50 Hz - Δf ≈ 50 - 1.7778 ≈ 48.2222 Hz

Expressed as a per unit change relative to 50 Hz:

Δf_pu = Δf / 50 ≈ 0.03555 per unit

The per unit area frequency response characteristic, therefore, describes how much power change results from a unit change in frequency, expressed as:

K_f = 1 / R_total = 1 / 112.5 MW/Hz ≈ 0.00889 Hz/MW

In per unit terms, on a 1000 MVA basis, this is:

K_f_pu = 1 / (R_total / system base power) = 1 / (112.5 / 1000) = 8.89 per unit Hz

Therefore, the area has a frequency response characteristic of approximately 8.89 per unit Hz, indicating the system's sensitivity to frequency deviations per MW change relative to a 1000 MVA system base.

Steady State Frequency Drop (b)

The steady-state frequency deviation is primarily determined by the total load change and the aggregate droop response. As calculated, the frequency drops from 50 Hz to approximately 48.2222 Hz; thus, the steady-state frequency will stabilize at this new value, indicating a frequency deviation of approximately 1.7778 Hz or 3.56% of the original frequency.

Increase in Turbine Mechanical Power Output (c)

Post-event, each generator increases its mechanical power output to compensate for the increased load, according to its droop and initial operating point.

The power increase ΔP_i for each unit is:

  • Unit 1: ΔP_1 = R1 × Δf = 50 MW/Hz × 1.7778 Hz ≈ 88.89 MW
  • Unit 2: ΔP_2 = R2 × Δf = 37.5 MW/Hz × 1.7778 Hz ≈ 66.67 MW
  • Unit 3: ΔP_3 = R3 × Δf = 25 MW/Hz × 1.7778 Hz ≈ 44.44 MW

Adding these to the initial power outputs, the new steady-state mechanical power outputs become:

  • Unit 1: 500 MW + 88.89 MW ≈ 588.89 MW
  • Unit 2: 375 MW + 66.67 MW ≈ 441.67 MW
  • Unit 3: 250 MW + 44.44 MW ≈ 294.44 MW

These adjustments demonstrate the dynamic response and capacity of each generator to maintain system stability after a sudden load increase.

Conclusion

This analysis underscores the importance of droop characteristics in power system stability. The system's frequency response characteristic provides a quantitative measure of how sensitive the interconnected system is to load disturbances. The steady-state frequency drop signifies the need for precise control settings to balance reliability and power quality, while the individual turbine responses highlight the roles of different units in restoring equilibrium after disturbances. As power systems evolve with increasing renewable integration and variable loads, understanding these fundamental responses remains crucial for designing resilient and adaptive energy networks.

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