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A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.?
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A power system consisting of two generating plants with fuel costs of ...
Problem Statement: Find the penalty factor of plant 1 in a power system consisting of two generating plants with fuel costs of C₁ = 0.05P²G1 + 20 PG1 + 1.5 and C₂ = 0.075 P²G2 + 22.5 PG2 + 1.6. The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2.
Solution:
Economical dispatch is a method used to determine the optimal power output of each generating unit in a power system, in order to meet the load demand at the lowest operating cost. The objective is to minimize the total fuel cost of the system, while satisfying the load demand and other constraints.
The incremental cost of a generating unit is the cost of producing an additional unit of power, and is given by the derivative of the cost function with respect to the power output. The incremental cost of each unit is equal at the optimal dispatch point, where the system cost is minimized.
Step 1: Calculate the incremental cost of each unit at 100 MW output.
Incremental cost of plant 1:
C₁' = dC₁/dP₁ = 0.1P₁ + 20
At 100 MW output, C₁' = 10,020 Rs/MW
Incremental cost of plant 2:
C₂' = dC₂/dP₂ = 0.15P₂ + 22.5
At 100 MW output, C₂' = 15,022.5 Rs/MW
Step 2: Calculate the incremental transmission loss of each unit.
Incremental loss of plant 1:
ΔL₁ = 0
Incremental loss of plant 2:
ΔL₂ = 0.2
Step 3: Calculate the penalty factor of each unit.
Penalty factor of plant 1:
PF₁ = ΔL₂ / (C₂' - C₁') = 0.2 / (15,022.5 - 10,020) = 0.00003339 Rs/MW²
Penalty factor of plant 2:
PF₂ = ΔL₁ / (C₁' - C₂') = 0 / (10,020 - 15,022.5) = 0
Conclusion: The penalty factor of plant 1 in the given power system is 0.00003339 Rs/MW². The penalty factor represents the cost of incremental transmission loss that is attributed to each unit, and is used to allocate the cost of transmission losses among the generating units. In this case, plant 1 has a lower incremental cost than plant 2, but it incurs a higher penalty factor due to the transmission losses caused by plant 2.
Solution:
Economical dispatch is a method used to determine the optimal power output of each generating unit in a power system, in order to meet the load demand at the lowest operating cost. The objective is to minimize the total fuel cost of the system, while satisfying the load demand and other constraints.
The incremental cost of a generating unit is the cost of producing an additional unit of power, and is given by the derivative of the cost function with respect to the power output. The incremental cost of each unit is equal at the optimal dispatch point, where the system cost is minimized.
Step 1: Calculate the incremental cost of each unit at 100 MW output.
Incremental cost of plant 1:
C₁' = dC₁/dP₁ = 0.1P₁ + 20
At 100 MW output, C₁' = 10,020 Rs/MW
Incremental cost of plant 2:
C₂' = dC₂/dP₂ = 0.15P₂ + 22.5
At 100 MW output, C₂' = 15,022.5 Rs/MW
Step 2: Calculate the incremental transmission loss of each unit.
Incremental loss of plant 1:
ΔL₁ = 0
Incremental loss of plant 2:
ΔL₂ = 0.2
Step 3: Calculate the penalty factor of each unit.
Penalty factor of plant 1:
PF₁ = ΔL₂ / (C₂' - C₁') = 0.2 / (15,022.5 - 10,020) = 0.00003339 Rs/MW²
Penalty factor of plant 2:
PF₂ = ΔL₁ / (C₁' - C₂') = 0 / (10,020 - 15,022.5) = 0
Conclusion: The penalty factor of plant 1 in the given power system is 0.00003339 Rs/MW². The penalty factor represents the cost of incremental transmission loss that is attributed to each unit, and is used to allocate the cost of transmission losses among the generating units. In this case, plant 1 has a lower incremental cost than plant 2, but it incurs a higher penalty factor due to the transmission losses caused by plant 2.
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A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.?
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A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.?.
A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A power system consisting of two generating plants with fuel costs of C₁ = 0.05P2G1 20 PG1 1.5 and C₂ = 0.075 P² G2 22.5 PG2 1.6 The system is operating on economical dispatch with 100 MW to power generation by each plant. The incremental transmission loss of plant 2 is 0.2. Find the penalty factor of plant 1.?.
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