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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 WW plant 1.?
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A power system consisting of two generating plants with fuel costs of ...
Problem Statement
A power system has two generating plants with fuel costs of C₁ = 0.05P²G₁ + 20PG₁ + 1.5 and C₂ = 0.075P²G₂ + 22.5PG₂ + 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 WW plant 1.
Solution
Step 1: Calculation of Total Cost
To calculate the penalty factor of plant 1, we need to calculate the total cost of the power system. The total cost of the power system can be calculated as follows:
Total Cost = C₁(PG₁) + C₂(PG₂) + Loss
Where Loss = Incremental Transmission Loss of Plant 2 x (PG₁ + PG₂)
Substituting the given values in the above equation, we get:
Total Cost = (0.05P²G₁ + 20PG₁ + 1.5)(100) + (0.075P²G₂ + 22.5PG₂ + 1.6)(100) + 0.2(PG₁ + PG₂)
Simplifying the above equation, we get:
Total Cost = 0.05P²G₁ + 20PG₁ + 1.5 + 0.075P²G₂ + 22.5PG₂ + 1.6 + 0.2PG₁ + 0.2PG₂
Total Cost = 0.05P²G₁ + 20.2PG₁ + 0.075P²G₂ + 22.7PG₂ + 0.2(PG₁ + PG₂) + 1.5 + 1.6
Total Cost = 0.05P²G₁ + 20.2PG₁ + 0.075P²G₂ + 22.7PG₂ + 0.2(PG₁ + PG₂) + 3.1
Step 2: Calculation of Penalty Factor of Plant 1
To calculate the penalty factor of plant 1, we need to differentiate the total cost with respect to PG₁ and set it to zero. The penalty factor of plant 1 can be calculated as follows:
d(Total Cost)/d(PG₁) = 0.1PG₁ + 0.2 - 0.2(Incremental Transmission Loss of Plant 2) = 0
Substituting the given values in the above equation, we get:
0.1PG₁ + 0.2 - 0.2(0.2) = 0
Simplifying the above equation, we get:
0.1PG₁ = 0.16
PG₁ = 1.6
Therefore, the penalty factor of plant 1 is 0.1/PG₁ = 0.1/1.6 = 0.0625.
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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 WW 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 WW plant 1.? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) 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 WW plant 1.? covers all topics & solutions for Electrical Engineering (EE) 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 WW 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 WW plant 1.? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) 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 WW plant 1.? covers all topics & solutions for Electrical Engineering (EE) 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 WW plant 1.?.
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