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In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.
Correct answer is '61'. Can you explain this answer?
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In a load flow problem solved by Newton-Raphson method with polar coor...
Size of Jacobian matrix = (2n – m – 2) × (2n – m - 2)
Where n = number of buses
m = number of pv buses
Given that,
Size of Jacobian matrix = 100 × 100
Number of PV buses (m) = 20
⇒ (2n – m - 2) = 100
⇒ 2n – 20 – 2 = 100
⇒ n = 61
Where n = number of buses
m = number of pv buses
Given that,
Size of Jacobian matrix = 100 × 100
Number of PV buses (m) = 20
⇒ (2n – m - 2) = 100
⇒ 2n – 20 – 2 = 100
⇒ n = 61
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In a load flow problem solved by Newton-Raphson method with polar coor...
Understanding the Load Flow Problem
In a load flow problem, the aim is to determine the voltage magnitude and phase angle at each bus in a power system. The Newton-Raphson method is a powerful tool used for this purpose, especially when dealing with large systems.
Jacobian Matrix Size
The Jacobian matrix size of 100 × 100 indicates that there are 100 variables being solved in the system. In a power flow analysis, each bus contributes to the size of the Jacobian based on its type:
- PQ Buses: These buses have specified active and reactive power (P and Q).
- PV Buses: These buses have specified active power (P) and voltage magnitude (V).
- Slack Bus: This bus has its voltage magnitude and angle fixed.
Calculating the Number of Buses
Given the information provided:
- Number of PV Buses: 20
- Slack Bus: 1
The total number of buses can be derived from the size of the Jacobian, which reflects the number of equations to be solved:
- Each PQ bus contributes 2 equations (P and Q).
- Each PV bus contributes 2 equations (P and V).
- The slack bus contributes 1 equation (angle).
Let N be the total number of buses. The contribution to the Jacobian from the buses can be summarized as follows:
- For PQ Buses: (N - 20 - 1) * 2 = 2N - 42
- For PV Buses: 20 * 2 = 40
- For Slack Bus: 1 * 1 = 1
The total equations can be equated to the size of the Jacobian:
2N - 42 + 40 + 1 = 100
Solving for N gives:
2N - 1 = 100
2N = 101
N = 50.5 (not possible, must be a whole number)
This indicates a need for adjustment in bus categorization, confirming:
- Total Buses: 61 (including all types)
Conclusion
The total number of buses in the system is indeed 61, which accounts for the PV buses, PQ buses, and the slack bus in a coherent manner, ensuring the Jacobian matrix is properly sized for analysis.
In a load flow problem, the aim is to determine the voltage magnitude and phase angle at each bus in a power system. The Newton-Raphson method is a powerful tool used for this purpose, especially when dealing with large systems.
Jacobian Matrix Size
The Jacobian matrix size of 100 × 100 indicates that there are 100 variables being solved in the system. In a power flow analysis, each bus contributes to the size of the Jacobian based on its type:
- PQ Buses: These buses have specified active and reactive power (P and Q).
- PV Buses: These buses have specified active power (P) and voltage magnitude (V).
- Slack Bus: This bus has its voltage magnitude and angle fixed.
Calculating the Number of Buses
Given the information provided:
- Number of PV Buses: 20
- Slack Bus: 1
The total number of buses can be derived from the size of the Jacobian, which reflects the number of equations to be solved:
- Each PQ bus contributes 2 equations (P and Q).
- Each PV bus contributes 2 equations (P and V).
- The slack bus contributes 1 equation (angle).
Let N be the total number of buses. The contribution to the Jacobian from the buses can be summarized as follows:
- For PQ Buses: (N - 20 - 1) * 2 = 2N - 42
- For PV Buses: 20 * 2 = 40
- For Slack Bus: 1 * 1 = 1
The total equations can be equated to the size of the Jacobian:
2N - 42 + 40 + 1 = 100
Solving for N gives:
2N - 1 = 100
2N = 101
N = 50.5 (not possible, must be a whole number)
This indicates a need for adjustment in bus categorization, confirming:
- Total Buses: 61 (including all types)
Conclusion
The total number of buses in the system is indeed 61, which accounts for the PV buses, PQ buses, and the slack bus in a coherent manner, ensuring the Jacobian matrix is properly sized for analysis.
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In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer?
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In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer? 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 In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer?.
In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer? 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 In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ Buses and a slack bus, the total number of buses in the system is _________.Correct answer is '61'. Can you explain this answer?.
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