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In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 x 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...
Given the size of bus is 100*100.
so [J]= 100
we have formula for [J] = [2n-m-2] 100= [2n-20-2]
total no.of buses ,n = 61
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In a load flow problem solved by Newton-Raphson method with polar coor...
Explanation:
Newton-Raphson method:
- Newton-Raphson method is an iterative numerical technique used to solve nonlinear equations.
- It is widely used in power system analysis for solving load flow problems.
- The method requires the calculation of the Jacobian matrix, which is a square matrix with the size equal to the number of buses in the system.
Polar coordinates:
- In load flow analysis, the bus voltage magnitude and angle are represented in polar coordinates.
- The Newton-Raphson method with polar coordinates involves the calculation of partial derivatives of power injections with respect to voltage magnitudes and angles.
Jacobian matrix size:
- The size of the Jacobian matrix in a load flow problem solved by the Newton-Raphson method with polar coordinates is equal to the number of buses in the system.
- In this question, the size of the Jacobian matrix is given as 100 x 100.
PV buses:
- PV buses are buses in the power system with a specified voltage magnitude and a variable active power injection.
- In load flow analysis, the voltage magnitude of PV buses is specified, and the active power injection is determined by the Newton-Raphson method.
- The number of PV buses in the system is given as 20.
Total number of buses:
- The total number of buses in the system can be determined by adding the number of PV buses, PQ buses, and the slack bus.
- The slack bus is the reference bus with a specified voltage magnitude and angle.
- Since the size of the Jacobian matrix is 100 x 100, the total number of buses in the system is 100.
- Subtracting the 20 PV buses from 100 gives the number of PQ buses and the slack bus, which is 80.
- Adding the slack bus gives a total of 81 buses in the system.
Answer:
The total number of buses in the system is 61.
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In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 x 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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