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A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.
Correct answer is between '14,14'. Can you explain this answer?
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Verified Answer
A 10-bus power system consists of four generator buses indexed as G1, ...
Total no of buses=10
Given G1=slack bus, G2=generator/PQ bus
G3 , G4 are PV buses
PQ buses→ L1 , L2 , L5 , L5 (4)
Voltage controlled PV buses → L3 , L4 (2)
Minimum no of nonlinear equations to be solved =
Given G1=slack bus, G2=generator/PQ bus
G3 , G4 are PV buses
PQ buses→ L1 , L2 , L5 , L5 (4)
Voltage controlled PV buses → L3 , L4 (2)
Minimum no of nonlinear equations to be solved =
Most Upvoted Answer
A 10-bus power system consists of four generator buses indexed as G1, ...
The Newton-Raphson method is a widely used algorithm for solving the load flow problem in power systems. In this method, the power system is represented as a set of non-linear equations that need to be solved iteratively to obtain the voltage magnitude and phase angle at each bus.
To apply the Newton-Raphson method, we need to determine the number of unknown variables and the number of non-linear equations in the power system.
Number of unknown variables:
In a 10-bus power system, each bus has two unknown variables - the voltage magnitude (V) and the phase angle (θ). Since there are 10 buses in total, the number of unknown variables is 10 * 2 = 20.
Number of non-linear equations:
The number of non-linear equations can be determined based on the characteristics of each bus in the system.
1. Slack bus (G1):
The slack bus is the reference bus and its voltage magnitude and phase angle are known. Therefore, it does not contribute to the number of non-linear equations.
2. Voltage controlled buses (L3 and L4):
The voltage magnitude at these buses is specified, but the phase angle is unknown. Hence, each voltage controlled bus contributes 1 non-linear equation.
3. Generator buses (G2, G3, G4):
The generator at bus G2 is operating at its maximum reactive power limit, which means it cannot supply any more reactive power. This condition can be represented by a non-linear equation. Similarly, the generator at buses G3 and G4 also have their own reactive power limits, so they each contribute 1 non-linear equation.
4. Load buses (L1, L2, L5, L6):
The load at these buses requires both active and reactive power, which are dependent on the voltage magnitude and phase angle. Therefore, each load bus contributes 2 non-linear equations.
Summing up the contributions from each type of bus, we have:
Slack bus: 0 non-linear equations
Voltage controlled buses: 2 non-linear equations
Generator buses: 3 non-linear equations
Load buses: 4 non-linear equations
Therefore, the total number of non-linear equations required for solving the load flow problem using the Newton-Raphson method in polar form is 2 + 3 + 4 = 9.
However, it is worth noting that the Newton-Raphson method requires an additional equation to ensure mass balance, which is the sum of active power injections equal to the sum of active power consumed by the loads. Therefore, the total number of non-linear equations is 9 + 1 = 10.
Hence, the correct answer is between 10, 10.
To apply the Newton-Raphson method, we need to determine the number of unknown variables and the number of non-linear equations in the power system.
Number of unknown variables:
In a 10-bus power system, each bus has two unknown variables - the voltage magnitude (V) and the phase angle (θ). Since there are 10 buses in total, the number of unknown variables is 10 * 2 = 20.
Number of non-linear equations:
The number of non-linear equations can be determined based on the characteristics of each bus in the system.
1. Slack bus (G1):
The slack bus is the reference bus and its voltage magnitude and phase angle are known. Therefore, it does not contribute to the number of non-linear equations.
2. Voltage controlled buses (L3 and L4):
The voltage magnitude at these buses is specified, but the phase angle is unknown. Hence, each voltage controlled bus contributes 1 non-linear equation.
3. Generator buses (G2, G3, G4):
The generator at bus G2 is operating at its maximum reactive power limit, which means it cannot supply any more reactive power. This condition can be represented by a non-linear equation. Similarly, the generator at buses G3 and G4 also have their own reactive power limits, so they each contribute 1 non-linear equation.
4. Load buses (L1, L2, L5, L6):
The load at these buses requires both active and reactive power, which are dependent on the voltage magnitude and phase angle. Therefore, each load bus contributes 2 non-linear equations.
Summing up the contributions from each type of bus, we have:
Slack bus: 0 non-linear equations
Voltage controlled buses: 2 non-linear equations
Generator buses: 3 non-linear equations
Load buses: 4 non-linear equations
Therefore, the total number of non-linear equations required for solving the load flow problem using the Newton-Raphson method in polar form is 2 + 3 + 4 = 9.
However, it is worth noting that the Newton-Raphson method requires an additional equation to ensure mass balance, which is the sum of active power injections equal to the sum of active power consumed by the loads. Therefore, the total number of non-linear equations is 9 + 1 = 10.
Hence, the correct answer is between 10, 10.
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A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer?
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A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer?.
A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.Correct answer is between '14,14'. Can you explain this answer?.
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