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In a power system with 100 buses, 1 bus is taken as slack bus, 15 buses are P\/ buses and rest are PQ buses. The number of variables to be solved by NR method in polar coordinates is
- a)100
- b)198
- c)200
- d)183
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a power system with 100 buses, 1 bus is taken as slack bus, 15 buse...
Hence, number of variables to be solved by NR method in polar coordinates = 183.
Most Upvoted Answer
In a power system with 100 buses, 1 bus is taken as slack bus, 15 buse...
The Newton-Raphson (NR) method is an iterative numerical technique used to solve power flow equations in power systems. It is commonly applied for solving the power flow problem in polar coordinates.
Given that there are 100 buses in the power system, let's analyze the number of variables involved in the NR method in polar coordinates.
1. Polar Coordinates:
In polar coordinates, each bus is represented by its voltage magnitude (V) and voltage angle (δ). These variables are used to describe the operating conditions of the power system.
2. Slack Bus:
The slack bus is the reference bus in the power system, and its voltage magnitude and angle are typically specified. Since it is the reference, its variables do not need to be solved using the NR method. Therefore, the slack bus contributes 0 variables.
3. PQ Buses:
PQ (P: active power, Q: reactive power) buses are buses where both the active and reactive power injections are specified. These buses have two unknown variables: voltage magnitude and angle. In total, there are 100 - 1 - 15 = 84 PQ buses in the system, contributing 2 * 84 = 168 variables.
4. PV Buses:
PV (P: active power, V: voltage magnitude) buses are buses where the active power injection and voltage magnitude are specified. These buses have one unknown variable: voltage angle. In total, there are 15 PV buses in the system, contributing 15 variables.
5. Total Variables:
The total number of variables to be solved using the NR method in polar coordinates is the sum of variables from PQ and PV buses, excluding the slack bus. Therefore, the total number of variables is 168 + 15 = 183.
Hence, the correct answer is option D) 183.
Given that there are 100 buses in the power system, let's analyze the number of variables involved in the NR method in polar coordinates.
1. Polar Coordinates:
In polar coordinates, each bus is represented by its voltage magnitude (V) and voltage angle (δ). These variables are used to describe the operating conditions of the power system.
2. Slack Bus:
The slack bus is the reference bus in the power system, and its voltage magnitude and angle are typically specified. Since it is the reference, its variables do not need to be solved using the NR method. Therefore, the slack bus contributes 0 variables.
3. PQ Buses:
PQ (P: active power, Q: reactive power) buses are buses where both the active and reactive power injections are specified. These buses have two unknown variables: voltage magnitude and angle. In total, there are 100 - 1 - 15 = 84 PQ buses in the system, contributing 2 * 84 = 168 variables.
4. PV Buses:
PV (P: active power, V: voltage magnitude) buses are buses where the active power injection and voltage magnitude are specified. These buses have one unknown variable: voltage angle. In total, there are 15 PV buses in the system, contributing 15 variables.
5. Total Variables:
The total number of variables to be solved using the NR method in polar coordinates is the sum of variables from PQ and PV buses, excluding the slack bus. Therefore, the total number of variables is 168 + 15 = 183.
Hence, the correct answer is option D) 183.
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