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A 1000 * 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are ________ (upto 2 decimal places).
Correct answer is '3500'. Can you explain this answer?
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A 1000 * 1000 bus admittance matrix for an electric power system has 8...
Number of buses = Number of diagonal elements = 1000
No. of non-zero elements = 8000
No. of non-zero off diagonal elements = 7000
No. of transmission lines
No. of non-zero elements = 8000
No. of non-zero off diagonal elements = 7000
No. of transmission lines
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A 1000 * 1000 bus admittance matrix for an electric power system has 8...
Number of Non-Zero Elements
Given that the 1000 * 1000 bus admittance matrix for the electric power system has 8000 non-zero elements, we need to determine the minimum number of branches (transmission lines and transformers) in the system.
Calculating the Number of Non-Zero Elements
To calculate the number of non-zero elements in the bus admittance matrix, we need to consider that each bus has a self-admittance value. Therefore, the total number of self-admittance elements in the matrix is 1000.
Since we have a total of 8000 non-zero elements, after subtracting the self-admittance elements, we are left with 8000 - 1000 = 7000 elements that represent admittance values between different buses.
Calculating the Number of Branches
To find the minimum number of branches, we can assume that each branch has two ends. Therefore, the total number of branches can be calculated by dividing the number of non-zero elements by 2.
Total Number of Branches = (Number of Non-Zero Elements - Number of Self-Admittance Elements) / 2
Total Number of Branches = (7000) / 2 = 3500
Explanation
The minimum number of branches in the electric power system is 3500. This means that there are 3500 transmission lines and transformers connecting different buses in the system.
In a power system, each branch represents a physical connection between two buses, such as a transmission line or a transformer. The admittance values in the bus admittance matrix represent the electrical characteristics of these branches.
By calculating the number of non-zero elements in the matrix and subtracting the number of self-admittance elements, we obtain the count of admittance values between different buses. Dividing this count by 2 gives us the minimum number of branches in the system.
Therefore, in this particular power system, there are a minimum of 3500 branches connecting the buses.
Given that the 1000 * 1000 bus admittance matrix for the electric power system has 8000 non-zero elements, we need to determine the minimum number of branches (transmission lines and transformers) in the system.
Calculating the Number of Non-Zero Elements
To calculate the number of non-zero elements in the bus admittance matrix, we need to consider that each bus has a self-admittance value. Therefore, the total number of self-admittance elements in the matrix is 1000.
Since we have a total of 8000 non-zero elements, after subtracting the self-admittance elements, we are left with 8000 - 1000 = 7000 elements that represent admittance values between different buses.
Calculating the Number of Branches
To find the minimum number of branches, we can assume that each branch has two ends. Therefore, the total number of branches can be calculated by dividing the number of non-zero elements by 2.
Total Number of Branches = (Number of Non-Zero Elements - Number of Self-Admittance Elements) / 2
Total Number of Branches = (7000) / 2 = 3500
Explanation
The minimum number of branches in the electric power system is 3500. This means that there are 3500 transmission lines and transformers connecting different buses in the system.
In a power system, each branch represents a physical connection between two buses, such as a transmission line or a transformer. The admittance values in the bus admittance matrix represent the electrical characteristics of these branches.
By calculating the number of non-zero elements in the matrix and subtracting the number of self-admittance elements, we obtain the count of admittance values between different buses. Dividing this count by 2 gives us the minimum number of branches in the system.
Therefore, in this particular power system, there are a minimum of 3500 branches connecting the buses.
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A 1000 * 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are ________ (upto 2 decimal places).Correct answer is '3500'. Can you explain this answer?
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