Test: Y Bus Matrix - Electrical Engineering (EE) MCQ

Concept:
When two inductances are connected in parallel and have a mutual effect then equivalent inductance can be calculated with the help of the following formula


First of all, calculate the equivalent reactance of two-line connected between buses 1 and 2


= -j6.45
and 

=-j3.33 pu
∴ Y22 = y12 + y23
= -j6.45 + (-j3.33)
=-j9.78 pu.

Bus Admittance Matrix:

• In a power system, Bus Admittance Matrix represents the nodal admittances of the various buses.
• Admittance matrix is used to analyze the data that is needed in the load or a power flow study of the buses.
• It explains the admittance and the topology of the network.

The following are the advantages of the bus admittance matrix.

• The data preparation of the bus admittance matrix is very simple.
• The formation of the bus admittance matrix and their modification is easy.
• The bus admittance matrix is a sparse matrix as most of the elements are zero and hence the memory require requirement to store the network data is less. Hence it is preferred to develop the equations for load flow studies.
  

For the above figure, the admittance matrix is as shown below.

• Diagonal elements of the Bus Admittance matrix are known as self-admittances and the off-diagonal elements are known as mutual admittances.
• The diagonal element Y_ii is the sum of all the admittances of the elements connected to the i^th bus.
• Y_ii = Σ y_ik , k = 1, 2, …n and k ≠ i
• The off-diagonal element Yij is equal to the minus of the admittance of the element connected between buses i and j.
• Y_ij = -y_ij

Some observations on the admittance matrix:

• Admittance matrix is a sparse matrix
• Diagonal elements are dominating
• Off diagonal elements are symmetric in terms of both position and value with respect to diagonal.
• The diagonal element of each node is the sum of the admittances connected to it
• Off diagonal element is negated admittance

Y bus matrix:

• In a power system, Bus Admittance Matrix represents the nodal admittances of the various buses.
• Admittance matrix is used to analyze the data that is needed in the load or a power flow study of the buses.
• It explains the admittance and the topology of the network.

The following are the advantages of the bus admittance matrix.

1. The data preparation of the bus admittance matrix is very simple.
2. The formation of the bus admittance matrix and its modification is easy.
3. The bus admittance matrix is a sparse matrix thus the computer memory requirement is less.
   

For the above figure, the admittance matrix is as shown below.

For formation of the Y bus matrix (using node voltage analysis) in power system network modelling KCL is used 
​Diagonal elements of the Bus Admittance matrix are known as self-admittances and the off-diagonal elements are known as mutual admittances.
Some observations on the admittance matrix:

• Off diagonal elements are symmetric in terms of both position and value with respect to diagonal.
• The diagonal element of each node is the sum of the admittances connected to it 
• Off diagonal element is negated admittance

Size of YBUS matrix = 1000 × 1000
Number of non-zero elements = 8000.
Number of diagonal elements = number of buses = 1000.
Number of non-zero off diagonal elements = 8000 – 1000 = 7000
Minimum number of branches = 7000/2 = 3500

T - parameter matrix,

Since A ≠ D, the network is asymmetric and hence Ybus and Zbus will also be asymmetric.

Concept:
For a 3 bus power system

For the above figure, the admittance matrix is as shown below.

Diagonal elements of the Bus Admittance matrix are known as self-admittances and the off-diagonal elements are known as mutual admittances.
Calculation:
Given bus admittance matrix of the uncompensated line is

By comparing the above matrix with standard 3 bus matrix
y₁₃ = -j4
y₃₂ = -j5
⇒ y₃₁ + y₃₂ + y₃₃ = -j8
⇒ y₃₃­ = j
After compensating, 
y₃₃ = j/2
Y_33(new) = -8.5 j.

Concept:

• In a power system, Bus Admittance Matrix represents the nodal admittances of the various buses.
• With the help of the transmission line, each bus is connected to various other buses.
• Admittance matrix is used to analyze the data that is needed in the load or a power flow study of the buses.
• It explains the admittance and the topology of the network.

I = [Y] V
Where,
I is the current of the bus in the vector form.
Y is the admittance matrix
V is the vector of the bus voltage.
For an n bus system, the order of admittance bus matrix is n×n.

Let series impedance each line is jy pu

From y_BUS, Y₁₂ = - y₁₂ = j20
⇒ y₁₂ = -j₂₀
From the diagram

⇒ y = j 0.1 pu

In order to solve such questions where the transformer is connected between the bus and you have to calculate the [Y]Bus matrix, then refer the whole circuit to one side with the help of the transformation ratio of the transformer.

Expression of the current is given by:

Above two expressions are written in the matrix form like below.

Bus admittance matrix:

Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios 1 : t_i &1 : t_j.

From the circuit shown above,

From equation (1) and (2), we get,