Thursday, 28 November 2019

Y Bus : Load Flow (Bus Admittance Matrix) Step By Step Formation

Y Bus : Load Flow (Bus Admittance Matrix) Step By Step Formation


Y Bus : Load Flow Formation Examples ,Y Bus to Z Bus Conversion, Property Of y bus matrix , Methods Of y bus Formation , Y Bus Admittance Matrix Solved Problems , y bus Calculator , Y Bus Formation Using Singular Transformation



Here We will discuss about Y bus Which Has Known As Many More Names Like , Y Matrix, Y Bus, Bus Admittance Matrix And Nodal Admittance Matrix.


First Of All We Have To Know What Is Y Bus In Power System.

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What Is Y Bus In Power System ?


The Y bus is often used in solving load flow problems. 

It has earned widespread applications due to its simplicity in data preparation, ease of formation and modification for network changes. 

Due to its sparsity it heavily reduces computer memory and time requirements.

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Formation of Y Bus (Bus Admittance Matrix)


Here, S1, S2, S3 are  power injections into bus 1, 2, 3.


y12, y23, y13 are line admittances between lines 1-2, 2-3, 1-3

y01sh/2, y02sh/2, y03sh/2 are half-line charging admittance between lines 1-2, 1-3 and 2-3

The half-line charging admittances connected to the same bus are at same potential and thus can be combined into one

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation
Y Bus : Load Flow (Bus Admittance Matrix) Step By Step Formation

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation


At bus 1, If we apply KCL ,



Where, V1, V2, V3 are voltage values at bus 1, 2, 3 respectively



Where,



Similarly by applying KCL at buses 2 and 3 we can derive the values of I2 and I3

Finally,





Y Bus Formation Example 

1) The impedance diagram shown below, convert all impedances to admittance and draw the admittance diagram. 

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation


Solution :

The Admittance Diagram :

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation

Applying To Each Bus :

Bus1 , Bus 2, Bus 3, Bus 4 Respectively,

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation

Rearranging The Equations :

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation

Introducing The Following Admittance :


Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation
So, The Equations Are :

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation

As We Can See In this example, since there is no connection between bus 1 and 4, Y14 = Y41 = 0 , similarly Y24 = Y42 = 0.


Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation

Load Flow And Y Bus (Bus Admittance Matrix) Step By Step Formation


Y Bus To Z Bus Conversion


Z Matrix can be Find by either inverting the Y bus network or by utilizing Z transport building calculation. 

The last technique is more enthusiastically to execute however increasingly useful and quicker (as far as PC run time and number of drifting point tasks every second) for a generally enormous framework.


Z Bus is the inverse of the Y Bus.

Properties Of Y Bus 

  • YBUS is a sparse matrix.
  • The diagonal elements are the sum of all the admittances connected to the respective nodes.
  • This off-diagonal elements are the negative of the sum of all the admittances connected directly between the nodes.
  • Sum of the elements in each column is zero, then the Ybus is singular.
  • A typical power system network, each bus is connected by few nearby bus, which cause many off diagonal elements to be zero.

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Need of Admittance matrix


  • Mathematical model and solution of electric network is the basis of modern power system analysis, i.e. in studies of power flow, fault analysis, and contingency analysis.
  • Electric network is constituted of transmission lines, transformers, parallel or series capacitors, and other static elements.
  • We can establish equivalent circuit of any complicated network and analyze it according to the AC circuit laws.
  • The electric network is represented by the linear lumped parameter model: for studies at synchronous frequency. Check it out the  Different types of Power Electronic Converters, Advantages and Disadvantages
  • For electromagnetic transient analysis.
  • Equivalent circuits described by distributed parameters.
  • First step for solving power flow problems is to develop nodal matrix


Advantages :


  • Data preparation is simple
  • It provides insight for developing algorithm in account for network change.
  • Sparsity technique enhances computational efficiency of power system problems.


Y Bus Calculator

Z bus is called the open circuit impedance matrix in circuit theory with the elements of Why we need to calculate Y Bus where we can calculate it from Z Bus?. 

A bus to the bus voltages. Thus, the admittance matrix relates nodal quantities. We encourage these ideas by introducing a simple example. 

We assume that all. Answer to Calculate the bus admittance matrix Y Bus and the bus impedance matrix Z Bus for the power system shown in Figure. 

Calculate the impedance base, ZB= (VB)2/SB; Calculate the current base, For a system with n buses, Ybus is an n by n symmetric matrix.

In short circuit analysis requires the determination of impedance bus matrices Zbus. Admittance bus matrices, Ybus, are. 

And These methods allow us to calculate the power flow, determine the voltages. 

The objective of a power flow study is to calculate the voltages The Y-bus is a square matrix with dimensions equal to the number of buses.

Simple load flow calculator in LabVIEW for three phase power LabVIEW based load flow calculator has . Determination of impedance through y bus matrix.

Methods Of Y Bus Formation :

The bus admittance matrix, formed in practice by either of the methods as under : 

(1) Direct Inspection Method
(2) Singular & Non-Singular Transformation
(3) Step by Step Method

Formation Of Y Bus Matrix By  Direct Inspection Method


Aim : To determine the admittance matrices for the given power system network.

Software Required : MATLAB

Theory: 


Bus admittance is often used in power system studies. 

In most of the power system studies it is required to form Y- bus matrix of the system by considering certain power system parameters depending upon the type of analysis.

Y-bus may be formed by inspection method, only if there is no mutual coupling between the lines.  Every transmission line should be represented  equivalent. 

Shunt impedances are added to diagonal element corresponding to the buses at which these are connected. The off diagonal elements are unaffected. 

The equivalent circuit of Tap changing transformers is included while forming Y-bus matrix.

Formation Of Y Bus Matrix :




where, 

Yii = Self admittance
Yij = Transfer admittance

Technique :

1. Enter the order window of the MATLAB. 

2. Make another M – document by choosing File - New – M – File 

3. Type and spare the program in the editorial manager window. 

4. Execute the program by either squeezing Tools – Run. 

5. View the outcomes.



Z BUS MATRIX Formation 


In case You Want To consider Z transport Matrix improvement first We need to consider Z transport lattice.

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Z-BUS MATRIX : 


The Z transport organize contains the driving point impedance of each and every center point with respect to a reference transport.

In addition, the driving point impedance of a center is indistinguishable impedance among it and the reference.

The off corner to corner are known as the trade Impedance between each transport of the framework and with each extraordinary vehicle concerning the reference transport. Check This Article: Equipments used in sub-stations

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The Z transport are generally called vehicle impedence framework which is worked from the branch containing data of the positive sequence,negative progression and zero game plan impedence.

During conventional purposes,the positive and negative game plan are managed comparably.

By and by We Learn About The FORMATION OF Z BUS MATRIX: 


The whole structure is amassed by starting with a lone part connected with the reference transport.

in case every segment is incorporated turn ,we have to change the system for that extra part.

All of the part added should be related with the system by a single center point or two center points.

There are a couple of sorts which are delineated underneath

TYPE 1: A branch from reference transport 

Expect current of 1.0pu is mixed into another vehicle Q ,related with the reference yet it will make no voltage on other buses.And also mixture of current into any vehicle of PN will convey no voltage on the new transport Q.

Y Bus : Load Flow (Bus Admittance Matrix) Step By Step Formation


Y Bus : Load Flow (Bus Admittance Matrix) Step By Step Formation


Z(i,q)=Z(q,i)=0

where I isn't identical to q

Z(q,q)=Z(p,q)

Hereafter from above condition the driving point impedance of new transport is impedance of new part included.

TYPE 2: 

A Branch not from reference transport 

Expect a current of 1.0pu is implanted into transport Q which is same as injecting the current on transport P.

Another center is been added to the Z transport network identifying with new transport Q.

The off diagonal parts of new line – column is same as the segment of transport P.

The diagonal part is Zq where q is Zp,P notwithstanding a plan line impedance .

Y Bus : Load Flow (Bus Admittance Matrix) Step By Step Formation


Z(i,q)=Z(i,p)

Z(q,i)=Z(p,i)

Z(qq)=Z(pp)+Z(p,q)

SOME IMPORTANT QUESTIONS RELATED TO Z-BUS 


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QUESTION 1 - What is Z transport matrix? 

Answer : Z transport network contains the driving point impedance of each and every center with respect to a reference transport.

Besides, the driving point impedance of a center point is proportionate impedance among it and the reference.

The off diagnol are known as the trade impedence between each transport of the framework and with each extraordinary vehicle concerning the reference transport.

The Z transport are generally called vehicle impedence grid which is worked from the branch containing data of the positive sequence,negative course of action and zero progression impedence.

During down to earth purposes,the positive and negative course of action are managed likewise.

QUESTION 2 - Write down rapidly about advancement of Z transport system? 

ANSWER - The whole system is assembled by starting with a singular part connected with the reference bus,and in case every segment is incorporated turn

we have to adjust the system for that extra segment.

All of the segment added should be related with the system by a singular center point or two centers

QUESTION 3 - Write down for the kind of Z transport course of action for a branch from reference transport? 

Answer - Suppose current of 1.0pu is mixed into another vehicle Q ,related with the reference yet it will make no voltage on various vehicles.

Also, besides mixture of current into any vehicle of PN will make no voltage on the new transport Q.

Z(i,q)=Z(q,i)=0 where I isn't identical to q

Z(q,q)=Z(p,q)

Hereafter from above condition the driving point impedence of new transport is impedence of new segment included.

QUESTION 4 - Write down for improvement of Z transport where a branch isn't from the reference transport? 

Answer - Suppose a current of 1.0pu is mixed into transport Q which is same as injecting the current on transport P.

Another center is been added to the Z transport lattice identifying with new transport Q.And the off diagnol segments of new segment – coloum is same as the segment of transport P.

The diagnol part is Zq where q is Zp,P notwithstanding a game plan line impedence .

Z(i,q)=Z(i,p)

Z(q,i)=Z(p,i)

Z(qq)=Z(pp)+Z(p,q)



What is a difference between Y-Bus And Z-Bus? 


Z transport is known as the open circuit impedance structure in circuit theory with the segments of the system known as the driving point and move impedance.

It is generally called vehicle impedance network. The course of action of a vehicle impedance arrange requires either structure inversion or the usage of included computations.

The Z transport is at any rate used for cut off.

Y transport is known as the short out acceptance organize or the nodal consent cross section, with the parts of the framework known as the driving point and move authorization.

It is generally called vehicle enlistment framework. Since in a power orchestrate each transport is related exceptionally to several distinct vehicles (a couple), the Y transport of a colossal framework is lacking ,

i.e, it has incalculable zeroes. The Y transport is consistently used in dealing with trouble stream issues.

It has expanded broad applications due to its straightforwardness in data preparation, effortlessness of game plan and alteration for arrange changes.

As a result of its sparsitv it energetically reduces PC memory And time required

Y Bus cross section is moreover called Bus Admittance organize is used in charge stream examination/load stream assessment in control system.

The system involves estimations of line acceptances and transport authorizations including half line charging consents.

This procedure is called as Inspection method. Various strategies, for instance, singular change is used if normal impedence/authorization are considered.

Z Bus structure is fabricated using Z transport building figuring where the impedences of the line thought about.

([Z] = [Y]^-1)

This arrangement can in like manner be used to assemble Impedence lattice from enlistment structure, anyway not used because they may apparently realize a lone system.

the Z transport network is utilized for lack assessment in the power system

Y transport will be transport enlistment organize which is used (generally) in Load stream examination.

This framework helps in finding estimations of P, Q, IVI and delta. The segments of grid are the enlistments of transmission lines between transports.

Z transport will be transport impedance arrange which is used in Fault examination. This network helps in finding the estimations of weakness current.

The parts of structure are the impedances of transmission line related between two vehicles

Focal points of Y-transport over Z-transport in load stream inspects?


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There are various differences between Bus Admittance Matrix and Bus Impedance framework and along these lines they find applications in different spaces. 

Here the summary out two or three the differentiations here:

1. Ybus is a Sparse Matrix that is most by far of parts are zero and hence less memory is required for limit however Zbus is a full grid and all segments are non-zero so more memory is required.

2. Weight Flow Studies incorporate Nodal Analysis and we wish to find the center or transport voltage and thus while confining KCL condition acceptance is a trademark choice when appeared differently in relation to impedance.

3. Ybus can be successfully formed using appraisal Method while Zbus building count is tangled.

4. Ybus can be adequately encircled using survey Method while Zbus building computation is befuddled.

5. Ybus can be successfully changed if there ought to be an event of any alterations in the power structure, for instance, extension of transmission line or removal of transmission line.

6. Common Impedances can be truly considered by the use of Singular Transformation Method of Ybus improvement

7. Zbus is used in lack examination since slanting parts address Thevenin Impedances however inclining segments of Ybus don't address Thevenin Admittances

8.Load stream looks at are done to find in a general sense the current. We understand that I V/Z and Z= 1/Y. From this time forward =Y*V. All these are lattices and thus division by structures is hard we use duplication using Y instead of isolating with Z

9. Y regards are little appeared differently in relation to Z. Thusly calculation gets less troublesome.

10. Easy to intertwine effect of basic coupling.

11. Y organize is even and there are an enormous number in it. Consequently it requires less memory as weight stream assessment are done in PCs.




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