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Anvesh Sameer

This course covers detailed approach to load flow studies in power systems. Various MCQS are solved with detailed explanation and tricks.

GATE (Graduate Aptitude Test in Engineering) 2020 & 2021 complete preparation with best educators. Know about the detailed syllabus, best books, exam pattern and dates, previous year question papers a

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English

Load Flow Studies

Model. & Perf. of Trans. Line

Power System

Electrical Engineering

GATE & ESE - EE, EC

GATE, ESE and IIT-JAM

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Test Preparation

Overview

Basics of load flow studies such as its importance, types of buses are classified

Terms you Need to Know

Y bus importance, y bus skeleton, y bus problems are discussed with detailed explanation.

In power engineering, nodal admittance matrix (or just admittance matrix) or Y Matrix or Ybus is an N x N matrix describing a power system with N buses. It represents the nodal admittance of the buses in a power system. In realistic systems which contain thousands of buses, the Y matrix is quite sparse. Each bus in a real power system is usually connected to only a few other buses through the transmission lines. The Y Matrix is also one of the data requirements needed to formulate a power flow study

Electric power transmission needs optimization in order to determine the necessary real and reactive power flows in a system for a given set of loads, as well as the voltages and currents in the system. Power flow studies are used not only to analyze current power flow situations, but also to plan ahead for anticipated disturbances to the system, such as the loss of a transmission line to maintenance and repairs. The power flow study would determine whether or not the system could continue functioning properly without the transmission line. Only computer simulation allows the complex handling required in power flow analysis because in most realistic situations the system is very complex and extensive and would be impractical to solve by hand. The Y Matrix is a tool in that domain. It provides a method of systematically reducing a complex system to a matrix than can be solved by a computer program. The equations used to construct the Y matrix come from the application of Kirchhoff’s current law and Kirchhoff’s voltage law to a circuit with steady-state sinusoidal operation. These laws give us that the sum of currents entering a node in the circuit is zero, and the sum of voltages around a closed loop starting and ending at a node is also zero. These principles are applied to all the nodes in a power flow system and thereby determine the elements of the admittance matrix, which represents the admittance relationships between nodes, which then determine the voltages, currents and power flows in the system.
The Y Matrix diagonal elements are called the self-admittances at the nodes, and each equals the sum of all the admittances terminating on the node identified by the repeated subscripts. The other admittances are the mutual admittances of the nodes, and each equals the negative of the sum of all admittances connected directly between the nodes identified by the double subscripts. The admittance matrix {\displaystyle Y} Y is typically a symmetric matrix as {\displaystyle y_{mn}=y_{nm}} y_{mn} = y_{nm}. However, extensions of the line model and models of other components such as transformers may make {\displaystyle Y} Y asymmetrical.[2]

For small transmission systems of about less than 10 nodes or buses, the Y matrix can be calculated manually. But for a realistic system with relatively large number of nodes or buses, say 1000 nodes, a computer program for computing Y is more practical to use

Y bus

Shunt elements

Tricks to solve modified y bus problems are discussed

Modified Y bus (part - 1)

Modified Y bus (part -2)

Newton Raphson method - jacobian matrix (1)

Newton raphson method - Jacobian matrix 2

What is Z Bus in power system?
Z bus is called the open circuit impedance matrix in circuit theory with the elements of the matrix known as the driving point and transfer impedance. It is also known as bus impedance matrix.

The formation of a bus impedance matrix requires either matrix inversion or the use of involved algorithms.The Z bus is however used for short circuit studies

Z denotes impedance and its reciprocal is admittance and denoted by Y. Z adds in series but not in parallel. On the other hand, Y is additive is parallel and we know that in power systems mostly loads are connected in parallel, that's why power system calculation are done in admittance matrix form Y rather than Z because it helps to simplify calculations. Once you have calculated Y, take inverse it you will find Z matrix.
Z Matrix or bus impedance matrix is an important tool in power system analysis. Though, it is not frequently used in power flow study, unlike Ybus matrix, it is, however, an important tool in other power system studies like short circuit analysis or fault study. The Zbus matrix can be computed by matrix inversion of the Ybus matrix. Since the Ybus matrix is usually sparse, the explicit Zbus matrix would by dense so memory intensive to handle directly

Electric power transmission needs optimization. Only Computer simulation allows the complex handling required. The Zbus matrix is a big tool in that box.
Because the Zbus is the inverse of the Ybus, it is symmetrical like the Ybus. The diagonal elements of the Zbus are referred to as driving-point impedances of the buses and the off-diagonal elements are called transfer impedances

Z bus

Z bus matrix construction algorithm

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Lessons

10 lessons • 2h 5m

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Overview

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Terms you Need to Know

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Y bus

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Shunt elements

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Modified Y bus (part - 1)

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Modified Y bus (part -2)

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Newton Raphson method - jacobian matrix (1)

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Newton raphson method - Jacobian matrix 2

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Z bus

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Z bus matrix construction algorithm