Ybus matrix
Encyclopedia
In power engineering
, Y Matrix or Ybus is an n x n symmetric 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
.
Ybus matrix form:
needs optimization. Only computer simulation
allows the complex handling required. The Ybus matrix is a tool in that domain.
of a power system, there are four main steps in creating the Y Matrix. First, the single line diagram is converted to an impedance diagram. Next, all voltage sources are converted to their equivalent current source representations. From here, the impedance diagram is then converted to an admittance diagram. Finally, the Y Matrix itself is created.
The admittances Y11, Y22,... Ynn 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.
For small transmission systems of about less than 10 nodes or buses, 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 Ybus is more practical to use.
Power engineering
Power engineering, also called power systems engineering, is a subfield of engineering that deals with the generation, transmission and distribution of electric power as well as the electrical devices connected to such systems including generators, motors and transformers...
, Y Matrix or Ybus is an n x n symmetric matrix describing a power system with n buses
Electrical bus
Electric bus is a bus powered by electric energy. "Electric bus" can also refer to:* Bus , used for connecting components of a computer or communication between computers* Busbars, thick conductors acting as nodes in electrical substations...
. It represents the nodal admittance
Admittance
In electrical engineering, the admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the inverse of the impedance . The SI unit of admittance is the siemens...
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
Power flow study
In power engineering, the power flow study is an important tool involving numerical analysis applied to a power system. A power flow study usually uses simplified notation such as a one-line diagram and per-unit system, and focuses on various forms of AC power...
.
Ybus matrix form:
Context
Electric power transmissionPower engineering
Power engineering, also called power systems engineering, is a subfield of engineering that deals with the generation, transmission and distribution of electric power as well as the electrical devices connected to such systems including generators, motors and transformers...
needs optimization. Only computer simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
allows the complex handling required. The Ybus matrix is a tool in that domain.
Design
Starting from the single line diagramOne-line diagram
In power engineering, a one-line diagram or single-line diagram is a simplified notation for representing a three-phase power system. The one-line diagram has its largest application in power flow studies. Electrical elements such as circuit breakers, transformers, capacitors, bus bars, and...
of a power system, there are four main steps in creating the Y Matrix. First, the single line diagram is converted to an impedance diagram. Next, all voltage sources are converted to their equivalent current source representations. From here, the impedance diagram is then converted to an admittance diagram. Finally, the Y Matrix itself is created.
The admittances Y11, Y22,... Ynn 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.
For small transmission systems of about less than 10 nodes or buses, 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 Ybus is more practical to use.