Smart grid topology identification using sparse recovery. Electric power transmission, distribution, and utilization lab exercise 1 instructions. The y bus is an n x n matrix n is the number of buses in the system a software package will calculate the y bus from the data provided by the user regarding the passive elements of the system transmission lines line shunts switched shunts capacitorsreactors bus shunts y bus matrix the admittance matrix. Consider the three bus network shown in figure that has five branch impedances and one current source. The formation of a bus impedance matrix requires eithe. Each bus in a real power system is usually connected to only a few other buses through the. Ybus building algorithm of power system using matlab blogger. Next we will teach you how to solve a y bus matrix. For many power networks, the admittance matrix is relatively sparse, whereas the impedance matrix is full. The formation of the bus admittance matrix and their modification is easy.
Sparse matrices dont have a lot of extra features, and some algorithms may not work for them. The bus admittance matrix plays a very important role in load flow analysis. The offdiagonal element is equal to the negative of the admittance between the nodes. Methods to efficiently order, store and work with large sparse matrices. Application of sparsity characteristics of power systems to. Nodal admittance matrix an overview sciencedirect topics. The bus admittance matrix is a square matrix of dimension n x n, where n is the number of network buses or nodes. It represents the nodal admittance of the buses in a power system. Admittance matrix most power system networks are analyzed by first forming the admittance matrix. Cots sparse matrix utilization in distribution power flow applications dino ablakovic, izudin dza. For a common bus admittance matrix with n nodes, if the average branch rate for each node is a, the sparsity of this matrix is. In power system, nodal admittance matrix or bus admittance matrix or y matrix or y bus is an n x n matrix describing a power system with n buses. The bus admittance matrix is a complex and symmetric matrix, but it is. Sparsity and decoupling in load power flow analysis archives.
Real and reactive power injected in a bus the complex power delivered to ith bus is given by. Modeling and solving of y bus matrices is an important part of power system analysis and design, and is used extensively in diagnosing, solving and finding problems in power systems especially different kind of faults. Formation of bus admittance matrix in a power system, power is injected into a bus from generators, while the loads are tapped from it. The lumped shunt admittances at the bus is taken as consideration. Make an initial estimate for the voltages at each bus update the voltage estimate for each bus in the system, one at a time, based on the estimates for the voltages and power flows at every other bus and the values of the bus admittance matrix. Formation of bus admittance matrix ybus s1, s2, s3 are net complex power injections into bus 1, 2, 3 respectively y12, y23, y are line admittances between lines 12, 23, y01sh2, y02sh2, y03sh2 are halfline charging admittance between lines 12, and 23 the halfline charging admittances connected to.
Therefore, the bus impedance matrix can be calculated with bus admittance matrix. It is known a self admittance matrix or driving point admittance. This paper, therefore, presents the application of power system sparsity characteristic to powerflow modelling and simulations to develop a model for storing the bus admittance matrix of power systems. Unlike current flowing through a branch and thus is a branch quantity, a current injection is a nodal quantity. Ive experimented a lot with solutions through numpy, scipy, and so forth, but i still dont know how to fix it. But before you do any of that stuff you first must know how to make a ybus matrix short form for admittance, often denoted in electrical equations as y, inverse of impedance z of a given power system, involving grids, transmission lines transformers and loads. Sparse matrix solution in optimal direct current loadflow using crout technique is. The bus admittance matrix systematic formulation of equations determined at. We create a bus admittance matrix ybus for the power system. Bus impedance matrix is the inversion of bus admittance matrix. The admittance matrix, a fundamental network analysis tool that we shall use heavily, relates current injections at a bus to the bus voltages.
Stepbystep formation of bus admittance matrix circuit. 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. Set up the 3x3 per unit bus admittance matrix for the system in figure 1. In 64bit matlab, however, double matrices with fewer than half of their elements nonzero are more efficient to store as sparse matrices. That is also a reason that the admittance matrix is very sparse.
The majority of load flow programs employ methods using the bus admittance matrix, as this method is found to be more economical. Application of sparsity characteristics of power systems. The bus admittance matrix is a sparse matrix thus the computer memory requirement is. I have a nxm matrix and i want to compute the nxn matrix of euclidean distances between the m points. Using those definitions, a matrix will be sparse when its sparsity is greater than 0.
In a real power system, each bus is usually connected to only a few other buses, hence the y bus matrix is sparse. A sparse matrix was passed, but dense data is required. Computing sparse pairwise distance matrix in r stack. The amount of current present in the bus can be calculated with the help of formation of the admittance matrix. Power flow analysis using graph based combination of.
Any modification like removal of any transmission line is difficult in case of ybus. In general, the diagonal terms y ii are the self admittance terms and are equal to the sum of the admittances of all devices incident to bus i. The diagonal terms, ykk, are the self admittance terms, equal to the sum of the admittances of all devices incident to bus k. In general, both matrices are nonsingular and symmetric. This is in contrast to what comes out of dist, for example, which would result in a dense matrix and. However, in spite of the fact that matlab is quite capable of matrix inversion for small dimension, you are not.
The admittance matrix is based upon kirchhoffs current law kcl, and it is easily formed and very sparse. Admittance matrix an overview sciencedirect topics. Analysis of complex power system faults and operating. Ybus building algorithm of power system using matlab nodal admittance matrix or ybus matrix is a matrix that contains admittances of the power system. In this work we especially exploit the concentration of nonzero elements in the corresponding sparse vectors around the main diagonal in the nodal admittance or structure matrix of the pn to improve the results. It not only stores the nodal admittance and line admittance of each bus, but also represents the topology structure of the power system. To study and analyze the complex power system, y bus or admittance matrix plays a significant role, since it is a sparse. Ybus and zbus both are used for designing and modeling of transmission system.
Software used matlab theory here a network model of power system is shown in figure 1. Cots sparse matrix utilization in distribution power flow. In the admittance matrix each nonzero offdiagonal element corresponds to a network branch connecting the pair of buses indicated by the row and column of the element. Sparsity is one of its greatest advantages as it heavily reduces computer memory and time requirements. As such, the admittance matrix is highly sparse matrix, of which each row has an average of fewer than four nonzero. With large systems ybus is a sparse matrix that is, most entries are zero. For a large power system, more than 90 % of offdiagonal elements are zero. By contrast, if most of the elements are nonzero, then the matrix is considered dense. Advantages of bus admittance matrix the bus admittance matrix is a sparse matrix i. The offdiagonal terms, y ij, are equal to the negative of the sum of the admittances joining the two buses. The offdiagonal terms, ykl, are equal to the negative of the admittance joining the two buses. Pdf a newton power flow for study purpose researchgate. The offdiagonal elements are equal to zero if there is no line between buses i and j, obviously, the bus admittance matrix is a sparse matrix. The number of zerovalued elements divided by the total number of elements e.
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. To study and analyze the complex power system, y bus or admittance matrix plays a significant role, since it is a sparse matrix and it is easy for calculations. With large systems y bus is a sparse matrix that is, most entries are zero. Hi guys, today we are going to teach you how to model a bus admittance matrix y bus of a given power system. There may be some buses with only generators and there may be other only with loads. Ybus admittance matrix formulation yousu chen pnnl december 18, 2015 this document is a description of how to formulate the ybus admittance matrix. What is the difference between dense and sparse matrices. Typically each row of the admittance matrix has an average of fewer than four nonzero elements. In fact, commercial codes for large lp problems seem to have predated codes for sparse linear equations even though solving a sparse lpproblem requires.
Comparison of newton raphson and gauss seidel methods. You use them when you need to work with matrices that would be too big for the. I know a sparse matrix simply does not include the zero entries, but since their allocation in the matrix can be very diverse, i am wondering whether that derivation from dense to sparse can be somehow automatized. The bus admittance matrix is sparse because each bus is only connected to a few nearby buses. In realistic systems which contain thousands of buses, the y matrix is quite sparse. Removal of shortcircuit element is easy in case of zbus. The number of zerovalued elements divided by the total number of elements is called the sparsity of the matrix. Designs of fast decoupled load flow for study purpose core. This is due to the fact that in power system network networks each node bus is connected to not more than three nodes. In the simplest form, the above matrix can be written as shown below. Some buses have generators and loads while some other may have static capacitors for reactive power compensation. How to model bus admittance matrix ybus of a given. Transmission lines run from bus i to bus j and are indexed by k.
To formulate ybus matrix by singular transformation. Za zc 1 2 3 ze zb zd i3 university of texas at austin. Generally, the sparse admittance matrix can be retained and the impedance matrix is calculated or built directly from the factorised admittance matrix. Ele b7 power systems engineering university of waterloo.
For large systems, y is a sparse matrix and it is structually symmetric. The bus admittance matrix is a sparse matrix thus the computer memory requirement is less. Conceptually, sparsity corresponds to systems with few pairwise interactions. It is very useful in load flow and stability analysis. It is known a selfadmittance matrix or driving point admittance. 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. Z bus or bus impedance matrix formation with example. Themajorapplication of sparse matrix techniques in optimization up to the present has been in the implementation of the simplex method for linear programming lp see, e.