For a systematic solution of power systems problems, a necessary prerequisite would be a solid theoretical and conceptual basis for ideas in modern power system analysis. An algorithm is developed for performing load flow study including all buses and lines of a power system network consisting of N buses and related interconnections.
LITERATURE REVIEW
The following are some of the many works dealing with the development of the Fast Discrete Load Flow (FDLF) method in power system analysis. An article by Horisberger et al.9 published in 1976 presents a static condition assessment procedure.
SCOPE OF THE PRESENT WORK
Chapter - 1 presents the general approach to the study of load flow, literature review and scope of the present work. Program D for this study and the results of the application of the program developed on a sample system.
INTRODUCTION
The purpose of the single line diagram is to concisely provide the essential information about the system. The information contained in a single line chart should therefore be expected to vary according to the problem at hand and according to the practice of the company producing the chart.
THE PER UNIT SYSTEM
Due to phase symmetry, it is usually . enough to represent only one phase, called the reference phase or phase. For appliances of the same general type, the p.u. voltage drops and losses are of the same order regardless of magnitude.
TRANSFORMERS
The n equivalent circuit elements, therefore, can be treated in the same way as the line elements. There are two ways in which a non-nominal transformer can be represented as shown in the figure above.
TRANSMISSION LINES AND CABLES22
In the load flow analysis of a power system, equipment such as23 buses, current transformers, switches, circuit breakers, etc. considered a negligible impedance and shunt elements such as potential transformers, lightning conductors and coupling capacitors are considered open circuit. In representing loads for load flow studies, . it is important to know the variation of real and reactive power with variation of voltage.
Ivl< e and ~ = tan-l ~ is the
MATRIX AND TYPES OF MATRICES
A matrix is defined as a rectangular array of numbers, called elements, arranged in a systematic manner with m rows and n columns. When the number of rows is equal to the number of columns, i.e. m= n, the matrix is called a square matrix and its order is equal to the number of rows ( or columns. The matrix formed from a principal matrix with the rejecting some of its columns or rows is called a sub-matrix of the main one.
If the rows and columns of an mxn matrix are interchanged, the result is the nxm matrix transposed and denoted by At if the original is A. If each element of a square matrix A is replaced by its co-factor, and then the matrix is transposed, it is resulting matrix an adjoint, which is denoted by A.
MATRIX OPERATIONS 3-4
Division does not exist in matrix algebra, except in the case of the division of a matrix by a scalar. But the purpose of division in solving equations is achieved by obtaining and manipulating the inverse matrix. We first need to define the unit matrix. A unit matrix U is a square matrix where all elements on the main diagonal are I and all off-diagonal elements are 0.
We define the inverse of a matrix A as the matrix that, when multiplied by A, results in the identity matrix. Therefore, the concept of the inverse of a matrix is useful in solving matrix equations. If the determinant is not zero, it is called a nonsingular matrix and a unique inverse exists.
BUS ADMITTANCE MATRIX
The diagonal elements of Yare are called the self-admittances and the off-diagonal elements are the mutual admittances.
FORMATION OF BUS ADMITTANCE MATRIX
The access matrix for shunt elements is usually diagonal, as there is normally no coupling between the components of each phase. Let's look at the following example system to illustrate the method for forming the bus access matrix. Assuming there is no interconnection in the system, many of the elements of the matrix will become zero.
The off-diagonal elements associated with different buses are just the sum of the admittances of the corresponding branches with negative sign. The general representation of the elements in accordance with the network configuration can be written as. Again, the bus admittance is a symmetric matrix along the main diagonal, the computer only needs to store the upper triangular bus input matrix and, during iteration, only these inputs are required, through an efficient sorting and compact storage scheme.
INTRODUCTION
ANALYTICAL DEFINITION AND BUS CLASSIFICATION
A P-V bus is one where the real power P is specified and the voltage magnitude is kept at a constant value by reactive power injection. It is necessary to find out the reactive power production QG and the phase angle of the bus, volt~ge. The concept of a swing bus is necessary because the I~ losses are not known in advance and it is therefore not possible to determine the injected real power at all the buses. It is customary to designate one of the voltage-controlled buses that generally has the largest generation as the swing bus.
In this bus, the real power Ps is not specified, but is calculated at the end of the calculation; Since we also need a reference phase in the system, the phase angle of the drive bus is also specified, generally as zero degrees.
DATA FOR LOAD FLOW STUDIES
Finally, there is the data required to effect changes in the system representation and operating conditions for tee calculation of subsequent cases. For interconnection studies, network connections are described using code numbers assigned to each bus, these numbers space the terminals of transmission lines and transformers. Code numbers are also used to identify the types of buses;8 the location of static capacitors, shunt reactors, and those elements in which off-nominal turns ratios of transformers are to be represented.
FORMULATION OF LOAD FLOW EQUATIONS
Mathematically, the complex load-flow equations are non-analytical and cannot be differentiated in complex form. This formulation results in a set of nonlinear simultaneous equations, two for each bus in the system.
NEWTON-RAPHSON METHOD USING YBUS'
- SYSTEM HAVING VOLTAGE CONTROL BUSES
Tile elements of the Jacobian are found by taking tile partial derivatives of the expressions for Pp and Qp and substituting into them the stresses assumed or calculated in the last previous iteration. All quantities in the linear equation (4.13) relate to interaction k, The linear equation when solved for lie,. In the Newton-Raphson method, the reactive power at a voltage-controlled bus is calculated at the end of an interaction using (4.23) and I V1 is kept at the specified value.
If a reactive power source (capacitor bank or .. synchronous condenser) of sufficient capacity cannot be provided, it is necessary to consider the limits of reactive power source at the voltage. The sequence of steps required to include the effect of voltage-controlled buses in the Fast decoupling-lterative method is shown in the flow diagram in Fig. Similarly, the reactive power changes are less sensitive to change in angle but mainly sensitive to change in voltage magnitude.
LIP]
COMPUTATION OF LINE ~LOWS AND SLACK BUS POWER
Let the line connecting bus P to bus q (Figure 4.2) have series admittance Ypq and total charge of the line. Here Ppq is the actual power flow from bus p to q and 0pq is the reactive power flow from bus p to q. Loose bus power is calculated by hopping the currents on the lines terminating on the loose bus.
INTRODUCTION 5-1
Initial voltages are specified for all busbars; for basic load currents, the P,Q buses are set to I + jO, while the P,V buses are set to V + jO. These conditions are accepted when the power discrepancies for all buses are less than a small specified tolerance. Once the solution is reached, the full terminal conditions for all buses, power flow and losses are calculated.
FEATURES OF THE COMPUTER PROGRAM
The basic algorithm used by a load flow program is depicted in Fig. 5.I. System data, such as bus power supply conditions, network connections and impedances, are read in and the access matrix is formed. The iteration cycle ends when the bus bar voltages and angles meet the specified conditions. Once a solution is reached, complete terminal conditions for all buses, line current and losses are calculated. and system totals can then be calculated.
Read the system data and the indicated loads and generation. Also read the voltage specification on the regulated buses. Update voltages and angles to meet specified load and generation conditions. Number of buses and lines. ii) Basic values. iii) Bus name and number .. iv) Specification of the bus ie. whether it is a swing bus or voltage-controlled bus or cargo bus. v) Bus voltage magnitude and phase angle with reference to the slack bus. vi) The value of the tolerance limit to be reached and the maximum number of iterations to be allowed.
DATA ASSEMBLY PROGRAM
PROGRAM FOR VOLTAGE CONTROLLED BUSES
PROGRAM FOR VOLTAGE AND POWER FLOW CALCULATION
OUTPUT PROGRAM
ADDITIONAL INPUT INFORMATIONS
ADDITIONAL OUTPUT INFORMATIONS
- DESCRIPTION OF.THE SAMPLE SYSTEM
- TEST RESULTS
- SUGGESTIONS FOR FURTHER WORK
- ARRILLAGA, J,
- B,M, WEEDY,
- TIE LINE CONTROL
Compared with the other methods, the convergence speed of the FOLF method is faster than any other method, requiring a relatively smaller number of iterations. However, in the FOLF method, the number of iterations is practically independent of the system size due to the quadratic characteristic of convergence. However, for large systems, the computing core requirements for the Jacobian matrix are very large in the figure, and for the calculation of the elements of the Jacobian for each iteration, it requires additional computing time.
On the contrary, the reduction in memory requirements with such assumptions and approximations of the FDLF method has made it attractive. The developed program can handle any size of power system network (just by changing the DIMENSION statements) depending on the size of the computer's memory. In this type of matrix, most of the elements are zero except for a few non-zero elements.
It primarily improves the tension conditions. both magnitude and phase ) of the bus where the voltage magnitude is less than the specified minimum. The self-admittances, Ypp (for bus p) and Yqq (for bus q) and the mutual admittance Ypq = Yqp' between buses p and q must be recalculated for each and every change in the tap of the TCUL transformer.
