Load Flow Study using Tellegen’s Theorem
Mini Project Report submitted to the Department of Electrical and Electronics Engineering in accordance with the academic requirement for the award of the degree.
SUBMITTED BY
AD SRIKANTH 05841A0232
LVS KARTHIK 05D91A0210
Department of Electrical and Electronics Engineering
Aurora’s Technological and Research Institute
(Affiliated to JNTU)
Parvathapur, Uppal, HYDERABAD – 500 039
CERTIFICATE
This is to certify that the Mini Project work titled
“Load Flow Study using Tellegen’sTheorem”
submitted by AD Srikanth and LVS Karthik of EEE, Aurora’s Technological & Research Institute, Parvathapur, Uppal, Hyderabad in accordance with the academic requirement for the award of degree Bachelor of Technology in Electrical and Electronics Engineering, is a bonafied work carried out by them from May 2008 to June 2008 under our guidance and supervision. The project report has not been submitted to any other University or other Institute.
Project Coordinator Project Expert Head of the Department
ACKNOWLEDGEMENTS
It gives us great pleasure in acknowledging the help received from various individuals in completing the project and presenting results. We are gratefully beholden beyond words to express deep sense of reverence and gratitude to our guide Mrs. Madhuri and her meticulous guidance, valuable suggestions, constructive criticism and wholehearted co-operation throughout the mini-project..
We are thankful to Mr./ Mrs. (Name & Designation of the Head of the organization where the candidate had done the project) for allowing me to do the Project work in (organization Name and address).
We take immense pleasure of dedicating our thanks to our principal Dr. Alka Mahajan for her moral help and encouragement during our project.
Project Associates
A.D.Srikanth
L.V.S. Karthik
INDEX
1. Abstract
2.Chapter 1 Introduction
1.1 Classical Load Flow Techniques
1.1.1 Limitations of Classical Load Flow methods
1.2 Load Flow Study of Distribution Networks
1.3 Objective of the Thesis
1.4 Generalized form of Tellegen Theorem
3. Chapter 2 Load Flow Solution formulation using exclusive
methods and Tellegen Theorem method
2.1 Introduction
2.2 Description of the radial Distribution network
2.3 Load Flow problem formulation using
tellegen theorem method
2.4 Distribution Network with main feeder
4.Chapter 3 Case study and analysis of load flow solutions methods
3.1 Case study: Load flow analysis of distribution network
with main feeder using Tellegen Theorem Method
3.2 Algorithm for the Distribution networks with
main feeder using Tellegen theorem method
3.2.1 Flow chart
3.3 SoftwareUsed(MATLAB)
3.3.1 Introduction to MATLAB
3.3.2 Starting MATLAB
3.3.3 Entering Source code in MATLAB
5. Chapter 4 Conclusions
4.1 Introduction
4.2 Conclusions on exclusive load flow methods
and Tellegen theorem method
Appendix:
X Source Code
X.1 Result
Bibliography
ABSTRACT
The present day distribution networks are enormously growing to meet the rapidly increasing demand of electrical power, but with a less attention towards its optimum growth. Due to this erratic and unplanned expansion, the real power losses have become appreciable, constituting the major portion of the overall system losses and with effect that, the operating voltage profile has become very poor. Such unplanned distribution network performance can be analyzed using an efficient load flow method and a solution to optimize the growth of the network can be obtained. Hence the distribution load flow study has become a vital tool for the analysis of Automated Distribution Systems .
The radial structure and the high resistance/reactance (R/X) ratios of the branches of the distribution networks, made the conventional load flow methods, like Fast Decoupled Load Flow ( FDLF ) and Newton-Raphson ( NR) unsuitable to provide the reasonable solution. Due to the topological specialty of the distribution networks and the non-applicability of the conventional load flow methods, the researchers preferred to develop exclusive load flow methods, are either loop-based or branch based methods, depending on the complexity of the distribution network.
The main principle involved in the exclusive load flow methods, is the “ principle of power conservation“ at a node of the network. The principle is that , the amount of power injected in to the node is equal to the sum of the power dissipated in the series branch and the power fed to the load. The principle of power conservation at the entire network level is known through an elegant theorem called “ Tellgen Theorem”.
The new load flow solution called “Tellegen theorm method” is developed on a distribution network with main feeder having 12 and 18 buses and on an another distribution network with main feeder and laterals having 28 and 33 buses. The voltage profile had chosen for the above networks are 440V and 110V.
Chapter 1
General Introduction
The electricity utility system is usually divided into three subsystems, which are generation, transmission and distribution. Further the distribution system is commonly broken down into three compenents: distribution subsations, distribution primary and secondary. At the subsation level, the voltage is reduced and the power is distributed in smaller amounts to the customers. Consequently, one substation will supply many customers with power. Thus, the number of transmission lines in the distribution systems is many times that of the transmission systems. Furthermore, most customers are connected to only one of the three phases in the distribution system. Therefore, the power flow on each of the lines is different and the system is typically ‘ unbalanced’. This characteristic needs to be counted for in load flow studies related to distribution networks.
A distribution circuit uses primary or main feeders and lateral distributiors. The main feeder originates from the substation and passes through the major load centers. The lateral distributors connect the individual load points to the main feeder with distribution transformers at their ends. Many distribution systems used in practice have a single circuit main feeder with wide range of resistance and reactance values. Thus a radial configured distribution network has a main feeder and a number of laterals emanate from the nodes of the main feeder.
The present day automated distribution systems are under continuous reformation. They are performing a number of jobs, like configuration management, continuous voltage control and routing of power through feeders by effective utilization of tie-switches and sectionalizing switches.
Since the distribution networks are under continuous expansion program to meet the present demand of power, but unfortunately a less attention is paid towards to the optimum growth. As a result, the real power losses have become appreciable and voltage profile has become very poor. The load flow analysis is the solution, through which any network can be analyzed to improve its performance.
The bus voltage angles are omitted in the problem formulation, because the radial loads use the voltage magnitudes as the most interested variable, and voltage phase angle is usually, less important compared to the magnitude of the voltage. Besides the difference among voltage phase angles in a feeder do not exceed a few degrees.
The Tellgen Theorem principle is applied to the radial distribution network, developing an objective equation, representing the total real and reactive powers injected in to the network. The equation is observed to be containing only the node voltage magnitudes, and the series-branch parameters, resistance and reactance. A proper bus and branch indexing scheme is implemented to read and retrieve the bus and load data.
The objective equation developed using the Tellgen theorem does not have either any higher order terms or any trigonometric terms. With effect that, it is observed that, the computation time and memory requirement is very much reduced. Further, a flat voltage profile assumption, which is used to initate the iteration process, has solved many other initial parameter assumption problems, that arose in the other solution techniques. It is proved that the memory requirement is reduced by 33.78% and the execution tims is saved about 35.44 %.
1.1 Classical Load Flow Techniques:
The classical load flow study methods used are guass – seidal load flow method (GS) Netwon- Raphson method(NR) and Fast Decoupled load flow method (FDLF).
(a) Gauss-seidal load (GS) method :
This is most primitive method of load flow study. A recursive expression for bus voltage Vp is developed from the load current flowing Ip through the bus ‘p’ and the power Sp injected to the bus.
The expression for the bus voltage magnitude Vp can be written as
Vp^(it+1) = ((Sp* / Ypp) / (1 / V*(it)p)) - Ypq / Ypp * Vq(it) - Ypq / Ypp * Vq^(it+1)
The iteration process begins with aflat voltage profile assumption to all the buses except the slack bus . the bus injected powers and the series branch admittance parameters are known and hence the bus voltages are updated using the eqn. A convergence check is made on these updated voltages and the iteration process is continued till the tolerance value is reached.
(b) Netwon Raphson (NR) method :
This method load flow study is a land mark in the load flow solution methods . the recursive power flow eqn’s for real and reactive powers (Pp , Qp) are used as core eqn’s.
The bus voltage vector is considered in two forms mainly rectangular form (V = e + jf)
And polar form (V=|V|angle).
If the rectangular form of voltage vector is used , the load flow method is called rectangular coordinate method and if the polar form of voltage vector is used , the load flow method is called rectangular polar coordinate method.
( c ) Fast Decoupled load flow method (FDLF) :
It is observed that , from the Netwon Raphson method , the changes , the changes in real power are very much influenced by the changes in load angle only and no influence due to the very magnitude changes . similarly the changes in reactive power (Q) are very much influenced by the changes in voltage magnitudes and no changes takes place due to the load angle changes . This formed the basis for the Fast decoupled load flow method and this method is called Approximate Netwon method.
The iteration procedure is same as the NR method and the memory and storage requirements are reduced considerably , the solution is a converged with the decoupling condition that the series branch conduction that the series branch conductance (Gpq) should be smaller series branch succeptance (Bpq).
1.1.1 Limitations of the classical load Flow methods :
The main limitation of the NR method is the large storage & large solution time. It is due to the repeated Formation and triangularization of jacobian matrix. Then by making certain approximations in the jacobian element values , an approximate network method , also called Fast Decoupled Load Flow (FDLF) method came into existence. It has been observed that the computational efficiency and reliability of FDLF method is higher than NR method and has been used as a main mathematical tool to compute load flow of transmission networks of power industry . The negative aspect of the FDLF method has been observed that the method failed to give converged solution for a network having high (R/X) ratios.
1.2 Load flow study of Distribution networks :
It is well known that the efficient load flow method is one of the most important and highly demanded software in the power industry, through which any network can be analyzed . The analysis of a distribution network has become an important area of activity for present day power system engineer.
The conservation of power principle at a node level was the main principle used in the load flow methods. The principle says that , at any node the power fed into the node is equal to the sum of the power dissipated in the series branch connected to that node .The distribution network is considered in two configurations namely distribution network with main feeder only and the other is distribution network with main feeder and laterals.
In the case of distribution network with main feeder only, the bus and branch numbering is simple and direct. In this method , the node voltages are computed iteratively. Initially the branch power flows are assumed to be zero. The branch power
flows are computed using the power flow equations and the terminal node voltages are updated and in turn the branch power losses are updated . A tolerance check is made to the updated branch power losses and the iteration power losses is continued till the convergence is obtained.
In the case of distribution network main feeder and laterals a proper bus and branch numbering scheme is used to read and retrieve the branch parameters and load values. In this configuration each lateral is treated as a main feeder of distribution network and the iteration process is continued for each lateral. Since the iteration process is carried in the forward direction of the power flow, the method is named “ Forward Sweeping Method”.
In another method “Dist Flow method”, the distribution network is reduced to a single branch network and by using the power flow Eqn’s , the real and reactive powers injected into the reduced network are determined in an iterative way. If convergence is not met , a new equivalent network is determined with the new parameters and the process is continued till the convergence is achieved. Then the node voltages and branch power losses are computed. The main advantage of this method is the efficiency is achieved by avoiding repeated computations of node voltage magnitudes.
.
1.3 Objective of the Thesis :
The thought for the development of new load flow method for the distribution network is initiated, when an attempt is made to find the load flow solution for a radial distribution network using the classical load flow methods. The majority of the classical load flow methods have problems, like non-convergence, high memory requirement, and large computation time. In that crisis, to overcome some of the problems, some of the exclusive load flow methods for distribution networks are studied. It is observed that the power conservation principle is used in all the exclusive load flow methods. If the same principle is applied to distribution networks, a better load flow is developed. Also it can be understood that, the conservation principle is a known reality and when it is used to find a new load flow solution of a network, that new load solution could also be a real and near to the practical solution.
The power conservation principle for the entire network is designated as a theorem called Tellegen theorem.
Hence, a part of the objective of this thesis work is to develop and formulate an efficient solution algorithm for the distribution networks using Tellegen theorem.
1.4 A Generalized form of Tellegen Theorem :
The electric network properties are analyzed from the impedance functions without a detailed knowledge of the circuit diagram. But certain properties like energy consumption and reciprocity of network could not be analyzed with the basic impedance functions. Usually the inner structure of the network is always taken into consideration for the energy distribution in the network . Hence a general theorem called Tellegen theorem has come into existence .
Among the theorems of circuit theory , Tellegen theorem is typical and solely depends upon the kirchoff’s laws and the topology of the network . The theorem applies to all electrical networks that obey kirchoff’s laws whether they are linear or non-linear.
Time invariant or time variant , reciprocal or non – reciprocal. The excitation is arbitrary and initial conditions are also immaterial. When specific assumptions are made concerning the network elements , the excitation and the initial conditions , tellegen theorem reduces to many useful network theorems .
The general Tellegen theorem is stated as followed
In any network configuration , Imagine branch currents "I " such that for every Node I=0, Assume branch voltages V such that for every mesh V =0 and for every branch let the Positive Direction Of 'The Current be from the "+" to the "-" Denoting the PositivePolarity Of the Voltage Fig. 1.1, Then VI = 0 Where the Summation Is Over All The Branches.
The theorem is represented mathematically in a basic form
v b Tib = 0
Where b varies from 1 to Nb where Nb is Total Number Of branches
For any mesh , the Kirchoff s Voltage law says that the sum Of the instantaneous Voltages are Zero i.e.. v = 0.
Let the Potentials of the arbitrary nodes 'M' and ‘N' are Vm and Vn respectively andvoltage across the branch Connecting 'M' and *N' nodes Is Vmn = Vm - Vn
Let the Current flowing through the branch Is I mn
Then the Product Of Voltage across the branch and Current flowing through the branch is called instantaneous power,
Vm Imn = (Vm – Vn ) Imn = Vm Imn – Vn Im
The Eqn [1.48] is applied to all the branches of the network , whose one of the node voltage is Vm and collect all the terms containing Vm.