IEEE P3002.2/D6, Oct 2015
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IEEE P3002.2 ™/D6 Draft Recommended Practice for Conducting Load-Flow Studies of Industrial and Commercial Power Systems
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Sponsor
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Technical Book Coordinating Committee of the IEEE
Society
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Approved
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Copyright © 2015 by the Institute of Electrical and Electronics Engineers, Inc. Three Park Avenue New York, New York 10016-5997, 10016-5997, USA
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All rights reserved.
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This document is an unapproved draft of a proposed IEEE Standard. As such, this document is subject to change. USE AT YOUR OWN RISK! Because this is an unapproved draft, this document must not be utilized for any conformance/compliance purposes. Permission is hereby granted for IEEE Standards Committee participants to reproduce this document for purposes of international standardization consideration. Prior to adoption of this document, in whole or in part, by another standards development development organization, permission permission must first be obtained from the IEEE Standards Activities Department ([email protected]). Other entities seeking permission to reproduce this document, in whole or in part, must also obtain permission from the IEEE Standards Activities Department.
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IEEE P3002.2/D6, Oct 2015
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Abstract: This recommended practice addresses activities related to load flow analysis, including design considerations for new systems, analytical studies for existing systems as well as operational and model validation considerations for industrial and commercial power systems. Load flow analysis includes steady-state power flow and voltage analysis along with considerations for optimal power flow calcula calculations. tions. This recomm recommended ended practice emphasiz emphasizes es the use of computer-aide computer-aided d analysis software with a list of desirable capabilities recommended to conduct a modern load flow study. It also presents examples of system data requirements and presents result analysis techniques.
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Keywords: load flow studies, load flow analysis, power flow, overload, over voltage, under voltage, power factor correction, impedance, overloads, voltage profile, electrical losses, voltage drop, compensation, cable ampacity, system validation, industrial loads, generation,
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IEEE P3002.2/D6, Oct 2015
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Abstract: This recommended practice addresses activities related to load flow analysis, including design considerations for new systems, analytical studies for existing systems as well as operational and model validation considerations for industrial and commercial power systems. Load flow analysis includes steady-state power flow and voltage analysis along with considerations for optimal power flow calcula calculations. tions. This recomm recommended ended practice emphasiz emphasizes es the use of computer-aide computer-aided d analysis software with a list of desirable capabilities recommended to conduct a modern load flow study. It also presents examples of system data requirements and presents result analysis techniques.
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Keywords: load flow studies, load flow analysis, power flow, overload, over voltage, under voltage, power factor correction, impedance, overloads, voltage profile, electrical losses, voltage drop, compensation, cable ampacity, system validation, industrial loads, generation,
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The Institute of Electrical and Electronics Engineers, Inc. 3 Park Avenue, New York, NY 10016-5997, USA Copyright © 20XX by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Published Published . Printed in the United United States of America. IEEE is a registered trademark in the U.S. Patent & Trademark Office, owned by the I nstitute of Electrical and Electronics Engineers, Incorporated. PDF: Print:
ISBN 978-0-XXXX-XXXX 978-0-XXXX-XXXX-X -X ISBN 978-0-XXXX-XXXX 978-0-XXXX-XXXX-X -X
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No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher.
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IEEE P3002.2/D6, Oct 2015
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IEEE P3002.2/D6, Oct 2015
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IEEE P3002.2/D6, Oct 2015
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Introduction
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This introduction is not part of IEEE P3002.2/D1, Draft Recommended Practice for Conducting Load-Flow Studies of Industrial and Commercial Power Systems.
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IEEE P3000 Series
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This recommended practice was developed by the Technical Books Coordinating Committee of the Industrial and Commercial Power Systems Department of the Industry Applications Society, as part of a project to repackage IEEE’s popular series of “color books.” The goal of this project is to speed up the revision process, eliminate duplicate material, and facilitate use of modern publishing and distribution technologies.
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When this project is completed, the technical material included in the thirteen “color books” will be included in a series of new standards — the most significant of which will be a new book, IEEE Standard 3000, “Recommended Practice for the Engineering of Industrial and Commercial Power Systems.” The new book will cover the fundamentals of planning, design, analysis, constructi on, installation, start-up, operation, and maintenance of electrical systems in industrial and commercial facilities. Approximately 60 additional “dot” standards, organized into the following categories, will provide in-depth treatment of many of the topics introduced by IEEE Standard 3000:
Power Systems Design (3001 series)
Power Systems Analysis (3002 series)
Power Systems Grounding (3003 series)
Protection and Coordination (3004 series)
Emergency, Stand-By Power, and Energy Management Systems (3005 series)
Power Systems Reliability (3006 series)
Power Systems Maintenance, Operations, and Safety (3007 series)
In many cases, the material in a “dot” standard comes from a particular chapter of a particular color book. In other cases, material from sever al color books has been combined into a new “dot” standard. The material in this recommended practice largely comes from IEEE 399 standard with emphasis towards practical load flow analysis.
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IEEE P3002.2/D6, Oct 2015
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IEEE P3002.2
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Recommended Practice for Conducting Load-Flow Studies of Industrial and Commercial Power Systems provides a recommended practice for load flow analysis of industrial and commercial power systems. It is likely to be of greatest value to the power-oriented engineer with limited experience in this area. It can also be an aid to all engineers responsible for the analysis of the operation of industrial and commercial power systems.
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Notice to users
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Laws and regulations
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Users of these documents should consult all applicable laws and regulations. Compliance with the provisions of this standard does not imply compliance to any applicable regulatory requirements. Implementers of the standard are responsible for observing or referring to the applicable regulatory requirements. IEEE does not, by the publication of its standards, intend to urge action that is not in compliance with applicable laws, and these documents may not be construed as doing so.
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Copyrights
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Updating of IEEE documents
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Users of IEEE standards should be aware that these documents may be superseded at any time by the issuance of new editions or may be amended from time to time through the issuance of amendments, corrigenda, or errata. An official IEEE document at any point in time consists of the current edition of the document together with any amendments, corrigenda, or errata then in effect. In order to determine whether a given document is the current edition and whether it has been amended through the issuance of amendments, corrigenda, or errata, visit the IEEE Standards Association web site at http://ieeexplore.ieee.org/xpl/standards.jsp , or contact the IEEE at the address listed previously.
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For more information about the IEEE Standards Association or the IEEE standards development process, visit the IEEE-SA web site at http://standards.ieee.org .
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Errata
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Errata, if any, for this and all other standards can be accessed at the following URL: http://standards.ieee.org/reading/ieee/updates/errata/index.html . Users are encouraged to check this URL for errata periodically.
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IEEE P3002.2/D6, Oct 2015
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Interpretations
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Current interpretations can be http://standards.ieee.org/reading/ieee/interp/ index.html.
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Patents
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[If the IEEE has not received letters of assurance prior to the time of publication, the following notice shall appear:]
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Attention is called to the possibility that implementation of this recommended practice may require use of subject matter covered by patent rights. By publication of this recommended practice, no position is taken with respect to the existence or validity of any patent rights in connection therewith. The IEEE is not responsible for identifying Essential Patent Claims for which a license may be required, for conducting inquiries into the legal validity or scope of Patents Claims or determining whether any licensing terms or conditions provided in connection with submission of a Letter of Assurance, if any, or in any licensing agreements are reasonable or non-discriminatory. Users of this recommended practice are expressly advised that determination of the validity of any patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Further information may be obtained from the IEEE Standards Association.
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[The following notice shall appear when the IEEE receives assurance from a known patent holder or patent applicant prior to the time of publication that a license will be made available to all applicants either without compensation or under reasonable rates, terms, and conditions that are demonstrably free of any unfair discrimination.]
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Attention is called to the possibility that implementation of this recommended practice may require use of subject matter covered by patent rights. By publication of this recommended practice, no position is taken with respect to the existence or validity of any patent rights in connection therewith. A patent holder or patent applicant has filed a statement of assurance that it will grant licenses under these rights without compensation or under reasonable rates, with reasonable terms and conditions that are demonstrably free of any unfair discrimination to applicants desiring to obtain such licenses. Other Essential Patent Claims may exist for which a statement of assurance has not been received. The IEEE is not responsible for identifying Essential Patent Claims for which a license may be required, for conducting inquiries into the legal validity or scope of Patents Claims, or determining whether any licensing terms or conditions provided in connection with submission of a Letter of Assurance, if any, or in any licensing agreements are reasonable or non-discriminatory. Users of this recommended practice are expressly advised that determination of the validity of any patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Further information may be obtained from the IEEE Standards Association.
accessed
at
the
following
URL:
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vi Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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IEEE P3002.2/D6, Oct 2015
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Participants
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At the time this draft recommended practice was submitted to the IEEE-SA Standards Board for approval, the Power Systems Analysis Editorial Working Group had the following membership:
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Farrokh Shokooh, Chair Albert Marroquin, Vice Chair Massimo Mitolo, Vice Chair
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Tanuj Khandelwal Haijun Liu Bill Roettger
11 Srikrishna Chitharanjan 12 Louie Powell 13 Daniel Ransom
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(to be supplied by IEEE)
14 Franklin Quilumba 15 Salman Kahrobaee 16 Mandar Manjarekar
The following members of the balloting committee voted on this recommended practice. Balloters may have voted for approval, disapproval, or abstention. (to be supplied by IEEE)
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Balloter1 Balloter2 Balloter3
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When the IEEE-SA Standards Board approved this trial-use recommended practice on , it had the following membership:
, Chair , Vice Chair , Past President , Secretary
SBMember1 SBMember2 SBMember3 *Member Emeritus
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49 SBMember7 50 SBMember8 51 SBMember9
Also included are the following nonvoting IEEE-SA Standards Board liaisons:
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, TAB Representative , NIST Representative , NRC Representative
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IEEE Standards Program Manager, Document Development IEEE Standards Program Manager, Technical Program Development vii Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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IEEE P3002.2/D6, Oct 2015
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IEEE P3002.2/D6, Oct 2015
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Contents
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1. Scope........................................................................................................................................... 1
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2. Normative references................................................................................................................. 1
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3. Introduction ................................................................................................................................ 1
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4. Analysis Objectives ................................................................................................................... 2
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5. System Simulation and Modeling............................................................................................. 4 5.1 Modeling Requirements...................................................................................................... 4 5.2 Overall Description of Example Industrial/Commercial Power System ......................... 5
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6. Required Input Data................................................................................................................... 4 6.1 General .................................................................................................................................. 4 6.2 System Data ......................................................................................................................... 4 6.3 Bus Data ............................................................................................................................... 5 6.4 Load Data .............................................................................................................................. 6 6.5 Generator Data..................................................................................................................... 7 6.6 Branch data .......................................................................................................................... 7 6.7 Transformer Data .................................................................................................................. 8 6.8 Example System Input Data .................................................................................................. 9
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7. Methodology and Standards...................................................................................................... 9 7.1 General .................................................................................................................................. 9 7.2 Overall Solution .................................................................................................................. 10 7.3 Problem Formulation .......................................................................................................... 10 7.4 Iterative Solution Algorithms .............................................................................................. 12 7.5 Gauss-Seidel iterative Technique ........................................................................................ 13 7.6 Newton-Raphson iterative Technique ................................................................................. 17 7.7 Comparison of Load Flow Solution Techniques ................................................................ 19 7.8 Load flow Source Models for Active and Reactive Power Limits and Controls ................ 20
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8. Model and Data Validation ..................................................................................................... 24
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9. Load flow Study Example....................................................................................................... 25 9.1 General ................................................................................................................................ 25 9.2 Load Flow Study Scenario Considerations ..................................................................... 27 9.3 Analysis of Load Flow Results ........................................................................................ 30
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10. Load Flow Analysis Results and Reports ............................................................................ 35
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11. Advanced Load Flow Applications ...................................................................................... 37
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12. Features of Analysis Tools.................................................................................................... 38
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13. Optimal Power Flow.............................................................................................................. 39
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14. Conclusions ............................................................................................................................ 40 ix Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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IEEE P3002.2/D6, Oct 2015
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15. Annex A – Reference and Additional Sources .................................................................... 40
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16. Annex B – Example System Input Data .............................................................................. 41
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IEEE P3002.2/D5, February, 2015
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Draft Recommended Practice for Conducting Load-Flow Studies of Industrial and Commercial Power Systems
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IMPORTANT NOTICE: This standard is not intended to ensure safety, security, health, or environmental protection in all circumstances. Implementers of the standard are responsible for determining appropriate safety, security, environmental, and health practices or regulatory requirements.
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This IEEE document is made available for use subject to important notices and legal disclaimers. These notices and disclaimers appear in all publications containing this document and may be found under the heading “Important Notice” or “Important Notices and Disclaimers Concerning IEEE Documents.” They can also be obtained on request from IEEE or viewed at http://standards.ieee.org/IPR/disclaimers.html .
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1. Scope
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This recommended practice describes how to conduct load-flow studies for industrial and commercial power systems. It will be of greatest value to the power-oriented engineer with limited experience in this area. It can also be an aid to all engineers responsible for the electrical design of industrial and commercial power systems.
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2. Normative references
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The following referenced documents are indispensable for the application of this document (i.e., they must be understood and used, so each referenced document is cited in text and its relationship to this document is explained). For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments or corrigenda) applies.
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IEEE Std. 399-1997, IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (IEEE Brown Book™)1.
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3. Introduction
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Load flow is also referred to as Power flow; these terms may be interchangeably used in this standard. This is the name given to a network solution that predicts steady-state currents, 1
IEEE publications are available from the Institute of Electrical and Electronics Engineers, 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331, USA.
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IEEE P3002.2/D5, February, 2015
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voltages, and real and reactive power flows through every branch and bus in the system. Load flow studies simulate operating conditions that cannot practically be experienced on the actual system because the system has not yet been built, because of the practical constraints of time, or because it would be unwise to expose the actual physical system to conditions that are potentially damaging. The end objective of the load flow study is not necessarily to arrive at hard, numerical performance parameters, but rather to gain insight into how the system performs over a range of operating scenarios.
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4. Analysis Objectives
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One of the most common computational procedures used in power system analysis is the load flow calculation. The planning, design, and operation of power systems require such calculations to analyze the steady-state (quiescent) performance of the power system under various operating conditions and to study the effects of changes in equipment configuration. The basic load flow question is this: given the load power consumption at all buses of a known electric power system configuration (e.g. network topology) and the power production at each generator, find the power flow in each line and transformer of the interconnecting network and the voltage magnitude and phase angle at each bus.
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For some types of equipment (e.g., photovoltaic solar arrays or wind farms), a time varying simulation, such as a time domain load flow may be required in order to fully understand the behavior of the electrical system over a period of time. These load flow solutions are performed using computer programs designed specifically for this purpose.
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Analyzing the solution of this problem for numerous conditions helps ensure that the power system is designed to satisfy its performance criteria while incurring the most favorable investment and operation costs.
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Some examples of the uses of load flow studies are to determine the following:
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Because the parameters of the elements such as lines and transformers are constant, the power system network itself is linear. However, in the power flow problem often involves specifying magnitudes of either real or reactive power, which then means that the relationship between voltage and current becomes nonlinear, and the same holds for the relationship between the real and reactive power consumption at a bus, or the generated real power and scheduled voltage magnitude at a generator bus. Thus, power flow calculation involves the solution of a set of nonlinear equations. This calculation gives the electrical response of the power system to a particular set of loads and generator power outputs. Power flows are an important part of power system operation and planning.
Component or circuit loadings
Steady-state bus voltages
Real and Reactive power flows
Transformer tap settings and Load Tap Changer actions
System Real and Reactive power losses and voltage drops
Generator exciter/regulator voltage set points
Undervoltage and overvoltage conditions for buses as well as equipment terminals 2 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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IEEE P3002.2/D5, February, 2015
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Performance under maximum, normal and minimum loading conditions
Performance under various operating configurations
Performance under emergency conditions (post contingency)
Requirement for either fixed or variable power factor improvement equipment
Load flow analysis has a great importance:
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1. To verify the operation of a network under various load and generation conditions
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2. To plan the future growth of both loads and generation
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3. To determine the best economical operation for existing systems
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4. To establish initial conditions for stability studies
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Also load flow results are very valuable for setting the proper protective devices to insure the safety of the system. In order to perform a load flow study, full data must be provided about the studied system, such as one-line diagram, parameters of transformers, cables and transmission lines, rated values of each equipment, and the real and reactive power for each load.
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Modern systems may be complex and have many paths or branches over which power can flow. Such systems form networks of series and parallel paths. Electric power flow in these networks divides among the branches until a balance is reached in accordance with Kirchhoff’s laws.
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There are generally two types of computer load flow programs — those intended for offline planning purposes, and those designed to operate in real-time, actively receiving input from the actual system. Most load flow planning studies use off-line software. On-line, or real-time load flows incorporate data input from the actual networks are becoming increasingly important in bridging the gap between static / planning network model and the model used by those responsible for actual system operation. Computer programs are also available that provide integrated off-line and real-time solutions for ‘what if’ predictive analysis. Such systems are able to integrate with existing plant Supervisory Control and Data Acquisition (SCADA) systems. Integrated real-time systems can therefore be used as planning and design tools as well as dispatching tool for the operator. And an additional level of sophistication is possible using so- called ‘optimal power flow’ modeling that applies constraints in the load flow solution to achieve objectives, such as minimum fuel cost, minimum power loss, flat voltage profile, etc.
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For industrial and commercial power systems, the load flow problem involves balanced, steadystate operation. Hence a single-phase, positive sequence model of the power system is typically sufficient. Three-phase or unbalanced load flow analysis software is available but is rarely needed in industrial power system applications.
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A load flow calculation determines the state of the power system for a given load and generation distribution. It represents a steady-state condition as if that condition had been held fixed for some time. There are situations in industrial applications where the issues of interest involve how those steady state conditions change over periods of minutes to hours as a consequence of changes in loading or generation; these applications can adequately simulated using conventional load flow tools by means of a series of simulations reflecting the pertinent 3 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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IEEE P3002.2/D5, February, 2015
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changes. On the other hand, concerns about how systems respond in the cycles-to-seconds time frame, perhaps as a consequence of short circuits or other disturbances, should be addressed using transient stability software. Power system transient stability is beyond the scope of this document.
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In actuality, line flows and bus voltages fluctuate constantly by small amounts because loads change constantly (e.g. lights, motors, and other loads are turned on and off). However, these small fluctuations can be ignored in calculating the steady-state effects on system equipment.
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As the load distribution, and possibly the network, will vary considerably during different time periods, it may be necessary to obtain load flow solutions representing different system conditions such as peak load, average load, or light load. These solutions will be used to determine either optimum operating modes for normal conditions, such as the proper setting of voltage control devices, or how the system will respond to abnormal conditions, such as line or transformer outages. Load flows form the basis for determining both when new equipment additions are needed and the effectiveness of new alternatives to solve present deficiencies and meet future system requirements.
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The load flow model is also the basis for several other types of studies such as short-circuit, stability, motor starting, and harmonic studies. The load flow model supplies the network data and provides an initial steady-state condition for these studies.
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5. System Simulation and Modeling
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5.1 Modeling Requirements
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Industrial plant electrical systems can be extensive. A simplified visual means of representing the complete system is essential to understanding the operation of the system under its various possible operating modes. The system one-line diagram serves this purpose. The one-line diagram is a single line representation of 3 , 2 , and 1 system identifying buses and interconnecting lines. Loads, generators, transformers, reactors, capacitors, etc., are all shown in their respective places in the system. In order to analyze any circuit, we use as a reference those points that are electrically distinct, that is, there is some impedance between them, which can sustain a potential difference. These reference points are called nodes. When representing a power system on a large scale, the nodes are called buses, since they represent an actual physical busbar where different components of the system meet. A bus is electrically equivalent to a single point on a circuit, and it marks the location of one of two things: a generator that injects power, or a load that consumes power.
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Drawing format will vary depending on the computer programs used and the preference of the users, but the one-line diagram should give the necessary network information in a clear, concise manner. The transfer of this data to the load flow program for analysis is discussed in the next section.
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It is necessary to know equipment parameters as well as their relationship to each other. Depending on the computer program being used, parameters may either be displayed directly on the one-line diagram, or may be listed in tables that accompany that diagram. Figure 1 is an example one-line diagram that will be used throughout this standard to illustrate some aspects of load flow studies.
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Bus names (or numbers) are displayed along with the bus nominal voltages. Interconnecting lines are usually shown with their impedance values and lengths entered. Equipment associated with a bus is shown connected to that bus. For instance, generators are shown connected to their bus with their equipment parameters specified, as illustrated in Figure 2. Similarly, loads are shown connected to bus Sub 2A in Figure 3. Motor loads are often indicated separately to aid in their modeling in short circuit and other studies. Each line originates on a bus and terminates on a different bus, as depicted in Figure 3. Transformers, like lines, are shown between two buses with the primary connected to one bus and the secondary to the other. Information to convey an offnominal turns ratio should be given when applicable.
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5.2 Overall Description of Example Industrial/Commercial Power System
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The sample system created to illustrate the process of performing a load flow analysis contains portions of different types of components which can be encountered in different heavy and light industrial power systems and or commercial installations. Figure 1 below shows the example system which will be used. The system contains the following component types which may be encountered for different systems:
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High voltage switchyard (heavy industrial facilities may own and be responsible for this part of the system) Medium voltage power distribution switchgear with multiple source feeders (common of large refinery and process driven facilities
20
Oil field and largely distributed pumping stations
21
Larger generation plant with dedicated unit transformer (~100+ MW capacity)
22
Smaller cogeneration components (~10’s MW capacity)
23
Double-ended secondary selective medium and low voltage switchgear configurations
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Emergency and critical system data backup systems (similar to “T ier 1” data center configurations). Larger industrial / commercial facilities may have data backup requirements with UPS units Large arc-furnace loads and harmonic filter similar to what may be found in large steel manufacturing plants. These components can be used to simulate the power factor correction and harmonic load flow content Synchronous motor compressors with excitation system control configurable to voltage or power factor support Adjustable speed drives (ASDs) or variable frequency drives which may be used for a variety of induction/synchronous motor control applications like and submersed pumping stations Building service power systems. Examples of industrial or institutional facilities which may have their own building power distribution system 5 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Example of micro grid application which includes renewable energy sources like photovoltaic (PV) installations and converter sources. Wind turbine generation which can take advantage of renewable energy sources available. The wind turbine system is used for distributed generation example load flow conditions.
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The one-line diagram of this system does not represent an actual installation which combines all of the individual components. The system was designed to be an educational tool for the purpose of explaining load flow concepts which may not be encountered in typical industrial/commercial installations. Furthermore, the intent of the example system used in this chapter is not to represent “best design practices” of industrial and commercial power systems. Figures 2~9 show the one-line diagrams of the individual components included in the example system.
12 13
Note that the example also contains 1-phase and multi-frequency components. The example does not extend to any dc elements.
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
m a r g a i D e n i L e n O m e t s y S e l p m a x E w o l F d a o L — 1 e r u g i F
. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d n 7 E a E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
1 2
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d l e i F l i O e h t f o
5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
m a r g a i D e n i L e n O — 2 e r u g i F
1
. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d n 8 E a E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
2 3 4
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1 2
Figure 3
— One-line
Diagram of the Wind Farm
Figure 4
— One-line
Diagram of the Bldg Service
3
4 5 6 7 8 9
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
1 n o i t a t s b u S e h t f o m a r g a i d e n i l e n O — 5 e r u g i F
. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d 0 E n a 1 E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
1 2 3
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
2 n o i t a t s b u S e h t f o m a r g a i d e n i l e n O — 6 e r u g i F
. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d n 1 E a E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
1 2
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
r e t n e C a t a D e h t f o
m a r g a i d e n i l e n O — 7 e r u g i F
. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d n 2 E a E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
1 2 3
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2 3
Figure 8
— Generating
Power Station Diagram
4
±
I>
TR:3
Dyn1
7.5 MVA 8 %Z
13.8/6.3 kV CB:22 Sub 2A
6.3 kV
CB:35
Lump5 5 6
M-6061 4000 kW
Figure 9
— Representation
of Loads, Lines, and Transformer
7
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6. Required Input Data
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6.1 General The data shown on the one-line describes the system configuration and the location and size of loads, generation, and equipment. It is organized into a list of data that defines the mathematical model for each power system component and how the components are connected together. The preparation of this data file is the foundation of all load flow analysis, as well as other analysis requiring the network model, such as short circuit and stability analysis. It is therefore essential that the data preparation be performed in a consistent, thorough manner. Data values must be as accurate as possible. Rounding and not including enough decimal places in certain parameters, can lead to erroneous results. Influential parameters must not be ignored. Tolerance values, wherever applicable, shall be considered for the calculations; the input uncertainty should always be conservatively taken into account; also a sensitivity analysis may help define proper data tolerance.
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In this sub- clause, data organization is shown in general terms and some comments are given on data preparation. The data are divided into the following categories (this organization is typical of most load flow analysis software): system data, bus data, generator data, branch data, and transformer data.
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Not too long ago, analysts were challenged by the fact that computer technology limited the number of node points that could be represented in a load flow model. This forced study engineers to be very creative about combining elements connected in series, or to choose to ignore elements that were judged to be irrelevant to the problem being solved. Modern simulation software running on modern computers is rarely constrained in this fashion. While is often necessary to build elaborate models of an entire system, experienced analysis understand that it is often still prudent to limit the extent of the model to include only those components and elements that are actually pertinent to the problem being addressed. Time typically relates to money, and it doesn’t make sense to invest any more time in data collection and model building than is needed to answer the question at hand.
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6.2 System Data
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Most load flow programs perform their calculations using a per unit representation of the system rather than working with actual volts, amperes, and ohms. The input of data to the program can either be in per unit or in physical units, depending on the design of the program. Converting the system data to a per unit representation requires the selection of a base kVA and base voltage. Selecting the base kVA and base voltage specifies the base impedance and base current. Computer programs automatically determine the other base kV based upon transformer turns ratios in the system.
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The system data specifies the base kVA (or MVA) for the entire system. A base 100 MVA) has traditionally been used for industrial studies, but other base values may also be chosen.
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The base kV is chosen for each voltage level. Selecting the nominal voltage to be the base voltage simplifies the analyses and reduces the chance of errors in interpretation of results.
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6.3 Bus Data
2 3 4
Buses represent the nodes of the electrical system and can be classified based on their conditions of load and/or generation. The bus data describe each bus and the load and shunts connected to that bus. The data include the following:
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Bus Name and/or bus number
Bus classification (Swing/Voltage Controlled/Load Bus)
Bus Service (In / Out) or Status
Bus nominal voltage
Bus rating / continuous amps
Initial per unit voltage and angle (to be discussed later)
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The bus ID may be a combination of characters and numbers, and is normally used only for identification purposes, allowing the user to give a descriptive name to the bus to make program output more easily understood. The bus ID should be unique in order to avoid errors while interpreting results.
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The bus classification allows the program to properly organize the buses for load flow solution. In general, there are three classifications for buses.
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1 Slack or Swing Bus The “swing” or “slack” bus is a special type of generator bus that is needed by the solution process. There is normally only one swing bus in a load flow model. In systems with strong grid interconnections, the grid connection is typically specified as the swing bus. In the absence of a grid connection, one generator must be selected as the swing bus. The swing bus is also referred to as the “infinite” bus. In reality, the power that the swing bus can release is finite, but very large with respect to the other generators of the system. During the operation, the voltage of this bus is always specified to remain constant in magnitude V and phase or angle θ, whereas, active and reactive powers will change according to the network. For this reason, this bus is also called the “ θ, V” bus. In addition to the generation assigned to the swing bus, this bus is responsible for supplying the losses of the system. The swing generator adjusts its scheduled power to supply the system MW and MVAR losses that are not otherwise accounted for, so that: power absorbed by loads plus power losses equals the power delivered by the swing bus plus power delivered by generator(s). 2. Generator or Voltage Controlled Bus During load flow simulations, the voltage magnitude at the voltage controlled bus is kept constant, and the reactive loading on the machine is adjusted as required to satisfy system conditions while maintaining that voltage. The active power supplied is kept constant at the value assigned to the generator. This most closely represents the situation with a generator where the voltage is controlled using the excitation and the power is controlled by the prime mover and the terminal voltage is regulated by an excitation system. A generator bus can also be used to represent a variable-reactive device where the voltage can be controlled by varying the value of the injected VAR to the bus. For the above reasons, this bus is also defined as the “P, V” bus, and the quantities θ and Q vary according to the network. 5 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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If a generator bus is not voltage regulated (e.g., an induction generator), the real power P and the reactive power Q are fixed in magnitude; thus, as load varies, the voltage magnitude V and the voltage θ angle vary. Induction generators are best represented as negative loads on load buses.
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The terms “load” bus and “generator” bus should not be taken literally, because the terms describe only the bus electrical behaviors, without necessarily implying the presence of equipment.
3. Load Bus In a load flow simulation, both the voltage magnitude and phase angle will change according to loading and network conditions. For simulation purposes, load buses are most often defined as having a ‘constant MVA’ characteristic which means that the complex power S= P = jQ will be held constant. Load buses are also defined as “P, Q” buses. That said, some load flow programs offer options for other forms of load bus modeling. For example, some kinds of static power conversion equipment might better be modeled as having constant real power, constant current characteristics. A load bus need not have load, it may simply be an interconnection point for two or more lines; in this case, Kirchhoff’s law requires that the sum of the real and reactive flows into the node equal the sum of the flows out of the bus.
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6.4 Load Data
20 21 22 23 24 25 26 27 28 29 30
In the load flow program, loads must be entered in a manner that is consistent with the design of the program. The most common scenario is for loads to be MW and MVAR at nominal voltage. As anticipated, the load is treated as a constant MVA, that is, independent of voltage. In some cases, a Constant Current or Constant Impedance component of load could also be entered so that the load is a function of voltage, as explained in IEEE Std 399-1997 (section 4.9). Shunts generally are entered in MVAR at nominal voltage. Care must be taken to ensure that the proper sign convention is used to differentiate between capacitive and reactive shunt loads. The load data are used to represent the load at various bus locations. Usually, the constant MVA load representation is used. Sometimes, the constant current or constant impedance type of load model may be used. Depending on the design of the software, load data may include some or all of the following:
31
-
Load Identification (either descriptive text or a unique load number)
32
-
Load Service (In/Out) or State
33
-
Real / Reactive power Rating
34
-
Rated Power factor
35
-
Loading in percent of nameplate or brake horsepower (BHP)
36
-
Load demand factor (continuous, intermittent or spare)
37 38
-
Load type for lumped loads (constant kVA, constant Z and/or constant I) and Load type ratio (% constant kVA, % constant Z, % constant I) 6 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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-
For motor loads, the efficiency and power factor of the machine, in percent, at 100%, 75%, and 50% loading, as well as the no-load and over loading conditions,
3 4
6.5 Generator Data
5 6 7 8
Generator data is entered for each generator in the system including any generator that may be connected to the designated system swing bus. The data defines the generator power output and how voltage is controlled by the generator. Depending on the design of the software, generator data may include some or all of the following:
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Generator identification (ID).
Generator nameplate ratings (rated MW, MVA, power factor and efficiency)
Generator operating mode (Swing, Voltage Control, MVAR Control, Power Factor Control) Operating real power output in MW (Voltage Control, MVAR Control, Power Factor Control)
Operating reactive power output in MVAR (MVAR Control)
Initial operating voltage angle in degrees (for the swing bus)
Operating power factor in percent (Power Factor Control)
Maximum reactive power output in MVAR (i.e., machine maximum reactive limit, Qmax)
Minimum reactive power input in MVAR (i.e., machine minimum reactive limit, Qmin)
Scheduled voltage in per unit (Swing, Voltage Control)
Generator Service (In/Out) or State
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Other items that might be included the model date are the generator MVA base and the generator’s internal impedance for use in short-circuit and dynamic studies. Computer programs may allow a generator to regulate a remote bus voltage although in most programs the control bus is usually the generator terminal bus / node.
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6.6 Branch data
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Data is also entered for each branch in the system. Herein the term “branch” refers to all elements that connect two buses including transmission lines, cables, series reactors, series capacitors, and transformers. In the real system, there may be multiple elements in series (e.g., an overhead transmission circuit that transitions into a cable circuit); when using modern simulation software that does not impose practical limits on the number of nodes in the model, it is preferable to treat each of these elements separately connected by a ‘node’. The data items include the following:
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From Bus / To Bus Identifications Branch Identification (especially if there are parallel branches connecting the specified From and To buses 7 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Branch Service (In/Out) or State
Physical length (Cable and Transmission Line)
Resistance in Ohms or Ohms per unit of length
Resistance in Ohms or percent on the chosen study base MVA
Reactance in Ohms or Ohms per unit length
Reactance in Ohms or percent on the chosen study base MVA base
Charging susceptance (shunt capacitance)
Line continuous amperage rating
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In industrial systems, overhead transmission lines and cable circuits are typically short, so the charging capacitance of these circuits is often immaterial. Hence, char ging susceptance is often omitted from industrial system load flow models. When susceptance is included, lines are represented by a model with series resistance and reactance and one-half of the charging susceptance placed on each end of the line. The resistance, reactance, and susceptance are usually input in either per unit or percent, depending on program design.
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Line ratings are normally input in amperes or MVA, depending on the design of the software. Current ratings can be converted to MVA with the formula:
18
ratingMVA =
3 kVBASE rating A
(1)
1000
19
A series reactor, series capacitor, or transformer would not have a charging susceptance term.
20
6.7 Transformer Data
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Additional data are required for transformers. These can either be entered as part of the branch data or as a separate data category depending on the particular load flow program being used. Depending on the design of the software, these additional data may include the following:
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Transformer Service (In/Out) or State
Transformer Identification
Rated MVA of the transformer based on transformer cooling class and number of cooling stages Transformer impedance (Z) in percent on stated MVA base. Some software may allow specifying positive and negative manufacturing tolerance values for transformer impedance. Three winding transformer impedance in percent on primary MVA base. Use caution to take the time to understand how the design of the software expects these impedances to be stated. The impedances of three-winding transformers can be stated either as determined by factory tests as separate primary-secondary, primary-tertiary, tertiary-secondary values on a stated base, or equivalent values to a fictitious center node, also on a specified base.
Fixed Tap setting in percent or kV, as require by the design of the software
Phase shift angle in degrees, if applicable 8 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Tap step size for automatic on-load tap changers
Maximum tap position for fixed and/or automatic on-load tap changers
Minimum tap position for fixed and/or automatic on-load tap changers
The organization of transformer tap data requires an understanding of the tap convention used by the load flow program to ensure the representation gives the correct boost or buck in voltage. Transformers with rated primary or secondary voltages that do not match the system nominal (base kV) voltages on the terminal buses will require an off-nominal tap representation in the load flow (and possibly require corresponding adjustment of the transformer impedance).
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6.8 Example System Input Data
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The example system described in section 5.2 and used for the load flow analysis example in section 9 has input data tables which are provided in Annex B. The input data listed in those tables is not limited to or may not follow the generic format of input data described in sections 6.1~6.7. The input data format can be different for different software simulation tools. The format of the computer simulation tool used to perform the load flow study described in section 9 was used to populate the data tables of Annex B.
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Note that the amount of input parameters required depends on the complexity and capability of the simulation tool used to perform a load flow analysis. For simplicity the tables in Annex B only contain the basic information which is considered “common” to most software analysis tools. Additional input parameters may be required to apply some of the analysis methods described in section 7; however, were omitted from this document; once again for simplicity purposes.
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7. Methodology and Standards
26
7.1 General
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Because load flow calculations involve solutions of a set of non-linear equations, manual solutions are impractical except for purely pedantic examples. Before digital computer solutions were available, load flow simulations were conducted using analog boards. In the very early days, these analog boards were simple dc devices with the elements of the power system represented by resistances. Obviously, the answers were not absolutely accurate, but were amazingly close enough for practical application.
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A special purpose analog boards called the ac network analyzer was developed in the late 1920s. Power system networks under study were represented by an equivalent, scaled-down network. The device allowed the analysis of a variety of operating conditions and expansion plans. The simulation setup time was long, and the time to conduct studies and record the results slowly made the network analyzers become cost ineffective. Furthermore, the large amount of hardware required led to their diminishing use. Only about 50 network analyzers were left in operational by the mid-1950s. 9 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Computers began to emerge in the late 1940s as computational tools. By the mid 1950s, largescale computers of sufficient speed and size to handle the requirements of a power system network calculation were available. Parallel to the hardware development, algorithms to efficiently solve the network equations were developed. Ward and Hale developed a successful load flow program using a modified Newton iterative procedure in 1956 [B5]. 1 The application of the Gauss-Seidel iteration algorithm followed soon after. Research in algorithms continued and the Newton-Raphson method was introduced in the early 1960s [B4]. Considerable research has been performed in the interim years to improve the performance of these al gorithms, making them more robust, able to handle additional power system components; the new algorithms accommodate much larger network sizes. These calculation algorithms persist to modern days and include adaptive methods which can adjust to higher system convergence demands.
12
7.2 Overall Solution
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A rough outline of solution of the power flow problem is the following: 1. Make an initial guess of all unknown voltage magnitudes and angles. It is common to use a "flat start" in which all voltage angles are set to zero and all voltage magnitudes are set to 100%. 2. Set an initial angle for the swing bus. The angle assigned to the swing bus is the reference for the bus voltage angles calculated for each other bus in the system. Some o engineers arbitrarily use 0 as the swing bus angle, but this typically results in negative signs on load bus voltage angles. A tradition going back to the days of ac network analyzers is to use an angle such as 50 o for the swing bus to avoid negative bus voltage angles in the final solution. 3. Solve the power balance equations using the most recent voltage magnitude and angle values. 4. Solve for the change in voltage angle and magnitude 5. Update the voltage magnitude and angles 6. If the solution is adequate as defined by a set of “stopping conditions”, terminate the simulation and report the results. If the solution is not adequate, return to step 3 to calculate a new solution.
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7.3 Problem Formulation
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The load flow calculation is a network solution problem. As explained in previous sections, and summarized in Table 1, for any power system, the variables given (i.e. the knowns) are:
33
Voltage V and phase θ at the swing bus;
34
Voltage V (in magnitude) and active power P, for “P,V” buses;
35
Active power P and reactive power Q for the “P, Q” buses.
36
The variables found (i.e. the unknowns) are:
37
voltage angle θ at the “P,V” buses
38
voltage angle θ and voltage magnitude V for the “P,Q” buses
1
The numbers in brackets correspond to those of the bibliography in section 20 10 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Table 1 — Known and Unknowns in Power Systems
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The determination of the above unknown quantities is possible by writing a system of equations, one equation for each of the above nodes, and then using a numerical method to solve those equations. Note that in theory, there does not have to be a solution to a set of non-linear equations. However, if the equations are properly written, the fact that they represent a practical power system means that there will be a solution. On the other hand, there are some special cases where the set of non-linear equations for a power system may have multiple solutions. Those cases form a special category of problem designated as ‘voltage stability’ that is beyond the scope of this document.
11 12 13
For modeling purposes, we can represent branches of networks by their branch admittance; therefore, all the voltages and currents in the network are related by the following matrix equation:
14 15
[ I ] = [Y ][V ] (2)
16 17 18 19 20 21 22 23 24
where
25 26
Because of the physical characteristics of generation and load, the terminal conditions at each bus (or node), are normally described in terms of active and reactive power ( P and Q).
27
The bus current at bus i is related to these quantities as follows:
[ I ] [V ] [Y ]
is the matrix of total positive sequence currents flowing into the network nodes (buses) is the matrix of positive sequence voltages at the network nodes (buses) is the nodal admittance matrix
Equation (2) is a linear algebraic equation with complex coefficients. If either [ I ] or [V ] are known, the solution for the unknown quantities could be obtained by application of various solution techniques for linear equations.
( P i jQi )
28
I i
29 30
where * designates the conjugate of a complex quantity. Combining Equations (2) and (3) yields Equation (4):
V i
(3)
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1 2 3 4 5 6
P jQ V Y V
(4)
Equation (4) constitutes a non-linear system of equations, generally of large dimensions which cannot be readily solved by closed-form matrix techniques. Because of this situation, load flow solutions are obtained by procedures involving numerical techniques based on iterative solution algorithms.
7 8
7.4 Iterative Solution Algorithms
9 10 11 12 13 14
Since the original technical papers describing digital load flow solution algorithms appeared in the mid-1950s, a seemingly endless collection of iterative schemes has been developed and reported. Many of these are variations of one or the other of two basic techniques that are in widespread use by the industry today: the Gauss-Seidel technique and the Newton-Raphson technique. The preferred techniques used by most commercial load flow software are variations of the Newton technique.
15 16 17 18
All of these techniques solve bus equations in admittance form, as described in the previous section. This system of equations has gained widespread application because of the simplicity of data preparation and the ease with which the bus admittance matrix can be formed and changed in subsequent cases.
19
In a load flow study, the primary parameters are as follows:
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
In order to define the load flow problem, it is necessary to specify two of the four quantities at each bus. For generating units, it is reasonable to specify P and |V | because these quantities are controllable through governor and excitation controls, respectively. For loads, one generally specifies the real power demand P and the reactive power Q. Since there are losses in the transmission system and these losses are not known before the load flow solution is obtained, it is necessary to retain one bus where P is not specified. At this bus, called a swing bus, | V | as well as θ, the swing-bus angle, are specified. Since θ is specified (that is, held constant during the load flow solution), it is the reference angle for the system. The swing bus is therefore also called the reference bus. Since the real power, P , and reactive power, Q, are not specified at the swing bus, these quantities are free to adjust to compensate transmission losses in the system.
36 37 38
Table 1 summarizes the standard electrical specifications for the three bus types. The classifications “generator bus” and “load bus” should not be tak en as absolute. There will, for example, be occasions where a pure load bus may be specified by P and |V |.
P Q |V | θ
is the active power into or out of the network is the reactive power into or out of the network is the magnitude of bus voltage is the angle of bus voltage referred to a common reference (the swing bus)
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With most software, the generator specification of holding the bus voltage constant and calculating the reactive power output will be overridden in the load flow solution if the generator reactive output reaches its maximum or minimum VAR limit. In this case, the generator reactive power will be held at the respective limit, and the bus voltage will be allowed to vary.
5
7.5 Gauss-Seidel iterative Technique
6 7 8 9 10 11 12
Descriptions of load flow solution techniques can become rather complicated, due more to the notation required for complex mathematics rather than the basic concepts of the solution method. In the following sections, therefore, the basic techniques are developed by considering their application to a dc circuit. Applications to ac problems are then a natural extension of the dc problem.
13 14
Table 2 — Load flow bus specifications
Bus type Load
P
Q
|V|
Usual load representation
Generator or synchronous condenser
Generator or synchronous condenser ( P = 0) with var limits Q – = minimum var limit Q+ = maximum var limit
when Q < Q g < Q+ (Q g is the source reactive power) -
Comments
θ
|V| is held as long as Q g is within limit
when Q g < Q or Q g > Q+
Swing
“Swing bus” must adjust net power to hold voltage constant essential for
15 16 17
The Gauss-Seidel solution algorithm is the easiest to understand. The performance of the GaussSeidel technique will be illustrated using the direct current circuit shown in Figure 10.
18 19 20
Bus 3 is a load bus with specified per unit power. Bus 2 is a generator bus with power specified, and Bus 1 is the swing bus with voltage specified. The voltages V 2 and V 3 are sought. From these, the branch flows can be calculated.
21
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I 1 Y 11 Y 12 Y 13 V 1 I Y Y Y V 2 21 22 23 2 I 3 Y 31 Y 32 Y 33 V 3
1
(5)
2 3 4 5
The process of creating the admittance matrix is embedded deeply within load flow software, so it is not something that the study engineer would ever have to do manually. But it is still helpful to understand the general principles involved in that process [B2], [B3], [B4]. The basic rules for construction of the Y matrix are:
6 7 8 9 10
1. The diagonal terms in the Y matrix are the sum of the admittances of the lines leaving a bus plus the admittance of any shunt elements connected to the bus, plus one-half of the charging admittance defined for each connected line. This means that the admittance matrix will always be a square matrix in which the number of diagonal elements equals the number of nodes in the system model.
11 12 13
2.The off-diagonal terms Y ij are the negative of the line admittances between buses i and buses j, where a connection between bus i and bus j is present. If there is no connection between bus I and bus j, the ij term is zero.
14 15
Figure 10
Y ij
16
1 Z ij
— Three-Bus dc network
(6)
17 18 19
Because there generally will not be an actual network connection between every possible pair of nodes in the system, the Y matrix tends to be very sparse (i.e. most of the off-diagonal terms are zero).
20
From Equation (5),
21 22
I 2 Y 21V 1 Y 22V 2 Y 23V 3
(7)
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1
V 2
2
Substituting
3
I 2
4
V 2
Y 22
P 2 V 2
I 2 Y 21V 1 Y 23V 3
(8)
(9)
1 P 2
Y 21V 1 Y 23V 3 Y 22 V 2
5
This is a nonlinear equation in V 2
6
For Bus 3, a similar procedure yields
7 8 9 10 11
V 3
(10)
1 P 3
Y 31V 1 Y 32V 2 Y 33 V 3
(11)
where the negative sign on P 3 is from the load sign convention. Equations (10) and (11) are in a form convenient for the application of the Gauss-Seidel iterative solution technique. The steps in this procedure are as follows:
12 13 14 15 16 17 18 19 20 21 22 23 24 25
The computed voltages are said to converge when, for each iteration, the voltages come closer and closer to the actual solution. Since the computation time increases linearly with the number of iterations, it is necessary to have the computer program check to precision of the solution after each iteration, and decide whether the last computed voltages are sufficient or whether further computations are required.
26 27 28 29
The criterion specifying the desired accuracy is called the “convergence criterion” . The number of iterations may be entered or changed in most load flow programs. For fast decoupled load flow algorithms the user can also change a solution acceleration factor; slowing the factor in case of convergence problem and increasing the factor for large network solutions.
1.
Step 1: Assign an estimate of V 2 and V 3 (for example, V 2 = V 3 = 1.0). Note that V 1 is fixed.
2.
Step 2: Compute a new value for V 2 using the initial estimates for V 2 and V 3 [see Equation (10)].
3.
Step 3: Compute a new value for
V 3 using
the initial estimate for V 3 and the just computed
value for V 2 [see Equation (11)]. 4.
Step 4: Repeat Step 2 and Step 3 using the latest computed voltages V 2 and V 3 until the solution is reached. One complete computation of V 2 and V 3 is one iteration.
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There are various ways to define when a solution has converged. One reliable convergence criterion is the power mismatch check in which the software determines the sum of the power flows (real and reactive) on all lines connected to each bus with the specified bus real and reactive power. The difference, which is the power mismatch, is a measure of how close the computed voltages are to an ideal, or exact, solution. The power mismatch tolerance is generally specified in the range of 0.01 to 0.0001 p.u. on the system MVA base. The total power mismatch is also printed in the output report of load flow programs and is an indication of how valid is the load flow solution. Ideally the power mismatch of the entire network should be 0 +j0. Power mismatch reporting should be done and reported at a bus level as well so that the user can understand which busess have buse have power power mism mismatch atch grea greater ter than the spec specified ified mis mismat match ch tole toleran rance ce and and there therefore fore repre represent sent the points poin ts that are con confound founding ing the iter iterativ ativee solu solution tion.. If the sour source ce of the iter iteratio ation n prob problem lem can be determined, there often model adjustments that can be made to make the network solve more quickly.
14 15 16
Another common convergence check evaluates the maximum change in any bus voltage from one iteration to the next. A solution with desired accuracy is assumed when the change is less than a specified small value, for example, 0.0001 p.u.
17
Some of the things that can lead to convergence difficulties include
18 19 20 21 22 23
Errors in the input data System is too weak to carry the load Insufficient VAR in the system to support the voltage Significant disparity in the magnitudes of element impedance that terminate at the same node.
24 25 26 27 28
A voltage check is dependent on the rate of convergence and is thus less reliable than the power mismatch check. However, the voltage check is much faster (computationally, on a digital computer) than the power mismatch check and since the power mismatch will be large until the voltage change is quite small, one may economically use a procedure where computation of mismatch is avoided until a small amount of voltage change occurs.
29 30 31 32 33 34
Solution of an ac circuit would be similar to the solution of a dc circuit except that both resistive and reactive impedances must be recognized, and the solution must calculate both voltages and angles. For the three-bus example, voltage magnitude and angle at Bus 1, generator power and bus voltage at Bus 2, and and real and reactive reactive load power power at bus 3 would be specified. specified. The load flow solution would determine the voltage angle and generator reactive power output of Bus 2 and the voltage magnitude and angle at Bus 3.
35
The ac version of Equations (9) and (10) can be obtained from Equation (4) as follows:
36 37 38 39 40
V i ( m )
1 P i jQi
i 1 N *( m1) Y ik V k ( m) Y ik V k ( m1) i 1, 2, ..., N 1 Y ii V i k 1 k i 1
(12)
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V , Y are complex voltage and admittance, respectively V * is the complex conjugate of V
3
7.6 Newton-Raphson iterative Technique
4 5 6 7
The Gauss-Seidel technique is inefficient, often requiring hundreds of iterations to achieve an acceptable solution. And it can fail to converge in some specialized instances. Problems that cannot be solved using the Gauss-Seidel technique may often be solved using the NewtonRaphson technique.
8 9 10 11
This approach uses the partial derivatives of the load flow relationships to estimate the changes in the independent variables required to find the solution. In general, the Newton Raphson technique achieves convergence using fewer iterations than the Gauss-Seidel technique. However, the computational effort per iteration is somewhat greater.
12 13
To apply the Newton-Raphson technique to the three-bus example in Figure 4, the bus powers are expressed as nonlinear functions of the bus voltage.
14 15 16 17 18 19 20
21
22 23 24
P 1 = V V 1 Y 1 V 1 Y 1 V 2 Y 1 V 3 1 ( Y 1 1 V 1 + Y 1 2 V 2 + Y 1 3 V 3) P 2 = V 2 V 2 ( Y Y 2 2 1 V V 1 1 + Y Y 2 2 2 V V 2 2 + Y Y 2 2 3 V V 3) 3) P 3 = V V 3 Y 3 V 1 Y 3 V 2 Y 3 V 3 3 ( Y 3 1 V 1 + Y 3 2 V 2 + Y 3 3 V 3)
(13)
Small changes in bus voltages ( ∆ V ) will cause corresponding, small changes in bus powers (∆ P ). ). A linearized approximation to the power change as a function of voltage changes can be obtained as follows:
P 1 P 1 V 1 P P 2 2 V P 3 1 P 3 V 1
P 1 V 2 P 2 V 2 P 3 V 2
P 1 V 3 V 1 P 2 V 2 V 3 P 3 V 3 V 3
(14)
or symbolically: [ΔP1] = [J][ΔV]
25 26 27 28 29
where [ J ], ], the Jacobian matrix, contains the partial deri vatives of power with respect to voltages for a particular set of voltages, V 1, 1, V 2, 2, and V 3, 3, that is, the partial derivations of Equation (13). When one or more of the voltages changes substantially, a new Jacobian matrix must be computed.
30 31
In the load flow problem, V 1 is specified; that is, ∆V 1 = 0. Also, since Δ P 1 does not enter the computations explicitly, Equation (14) may be reduced to 17 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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2 3 4 5 6 7 8
P 2 P 2 V 2 P P 3 3 V 2
(15)
Changes in V 2 and V 3 due to changes in P in P 2 and P and P 3 are obtained by inverting [ J ] to obtain [ΔV] = [J] – 1[ΔP] P]
(16)
The Newton-Raphson load flow solution method is then as follows: a)
Step 1: Assign estimates of V 2 and V 3 (for example, V 2 = V 3 = 1.0).
b)
Step 2: Compute P Compute P 2 and and P P 3 from Equation (13).
c)
Step 3: Compute the differences ( Δ P ) between computed and specified powers:
9 10
Δ P 2 = P 2 – – P P ′ 2
(17)
Δ P 3 = P 3 – P ′ 3
11 12 13 14 15
P 2 V 3 V 2 P 3 V 3 V 3
Where the “prime” indicates specified value d)
Step 4: because the condition Δ P ≠ 0 is caused by errors in the voltages, the voltages should be incorrect by an amount that is closely approximated by Δ V as evaluated from Equation (16).
16
Therefore, the new estimate for the bus voltages is
17
V 2 V 2 1 P 2 J V P 3 new V 3 old 3
18 19 20 21 22
(18)
This is the basic equation in the Newton-Raphson method. The negative sign is becausee of the way Δ P was defined. becaus e)
Step 5: ReRe-compute compute and “invert” the Jacobian matrix using the last computed voltages and compute the new estimate for the voltages using Equations (17) and (18). Repeat this procedure until Δ P 2 and Δ P 3 are less than a small value (convergence criterion).
23 24 25
The convergence of the Newton-Raphson technique is not asymptotic as was the case with the Gauss-Seidel iterative scheme. The convergence is very rapid for the first few iterations and slows as the solution is neared.
26
For the ac load flow solution, the Jacobian matrix may be arranged as follows:
27
P J 1 J 2 Q J J V 4 3
(19) 18
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Where the complex bus voltage is written in polar coordinates, | V | . The Jacobian matrix can be arranged in many different ways to fit the particular programming techniques selected. An approximation to the Newton-Raphson formulation can be obtained by observing that, for a small change in the magnitude of bus voltage Δ |V |, the real power, P , does not change appreciably. Similarly, for a small change in bus voltage phase angle Δ , the reactive power, Q, does not change very much.
8
Thus, in Equation (19):
9
J 2 P 0
(20)
V
P 0
10
J 3
11 12 13
This allows Equation (19) to be “decoupled” into the following form:
14
(21)
P J 1
(22)
15 16 17 18 19 20 21 22 23 24
Q J V
(23)
4
Note that these two equations can be solved independently and sequentially, thereby reducing the storage and solution time requirements compared to using the full Jacobian. The decoupled Newton-Raphson technique may be used in applicatio ns where computational speed is important and the starting solution is close to the actual solution. This situation often occurs where a series of contingencies are being investigated about a previously solved reference case. However, the decoupled technique does not work well for systems with large branch resistance to reactance ratios, such as often found in industrial systems.
25 26
7.7 Comparison of Load Flow Solution Techniques
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The two techniques described in the previous sub clauses are the basic load flow solution techniques. There are many variations and improvements to these techniques that have been developed and incorporated into load flow programs to improve the starting or convergence characteristics.
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Although it is useful to understand how load flow solution techniques work, it is more important to understand the characteristics that these techniques exhibit. Because their convergence characteristics are dependent upon network, load, and generator conditions, each of the iterative techniques discussed has its own strengths and weaknesses.
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Gauss-Seidel methods generally exhibit poor convergence characteristics when compared to Newton methods and thus are not used as often for practical power flow solutions. Most of the more recent research into load flow solution techniques has centered on Newton methods. Variations of the Newton methods have been developed to overcome the weaknesses of the original methods, especially the ability to converge from a poor initial voltage estimate. That said, some modern software offers both Gauss-Seidel and Newton-Raphson solutions. In some cases, the study engineer must choose the method to be applied. Some tools use on method to develop an initial set of bus voltage and angles, and then switches to the alternate method to finish the solution.
10 11 12
The modified Newton methods employed by commercial load flow programs combine good convergence characteristics and solution algorithm robustness. Details on these algorithms are available in the references.
13 14
7.8 Load flow Source Models for Active and Reactive Power Limits and Controls
15 16 17 18 19 20 21 22
Traditional load flow modeling as described in sections 6.3 and 7.3 require a “slack bus” (swing bus) and “P-V” and “P-Q” buses to achieve a solution. The behavior of the generator controls, and the limits in active and reactive power generation of most modern sources of power, are not exactly modeled by the use these “traditional” load flow solution modes. Controls and limiters reduce the amount of active and reactive power generation under steady-state and transient conditions. Furthermore, the application and selection of the load flow modes of operation in a simulation shall be determined based on the mode of operation of the controllers of each of the main elements of a generator as shown in figure 11 for each of the machines in a system.
23 24 25 26 27
Figure 11
— Synchronous Generator Controls
If the system voltage and frequency from the load flow solution are not within a specific range, the generators will not be able to provide the desired voltage or power output. The following table shows how the modes of operation are related to the actual operational mode of the
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1 2
generator as described in figure 11. The table also describes which parameters are used as set points.
3
Table 3 — Synchronous Generator Operating Mode for LF Studies
LF Mode Swing
Controlled Parameter V, Speed
AVR Mode
GOV Mode
Pe Limit
Qe Limit
Voltage Control
Isochronous
Pmax / P rated
OEL 1 & UEL 2
P-V
V, Pe
Voltage Control
Droop
N/A
OEL & UEL
P-Q P-Q
4
Qe, Pe MVAR Control Droop N/A Qe, Pe PF Control Droop P max / P rated 1&2 over and under excitation limit controls of the synchronous generator
N/A OEL & UEL
5 6 7 8 9 10 11 12
Table 3 introduced several generation control elements and modes of operation. Load flow solutions are considered to be steady-state snapshots or a power system operating with different control limits. The term isochronous and droop represent the mode of operation of the governor speed and load controller. The terms voltage control, MVAR control and power factor control indicate the mode of operation of the automatic voltage regulator of the excitation system. The terms OEL and UEL stand for over and under excitation limiters. The term P max stands for maximum prime mover mechanical power.
13 14 15 16
Synchronous generators have physical output limits. Heating effects physically limit the maximum power and current output of a generator. The prime mover has a physical limit on the amount of energy it can convert to mechanical torque. The generator capability curve showin in figure 12 shows some of the electrical power output physical limits of a generator.
Max Pe Out ut
17 18
Figure 12
— Synchronous Generator Capability Curve
19
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The main purpose of the controls and limiters is to stay within the desired operating range (i.e. leading or lagging power factor, bus voltage range, etc). However, when the generator output reaches overload conditions under steady-state operation, the generators will also adjust their active and reactive power output (based on safety-margin protective limits as defined). These controls may cause a transition in the mode of operation of load flow programs based on the reactive power output characteristics.
7 8 9
This means that under some load flow solutions, the generator may be operating in the P-V mode, but then switch to P-Q (MVAR control mode or Power Factor control mode). This transition point may be critical for simulating voltage stability limits in load flow simulations.
10 11 12 13 14 15
The following image shows an example of an actual generator capability curve with an actual OEL and UEL limiter curves. The arrows indicate the region boundary where the load flow simulation would switch from P-V to P-Q. The UEL and OEL would prevent the generator from overheating and reduce the reactive power output of the generator. In load flow solutions, it is critical to determine how much reactive power can be provided and thus the load flow solution should include considerations on such limits.
16 17 P-Q
18
P-V
19 20 21
P-V
22 23
P-Q
24 25 26
Figure 13
— Gen P-V to P-Q Switch Region Map
27 28 29 30 31
The OEL operation follows a thermal capability limit similar to the one shown in the figure below. Note that for the purpose of load flow analysis (single snap shot of the system operation), it may be considered that the overload time is long and that the generator reactive power output will be limited in similar fashion as it is shown in the figure above (represented as a line).
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Figure 14
— OEL Limiter Inverse Time overcurrent Chart
Similar to generators, other types of sources like power electronic converters (Inverters) have controls which limit the active and reactive power output. The limits on the converter sources are established based on the system voltage (input terminal voltage) and active power being generated by the source. The limits on the reactive power are typically represented by two main types of curves called P-Q and Q-V curves. Figure 15 shows generic examples of what the curves may look like for different devices.
9 10
P-Q P-Q
11 12
P-V P-V
13 14 15 16
Figure 15
— Converter P-Q and Q-V Reactive Power Limits
17 18 19 20 21 22
The P-Q & Q-V curves may have different shapes and range of operation. The bounded area typically represents the P-V operating region of the converter. This means that the power electronics (firing angle and pulse width modulation controls) have the ability to control the output voltage at the terminal of the device within the specified region. Outside the operating region bounded by the curves, the converter source will operate as a P-Q source.
23 24 25
The P-Q curve plots the active power generated vs. the reactive power limits of the converter. The Q-V curve shows the dependency of the source on the terminal voltage output of the converter. This means that the reactive power is limited by the generated kW and the terminal voltage.
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It is important to determine the amount of reactive power available in a system. This becomes a requirement for most systems with power converter which interconnect to a power grid (utility). Load flow simulations in power system analysis software may require several iterations to determine the reactive power capability of a photovoltaic or wind turbine converter system. The reason is that the reactive power limits apply to each individual converter. Typically a controller supervises the flow of each converter source depending on the electrical distance of the impedance elements in the collector system.
8 9 10 11
The example selected for load flow analysis contains examples of both photo-voltaic and wind turbine power converters interconnected to a main industrial complex. With the advent of distributed generation and renewable energy sources, the load flow simulations need to be capable of modeling interactions within different types of voltage sources.
12 13 14
8. Model and Data Validation
15 16 17
Load flow models should be validated prior to issuing any recommended changes to the system. Load flow validation may be performed by acquiring actual values of electrical variables in the system, and compare the simulation results with actual system measurements.
18 19 20 21
For existing systems, the network configuration, load, and generation are often chosen to match a known operating condition, so that results can be compared to values obtained from operating experience to help validate the model. The base case represents the system in the normal operating mode supplying normal loading conditions.
22 23 24 25
That said, the usual purpose of load flow simulation is to gain insight into the performance of a system in response to various operating contingencies, and it is possible that there will not be exact numerical correlation between simulation results and measurements taken from the actual system for all corresponding conditions.
26 27 28 29
The reason for performing load flow validation is to benchmark the power flow model with actual operating condition under normal loading and network topology. Once a benchmark is achieved via load flow validation techniques then any simulation performed thereafter will be using more accurate loading, generation and network topology.
30 31 32 33
There are special situations where the tolerance between acceptable and unacceptable operation are especially tight, and it is necessary to use a load flow simulation model to make planning decisions that required more exact correlation. In those instances, the study engineer will be challenged to be more exacting about determining the system parameters and developing the system model.
34
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9. Load flow Study Example
2
9.1 General
3 4 5
As anticipated, to illustrate the use of a load flow program, the example system of Figure 1~10 will be referenced in the load flow study example. The example system overall description was provided in section 5.2, its input data parameters in section 6.8 and Annex B.
6 7 8
Most load flow programs have data checking and analysis routines to help find data input errors. These include a check of the network topology to see that all in-service buses are connected to the swing bus and range checking of certain data items to flag uncharacteristic values.
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
A fundamental check of the base case is to examine the ability of the load flow solution to converge. As noted in section 7, convergence should lead to a very small amount of MW and MVAR mismatch on every bus, where the mismatch is simply the sum of all the active and reactive powers entering the bus. The mismatch should ideally equal zero to satisfy Kirchhoff’s laws; however, a small mismatch is acceptable provided its percentage is small in comparison to the total bus load; a small amount of mismatch will not adversely affect the accuracy of the calculated bus voltages. If the load flow solution cannot approach this point for a known normal operating condition, then a problem in the system model is indicated. Scanning of the load flow output to see buses with large values of mismatch or abnormal voltages will often help find the problem area. The problem could be incomplete or inconsistent data. Short lowimpedance lines in close proximity with long lines may make convergence difficult. Very lowimpedance lines will likely cause convergence problems unless the load flow program contains special logic in the solution techniques to handle them. Engineering judgment is needed to determine whether it is more appropriate to model these elements explicitly or to lump them with adjacent elements.
24 25 26 27
Most load flow programs have the ability to take a solved load flow case and store all the necessary data including the solution in an electronic file. Electronic storage allows easy retrieval of the load flow case to incorporate future changes or to perform outage condition studies.
28 29 30 31 32 33
For each bus, the bus voltage magnitude and angle are calculated. The voltage magnitude may be presented in per unit or kV (or both may be listed). Each line going from that bus to another bus is listed, providing the MW and MVAR flow (or kW and kVAR) on the line out of the “from” bus. A negative flow means the flow is coming into the “from” bus. For transformers, the tap is also listed. If there is significant mismatch on the bus, it will also be listed. Different programs will use somewhat different formats; but all programs will present basically the same information.
34 35 36 37
A concise and usually more informative method of presenting load flow results is to display these graphically on the system one-line diagram. System flows can be quickly analyzed from this visual presentation that relates system configuration, operating conditions, and equipment parameters. Figure 16 displays load flow results in graphical form.
38 39 40
This figure shows the voltages on all buses and flows on all lines. Besides the o utput data, t he system configuration is clearly shown: which buses are supplied by each feeder, loads being modeled, generator output, transformer tap ratios, and shunt capacitor values.
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Figure 16
— Example of Graphical Load Flow Results
3 4 5 6
Most commercial load flow programs will generate such drawings. Output format will vary. In Figure 16, the power flows are shown near one of the buses and arrows indicate the direction of the MW and the MVAR flow.
7 8 9
Load flow output as shown in Figure 13 provides an effective means to document study results. Case titles or text on the drawing should indicate the system conditions being analyzed. In our particular case, the scenario shown is “ normal ”.
10 11 12 13 14
Table 4 presents information which is typically dependent on the process and system reliability and continuity of operation requirements. If process continuity is of high importance then the load flow study must include scenarios which show that the system can properly function under special circumstances like the loss or maintenance of one substation transformer or protective device.
15 16
The following major configurations as described in Table 4 will be used in the load flow study example provided in this section.
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Table 4 — Example System Switching Modes of Operation (Configurations) Configuration
Normal
Description
Process Description
Tie-breakers normally open. Co-generation
Normal process.
Tie-Closed
Tie-breakers in closed position. Bypass some feeders with alternate transformer supply
Normal process with potential component failure (loss) or component maintenance
Co-Gen off
Co-generator is not operational. Tie-breakers normally open. Minimum system loading and generation.
turnaround or temporary transition mode of operation
2 3 4 5 6
The configurations listed in Table 4 represent only the most common configurations used for an industrial power system. The number of switching configurations and operating modes may be large for some systems. Typically “at least one” load flow simulation sh ould be performed for each configuration in a power system.
7 8
9.2 Load Flow Study Scenario Considerations
9 10 11
Power system load flow analysis needs to consider all the modes of operation and system switching configuration required to keep continuous operation of critical loads. The system power flow performance can be evaluated by means of different study scenarios or case studies.
12 13
The load flow analysis scenario selection can be made by considering some of the following aspects.
14 15 16 17 18 19 20 21 22 23 24
Multiple and/or redundant power sources in and out of service (co-gen, peak shaving, emergency power supply, etc) Position (open or closed) of circuit breakers and switches (i.e. main-tie-main circuit breaker configurations). System loading demand should be considered. Both maximum and minimum loading conditions can be useful to determine the system operating limits (i.e. under and over voltage conditions). Tap positions of on-load-tap-changer transformers. The removal or failure of auto transformers and voltage regulators should be given consideration as additional scenarios. Inadequate transformer tap settings may lead to high voltage variations and circulating current which will cause unnecessary transformer overheating.
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Branch parameter variation, including the length and impedance tolerance. The effect of operating and ambient temperature on the resistance of cables and overhead lines should be considered. Load variation based on changes in voltage and frequency. The study shall consider the actual load composition including constant kVA, constant impedance, and constant current types of loads. The effect of voltage and frequency variation may also be expressed by using exponential and polynomial load functions. Source control modes need to be considered. Voltage control, power factor, MVAR and swing modes should be considered including the actual limits applicable to each source as described in section 7.8. Presence of electronic power converters, VAR compensators, and other specialized devices that impose non-linearity on operation of the system. Simplified, but adequately accurate models should be incorporated into load flow scenarios. Presence of series capacitors, negative/small impedances, to be modeled with specially enhanced load flow methods, in addition to Newton-Raphson and Gauss Seidel techniques.
17 18 19
When load flow studies are conducted for industrial applications, there are usually a relative small, finite number of practical scenarios to consider. It is left to the study engineer to identify those scenarios and formulate the necessary cases for simulation.
20 21
For the purpose of the example used for load flow analysis, there are three basis scenarios considered for the load flow analysis.
22
Table 5 — Load Flow Scenarios Scenario
NormalLF
Loading
Generation
Configuration
Normal
Normal
Normal
MaximumLF
Max Load
Max Gen
Tie-Closed
MinimumLF
Min Load
Min Gen
CoGenOff
Comments
Base scenario: Normally-open tie breakers. Normal loading and generation. Used to determine normal operating condition load flow results Determine if equipment overload occurs with maximum loading and loss of one transformer. Main purpose is to determine equipment overloads With minimum process load and no co-gen. Used to determine if there are any overloads or undervoltage conditions.
23 24 25 26
Note that positive impedance, resistance and length adjustments were applied with the maximum and normal load flow scenarios. Negative adjustments may be used in some situations with minimum load flow simulations, but not applied in this example.
27 28
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and be able to compare the results to find the worst-case results amongst all cases. This will be further discussed in section 10.
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9.3 Analysis of Load Flow Results
2 3 4 5
Now that a load flow has been run for the base and maximum and minimum conditions, it is time to analyze the results and use the information to determine what can be done to correct or improve the system operation. The analysis of the load flow results may reveal problems as described below:
6 7 8 9 10 11 12 13 14 15 16
Over and undervoltage conditions (i.e. voltage profile, voltage drops) Equipment overload/under-utilized conditions (transformer power and current overloads, cable ampacity values exceeded, switchgear continuous current above rated values, etc) System power factor (operating below desired power factor) Incorrect voltage and angle tap settings for looped systems; which may lead to circulating currents and equipment overheating Generator / Source overload conditions (active and reactive power overloads) Spin reserve limits, total generation and total load of the system under each configuration Steady-state frequency and voltage stability limits (maximum system loading limits beyond which the system voltage and frequency may collapse).
17 18
The previous list of items which should be considered in the analysis is only a sample and the comprehensive list will depend on the system design and topology.
19 20
Now that some of the analysis criteria have been established, they can be applied to the example system load flow results.
21 22
9.3.1 Bus Voltage Profile Analysis
23 24 25 26 27
Table 6 shows the undervoltage issues (i.e. voltage drops in excess of 5 %). Typical over and undervoltage limits are determined based on the type of system and voltage level. ANSI C84.1 voltage limits are ± 5 %. The maximum normal utilization voltage limit is -10%. That is the voltage drop can be as high as 10% from the bus nominal voltage for some equipment. For this example a voltage variation of ± 5 % is considered as a potential problem.
28
Table 6 — Voltage Profile Analysis Bus ID B:10 Sub 2C 820 Sub 2A Sub 2B
Nom. kV 0.4 6.3 6.3 6.3 6.3
1
Limit Violation (%) 88.04 88.58 88.69 88.76 88.76
Scenario Maximum LF Maximum LF Maximum LF Maximum LF Maximum LF
Condition Undervoltage Undervoltage Undervoltage Undervoltage Undervoltage
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1 2 3 4
Bus ID Nom. kV Limit Violation (%) Scenario Bus20 0.4 89.47 Maximum LF B:11 0.23 90.23 Maximum LF Maximum LF MCC 2 0.4 90.71 B:12-1-2 0.48 90.83 Maximum LF Maximum LF B:13-1-2 0.48 90.83 Bus 1A-1-2 4.16 91.93 Maximum LF Maximum LF Bus 1B-1-2 4.16 91.93 2A 0.4 103.17 Minimum LF B:11 4.16 103.06 Minimum LF Minimum LF Bus5 0.23 102.81 1 Note that there is some marginal overvoltage conditions on some buses.
Condition Undervoltage Undervoltage Undervoltage Undervoltage Undervoltage Undervoltage Undervoltage Overvoltage Overvoltage Overvoltage
Note that over and undervoltage conditions can be corrected using several techniques; which include the use of synchronous condensers, capacitor banks, transformer tap adjustments, and increase in reactive power generation, etc.
5 6
9.3.2 Equipment Overload Analysis
7 8 9 10 11
The analysis of equipment overloads can be done from the load flow results. Typically, overload conditions will be detected under the conditions with the highest load; however, lightly loaded conditions may also have overload problems if the switching configuration allows for certain equipment to be in operation with unusually high load. The analysis should include all scenarios performed in the load flow study.
12 13 14 15 16
Overload conditions are typically determined by comparing the maximum power or current flow from the load flow scenarios against the equipment maximum rating considering additional available cooling stages (transformers), cable installation and derating procedures, generator maximum power output based on available generation (active and reactive power), etc. Table 7 shows some of the overloads detected by inspecting the load flow results.
17
Table 7 — Overloaded Equipment Analysis Element ID C:6 TR12-1 EDG:1
Type 3φ Cable 3φ Xfmr Generator
Rating 151 A 3.5 MVA 7 MVAR
Loading % 107.9 % 110.7 % 101 %
Overload Condition Exceeds derated ampacity Exceeds max MVA rating Reached max MVAR limit
Scenario Maximum LF Maximum LF Maximum LF
18 19 20
Other potential overload conditions which may be determined from a typical load flow study may include:
21 22 23
24
Switchgear, MCC, panelboards, switchboards, protective device and switching elements continuous current ratings Current limiting reactor rated full load Amp rated impedance 31 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Transmission line (overhead bare conductors) current capacity Capacitor rated current and rated voltage overloads (may require harmonic load flow analysis, but fundamental frequency overload would be determined from basic load flow analysis).
5
Inverter / power electronic converters rated current and reactive power limits
6
Synchronous motor excitation system limits (over and under excitation limits)
7 8 9
General source limits like wind-turbine reactive power limits, induction generator overloads, regenerative-drive over and under voltage problems, motor-generator (MG) device power factor problems, etc.
10 11
9.3.3 Power Flow Correction Analysis
12 13 14 15
The purpose of a load flow analysis is not limited to determining equipment overloads and voltage profile problems, but it also includes the analysis of the power flows and how they can be improved to reduce system losses and maintain certain operating restrictions under normal operating conditions.
16
Examples of system power flow improvements include some of the following:
17 18 19 20 21 22 23 24 25 26 27 28
Power factor correction Power flow operating requirements handed down by regulating authorities (reactive power demand based on point of common coupling voltage fluctuations) Voltage profile improvement by reactive power support (i.e. the use and selection of static VAR compensators, capacitor banks, automatic capacitor switching, and adjustable speed drives to reduce reactive power demand) Reduction of real power losses in branch elements like cables and transformers by better selection of transformer tap positions, better current limiting device selection .
The following analysis conclusions were made from the load flow analysis in the example system. Only the larger transformer elements are included in the table (i.e. only branch elements with MVA capacity > 3 MVA were considered).
29 30 31
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Table 8 — Power Factor Analysis Results (for some key transformers > 3 MVA)
#
1 2 3 4 5 6 7
ID
From Bus
To Bus
TR:9 TR:3 TR:4 3WTR:1 3WTR:1 3WTR:1 3WTR:1
Arc Furnace Bus 45 MAIN4A3 Bus F Bus E Bus F Bus E
2A Sub 2A Sub 2B Bus 14 & 15 Bus 102 sec & 12 Bus 14 & 15 Bus 102 sec & 12
Max Rating (MVA) 10.5 9.85 9.85 56 56 56 56
PF %
Scenario
76.5 81.9 84.5 92.8 92.8 95.8 95.8
MaximumLF MaximumLF MaximumLF MaximumLF MaximumLF Normal LF Normal LF
2 3 4 5 6 7 8
Improvements in system operation which can be determined from the load flow analysis are usually made by using the operating modes which are most commonly applied such as the “normal” or “maximum loading” scenarios. Applying system design changes on special operating configurations; which occur infrequently, is not typically required or may not be cost effective. The small improvement in energy consumption or penalty reduction may not justify the additional equipment cost.
9 10 11 12 13 14 15 16 17
The low factors described in Table 8 (rows 1~3), are easily corrected since the system contains harmonic filters (which add power factor correction VARs) and also synchronous condensers. The power factor for this system going towards the utility connection is approximately 92% (rows 4 & 5) during maximum load conditions. Depending on the contract with the utility, it a power factor of 95% (rows 6 & 7) or higher were required during the entire operational time of the system, then some additional capacitor banks would have to be installed and switched on during maximum load conditions. The location and voltage level of the capacitors being installed is not determined from load flow power factor correction alone, but harmonic load flow and s witching transient analysis as well.
18 19 20 21 22
Before the installation of the synchronous condensers and harmonic filters, the power factor of the system going towards the utility connection would be 87.4%, way below the required 95%. A load flow scenario without these elements would easily show the low power factor condition (Figure 17).
23 24 25
Another element which plays a major role in power factor improvement is the variable frequency drive; which operates with an input power factor between 94 to 95%.
26 27
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
n o i t c e r r o C r o t c a F r e w o P t u o h t i w s t l u s e R w o l F d a o L —
. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d 4 E n a 3 E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
7 1 e r u g i F
1 2
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Analysis of the system load flow outputs after each set of changes results in the system being gradually tuned to obtain the most efficient and reliable operation. Experience with load flows improves the engineer’s ability to make corrections with a minimu m number of load flow solutions. However, it is stressed that any change affects the whole system, and a cure at one spot can create unexpected problems at another location in the system. For this reason, it is better not to make too many changes in a single run as the effects on the system may be difficult to understand. Each change case should be documented showing changes made and results obtained in order to keep future changes consistent with improving the system. Furthermore each system change also needs to be evaluated under short-circuit, harmonic analysis, switching transients, etc, etc further requiring the need for computer simulation tools which can handle all of these analysis.
12 13
10. Load Flow Analysis Results and Reports
14 15 16 17 18 19 20 21
All the essential output data and results from the analysis must be reported in an organized fashion, describing the parameters for each bus: bus voltages and phase angles, branch flows and voltage drops, load power consumption, and reactive powers. In industrial system studies, the number of cases that must be simulated to assess scenarios of interest is usually finite, and flow diagrams are the most common form of documentation. The challenge for the study engineer is to then recognize when the diagram shows undesirable circuit flows or bus voltages, and to suggest solutions to remediate those issues. Typically, it would be expected that additional simulations be done to demonstrate the efficacy of the suggested solutions.
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Flow diagrams are often impractical on larger systems. Instead, the usual practice is to instruct the software to recognized instances where the flow through a path exceeds the rating of that path, or where the voltage on a bus falls outside a specified voltage tolerance for that bus. Then, those ‘criteria violations’ are summarized in a table. In those cases, the concern is not so much for how the criteria violations come about as it is for the fact that they occur, and the job of the study engineer is to find system operating solutions that minimize the number of reported violations.
29 30
The report may also flag abnormal operating conditions, such as overloaded cables and over- or under-voltage buses
31 32 33 34 35 36
As an example, operating voltages below a certain threshold, as established by the criteria chosen for the Load Flow Study (e.g. 94.2 %), are put in evidence in the report for affected busses, so that corrective steps can be taken. Namely, the regulation features of load tap changers, if present in transformers, can be applied to regulate the bus voltage. Fixed taps can also be used, but their settings must be verified in both maximum and minimum load conditions, to prevent the occurrence of overvoltages.
37 38
Figures 18~20 shows small portions of the load flow reports for each of the scenarios performed in the previous section for the load flow study.
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Figure 18
— Portion
of Normal Load Flow Report
3
4 5
Figure 19
— Portion
of Maximum Load Flow Report
Figure 20
— Portion
of Minimum Load Flow Report
6 7 8 9 10 11 12 13 14 15
Load flow analysis if individual reports may be time consuming when the bottom line or lowest voltage results are needed. It is more practical to use comparison tools which would allow for the analysis of multiple simulation results. Tools of this nature would then provide a numerical comparison analysis between all the load flow scenario results and automatically determine which the worst-case result is for each of the conditions being analyzed as described in section 9.3. Table 9 shows an example of how the output of a multiple result analysis/comparison tool could look like. 36 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Table 9 — Multiple Load Flow Result Analysis Tool Output ID
TR:3 TR12-1 C:6 C:1 C:2 TX KA 135 TX RC 91 TX RC 104
From Bus 45 84-1-2 Bus A Bus14 102 Sec C:26 C:19-1 C:3-1
To Bus
Type
Rating
Allowable
Sub 2A Bus 1A-1-2 Arc Furnace B Bus A Bus A F:KA135 F:RC91 F:RC104
Transf. 2W Transf. 2W Cable Cable Cable Transf. 2W Transf. 2W Transf. 2W
7.5 MVA 2.5 MVA 1 - 1/C 1/0 2 - 1/C 350 2 - 1/C 350 0.3 MVA 0.3 MVA 0.3 MVA
9.853 MVA 3.5 MVA 151 A 824.4 A 824.4 A 0.3 MVA 0.3 MVA 0.3 MVA
Max LF % 138 110.6 107.1 105.3 103.7 91.2 90.4 90
Min LF % 39.9 60.7 68.1 35.8 34.9 99.6 30.6 22.3
Norm. LF % 65.5 42.9 72.3 67.7 66.3 93.8 77.9 74.9
2 3 4 5 6
Table 9 shows the under most situations the overload in equipment would occur during the Max LF (Maximum Load Flow) scenario that was performed in section 9. The comparison tool in this case marks the problem areas visually with maroon color and marginally overloaded equipment with magenta color. These are visual comparison aids.
7 8 9 10
The benefits of such analysis/comparison tools are many, but include the reduction in analysis time and cost; and the removal of human, error since the extraction of the violations and problem areas would not be performed manually. One final benefit could be the automatic comparison of the “recommended” solution simulations against the original load flow results without correction.
11 12
11. Advanced Load Flow Applications
13 14 15
Load flow simulations are sometimes employed for purposes other than simulation of steady state system performance. These are specialized applications that the study engineer should at least be familiar with.
16 17 18 19 20
One application is calculation of short circuit currents. For conventional load flow analysis it is sufficient to specify only one swing bus in the system. However, it is possible to calculate short circuit currents by designating a chosen ‘fault bus’ as a swing bus, and specifying that the voltage on that bus must be zero. The simulation will then yield real and reactive power flows that correspond to the currents that will flow to a three-phase short circuit at that designated bus.
21 22 23 24 25
It is important to recognize that this kind of short circuit calculation may be useful to determine current magnitudes for analyzing relay performance, and also to predict the voltage impact of short circuits in power quality studies, but because the calculation method does not conform to either IEEE or IEC requirements, the results should not be used to evaluate the application of fault interrupting devices.
26 27 28 29 30
A related application is to use load flow simulations to assess the impact of step changes in system loading (or changes in system configuration) on steady-state system voltages. An example of this might be the case where the study engineer wants to know how voltages are affected when a piece of metal enters a rolling mill, when a motor starts, or when a capacitor bank is switched on or off the system. These situations can be analyzed by performing two successive 37 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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load flow simulations; the first is a steady state load flow simulation of the system immediately prior to the change, while the second is a simulation with the change having been made. To be most accurate, the system model must allow specification of an internal reactance for each generator, and the second simulation must be conducted with the voltage behind that internal reactance (ideally, the saturated, or rated voltage transient reactance, x’dv) held constant at the level determined in the initial simulation [B7]. Some commercial load flow programs are designed to accommodate that kind of modeling directly, but there are usually ways that programs that do not have that facility can be used to yield the same effect.
9
12. Features of Analysis Tools
10 11 12
Many load flow programs are presently available, both in the public domain and as commercial products. Load flow programs differ in the ease of use, program accuracy, program documentation, program sophistication, such as feature set and, of course, cost.
13 14 15 16 17 18 19 20 21 22
There is a wide range in the level of sophistication in the available programs. There is a corresponding range in the level of user need for this sophistication. The more sophisticated programs may contain several load flow solution techniques allowing for easier solution of a wide range of problems, more data checking activities to help in debugging data input errors, more data handling activities to ease changes to system data or configuration, graphic display of load flow results, ability to handle much larger networks, the modeling of additional power system components, and the incorporation of additional control functions into the solution techniques as well as time saving techniques and study case options to generate required scenarios. Industrial and commercial power systems of today along with their users need a high level of sophistication from computer power system simulation programs to analyze the power systems.
23 24 25 26
The following are the key features of a load flow program that should be used for industrial and commercial applications. These requirements have been separated into minimum requirements for software intended for industrial applications, and optional requirements that offer more flexibility or functionality.
27
Minimum requirements;
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Power flow simulation with multiple loading and generation conditions Power factor improvement simulation In the not-too-distant past, load flow programs were limited in the number of buses that could be modeled. Because the number of nodes in the network model determines the size of the bus admittance (Y) matrix that is calculated during the simulation, this limitation was related to the amount of memory available in the computer being used. Computer technology has advanced to the point where memory limitations are no longer a real concern, but software publishers often still impose bus-count limitations as part of a product marketing strategy. The software chosen should be dimensioned sufficiently to model the system to be studies. User-controlled load flow calculation convergence parameters Automatically adjust transformer (two and three winding) tap and LTC and voltage regulator settings Automatic generator voltage regulator actions Depict power flow results graphically Detailed real & reactive power losses calculation and reporting 38 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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Option to update initial conditions to improve convergence Save load flow solution parameters for each scenario Save changes so that studies can be re-run Conduct unlimited “what if” studies within one database Calculate power flows, losses, voltage drop, bus voltages, currents, & power factors Bus, transformer, line, cable and generator overload warnings Load flow database integrated with the databases required for other related studies (including but not limited to short circuit studies, motor starting studies, stability studies, harmonic studies, etc)
Optional functionality: Automatically execute simulations for every practical single and/or multiple contingency scenario, evaluating all critical & marginal limit violations. Violation alerts ideally should be displayed in alert windows and tabular reports Automatic temperature correction for the thermal capacities of circuit elements may be important on Modeling of phase-shifting transformers Compare & analyze multiple reports using specific routines Auto-run load flow mode based on system changes Solve either three-phase or single-phase system load flow Update loading for DC load flow calculations. Considers power factor and efficiency at no-load & over-load conditions
An alternative to in-house use of a load flow program is to use consultants who can do the analysis and present the facility engineer with a complete report including a technical analysis of the computer output together with their findings and recommendations on system improvement. Consultants have the advantage of having the experience required to efficiently execute studies and correctly interpret results. However, it is still important for the industrial facility engineer to understand the data requirements, how a study is performed, how valid are the assumptions and results as well as how sound are the suggested changes to the system.
31 32
13. Optimal Power Flow
33 34 35 36
Beyond the straightforward power flow program that simply calculates the variables pertaining to a single, existing system condition, there are more involved programs that have the ability to account for other limiting criteria that affect operation of the system. These programs are known as optimal power flow (OPF).
37 38 39 40 41 42 43
In traditional load flow studies, the final settings of control parameters are based on the engineer’s experience and judgment. Sometimes an iterative process is required to reach the final overall satisfactory settings. This process can be time consuming for large systems. These control parameters typically are: transformer LTC settings, generator MW generation or fuel cost, generator AVR settings or reactive power generation, series and shunt static VAR compensation device settings, the amount of load shed, etc. In practice, any of those control settings or any combination of these controls can be used in a particular system.
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The Optimal Power Flow Study employs optimization techniques to automatically adjust the power system control settings while at the same time it solves the load flow equation. In addition, the OPF should include a range of optimization or security criteria for the system and enforce limits on system quantities (bus voltage, line flow, etc.) during the optimization process. These optimization criteria are generally called objectives, such as the system performance indexes, whereas the limits are called constraints.
7
14. Conclusions
8 9 10 11 12 13 14 15
It should be evident to designers and operators of industrial plant electrical systems, as well as to utility system engineers, that a tool that predicts the performance of their electrical systems under various actual steady state operating conditions that is very valuable. Such a tool can be used to prevent expensive outages, damaged equipment, and possibly even loss of life. The load flow solution provides a means to study systems under real or hypothetical conditions. The solution results should be evaluated and analyzed with respect to optimum present and future operation. This leads to a diagnosis of the system as it exists. The analysis can also point the way to improved operation and provide a meaningful basis for future system planning.
16
15. Annex A – Reference and Additional Sources
17
Additional information may be found in the following sources:
18 19 20
[B1] Brown, H. E., Solution of Large Networks by Matrix Methods , New York, NY: John Wiley and Sons, 1975.
21 22
[B2] Stagg, G. W., and El-Abiad, A. H., Computer Methods in Power System Analysis , New York, NY: McGraw-Hill, 1968.
23 24
[B3] Stevenson, W. D., Elements of Power System Analysis, New York, NY: McGraw-Hill, 1975.
25 26
[B4] Tinney, W. F., and Hart, C. E., “Power flow solution by Newton’s method,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-86, pp. 1444 – 1460, Nov. 1967.
27 28
[B5] Ward, J. B., and Hale, H. W., “Digital Computer Solution of Power Flow Problems,” AIEE Transactions, Part III — Power Apparatus and Systems , vol. 75, pp. 398 – 404, June 1956.
29 30
[B6] Wood, A. J., and Wollenberg, B. F., Power Generation, Operation and Control , New York, NY: John Wiley and Sons, 1984.
31 32
[B7] Concordia, Charles, Synchronous Machines, Theory and Practice, New York, NY, John Wiley and Sons, 1951
33 34
[B8] IEEE Std 141-1993, IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (IEEE Red Book).
35 36
40 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
Authorized licensed use limited to: Power Engineers Inc. Downloaded on February 25,2016 at 19:29:05 UTC from IEEE Xplore. Restrictions apply.
IEEE P3002.2/D5, February, 2015
1
16. Annex B – Example System Input Data
2
This section provides all input tables for the sample system used in this chapter.
3 4
5 6 7
8 9 10 11 12
1
Table B.1 Generator Data Rated Rated LF Gen Qmax PF% EFF Mode MW Mvar
ID
Rated kV
Rated MVA
EDG:1
13.8
11.765
85
95
PV1
10
Main Gen
13.8
88.235
85
95
PV
75
Qmin Mvar
Pmin MW
Xd’
6.2
-4.2
0
22.8
48
-24
0
22.8
%
Constant power output with voltage regulation
Table B.2 Utility Source Data ID
Rated kV
LF Mode
U1
138
Swing
U2
138
1
%V
MVAsc
X/R
R 1 %
R 2 %
R 0 %
X1 %
X2 %
X0 %
1
101
1200
35
0.238
0.238
0.381
8.32
8.32
8.32
Swing
101
1500
25
0.266
0.266
0.266
6.66
6.66
6.66
swing mode is defined as constant voltage, frequency and angle at the output of the utility connection
Table B.3 Two-winding Transformer Data Sec Z1 X1/R 1 Fixed Tap Conn. kV % Ratio % Prim-Sec
ID
Rated MVA
Prim kV
Angle Degree
Max 1 MVA
AUX:1
2.5
13.8
4.16
4.8
4.7
0.0
ΔY
30
2.5
GSU:1
75
138
13.8
9
3.1
5.0
ΔY
30
112
T6-1
3
13.8
4.16
6.4
12.3
-2.5
ΔY
30
3
T8-1
1
4.16
0.48
5.6
5.8
-2.5
ΔY
30
1.288
TR:3
7.5
13.8
6.3
8
14.2
-2.5
ΔY
30
12.317
TR:4
7.5
13.8
6.3
8
14.2
-2.5
ΔY
30
12.317
TR:5
3
13.8
0.48
5.8
14.2
-2.5
ΔY
30
4.2
TR:6
3
13.8
0.48
5.8
14.2
-2.5
ΔY
30
4.2
TR:7
1
13.8
4.16
5.5
5.8
0.0
ΔΔ
0
1
TR:8
1
13.8
4.16
5.5
5.8
0.0
ΔY
30
1
TR:9
7.5
13.8
4.16
6.4
14.2
-2.5
ΔY
30
10.5
41 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
Authorized licensed use limited to: Power Engineers Inc. Downloaded on February 25,2016 at 19:29:05 UTC from IEEE Xplore. Restrictions apply.
IEEE P3002.2/D5, February, 2015
ID
Rated MVA
Prim kV
Sec kV
Z1 %
X1/R 1 Ratio
Fixed Tap %
Conn. Prim-Sec
Angle Degree
Max 1 MVA
TR:10
0.5
0.48
0.12
4.8
4.7
0.0
ΔY
30
0.5
TR:11
0.5
0.48
0.12
4.8
4.7
0.0
ΔY
30
0.5
TR12-1
2.5
13.8
4.16
6.5
12.5
-2.5
ΔY
30
3.5
TR:13
3
0.575
34.5
5.8
14.2
0.0
ΔY
-30
4.2
TR:141-1
1
4.16
0.48
5.4
5.8
0.0
ΔY
30
1.29
TR:15
10
34.5
138
7.8
12.1
0.0
ΔY
-30
14
TR:16
1
6.3
0.4
5
5.8
-5.0
ΔY
30
1.726
TR:17
300
0.4
0.23
4
3.1
-2.5
ΔY
30
336
TR:18
0.75
13.8
0.48
5.8
4
0.0
ΔY
30
4.2
TR:19
225
0.48
0.24
4.8
4.7
-5.0
1-Ph AB
-
4200
TR:20
125
0.48
0.20 8
3
3.5
-5.0
ΔY
30
4200
TR:21
3
0.575
34.5
5.8
14.2
0.0
ΔY
-30
4.2
TR:22
75
13.8
0.24
3.7
2.9
0.0
1-Ph AB
-
75
TR:23
125
13.8
0.48
3.7
3.6
0.0
1-Ph AB
-
125
TR:25
3
0.575
34.5
5.8
14.2
0.0
ΔY
-30
4.2
TR:27
15
138
12.4 7
6.7
12.1
0.0
ΔY
30
17.831
225
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
225
150
12.47
0.48
3.7
3.6
0.0
ΔΔ
0
150
225
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
225
113
12.47
0.48
3.7
3.6
0.0
ΔΔ
0
113
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
500
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
500
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
225
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
225
TX CAN 86 TX KA 52 TX KA 84 TX KA 90 TX KA 135 TX KA 152 TX RC 91 TX RC 93 TX RC 104 TX RC 117
42 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
Authorized licensed use limited to: Power Engineers Inc. Downloaded on February 25,2016 at 19:29:05 UTC from IEEE Xplore. Restrictions apply.
IEEE P3002.2/D5, February, 2015
ID
1 2 3
TX RC 130 TX SAC 24 TX SG 17 TX SG 22 1
Rated MVA
Prim kV
Sec kV
Z1 %
X1/R 1 Ratio
Fixed Tap %
Conn. Prim-Sec
Angle Degree
Max 1 MVA
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
225
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
225
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
300
12.47
0.48
5.2
5.1
0.0
ΔΔ
0
300
Transformer maximum loading is accomplished with a dditional cooling stages.
43 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
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0 9
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3 8 0 . 0
3 8 0 . 0
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6 4 0 . 0
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8 0 . 3 0 1
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2 2 0 . 0
8 2 1 . 0
1 2 1 . 0
8 2 0 . 0
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4 7 0 . 0
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1
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8 7 4 *
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5 1
5 1
6 . 6
6 . 6
6 . 0
6 . 0
5
0 2 1 s u B
9 1 1 s u B
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C 2 b u S
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R T M D F V
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1
Authorized licensed use limited to: Power Engineers Inc. Downloaded on February 25,2016 at 19:29:05 UTC from IEEE Xplore. Restrictions apply.
y t d e i c w a o l p l m A A
4 5 4 . 8 4 9
9 9 8 . 9 4 8
0
0 4 0 . 1 1 3
9 2 9 . 2 2 1
3 3 1 . 5 6
7 5 6 . 9 3 4
3 3 1 . 5 6
6 5 1 . 1 1 4
7 5 6 . 9 3 4
9 8 1 . 2 4 2
2 4 1 . 0 6 4
7 . 9 1 1
9 6 5 . 4 0 3
8 4 7 . 3 0 1
9 7 2 . 8 3 1
x p 5 a m 7 ◦ e C M T
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5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
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e s m 0 a e p C ◦ 9 T B
5 7
5 7
5 7
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5 7
0 9
5 7
0 9
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0 9
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0 9
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8 7 0 . 0
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7 8 0 . 0
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7 9 0 . 0
7 9 0 . 0
4 5 0 . 0
3 0 1 . 0
7 9 0 . 0
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3 3 0 . 0
7 2 1 . 0
0 1 3 . 0
1 8 0 . 0
0 1 3 . 0
1 6 0 . 0
1 8 0 . 0
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2 6 2 . 0
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p # / C
2
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1
1
1
2
1
1
2
1
2
1
2
1
2
. n e o p y C T
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u C
u u u u u u u u u u u C C C C C C C C C C C
. e l u s p y n T I
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Ω 1
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
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0 0 5
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4
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4
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6
h t g t f n e L
0 0 0 1
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0 0 1
0 5 1
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4 4 8 5
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0 5 3
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0 2 1 *
5 0 4 2
d e V t a k R
8 3 1
6 . 0
6 . 0
6 . 0
6 . 0
6 . 0
5
6 . 0
5 3
5
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6
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6
6 . 0
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o s u T B
5 1 : s u B
A 9 2 8 0 - 1 4 1 s u 2 B M
1 6 0 6 M
1 5 s u B
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1 H A
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m s u o r B F
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9 0 1 2 1 : 2 : 2 : 2 : C C C C
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. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d 5 E n a 4 E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
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Authorized licensed use limited to: Power Engineers Inc. Downloaded on February 25,2016 at 19:29:05 UTC from IEEE Xplore. Restrictions apply.
y t d e i c w a o l p l m A A
9 7 2 . 8 3 1
7 8 2 . 3 5 2
7 5 6 . 9 3 4
9 6 4 . 1 3 1
9 8 1 . 2 4 2
1 0 5 . 4 2
1 0 5 . 4 2
5 1 2 . 8 7
7 5 6 . 9 3 4
5 1 2 . 8 7
5 1 2 . 8 7
5 1 2 . 8 7
9 7 2 . 4 4 1
9 7 2 . 4 4 1
9 7 2 . 4 4 1
9 7 2 . 4 4 1
x p 5 a m 7 ◦ e C M T
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5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
e s m 5 a e p C ◦ 7 T B
0 9
0 9
0 9
0 9
0 9
0 9
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0 9
5 7
5 7
5 7
0 9
0 9
0 9
0 9
3 5 0 . 0
5 1 1 . 0
7 3 0 . 0
7 8 0 . 0
7 9 0 . 0
9 0 1 . 0
9 0 1 . 0
9 3 0 . 0
7 3 0 . 0
9 3 0 . 0
9 3 0 . 0
9 3 0 . 0
0 4 0 . 0
0 4 0 . 0
0 4 0 . 0
0 4 0 . 0
0 1 5 . 0
7 8 0 . 0
1 8 0 . 0
2 4 3 . 0
5 3 1 . 0
5 6 2 . 4
5 6 2 . 4
2 0 2 . 0
1 8 0 . 0
2 0 2 . 0
2 0 2 . 0
2 0 2 . 0
4 8 1 . 0
4 8 1 . 0
4 8 1 . 0
4 8 1 . 0
p # / C
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
. n e o p y C T
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. e l u s p y n T I
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5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
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r r e e r e r e E b b b b R R R R P b R P b b P P P P L u E b u u u E E E E X R R R R
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1
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h t g t f n e L
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d e V t a k R
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5 2
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1
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6 . 0
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5
6 . 0
6 . 0
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A
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1 1 V O M
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4 8 A K
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0 0 P 5 9 4 P A 1 A C A K C
2 5 1 A K
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m s u o r B F
2 1 B 1 : s u B
6 1 s u B
2 1 B 1 : s u B
0 1 : B
8 1 s u B
2 1 2 1 : B
2 1 3 1 : B
4 8 A K : F
2 1 B 1 : s u B
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4 0 1 C R : F
0 3 1 C R : F
4 1 R 1 F : C
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. e g n a h c o t . d t e c e v r j e b s u s e , r t f s t a r h g D i r s l l d A r a . d 6 E n a 4 E t E I S 5 E 1 E 0 E 2 I d © t e h v g o r i r p y p p a o n C u n a s i s i h T
e l e l e l e e l e l e l e e 2 l e e l e e l e e l e l 2 - b 2 l - 2 - 6 l - 7 l 0 2 3 b 2 8 b 9 l 0 b 1 l 2 b 3 b b b b b b - b 4 b 5 b 6 b a 9 a 1 b a 1 a 1 a 1 a a a 1 a a 1 a 1 a 1 a 2 a 2 a 2 a 2 C C C 1 C C C 1 C 1 C C 1 C C C C C C C
Authorized licensed use limited to: Power Engineers Inc. Downloaded on February 25,2016 at 19:29:05 UTC from IEEE Xplore. Restrictions apply.
y t d e i c w a o l p l m A A
2 2 6 . 2 0 1
2 2 6 . 2 0 1
2 2 6 . 2 0 1
2 2 6 . 2 0 1
2 2 6 . 2 0 1
2 2 6 . 2 0 1
2 2 6 . 2 0 1
2 2 6 . 2 0 1
9 8 3 . 1 0 2
8 7 4 . 9 7 1
1 7 9 . 6 7 1
7 2 7 . 2 4
2 9 0 . 7 0 1
8 7 1 . 2 1 4
0
x p 5 a m 7 ◦ e C M T
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5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
5 7
e s m 5 a e p C ◦ 7 T B
5 7
5 7
5 7
5 7
5 7
5 7
5 7
0 9
0 9
0 9
0 9
0 9
5 7
5 7
8 3 0 . 0
8 3 0 . 0
8 3 0 . 0
8 3 0 . 0
8 3 0 . 0
8 3 0 . 0
8 3 0 . 0
8 3 0 . 0
5 9 0 . 0
4 4 1 . 0
7 4 0 . 0
8 3 1 . 0
6 . 9 2 1
2 4 0 . 0
8 6 0 . 0
0 6 1 . 0
0 6 1 . 0
0 6 1 . 0
0 6 1 . 0
0 6 1 . 0
0 6 1 . 0
0 6 1 . 0
0 6 1 . 0
8 0 1 . 0
8 2 4 . 0
7 4 1 . 0
0 3 3 . 2
4 9 4
8 2 0 . 0
2 6 0 . 0
p # / C
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
. n e o p y C T
u u u u u u u u u u u u u C C C C C C C C C C C C C
u C
u C
. e l u s p y n T I
r e r e r e r e r e r e r e r e R E b b b b b b b b R E P P b b b b b b b b P P L u u u u u u u u E X E L X R R R R R R R R
Ω 1
X Ω 1
R 1
5 1 0 2 , y r a u r b e F , 5 D / 2 . 2 0 0 3 P E E E I
/ i l e G z i W m c 1 S k A
r e E b P b 2 L u X R
r e b 2 b u R
1
1
1
1
1
1
1
0 / 2
0 / 1
0 / 1
*
*
0 5
0 0 5
0 0 5
0 1
h t g t f n e L
5 2 3
5 2 3
5 2 3
5 2 3
5 2 3
5 2 3
5 2 3
5 2 3
7 7 7
0 5 6
5 5 4
0 3 2 *
0 2 1 *
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IEEE P3002.2/D5, February, 2015
1
Table B.10 Load Data ID
Rated kV
Rated kVA
Rated PF
Constant MW%
Constant Z%
Phases
Loading % (kVA) Max/Norm/Min
Lump1
6
1000
85.0
80
20
3φ
90/55/55
Lump10
0.48
2000
98.0
80
20
3φ
75/55/55
Lump1-1-2
0.48
400
80.0
80
20
3φ
100/75/0
Lump12
0.48
2000
98.0
80
20
3 φ
75/55/55
Lump2-2
0.48
350
80.0
80
20
3φ
100/75/25
Lump5
6
2000
85.0
80
20
3φ
85/75/65
Lump7
13.8
15000
85.0
80
20
3φ
90/75/20
Lump8
13.8
15000
85.0
80
20
3φ
95/75/20
Lump9
4.16
1500
85.0
80
20
3 φ
115/100/50
Recreation Center
0.24
75
85.0
80
20
1φ AB
90/90/10
Warehouse A
0.48
125
85.0
80
20
1φ AB
75/65/50
4.16
6500
78.0
0
100
3φ
80/50/10
0.23
250
95.0
0
100
3φ
85/85/80
Load1-1-2
0.48
35
85.0
0
100
3φ
90/60/20
Load2-2
0.48
30
83.0
0
100
3φ
90/60/20 0 /100/ 0
Arc Furnace Load ICCRPANEL A
*Panelboard
A
0.24
200
100
0
100
1φ AB
*Panelboard
B
0.24
120
85
0
100
3φ
* PDU1
0.48
150
100
0
100
3φ
* PDU2
0.48
150
100
0
100
3φ
* Servers
#1
0.12
225
100
0
100
3φ
* Servers
#2
0.12
75
100
0
100
3φ
0 /100/ 0 0 /100/ 0 0 /100/ 0 0 /100/ 0 0 /100/ 0
2 3 4 5
54 Copyright © 2015 IEEE. All rights reserved. This is an unapproved IEEE Standards Draft, subject to change.
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