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Copyright © 2015 IEEE. All rights reserved.This is an unapproved IEEE Standards Draft, subject to change.

IEEE P3002.2 ™/D61Draft Recommended Practice for Conducting Load-Flow Studies of Industrial and2Commercial Power Systems3

Sponsor4

Technical Book Coordinating Committee5of the6

IEEE Society7

Approved 8

IEEE-SA Standards Board 91011

Copyright © 2015 by the Institute of Electrical and Electronics Engineers, Inc.12Three Park Avenue13

New York, New York 10016-5997, USA14

All rights reserved.15

This document is an unapproved draft of a proposed IEEE Standard. As such, this document is16subject to change. USE AT YOUR OWN RISK! Because this is an unapproved draft, this17document must not be utilized for any conformance/compliance purposes. Permission is hereby18granted for IEEE Standards Committee participants to reproduce this document for purposes of19international standardization consideration. Prior to adoption of this document, in whole or in20

part, by another standards development organization, permission must first be obtained from the21IEEE Standards Activities Department ([email protected]). Other entities seeking permission to22reproduce this document, in whole or in part, must also obtain permission from the IEEE23Standards Activities Department.24

IEEE Standards Activities Department25445 Hoes Lane26Piscataway, NJ 08854, USA27

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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.


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This is an unapproved IEEE Standards Draft, subject to change.

Introduction1

This introduction is not part of IEEE P3002.2/D1, Draft Recommended Practice for Conducting2Load-Flow Studies of Industrial and Commercial Power Systems.3

IEEE P3000 Series4

This recommended practice was developed by the Technical Books Coordinating Committee of5the Industrial and Commercial Power Systems Department of the Industry Applications Society,6as part of a project to repackage IEEE’s popular series of “color books.” The goal of this project7is to speed up the revision process, eliminate duplicate material, and facilitate use of modern8

publishing and distribution technologies.9

When this project is completed, the technical material included in the thirteen “color books” will10 be included in a series of new standards — the most significant of which will be a new book, IEEE11Standard 3000, “Recommended Practice for the Engineering of Industrial and Commercial Power12Systems.” The new book will cover the fundamentals of planning, design, analysis, constructi on,13

installation, start-up, operation, and maintenance of electrical systems in industrial and14 commercial facilities. Approximately 60 additional “dot” standards, organized into the following15categories, will provide in-depth treatment of many of the topics introduced by IEEE Standard163000:17

Power Systems Design (3001 series)18

Power Systems Analysis (3002 series)19

Power Systems Grounding (3003 series)20

Protection and Coordination (3004 series)21

Emergency, Stand-By Power, and Energy Management Systems (3005 series)22

Power Systems Reliability (3006 series)23

Power Systems Maintenance, Operations, and Safety (3007 series)24

25

In many cases, the material in a “dot” standard comes from a particular chapter of a particular26color book. In other cases, material from sever al color books has been combined into a new “dot”27standard.28

29The material in this recommended practice largely comes from IEEE 399 standard with emphasis30towards practical load flow analysis.31

32



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vCopyright © 2015 IEEE. All rights reserved.


IEEE P3002.21

Recommended Practice for Conducting Load-Flow Studies of Industrial and Commercial Power2Systems provides a recommended practice for load flow analysis of industrial and commercial3

power systems. It is likely to be of greatest value to the power-oriented engineer with limited4

experience in this area. It can also be an aid to all engineers responsible for the analysis of the5 operation of industrial and commercial power systems. 6

Notice to users7

Laws and regulations8

Users of these documents should consult all applicable laws and regulations. Compliance with the9 provisions of this standard does not imply compliance to any applicable regulatory requirements.10Implementers of the standard are responsible for observing or referring to the applicable11regulatory requirements. IEEE does not, by the publication of its standards, intend to urge action12that is not in compliance with applicable laws, and these documents may not be construed as13

doing so.14

Copyrights15

This document is copyrighted by the IEEE. It is made available for a wide variety of both public16and private uses. These include both use, by reference, in laws and regulations, and use in private17self-regulation, standardization, and the promotion of engineering practices and methods. By18making this document available for use and adoption by public authorities and private users, the19IEEE does not waive any rights in copyright to this document.20

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been amended through the issuance of amendments, corrigenda, or errata, visit the IEEE27Standards Association web site at http://ieeexplore.ieee.org/xpl/standards.jsp , or contact the IEEE28at the address listed previously.29

For more information about the IEEE Standards Association or the IEEE standards development30 process, visit the IEEE-SA web site at http://standards.ieee.org .31

Errata32

Errata, if any, for this and all other standards can be accessed at the following URL:33http://standards.ieee.org/reading/ieee/updates/errata/index.html . Users are encouraged to check34this URL for errata periodically.35



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Interpretations1

Current interpretations can be accessed at the following URL:2http://standards.ieee.org/reading/ieee/interp/3index.html. 4

Patents5

[If the IEEE has not received letters of assurance prior to the time of publication, the following6notice shall appear:]7

Attention is called to the possibility that implementation of this recommended practice may8require use of subject matter covered by patent rights. By publication of this recommended9

practice, no position is taken with respect to the existence or validity of any patent rights in10connection therewith. The IEEE is not responsible for identifying Essential Patent Claims for11which a license may be required, for conducting inquiries into the legal validity or scope of12Patents Claims or determining whether any licensing terms or conditions provided in connection13with submission of a Letter of Assurance, if any, or in any licensing agreements are reasonable or14

non-discriminatory. Users of this recommended practice are expressly advised that determination15of the validity of any patent rights, and the risk of infringement of such rights, is entirely their16own responsibility. Further information may be obtained from the IEEE Standards Association.17

[The following notice shall appear when the IEEE receives assurance from a known patent18holder or patent applicant prior to the time of publication that a license will be made available19to all applicants either without compensation or under reasonable rates, terms, and conditions20that are demonstrably free of any unfair discrimination.]21

Attention is called to the possibility that implementation of this recommended practice may22require use of subject matter covered by patent rights. By publication of this recommended23

practice, no position is taken with respect to the existence or validity of any patent rights in24

connection therewith. A patent holder or patent applicant has filed a statement of assurance that it25 will grant licenses under these rights without compensation or under reasonable rates, with26reasonable terms and conditions that are demonstrably free of any unfair discrimination to27applicants desiring to obtain such licenses. Other Essential Patent Claims may exist for which a28statement of assurance has not been received. The IEEE is not responsible for identifying29Essential Patent Claims for which a license may be required, for conducting inquiries into the30legal validity or scope of Patents Claims, or determining whether any licensing terms or31conditions provided in connection with submission of a Letter of Assurance, if any, or in any32licensing agreements are reasonable or non-discriminatory. Users of this recommended practice33are expressly advised that determination of the validity of any patent rights, and the risk of34infringement of such rights, is entirely their own responsibility. Further information may be35obtained from the IEEE Standards Association.36

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viiCopyright © 2015 IEEE. All rights reserved.


Participants1

At the time this draft recommended practice was submitted to the IEEE-SA Standards Board for2approval, the Power Systems Analysis Editorial Working Group had the following membership:3

Farrokh Shokooh, Chair 4

Albert Marroquin, Vice Chair 5Massimo Mitolo, Vice Chair 6

7Tanuj Khandelwal8Haijun Liu9Bill Roettger10

Srikrishna Chitharanjan11Louie Powell12Daniel Ransom13

Franklin Quilumba14Salman Kahrobaee15Mandar Manjarekar16

1718

The following members of the balloting committee voted on this19recommended practice. Balloters may have voted for approval, disapproval, or abstention.20

21(to be supplied by IEEE)22

23Balloter124Balloter225Balloter326

Balloter427Balloter528Balloter629

Balloter730Balloter831Balloter932

3334

When the IEEE-SA Standards Board approved this trial-use recommended practice on , it had the following membership:36

(to be supplied by IEEE)37, Chair 38

, Vice Chair39

, Past President40, Secretary41

42SBMember143SBMember244SBMember345

SBMember446SBMember547SBMember648

SBMember749SBMember850SBMember951

*Member Emeritus525354

Also included are the following nonvoting IEEE-SA Standards Board liaisons:55

, TAB Representative 56

, NIST Representative 57 , NRC Representative 58

59 IEEE Standards Program Manager, Document Development60

6162

IEEE Standards Program Manager, Technical Program Development63



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Contents1

1. Scope........................................................................................................................................... 1 2

2. Normative references ................................................................................................................. 1 3

3. Introduction ................................................................................................................................ 1 4

4. Analysis Objectives ................................................................................................................... 2 5

5. System Simulation and Modeling ............................................................................................. 4 65.1 Modeling Requirements ...................................................................................................... 4 75.2 Overall Description of Example Industrial/Commercial Power System ......................... 5 8

6. Required Input Data ................................................................................................................... 4 96.1 General .................................................................................................................................. 4 106.2 System Data ......................................................................................................................... 4

11

6.3 Bus Data ............................................................................................................................... 5

12 6.4 Load Data .............................................................................................................................. 6 136.5 Generator Data..................................................................................................................... 7 146.6 Branch data .......................................................................................................................... 7 156.7 Transformer Data .................................................................................................................. 8

166.8 Example System Input Data .................................................................................................. 9 17

7. Methodology and Standards ...................................................................................................... 9 18

7.1 General .................................................................................................................................. 9 197.2 Overall Solution .................................................................................................................. 10 207.3 Problem Formulation .......................................................................................................... 10 217.4 Iterative Solution Algorithms .............................................................................................. 12 22

7.5 Gauss-Seidel iterative Technique ........................................................................................ 13

23 7.6 Newton-Raphson iterative Technique ................................................................................. 17

247.7 Comparison of Load Flow Solution Techniques ................................................................ 19 257.8 Load flow Source Models for Active and Reactive Power Limits and Controls ................ 20 26

8. Model and Data Validation ..................................................................................................... 24 27

9. Load flow Study Example ....................................................................................................... 25 289.1 General ................................................................................................................................ 25

299.2 Load Flow Study Scenario Considerations ..................................................................... 27 309.3 Analysis of Load Flow Results ........................................................................................ 30 31

10. Load Flow Analysis Results and Reports ............................................................................ 35

32

11. Advanced Load Flow Applications ...................................................................................... 37 33

12. Features of Analysis Tools .................................................................................................... 38 34

13. Optimal Power Flow.............................................................................................................. 39 35

14. Conclusions ............................................................................................................................ 40

36



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15. Annex A – Reference and Additional Sources .................................................................... 40 1

16. Annex B – Example System Input Data .............................................................................. 41

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1Copyright © 2015 IEEE. All rights reserved.


Draft Recommended Practice for Conducting Load-Flow Studies of Industrial and1Commercial Power Systems2

IMPORTANT NOTICE: This standard is not intended to ensure safety, security, health, or3environmental protection in all circumstances. Implementers of the standard are responsible4 for determining appropriate safety, security, environmental, and health practices or regulatory5requirements.6

This IEEE document is made available for use subject to important notices and legal7

disclaimers.8These notices and disclaimers appear in all publications containing this document and may9be found under the heading “Important Notice” or “Important Notices and Disclaimers10Concerning IEEE Documents.” They can also be obtained on request from IEEE or viewed at11http://standards.ieee.org/IPR/disclaimers.html .12

1. Scope13

This recommended practice describes how to conduct load-flow studies for industrial and14commercial power systems. It will be of greatest value to the power-oriented engineer with15limited experience in this area. It can also be an aid to all engineers responsible for the electrical16design of industrial and commercial power systems.17

2. Normative references18

The following referenced documents are indispensable for the application of this document (i.e.,19they must be understood and used, so each referenced document is cited in text and its20relationship to this document is explained). For dated references, only the edition cited applies.21For undated references, the latest edition of the referenced document (including any amendments22or corrigenda) applies.23

IEEE Std. 399-1997, IEEE Recommended Practice for Industrial and Commercial Power Systems24Analysis (IEEE Brown Book™)1.25

3. Introduction26

Load flow is also referred to as Power flow; these terms may be interchangeably used in this27standard. This is the name given to a network solution that predicts steady-state currents,28

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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voltages, and real and reactive power flows through every branch and bus in the system. Load1flow studies simulate operating conditions that cannot practically be experienced on the actual2system because the system has not yet been built, because of the practical constraints of time, or3

because it would be unwise to expose the actual physical system to conditions that are potentially4damaging. The end objective of the load flow study is not necessarily to arrive at hard, numerical5

performance parameters, but rather to gain insight into how the system performs over a range of6

operating scenarios.78

Because the parameters of the elements such as lines and transformers are constant, the power9system network itself is linear. However, in the power flow problem often involves specifying10magnitudes of either real or reactive power, which then means that the relationship between11voltage and current becomes nonlinear, and the same holds for the relationship between the real12and reactive power consumption at a bus, or the generated real power and scheduled voltage13magnitude at a generator bus. Thus, power flow calculation involves the solution of a set of14nonlinear equations. This calculation gives the electrical response of the power system to a15

particular set of loads and generator power outputs. Power flows are an important part of power16system operation and planning.17

4. Analysis Objectives18

One of the most common computational procedures used in power system analysis is the load19flow calculation. The planning, design, and operation of power systems require such20calculations to analyze the steady-state (quiescent) performance of the power system under various21operating conditions and to study the effects of changes in equipment configuration. The basic22load flow question is this: given the load power consumption at all buses of a known electric23

power system configuration (e.g. network topology) and the power production at each generator,24find the power flow in each line and transformer of the interconnecting network and the voltage25magnitude and phase angle at each bus.26

For some types of equipment (e.g., photovoltaic solar arrays or wind farms), a time varying27simulation, such as a time domain load flow may be required in order to fully understand the28

behavior of the electrical system over a period of time. These load flow solutions are performed29using computer programs designed specifically for this purpose.30

Analyzing the solution of this problem for numerous conditions helps ensure that the power31system is designed to satisfy its performance criteria while incurring the most favorable32investment and operation costs.33

Some examples of the uses of load flow studies are to determine the following:34

Component or circuit loadings35

Steady-state bus voltages36

Real and Reactive power flows37

Transformer tap settings and Load Tap Changer actions38

System Real and Reactive power losses and voltage drops39

Generator exciter/regulator voltage set points40

Undervoltage and overvoltage conditions for buses as well as equipment terminals41



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Performance under maximum, normal and minimum loading conditions1

Performance under various operating configurations2

Performance under emergency conditions (post contingency)3

Requirement for either fixed or variable power factor improvement equipment4

5

Load flow analysis has a great importance:6

1. To verify the operation of a network under various load and generation conditions7

2. To plan the future growth of both loads and generation8

3. To determine the best economical operation for existing systems9

4. To establish initial conditions for stability studies10

Also load flow results are very valuable for setting the proper protective devices to insure the11safety of the system. In order to perform a load flow study, full data must be provided about the12

studied system, such as one-line diagram, parameters of transformers, cables and transmission13lines, rated values of each equipment, and the real and reactive power for each load.14

Modern systems may be complex and have many paths or branches over which power can flow.15Such systems form networks of series and parallel paths. Electric power flow in these16networks divides among the branches until a balance is reached in accordance with17Kirchhoff’s laws. 18

There are generally two types of computer load flow programs — those intended for offline19 planning purposes, and those designed to operate in real-time, actively receiving input from the20actual system. Most load flow planning studies use off-line software. On-line, or real-time load21flows incorporate data input from the actual networks are becoming increasingly important in22

bridging the gap between static / planning network model and the model used by those responsible23for actual system operation. Computer programs are also available that provide integrated off-line24and real-time solutions for ‘what if’ predictive analysis. Such systems are able to integrate with25existing plant Supervisory Control and Data Acquisition (SCADA) systems. Integrated real-time26systems can therefore be used as planning and design tools as well as dispatching tool for the27operator. And an additional level of sophistication is possible using so-called ‘optimal power28flow’ modeling that applies constraints in the load flow solution to achieve objectives, such as29minimum fuel cost, minimum power loss, flat voltage profile, etc.30

For industrial and commercial power systems, the load flow problem involves balanced, steady-31state operation. Hence a single-phase, positive sequence model of the power system is typically32sufficient. Three-phase or unbalanced load flow analysis software is available but is rarely33

needed in industrial power system applications.34

A load flow calculation determines the state of the power system for a given load and35generation distribution. It represents a steady-state condition as if that condition had been held36fixed for some time. There are situations in industrial applications where the issues of interest37involve how those steady state conditions change over periods of minutes to hours as a38consequence of changes in loading or generation; these applications can adequately simulated39using conventional load flow tools by means of a series of simulations reflecting the pertinent40



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changes. On the other hand, concerns about how systems respond in the cycles-to-seconds time1frame, perhaps as a consequence of short circuits or other disturbances, should be addressed2using transient stability software. Power system transient stability is beyond the scope of this3document.4

In actuality, line flows and bus voltages fluctuate constantly by small amounts because loads5

change constantly (e.g. lights, motors, and other loads are turned on and off). However, these6small fluctuations can be ignored in calculating the steady-state effects on system equipment.7

As the load distribution, and possibly the network, will vary considerably during different time8 periods, it may be necessary to obtain load flow solutions representing different system conditions9such as peak load, average load, or light load. These solutions will be used to determine either10optimum operating modes for normal conditions, such as the proper setting of voltage control11devices, or how the system will respond to abnormal conditions, such as line or transformer12outages. Load flows form the basis for determining both when new equipment additions are13needed and the effectiveness of new alternatives to solve present deficiencies and meet future14system requirements.15

The load flow model is also the basis for several other types of studies such as short-circuit,16stability, motor starting, and harmonic studies. The load flow model supplies the network data and17

provides an initial steady-state condition for these studies.18

5. System Simulation and Modeling19

5.1 Modeling Requirements 20

Industrial plant electrical systems can be extensive. A simplified visual means of representing the21complete system is essential to understanding the operation of the system under its various22

possible operating modes. The system one-line diagram serves this purpose. The one-line diagram23is a single line representation of 3, 2, and 1 system identifying buses and interconnecting24

lines. Loads, generators, transformers, reactors, capacitors, etc., are all shown in their respective25 places in the system. In order to analyze any circuit, we use as a reference those points that are26electrically distinct, that is, there is some impedance between them, which can sustain a potential27difference. These reference points are called nodes. When representing a power system on a large28scale, the nodes are called buses, since they represent an actual physical busbar where different29components of the system meet. A bus is electrically equivalent to a single point on a circuit, and30it marks the location of one of two things: a generator that injects power, or a load that consumes31

power.32

Drawing format will vary depending on the computer programs used and the preference of the33users, but the one-line diagram should give the necessary network information in a clear,34concise manner. The transfer of this data to the load flow program for analysis is discussed in35

the next section.36

It is necessary to know equipment parameters as well as their relationship to each other. Depending37on the computer program being used, parameters may either be displayed directly on the one-line38diagram, or may be listed in tables that accompany that diagram. Figure 1 is an example one-line39diagram that will be used throughout this standard to illustrate some aspects of load flow studies.40



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Bus names (or numbers) are displayed along with the bus nominal voltages. Interconnecting lines1are usually shown with their impedance values and lengths entered. Equipment associated with a2

bus is shown connected to that bus. For instance, generators are shown connected to their bus3with their equipment parameters specified, as illustrated in Figure 2. Similarly, loads are shown4connected to bus Sub 2A in Figure 3. Motor loads are often indicated separately to aid in their5modeling in short circuit and other studies. Each line originates on a bus and terminates on a6

different bus, as depicted in Figure 3. Transformers, like lines, are shown between two buses with7the primary connected to one bus and the secondary to the other. Information to convey an off-8nominal turns ratio should be given when applicable.9

5.2 Overall Description of Example Industrial/Commercial Power System 10

The sample system created to illustrate the process of performing a load flow analysis contains11 portions of different types of components which can be encountered in different heavy and light12industrial power systems and or commercial installations. Figure 1 below shows the example13system which will be used. The system contains the following component types which may be14encountered for different systems:15

High voltage switchyard (heavy industrial facilities may own and be responsible for this16 part of the system)17

Medium voltage power distribution switchgear with multiple source feeders (common of18large refinery and process driven facilities19

Oil field and largely distributed pumping stations20

Larger generation plant with dedicated unit transformer (~100+ MW capacity)21

Smaller cogeneration components (~10’s MW capacity) 22

Double-ended secondary selective medium and low voltage switchgear configurations23

Emergency and critical system data backup systems (similar to “Tier 1” data center24configurations). Larger industrial / commercial facilities may have data backup25requirements with UPS units26

Large arc-furnace loads and harmonic filter similar to what may be found in large steel27manufacturing plants. These components can be used to simulate the power factor28correction and harmonic load flow content29

Synchronous motor compressors with excitation system control configurable to voltage30or power factor support31

Adjustable speed drives (ASDs) or variable frequency drives which may be used for a32variety of induction/synchronous motor control applications like and submersed pumping33stations34

Building service power systems. Examples of industrial or institutional facilities which35may have their own building power distribution system36



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Example of micro grid application which includes renewable energy sources like1 photovoltaic (PV) installations and converter sources.2

Wind turbine generation which can take advantage of renewable energy sources3available. The wind turbine system is used for distributed generation example load flow4conditions.5

The one-line diagram of this system does not represent an actual installation which combines all6of the individual components. The system was designed to be an educational tool for the purpose7of explaining load flow concepts which may not be encountered in typical industrial/commercial8installations. Furthermore, the intent of the example system used in this chapter is not to9represent “best design practices” of industrial and commercial power systems. Figures 2~9 show10the one-line diagrams of the individual components included in the example system.11

Note that the example also contains 1-phase and multi-frequency components. The example does12not extend to any dc elements.13

14

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Figure 3 — One-line Diagram of the Wind Farm2

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Figure 4 — One-line Diagram of the Bldg Service5

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I E E E P 3 0 0 2 . 2

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1

2

Figure 8 — Generating Power Station Diagram3

4

5

Figure 9 — Representation of Loads, Lines, and Transformer6

7

Sub 2A6.3 kV

±

I>

TR:3

8 %Z

7.5 MVA

13.8/6.3 kV

Dyn1

CB:22

Lump5

CB:35CB:35

M-60614000 kWM-60614000 kW

Lump5

Sub 2A6.3 kV

TR:3

8 %Z

7.5 MVA

13.8/6.3 kV

Dyn1

CB:22



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6. Required Input Data1

6.1 General2The data shown on the one-line describes the system configuration and the location and size of3loads, generation, and equipment. It is organized into a list of data that defines the mathematical4model for each power system component and how the components are connected together. The5

preparation of this data file is the foundation of all load flow analysis, as well as other analysis6requiring the network model, such as short circuit and stability analysis. It is therefore essential7that the data preparation be performed in a consistent, thorough manner. Data values must be as8accurate as possible. Rounding and not including enough decimal places in certain parameters,9can lead to erroneous results. Influential parameters must not be ignored. Tolerance values,10wherever applicable, shall be considered for the calculations; the input uncertainty should always11

be conservatively taken into account; also a sensitivity analysis may help define proper data12tolerance.13

In this sub- clause, data organization is shown in general terms and some comments are given on14data preparation. The data are divided into the following categories (this organization is typical of15most load flow analysis software): system data, bus data, generator data, branch data, and16

transformer data.17

Not too long ago, analysts were challenged by the fact that computer technology limited the18number of node points that could be represented in a load flow model. This forced study19engineers to be very creative about combining elements connected in series, or to choose to20ignore elements that were judged to be irrelevant to the problem being solved. Modern simulation21software running on modern computers is rarely constrained in this fashion. While is often22necessary to build elaborate models of an entire system, experienced analysis understand that it is23often still prudent to limit the extent of the model to include only those components and elements24that are actually pertinent to the problem being addressed. Time typically relates to money, and it25doesn’t make sense to invest any more time in data collection and model building than is needed26to answer the question at hand.27

6.2 System Data28

Most load flow programs perform their calculations using a per unit representation of the system29rather than working with actual volts, amperes, and ohms. The input of data to the program can30either be in per unit or in physical units, depending on the design of the program. Converting the31system data to a per unit representation requires the selection of a base kVA and base voltage.32Selecting the base kVA and base voltage specifies the base impedance and base current. Computer33

programs automatically determine the other base kV based upon transformer turns ratios in the34system.35

The system data specifies the base kVA (or MVA) for the entire system. A base 100 MVA)36

has traditionally been used for industrial studies, but other base values may also be chosen.37

The base kV is chosen for each voltage level. Selecting the nominal voltage to be the base voltage38simplifies the analyses and reduces the chance of errors in interpretation of results.39



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6.3 Bus Data1

Buses represent the nodes of the electrical system and can be classified based on their conditions2of load and/or generation. The bus data describe each bus and the load and shunts connected to3that bus. The data include the following:4

Bus Name and/or bus number5 Bus classification (Swing/Voltage Controlled/Load Bus)6

Bus Service (In / Out) or Status7

Bus nominal voltage8

Bus rating / continuous amps9

Initial per unit voltage and angle (to be discussed later)10

11

The bus ID may be a combination of characters and numbers, and is normally used only for12identification purposes, allowing the user to give a descriptive name to the bus to make13

program output more easily understood. The bus ID should be unique in order to avoid errors14while interpreting results.15

The bus classification allows the program to properly organize the buses for load flow solution. In16general, there are three classifications for buses.17

181 Slack or Swing Bus19The “swing” or “slack” bus is a special type of generator bus that is needed by the solution20

process. There is normally only one swing bus in a load flow model. In systems with strong grid21interconnections, the grid connection is typically specified as the swing bus. In the absence of a22grid connection, one generator must be selected as the swing bus.23The swing bus is also referred to as the “infinite” bus. In reality, the power that the swing bus can24release is finite, but very large with respect to the other generators of the system. During the25operation, the voltage of this bus is always specified to remain constant in magnitude V and phase26or angle θ, whereas, active and reactive powers will change according to the network. For this27reason, this bus is also called the “θ, V” bus. 28In addition to the generation assigned to the swing bus, this bus is responsible for supplying the29losses of the system. The swing generator adjusts its scheduled power to supply the system MW30and MVAR losses that are not otherwise accounted for, so that: power absorbed by loads plus31

power losses equals the power delivered by the swing bus plus power delivered by generator(s).3233

2. Generator or Voltage Controlled Bus34During load flow simulations, the voltage magnitude at the voltage controlled bus is kept constant,35and the reactive loading on the machine is adjusted as required to satisfy system conditions while36maintaining that voltage. The active power supplied is kept constant at the value assigned to the37generator. This most closely represents the situation with a generator where the voltage is38controlled using the excitation and the power is controlled by the prime mover and the terminal39voltage is regulated by an excitation system.40A generator bus can also be used to represent a variable-reactive device where the voltage can be41controlled by varying the value of the injected VAR to the bus. For the above reasons, this bus is42also defined as the “P, V” bus, and the quantities θ and Q vary according to the network. 43



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If a generator bus is not voltage regulated (e.g., an induction generator), the real power P and the1reactive power Q are fixed in magnitude; thus, as load varies, the voltage magnitude V and the2voltage θ angle vary. Induction generators are best represented as negative loads on load buses.3

43. Load Bus5In a load flow simulation, both the voltage magnitude and phase angle will change according to6

loading and network conditions. For simulation purposes, load buses are most often defined as7having a ‘constant MVA’ characteristic which means that the complex power S= P = jQ will be8held constant. Load buses are also defined as “P, Q” buses. That said, some load flow programs9offer options for other forms of load bus modeling. For example, some kinds of static power10conversion equipment might better be modeled as having constant real power, constant current11characteristics.12A load bus need not have load, it may simply be an interconnection point for two or more lines; in13this case, Kirchhoff’s law requires that the sum of the real and reactive flows into the node equal14the sum of the flows out of the bus.15

The terms “load” bus and “generator” bus should not be taken literally, because the terms describe16only the bus electrical behaviors, without necessarily implying the presence of equipment.17

18

6.4 Load Data19

In the load flow program, loads must be entered in a manner that is consistent with the design of20the program. The most common scenario is for loads to be MW and MVAR at nominal voltage.21As anticipated, the load is treated as a constant MVA, that is, independent of voltage. In some22cases, a Constant Current or Constant Impedance component of load could also be entered so23that the load is a function of voltage, as explained in IEEE Std 399-1997 (section 4.9). Shunts24generally are entered in MVAR at nominal voltage. Care must be taken to ensure that the proper25sign convention is used to differentiate between capacitive and reactive shunt loads.26The load data are used to represent the load at various bus locations. Usually, the constant MVA27load representation is used. Sometimes, the constant current or constant impedance type of load28model may be used. Depending on the design of the software, load data may include some or all29of the following:30

- Load Identification (either descriptive text or a unique load number)31

- Load Service (In/Out) or State32

- Real / Reactive power Rating33

- Rated Power factor34

- Loading in percent of nameplate or brake horsepower (BHP)35

- Load demand factor (continuous, intermittent or spare)36

- Load type for lumped loads (constant kVA, constant Z and/or constant I) and Load type37ratio (% constant kVA, % constant Z, % constant I)38



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- For motor loads, the efficiency and power factor of the machine, in percent, at 100%,175%, and 50% loading, as well as the no-load and over loading conditions,2

3

6.5 Generator Data4

Generator data is entered for each generator in the system including any generator that may be5connected to the designated system swing bus. The data defines the generator power output and6how voltage is controlled by the generator. Depending on the design of the software, generator7data may include some or all of the following:8

Generator identification (ID).9

Generator nameplate ratings (rated MW, MVA, power factor and efficiency)10

Generator operating mode (Swing, Voltage Control, MVAR Control, Power Factor11Control)12

Operating real power output in MW (Voltage Control, MVAR Control, Power Factor13

Control)14 Operating reactive power output in MVAR (MVAR Control)15

Initial operating voltage angle in degrees (for the swing bus)16

Operating power factor in percent (Power Factor Control)17

Maximum reactive power output in MVAR (i.e., machine maximum reactive limit,18Qmax)19

Minimum reactive power input in MVAR (i.e., machine minimum reactive limit, Qmin)20

Scheduled voltage in per unit (Swing, Voltage Control)21

Generator Service (In/Out) or State22

23

Other items that might be included the model date are the generator MVA base and the24generator’s internal impedance for use in short-circuit and dynamic studies. Computer programs25may allow a generator to regulate a remote bus voltage although in most programs the control bus26is usually the generator terminal bus / node.27

6.6 Branch data28

Data is also entered for each branch in the system. Herein the term “branch” refers to all29elements that connect two buses including transmission lines, cables, series reactors, series30capacitors, and transformers. In the real system, there may be multiple elements in series (e.g., an31overhead transmission circuit that transitions into a cable circuit); when using modern simulation32

software that does not impose practical limits on the number of nodes in the model, it is preferable33 to treat each of these elements separately connected by a ‘node’. The data items include the34following:35

36

From Bus / To Bus Identifications37

Branch Identification (especially if there are parallel branches connecting the specified38From and To buses39



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Branch Service (In/Out) or State1

Physical length (Cable and Transmission Line)2

Resistance in Ohms or Ohms per unit of length3

Resistance in Ohms or percent on the chosen study base MVA4

Reactance in Ohms or Ohms per unit length5

Reactance in Ohms or percent on the chosen study base MVA base6

Charging susceptance (shunt capacitance)7

Line continuous amperage rating8

9

In industrial systems, overhead transmission lines and cable circuits are typically short, so the10charging capacitance of these circuits is often immaterial. Hence, charging susceptance is often11omitted from industrial system load flow models. When susceptance is included, lines are12represented by a model with series resistance and reactance and one-half of the charging13susceptance placed on each end of the line. The resistance, reactance, and susceptance are14usually input in either per unit or percent, depending on program design.15

Line ratings are normally input in amperes or MVA, depending on the design of the software.16Current ratings can be converted to MVA with the formula:17

ratingMVA =1000

ratingkV3 ABASE (1)18

A series reactor, series capacitor, or transformer would not have a charging susceptance term.19

6.7 Transformer Data20

Additional data are required for transformers. These can either be entered as part of the branch21data or as a separate data category depending on the particular load flow program being used.22

Depending on the design of the software, these additional data may include the following:23

24

Transformer Service (In/Out) or State25

Transformer Identification26

Rated MVA of the transformer based on transformer cooling class and number of27cooling stages28

Transformer impedance (Z) in percent on stated MVA base. Some software may allow29specifying positive and negative manufacturing tolerance values for transformer30impedance.31

Three winding transformer impedance in percent on primary MVA base. Use caution to32take the time to understand how the design of the software expects these impedances to be33stated. The impedances of three-winding transformers can be stated either as determined34

by factory tests as separate primary-secondary, primary-tertiary, tertiary-secondary values35on a stated base, or equivalent values to a fictitious center node, also on a specified base.36

Fixed Tap setting in percent or kV, as require by the design of the software37

Phase shift angle in degrees, if applicable38



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Tap step size for automatic on-load tap changers1

Maximum tap position for fixed and/or automatic on-load tap changers2

Minimum tap position for fixed and/or automatic on-load tap changers3

4

The organization of transformer tap data requires an understanding of the tap convention used by5the load flow program to ensure the representation gives the correct boost or buck in voltage.6Transformers with rated primary or secondary voltages that do not match the system nominal7(base kV) voltages on the terminal buses will require an off-nominal tap representation in8the load flow (and possibly require corresponding adjustment of the transformer impedance).9

10

6.8 Example System Input Data 11

The example system described in section 5.2 and used for the load flow analysis example in12section 9 has input data tables which are provided in Annex B. The input data listed in those13tables is not limited to or may not follow the generic format of input data described in sections146.1~6.7. The input data format can be different for different software simulation tools. The format15of the computer simulation tool used to perform the load flow study described in section 9 was16used to populate the data tables of Annex B.17

Note that the amount of input parameters required depends on the complexity and capability of18the simulation tool used to perform a load flow analysis. For simplicity the tables in Annex B19only contain the basic information which is considered “common” to most software analysis20tools. Additional input parameters may be required to apply some of the analysis methods21described in section 7; however, were omitted from this document; once again for simplicity22

purposes.23

24

7. Methodology and Standards25

7.1 General26

Because load flow calculations involve solutions of a set of non-linear equations, manual27solutions are impractical except for purely pedantic examples. Before digital computer solutions28were available, load flow simulations were conducted using analog boards. In the very early29days, these analog boards were simple dc devices with the elements of the power system30represented by resistances. Obviously, the answers were not absolutely accurate, but were31amazingly close enough for practical application.32

A special purpose analog boards called the ac network analyzer was developed in the late 1920s.33Power system networks under study were represented by an equivalent, scaled-down network.34The device allowed the analysis of a variety of operating conditions and expansion plans. The35simulation setup time was long, and the time to conduct studies and record the results slowly36made the network analyzers become cost ineffective. Furthermore, the large amount of hardware37required led to their diminishing use. Only about 50 network analyzers were left in operational by38the mid-1950s.39



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Computers began to emerge in the late 1940s as computational tools. By the mid 1950s, large-1scale computers of sufficient speed and size to handle the requirements of a power system2network calculation were available. Parallel to the hardware development, algorithms to3efficiently solve the network equations were developed. Ward and Hale developed a successful4load flow program using a modified Newton iterative procedure in 1956 [B5].1 The application5of the Gauss-Seidel iteration algorithm followed soon after. Research in algorithms continued6

and the Newton-Raphson method was introduced in the early 1960s [B4]. Considerable research7has been performed in the interim years to improve the performance of these algorithms, making8them more robust, able to handle additional power system components; the new algorithms9accommodate much larger network sizes. These calculation algorithms persist to modern days10and include adaptive methods which can adjust to higher system convergence demands.11

7.2 Overall Solution12

A rough outline of solution of the power flow problem is the following:131. Make an initial guess of all unknown voltage magnitudes and angles. It is common to use14

a "flat start" in which all voltage angles are set to zero and all voltage magnitudes are set15to 100%.16

2. Set an initial angle for the swing bus. The angle assigned to the swing bus is the17reference for the bus voltage angles calculated for each other bus in the system. Some18engineers arbitrarily use 0

o as the swing bus angle, but this typically results in negative19

signs on load bus voltage angles. A tradition going back to the days of ac network20analyzers is to use an angle such as 50o for the swing bus to avoid negative bus voltage21angles in the final solution.22

3. Solve the power balance equations using the most recent voltage magnitude and angle23values.24

4. Solve for the change in voltage angle and magnitude255. Update the voltage magnitude and angles266. If the solution is adequate as defined by a set of “stopping conditions”, terminate the27

simulation and report the results. If the solution is not adequate, return to step 3 to28

calculate a new solution.29

7.3 Problem Formulation30

The load flow calculation is a network solution problem. As explained in previous sections, and31summarized in Table 1, for any power system, the variables given (i.e. the knowns) are:32

Voltage V and phase θ at the swing bus; 33

Voltage V (in magnitude) and active power P, for “P,V” buses; 34

Active power P and reactive power Q for the “P, Q” buses. 35

The variables found (i.e. the unknowns) are:36

voltage angle θ at the “P,V” buses37

voltage angle θ and voltage magnitude V for the “P,Q” buses38

1 The numbers in brackets correspond to those of the bibliography in section 20



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Table 1 — Known and Unknowns in Power Systems1

2

The determination of the above unknown quantities is possible by writing a system of equations,3one equation for each of the above nodes, and then using a numerical method to solve those4equations. Note that in theory, there does not have to be a solution to a set of non-linear5equations. However, if the equations are properly written, the fact that they represent a practical6

power system means that there will be a solution. On the other hand, there are some special cases7where the set of non-linear equations for a power system may have multiple solutions. Those8cases form a special category of problem designated as ‘voltage stability’ that is beyond the scope9of this document.10

For modeling purposes, we can represent branches of networks by their branch admittance;11therefore, all the voltages and currents in the network are related by the following matrix12equation:13

[ I ] = [Y ][V ]14(2)15

where1617

[ I ] is the matrix of total positive sequence currents flowing into the network nodes (buses)18

[V ] is the matrix of positive sequence voltages at the network nodes (buses)19[Y ] is the nodal admittance matrix20

21Equation (2) is a linear algebraic equation with complex coefficients. If either [ I ] or [V ] are22known, the solution for the unknown quantities could be obtained by application of various23solution techniques for linear equations.24

Because of the physical characteristics of generation and load, the terminal conditions at each bus25(or node), are normally described in terms of active and reactive power ( P and Q).26

The bus current at bus i is related to these quantities as follows:27

i

iii

V Q P I ) j( (3)28

where * designates the conjugate of a complex quantity. Combining Equations (2) and (3) yields29Equation (4):30

31



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V Y V

Q P

j (4)1

2Equation (4) constitutes a non-linear system of equations, generally of large dimensions which3

cannot be readily solved by closed-form matrix techniques. Because of this situation, load flow4 solutions are obtained by procedures involving numerical techniques based on iterative5solution algorithms.6

7

7.4 Iterative Solution Algorithms8

Since the original technical papers describing digital load flow solution algorithms appeared9in the mid-1950s, a seemingly endless collection of iterative schemes has been developed and10reported. Many of these are variations of one or the other of two basic techniques that are in11widespread use by the industry today: the Gauss-Seidel technique and the Newton-Raphson12

technique. The preferred techniques used by most commercial load flow software are variations13of the Newton technique.14

All of these techniques solve bus equations in admittance form, as described in the previous15section. This system of equations has gained widespread application because of the simplicity of16data preparation and the ease with which the bus admittance matrix can be formed and changed in17subsequent cases.18

In a load flow study, the primary parameters are as follows:19

20 P is the active power into or out of the network21

Q is the reactive power into or out of the network22 |V | is the magnitude of bus voltage23θ is the angle of bus voltage referred to a common reference (the swing bus)24

25In order to define the load flow problem, it is necessary to specify two of the four quantities at26each bus. For generating units, it is reasonable to specify P and |V | because these quantities are27controllable through governor and excitation controls, respectively. For loads, one generally28specifies the real power demand P and the reactive power Q. Since there are losses in the29transmission system and these losses are not known before the load flow solution is obtained, it is30necessary to retain one bus where P is not specified. At this bus, called a swing bus, |V | as well31as θ, the swing-bus angle, are specified. Since θ is specified (that is, held constant during the32load flow solution), it is the reference angle for the system. The swing bus is therefore also called33

the reference bus. Since the real power, P , and reactive power, Q, are not specified at the swing34 bus, these quantities are free to adjust to compensate transmission losses in the system.35

Table 1 summarizes the standard electrical specifications for the three bus types. The36classifications “generator bus” and “load bus” should not be tak en as absolute. There will, for37example, be occasions where a pure load bus may be specified by P and |V |.38



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With most software, the generator specification of holding the bus voltage constant and1calculating the reactive power output will be overridden in the load flow solution if the generator2reactive output reaches its maximum or minimum VAR limit. In this case, the generator reactive3

power will be held at the respective limit, and the bus voltage will be allowed to vary.4

7.5 Gauss-Seidel iterative Technique5

Descriptions of load flow solution techniques can become rather complicated, due more to6the notation required for complex mathematics rather than the basic concepts of the solution7method. In the following sections, therefore, the basic techniques are developed by8considering their application to a dc circuit. Applications to ac problems are then a natural9extension of the dc problem.10

1112

Table 2 — Load flow bus specifications13

14

Bus type P Q |V| θ Comments

Load Usual load representation

Generator or synchronouscondenser

whenQ- < Q g < Q

+

(Q g is the sourcereactive power)

Generator or synchronouscondenser( P = 0) with var limits Q – = minimum var limit

Q+ = maximum var limit

when

Q g < Q-

or

Q g > Q+

|V| is held as long as Q g is

within limit

Swing “Swing bus” must adjust net

power to hold voltage

constant essential for

15The Gauss-Seidel solution algorithm is the easiest to understand. The performance of the Gauss-16

Seidel technique will be illustrated using the direct current circuit shown in Figure 10.17

Bus 3 is a load bus with specified per unit power. Bus 2 is a generator bus with power18specified, and Bus 1 is the swing bus with voltage specified. The voltages V 2 and V 3 are sought.19From these, the branch flows can be calculated.20

The system equations on an admittance basis are from Equation (2).21



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3231212

22

2

1V Y V Y I

Y V (8)1

Substituting2

2

22

V P I (9)3

323121

2

2

22

2

1V Y V Y

V

P

Y V (10)4

This is a nonlinear equation in V 2 5

For Bus 3, a similar procedure yields6

232131

3

3

33

3

1V Y V Y

V

P

Y V (11)7

8

where the negative sign on3

P is from the load sign convention.9

Equations (10) and (11) are in a form convenient for the application of the Gauss-Seidel iterative10solution technique. The steps in this procedure are as follows:11

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.12

2. Step 2: Compute a new value for V 2 using the initial estimates for V 2 and V 3 [see Equation13 (10)].14

3. Step 3: Compute a new value for3

V using the initial estimate for V 3 and the just computed15

value for V 2 [see Equation (11)].16

4. Step 4: Repeat Step 2 and Step 3 using the latest computed voltages V 2 and V 3 until the17solution is reached. One complete computation of V 2 and V 3 is one iteration.18

19

20

The computed voltages are said to converge when, for each iteration, the voltages come closer21and closer to the actual solution. Since the computation time increases linearly with the number22of iterations, it is necessary to have the computer program check to precision of the solution after23

each iteration, and decide whether the last computed voltages are sufficient or whether further24computations are required.25

The criterion specifying the desired accuracy is called the “convergence criterion”. The number of26iterations may be entered or changed in most load flow programs. For fast decoupled load flow27algorithms the user can also change a solution acceleration factor; slowing the factor in case of28convergence problem and increasing the factor for large network solutions.29



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There are various ways to define when a solution has converged. One reliable convergence1criterion is the power mismatch check in which the software determines the sum of the power2flows (real and reactive) on all lines connected to each bus with the specified bus real and3reactive power. The difference, which is the power mismatch, is a measure of how close the4computed voltages are to an ideal, or exact, solution. The power mismatch tolerance is generally5specified in the range of 0.01 to 0.0001 p.u. on the system MVA base. The total power mismatch is6

also printed in the output report of load flow programs and is an indication of how valid is the load7flow solution. Ideally the power mismatch of the entire network should be 0 +j0. Power mismatch8reporting should be done and reported at a bus level as well so that the user can understand which9

buses have power mismatch greater than the specified mismatch tolerance and therefore represent the10 points that are confounding the iterative solution. If the source of the iteration problem can be11determined, there often model adjustments that can be made to make the network solve more12quickly.13

Another common convergence check evaluates the maximum change in any bus voltage from one14iteration to the next. A solution with desired accuracy is assumed when the change is less than a15specified small value, for example, 0.0001 p.u.16

Some of the things that can lead to convergence difficulties include17

Errors in the input data18 System is too weak to carry the load19 Insufficient VAR in the system to support the voltage20 Significant disparity in the magnitudes of element impedance that terminate at the same21

node.2223

A voltage check is dependent on the rate of convergence and is thus less reliable than the24 power mismatch check. However, the voltage check is much faster (computationally, on a25digital computer) than the power mismatch check and since the power mismatch will be large until26

the voltage change is quite small, one may economically use a procedure where computation of27mismatch is avoided until a small amount of voltage change occurs.28

Solution of an ac circuit would be similar to the solution of a dc circuit except that both resistive29and reactive impedances must be recognized, and the solution must calculate both voltages and30angles. For the three-bus example, voltage magnitude and angle at Bus 1, generator power and31

bus voltage at Bus 2, and real and reactive load power at bus 3 would be specified. The load flow32solution would determine the voltage angle and generator reactive power output of Bus 2 and the33voltage magnitude and angle at Bus 3.34

The ac version of Equations (9) and (10) can be obtained from Equation (4) as follows:35

1...,,2,11

1

)1(1

1

)(

)1(*

)(

N iV Y V Y V

jQ P

Y V

N

ik

m

k ik

i

k

m

k ik m

i

ii

ii

m

i (12)36

Where:37 N is the number of buses in the system, and the swing bus is bus N38m is the present iteration number39i,k are bus indices40



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V , Y are complex voltage and admittance, respectively1V * is the complex conjugate of V2

7.6 Newton-Raphson iterative Technique3

The Gauss-Seidel technique is inefficient, often requiring hundreds of iterations to achieve an4acceptable solution. And it can fail to converge in some specialized instances. Problems that5ca