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Calculation of Load Flow, Prospective Fault Currents and Transient Disturbances
CHAPTER
Calculation of Load Flow, Prospective Fault Currents and Transient Disturbances
6
FAULT CALCULATION The following calculations and information are not exhaustive but are intended to give the reader sufficient knowledge to enable switchgear of adequate load and fault current rating to be specified. The subject may be studied in more detail by reading the relevant documents listed in Appendix 1. The nomenclature used is generally as given in ‘Power System Protection’ (IET). When a short circuit occurs in a distribution switchboard, the resulting fault current can be large enough to damage both the switchboard and associated cables due to thermal and electromagnetic effects. The thermal effects will be proportional to the duration of the fault current to a large extent and this time will depend on the characteristics of the nearest upstream automatic protective device which should operate to clear the fault. Arcing faults due to water or dirt ingress are most unlikely in the switchboards of land-based installations, but from experience, they need to be catered for offshore. For switchboards operating with generators of 10 MW or more, it is usually not difficult to avoid the problem of long clearance times for resistive faults. However, with the smaller generators clearance times of several seconds may be required because of the relatively low prospective fault currents available. (See PART 4 Chapter 4) With small emergency generators, pilot exciters are not normally provided and the supply for the main exciter is derived from the generator output. This arrangement is not recommended, as it allows the collapse of generator output current within milliseconds of the onset of a fault. With such small generators even sub-transient fault currents are small, and it is unlikely that downstream protection relays set to operate for ‘normal’ generation will have operated before the output collapse. It is usual to provide a fault current maintenance unit as shown in Fig. 4.6.2. This device is basically a ‘compounding’ circuit which feeds a current proportional to output current back to the exciter field. When the output current reaches a threshold value well above normal load current, a relay operates, switching in the compounding circuit. Thus a high output current is maintained by this feedback arrangement until definite time overcurrent protection, set to prevent the generator thermal rating being exceeded, operates. A worked example for use in setting Main Generator Protection is given in PART 4 Chapter 5. Offshore Electrical Engineering Manual. https://doi.org/10.1016/B978-0-12-385499-5.00026-1 Copyright © 2018 Elsevier Inc. All rights reserved.
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CHAPTER 6 Calculation of Load Flow, Fault Currents
FIGURE 4.6.1 Equivalent voltage source method.
FIGURE 4.6.2 Schematic of small generator fault current maintenance circuit.
STANDARD METHODS OF CALCULATION There are several ways to calculate the short circuit current for a marine electrical system, some very simple as the example in PART 4 Chapter 7, others more complex are listed in the table below. The complexity of the calculation is not always an indication as to the efficacy of the result.
IEC 60909
Type of Circuit
Standard Specification
Systems of ships and mobile & fixed offshore units Primarily for landbased systems
IEC 61363
All systems
IEEE 141/ANSI C37
IEC 60909
Method of Calculation Breaking Current
Making Current
Ac decrement based Dc and ac decrements on generator transient calculated impedance Use of c and k factors. Refer to IEC TR 60909-1 Use of impedance correction factors for rotating machines can significantly affect results.
IEC 61363 Calculation methods that include generator and motor short circuit decrement will tend to produce the lowest acceptable values of short circuit current. As ship and offshore systems normally consist of ‘Island’ generation where machine decrement has significant effect, IEC Standard 61363-1, usually, produces the most accurate result, i.e., it produces study results that represent conditions that may affect typical marine or offshore installations more significantly than land-based systems, including more emphasis on generator and motor decay. Where feeder cable impedance tends to reduce decrement effects, the study can take advantage of the Equivalent Generator approach outlined in IEC 61363-1 section 7. For more simple marine electrical systems, the equivalent generator method will involve extensive calculations and produce results little different from more simple methods. In this case, IEC 60909 may be a better choice for your study.
IEC 60909 The calculation method, used in the IEC Standard 60909 determines the short circuit currents at the location F using equivalent voltage source:
cUn √ 3
This source is defined as the voltage of an ideal source applied at the short circuit location in the positive sequence system, whereas all other sources are ignored. All network components are replaced by their internal impedances (see Fig. 4.6.1).
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CHAPTER 6 Calculation of Load Flow, Fault Currents
In the calculation of the maximum short circuit currents, a voltage factor c is assumed (from IEC60038) for cmax, for Low (Table 1), Medium (Table 2) and High (Table 3) voltage levels. According to Fig. 4.6.1, in the case of balanced short circuits, the initial symmetrical short circuit current is calculated by:
cUn Ik″ = √ 3 . ZQ
IEEE141/ANSI37 The decrement factors used by the ANSI SCC give reasonable decays provided the X/R ratios are within the intervals specified in the IEEE Application Guide for AC High Voltage Circuit Breakers Rated on a Symmetrical Current Basis. Your client may specify which study method is to be used, but if the installation is mobile, then it would be advisable to follow a global standard such as ABS or DNV GL for guidance on which study method to use.
DIGITAL METHODS OF FAULT CALCULATION In digital fault calculation, an admittance matrix is formed which is extended to include the source admittances, and the matrix is then reduced to a single impedance connected between the neutral (zero node) and the point of fault.
DIGITAL SIMULATION OF SYSTEM DISTURBANCES When designing large offshore power systems, it is vital that the response of the system to the starting of large motors, and the application of phase-to-phase or earth faults, have been analysed to a reasonable degree of certainty, so that the risk of dangerous operating conditions and system instability can be avoided as much as possible. The digital computer programs used in such analysis have the following elements: 1. The program will obtain its basic system data, including models of all generators, governors, AVRs etc. and network configuration, from data stored in various input files. Models for such devices as AVRs, prime movers etc. are in the form of differential equations. 2. Having obtained the necessary input data and initialized the system, the program uses a step-by-step implicit trapezoidal method of simultaneously solving the large number of differential equations involved. Iterative methods are used at each step to obtain the desired accuracy (usually 99.95%). 3. After a defined simulated period, the program stops and creates an output file containing the values of all variables calculated at each step. 4. For faster and more user-friendly interpretation of this output data, graphics subroutines are used to plot the variables against time.
ETAP Short Circuit Analysis Software
Suitable program suites are available commercially from the organizations listed in the Bibliography section.
TRANSIENT SIMULATIONS AND HARMONIC ANALYSIS Most of the commercial programs available have other modules, including simulation of generator outages and transient system upsets such as the starting of large electrical drives. It is essential that such studies are carried out prior to specifying main generation and switchgear ratings in order to ensure the system is going to be stable. If it is expected that a large proportion of the electrically driven machinery is of variable frequency or variable speed, harmonic analysis is also essential in order to calculate the percentage Total Harmonic Distortion (%THD). It is important that the grouped capacitance of lighting and any other large capacitive load is included in the model. The following are examples of short circuit analysis and other outputs from three proprietary programs available. There are a many more programs available on the market, some of which are available free from switchgear manufacturers. The author is not recommending any particular software, and to some extent, suitability of the program will depend on: • The particular engineer’s experience • What particular graphic outputs are required • Whether other results such as harmonic analysis, arc-flash studies, relay discrimination graphs, etc., are required • The hardware and software available for the program to run on • Client and project preference
ETAP SHORT CIRCUIT ANALYSIS SOFTWARE Etap.com Operation Technology, Inc. ©2017. ETAP Short Circuit software program allows for fault calculations based on ANSI/IEEE, IEC and GOST standards. The user-friendly interface, combined with powerful analysis engine, saves hours of tedious hand calculations and takes the guesswork out of fault analysis by automating the process with multiple calculation and result analysis tools. ETAP Short Circuit Software Key Features: • IEC Standard 60909 • IEC Standard 61363 • ANSI/IEEE Standards C37 & UL 489 • GOST (Russian) Standards R-52735 • Unbalanced L-G, L-L, and L-L-G faults analysis • Device evaluation for 3- and 1-phase systems
• Determine worst case device duty results • Display critical and marginal alerts • Load terminal short circuit calculation • Generator circuit breaker evaluation • Comprehensive short circuit plots & reports
241
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CHAPTER 6 Calculation of Load Flow, Fault Currents
Built-in intelligence allows it to automatically apply all factors and ratios required for high- and low-voltage device duty evaluation. Overstressed device alarms are displayed on the one-line diagram and reports. The short circuit module seamlessly integrates with the ETAP Protection & Coordination and Arc Flash Analysis programs.
IEC 61363 individual phase fault current.
ETAP Short Circuit Analysis Software
Report Analyser to Compare Studies and Identify Worst Case.
ETAP ANSI Short Circuit Features
ETAP IEC Short Circuit Features
• Determine maximum and minimum short circuit fault currents • Calculate ½ cycle, 1.5–4 and 30 cycle balanced and unbalanced faults • Check momentary and interrupting device capabilities • Check closing & latching capabilities • Evaluate symmetrical or total rated circuit breakers • Special handling of generator circuit breakers • Interrupting duty as a function breaker contact parting time • Standard and user-definable contact parting time • Automatically includes No AC Decay (NACD) ratio • User options for automatic adjustment of HVCB rating
• Unbalanced L-G, L-L and L-L-G faults analysis • Transient short circuit calculations to generate individual A, B and C phase currents • Compares device ratings with calculated short circuit values • User-definable voltage C factor • Service or ultimate short circuit current ratings for LVCB breaking capability • User-definable R/X adjustment methods for Ip (method A, B, or C) • Negative or positive ″impedance adjustments for max/min Ik and Ik • Automatic application of K correction factors (i.e., KT, KG, KSO) • Automatically determines meshed and non-meshed networks for calculating Ib, Ik and Idc • Considers both near and far from generator short circuits
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Short Circuit Duty Summary Report Generator Circuit Breaker 3-Phase Fault Currents: (Prefault Voltage = 102% of the Bus Nominal Voltage) Circuit Breaker ID
Type
CB4
5 cy Sym CB
Momentary Duty (@ 1/2 Cycle)
Interrupting Duty (@ Contact Parting Time)
Source and Generator PF
Symm. kA rms
Asymm. kA rms
Asymm. kA Peak
Symm. kA rms
Asymm. kA rms
Symm. kA Peak
DC Fault Current (kA)
Degree of Asymm. (%)
Gen-lagging PF Gen-leading PF Gen-no load Sys-lagging PF Sys-leading PF
1.853 1.558 1.628 8.660 8.969
4.575 4.472 4.463 14.155 14.660
6.803 6.396 6.458 23.444 24.280
1.809 1.518 1.583 8.625 8.935
3.517 3.382 3.388 11.228 11.631
2.559 2.146 2.239 12.198 12.635
3.016 3.022 2.996 7.188 7.446
117.85 140.81 133.82 58.93 58.93
Sys-no load
8.867
14.492
24.003
8.828
11.492
12.485
7.358
58.93
CHAPTER 6 Calculation of Load Flow, Fault Currents
Generator Circuit Breaker Evaluation per IEEE C37.013
Unbalanced Short Circuit Analysis for Multiple and Single Phase Systems
UNBALANCED SHORT CIRCUIT ANALYSIS FOR MULTIPLE AND SINGLE PHASE SYSTEMS The ETAP Unbalanced Short Circuit module applies 3-phase system modeling to represent unbalanced 3-phase systems, as well as 1-phase systems including panel, UPS and distribution transformers. It fully captures the effect of unbalanced systems, including unbalanced loads, transmission components, special distribution transformers and coupling between transmission lines.
Display fault current in phase/sequence for any fault types.
245
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CHAPTER 6 Calculation of Load Flow, Fault Currents
IPSA SHORT CIRCUIT ANALYSIS SOFTWARE
IPSA Short Circuit Analysis Software
247
248
CHAPTER 6 Calculation of Load Flow, Fault Currents
POWER TOOLS FOR WINDOWS
Power Tools for Windows
249
250
CHAPTER 6 Calculation of Load Flow, Fault Currents
PROVING THE SOFTWARE A set of example manual fault calculations with full workings should be available, for comparison with a set of input data (generated by the proposed software) and output results printout, (using identical input data) and carried out with the software, which is intended will be used for the proposed study. This ‘proving’ example should be run on the hardware and software (e.g., Windows 10) intended to be used in the study, even if it has been run successfully before on other hardware. Such calculations are essential to ensure that: • The software is operating properly in the environment it is running on (e.g., Windows 10). • The client can be confident of the software and consequently more confident of the results.
MANUAL CALCULATIONS The engineer running the study needs to have a reasonable indication as to results expected and can check the input network and data before running the program, or rerunning the program if not happy with the initial result. It is recommended that programs such as MatLab or Mathcad are used for the ‘manual’ calculation rather than a spreadsheet template, as spreadsheets may introduce rounding errors. With such programs the workings can be demonstrated more easily by adding explanatory notes etc. Please refer to PART 4 Chapter 5 for an example fault calculation. Please refer to PART 4 Chapter 7 for example relay studies.
Calculation of Load Flow, Prospective Fault Currents and Transient Disturbances
6
FAULT CALCULATION The following calculations and information are not exhaustive but are intended to give the reader sufficient knowledge to enable switchgear of adequate load and fault current rating to be specified. The subject may be studied in more detail by reading the relevant documents listed in Appendix 1. The nomenclature used is generally as given in ‘Power System Protection’ (IET). When a short circuit occurs in a distribution switchboard, the resulting fault current can be large enough to damage both the switchboard and associated cables due to thermal and electromagnetic effects. The thermal effects will be proportional to the duration of the fault current to a large extent and this time will depend on the characteristics of the nearest upstream automatic protective device which should operate to clear the fault. Arcing faults due to water or dirt ingress are most unlikely in the switchboards of land-based installations, but from experience, they need to be catered for offshore. For switchboards operating with generators of 10 MW or more, it is usually not difficult to avoid the problem of long clearance times for resistive faults. However, with the smaller generators clearance times of several seconds may be required because of the relatively low prospective fault currents available. (See PART 4 Chapter 4) With small emergency generators, pilot exciters are not normally provided and the supply for the main exciter is derived from the generator output. This arrangement is not recommended, as it allows the collapse of generator output current within milliseconds of the onset of a fault. With such small generators even sub-transient fault currents are small, and it is unlikely that downstream protection relays set to operate for ‘normal’ generation will have operated before the output collapse. It is usual to provide a fault current maintenance unit as shown in Fig. 4.6.2. This device is basically a ‘compounding’ circuit which feeds a current proportional to output current back to the exciter field. When the output current reaches a threshold value well above normal load current, a relay operates, switching in the compounding circuit. Thus a high output current is maintained by this feedback arrangement until definite time overcurrent protection, set to prevent the generator thermal rating being exceeded, operates. A worked example for use in setting Main Generator Protection is given in PART 4 Chapter 5. Offshore Electrical Engineering Manual. https://doi.org/10.1016/B978-0-12-385499-5.00026-1 Copyright © 2018 Elsevier Inc. All rights reserved.
237
238
CHAPTER 6 Calculation of Load Flow, Fault Currents
FIGURE 4.6.1 Equivalent voltage source method.
FIGURE 4.6.2 Schematic of small generator fault current maintenance circuit.
STANDARD METHODS OF CALCULATION There are several ways to calculate the short circuit current for a marine electrical system, some very simple as the example in PART 4 Chapter 7, others more complex are listed in the table below. The complexity of the calculation is not always an indication as to the efficacy of the result.
IEC 60909
Type of Circuit
Standard Specification
Systems of ships and mobile & fixed offshore units Primarily for landbased systems
IEC 61363
All systems
IEEE 141/ANSI C37
IEC 60909
Method of Calculation Breaking Current
Making Current
Ac decrement based Dc and ac decrements on generator transient calculated impedance Use of c and k factors. Refer to IEC TR 60909-1 Use of impedance correction factors for rotating machines can significantly affect results.
IEC 61363 Calculation methods that include generator and motor short circuit decrement will tend to produce the lowest acceptable values of short circuit current. As ship and offshore systems normally consist of ‘Island’ generation where machine decrement has significant effect, IEC Standard 61363-1, usually, produces the most accurate result, i.e., it produces study results that represent conditions that may affect typical marine or offshore installations more significantly than land-based systems, including more emphasis on generator and motor decay. Where feeder cable impedance tends to reduce decrement effects, the study can take advantage of the Equivalent Generator approach outlined in IEC 61363-1 section 7. For more simple marine electrical systems, the equivalent generator method will involve extensive calculations and produce results little different from more simple methods. In this case, IEC 60909 may be a better choice for your study.
IEC 60909 The calculation method, used in the IEC Standard 60909 determines the short circuit currents at the location F using equivalent voltage source:
cUn √ 3
This source is defined as the voltage of an ideal source applied at the short circuit location in the positive sequence system, whereas all other sources are ignored. All network components are replaced by their internal impedances (see Fig. 4.6.1).
239
240
CHAPTER 6 Calculation of Load Flow, Fault Currents
In the calculation of the maximum short circuit currents, a voltage factor c is assumed (from IEC60038) for cmax, for Low (Table 1), Medium (Table 2) and High (Table 3) voltage levels. According to Fig. 4.6.1, in the case of balanced short circuits, the initial symmetrical short circuit current is calculated by:
cUn Ik″ = √ 3 . ZQ
IEEE141/ANSI37 The decrement factors used by the ANSI SCC give reasonable decays provided the X/R ratios are within the intervals specified in the IEEE Application Guide for AC High Voltage Circuit Breakers Rated on a Symmetrical Current Basis. Your client may specify which study method is to be used, but if the installation is mobile, then it would be advisable to follow a global standard such as ABS or DNV GL for guidance on which study method to use.
DIGITAL METHODS OF FAULT CALCULATION In digital fault calculation, an admittance matrix is formed which is extended to include the source admittances, and the matrix is then reduced to a single impedance connected between the neutral (zero node) and the point of fault.
DIGITAL SIMULATION OF SYSTEM DISTURBANCES When designing large offshore power systems, it is vital that the response of the system to the starting of large motors, and the application of phase-to-phase or earth faults, have been analysed to a reasonable degree of certainty, so that the risk of dangerous operating conditions and system instability can be avoided as much as possible. The digital computer programs used in such analysis have the following elements: 1. The program will obtain its basic system data, including models of all generators, governors, AVRs etc. and network configuration, from data stored in various input files. Models for such devices as AVRs, prime movers etc. are in the form of differential equations. 2. Having obtained the necessary input data and initialized the system, the program uses a step-by-step implicit trapezoidal method of simultaneously solving the large number of differential equations involved. Iterative methods are used at each step to obtain the desired accuracy (usually 99.95%). 3. After a defined simulated period, the program stops and creates an output file containing the values of all variables calculated at each step. 4. For faster and more user-friendly interpretation of this output data, graphics subroutines are used to plot the variables against time.
ETAP Short Circuit Analysis Software
Suitable program suites are available commercially from the organizations listed in the Bibliography section.
TRANSIENT SIMULATIONS AND HARMONIC ANALYSIS Most of the commercial programs available have other modules, including simulation of generator outages and transient system upsets such as the starting of large electrical drives. It is essential that such studies are carried out prior to specifying main generation and switchgear ratings in order to ensure the system is going to be stable. If it is expected that a large proportion of the electrically driven machinery is of variable frequency or variable speed, harmonic analysis is also essential in order to calculate the percentage Total Harmonic Distortion (%THD). It is important that the grouped capacitance of lighting and any other large capacitive load is included in the model. The following are examples of short circuit analysis and other outputs from three proprietary programs available. There are a many more programs available on the market, some of which are available free from switchgear manufacturers. The author is not recommending any particular software, and to some extent, suitability of the program will depend on: • The particular engineer’s experience • What particular graphic outputs are required • Whether other results such as harmonic analysis, arc-flash studies, relay discrimination graphs, etc., are required • The hardware and software available for the program to run on • Client and project preference
ETAP SHORT CIRCUIT ANALYSIS SOFTWARE Etap.com Operation Technology, Inc. ©2017. ETAP Short Circuit software program allows for fault calculations based on ANSI/IEEE, IEC and GOST standards. The user-friendly interface, combined with powerful analysis engine, saves hours of tedious hand calculations and takes the guesswork out of fault analysis by automating the process with multiple calculation and result analysis tools. ETAP Short Circuit Software Key Features: • IEC Standard 60909 • IEC Standard 61363 • ANSI/IEEE Standards C37 & UL 489 • GOST (Russian) Standards R-52735 • Unbalanced L-G, L-L, and L-L-G faults analysis • Device evaluation for 3- and 1-phase systems
• Determine worst case device duty results • Display critical and marginal alerts • Load terminal short circuit calculation • Generator circuit breaker evaluation • Comprehensive short circuit plots & reports
241
242
CHAPTER 6 Calculation of Load Flow, Fault Currents
Built-in intelligence allows it to automatically apply all factors and ratios required for high- and low-voltage device duty evaluation. Overstressed device alarms are displayed on the one-line diagram and reports. The short circuit module seamlessly integrates with the ETAP Protection & Coordination and Arc Flash Analysis programs.
IEC 61363 individual phase fault current.
ETAP Short Circuit Analysis Software
Report Analyser to Compare Studies and Identify Worst Case.
ETAP ANSI Short Circuit Features
ETAP IEC Short Circuit Features
• Determine maximum and minimum short circuit fault currents • Calculate ½ cycle, 1.5–4 and 30 cycle balanced and unbalanced faults • Check momentary and interrupting device capabilities • Check closing & latching capabilities • Evaluate symmetrical or total rated circuit breakers • Special handling of generator circuit breakers • Interrupting duty as a function breaker contact parting time • Standard and user-definable contact parting time • Automatically includes No AC Decay (NACD) ratio • User options for automatic adjustment of HVCB rating
• Unbalanced L-G, L-L and L-L-G faults analysis • Transient short circuit calculations to generate individual A, B and C phase currents • Compares device ratings with calculated short circuit values • User-definable voltage C factor • Service or ultimate short circuit current ratings for LVCB breaking capability • User-definable R/X adjustment methods for Ip (method A, B, or C) • Negative or positive ″impedance adjustments for max/min Ik and Ik • Automatic application of K correction factors (i.e., KT, KG, KSO) • Automatically determines meshed and non-meshed networks for calculating Ib, Ik and Idc • Considers both near and far from generator short circuits
243
244
Short Circuit Duty Summary Report Generator Circuit Breaker 3-Phase Fault Currents: (Prefault Voltage = 102% of the Bus Nominal Voltage) Circuit Breaker ID
Type
CB4
5 cy Sym CB
Momentary Duty (@ 1/2 Cycle)
Interrupting Duty (@ Contact Parting Time)
Source and Generator PF
Symm. kA rms
Asymm. kA rms
Asymm. kA Peak
Symm. kA rms
Asymm. kA rms
Symm. kA Peak
DC Fault Current (kA)
Degree of Asymm. (%)
Gen-lagging PF Gen-leading PF Gen-no load Sys-lagging PF Sys-leading PF
1.853 1.558 1.628 8.660 8.969
4.575 4.472 4.463 14.155 14.660
6.803 6.396 6.458 23.444 24.280
1.809 1.518 1.583 8.625 8.935
3.517 3.382 3.388 11.228 11.631
2.559 2.146 2.239 12.198 12.635
3.016 3.022 2.996 7.188 7.446
117.85 140.81 133.82 58.93 58.93
Sys-no load
8.867
14.492
24.003
8.828
11.492
12.485
7.358
58.93
CHAPTER 6 Calculation of Load Flow, Fault Currents
Generator Circuit Breaker Evaluation per IEEE C37.013
Unbalanced Short Circuit Analysis for Multiple and Single Phase Systems
UNBALANCED SHORT CIRCUIT ANALYSIS FOR MULTIPLE AND SINGLE PHASE SYSTEMS The ETAP Unbalanced Short Circuit module applies 3-phase system modeling to represent unbalanced 3-phase systems, as well as 1-phase systems including panel, UPS and distribution transformers. It fully captures the effect of unbalanced systems, including unbalanced loads, transmission components, special distribution transformers and coupling between transmission lines.
Display fault current in phase/sequence for any fault types.
245
246
CHAPTER 6 Calculation of Load Flow, Fault Currents
IPSA SHORT CIRCUIT ANALYSIS SOFTWARE
IPSA Short Circuit Analysis Software
247
248
CHAPTER 6 Calculation of Load Flow, Fault Currents
POWER TOOLS FOR WINDOWS
Power Tools for Windows
249
250
CHAPTER 6 Calculation of Load Flow, Fault Currents
PROVING THE SOFTWARE A set of example manual fault calculations with full workings should be available, for comparison with a set of input data (generated by the proposed software) and output results printout, (using identical input data) and carried out with the software, which is intended will be used for the proposed study. This ‘proving’ example should be run on the hardware and software (e.g., Windows 10) intended to be used in the study, even if it has been run successfully before on other hardware. Such calculations are essential to ensure that: • The software is operating properly in the environment it is running on (e.g., Windows 10). • The client can be confident of the software and consequently more confident of the results.
MANUAL CALCULATIONS The engineer running the study needs to have a reasonable indication as to results expected and can check the input network and data before running the program, or rerunning the program if not happy with the initial result. It is recommended that programs such as MatLab or Mathcad are used for the ‘manual’ calculation rather than a spreadsheet template, as spreadsheets may introduce rounding errors. With such programs the workings can be demonstrated more easily by adding explanatory notes etc. Please refer to PART 4 Chapter 5 for an example fault calculation. Please refer to PART 4 Chapter 7 for example relay studies.