EMO Wiki - User contributions [en]

EMO:Loading and editing Transmission System Data

2016-02-26T03:02:19Z

WoodsM: /* Editing Loaded Circuit Data */

{{#hidens:}}
=== Loading Transmission Data ===
<span style="color:#2E5894">
'''>> To load Transmission data in to your forecast Definition:'''
#Click the '''Load Data button''' (or use the '''Data > Load Data''' option in the Menu bar of the '''''Forecast Definition Window''''' to open the '''''Load Data Window''''')
#Use the '''Load Transmission Data Dialogue''' to specify the details of the Transmission data you wish to use

Tip: Remember to select a data range for the Transmission data that fully covers the Forecast Definition Effective Date Range.

=== Manual Constraints ===
In Forecast mode, EMO loads all of the constraints extracted from the SPD daily data files into the Forecast for you. It also loads Manual Constraints from the SO's web site available at http://www.systemoperator.co.nz/system-operations/security-management/security-constraints (part way down this page is the ''Manual Constraints Post SFT (updated dd ddd yyyy)'' workbook). The Manual constraints are, by default, set to inactive status, so you need to decide which of these constraints you need (if any) and set them to active.

=== Editing Loaded Circuit Data ===
Data for individual Circuits can be edited using the '''''Edit Circuit Information Window''''' accessed by double-clicking a circuit in the loaded circuit data panel on the Forecast Definition Window.

These edited fields are equivalent to the values in the [[EMO:Circuits Information Grid|Circuits Information Grid]]:
*'''Name'''
*'''From'''
*'''To'''
*'''CircuitType'''
*'''Resistance'''
*'''Reactance'''
*'''Fixed Loss'''

Also the following fields can be defined:
*'''Summer, Shoulder, Winter''' : these fields defined the default capacity in the three temperature phases
*'''Re-Rated''': NOT EDITABLE, this field shows if there are any rerating entries relating to this circuit
*'''SFT Protection Factors''': These factors control the generation of automatic SFT constraints, if that feature is being used. For more information see [[EMO:SFT Constraints|SFT Constraints]].
These values are only required for Line, not Transformers or Switches. The values are in the format <Summer PF>,<Summer PFQ>;<Winter PF>,<Winter PFQ>;<Shoulder PF>,<Shoulder PFQ>

*'''Included''': allows circuits to be removed from the forecast.

=== Editing Loaded Equation Constraint Data ===
Equation Constraint data can be edited using the '''''Edit Equation Constraint Information''''' Window accessed by double-clicking an equation in the loaded equations data panel on the Forecast Definition Window.

[[Main Page|Home]]

EMO:Loading and editing Transmission System Data

2016-02-26T03:01:42Z

WoodsM: /* Editing Loaded Circuit Data */

{{#hidens:}}
=== Loading Transmission Data ===
<span style="color:#2E5894">
'''>> To load Transmission data in to your forecast Definition:'''
#Click the '''Load Data button''' (or use the '''Data > Load Data''' option in the Menu bar of the '''''Forecast Definition Window''''' to open the '''''Load Data Window''''')
#Use the '''Load Transmission Data Dialogue''' to specify the details of the Transmission data you wish to use

Tip: Remember to select a data range for the Transmission data that fully covers the Forecast Definition Effective Date Range.

=== Manual Constraints ===
In Forecast mode, EMO loads all of the constraints extracted from the SPD daily data files into the Forecast for you. It also loads Manual Constraints from the SO's web site available at http://www.systemoperator.co.nz/system-operations/security-management/security-constraints (part way down this page is the ''Manual Constraints Post SFT (updated dd ddd yyyy)'' workbook). The Manual constraints are, by default, set to inactive status, so you need to decide which of these constraints you need (if any) and set them to active.

=== Editing Loaded Circuit Data ===
Data for individual Circuits can be edited using the '''''Edit Circuit Information Window''''' accessed by double-clicking a circuit in the loaded circuit data panel on the Forecast Definition Window.

These edited fields are equivalent to the values in the [[EMO:Circuits Information Grid|Circuits Information Grid]]:
*'''Name'''
*'''From'''
*'''To'''
*'''CircuitType'''
*'''Resistance'''
*'''Reactance'''
*'''Fixed Loss'''

As well as these fields the following fields can be defined:
*'''Summer, Shoulder, Winter''' : these fields defined the default capacity in the three temperature phases
*'''Re-Rated''': NOT EDITABLE, this field shows if there are any rerating entries relating to this circuit
*'''SFT Protection Factors''': These factors control the generation of automatic SFT constraints, if that feature is being used. For more information see [[EMO:SFT Constraints|SFT Constraints]].
These values are only required for Line, not Transformers or Switches. The values are in the format <Summer PF>,<Summer PFQ>;<Winter PF>,<Winter PFQ>;<Shoulder PF>,<Shoulder PFQ>

*'''Included''': allows circuits to be removed from the forecast.

=== Editing Loaded Equation Constraint Data ===
Equation Constraint data can be edited using the '''''Edit Equation Constraint Information''''' Window accessed by double-clicking an equation in the loaded equations data panel on the Forecast Definition Window.

[[Main Page|Home]]

EMO:Loading and editing Transmission System Data

2016-02-26T03:00:21Z

WoodsM: /* Editing Loaded Circuit Data */

{{#hidens:}}
=== Loading Transmission Data ===
<span style="color:#2E5894">
'''>> To load Transmission data in to your forecast Definition:'''
#Click the '''Load Data button''' (or use the '''Data > Load Data''' option in the Menu bar of the '''''Forecast Definition Window''''' to open the '''''Load Data Window''''')
#Use the '''Load Transmission Data Dialogue''' to specify the details of the Transmission data you wish to use

Tip: Remember to select a data range for the Transmission data that fully covers the Forecast Definition Effective Date Range.

=== Manual Constraints ===
In Forecast mode, EMO loads all of the constraints extracted from the SPD daily data files into the Forecast for you. It also loads Manual Constraints from the SO's web site available at http://www.systemoperator.co.nz/system-operations/security-management/security-constraints (part way down this page is the ''Manual Constraints Post SFT (updated dd ddd yyyy)'' workbook). The Manual constraints are, by default, set to inactive status, so you need to decide which of these constraints you need (if any) and set them to active.

=== Editing Loaded Circuit Data ===
Data for individual Circuits can be edited using the '''''Edit Circuit Information Window''''' accessed by double-clicking a circuit in the loaded circuit data panel on the Forecast Definition Window.

These edited fields are equivalent to the values in the [[Circuits Information Grid]]:
*'''Name'''
*'''From'''
*'''To'''
*'''CircuitType'''
*'''Resistance'''
*'''Reactance'''
*'''Fixed Loss'''

As well as these fields the following fields can be defined:
*'''Summer, Shoulder, Winter''' : these fields defined the default capacity in the three temperature phases
*'''Re-Rated''': NOT EDITABLE, this field shows if there are any rerating entries relating to this circuit
*'''SFT Protection Factors''': These factors control the generation of automatic SFT constraints, if that feature is being used. For more information see [[EMO:SFT Constraints|SFT Constraints]].
These values are only required for Line, not Transformers or Switches. The values are in the format <Summer PF>,<Summer PFQ>;<Winter PF>,<Winter PFQ>;<Shoulder PF>,<Shoulder PFQ>

*'''Included''': allows circuits to be removed from the forecast.

=== Editing Loaded Equation Constraint Data ===
Equation Constraint data can be edited using the '''''Edit Equation Constraint Information''''' Window accessed by double-clicking an equation in the loaded equations data panel on the Forecast Definition Window.

[[Main Page|Home]]

EMO:Circuits Information Grid

2016-02-26T01:35:15Z

WoodsM: /* Data Types */

{{#hidens:}}
=== Access ===
The '''Circuits Tab''' in the '''''[[EMO:Main Window Display Panel|Main Window Display Panel]]'''''.

=== Purpose ===
To display '''''Dynamic Information''''' related to all Circuits for a '''''Current Data Set'''''.

=== Data Types ===
{|class="wikitable"
! Column !! Description
|-
|
:''Name''
|
:Circuit Name (as provided by Transpower or user-named)
|-
|
:''From/To Node''
|
:The nodes linked by the Circuit. The From and To designations are used for reference when calculating flow direction:
*Flow FROM => TO is +ve
*Flow TO => FROM is -ve
|-
|
:''IsHVDC Indicator''
|
:Indicates the Circuit is included in the HVDC Modelling when checked
|-
|
:''Resistance''
|
:Circuit resistance (in Ω)
|-
|
''Reactance''
|
:Circuit reactance (in Ω)
|-
|
:''Fixed Losses''
|
:Fixed losses (in MW) associated with the Circuit
|-
|
:''Capacity''
|
:Capacity of the Circuit (in MW) for the current period
|-
|
:''Powerflow''
|
:Flow in Circuit (in MW) for the current period
|-
|
:''P.S.''
|
:The price separation across the nodes connected by the Circuit after deducting Price differences due to losses. This is useful for identifying Circuits affected by Equation Constraints.
|-
|
:''Losses''
|
:The Losses (in MW) associated with the line for the current period
|-
|
:''Loading''
|
:Percentage of total capacity used in the Current Period expressed as a number between 0 and 1
|
|-
|
:''SFT PF''
|
:The SFT protection factor - See [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]]. This is valid for lines only
|
|-
|
:''SFT PFQ''
|
:The SFT curvature - See [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]]. This is valid for lines only
|
|-
|
:''SFT Threshold''
|
:The SFT Threshold - See [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]]. This is valid for lines only
|
|-
|
:''SFT Tmax''
|
:The Thermnal limit of the circuit - See [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]]. This is valid for lines only
|}

NOTE: Double-clicking on any row will open a separate '''''[[EMO:Circuits Information Window|Circuit Information Window]]''''' for the associated Circuit.

[[Main Page|Home]]

EMO:SFT Calculator

2016-02-11T20:48:48Z

WoodsM:

The SFT Calculator is provided so the PF and PFQ can be estimated for lines that don't exist on the grid yet. As explained in [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]] these two values are used be EMO to generate SFT constraints, so they will be needed if a line is added to a forecast and needs to be included in the SFT modelling.

[[File:SFTCalculator.png]]

The SFT Calculator is opened from the Data menu. A dialog box appears from which an existing line can be chosen to provide starting values in the calculator. Once the calculator is open the conductor properties and the cable configuration can be changed. The resulting thermal limit and PF and PFQ values will be automatically updated as changes are made.

EMO:SFT Calculator

2016-02-11T20:48:25Z

WoodsM:

The SFT Calculator is provided so the PF and PFQ can be estimated for lines that don't exist on the grid yet. As explained in [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]] these two values are used be EMO to generate SFT constraints, so they will be needed if a line is added to a forecast and needs to be included in the SFT modelling.
[[File:SFTCalculator.png]]

The SFT Calculator is opened from the Data menu. A dialog box appears from which an existing line can be chosen to provide starting values in the calculator. Once the calculator is open the conductor properties and the cable configuration can be changed. The resulting thermal limit and PF and PFQ values will be automatically updated as changes are made.

EMO:SFT Calculator

2016-02-11T20:47:34Z

WoodsM:

The SFT Calculator is provided so the PF and PFQ can be estimated for lines that don't exist on the grid yet. As explained in [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]] these two values are used be EMO to generate SFT constraints, so they will be needed if a line is added to a forecast and needs to be included in the SFT modelling.
[[File:SFT Calculator.png]]

The SFT Calculator is opened from the Data menu. A dialog box appears from which an existing line can be chosen to provide starting values in the calculator. Once the calculator is open the conductor properties and the cable configuration can be changed. The resulting thermal limit and PF and PFQ values will be automatically updated as changes are made.

File:SFTCalculator.png

2016-02-11T20:46:26Z

WoodsM:

EMO:SFT Calculator

2016-02-11T20:44:05Z

WoodsM: Created page with "The SFT Calculator is provided so the PF and PFQ can be estimated for lines that don't exist on the grid yet. As explained in [[EMO:How EMO models SFT constraints|How EMO mod..."

The SFT Calculator is provided so the PF and PFQ can be estimated for lines that don't exist on the grid yet. As explained in [[EMO:How EMO models SFT constraints|How EMO models SFT constraints]] these two values are used be EMO to generate SFT constraints, so they will be needed if a line is added to a forecast and needs to be included in the SFT modelling.
[[File:Example.jpg]]

The SFT Calculator is opened from the Data menu. A dialog box appears from which an existing line can be chosen to provide starting values in the calculator. Once the calculator is open the conductor properties and the cable configuration can be changed. The resulting thermal limit and PF and PFQ values will be automatically updated as changes are made.

EMO:SFT Constraints

2016-02-11T20:28:23Z

WoodsM:

In February 2014, the Auto-SFT feature was made available in EMO version 5. There are often times when a market participant knows that some future event will impact on its operations and financial outcomes, resulting in a need to study the event beforehand. But what constraints will there be in the market at that point in time? Is history a good guide?

We know of many constraints that may apply as they are published in the list of Manual Constraints on the SO's web site (see the[[EMO:Constraint Overview|Constraint Overiew page]]), but since the introduction of SFT it is entirely possible that some future event may produce SFT constraints that were hitherto not observed in published market data, and this is where EMO's Auto-SFT feature can help.

Disclaimer: EMO's Auto-SFT feature cannot produce all possible future constraints for you. We are limited in our ability to access data that is used by the SO in formulating SFT constraints (so we have to make approximations), and there are some forms of SFT constraint that are not readily created. You should view EMO's SFT constraints as a good approximation to most of the SFT constraints that could arise in future.

[[EMO:SFT Overview|SFT Overview]]

[[EMO:How EMO models SFT constraints|How EMO models SFT constraints]]

[[EMO:Viewing SFT Constraints in EMO|Viewing SFT Constraints in EMO]]

[[EMO:SFT Calculator|SFT Calculator]]

[[Main Page|Home]]

EMO:Use of line conductor information in SFT

2015-12-21T01:03:58Z

WoodsM: /* Conductor Parameters */

The behaviour of SFT constraints is now derived from information about the thermal characteristics of the lines involved. The information required by EMO to do this derivation is contained in two files, the Conductor Parameters file and the Circuit Configuration file.

Both these files are provided by Energy Link in the automatic downloads made by EMO. They will appear in the <Data>/Inputs/Grid/SFT directory. The Circuit Configuration file can be overridden by a manually edited file however. This is done by placing a file with the correct name format into a directory at <Data>/Inputs/Grid/SFT/Manual.

==Conductor Parameters==

The Conductor Parameters file contains information on the properties of the different types of conductors used in transpower lines. This is a csv file with a heading line and the following columns. The file is named 'Conductor_Parameters_<yyyyMMdd>.csv' where <yyyyMMdd> is the creation date. A number of these files may appear together but only the one with the latest date will be loaded.

{|class="wikitable"
! Column !! Meaning
|-
!Conductor Code
|
:This is the code used to identify this type of cable
|-
!Conductor Description
|
:a description, for reference only
|-
!Absorbivity
|
:Average absorbance, the proportion of incoming radiative energy that is absorbed over naturally occurring frequencies
|-
!Coefficient of Resistance
|
:The rate of change in resistance as temperature is increased
|-
!Resistance @20 C ohms/km
|
:Electrical resistance
|-
!Mass per unit lemgth gm/cm
|
:The mass or weight of the cable
|-
!Diameter mm
|
:Diameter of the cable
|-
!Emissivity
|
:Physical emissivity, which determines the rate at which heat is lost through radiation
|-
!Specific Heat Capacity Cal/g/C
|
:Physical heat capacity, the amount of energy required to raise the temperature in the cable material
|}

==Circuit Configuration==
The Circuit Configuration describes the configuration of the circuit with regard to the cable type and number and the offload time used.
The file is named 'Circuit Configuration_<yyyyMMdd>.csv' where <yyyyMMdd> is the creation date. A number of these files may appear together but only the one with the latest date will be loaded.

{|class="wikitable"
! Column !! Meaning
|-
!Branch Id
|
:The branch id is used as the name of the circuit in EMO
|-
!Date
|
:The date from which the information in the row is valid. If this column is empty the information is valid from teh earliest date possible
|-
!Limiting Conductor
|
:the name of the cable type used in the conductor that sets the thermal limit of the line. This name needs to appear in the conductor code column in the Conductor Parameters file
|-
!Number of Conductors
|
:the number of conductors used in the line.
|-
!SFT_Status (Y/N)
|
:whether to apply SFT to theis line
|-
!Offload time (minutes)
|
:the SFT offload time, or time window in which a thermal overload can occur.
|-
!Threshold
|
:The threshold after which the constraint will be shown by EMO. This is expressed as a percentage of the constraint limit.
|}

EMO:Use of line conductor information in SFT

2015-12-20T22:49:42Z

WoodsM:

The behaviour of SFT constraints is now derived from information about the thermal characteristics of the lines involved. The information required by EMO to do this derivation is contained in two files, the Conductor Parameters file and the Circuit Configuration file.

Both these files are provided by Energy Link in the automatic downloads made by EMO. They will appear in the <Data>/Inputs/Grid/SFT directory. The Circuit Configuration file can be overridden by a manually edited file however. This is done by placing a file with the correct name format into a directory at <Data>/Inputs/Grid/SFT/Manual.

==Conductor Parameters==

The Conductor Parameters file contains information on the properties of the different types of conductors used in transpower lines. This is a csv file with a heading line and the following columns. The file is named 'Conductor_Parameters_<yyyyMMdd>.csv' where <yyyyMMdd> is the creation date. A number of these files may appear together but only the one with the latest date will be loaded.

{|class="wikitable"
! Column !! Meaning
|-
!Conductor Code
|
:This is the code used to identify this type of cable
|-
!Conductor Description
|
:a description, for reference only
|-
!Absorbivity
|
:Average absorbance, the proportion of incoming radiative energy that is absorbed over naturally occurring frequencies
|-
!Coefficient of Resistance
|
:The rate of change in resistance as temperature is increased
|-
!Resistance @20 C ohms/km
|
:Electrical resistance
|-
!Mass per unit lemgth gm/cm
|
:The mass or weight of the cable
|-
!Diameter mm
|
:Diameter of the cable
|-
!Emissivity
|
:Physical emissivity, which determines the rate at which heat is lost through radiation
|-
!Specific Heat Capacity Cal/g/C
|
:Physical heat capacity, the amount of energy contained in a temperature rise in the cable material
|}

==Circuit Configuration==
The Circuit Configuration describes the configuration of the circuit with regard to the cable type and number and the offload time used.
The file is named 'Circuit Configuration_<yyyyMMdd>.csv' where <yyyyMMdd> is the creation date. A number of these files may appear together but only the one with the latest date will be loaded.

{|class="wikitable"
! Column !! Meaning
|-
!Branch Id
|
:The branch id is used as the name of the circuit in EMO
|-
!Date
|
:The date from which the information in the row is valid. If this column is empty the information is valid from teh earliest date possible
|-
!Limiting Conductor
|
:the name of the cable type used in the conductor that sets the thermal limit of the line. This name needs to appear in the conductor code column in the Conductor Parameters file
|-
!Number of Conductors
|
:the number of conductors used in the line.
|-
!SFT_Status (Y/N)
|
:whether to apply SFT to theis line
|-
!Offload time (minutes)
|
:the SFT offload time, or time window in which a thermal overload can occur.
|-
!Threshold
|
:The threshold after which the constraint will be shown by EMO. This is expressed as a percentage of the constraint limit.
|}

EMO:Use of line conductor information in SFT

2015-12-20T22:42:19Z

WoodsM:

The behaviour of SFT constraints is now derived from information about the thermal characteristics of the lines involved. The information required by EMO to do this derivation is contained in two files, the Conductor Parameters file and the Circuit Configuration file

==Conductor Parameters==

The Conductor Parameters file contains information on the properties of the different types of conductors used in transpower lines. This is a csv file with a heading line and the following columns

{|class="wikitable"
! Column !! Meaning
|-
!Conductor Code
|
:This is the code used to identify this type of cable
|-
!Conductor Description
|
:a description, for reference only
|-
!Absorbivity
|
:Average absorbance, the proportion of incoming radiative energy that is absorbed over naturally occurring frequencies
|-
!Coefficient of Resistance
|
:The rate of change in resistance as temperature is increased
|-
!Resistance @20 C ohms/km
|
:Electrical resistance
|-
!Mass per unit lemgth gm/cm
|
:The mass or weight of the cable
|-
!Diameter mm
|
:Diameter of the cable
|-
!Emissivity
|
:Physical emissivity, which determines the rate at which heat is lost through radiation
|-
!Specific Heat Capacity Cal/g/C
|
:Physical heat capacity, the amount of energy contained in a temperature rise in the cable material
|}

==Circuit Configuration==
This describes the configuration of the circuit with regard to the cable type and number and the offload time used.

The Conductor Parameters file contains information on the properties of the different types of conductors used in transpower lines. This is a csv file with a heading line and the following columns

{|class="wikitable"
! Column !! Meaning
|-
!Branch Id
|
:The branch id is used as the name of the circuit in EMO
|-
!Date
|
:The date from which the information in the row is valid. If this column is empty the information is valid from teh earliest date possible
|-
!Limiting Conductor
|
:the name of the cable type used in the conductor that sets the thermal limit of the line. This name needs to appear in the conductor code column in the Conductor Parameters file
|-
!Number of Conductors
|
:the number of conductors used in the line.
|-
!SFT_Status (Y/N)
|
:whether to apply SFT to theis line
|-
!Offload time (minutes)
|
:the SFT offload time, or time window in which a thermal overload can occur.
|-
!Threshold
|
:The threshold after which the constraint will be shown by EMO. This is expressed as a percentage of the constraint limit.
|}

EMO:Use of line conductor information in SFT

2015-12-20T21:45:36Z

WoodsM: /* Conductor Parameters */

EMO:Use of line conductor information in SFT

2015-12-20T21:45:12Z

WoodsM: Created page with "The behaviour of SFT constraints is now derived from information about the thermal characteristics of the lines involved. The information required by EMO to do this derivatio..."

EMO:How EMO models SFT constraints

2015-12-20T20:02:50Z

WoodsM: /* Estimating the constraint curves used by SPD */

EMO:How EMO models SFT constraints

2015-12-20T20:00:31Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-20T19:55:12Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T03:32:07Z

WoodsM: /* Estimating the constraint curves used by SPD */

EMO:How EMO models SFT constraints

2015-12-18T03:29:28Z

WoodsM: /* Estimating the constraint curves used by SPD */

EMO:How EMO models SFT constraints

2015-12-18T03:26:24Z

WoodsM: /* Estimating the constraint curves used by SPD */

EMO:How EMO models SFT constraints

2015-12-18T03:24:18Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T03:21:15Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T03:20:54Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T02:30:09Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T02:22:55Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T02:20:41Z

WoodsM: /* SFT constraint modelling in EMO */

EMO:How EMO models SFT constraints

2015-12-18T02:18:18Z

WoodsM: /* SFT constraint modelling in EMO */

File:ScreenShot SFT.PNG

2015-12-18T02:17:25Z

WoodsM: uploaded a new version of "File:ScreenShot SFT.PNG"

EMO:How EMO models SFT constraints

2015-12-18T02:14:33Z

WoodsM: /* Estimating the constraint curves used by SPD */

EMO:Estimation From Historical Constraints

2015-12-18T00:51:33Z

WoodsM: Created page with "The power flows used in this relationship are from an AC power flow model, which is constructed using the SPD solution in conjunction with reactive power modelling and a detai..."

The power flows used in this relationship are from an AC power flow model, which is constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is an inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre-post power flow constraint for each line. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(( \underline{C}, \underline{C} )\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to. Given that the constraint is a quadratic function and we know one point on the function there are two degrees of freedom left to estimate. Here we look at estimating \(\beta\), the slope of the curve at \(( \underline{C}, \underline{C} )\), and \(\alpha\), the rate of change in that slope with respect to \(F_{m}\).

The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre-post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. Given all equations associated with a particular combination of SFT constraint and thermal environment, we are looking for values of \(\alpha\) and \(\beta\) which have the following relationships. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appears to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

EMO:How EMO models SFT constraints

2015-12-18T00:51:22Z

WoodsM: /* Estimating the constraint curves used by SPD */

EMO:How EMO models SFT constraints

2015-12-18T00:50:52Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints involving two lines. For example:
-0.902 × OHK_WRK.1+1.274 × THI_WKM1.1 ≤ 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage (the contingent line). The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the ''protected line'' and \(F_{c}\) is the flow on the ''contingent line''.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency.

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==

[[EMO:Estimation From Historical Constraints|Estimation From Historical Constraints]]

The power flows used in this relationship are from an AC power flow model, which is constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is an inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre-post power flow constraint for each line. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(( \underline{C}, \underline{C} )\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to. Given that the constraint is a quadratic function and we know one point on the function there are two degrees of freedom left to estimate. Here we look at estimating \(\beta\), the slope of the curve at \(( \underline{C}, \underline{C} )\), and \(\alpha\), the rate of change in that slope with respect to \(F_{m}\).

The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre-post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. Given all equations associated with a particular combination of SFT constraint and thermal environment, we are looking for values of \(\alpha\) and \(\beta\) which have the following relationships. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appears to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot SFT.PNG|863px|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column "'''SFT PF'''"). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto-SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 above, a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Where A is equal to the protection factor on the protected line. Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:SFT Constraints

2014-02-19T02:04:01Z

WoodsM:

EMO:SFT Overview

2014-02-19T02:02:09Z

WoodsM:

[[File:SFT simple example.png|right]]
The principle behind SFT is simple: if one circuit in the grid has an unplanned outage, then every other line in the grid could then become overloaded. Therefore we need to limit the flow on some circuits just in case there is an outage. For example, the figure shows a portion of a grid where three identical circuits are in parallel between nodes A and B, so the total power flow is divided equally across the three. If one circuit trips, then the other two will each end up carrying 50% more power than they did prior to the trip. Under an SFT approach, each circuit would have two constraints each looking like

''Flow in protected circuit + 0.5 × flow in contingent circuit ≤ Capacity''

where there is one constraint for each of the other two circuits. For example, if each circuit carries 100 MW, then after one circuit trips the remaining lines will each carry 150 MW. If the circuit capacity is 150 MW, then the constraints would be ''Flow in protected circuit + 0.5 × flow in contingent circuit ≤ 300''.

So in principle, the SFT process:
*outages each and every circuit in turn;
*for each circuit outaged, check the loading on every other circuit;
*formulate constraints to protect any circuits that are overload.

In practice, circuits on the grid typically have more capacity than is apparent, because their respective capacity ratings are based on steady-state operation, whereas after a circuit trips the SO re-dispatches the market during the 15 minute off-load time, during which time a lot can change. In steady state, the thermal capacity rating of a circuit is determined by how much it sags due to it being heated as power flows through it: there are statutory limits on the distance between transmission circuits and the ground, or objects on the ground (trees, etc). Lines lengthen as they heat due to power flowing in them (and due to changes in ambient conditions) which is why they sag.

If a circuit is already loaded at its capacity rating, then it is assumed to be at maximum allowable sag and therefore the simple approach above applies. But, if a line is running below its capacity rating, then if it suddenly carries more power due to the tripping of another line, it will take some minutes before the additional heat produces additional sag: for this reason, the SFT constraints can typically allow a circuit to be loaded higher after another circuit trips than might be expected.

EMO:How EMO models SFT constraints

2014-02-03T00:18:26Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from an AC power flow model, which is constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint for each line. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(( \underline{C}, \underline{C} )\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to. Given that the constraint is a quadratic function and we know one point on the function there are two degrees of freedom left to estimate. Here we look at estimating \(\beta\), the slope of the curve at \(( \underline{C}, \underline{C} )\), and \(\alpha\), the rate of change in that slope with respect to \(F_{m}\).

The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. Given all equations associated with a particular combination of SFT constraint and thermal environment we are looking for values of \(\alpha\) and \(\beta\) which have the following relationships. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot_SFT_1.PNG|863px|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Where A is equal to the protection factor on the protected line. Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-03T00:12:16Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(( \underline{C}, \underline{C} )\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to. Given the constraint is a quadratic function and we know one point on the function there are two degrees of freedom left to estimate. Here we look at estimating \(\beta\), the slope of the curve at \(( \underline{C}, \underline{C} )\), and \(\alpha\), the rate of change in that slop with respect to \(F_{m}\).

The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are values of \(\alpha\) and \(\beta\) for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot_SFT_1.PNG|863px|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Where A is equal to the protection factor on the protected line. Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-03T00:06:26Z

WoodsM: /* SFT constraint modelling in EMO */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot_SFT_1.PNG|863px|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Where A is equal to the protection factor on the protected line. Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-02T23:17:26Z

WoodsM: /* SFT constraint modelling in EMO */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot_SFT_1.PNG|863px|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-02T23:15:44Z

WoodsM: /* SFT constraint modelling in EMO */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot_SFT_1.PNG|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-02T23:13:40Z

WoodsM:

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
[[File:ScreenShot_SFT_10.PNG|thumb|none|Diagram 1. SFT Protection factor trait in EMO]]

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-02T23:11:18Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

== SFT constraint modelling in EMO ==
File:Figure_SFT_10.PNG|SFT Protection factor trait in EMO

Among the traits shown for a circuit in EMO is the SFT protection factor (shown here under the column SFT). There is no trait currently for the SF constraint curvature. The SFT protection factor will determine the nature of the SFT constraints generated by EMO. Setting the SFT protection factor to a high number will tend to relax any constraints on that line.
When making a dispatch with Auto SFT on EMO will search for lines that may be overloaded by an outage in another line. The effect of an outage at the contingent line (C) on the power flow on the protected line (M) can be estimated as a proportion of the flow on C being transferred to M.

{|
|style="width: 100px"|'''Equation 4.'''
|\[F'_{m} = F_{m} + B{F}_{m}\]
|}

Where \(F'_{m}\) is the post-contingent flow on the protected line.
To ensure the point \(( F_{m}\), \(F'_{m})\) does not lie outside the physical SFT constraint in Diagram 1 a linear constraint is added to the dispatch model as follows

{|
|style="width: 100px"|'''Equation 5.'''
|\[AF_{m} + BF_{c} \leq A \underline{C}\]
|}

Once the exposed lines are identified and the related constraints are added to the model the dispatch is reiterated. Eventually all relevant SFT constraints should be found and applied.

EMO:How EMO models SFT constraints

2014-02-02T22:37:43Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT constraint curvature’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

EMO:How EMO models SFT constraints

2014-02-02T20:22:07Z

WoodsM:

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at \(F_{m}\) is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We have the arc flows \(F_{m}\) from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT protection factor variation’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

EMO:How EMO models SFT constraints

2014-02-02T20:19:36Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the tangent of this curve at Fm is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We can also the arc flows from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT protection factor variation’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

EMO:How EMO models SFT constraints

2014-01-31T03:55:19Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point \(\big( \underline{C}, \underline{C} \big)\) where \(\underline{C}\) is the thermal capacity of the line, which is a value we do have access to.
The slope of the curve is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We can also the arc flows from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(\underline{C} - \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq \underline{C} + \frac{ \alpha }{2} \big(\underline{C} - \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the \(\big( \underline{C}, \underline{C} \big)\) point, probably due to the effects of reactive power flows. For these reasons the best fit is currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT protection factor variation’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

EMO:How EMO models SFT constraints

2014-01-31T03:45:46Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point (C, C) where C is the thermal capacity of the line, which is a value we do have access to.
The slope of the curve is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We can also the arc flows from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[A \simeq \alpha \big(C- \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq C+ \frac{ \alpha }{2} \big(C- \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the (C, C) point, probably due to the effects of reactive power flows. For these reasons the best fit for a and ß are currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT protection factor variation’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

EMO:How EMO models SFT constraints

2014-01-28T21:08:32Z

WoodsM: /* Estimating the constraint curves used by SPD */

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point (C, C) where C is the thermal capacity of the line, which is a value we do have access to.
The slope of the curve is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We can also the arc flows from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[C \simeq \alpha \big(C- \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq C+ \frac{ \alpha }{2} \big(C- \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the (C, C) point, probably due to the effects of reactive power flows. For these reasons the best fit for a and ß are currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT protection factor variation’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>

File:Graph SFT 4.PNG

2014-01-28T21:07:52Z

WoodsM:

EMO:How EMO models SFT constraints

2014-01-28T21:07:40Z

WoodsM:

== SFT constraints in SPD ==
The aim of automatic SFT constraint modelling in EMO is to model the SFT constraints that are generated as part of the dispatch and pricing solution in SPD. These constraints are designed to avoid thermal overloading of a line in the event of the unexpected outage of any other line.
SFT constraints appear in the dispatch and pricing optimisation model as linear constraints between two lines. For example:
-0.902*OHK_WRK.1+1.274*THI_WKM1.1 <= 605.79
In this case THI_WKM1.1 is the line being protected from overload and OHK_WRK.1 is the line which may cause overload in THI_WKM1.1 if it has an outage. The general form of the SFT constraint is
{|
|style="width: 100px"|'''Equation 1.'''
|\[ A F_{m} + B F_{c} \leq C \]
|}

Where \(F_{m}\) is the flow on the protected line and \(F_{c}\) is the flow on the contingent line.
The physical nature of the SFT constraint depends on various characteristics of the line being protected, the thermal environment and the mitigating measures available if an outage occurs. The constraint can be expressed as a function of the loading on the line before an outage occurs (pre-contingent) and the loading after an outage occurs (post-contingent). The higher the line is loaded pre-contingency the greater its expected temperature, giving it less capacity to absorb extra power in the event of a contingency

The physical constraint on the protected line that is modelled with SFT is shown in the diagram 1. This constraint will depend on the thermal environment
[[File:Diagram_SFT_1.PNG|500px|thumb|none|Diagram 1. Physical SFT constraint on a single line]]

In SPD the constraint above is modelled as a linear constraint which represents a tangent of the physical constraint at the point where the pre-contingent power flow matches the power flow in the solution of SPD. Because the constraint may affect dispatch this is an iterative process, the resulting constraint is shown in diagram 2.
[[File:Diagram_SFT_2.PNG|500px|thumb|none|Diagram 2. Physical SFT constraint on a single line]]

== Estimating the constraint curves used by SPD ==
The power flows used in this relationship are from and AC power flow model, which will be constructed using the SPD solution in conjunction with reactive power modelling and a detailed model of the transmission grid componentry. The full information for creating this AC model is not available to us, so there is inevitable degree of approximation in estimating SFT constraints from our point of view.
To model this constraint in EMO we also need to estimate the nature of the pre/post power flow constraint as much as it relates to the SPD solution. We do not currently have access to the definitions of these functions, but we are informed that they are quadratic functions and they will pass through the point (C, C) where C is the thermal capacity of the line, which is a value we do have access to.
The slope of the curve is given explicitly in the resulting constraint equation in SPD, being negative the value A in Equation 1.
We can also the arc flows from the SPD solution so, given enough instances of an SFT equation for a particular protected line, we might be able to estimate its pre/post constraint curve. We are informed that the thermal environment used for each curve is purely dependent on the Summer/Shoulder/Winter designation of the trading period so we can make a sample of all the constraints that fall into each category.

To estimate the curve then we can try to find the linear relationship between the slope and the pre-contingent flow. What we are looking for in the equations we are seeing in SPD are two values, call them \(\alpha\) and \(\beta\), for which the following relationships exist over all instances of a particular combination of SFT constraint and thermal environment. If a good fit for these values can be found the quadratic curve can be estimated.

{|
|style="width: 100px"|'''Equation 2.'''
|\[C \simeq \alpha \big(C- \underline{F}_{m} \big)+\beta\]
|}

{|
|style="width: 100px"|'''Equation 3.'''
|\[C \simeq C+ \frac{ \alpha }{2} \big(C- \underline{F}_{m} \big)^{2}\]
|}

However there appears to be no significant and reliable correlation between the tangent slope of the SFT constraints (A in Equation 1) and the power flows in the solution in the data we have analysed to date. What correlation there is appear to be overshadowed by the variability in the limit, which is sometimes seen to fall below the (C, C) point, probably due to the effects of reactive power flows. For these reasons the best fit for a and ß are currently calculated by setting \(\alpha\) to 0 and \(\beta\) to the average slope A.

These values are delivered to EMarketOffer using the AverageLineProtectionFactors<date>.csv file in the <EMO Data Dir>/Inputs/Grid/SFT directory. Lines for which we have no data have these values set to 0 and 1.04, which is the average protection value for lines which are not under enhanced protection schemes.

The \(\alpha\) and \(\beta\) values can then be used to generate slopes and constraint limits for all values of \(F_{m}\), they are referred to here as the ‘SFT protection factor variation’ and the ‘SFT protection factor’ respectively. Only the latter currently appears in EMO as an input value against each line, the variation value being set to zero.

Some examples of constraint variation are shown in the figures below:
<gallery mode="nolines" widths=400px heights=400px>
File:Graph_SFT_1.PNG|Figure 1: Summer SFT constraints on the NSY_ROX.1 line (contingent line CYD_TWZ1.1)
File:Graph_SFT_2.PNG|Figure 2: Summer SFT constraints on the OAM_STU_WTK2.2 line (contingent line OAM_BPT_WTK1.2)
File:Graph_SFT_3.PNG|Figure 3: Winter SFT constraints on the ARI_KIN1.1 line (contingent line ARI_KIN2.1)
File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)
</gallery>
[[File:Graph_SFT_4.PNG|Figure 3: Winter SFT constraints on the KIN_TRK1.1 line (contingent line HAM_WKM.1)]]