# PTDF and OTDF Sensitivity Functions

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```Use of PDTF’s and ODTF’s
Powerworld PDTF and ODTF
Sensitivity Functions
Example – Path Utilization
Tool (PUF Diagram)
Powerworld June 30, 2015 Users Group Meeting
1
Topic of Discussion




PDTF’s – What are they?
Demonstration of how they can be used to
develop a useful tool.
Development of Power Transfer Diagram
(Excel Spreadsheet/Diagram)
ODTF’s – What are they?
How are they different from
PDTF’s?
Powerworld June 30, 2015 Users Group Meeting
2
PDTF’s




Power Transfer Distribution Factors (PTDF)
PDTF is defined as the incremental impact on
the transmission system of a transfer of power
between two points in the power system
PTDFs demonstrate a linear impact
(i.e. is a linear sensitivity function)
They provide what percent of the transfer
appears on each transmission line in the
power system
Powerworld June 30, 2015 Users Group Meeting
3
PTDF Calculation

PTDFs are calculated using the factored
power flow Jacobian (Jacobian is a
linearized matrix of partial derivatives of P
and Q with respect to angle and voltage
magnitude)
∆|V| = [J(V*)]-1 ∆P
∆P - Change in power injections
associated with a power transfer
∆|V| - Change in system voltages,
therefore flows on each transmission
branch can be calculated
Powerworld June 30, 2015 Users Group Meeting
4
Specifying Transfer for PDF
Calculation


Must specify a seller (source) and buyer
(sink) for a power transfer
Options for Seller and Buyer:




Area, Zone, or Super Area - Generators in region
participate according to participation factors
Slack – Slack generator provides
Injection Group – Loads/Generators participate
based on each element of the group
Bus – Power comes from/to this bus
Powerworld June 30, 2015 Users Group Meeting
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Calculation Method for PTDF

Specify a Calculation Method
Linearized AC (includes losses)
 Lossless DC – DC power flow (no losses)
 Lossless DC with Phase Shifters –
Modification of lossless DC that forces phase
shifters to hold flow across them

Powerworld June 30, 2015 Users Group Meeting
6
PTDF Display
Powerworld June 30, 2015 Users Group Meeting
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Example: Power Transfer Path
Utilization Diagram (PUF Diagram)

Develop an Excel Spreadsheet
Diagram that provides a visual
effect of power transfers across
transfer paths in the NW from one
area to another.
Powerworld June 30, 2015 Users Group Meeting
8
Powerworld Files Used



Installed Interface Groups to model
transfer paths of interest
Used the PTDF to do a linearized
AC power transfer from bus (center
of area of seller) to bus (center of
area of buyer – common point)
Used the superposition principle to
allow determine from any one bus
to another
Powerworld June 30, 2015 Users Group Meeting
9
Excel Spreadsheet (Data)–
PODFs for Interfaces
Used AC Linearized Method for Determination of Factors
POR ‐ Area/Bus (Transfer FROM Bus)
Sea N ‐ Monroe 500
Sea S ‐ Maple Valley 500
Paul ‐ Paul 500
Allston ‐ Allston 500
Allston ‐ Trojan 230
PDX/Salem ‐ Troutdale 230
PDX/Salem ‐ Keeler 230
PDX/Salem ‐ Pearl 230
Eugene ‐ Alvey 230
S Oregon ‐ Meridian 230
Malin ‐ Malin 500
Cent OR ‐ Redmond 230
Big Eddy ‐ Big Eddy 230
John Day ‐ John Day 500
Bonneville ‐ Bonneville 230
Idaho ‐ Boise Bench 230
Mid C ‐ Midway 230
Mid C ‐ Hanford 500
Coulee ‐ Coulee 500
Slatt ‐ Slatt 500
McNary ‐ McNary 500
Walla Walla ‐ Walla Walla 230
NE Wash ‐ Bell 500
Montana ‐ Broadview 500
Wyoming ‐ Dave Johnston 230
Utah/Colorado ‐ Bonanza 345
Ariz/N Mex ‐ Palo Verde 500
Nevada ‐ Harry Allen 500
California ‐ Telsa 500
Canada ‐ Nicola 500
System Specific Values (POR‐POD)
POR (From Bus)
POD (To Bus)
Existing System (Big Eddy‐Knight) ‐ Case 1
POD ‐ Boise Bench 230 (Transfer TO Bus)
Path Transfer (% Change)
West of West of North of Nelway‐
North of West of West of West of Monroe‐ Raver‐ Paul‐
S of S of S of Cascades BC‐NW
Cascades John Boundary
Hanford McNary
Slatt John Day
Echo Lake Paul Allston Allston Salem Eugene
South
North
Day
Matl
MT‐NW
ID‐NW
Hmwy‐
Sum Lk
COI
PDCI
Alturas‐
Reno
S Ore Import
W of Col River
Tot‐2
52.1
‐11.1
‐4.0
‐3.1
‐2.7
‐1.6
‐1.9
‐1.7
‐1.2
‐1.0
‐0.8
‐0.9
‐1.1
‐1.0
‐1.6
0.0
0.2
‐0.7
2.8
‐0.8
‐0.6
0.2
4.1
3.9
1.1
0.2
‐0.4
‐0.4
‐0.8
36.4
13.4
14.9
‐38.3
‐27.6
‐22.2
‐9.3
‐13.4
‐10.9
‐5.3
‐3.7
‐2.2
‐2.3
‐2.7
‐1.4
‐10.1
0.0
5.5
4.6
9.3
‐0.5
0.2
2.4
7.2
5.3
1.0
‐0.2
‐1.5
‐1.5
‐2.2
10.6
16.3
17.9
48.0
‐34.7
‐24.7
‐11.0
‐16.0
‐13.2
‐6.5
‐4.6
‐2.7
‐2.9
‐3.3
‐1.8
‐11.7
0.0
6.9
5.5
11.4
‐0.7
0.3
3.0
9.0
6.6
1.2
‐0.3
‐1.8
‐1.9
‐2.7
13.0
19.6
21.6
49.0
61.7
66.6
‐13.5
‐19.5
‐15.8
‐7.7
‐5.5
‐3.2
‐3.4
‐3.9
‐2.1
‐14.7
0.0
8.2
6.5
13.6
‐0.8
0.3
3.5
10.8
7.9
1.5
‐0.3
‐2.2
‐2.2
‐3.2
15.5
9.9
10.1
12.1
13.2
13.4
14.0
15.4
16.0
‐69.8
‐40.3
‐8.8
1.5
9.5
7.9
13.1
0.0
9.6
9.5
9.3
8.5
8.6
7.4
8.5
6.7
‐0.6
‐3.0
‐7.1
‐7.1
‐9.5
8.5
8.7
9.0
10.8
11.7
11.9
12.4
13.6
14.2
25.8
‐31.0
‐7.8
1.3
8.4
7.0
11.6
0.0
8.5
8.4
8.2
7.5
7.6
6.6
7.6
6.0
‐0.5
‐2.6
‐6.3
‐6.3
‐8.4
7.5
‐73.3
‐74.8
‐49.3
‐37.8
‐33.0
‐12.9
‐19.1
‐15.2
‐7.0
‐4.8
‐2.6
‐2.7
‐3.0
‐1.2
‐14.2
0.0
9.8
8.0
15.5
0.2
1.1
3.8
8.1
3.8
0.2
‐0.7
‐2.0
‐2.0
‐2.6
‐54.3
58.1
59.1
‐16.1
‐15.2
‐13.6
‐17.1
‐16.9
‐18.3
‐20.3
‐19.6
‐18.6
‐19.4
‐18.9
‐22.2
‐12.6
0.0
45.8
66.2
58.0
‐23.5
‐21.8
20.9
54.3
45.3
8.3
‐2.1
‐12.5
‐12.6
‐18.1
51.3
49.6
50.2
30.1
21.2
17.7
2.8
6.8
3.3
‐3.6
‐4.9
‐6.1
‐6.3
‐5.0
‐8.9
7.3
0.0
44.2
‐25.2
51.8
‐10.0
‐7.9
11.0
33.3
20.4
4.6
0.2
‐3.7
‐3.8
‐5.8
42.0
‐1.6
‐2.1
‐7.1
‐9.4
‐10.4
‐13.8
‐13.3
‐13.6
‐15.0
‐15.3
‐15.3
‐15.6
‐15.7
‐17.5
‐12.8
0.0
3.6
‐0.4
‐0.1
‐20.1
58.0
23.6
3.0
3.3
‐4.4
‐7.3
‐12.7
‐12.7
‐15.7
‐0.5
10.4
10.2
4.9
2.6
1.9
‐2.1
‐1.3
‐2.7
‐6.6
‐8.5
‐10.3
‐10.0
‐5.4
‐9.4
0.0
0.0
11.8
14.8
11.7
62.3
26.8
14.7
12.4
10.8
‐0.2
‐3.5
‐7.8
‐7.9
‐10.2
9.8
‐14.8
‐15.5
‐23.9
‐27.8
‐29.1
‐40.3
‐34.4
‐35.8
‐24.3
‐11.4
2.8
‐5.3
‐59.1
21.1
‐35.4
0.0
‐15.7
‐10.3
‐12.6
6.8
3.1
‐5.8
‐10.4
‐7.8
‐1.4
0.3
1.6
1.6
2.3
‐12.3
‐9.6
‐11.1
‐34.8
‐45.6
‐49.4
‐69.0
‐63.1
‐67.1
‐62.6
‐35.0
‐5.6
4.7
12.5
10.2
‐60.4
0.0
‐3.2
2.8
‐4.4
9.4
8.5
3.7
‐2.4
‐1.3
‐2.1
‐2.6
‐4.9
‐4.9
‐6.3
‐7.0
‐5.8
‐3.5
‐2.3
‐2.0
‐1.9
‐1.4
‐1.5
‐1.4
‐1.2
‐1.0
‐0.9
‐1.0
‐1.1
‐1.1
‐1.4
0.0
‐1.3
‐1.2
‐1.1
‐1.0
‐0.8
‐0.1
3.4
4.8
1.4
0.4
‐0.4
‐0.4
‐0.8
73.5
4.5
2.6
1.6
1.3
1.2
0.8
0.9
0.9
0.7
0.6
0.5
0.5
0.6
0.6
0.8
0.0
0.6
0.6
0.3
0.5
0.4
‐0.2
‐3.9
‐1.7
‐0.3
0.0
0.3
0.3
0.5
15.1
2.0
1.5
1.1
1.0
0.9
0.8
0.8
0.8
0.7
0.6
0.5
0.6
0.7
0.6
0.8
0.0
0.9
0.7
0.9
0.6
0.6
0.4
‐0.1
‐3.7
‐1.3
‐0.5
0.1
0.1
0.4
4.9
‐6.9
‐7.3
‐7.0
‐6.8
‐6.7
‐6.5
‐6.6
‐6.5
‐5.8
‐4.9
‐3.9
‐5.0
‐6.3
‐6.1
‐6.5
0.0
‐7.5
‐7.4
‐8.1
‐6.4
‐6.7
‐6.9
‐11.7
71.5
20.9
8.6
1.2
0.9
‐2.7
‐4.1
‐68.1
‐69.1
‐70.4
‐71.4
‐71.3
‐73.2
‐73.4
‐73.3
‐74.9
‐76.5
‐76.4
‐75.2
‐72.2
‐71.8
‐71.2
0.0
‐69.7
‐69.6
‐66.9
‐71.5
‐71.2
‐76.5
‐65.2
‐57.7
‐35.3
‐34.3
‐60.3
‐59.9
‐77.4
‐60.4
‐37.2
‐37.9
‐39.2
‐40.0
‐40.1
‐41.6
‐41.7
‐41.8
‐43.7
‐46.0
‐47.4
‐44.9
‐41.2
‐41.3
‐40.2
0.0
‐37.9
‐38.3
‐36.4
‐40.5
‐39.0
‐30.7
‐34.4
‐29.6
‐15.7
‐15.1
‐34.0
‐33.6
‐47.1
‐32.8
11.9
12.2
12.9
13.2
13.3
13.9
14.0
14.1
15.2
16.4
19.3
15.2
13.8
13.8
13.4
0.0
12.3
12.5
11.6
13.5
12.9
9.9
10.3
6.5
‐14.3
‐24.0
‐56.4
‐55.5
‐78.9
10.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.4
1.4
1.5
1.6
1.6
1.6
1.7
1.7
1.9
2.4
2.1
2.0
1.6
1.6
1.6
0.0
1.4
1.5
1.4
1.6
1.5
1.2
1.3
1.0
‐0.3
‐0.8
‐0.8
‐1.4
1.2
1.2
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
‐3.0
‐88.2
3.0
2.3
1.0
1.1
0.7
0.0
0.8
0.9
0.8
1.0
1.0
0.7
0.7
0.6
‐0.3
‐0.7
‐0.6
‐1.2
1.6
0.7
‐7.0
‐7.2
‐7.7
‐7.9
‐8.0
‐8.4
‐8.5
‐8.6
‐9.6
‐11.3
‐12.3
‐9.6
‐8.3
‐8.3
‐8.1
0.0
‐7.3
‐7.4
‐6.8
‐8.1
‐7.7
‐5.8
‐5.8
‐2.7
16.5
25.3
‐33.1
‐30.2
‐19.1
‐6.0
‐9.7
‐10.0
‐10.5
‐10.9
‐10.9
‐11.5
‐11.6
‐11.7
‐12.9
‐15.0
‐16.4
‐12.8
‐11.3
‐11.3
‐11.1
0.0
‐10.0
‐10.2
‐9.5
‐11.1
‐10.5
‐8.1
‐8.3
‐5.1
13.1
21.6
51.7
50.2
‐25.9
‐8.4
2.5
27.8
35.0
‐61.4
‐4.6
‐4.1
38.9
‐6.6
‐29.1
67.4
24.2
30.9
54.1
1.2
‐0.9
‐0.4
0.1
0.2
1.0
‐0.3
0.0
‐0.1
0.3
0.2
0.4
McNary ‐ McNary 500
Allston ‐ Allston 500
Powerworld June 30, 2015 Users Group Meeting
10
Sample Output
Transfer Path Impact Diagram
BC‐NW
1.2
Canada
Derived from 2015 HS4 WECC Base Case
Note: Arrow Denotes Normal Direction of Positive Path Flow
MATL
Seattle ‐ N
‐0.4
Nlwy‐Bdry
Monroe‐
Echo Lake
Seattle ‐ S/
Olympic Pen
‐0.9
Coulee
2.5
POR (FROM Area)
POD (TO Area)
Transfer Amount
McNary ‐ McNary 500
Allston ‐ Allston 500
100
MW
W of Cascades
North
N of Hanford
38.9
NE Wash
‐29.1
Montana
Raver ‐ Paul
N of John Day
(500 kV Only)
27.8
MT ‐ NW
0.1
‐6.6
Paul
Mid C/
Hanford
Paul ‐ Allston
35.0
W of Cascades ‐ South
54.1
Walla Walla
Allston
W of McNary
W of John Day
S of
Allston
Bonneville
Big Eddy/
The Dalles
‐61.4
SW Wash/
Portland/
Salem/N Coast
30.9
67.4
Slatt/
Grassland
John Day
McNary/
Roundup
W of Slatt
24.2
Wyoming
ID ‐ NW
0.2
S of Salem
Central
Oregon
‐4.6
Eugene/
S Coast
Hemingway‐
Summer Lk
1.0
Idaho
S of Eugene
‐4.1
Malin/
KFalls/Capt Jk
S Ore Import
0.3
S Oregon
Alturas‐Reno
COI
PDCI
0.0
Utah/Colo.
‐0.1
Tot‐2
Nevada
0.2
‐0.3
Ariz/N Mex
California
W of Col Rvr
0.4
Powerworld June 30, 2015 Users Group Meeting
11
Line Outage Distribution
Factors (LODF)



LODFs are similar to PTDF
linearized calculation
Calculate the impact of opening
(outage) or closing a branch
Calculated the percent of power
flow specified for a transmission
line that occurs due to switching
will appear on other lines
Powerworld June 30, 2015 Users Group Meeting
12
LODF Diagram
Powerworld June 30, 2015 Users Group Meeting
13
LODF Matrix
Powerworld June 30, 2015 Users Group Meeting
14
More Information
Good Tutorial available on the Powerworld
website: http://www.powerworld.com
Under Training &amp; Events, Online Training, in
the Topic I11: Linear Sensitivity Analysis
Powerworld June 30, 2015 Users Group Meeting
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Questions?
Powerworld June 30, 2015 Users Group Meeting
16
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