17-04-2025 © Deep Kiran, IIT Roorkee (2025) 1
EEN/L-671:
RESTRUCTURED POWER
SYSTEMS
LECTURE 35: Transmission Pricing
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 2
Methods Considering Power Flows
• Use of DC power flow
• Usage based on tracing results (Tracing)
• Marginal Participation Method (MP)
• Equivalent bilateral exchange (EBE)
• Other line usage factors based on sensitivities
• Salient Features:
• Simulate a transaction or obtain a snap shot for pool
• Find out contribution of each transaction or individual entity into line
flows
• Attribute cost of line in proportion to participation of each
transaction or entity
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 3
DC Power Flow Based MW-Mile Method
S. Reactance Ll Pmax
Element Wl
No. (pu) (km) (MW)
1 1-3 0.2 200 0.25 100
T1=65 MW T2=35 MW 2 2-3 0.25 100 0.5 50
3 1-2 0.4 100 0.5 50
G2
G1 𝑀𝑊𝑀𝑖𝑙𝑒𝑡 = 𝑊𝑙 𝑀𝑊𝑡,𝑙 𝐿𝑙
𝑙
𝑇𝐶 = 10000
Line Line Line
MWMilet TCt
1-3 2-3 1-2
T1= Flow (MW) 50 15 15
65 4000 6400
MW MWMilet,l 2500 750 750
T1=65 MW
T2= Flow (MW) 10 25 10
T2=35 MW 35 2250 3600
MW MWMilet,l 500 1250 500
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 4
Power flow tracing
L4
100 MW
50 MW
A 71
1 5
29
1
22
2 4
64 18
3
B L1
15 MW L2 L3
45 MW 40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 5
Power flow tracing
Line flow decomposition into generator components
Line usage by generators
Gen 1 Gen 2 … Gen m
Line 1 A11 A12 … A1m
Line 2 A21 A22 … A2m
… … … … …
Line i Ai1 Ai2 … Aim
Aij is power flow component of jth generator on ith line
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 6
Power flow tracing
Load-generation interaction
Gen 1 Gen 2 … Gen n
Load 1 B11 B12 … B1n
Load 2 B21 B22 … B2n
… … … … …
Load m Bm1 Bm2 … Bmn
Bij is power provided by jth generator to ith load
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 7
Power flow tracing
L4
100 MW
50 MW
A 71
1 5
29
1
22
2 64 18 4
3
B L1
15 MW L2 L3
45 MW 40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 8
Power flow tracing
Line flow decomposition into load components
Line usage by loads
Load 1 Load 2 … Load n
Line 1 C11 C12 … C1n
Line 2 C21 C22 … C2n
… … … … …
Line i Ci1 Ci2 … Cin
Cij is power flow component of jth load on ith line
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 9
Power flow tracing
Generator-load interaction
Load 1 Load 2 … Load m
Gen 1 D11 D12 … D1m
Gen 2 D21 D22 … D2m
… … … … …
Gen n Dn1 Dn2 … Dnm
Dij is power received by jth load from ith generator including losses
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 10
Power flow tracing
Line loss allocation to loads and generators
Loss sharing by loads and generators
Load Load Load
… Gen 1 Gen 2 … Gen m
1 2 n
Line 1 L11 L12 … L1n G11 G12 … G1m
Line 2 L21 L22 … L2n G21 G22 … G2m
… … … … … … … … …
Line i Li1 Li2 … Lin Gi1 Gi2 … Gim
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 11
What is Power Tracing?: Definition
• Power Tracing is a tool, applied Post-facto on power flow
snap-shot that provides complete power audit information
like:
• Share of loads in Generation
• Generators’ contribution in Loads
• Decomposition of Transmission line flows into Generator and Load
Components
• Loss allocation to generators and Loads
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 12
Power tracing
State estimation
Data solution or
metered data
Algorithm Power tracing
Transmission line
Results Loss allocation flow
decomposition
Load-generator
interaction
Point-of-
Ex-post Tractability of
Applications Loss pricing
connection ex-
ante transmission
pricing
transmission cost
allocation
bilateral
transactions
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 13
Fundamentals of power tracing
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 14
What are pre-requisites of Power Tracing?
• State Estimation Solution
• Or
• Power flows over lines and,
• Injections at generator and load buses and,
• Network topology (single line diagram)
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 15
Power Tracing: Two Versions
• Downstream Algorithm
• Generator Side Statements
• Each Generator’s contribution in Transmission Line flows
• Each Generator’s contribution in Transmission Line losses
• Net power sent to a particular load
• Upstream Algorithm
• Load Side Statements
• Each Load’s contribution in Transmission Line flows
• Each Load’s contribution in Transmission Line losses
• Power received from a particular generator including losses
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 17
Proportionate Sharing Principle
j k
40 60
70 30
m l
Line Share of line j-i Share of line k-i
40 60
i-m 70 × = 28 70 × = 42
100 100
40 60
i-l 30 × = 12 30 × = 18
100 100
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 18
Graph Theoretic Approach
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 19
Graph Theoretic Approach: Downstream
Tracing Concept
• Proved Lemma:
• A finite nodes power system without circular flows has at least one
pure source
• Symbolic node elimination
• Tops Down Approach
• Starts at ‘Pure Source’
• Ends at ‘Pure Sink’
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 20
Downstream Algorithm: Various
Decompositions
j 40 60 k
i
30 30 40
m l n
Decomposition Formula
𝐺 𝑃𝐺𝑣𝑖𝑟𝑡
Line flow decomposition 𝑃𝑙𝑚 = 𝑁𝑔 𝑣𝑖𝑟𝑡 𝑃𝑙𝑚
σ𝑖=1 𝑃𝐺
𝑠 𝑟
𝑃𝐺𝑣𝑖𝑟𝑡
Loss decomposition 𝐿𝑜𝑠𝑠𝑃𝑙𝑚 = (𝑃𝑙𝑚 − 𝑃𝑙𝑚 )
𝐺𝑖
σ𝑁𝑔 𝑣𝑖𝑟𝑡
𝑖=1 𝑃𝐺
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 21
Graph Theoretic Approach: Downstream
Tracing
L4
100 MW Line Gen A’s flow Gen B’s flow
50 MW
1-2 29 0
A 71 71A 2-3 29 35
1 5 3-4
3-5
1-5 71 0
5-4
29 Generator-load interaction
1
Load Gen A Gen B
22
L1 0 15
L2 20.4 24.6
L3
29A
2 4
64 18 L4
3
B L1
50 MW 15 MW
35 L2 L3
45 MW 40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 22
Graph Theoretic Approach: Downstream
Tracing
L4
Line Gen A’s flow Gen B’s flow
50 MW
1-2 29 0
71A 2-3 29 35
5 3-4
3-5
1-5 71 0
5-4
Generator-load interaction
1
Load Gen A Gen B
22
L1 0 15
L2 20.4 24.6
L3
29A
2 35B 4
64 18 L4
3
B
35 MW 29A
L2 L3
45 MW 40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 23
Graph Theoretic Approach: Downstream
Tracing
L4
Line Gen A’s flow Gen B’s flow
50 MW
1-2 29 0
71A 2-3 29 35
5 3-4 8.2 9.8
3-5 0.45 0.55
1-5 71 0
5-4
Generator-load interaction
1
Load Gen A Gen B
22
L1 0 15
L2 20.4 24.6
L3
10.4B
4 L4
18
3
8.6A L3
40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 24
Graph Theoretic Approach: Downstream
Tracing
L4
Line Gen A’s flow Gen B’s flow
50 MW
1-2 29 0
71.45A 2-3 29 35
0.55B 5 3-4 8.2 9.8
3-5 0.45 0.55
1-5 71 0
5-4
Generator-load interaction
Load Gen A Gen B
22
L1 0 15
L2 20.4 24.6
L3
8.2A 4 L4 49.6 0.4
9.8B
L3
40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 25
Graph Theoretic Approach: Downstream
Tracing
Line Gen A’s flow Gen B’s flow
1-2 29 0
21.85A 2-3 29 35
0.15B 5 3-4 8.2 9.8
3-5 0.45 0.55
1-5 71 0
5-4 21.85 0.15
Generator-load interaction
Load Gen A Gen B
22
L1 0 15
L2 20.4 24.6
L3
8.2A 4 L4 49.6 0.4
9.8B
L3
40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 26
Graph Theoretic Approach: Downstream
Tracing
Line Gen A’s flow Gen B’s flow
1-2 29 0
2-3 29 35
3-4 8.2 9.8
3-5 0.45 0.55
1-5 71 0
5-4 21.85 0.15
Generator-load interaction
Load Gen A Gen B
L1 0 15
L2 20.4 24.6
L3 30.05 9.95
30.05A 4 L4 49.6 0.4
9.95B
L3
40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 27
Upstream Tracing is dual of Downstream
Tracing
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 28
Graph Theoretic Approach: Upstream
Tracing Concept
• Proved Lemma:
• A finite nodes power system without circular flows has at least one
pure sink
• Symbolic Node Elimination
• Bottoms Up Approach
• Starts at ‘Pure Sink’
• Ends at ‘Pure Source’
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 29
Downstream Algorithm: Various
Decompositions
j 40 60 k
i
30 30 40
m l n
Decomposition Formula
𝐿 𝑃𝐿𝑣𝑖𝑟𝑡
Line flow decomposition 𝑃𝑙𝑚 = 𝑃𝑙𝑚
σ𝑁𝑙
𝑖=1 𝑃𝐿
𝑣𝑖𝑟𝑡
𝑠 𝑟
𝑃𝐿𝑣𝑖𝑟𝑡
Loss decomposition 𝐿𝑜𝑠𝑠𝑃𝑙𝑚 = (𝑃𝑙𝑚 − 𝑃𝑙𝑚 )
𝐿𝑖
σ𝑁𝑙
𝑖=1 𝑃𝐿
𝑣𝑖𝑟𝑡
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 30
Graph Theoretic Approach: Upstream
Tracing
L4
100 MW
50 MW
A 71 L1’s L2’s L3’s L4’s
Line
5 flow flow flow flow
1
1-2 0 20.4 8.3 0.3
2-3 0 45 18.3 0.7
3-4 0 0 18 0
29 3-5 0 0 0.3 0.7
1 1-5 0 0 21.7 49.3
22
5-4 0 0 22 0
Load-Generator interaction
Gen L1 L2 L3 L4
2 4 A 0 20.4 30 49.6
64 18
3 B 15 24.6 10 0.4
B L1
50 MW 15 MW
35 L2 L3
45 MW 40 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 31
Graph Theoretic Approach: Upstream
Tracing
L4
100 MW
50 MW
A 71 L1’s L2’s L3’s L4’s
Line
5 flow flow flow flow
1
1-2 0 20.4 8.3 0.3
2-3 0 45 18.3 0.7
22L3 3-4 0 0 18 0
29 3-5 0 0 0.3 0.7
1 1-5 0 0 21.7 49.3
5-4 0 0 22 0
Load-Generator interaction
Gen L1 L2 L3 L4
2 A 0 20.4 30 49.6
64
3 B 15 24.6 10 0.4
B
35 MW L2 18L3
45 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 32
Graph Theoretic Approach: Upstream
Tracing
100 MW
A
L1’s L2’s L3’s L4’s
Line
flow flow flow flow
1 21.7L3+49.3L4 1-2 0 20.4 8.3 0.3
2-3 0 45 18.3 0.7
3-4 0 0 18 0
29 3-5 0 0 0.3 0.7
1-5 0 0 21.7 49.3
5-4 0 0 22 0
Load-Generator interaction
Gen L1 L2 L3 L4
2 A 0 20.4 30 49.6
64
3 B 15 24.6 10 0.4
B
35 MW L2 18.3L3+0.7L4
45 MW
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 33
Graph Theoretic Approach: Upstream
Tracing
100 MW
A
L1’s L2’s L3’s L4’s
Line
flow flow flow flow
1 21.7L3+49.3L4 1-2 0 20.4 8.3 0.3
2-3 0 45 18.3 0.7
3-4 0 0 18 0
29 3-5 0 0 0.3 0.7
1-5 0 0 21.7 49.3
5-4 0 0 22 0
Load-Generator interaction
Gen L1 L2 L3 L4
2 A 0 20.4 30 49.6
B 15 24.6 10 0.4
B
35 MW 45L2+18.3L3+0.7L4
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 34
Graph Theoretic Approach: Downstream
Tracing
100 MW
A
L1’s L2’s L3’s L4’s
Line
flow flow flow flow
1 21.7L3+49.3L4 1-2 0 20.4 8.3 0.3
2-3 0 45 18.3 0.7
3-4 0 0 18 0
29 3-5 0 0 0.3 0.7
1-5 0 0 21.7 49.3
5-4 0 0 22 0
Load-Generator interaction
Gen L1 L2 L3 L4
2 A 0 20.4 30 49.6
B 15 24.6 10 0.4
20.4L2+8.3L3+0.3L4
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 35
Graph Theoretic Approach: Upstream
Tracing
100 MW
A
L1’s L2’s L3’s L4’s
Line
flow flow flow flow
1 20.4L2+30L3+49.6L4 1-2 0 20.4 8.3 0.3
2-3 0 45 18.3 0.7
3-4 0 0 18 0
3-5 0 0 0.3 0.7
1-5 0 0 21.7 49.3
5-4 0 0 22 0
Load-Generator interaction
Gen L1 L2 L3 L4
A 0 20.4 30 49.6
B 15 24.6 10 0.4
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 36
Attendance
• MS Teams: l6ahq8m
• Please ensure 75% of attendance for ETE.
• Deadline for term paper work: 20th April 2025
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 38
Graph Theoretic Approach: Payment
Contributions Factors Cost (₹1000/ line) Total
cost
1-2 2-3 3-4 3-5 1-5 5-4 1-2 2-3 3-4 3-5 1-5 5-4 1-2 2-3 3-4 3-5 1-5 5-4
Gen A 29 29 8.2 0.45 71 21.85 0.50 0.23 0.23 0.23 0.50 0.50 500 227 228 225 500 497 2176
Gen B 0 35 9.8 0.55 0 0.15 0.00 0.27 0.27 0.28 0.00 0.00 0.00 273 272 275 0.00 3 824
L1 0 0 0 0 0 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
L2 20.4 45 0 0 0 0 0.35 0.35 0.00 0.00 0.00 0.00 352 352 0.00 0.00 0.00 0.00 703
L3 8.3 18.3 18 0.3 21.7 22 0.14 0.14 0.50 0.15 0.15 0.50 143 143 500 150 153 500 1589
L4 0.3 0.7 0 0.7 49.3 0 0.01 0.01 0.00 0.35 0.35 0.00 5 5 0.00 350 347 0.00 708
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 39
Marginal Participation Method
• Incremental power flow change in each line is calculated
for 1 MW incremental change of demand or generation at
each node.
• Using this information, usage index for a particular time
span is calculated for each node.
• Marginal participation factor for each node is evaluated.
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 40
Marginal Participation Method
• 𝑈𝑘𝑐 = |𝐹𝑐𝑘 − 𝐹𝑐 𝑃𝑘
• 𝐹𝑐 ➔ Power flow of line ‘c’
• 𝐹𝑐𝑘 ➔ Power flow in line ‘c’ when nodal injection of bus ‘k’
is increased by 1 MW
• 𝑃𝑘 ➔ Original nodal injection at bus ‘k’
• 𝑈𝑘𝑐 ➔ Usage factor of bus ‘k’ over line ‘c’
𝑈𝑘𝑐
• 𝑝𝑎𝑟𝑡𝑘𝑐 =
σ𝑘 𝑈𝑘𝑐
• Make charges proportional to 𝑝𝑎𝑟𝑡𝑘𝑐
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 41
Marginal participation method
1 MW
Change in line flow Participation factor
A
∆L A-B B-C B-D C-D A-B B-C B-D C-D
1 MW
1000₹ B 0.33 MW C D 1 0.33 0.66 0.33 0.33 0.33 0.66 0.5
500₹ C 1 0.66 0.33 0.33 0.33 0.66 0.33 0.5
B 1 0 0 0 0.33 0 0 0
A 0 0 0 0 0 0 0 0
Payment for each line
Payment
D (₹)
∆L A-B B-C B-D C-D
1 MW D 333 167 133 150 783
C 333 333 67 150 883
B 333 0 0 0 333
A 0 0 0 0 0
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 42
Equivalent Bilateral Exchange Method
(EBE)
• Every generator is assumed to have share in every load
• Share is found by proportionality principle
• Requires knowledge of network parameters
• Works on DC power flow model
17-04-2025 © Deep Kiran, IIT Roorkee (2025) 43
Equivalent Bilateral Exchange Method
(EBE)
• Step 1: Obtain DC power flow solution
𝑃𝐺𝑖 𝑃𝐷𝑗
• Step 2: 𝐺𝐷𝑖𝑗 =
𝑃𝐷
• PD is total system demand (𝑃𝐷 = σ𝑗 𝑃𝐷𝑗 = σ𝑖 𝑃𝐺𝑖 )
• Step 3: Solve a DC load flow consisting of a single power
injection of GDij at bus i and the load at bus j.
𝑖𝑗 𝑖𝑗
• 𝑃𝑙𝑚 = |𝑃𝑇𝐷𝐹𝑙𝑚 |𝐺𝐷𝑖𝑗
• Step 4: The costs of the line lm can be attributed to this
equivalent bilateral exchange in linear proportion to the
usage
