Nodal Pricing Basics

1

Nodal Pricing Basics

Drew Phillips

Market Evolution Program

2

Agenda

What is Nodal Pricing? Impedance, Power Flows Losses and Limits Nodal Price Examples

• No Losses or Congestion • Congestion Only

– Impact of Transmission Rights• Losses Only

How DSO Calculates Nodal Prices

3

What is Nodal Pricing?

Nodal Pricing = Locational Marginal Pricing (LMP)= Locational Based Marginal Pricing (LBMP)

Nodal Pricing is a method of determining prices in which market clearing prices are calculated for a number of locations on the transmission grid called nodes• Each node represents the physical location on the transmission

system where energy is injected by generators or withdrawn by loads

Price at each node represents the locational value of energy, which includes the cost of the energy and the cost of delivering it, i.e., losses and congestion

IMO publishes nodal prices for information purposes; they are referred to as shadow prices

4

What causes locational differences?

Losses Due to the physical characteristics of the transmission system,

energy is lost as it is transmitted from generators to loads Additional generation must be dispatched to provide energy in

excess of that consumed by load

Transmission congestion Prevents lower cost generation from meeting the load; higher

cost generation must be dispatched in its place

In both cases, the associated costs are allocated to each node in a manner that recognizes their individual contribution to/impact on these extra costs

5

Impedance, Power Flows, Losses and Limits

6

Impedance and its effect on power flows

Impedance Is a characteristic of all transmission system elements Signifies opposition to power flow A higher impedance path indicates more opposition to power flow and greater

losses

Impedance between two points on the grid is related to: Line length Number of parallel paths Voltage level Number of series elements such as transformers

Impedance will be lower where there are: Shorter transmission lines More parallel paths Higher voltage Fewer series transformers

7

Relative Impedance and Power Flow

115 kV

230 kV

Gen Load

Energy will flow preferentially on the 230 kV path:• Higher voltage• More lines in parallel• Fewer transformers

Transformer

8

Power Flows

Power will take all available paths to get from supply point to consumption point

Power flow distribution on a transmission system is a function of:• Location and magnitude of generation• Location and magnitude of load• Relative impedance of the various paths between generation

and load

The following examples ignore the effect of losses

9

Power Flows

All lines have equal impedance Path W-S-E-N has three times the impedance of path W-N Flow divides inversely to impedance If W Gen supplies N Load, flow W-S-E-N is one third flow W-N If N Load is 100 MW, 75 MW flows on path W-N, 25 MW flows on path W-S-

E-N

N Load

W Gen

N

W

S

E

75 %

25 %

E Gen

10

What if E Gen supplies N Load?

Path E-S-W-N has three times the impedance of path W-N Flow divides inversely to impedance If E Gen supplies N Load, flow E-S-W-N is one third flow E-N If N Load is 100 MW, 75 MW flows on path E-N, 25 MW flows on

path E-S-W-N

N Load

N

W

S

E

25 %

75 %

E Gen

11

40 MW60 MW

Superposition

What if W Gen supplies 60 MW and E Gen supplies 40 MW to N Load?

Both W Gen and E Gen’s output will flow in proportion to the impedance of the paths to N Load

Resulting line flows represent the net impact of their flow distribution

N Load

W Gen

N

W

S

E E Gen

100 MW

40 MW10 MW

30 MW

45 MW

15 MW

60 MW60 MW

5 MW(15 – 10) 5 MW (15 – 10)

45 MW55 MW (15 + 30)(45 + 10)

12

Loss Comparison for 100 km Lines

115 kV

230 kV

500 kV

90 MW

90 MW

90 MW 79.5 MW

88.5 MW

89.9 MW180 A

390 A

780 A

• Losses are:• proportional to Current2 x Resistance (I2R)• lower on higher voltage lines because resistance

is lower and current flow is lower for a given MW flow

Current (Amps) A

13

Loss Comparison

Losses are higher on a line that is heavily loaded for the same increase in current

Current (I)

Loss

es (M

W)

=

14

Security Limits

Security limits are the reliability envelope in which the market operates

Power will take all available paths to get from supply point to consumption point

Transmission lines do not control or limit the amount of power they convey

Power flows are managed by dispatching the system (normally via dispatch instructions and interchange scheduling)

Must respect current conditions and recognized contingencies

15

Nodal Price Examples

16

How are nodal prices derived?

Marginal cost is the cost of the next MW; the marginal generator is the generator that would be dispatched to serve the next MW

• This is the basis of our current unconstrained market clearing price A nodal price is the cost of serving the next MW of load at a given

location (node) Nodal prices are formulated using a security constrained dispatch and

the costs of supply are based upon participant offers and bids Nodal prices consist of three components:

Nodal Price

Marginal Cost of Generation

Marginal Cost of Losses

Marginal Cost of

Transmission Congestion

= + +

17

Current Pricing Scheme

NodalPrices

Currently calculated for information purposes only

IMOMarket

Participants

UnconstrainedCalculation

• ignores physical limitations

MarketSchedule

UniformPrice

ConstrainedCalculation

• considers physical limitations

DispatchSchedule

Bids/Offers CMSCBids/

Offers

Dispatchableresources

produce or consume MWs

$

18

Nodal Price Calculations

No Congestion or Losses With Congestion With Losses

Process: Determine least cost dispatch to serve load Determine resulting power flows to ensure security limits are

respected Calculate prices by determining the dispatch for one additional

MW at each node (while still respecting all limits)

19

No Congestion or Losses

20

Transmission Limit = 85 MW

No Congestion or Losses: Dispatch

Least cost solution would have W Gen supply all 100 MW to N Load, based on W Gen’s offer price

Resultant flow is within limits Nodal price is the cost of serving the next MW What are the prices at each node?

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

0 MW

Dispatch

125 @ $35

Offer

25 MW

75 MW 25 MW

25 MW

21


No Congestion or Losses: Node N Price

Price at Node N is the cost of supplying next 1 MW to N Least cost solution would have W Gen supply the next MW to N, based

on W Gen’s offer price Resultant flow would be within limits (net of existing flow and increment to

serve additional 1 MW at Node N) W Gen is the marginal generator and Node N price = $30

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen 125 @ $35

Offer

$30

+ 1 MW

0 MW

Dispatch

100 MW

Dispatch

+1 MW

25.25 MW

75.75 MW 25.25 MW

25.25 MW

(25 + .25)(75 + .75)

(25 + .25) (25 + .25)

22


No Congestion or Losses: Node W Price

Price at Node W is the cost of supplying next 1 MW at W Least cost solution would have W Gen supply the next MW to W,

based on W Gen’s offer price Resultant flow would be within limits (net flow change is zero) W Gen is the marginal generator and Node W price = $30

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

+1 MW

0 MW

Dispatch

125 @ $35

Offer

25 MW

75 MW 25 MW

25 MW

$30

+ 1 MW

23


No Congestion or Losses: Node E Price

Price at Node E is the cost of supplying next 1 MW to E Least cost solution would have W Gen supply the next MW to N, based


serve additional 1 MW at Node E) W Gen is the marginal generator and Node E price = $30

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

+1 MW

0 MW

Dispatch

125 @ $35

Offer$30

+ 1 MW

25.5 MW

75.5 MW 24.5 MW

25.5 MW

(25 - .5)(75 + .5)

(25 + .5) (25 + .5)

24


No Congestion or Losses: Node S Price

Price at Node S is the cost of supplying next 1 MW at S Least cost solution would have W Gen supply the next MW to S, based


serve additional 1 MW at Node S) W Gen is the marginal generator and Node S price = $30

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

+1 MW

0 MW

Dispatch

125 @ $35

Offer

$30

+ 1 MW

24.75 MW

75.25 MW 24.75 MW

25.75 MW

(25 - .25)(75 + .25)

(25 + .75) (25 - .25)

25

Summary

The previous examples demonstrate the method used to derive nodal prices

As we would expect, the nodal prices at all nodes on a transmission system will be the same in the absence of losses and congestion

Unfortunately, no such transmission system exists The following examples will apply the same method to illustrate the

calculation under conditions of congestion and then losses Examples:

• are not representative of how the IMO-controlled grid is dispatched and therefore the impact on nodal prices is entirely fictitious; these scenarios were designed to illustrate a concept while keeping the calculation as simple as possible

• are for illustrative purposes only and do not imply a settlement basis for a nodal pricing methodology for Ontario

26

Congestion, No Losses

27

Transmission Limit = 75.2 MW

Congestion (No Losses): Dispatch

Assume the transmission limit is reduced; dispatch can be solved as in the no congestion case, but what is the effect on nodal prices?

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

0 MW

Dispatch

125 @ $35

Offer

25 MW

75 MW 25 MW

25 MW

28

0 MW

Dispatch

+1.1 MW

100 MW

Dispatch

-.1 MW


Congestion (No Losses): Node N Price

An increase in output of 1 MW by either W Gen or E Gen alone will increase the W-N line flow over the limit; we must redispatch the system using both generators

If we reduce W Gen output by 0.1 MW (75% of the reduction will appear on W to N flow) and increase E Gen output by 1.1 MW (25% flows from N to W), net effect is on line W-N is a flow increase of .2 MW

This is the lowest cost way to meet an additional 1 MW at N Node N price = $35.50 (1.1 X $35 – 0.1 X $30)

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen 125 @ $35

Offer

24.7 MW

75.2 MW 25.8 MW

24.7 MW

$35.50

+ 1 MW

29

100 MW

Dispatch

+.4 MW

0 MW

Dispatch

+.6 MW


Congestion (No Losses): Node E Price


If we increase W Gen output by 0.4 MW (75% flows from W to N) and increase E Gen output by .6 MW (0% flows from N to W), net effect is on line W-N is a flow increase of .2 MW

This is the lowest cost way to meet an additional 1 MW at E Node E price = $33 (0.6 X $35 + 0.4 X $30)

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen 125 @ $35

Offer

25.2 MW

75.2 MW 24.8 MW

25.2 MW

$33

+ 1 MW

30


Congestion (No Losses): Node S Price


If we increase W Gen output by 0.8 MW (75% flows from W to N) and increase E Gen output by .2 MW (25% flows from N to W), net effect is on line W-N is a flow increase of .2 MW

This is the lowest cost way to meet an additional 1 MW at E Node S price = $31 (0.2 X $35 + 0.8 X $30)

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen 125 @ $35

Offer

24.6 MW

75.2 MW 24.8 MW

25.6 MW $31

+ 1 MW

0 MW

Dispatch

+.2 MW

100 MW

Dispatch

+.8 MW

31


Congestion (No Losses): Node W Price

Least cost solution would have W Gen supply the next MW to W, based on W Gen’s offer price

W Gen can meet the additional MW at Node W without affecting the transmission system (net flow change is zero)

W Gen is the marginal generator and Node W price = $30

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

+1 MW

0 MW

Dispatch

125 @ $35

Offer

25 MW

75 MW 25 MW

25 MW

$30

+ 1 MW

32


Congestion (No Losses): Summary

System is congested on line W-N Combination of W Gen and E Gen redispatch is necessary to meet incremental loads

at Node N,E and S If W Gen and N Load are settled at their respective nodal prices, the difference will

result in a settlement surplus Surplus due to the congestion component of different nodal prices is used to fund

transmission rights

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

0 MW

Dispatch

125 @ $35

Offer

25 MW

75 MW 25 MW

25 MW

$30

$31

$33

$35.50

33

Transmission Rights

Provide a hedge against congestion charges between two locations Transmission rights holders receive the difference in congestion charges

between the two locations defined by the transmission right Using our example:

• Price at N - Price at W = Congestion Charge• $35.5 - $30 = $5.50/MW

If N load holds 100 MW of transmission rights, they will receive 100 x $5.50 = $550

N Load:• Pays 100 x $35.50 = $3550 for energy• Receives 100 x $5.50 = $550 for transmission rights• Net = $3000

W Gen is paid 100 x $30 = $3000

34


Exercise One

Assume the transmission limit is on line S-E (for simplicity we’ll allow flow to equal the limit, although in reality flow must be less than the limit)

The load at N is being served by W Gen with flows on the transmission system as shown

What are the nodal prices at N and S?

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

100 MW

Dispatch

0 MW

Dispatch

125 @ $35

Offer

25 MW

75 MW 25 MW

25 MW

35


Exercise Answer: Node N Price

W Gen cannot be used as sole supply as any increase in output will increase the S-E line flow; must redispatch the system

Must increase W Gen output by 0.5 MW (25% flows from S to E) and increase E Gen output by 0.5 MW (25% flows from E to S)

Resultant flow would be within limits Node N price = $32.50 (0.5 X $35 + 0.5 X $30)

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen 125 @ $35

Offer

$32.50

25 MW

75.5 MW 25.5 MW

25 MW

(25 +.125 – .125) (25 +.125 – .125)

(25 +.125 + .375)(75 +.375 + .125)

+ 1 MW

100 MW

Dispatch

+.5 MW

0 MW

Dispatch

+.5 MW

36


Exercise Answer: Node S Price

W Gen can be used as sole supply; the increase in output to serve Node S will decrease the S-E line flow

Increase W Gen output by 1.0 (75% flows from E to S) Resultant flow would be within limits Node S price = $30

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen 125 @ $35

Offer

$30

+ 1 MW

0 MW

Dispatch

100 MW

Dispatch

+1 MW

24.75 MW

75.25 MW 24.75 MW

25.75 MW

(25 + .75) (25 - .25)

(25 - .25)(75 + .75)

37

Losses, No Congestion

38

Losses (No Congestion): Dispatch

Least cost solution would have W Gen supply all 100 MW to N Load due to its lower offer price, but due to losses must generate 104 MW

Resultant flow is within limits Nodal price is the cost of serving the next MW What are the prices at Node N?

N Load

W Gen

N

W

S

E

100 MW

125 @ $30

Offer

E Gen E Gen

104 MW

Dispatch

0 MW

Dispatch

125 @ $35

Offer78 MW

75 MW

26 MW

25 MW

39

104 MW

Dispatch

+1.04 MW

Losses (No Congestion): Node N Price

Price at node N is the cost of supplying next 1 MW W Gen must generate an additional 1.04 MW to N to deliver 1 MW at Node N Resultant flow would be within limits Node N price = $31.20 (1.04 X $30) Prices at Nodes E and S would be similarly calculated Price at Node W = $30 as an increment of load can be supplied from W Gen with no

impact to transmission flows

N Load

W Gen

N

W

S

E

101 MW

125 @ $30

Offer

E Gen E Gen

0 MW

Dispatch

125 @ $35

Offer78.9 MW

75.75 MW

26.3 MW

25.25 MW$31.20

40

Summary

When more than one generator is on the margin, prices may be:• higher than any offer • lower than any offer (and could even be negative)

For additional examples see the Market Evolution Day Ahead Market web page and in particular: http://www.theimo.com/imoweb.pubs/consult/mep/dam_wg_2003sep16_LMPexamples.pdf

Even when there is no congestion on the transmission system directly connecting them, prices may be different between two nodes due to:• losses and/or• their differing impact on congested paths elsewhere in the system

If a generator is partially dispatched: nodal price = offer price If a generator is fully dispatched: nodal price > than offer price If a generator is not dispatched: nodal price < than offer price

http://www.theimo.com/imoweb.pubs/consult/mep/dam_wg_2003sep16_LMPexamples.pdf

41

How the Dispatch Scheduling Algorithm (DSO) Calculates Nodal Prices

42

Dispatch Scheduling Optimizer (DSO)

Two methods are available to calculate nodal prices:1) calculate nodal prices at each node directly (as in previous

examples)2) calculate a reference node price then derive prices at all other

nodes

The DSO uses method 2 as it requires less computing power and is faster:• It yields the same results as method 1• It does not matter which node is chosen as the reference bus

43

Marginal Cost of Generationλs

System Marginal Cost at Reference Node

Marginal Cost of Losses

Marginal Cost of

Transmission Congestion

Cost of transmission limits incurred for the next MW of load at the node

Σ αnk*μk

Calculate Nodal Prices

LMP

Nodal Price

λn = + +

Cost of losses incurred for the next MW of load at the node

(DFn - 1)* λs

44

Inputs

Offers and bids Forecast demand for the next interval based upon a snapshot of

current demand modified by the expected +/- in the next interval Load profile based upon the current system snapshot Physical model of the transmission system Security limits Penalty Factors (losses)

• represent losses between nodes and the reference bus• IMO uses fixed losses for each node based on historical

power flows

45

Penalty Factors

Represent incremental impact on losses for generation or load at each node based on a representative power flow distribution on the grid

If PF > 1: losses are incurred for each MW delivered to Richview If PF < 1: losses are reduced for each MW delivered to Richview

Gen D

Gen C

Richview

Gen AGen B

PF = .95

= - 5.3% lossesPF = 1.01

= 1% losses

PF = .9

= - 11.2% losses

PF = 1.3

= 23% losses

Load Z

PF = .97

= - 3.1% losses

Non-dispatchable

46

Nodal Price Calculation in DSO

DSO Calculation 1

• Bids and Offers• Forecast Load• System Limits

• Penalty Factors

• Transmission Model• Load Profile

• Congestion Impact

• Richview Nodal Price

• Dispatch Instructions

DSO Calculation 2

• Richview Nodal Price• Congestion Impact

• Penalty Factors

• All Other Nodal Prices

47

Reference Bus Merit Order

Delivery Point Offer/Bid Stack

Gen C 100 MW @ $60

Gen B 100 MW @ $70

Gen A 100 MW @ $75

Gen D 100 MW @ $50

.95

1.01

.90

1.3

Penalty Factors

Gen C 100 MW @ $57

Gen B 100 MW @ $70.7

Gen A 100 MW @ $67.5

Gen D 100 MW @ $65

Richview Equivalent Offer/Bid Stack

Subsequent calculation addresses quantity differences due to the effect of losses

48

Effective Price

Delivery Point Offer/Bid Stack

Gen D 100 MW @ $50 1.3

Penalty Factors

Gen D 100 MW @ $65


If we generate 100 MW at Gen D, only 100/1.3 or 76.9 MW shows up at Richview due to losses

100 MW at Gen D costs 100 x $50 = $5,000, which only yields 76.9 MW at Richview, resulting in an effective price of $5000/76.9 MW = $65 /MW

49

Determine Unconstrained Economic Solution

Current system demand +/- forecast change in next interval


Gen C 100 MW @ $57

Gen B 100 MW @ $70.7

Gen A 100 MW @ $67.5

Gen D 100 MW @ $65Forecast Demand

50

Introduce Physical Network

Allocate forecast demand to nodes based on load profile of current system

Run load flow to solve power balance using offers and bids at appropriate nodes, physical characteristics of transmission system and system limits

Determine System Marginal Cost at Richview

1%

2%6%5%

3%

3%

10%

2%

4%

4%

5%4%Richview

Gen D

Gen CGen A

Gen B

Load Z

51

System Marginal Cost: No Congestion

If power balance is solved without any need to redispatch to respect limits; there is no congestion and the system marginal cost will equal that determined in the purely economic merit order i.e., Gen D will set the system marginal cost

System Marginal Cost (λs) = $65

Gen C 100 MW @ $57

Gen B 100 MW @ $70.7

Gen A 100 MW @ $67.5

Gen D 100 MW @ $65Forecast Demand

52

Nodal Prices: No Congestion

Offer Price

Gen C

Gen B

Gen A

$60

$70

$75

0.95

1.01

0.90

$3.42

-$0.64

$7.22

Penalty Factor

Losses Cost

0

0

0

Congestion Cost

$68.42

$64.36

$72.22

Gen D $50 1.30 -$15.00 0 $50.00

Nodal Price

Richview = λs $65.00

Load Z N/A 0.97 $2.01 0 $67.01

53

$68.42

$50.00

Nodal Prices and Dispatch: No Congestion

Offer prices: Gen A $75 Gen B $70 Gen C $60 Gen D $50Which generators should be dispatched?

$65.00Gen D

Gen C

Richview

Gen AGen B $64.36

$72.22

Fully dispatched

Partially dispatched

54

Congestion

If a transmission limit on the line from Gen D prevents its economic dispatch another more expensive resource must be dispatched to meet demand

This congestion will raise the system marginal cost and affect nodal prices throughout the system

Gen D

Gen C

Richview

Gen AGen B

Binding Transmission Limit

Line 1

Load Z

55

System Marginal Cost: Congestion

Congestion on Line 1 from Gen D: redispatch from economic merit order to respect limit

System marginal cost is now set by Gen A System Marginal Cost (λs) = $67.5 There is a cost associated with the Line 1 transmission

limit

Gen C 100 MW @ $57

Gen B 100 MW @ $70.7

Gen A 100 MW @ $67.5

Gen D 90 MW @ $65 Forecast Demand

56

Line 1 Transmission Limit Cost

Determine transmission limit cost by relaxing constraint by 1 MW and measuring impact on total system costs

Note: results are rounded on the following diagrams


Gen D

Gen C

Richview

Gen AGen B

Line 1

Load Z

57

Line 1 Transmission Limit Cost

Increase Gen D by 1 MW results in +.7692 MW at Richview due to losses

To maintain the generation/load balance we must reduce Gen A by .6923 MW

Net cost is $50 x 1 MW - $75 x .6923 MW = -$1.92

Gen D

Gen C

Richview

Gen AGen B

- 11.2% losses

+1 MW 23% losses

+.77 MW

-.69 MW

Load Z

58

Nodal Prices: Congestion

Richview = λs

Offer Price

Gen C

Gen B

Gen A

Gen D

$60

$70

$75

$50

0.95

1.01

0.90

1.30

$3.55

-$0.67

$7.50

-$15.58

Penalty Factor

Losses Cost

0

0

0

-1.92

Congestion Cost

$71.05

$66.83

$75.00

$50.00

Nodal Price

$67.50

Load Z N/A 0.97 $2.09 0 $69.59

59

$71.05

$50.00

Nodal Prices and Dispatch: Congestion

Offer prices: Gen A $75 Gen B $70 Gen C $60 Gen D $50Which generators should be dispatched?

$67.50Gen D

Gen C

Richview

Gen AGen B $66.83

$75.00


Line 1

Partially dispatched

Partially dispatchedFully dispatched

60

Nodal Price Comparison

Gen C

Gen B

Gen A

Gen D

$68.42

$64.36

$72.22

$50.00

Nodal Price(No Congestion)

$71.05

$66.83

$75.00

$50.00

Richview = λs $65.00 $67.50

Nodal Price(Congestion)

Load Z $67.01 $69.59

61

Getting Nodal Price Information

Nodal prices available on IMO FTP site only (in .csv format) Go to Market Data page:

• http://www.theimo.com/imoweb/marketdata/marketData.asp Scroll down to hyperlink:

• ftp://aftp.theimo.com/pub/reports/PUB/ Select DispConsShadowPrice folder Choose report date and hour i.e., Sept 20 for Hour 1:

• PUB_DispConsShadowPrice_2003092001.csv

1 6 RICHVIEW-230.G_SLACKA 36.13 1.12 0.77 0.77 DSO-RD;

Hour Interval NodeOperating Reserve

10S/10NS/30Energy

Documents

Nodal Pricing Basics