Simulation of Alberta Pool Prices

Scott MacDonald

Outline

• High level observations of Alberta power market since deregulation

– Load growth, Generation, Historical pool prices

• Challenges of simulating prices– What drives price spikes?– Alberta’s merit order

• Description of model• Results

Alberta Marginal Cost ($/MWh)

0

50

100

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350

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

MW

$/MWh

Wind, Hydro, Biomass

Base Gas

Coal

Peaking Gas,Dispatchable Hydro

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec5000

5500

6000

6500

7000

7500

8000

8500

9000Peak load growth by month 2000 - 2007

Sys

tem

De

ma

nd

(M

W)

20002001200220032004200520062007

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec5000

5500

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6500

7000

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8000

8500

9000Off peak load growth by month 2000 - 2007

Sys

tem

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ma

nd

(M

W)

20002001200220032004200520062007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23250

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500M

W

Hour Ending

SCADA Generation Data for Wind On 10/02/2007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2350

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MW

Hour Ending

SCADA Generation Data for Hydro On 10/02/2007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 234300

4400

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MW

Hour Ending

SCADA Generation Data for Coal On 10/02/2007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 231950

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MW

Hour Ending

SCADA Generation Data for Gas On 10/02/2007

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Time (hours)

Sys

tem

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ma

nd

(M

W)

Load Duration Curve for 2006

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Time (hours)

Pric

e $

/MW

h

0 1000 2000 3000 4000 5000 6000 7000 80005000

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Time (hours)

Sys

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ma

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(M

W)

Load Duration Curve for 2007

0 1000 2000 3000 4000 5000 6000 7000 80000

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Time (hours)

Pric

e $

/MW

h

Summary of Off Peak Prices2000 2001 2002 2003 2004 2005 2006 2007

Jan $33.69 $111.68 $18.32 $66.04 $42.53 $46.08 $46.08 $43.27Feb $36.20 $93.16 $14.46 $56.98 $43.99 $34.90 $38.76 $59.01Mar $37.49 $73.12 $43.40 $85.43 $34.09 $38.10 $33.74 $37.29Apr $60.11 $85.25 $27.60 $36.71 $37.90 $39.64 $26.37 $29.26May $31.05 $61.85 $21.61 $39.61 $50.64 $31.00 $27.74 $19.83Jun $50.54 $41.34 $14.52 $25.59 $48.34 $33.21 $27.92 $27.44Jul $56.24 $37.22 $14.13 $65.10 $45.66 $28.20 $76.76 $86.89Aug $69.34 $36.91 $19.22 $42.05 $33.90 $63.50 $46.65 $34.83Sep $79.99 $22.74 $27.38 $28.67 $40.10 $34.10 $43.85 $35.49Oct $140.81 $29.74 $28.16 $39.63 $44.37 $95.66 $96.59 $44.47Nov $112.12 $21.68 $43.96 $42.80 $31.33 $83.86 $58.41Dec $142.30 $23.49 $58.59 $35.08 $47.11 $53.92 $49.19

Summary of On Peak Prices2000 2001 2002 2003 2004 2005 2006 2007

Jan $56.53 $145.33 $35.74 $90.97 $66.61 $53.53 $92.66 $73.36Feb $55.12 $134.44 $28.30 $99.42 $50.13 $48.49 $65.56 $84.15Mar $105.87 $114.65 $64.39 $93.24 $48.50 $49.60 $51.54 $70.72Apr $120.45 $138.40 $57.73 $62.57 $62.24 $57.68 $56.02 $69.60May $66.55 $107.47 $54.03 $68.70 $80.13 $63.49 $76.86 $68.97Jun $147.78 $79.85 $71.59 $59.57 $70.44 $71.16 $86.28 $66.25Jul $177.63 $66.29 $35.29 $104.38 $64.42 $45.28 $168.81 $210.02Aug $297.97 $63.54 $41.27 $66.34 $63.00 $106.26 $92.83 $97.29Sep $246.65 $35.69 $60.35 $54.56 $68.20 $103.68 $110.80 $60.12Oct $342.40 $54.20 $56.07 $87.62 $68.49 $142.86 $235.51 $80.54Nov $312.21 $41.80 $87.42 $60.37 $53.49 $154.71 $139.86Dec $225.67 $41.60 $80.57 $51.02 $74.26 $138.50 $87.98

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 310

100

200

300

400

500

600

700

800

900

1000P

rice

$/M

Wh

Time (days)

Example of a low settling month - July 2005Mean: 37.7471 Std: 35.0434

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 310

100

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1000P

rice

$/M

Wh

Time (days)

Example of a high settling month - July 2007Mean: 155.735 Std: 259.7324

1000 2000 3000 4000 5000 6000 7000 80000

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Cummulative Supply (MW)

Pric

e $

/MW

h

Merit order for July 12, 2005

Hour Ending 4Hour Ending 8Hour Ending 15Hour Ending 21

7900 7950 8000 8050 8100 8150 8200 8250 8300 8350 84000

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Cummulative Supply (MW)

Pric

e $

/MW

h

Merit order for July 12, 2005 (close up)

Hour Ending 15

System Marginal Price

• Pool Price is the time weighted average of the SMP

• Intersection of Alberta Internal Load (AIL) and merit curve determines the price

• SMP remains constant as long as AIL is on the price setting block

• Many factors effect the merit order (Wind, Imports, DCR)

Sample SMP Calculation

PostTime SMP($/MWh)

AIL(MW)

DCR(MW)

BC (MW)

SK(MW)

WIND(MW)

15:48 54.10 8276 512 109 -126 429

Adjusted Load = AIL + SK – WIND – 0.44*DCR

= 7496 MW

7496 MW (intersect with merit curve) implies SMP = 52.80 $/MWh

Description of Price Simulation Model

• Very simple (perhaps too simple?)• Good:

– Reproduces historically “reasonable” CDFs– Stats are inline with history– Spikes happen in the right hour endings (8-23)– Back tests calculate margins with 1 to 1.5 std of mean

• Bad:– Fails to reproduce the large number of $10/MWh hours.

(Coal units marginal price)– Over parameterized?– Assumes that history is likely to repeat itself

Model Process

1. Query historical data from SQL database2. Create shaping matrix3. Create noise vector4. Create price path

Shaping Matrix(for one month)

Mon Tue Wed Thu Fri Sat SunP_1,{1:24} … … … … … …P_2,{1:24} … … … … … …P_3,{1:24} … … … … … …P_4,{1:24} … … … … … …Notation:

P_i,{1:24}

Day OccurrenceHours 1 through 24

Shaping Matrix(aggregate)

Mon Tue Wed Thu Fri Sat SunM(P_{1:4},{1:24},1)

… … … … … …

M(P_{1:4},{1:24},2)

… … … … … …

M(P_{1:4},{1:24},3)

… … … … … …

M(P_{1:4},{1:24},4)

… … … … … …Notation, M = mean()

P_{1:4},{1:24},i

Day OccurrenceHours 1 through 24

Year Label

Mon Tue Wed Thu Fri Sat Sun

HE 4

HE 8

HE 12

HE 16

HE 20

HE 24

Aggregate scalars (normalized to peak of month) for month 1

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1

Mon Tue Wed Thu Fri Sat Sun Mon0

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1

Mon Tue Wed Thu Fri Sat Sun

HE 4

HE 8

HE 12

HE 16

HE 20

HE 24

Aggregate scalars (normalized to peak of month) for month 5

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Mon Tue Wed Thu Fri Sat Sun Mon0

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Mon Tue Wed Thu Fri Sat Sun

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HE 24

Aggregate scalars (normalized to peak of month) for month 9

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Mon Tue Wed Thu Fri Sat Sun Mon0

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Mon Tue Wed Thu Fri Sat Sun

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HE 24

Aggregate scalars (normalized to peak of month) for month 7

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Mon Tue Wed Thu Fri Sat Sun Mon0

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1

Noise Vector

• Skip the details• Broken out into peak (HE 8-23) and off peak

(everything else)• Remove seasonality by doing

– log(P_i) – mean(log(P_month))

Create Price Path (pseudocode)1. Tmp_(i,j) = Smat(i,j) + X*Smat_std(i,j)

where X ~ a + b*U(0,1) random variable2. Tmp = flatten(Tmp)3. S = S*c

where c is scaling constant4. On_peak_chain = emprand(Nvec_on)5. Off_peak_chain = emprand(Nvec_off)6. IF (HE is peak):

P = log(S) + On_peak_chainElse:

P = log(S) + Off_peak_chain7. P = exp(P) + X

where X ~ a + b*U(0,1) random variable

0 50 100 1500

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$ (CAD)

Pro

ba

bili

tyHistogram of mean of price paths. Mean: 84.9754 std: 29.2083

0 20 40 60 80 100 1200

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$ (CAD)

Pro

ba

bili

tyHistogram of mean of off peak price paths. Mean: 64.0045 std: 26.4742

-20 0 20 40 60 80 100 120 140 160 1800

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$ (CAD)

Pro

ba

bili

tyHistogram of mean of peak price paths. Mean: 100.3004 std: 32.3465

Min Max Mean Median Std0

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1000Statistics of simulated price paths and historical prices

$ (

CA

D)

Simulated2003200420052006

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Empirical CDF

Simulated2003200420052006

Conclusion

• Thin supply stack causes wild price variation• Generators dispatching intelligently

– Scarcity pricing, shadow bidding

• Naïve approach seems to yield reasonable results (back tested over 1 year of data)

• Flexible tool to allow users to assess the risk of various hedge scenarios (7x24, 6x16, etc)