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Modelling incentives and regulation in wholesale electricity markets. Andy Philpott Electric Power Optimization Centre The University of Auckland (www.esc.auckland.ac.nz/epoc) (with acknowlegements to Geoff Pritchard and Golbon Zakeri). What is the purpose of this talk?.

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modelling incentives and regulation in wholesale electricity markets
Modelling incentives and regulation in wholesale electricity markets

Andy Philpott

Electric Power Optimization Centre The University of Auckland

(www.esc.auckland.ac.nz/epoc)

(with acknowlegements to Geoff Pritchard and Golbon Zakeri)

what is the purpose of this talk
What is the purpose of this talk?
  • New Zealand faces some huge technical challenges in energy supply and delivery.
  • This needs lots of research and development into new technology which is where NERI is currently focused.
  • But technology is not enough – we need to understand the economic institutions for implementing this technology.
  • Our work at EPOC studies how these institutions (e.g. taxes, trading schemes, regulations etc.) work using models.
  • These models try to help us design mechanisms that will induce “optimal” behaviour in the agents of wholesale electricity markets – i.e. we study incentives and how they work.
summary
Summary
  • What is the wholesale electricity market?
  • Examples of incentive/regulation problems
    • Generator offering
    • Transmission planning
    • Wind power
    • Emissions trading
  • Takeaway: new energy technology is necessary but not sufficient without understanding the market mechanisms under which we expect it to be adopted.
nzem is a uniform price auction e g single node

price

T1(q)

quantity

demand

NZEM is a uniform price auction (e.g. single node)

price

T2(q)

p

quantity

price

combined offer stack

p

quantity

slide5

Example

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

Thermal B: 400 @ $50

Load 500

slide6

Least-cost dispatch

100

150

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

250

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

200

50

Thermal B: 400 @ $50

Load 500

slide7

Least-cost dispatch with nodal prices

$45

100

150

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

250

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

200

50

Thermal B: 400 @ $50

Load 500

$50

  • Load pays $25000 (=$50*500)
  • Hydro makes profit $4000 and Wind makes profit $4500
  • System operator makes congestion rent of $1250
  • The dispatch has total cost $15250
the actual nzem
The actual NZEM
  • Generators specify supply curves defining prices at which they will generate.
  • Curves fixed for each (1/2) hour
  • Linear programming model runsevery five minutes to determine
    • who produces how much
    • electricity flows in grid
    • spot price of electricity at each grid exit point around the country (244 of these)
wholesale electricity prices

6am-9am

3am-6am

Wholesale electricity prices

Five Minute Wholesale Electricity Prices on 28/08/06 ($/MWh)

Source: comitfree

Otahuhu

Benmore

Time of Day

slide11

$89

$89

Example 1: Dispatch with strategic bidding

$45

100

150

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

250

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

200

50

Thermal B: 400 @ $50

Load 500

$50

  • Load pays $19500 extra (=$39*500)
  • Hydro makes extra $7800 and Thermal B makes extra $1950
  • System operator makes extra congestion rent of $9750
  • The dispatch is exactly the same, with cost $15250
slide12

Thermal A: 400 @ $45

149 @ $45

51

249

149

$50

Example 2: Dispatch with strategic withholding

$45

100

150

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

250

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

200

50

Thermal B: 400 @ $50

Load 500

$50

  • Load pays no extra money
  • System operator congestion rent goes down by $1250 to $0
  • Wind makes $500 more, Thermal A makes $745 more…

Total cost of dispatch is $15255 which is $5 more than original cost!!

slide13

Strategic behaviour by firms can result in higher prices and a wealth transfer between agents.

  • Strategic behaviour by firms can result in dispatch inefficiency.
  • Prices that do not truly represent the cost of shortage can lead to inefficiencies in the wider economy.
  • Dispatch inefficiency is a deadweight loss ($5 in example)
  • Q: How bad can it get?
  • Q: How do we prevent it?

What can we learn from this example?

slide14

J.F. Nash Jr., Equilibrium points in n-person games,

Proc Nat. Acad. Sci.USA, 36 (1950) 48-49.

slide15

If generators offer at marginal cost

Load = 500 - p

Expect the price to be $50

a=450

b=450

Line contains no flow.

Thermals make no profit.

Load has high welfare.

Thermal A: 500 @ $50

a

Capacity 1000

lossless

Thermal B: 500 @ $50

b

Load = 500 - p

slide16

If generators withhold strategically

Load = 500 - p

Total load = 1000-2p

p = 500-(a+b)/2

A solves:

max (p-50)a

Bsolves:

max (p-50)b

Thermal A: 500 @ $50

a

Capacity 1000

lossless

(500-(a+b)/2-50)a

has maximum at

a = 450-b/2

(500-(a+b)/2-50)b has maximum at

b = 450-a/2

Thermal B: 500 @ $50

b

Load = 500 - p

slide17

(300,300)

Example of Cournot-Nash equilibrium

Load = 500 - p

Total load = 1000-2p

p = 500-(a+b)/2

A solves:

max (p-50)a

Bsolves:

max (p-50)b

$200

Thermal A: 500 @ $50

300

Capacity 1000

lossless

(500-(a+b)/2-50)a

has maximum at

a = 450-b/2

(500-(a+b)/2-50)b has maximum at

b = 450-a/2

Thermal B: 500 @ $50

300

$200

Load = 500 - p

slide18

Thermals each make profit of $45000.

Load decreases welfare by $56250.

Example of Cournot-Nash equilibrium

Price = $200

Load = 500 - p

$200

Thermal A: 500 @ $50

300

Deadweight loss is $11250 x 2

No flow in the line

Capacity 1000

lossless

Thermal B: 500 @ $50

300

$200

Load = 500 - p

slide19

What if the line has zero capacity?

Load = 500 - p

Each load = 500-p

p = 500-a

A solves:

max (p-50)a

Thermal A: 500 @ $50

a

Capacity 0

lossless

(500-a-50)a

has maximum at

a = 225

(500-b-50)b

has maximum at

b = 225

Thermal B: 500 @ $50

b

Load = 500 - p

slide20

What if the line has zero capacity?

Load = 500 - p

$275

Each load = 500-p

p = 500-a

A solves:

max (p-50)a

Thermal A: 500 @ $50

225

Capacity 0

lossless

(500-a-50)a

has maximum at

a = 225

(500-b-50)b

has maximum at

b = 225

Thermal B: 500 @ $50

225

$275

Load = 500 - p

slide21

Thermals each make profit of $50625.

What if the line has zero capacity?

Price = $275

Load = 500 - p

$275

Thermal A: 500 @ $50

225

Deadweight loss is $25312.50 x 2

Capacity 0

lossless

Thermal B: 500 @ $50

225

$275

Load = 500 - p

The transmission line has significant value in encouraging competition even though it might never transport any electricity.

does this matter in practice
Does this matter in practice?

Clause 10 of the Grid Investment Test states:

“Competition Benefits may be included in the market benefits of a proposed investment or alternative project if the Board reasonably considers this appropriate, provided the competition benefits can be separately identified and calculated”

NZElectricity Commission 2006, Grid Investment Test.

new zealand example downward 2007

AKL

CNI

SI

New Zealand example (Downward 2007)

Northland/Auckland

Demand

2010 – 2288 MW

2015 – 2631 MW

2020 – 2987 MW

Strategic Generators

Huntly + E3P (1413 MW)

Otahuhu B (390 MW)

Central North Island

Demand

2010 – 1794 MW

2015 – 1954 MW

2020 – 2109 MW

Strategic Generators

Waikato Hydro (776 MW)

Lower North Island and South Island

Demand

2010 – 3211 MW

2015 – 3492 MW

2020 – 3721 MW

Strategic Generators

Taranaki CC (365 MW)

Waitaki Hydro (2718 MW)

Clutha Hydro (1000MW)

slide24

New Zealand example

Source: Anthony Downward, EPOC

slide25

Incentives for wind generation

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

Thermal B: 400 @ $50

Load 500

Source: Geoff Pritchard, EPOC WW2007

slide26

Least-cost dispatch

100

150

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

250

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

200

50

Thermal B: 400 @ $50

Load 500

The best solution, on the assumption that the wind forecast is accurate.

Source: Geoff Pritchard, EPOC WW2007

slide27

Wind above forecast

100

150

Wind: 120 actual, @ $0

Thermal A: 400 @ $45

spill 20

250

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

200

50

Thermal B: 400 @ $50

Load 500

Wind is spilled – cheap energy is lost.

Source: Geoff Pritchard, EPOC WW2007

slide28

Wind below forecast

80

150

Wind: 80 actual, @ $0

Thermal A: 400 @ $45

230

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

220

50

Thermal B: 400 @ $50

Load 500

Wind shortfall is made up with expensive water.

Source: Geoff Pritchard, EPOC WW2007

are better forecasts needed
Are better forecasts needed?

Electricity Commission WGIP report June 2007

slide30

A flexible dispatch

100

125

Wind: 100 forecast, @ $0

Thermal A: 400 @ $45

225

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

175

100

Thermal B: 400 @ $50

Load 500

  • Spare capacity on transmission line.
  • Spare capacity in cheap hydro offer.

Source: Geoff Pritchard, EPOC WW2007

slide31

Wind above forecast

120

125

Wind: 120 actual, @ $0

Thermal A: 400 @ $45

245

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

155

100

Thermal B: 400 @ $50

Load 500

Surplus wind is matched to hydro decrease.

Source: Geoff Pritchard, EPOC WW2007

slide32

Wind below forecast

80

125

Wind: 80 actual, @ $0

Thermal A: 400 @ $45

205

Capacity 250

lossless

Hydro: 200 @ $30,

200 @ $90

195

100

Thermal B: 400 @ $50

Load 500

Lack of wind is matched by hydro.

Source: Geoff Pritchard, EPOC WW2007

slide33

Optimizing dispatch as a stochastic LP

Generators offer to sell quantities qi , ask prices pi ,regulation margins ri

We find dispatches xi and Zi to

minimize S (pi xi + E[ (pi +ri)(Zi - xi)+ - (pi -ri)(Zi - xi)- ] )

(expected cost of power, at offered prices, including re-dispatch)

so that

  • demand is met (at both 1st and 2nd stages)
  • transmission network is operated within capacity
  • (xi , Zi ) satisfy plant constraints

Source: Geoff Pritchard, EPOC WW2007

slide34

Example

Wind: capacity 40, @ $0

scenarios0, 10, 20, 30

probabilities0.5, 0.2, 0.2, 0.1

Hydro 1: 40 @ $39 (+/- $2)

Hydro 2: 40 @ $40 (+/- $5)

Load 60

  • Ensemble forecast for wind. Most likely scenario is 0.
  • Hydros compete on both energy and regulation.
  • What to dispatch?

Source: Geoff Pritchard, EPOC WW2007

slide35

Optimal hedged dispatch (initial)

Wind: capacity 40, @ $0

scenarios0, 10, 20, 30

probabilities0.5, 0.2, 0.2, 0.1

30

Hydro 1: 40 @ $39 (+/- $2)

10

20

Hydro 2: 40 @ $40 (+/- $5)

Load 60

  • Hydros dispatched “out of order” to keep regulation cost down.

Source: Geoff Pritchard, EPOC WW2007

slide36

Optimal hedged re-dispatch

Wind: capacity 40, @ $0

scenarios0, 10, 20, 30

probabilities0.5, 0.2, 0.2, 0.1

Hydro 1: 40 @ $39 (+/- $2)

0, 10, 20, 30

40, 30, 20, 10

Hydro 2: 40 @ $40 (+/- $5)

20

Load 60

  • Hydro 1 wins the regulation business.

Source: Geoff Pritchard, EPOC WW2007

slide37

Initial dispatch prices

  • p – the marginal cost of an additional unit of load

in the initial dispatch.

  • This is an appropriate price at which to trade energy,

where that energy was present in the initial dispatch.

  • Applies to:
    • inflexible load and generation
    • some flexible and intermittent generation

Source: Geoff Pritchard, EPOC WW2007

slide38

Re-dispatch prices

  • pR– the marginal cost of an additional unit of load

in a re-dispatch.

  • This is an appropriate price at which to trade energy,

where that energy was added in a re-dispatch.

  • Applies to:
    • some flexible and intermittent generation (both hydro & wind)

Source: Geoff Pritchard, EPOC WW2007

slide39

Example: initial dispatch prices

Wind: capacity 40, @ $0

scenarios0, 10, 20, 30

probabilities0.5, 0.2, 0.2, 0.1

30

Hydro 1: 40 @ $39 (+/- $2)

10

20

Hydro 2: 40 @ $40 (+/- $5)

$40

Load 60

  • Marginal additional load would be met by Hydro 2.
  • The quantities xi are sold @ $40; load pays $40.

Source: Geoff Pritchard, EPOC WW2007

slide40

Example: re-dispatch prices

Wind: capacity 40, @ $0

scenarios0, 10, 20, 30

probabilities0.5, 0.2, 0.2, 0.1

Hydro 1: 40 @ $39 (+/- $2)

0, 10, 20, 30

40, 30, 20, 10

Hydro 2: 40 @ $40 (+/- $5)

10

30

20

$41, $41, $37, $37

Load 60

  • 1st scenario: Wind buys back 10 @ $41; Hydro 1 sells 10 @ $41
  • 2nd scenario: no re-dispatch
  • 3rd scenario: Wind sells 10 @ $37; Hydro 1 buys back 10 @ $37
  • 4th scenario: Wind sells 20 @ $37; Hydro 1 buys back 20 @ $37

Source: Geoff Pritchard, EPOC WW2007

slide41

Average selling prices

Wind: capacity 40, @ $0

scenarios0, 10, 20, 30

probabilities0.5, 0.2, 0.2, 0.1

Hydro 1: 40 @ $39 (+/- $2)

0, 10, 20, 30

40, 30, 20, 10

Hydro 2: 40 @ $40 (+/- $5)

20

$41, $41, $37, $37

Load 60

  • Average selling price achieved
  • = (expected revenue) / (expected generation)
  • Wind: $38.11
  • Hydro 1: $40.55
  • Hydro 2: $40

Source: Geoff Pritchard, EPOC WW2007

a price for uncertainty
A price for uncertainty
  • Prices earned by less predictable wind generation are lower on average.
  • Prices earned by flexible generation are higher on average.
  • Prices paid by less predictable loads are higher on average.
  • New wind generation that decreases variation will increases price for all.
  • Revenue adequate dispatch model means that wind backup can be suitably rewarded.
emissions trading
Emissions trading
  • NZ ETS is a cap-and-trade scheme.
  • How can generators act strategically in this setting?
  • Little work done here, but see e.g. Chen, Hobbs et al 2007.
  • Example conjecture: withholding generation decreases emissions so that emission permits become cheaper, and so are acquired by competitive firms who will increase output in equilibrium.
  • Alternative is a carbon tax.
  • Example conjecture: A $20/MWh carbon tax on thermal plant just increases the consumer’s price by $20/MWh with windfall to hydro.
  • Try this out with a very stylized example…
slide44

Example: Least-cost dispatch

Load = 500 - p

Expect the price to be $50

a=450

b=450

Line contains no flow.

Thermals make no profit.

Load has high welfare.

$50

Thermal A: 500 @ $50

a

Capacity 1000

lossless

Hydro B: 500 @ $50

b

$50

Load = 500 - p

slide45

360

70

500

Least-cost dispatch with CO2 tax

Load = 500 - p

$70

Thermal A: 500 @ $50

plus $20 CO2 tax

Capacity 1000

Hydro B: 500 @ $50

$70

Load = 500 - p

Price increases by $20. The carbon tax has been transferred to consumers.

Hydro B makes $10000 profit.

slide46

(300,300)

Cournot-Nash equilibrium

Load = 500 - p

Total load = 1000-2p

p = 500-(a+b)/2

A solves:

max (p-50)a

Bsolves:

max (p-50)b

$200

Thermal A: 500 @ $50

300

Capacity 1000

lossless

(500-(a+b)/2-50)a

has maximum at

a = 450-b/2

(500-(a+b)/2-50)b has maximum at

b = 450-a/2

Hydro B: 500 @ $50

300

$200

Load = 500 - p

slide47

273

(273,313)

20

313

Cournot-Nash equilibrium with CO2 tax

Load = 500 - p

Total load = 1000-2p

p = 500-(a+b)/2

A solves:

max (p-50+20)a

Bsolves:

max (p-50)b

$206.66

Thermal A: 500 @ $50

plus $20 CO2 tax

Capacity 1000

(500-(a+b)/2-70)a

has maximum at

a = 430-b/2

(500-(a+b)/2-50)b has maximum at

b = 450-a/2

Hydro B: 500 @ $50

$206.66

Load = 500 - p

Price increases by only $6.66.

the takeaways
The takeaways
  • Markets are intended to provide incentives for agents to make optimal decisions.
  • Understanding these is essential to formulating energy policy.
  • For a poor market design, strategic behaviour might make decisions inefficient.
  • Regulation is intended to restore some efficiency.
  • Nash equilibrium models are indispensible in understanding whether incentives and or regulation will deliver the desired outcomes.
the last word is incentives
The last word is incentives

Robert Aumann

Nobel Prize Lecture

December 8, 2005