Dr. Geoffrey Pritchard

1
Dispatch Pricing
with Uncertainty Intermittency

• Dr. Geoffrey Pritchard
• University of Auckland

2
NZ has a large wind resource

• 500 MW now installed or committed.
• many more sites under investigation or seeking
  consents.
• 3000 MW potential
• but this ignores system integration issues.

3
Wind is unpredictable and variable

• Wind forecast error exceeds load forecast error
  in NI with gt370 MW wind.
• (WGIP, 2 hour forecasts, 1-month return
  period events)
• Wind variability is about half of load
  variability in NI with 1600 MW wind.
• (WGIP, 10 sec or 5 min periods, 1-month
  return period events)

4
Accommodating uncertainty (wind and
load)

• Processes
• 5-minute re-dispatch
• Frequency-keeping
• Technologies
• Hydro
• Fast gas turbine
• Responsive loads (EV battery charging?)

5
Wind/hydro matching

• Why not pair off each wind farm with a hydro?
• transmission implications if not co-located.
• doesnt make full use of hydro flexibility.
• doesnt allow wind farms to match with each
  other.
• Matching might be done better at the power system
  level.

6
The dispatch process (at present)
-2hr
0
30min

• Generator offers close
• Loads, wind forecast
• SPD run to find optimal dispatch

• Actual loads, wind
• SPD re-dispatch every 5 min
• Frequency-keepers adjust continuously

7

• Could the system operation / market be extended
  to treat uncertainty optimally?

8
Example
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
Thermal B 400 _at_ 50
Load 500

• Wind forecast may be inaccurate.
• Hydro can be re-dispatched in response, thermals
  cant.
• What to dispatch?

9
Least-(forecast)-cost dispatch
100
150
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
The best solution, on the assumption that the
wind forecast is accurate.
10
Wind above forecast
100
150
Thermal A 400 _at_ 45
Wind 120 actual, _at_ 0
spill 20
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
Wind is spilled cheap energy is lost.
11
Wind below forecast
80
150
Thermal A 400 _at_ 45
Wind 80 actual, _at_ 0
230
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
220
50
Thermal B 400 _at_ 50
Load 500
Wind shortfall is made up with expensive water.
12
Better forecasting?

• Forecast errors in either direction incur high
  penalties
• so smaller errors would certainly help.
• Can the penalties themselves be reduced?

13
Hedging vs. uncertainty
100
125
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
225
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
175
100
Thermal B 400 _at_ 50
Load 500

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

14
Wind above forecast
120
125
Thermal A 400 _at_ 45
Wind 120 actual, _at_ 0
245
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
155
100
Thermal B 400 _at_ 50
Load 500
Surplus wind is matched to hydro.
15
Wind below forecast
80
125
Thermal A 400 _at_ 45
Wind 80 actual, _at_ 0
205
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
195
100
Thermal B 400 _at_ 50
Load 500
Surplus wind is matched to hydro.
16
Hedged vs. conventional dispatch
100
125 (25 less)
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
225 (25 less)
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
175 (25 less)
100 (50 more)
Thermal B 400 _at_ 50
Load 500

• Adjustment Thermal A -gtThermal B costs 5,
• but allows chance to save water worth 30.
• Adjustment Hydro -gtThermal B costs 20,
• but allows chance to save 60 on water.

17
Is the hedged dispatch better?

• Depends on the probabilities involved.
• The more uncertainty in the wind, the more
  hedging will be worthwhile.

18

• Allowing for uncertainty in one offer (or load)
  affects the dispatch of other offers, even those
  that are not uncertain themselves.

19
What not to conclude from the example

• Hedged dispatch means higher thermal fuel burn.
• Other, similar examples adjust dispatch away from
  thermals.
• The transmission network is the essential
  element.
• Other, similar examples have one node, no lines.

20

• Could the system operation / market be extended
  to treat uncertainty optimally?

21
Market principles There is only one market

• No separate day-ahead and regulating market
• (as in Nordpool etc.)
• No separate markets for ancillary services.
• Exception the present frequency-keeping auction.
• Not an exception instantaneous reserve
  (co-optimized).
• A generator shouldnt have to choose which market
  to offer into.
• Potential arbitrage, illiquidity, market power
  issues.

22
Instantaneous reserve

• IR is insurance against truly rare events.
• Includes the effect of exceptional weather on
  wind farms
• But not most wind fluctuations.

23
Optimizing dispatch (conventional)

• Generators offer to sell tranches qi, ask prices
  pi
• We find dispatches xi to
• minimize S pi xi (cost of power,
  at offered prices)
• so that
• demand is met
• transmission network is operated within capacity
• 0 lt xi lt qi

24
Optimizing dispatch (hedged)

• One approach
• Generators offer to sell tranches qi, asking
  prices pi
• We find dispatches
• xi (1st stage initial dispatch)
• Zi (2nd stage real-time, contingent on random
  events)
• Three kinds of offer
• Inflexible (thermal), no re-dispatching, Zi
  xi
• Flexible (hydro), arbitrary re-dispatching, 0lt
  xi lt qi, 0lt Zi lt qi
• Intermittent (wind), 0lt xi lt qi, 0lt Zi lt Si
  (random)

25
Optimizing dispatch (hedged)

• Generators offer to sell tranches qi, ask prices
  pi
• Flexible plant may also offer
• to sell additional power via re-dispatch, ask
  price pi ri
• to buy back power via re-dispatch, bid price pi -
  ri
• where ri is a regulation margin.

26
Optimizing dispatch (hedged)

• Generators offer to sell tranches 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

27
Example
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)
Hydro 2 40 _at_ 40 (/- 5)
Load 60

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

28
Optimal hedged dispatch (initial)
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)
30
10
20
Hydro 2 40 _at_ 40 (/- 5)
Load 60

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

29
Optimal hedged re-dispatch
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)
0, 10, 20, 30
40, 30, 20, 10
Hydro 2 40 _at_ 40 (/- 5)
20
Load 60

• Hydro 1 wins the regulation business.

30
Market pricing (conventional)

• Conventional spot price the marginal cost of a
  unit of additional load.
• This is an appropriate price at which to trade
  spot energy.
• This already varies by
• location (in the network)
• time (of day).

31
Market pricing (hedged)

• We have now introduced an economic distinction
  between
• initial dispatch and re-dispatch.

32
Initial dispatch prices

• pn the marginal cost of an additional unit of
  load at node n
• 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

33
Re-dispatch prices

• pnR the marginal cost of an additional unit of
  load at node n
• 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)

34
Example initial dispatch prices
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)
30
10
20
Hydro 2 40 _at_ 40 (/- 5)
40
Load 60

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

35
Example re-dispatch prices
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)
0, 10, 20, 30
40, 30, 20, 10
Hydro 2 40 _at_ 40 (/- 5)
20
41, 41, 37, 37
Load 60

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

36
Average selling prices
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)
0, 10, 20, 30
40, 30, 20, 10
Hydro 2 40 _at_ 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

37
Example multiple wind farms
Wind 1 capacity 100, _at_ 0 scenarios 40, 40, 45,
55, 50, 50, 50, 60
Thermal 100 _at_ 58
Hydro 30 _at_ 40 (/- 4) 60 _at_ 60
(/- 4)
Wind 2 capacity 100, _at_ 0 scenarios 40, 50, 50,
60, 50, 55, 60, 60
Wind 3 capacity 100, _at_ 0 scenarios 45, 50, 60,
50, 45, 55, 40, 55
Load 300
equally likely scenarios
38
Correlations between wind farms
Wind 2
Wind 3
Wind 3
Wind 1
Wind 2
Wind 1

• Wind 1 and Wind 2 are somewhat correlated
• Wind 3 is relatively uncorrelated

39
Initial dispatch
Wind 1 capacity 100, _at_ 0 scenarios 40, 40, 45,
55, 50, 50, 50, 60
Thermal 100 _at_ 58
95
50
Hydro 30 _at_ 40 (/- 4) 60 _at_ 60
(/- 4)
50
58
Wind 2 capacity 100, _at_ 0 scenarios 40, 50, 50,
60, 50, 55, 60, 60
55
50
Wind 3 capacity 100, _at_ 0 scenarios 45, 50, 60,
50, 45, 55, 40, 55
Load 300
equally likely scenarios

• Hydro is dispatched ahead of thermal to
  facilitate regulation.
• Thermal is marginal at 58.
• In some scenarios, the wind farms can trade with
  each other.
• Average overall selling prices achieved
• Thermal 58, Hydro 59.01,
• Wind 1 57.54, Wind 2 57.60, Wind 3
  57.80

40
Revenue adequacy

• Conventional
• (Total payments received from loads)
• minus
• (Total payments to generators)
• gives a non-negative surplus. (Loss
  constraint rental.)
• The same is true with optimal hedged dispatch
  and re-dispatch pricing, in all
  scenarios.

41
Another example
Thermal 2 100 _at_ 45
Wind 2 60 _at_ 0
Wind 1 60 _at_ 0
Hydro 50 _at_ 42 (/- 10) 60 _at_ 80
(/- 10)
Thermal 1 100 _at_ 40
capacity 150
Load 264
Wind farms treated as deterministic (i.e.
accurately forecast).
42
Conventional dispatch
Thermal 2 100 _at_ 45
0
Wind 2 60 _at_ 0
60
60
Wind 1 60 _at_ 0
41
41.5
40.5
99
Hydro 50 _at_ 42 (/- 10) 60 _at_ 80
(/- 10)
Thermal 1 100 _at_ 40
45
40
42
42.5
capacity 150
Load 264
Spring washer effect a very constrained
solution.
43
Hedged version of the problem
Thermal 2 100 _at_ 45
Wind 1 capacity 100, _at_ 0 scenarios 30, 50, 60,
70, 90 equally likely
Wind 2 capacity 100, _at_ 0 scenarios 30, 50, 60,
70, 90 equally likely
Hydro 50 _at_ 42 (/- 10) 60 _at_ 80
(/- 10)
Thermal 1 100 _at_ 40
capacity 150
Wind farms independent
Load 264
Ensemble forecast for wind farms. Note 60 is
still the best forecast for each wind farm.

44
Hedged dispatch and pricing
Thermal 2 100 _at_ 45
45 (45 more)
Wind 1 capacity 100, _at_ 0 scenarios 30, 50, 60,
70, 90 equally likely
Wind 2 capacity 100, _at_ 0 scenarios 30, 50, 60,
70, 90 equally likely
60
60
45
42.5
47.5
69 (30 less)
Hydro 50 _at_ 42 (/- 10) 60 _at_ 80
(/- 10)
Thermal 1 100 _at_ 40
40
50
52.5
capacity 150
30 (15 less)
Load 264

• Hydro dispatch is reduced to avoid the risk of
  using 80 water.
• Line is not at capacity (it carries 145)
• - this facilitates regulation by maintaining
  flexibility.
• Prices anticipate a possible spring-washer upon
  re-dispatch.

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Dispatch Pricing
with Uncertainty Intermittency

• Dr. Geoffrey Pritchard
• University of Auckland