1. Wind Power & Grid Operation Dr. Geoffrey Pritchard University of Auckland

2. Wind forecasting Generation dispatched 2 hours in advance of real time. Forecasts used for loads, wind. Re-dispatch / frequency-keeping required when forecasts turn out to be wrong. Need to understand probability distribution of forecast error.

3. Centralised Data Set Electricity Commission data. Includes half-hourly metered output by all power stations, including wind farms. Useful data for –Tararua I (4 years), I+II (3.8 years), III (8 months) –Te Apiti (3.4 years) –Hau Nui (2 years) –White Hill (6 months)

6. Unforecasted component of wind The relevant quantity for grid operation is Unforecasted output = (actual output) – (forecast output) Forecast is usually simple persistence (i.e. forecast no change).

7. Simple persistence forecast @ -2hr -2hr 0+30min Generator offers close Wind forecast is actual output in TP-5 Actual wind observed TP TP-1TP-2TP-3TP-4TP-5 Unforecasted wind in TP = (output in TP) – (output in TP-5)

11. Scenario selection problem NZ wind farms: 6-30 distinct sites Need a tractable collection of model scenarios for unforecasted wind at all sites Historical data: too many/too few scenarios

12. Example: 2 sites Reduce the following to 5 model scenarios:

13. Example: 2 sites Reduce the following to 5 model scenarios:

14. 2 sites, transmission unconstrained Only the total unforecasted output matters – so we really have only 3 scenarios

15. 2 sites, transmission unconstrained An improvement – 5 different scenarios

16. Optimal dispatch problem (SPD) Generators offer to sell tranches q i, asking prices p i We find dispatches x i to minimize  p i x i (cost of power, at offered prices) so that –(forecast) demand is met –transmission network is operated within capacity –0 < x i < q i

17. Deterministic dispatch problem minimize x c(x) (dispatch decision) (Cost of dispatch, valuing power at offered prices.)

18. Stochastic dispatch problem minimize x E[ c(x,W) ] (dispatch decision) (random wind/load outcome) (Expected cost of dispatch and re-dispatch.)

19. Example Hydro: 50 @ $42 60 @ $80 Load 264 Thermal B: 100 @ $45 Wind B: 60 @ $0 Wind A: 60 @ $0 Thermal A: 100 @ $40 capacity 150 Wind farm offers are forecasts only.

20. Dispatch solution Hydro: 50 @ $42 60 @ $80 Load 264 Thermal B: 100 @ $45 Wind B: 60 @ $0 Wind A: 60 @ $0 Thermal A: 100 @ $40 145/150 (different from the standard optimal dispatch) 45 30 69 60

24. Wasserstein distance Distance between a true probability distribution  and a model-scenario representation : d W (,) = E  [ distance to nearest model scenario ]

25. Wasserstein approximations are good for stochastic optimization in general, i.e. devoid of the context of a particular problem. Can adapt it for a more specific class of problems by re-defining the distance between scenarios. Wasserstein distance

27. First solve the dispatch problem using only forecast wind (SPD). Then generate relevant model scenarios for unforecasted wind at all sites. Now re-solve allowing for re-dispatch costs created by the model scenarios (robust solution). A way forward?

28. Dr. Geoffrey Pritchard University of Auckland Wind Power & Grid Operation

29. NZ has a large wind resource 500 MW now installed or under construction –many more sites under investigation or seeking consents. 3000+ MW potential –but this ignores system integration issues.