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

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.

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)

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).

Simple persistence -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)

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

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

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

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

2 sites, transmission unconstrained An improvement – 5 different scenarios

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

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

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

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

Dispatch solution Hydro: $42 $80 Load 264 Thermal B: $45 Wind B: $0 Wind A: $0 Thermal A: $40 145/150 (different from the standard optimal dispatch)

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

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

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?

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

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