Value of Forecasts in Unit Commitment Problems

Transcription

1 Tim Schulze, Andreas Grothery and School of Mathematics

2 Agenda Motivation Unit Commitemnt Problem British Test System Forecasts and Scenarios Rolling Horizon Evaluation Comparisons Conclusion

3 Our Motivation - Wind Power Uncertainty Increasing supply from volatile renewable sources predictability problem Green UK goal: 30GW installed capacity of wind by How much would knowing the wind generation profile 48 hours ahead reduce national generaton costs? What is added value of stochastic models over deterministic ones?

4 Unit Commitment Problem: Deterministic 24h ahead minimum cost schedules (on/off and production) Constraints: demand-generation balance, spinning reserve, up/downtimes, ramp rates Large MILP, solve by B&B Load Wind = Thermal + Water Gen Capacity of Thermal + Water Gen Min Up Min Down Time

5 Unit Commitment Problem: Stochastic Multiple scenarios with different residual loads (after wind) Tree structure: scenario information revealed over time Problem: size of the model increases quickly in the number of scenarios. Use a scenario decomposition solution approach Load Wind = Thermal + Water Gen Capacity of Thermal + Water Gen Notification > Heating Min Up Min Down Time

6 Supply Demand Gas Coal Nuclear Renewable Wind Demand

7 British Test System: Overview Centrally operated model of the expected 2020 British National Grid Minimise levelised cost including CO2, with markup for capital, O&M and decommissioning cost Z1 Z4 Z3 Z5 Z6 Z2 Z7 130 conventional generators NI 160 wind farms 30% installed capacity Pump storage: 2 Scotland, 2 Wales IE Z9 Z8 Z11 Z10 Z12 Interconnectors: Ireland, France, Netherlands Z13 Z17 Z16 Z14 Z15 FR NL

8 British Test System: Transmission B1 17 nodes, corresponding to National Grid study zones 27 transmission links, only real power variables, no losses, no phase angles transmission limits: single line and boundary import/export constraints local generation/demand, but global reserve B1 B2 B3 B3 B4 NI IE Z1 Z4 Z3 Z5 Z6 B5 B6 B7 B11 B16 Z2 B2 B4 B5 B6 Z7 Z8 Z9 B7 Z10 B11 B8 B16 B9 B8 B17 Z11 B9 B12 Z12 Z13 B14 Z14 B15 B10 B13 Z17 Z16 Z15 B13 B10 B12 B15 FR NL

9 British Test System: Flexibility Wind generation is unpredictable. Flexibilty to deal with this comes from: Ability to ramp up and down generators Start fast-start units B3 B1 B2 B3 B4 B5 Z1 Z3 Z5 Z4 Z6 B1 Z2 B4 Z7 B2 B5 B6 Use pump storage NI B6 B7 Eat into the response (15sec) margin Eat into reserve (20 min) margin. IE B7 B11 B16 Z9 Z8 Z10 B11 B8 B16 B9 B8 B17 Z11 B12 B9 Z12 Z13 B14 Z14 B15 B10 B13 Z17 Z16 Z15 B13 B10 B12 B15 FR NL

10 60 Demand Wind Power GW LMPs ($/MWh) Z1 Z2 Other Stored: GWh 10 5 Z1 Z4 Z Days (based on scaled up Jan 2010 wind and demand with perfect foresight)

11 Forecast & Scenario Simulation: Overview Required: Available: historic wind data historic point forecasts scenarios historic regional wind speeds scenario generation techniques for forecast errors Point forecasts need to be synthesized

12 Forecast & Scenario Simulation: Overview Required: Available: historic wind data historic point forecasts scenarios historic regional wind speeds scenario generation techniques for forecast errors Point forecasts need to be synthesized

13 Forecast & Scenario Simulation: Overview Required: Available: historic wind data historic point forecasts scenarios historic regional wind speeds scenario generation techniques for forecast errors Point forecasts need to be synthesized

14 Synthesizing Point Forecasts State of the art wind power forecasts combine NWP and TS models Our forecasts should match their error statistics Step 1: Get Pattern Forecasts as average of matching past wind patterns Step 2: Pattern Forecasts are unreliable 6h ahead, so use weighted average of pattern forecast and shifted real wind Synthesised Forecast 20% Error [% Installed Capacity] 15% 10% Persistence 5% PatternFC Synthesised 0% Hours ahead Error statistics of forecasts for the year 2010.

15 Synthesizing Point Forecasts State of the art wind power forecasts combine NWP and TS models Our forecasts should match their error statistics Step 1: Get Pattern Forecasts as average of matching past wind patterns Step 2: Pattern Forecasts are unreliable 6h ahead, so use weighted average of pattern forecast and shifted real wind Synthesised Forecast 20% Error [% Installed Capacity] 15% 10% Persistence 5% PatternFC Synthesised 0% Hours ahead Error statistics of forecasts for the year 2010.

16 Scenario Simulation and Selection 1. Once point forecasts are available, fit correlated ARMA(1, 1) models to regional error time series 2. Simulate 500+ error scenarios 3. Add errors to point forecasts, translate wind speeds to load factors 4. Select scenarios and merge into a tree Example selecting six scenarios in the region North Wales.

17 Scenario Simulation and Selection 1. Once point forecasts are available, fit correlated ARMA(1, 1) models to regional error time series 2. Simulate 500+ error scenarios 3. Add errors to point forecasts, translate wind speeds to load factors 4. Select scenarios and merge into a tree Example selecting six scenarios in the region North Wales.

18 Rolling Horizon Evaluation Procedure Schedule: Get system state (state) and wind forecast (wf). Schedule: Generate a 24 hour schedule starting 3,6 or 8 hours ahead Dispatch: Get current wind forecast and state and most recent schedule Dispatch. Adjust the generator outputs and commitment of flexible generators to match actual wind state, wf C Scheduling Procedure Schedule 24h schedule Dispatch Procedure state, wf Dispatch 24h schedule state, wf state, wf C Schedule 24h schedule Dispatch 24h schedule state, wf state, wf C schedule Schedule 24h schedule Dispatch 24h state Time Time

19 Rolling Evaluation: 3 hour schedule revision Use the wind forecast from three hours ago, solve det. model... or a stochastic model. Fix first stage commitments. Realize three hours of real wind, adapt OCGT, PS, shed load, remaining reserve. Beyond three hours use the next forecast. Roll three hours forward and repeat.

20 Rolling Evaluation: 3 hour schedule revision Use the wind forecast from three hours ago, solve det. model... or a stochastic model. Fix first stage commitments. Realize three hours of real wind, adapt OCGT, PS, shed load, remaining reserve. Beyond three hours use the next forecast. Roll three hours forward and repeat.

21 Rolling Evaluation: 3 hour schedule revision Use the wind forecast from three hours ago, solve det. model... or a stochastic model. Fix first stage commitments. Realize three hours of real wind, adapt OCGT, PS, shed load, remaining reserve. Beyond three hours use the next forecast. Roll three hours forward and repeat.

22 Rolling Evaluation: 3 hour schedule revision Use the wind forecast from three hours ago, solve det. model... or a stochastic model. Fix first stage commitments. Realize three hours of real wind, adapt OCGT, PS, shed load, remaining reserve. Beyond three hours use the next forecast. Roll three hours forward and repeat.

23 Comparisons How does total cost depend on the combination of: Frequency of revising the schedule 24h: Reschedule every 24h using forecast 8-32h ahead 6h: Reschedule every 6h using forecast 6-30h ahead 3h: Reschedule every 3h using forecast 3-27h ahead Scheduling method Perf: Det: Perfect foresight: use actual wind Deterministic: use synthetic wind forecast and extra reserve margins based on a range of percentages of forecast wind Stoch: Stochastic: use a tree of 12 wind scenarios generated from synthetic forecasts In all cases the evaluation uses 2 years data and dispatch is repeated every 3 hours The dispatch uses actual wind for 3 hours + forecast for next 21 hours.

24 Cost Comparison: 3,6 and 24h Rolling, Stoch vs Det Daily average cost $98M $97M $96M 24h Det 24h Stoch 6h Det 6h Stoch 3h Det 3h Stoch Perfect $95M Deterministic reserve margin (GW)

25 Cost Breakdown: Stoch vs Det 6h Rolling Daily average cost $96M $95.5M $95M Deterministic 6h Load Res OCGT Gen Stochastic 6h $94.5M Deterministic reserve margin (GW)

26 Cases: all 3 hour revisions Pat: Normal network, Pattern forecast Norm: Normal network, Sythesized forecast Z1: 2 extra pump systems in Z1 Daily average cost $95.6M $95.4M $95.2M $95M $94.8M Best Deterministic Stochastic Perfect Z4: Double pump capacity in Z4 NoN: No network constraints NoS: No pump storage $94.6M $94.4M Pat Norm Z4 Z1 NoN NoS Case

27 Conclusion Need to evaluate data in context of decisions using it. Value of perfect forecast was $350k-$1200 daily for 3-24h updates Synthesised forecast was $75k cheaper than Pattern forcast. Compared to deterministic scheduling with best reserve margins, stochastic scheduling saved $100k-$300k daily for 3-24h updates Cost depends significantly on the frequency at which commitments are revised. Don t know how muchof the gap to Perfect would close state of the art forecasts better scenario trees generation methods

28 Conclusion Need to evaluate data in context of decisions using it. Value of perfect forecast was $350k-$1200 daily for 3-24h updates Synthesised forecast was $75k cheaper than Pattern forcast. Compared to deterministic scheduling with best reserve margins, stochastic scheduling saved $100k-$300k daily for 3-24h updates Cost depends significantly on the frequency at which commitments are revised. Don t know how muchof the gap to Perfect would close state of the art forecasts better scenario trees generation methods

29 Expected Loss Costs for Reserve and Response shedding Besides wind, major uncertainty are failures (assume independent) Expected loss based cost, assuming generators fail every 150 days Planning: Stochastic models treat reserve as soft constraint Response $500k Response & Reserve $400k $15k $300k $10k $200k $100k $5k $0k $0k 0 1,500 3,000