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A simplified approach for optimizing hydropower generation scheduling. Frode Kjærland & Berner Larsen Bodø Graduate School of Business at the University of Nordland IAEE – Stockholm, Sweden , June 21 st 2011. Background.
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A simplified approach for optimizing hydropower generation scheduling Frode Kjærland & Berner Larsen Bodø GraduateSchoolof Business at the University of Nordland IAEE – Stockholm, Sweden, June 21st 2011
Background • Optimizing hydropower scheduling for a small producer in a Nordic context • Hydropower producers face a number of dynamic factors which affect short term production planning. • Each day a decision has to be made concerning if and which of the 24 hours the consecutive day one commits generation • Short term planning is also coupled to more long-term planning • Peak load producer has to pick the hours with highest prices • Adapt to uncertainty in prices (fluctuate over the day, week, season and years). Also uncertainty in precipitation, reservoir level, risk of flood
Background and relatedresearch • The physical Nordic electricity market • Regulation • ”One dayahead” – market, Nord Pool Spot • The industryoptimizeaccording to industry software (typicallybasedonFosso et. al.,1999) • Therearedifferentdynamicmanagementtools (Hong Ling et. al.,2008; Fleten & Wallace ,2001) • Obvious benefit in postponing generation to high price seasons (Näsäkkälä & Keppo, 2008) • A small participant with less resources and competence needs simpler rules
The Model • The model presented is based on a P-value which decides whether to produce the actual hour the following day or not. • The P-value indicates a percentile of the sorted hourly prices that are in the lagged database. • When the spot price of NO4 (area price in Northern Norway) a current day is greater than the lower100P % percentile of the spot price of NO4 for the last two years, the producer will commit a bid for this hour (with full capacity) - and visa versa. • P indicates percentile, meaning that if, for example, P = 0.6, the model will calculate the 60% percentile of the Z Spot prices for NO4 for the last 17.520 hours. This means that all spot prices <Z constitute 60% of spot prices for NO4 in this period.
More modeldescription • If the turbine capacity implies that we have to produce only 100p % of the hours each year on the average, we try to pick the hours which have the 100p % highest prices. • We do this by computing the 100(1-p) % lower percentile Q of the hourly spot prices of NO4 the last two years (17 520 hours). • We compute the percentile Q by sorting these 17 520 numbers in ascending order. Let xi be the ith of these numbers, i = 1; : : ; 17 520. If (1-p)17519 is an integer, then Q = x1+(1-p)17519. If not, we use linear interpolation between x˪1+(1-p)17519˩ and x˹1+(1-p)17519˥ to find Q. • If the spot price is larger than Q, the producer will commit a bid for this hour tomorrow, and vice versa. • In this way we try to achieve that production is only in the hours with the 100p % highestprices. • For each of the 24 hours the current hourly price is compared to the percentile Q explained above.
Data – samplepower plants • Small producer (price taker) which control (parts) of two hydropower plants, A and B, located in the price area NO4 (Northern Norway) • The plants are “virtual” power plants. Hence, they can produce according to full capacity and not “best point”
Data II • We have used the following data to conduct simulations (programmed in R). The data is collected from the producer and Nord Pool Spot: • Characteristics of the actual power plants; A and B.• Production data for the power plants 2002-2009 - hourly level.• Data for inflow and water reservoir levels of plant A and B.• Income from the same period – also on hourly level.• Spot price data - area price (NO4) (hourly rates) for 2000-09. • The simulations are conducted from 07/01/2002 through to 12/27/2009, i.e. 416 weeks. • For each of the 24 hours the current hourly price is compared to the accumulated prices of the lagged hourly prices from the last two years (17.520 hours).
KEY ASPECT OF THE MODEL • The plants have to possess considerable flexibility both in reservoirs and turbine capacity to be suitable for this approach. • Minimum water reservoir level is set to 15 % (can easily be changed). • We make simulations on three types of strategy: • Applying the model for different P-values • Monday to Friday, September to April– hours 5-24 • All days – hours 1-7/22-24 (meaningless, but illustrative)
Discussion • Focusonachievedaverageprice (NOK/MWh) -correctedfor differentsimulated water reservoirlevels in the end oftheperiod • The modelcapturemuchofthe market dynamics. • The highestP-valuesprovidethehighestrevenue. The ”tougher” approch, the more is thehighestpricesexploited (Wolfgang et al., 2009) • Highvolatility in generetion/income – problematic for publicowners • The simulatedperiod (2002-09) is charachterized by increasingprices in general
Main findings • Simulatedachievedaveragepriceincreasewith14 % from evening/nights to peakloadonweeklybasis in Sept-April. • Simulatedachievedaverageprice is close to 20 % highercompared to theMonday-Friday 5-24 strategy. • Therearesignificantgains in applyingthemodelcompared to actualgeneretion/income (10s of millions NOK)
Conclusions and Implications • The approachmay be (to someextent) difficult to implement for smallparticipants. • The approach do givehighvariation in income – however; feasablewhenhighturbinecapacity and highdegreeofregulation. • The modelassumesnobig, long lasting shocks. If so - themodel has to be modified.
