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The Journal of Energy Markets (2343) Volume 5/Number 3, Fall 2012

A simplified approach for optimizing

hydropower generation scheduling

Frode Kjrland

Bod Graduate School of Business, University of Nordland, PO Box 1490,

8049 Bod, Norway; email: [email protected]

and

Trondheim Business School, Jonsvannsveien 82, 7004 Trondheim, Norway

Berner Larsen

Bod Graduate School of Business, University of Nordland, PO Box 1490,

8049 Bod, Norway; email: [email protected]

This paper presents a simplified model for optimizing hydropower scheduling for

a small producer with a high degree of flexibility. The approach involves selecting

the hours with the highest prices. The power plants run at full capacity all hours

of the next days when hourly spot prices are greater than the upper p percentile

of the hourly spot prices for the last two years (17 520 hours), and do not run

otherwise. The simulations foran eight-year period, 20029, show a considerable

increase in income. The producer can achieve 19% more income compared with

a more naive strategy of generating at peak hours on weekdays. Our simulations

also show that an optimal choice ofp is a value lower than the load factor of the

plants, due to the general increase in prices in the studied period.

1 INTRODUCTION

The purpose of this paper is to apply a simplified model for a hydropower producer

in order to optimize the generation scheduling for maximizing revenue. Hydropower

producers face a number of dynamic factors affecting short-term production planning.

Each day a decision has to be made concerning whether to operate and, if so, which

of the twenty-four hours of the next day one ought to commit to generation. However,

such short-term planning is also coupled with more long-term planning. We present

a simple model for a small participant controlling two plants with considerably large

reservoirs and relatively high turbine capacity and also suggest simple rules for

everyday decisions concerning the next day in order to increase profits.

We thank participants at the ElCarbonRisk seminar at Skeikampen in April 2011, participants at

the 34th IAEE conference in Stockholm in June 2011 and anonymous referees, including two

participants in the industry, for valuable comments.

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24 F. Kjrland and B. Larsen

Several approaches have been discussed in the literature to solve short-term oper-

ation scheduling problems for a hydropower producer in order to maximize revenue.

A peakload producer in the context of the Nordic electricity market has to pick the

hours with the highest prices. Prices fluctuate over the day, week, season and year.

Hence, the uncertainty in future precipitation, temperature, reservoir level, short- and

long-term prices, riskof flood, etc,has to be taken into account when making decisions

concerning generation scheduling.

1.1 Literature review

Optimization of hydropower generation has been addressed in several studies in the

researchliterature on the subject. Revenues fromhydropower generation are uncertain

due to the uncertainty regarding both price and production. The stochastic conditions

in the spot and forward prices, as wellas inflow andproduction capabilities, emphasize

the need to incorporate some form of dynamic management tool, which is discussedin general terms in, for example, Hongling et al (2008), Labadie and Stitt (2004),

Yamin (2004) and Fleten and Wallace (2002). Moreover, there are a number of studies

applying some type of mathematical programming, such as Chang et al (2001) and

Wang (2009). The approach that is most similar to the model presented in this paper

is the so-called peak-shaving method (see, for example, Simopoulos et al (2007)).

However, many of these studies concern the aggregate system level and do not focus

on the generator as the unit of analysis.

The different types of models make various simplifying assumptions in order to

reduce the complexity of hydropower scheduling. Furthermore, there is an abundance

of contexts relating to market environment, regulation and energy system. There are

also quite a few studies related to Norwegian hydropower production. Norway is the

worlds sixth largest hydropower producer, but, after Iceland, it is the country with the

highest percentage of total hydropower electricity production. It is therefore natural

that the optimization of hydropower generation has been the subject of several studies

in a Norwegian (and Nordic) context.

Because of all these issues, software has been used extensively to help produc-

ers adapt in order to maximize profits. Fosso et al (1999) conceptually describe an

approach where water valuecalculationsand forecasts of future spot prices are key ele-

ments in long-term, medium-term and short-term scheduling. Nskkl and Keppo

(2008) focus on the forward curve dynamics and show how forwardprices can be used

for postponing generation to high-price seasons. Their study includes an empirical

application to a Norwegian hydro producer. Recent studies concerning water schedul-

ing problems in a Spanish context, such as Prez-Daz et al (2010a,b), also include

forecasts of electricity prices. Their approaches are based on dynamic programming

and nonlinear programming, respectively. An empirical study of thirteen Norwegian

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A simplified approach for optimizing hydropower generation scheduling 25

hydropower producers (Fleten et al (2008)) also shows the extensive use of forward

price information in scheduling.

Our approach is fundamentally different. We do not incorporate any forward

price information, forecasts or observed prices from the financial market. The model

described in this paper leans on historical price information. Our model is also simpler

and itis unique because ofthe use ofthep percentile of the historical spot prices rather

than any type of linear/nonlinear programming or operation management. Still, the

results are useful for producers controlling reservoirs with a high degree of flexibility.

1.2 The Nordic electricity market

The Nordic electricity market, in particular the Norwegian electricity market, has

some special properties due to the dominance of hydro. In Norway, about 97% of

electricity generation is hydropower (about 50% in the Nordic countries overall).

The capacity in Norwegian reservoirs is about 84 TWh, representing about 70% ofnormalannual production (approximately 121 TWh).Hence, many generators possess

the flexibility to adapt so that more can be produced when prices are relatively high.

However, several risky aspects must be addressed, such as uncertain future prices,

uncertain inflows, uncertain production volume, risk of flooding and/or excessively

low water reservoir levels (governed by the regulation license).

The physical production of electricity is organized in two markets: the regulator

market and a day ahead market (Benth et al (2008)). Nord Pool Spot is the Nordic

power exchange for actual generation. It has evolved from being a Norwegian power

exchange to operating in Denmark, Finland and Sweden as well. Elspot is the market

for physical contracts and is an auction-based one day in advance market for each

hour of the following day. Approximately 70% of Nordic consumption is traded atElspot.

Each day, both buyers and sellers submit prices and volumes for each of the twenty-

four hours of the following day. This market closes at 12 noon everyday. On this basis,

a derived price is set for each of the twenty-four hours of the following day. Because

of constraints in the grid, these prices can be different in the different price zones. 1

The average price is the so-called system price (which assumes no bottlenecks in the

system and is therefore a theoretical national spot price). Strictly speaking, the spot

price is a forward contract with delivery in a specific hour the next day.

The financial market is operated by NASDAQ OMX (formerly Eltermin). This is a

different arena to the physical markets. In this market there are a significant number of

futures and forward contracts ranging from several weeks to five years ahead (Nord

Pool (2009)). These contracts are settled against the system price in the delivery

1 Norway was divided up into five areas in 2011.

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FIGURE 1 Spot price (area price) of NO4 in 20029.

100

200

300

400

500

Month

NOK/MWh

01/2002 01/2004 01/2006 01/2008 12/2009

Monthly average (ninety-six observations) in Norwegian kroner/megawatt (NOK/MW). 1 7.80 NOK in August2011.The figure includes a trend line.

period. In reality, one can say that these forward contracts are what the textbooks

refer to as swaps, since the settlement of these contracts is to exchange a floating

electricity price (system price) for a fixed price (futures or forward price).

Largely because of the variability and uncertainty in rainfall and temperature, short-

term prices (spot and short forward) tend to be very volatile. Reservoir levels, recent

rainfall and weather forecasts have a significant impact on short-term prices. There-

fore, short-term electricity prices are sometimes termed weather derivatives. In

Figure 1 we have plotted data for the monthly average area price NO4, which is the

relevant spot price for the analysis later in this paper (until January 11, 2010, this was

NO3). The figure shows that prices have been rising throughout the period 20029.

Although prices fluctuate according to the seasons, there has been a general increasing

trend over the period. This is due to the growing demand without a corresponding

increase in supply (Kjrland (2009)). The figure also demonstrates the high volatility

in Norwegian electricity spot prices, showing the attractiveness of generating during

peak price periods. One can also observe three shocks during this period. In 20023

there was a shock winter, when the combination of low reservoir levels due to a

dry autumn in 2002, with very little rainfall, together with cold temperatures resulted

in extremely high spot prices. However, the summer of 2006 (low reservoir levels



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because of a cold winter, dry summer and reduced capacity of Swedish nuclear ther-

mal power) and the fall/early winter of 2008 (unusually low rainfall in early fall and,

hence, low reservoir levels) were also characterized by high spot prices.

2 THE MODEL

The idea of the model is to pick the hours with the highest prices. As mentioned,

electricity prices vary significantly over years, seasons, weeks and during the day.

Since the physical turnover at Nord Pool Spot takes place on an hourly basis, there

will naturally be a significant gain by adapting production to the hours with the highest

price, typically during daytime on weekdays and typically in winter. This approach

is based on a daily decision for submitting a bid for each of the twenty-four hours

the following day with full capacity if the price is above a threshold and nothing

otherwise.

Suppose that a hydropower plant has a load factor ofQ%, meaning that the middleyearly generation is produced in Q% of the hours of the year when running at full

capacity. Suppose further that we have a database with the spot price for each hour in

a given period of some years. Obviously, the revenue is maximized for this period if it

is possible to run the plant at capacity at all the hours when the price is larger than the

upper Q percentile of all the prices in the database. This means that the plant is run at

full capacity at all the hours with the Q% highest prices in the database, and is not run

otherwise. However, we cannot use this algorithm without adjustments, as we do not

know the prices for all the hours in the period when the decision about production is

made. In addition, the reservoir capacity may be too small to store all the water when

the plant is not running, and there may be too little water to run the plant at capacity

every hour the price constraints are duly satisfied. Therefore, we make the following

adjustments to the algorithm.

Instead of letting the price threshold be the upper Q percentile of all the prices

in the database, we let the price threshold be the upperp percentile of the17520

latest hour prices (two years) when the bid is submitted. (When p is given, this

percentile may be computed before the bid is submitted.)

If the reservoir level is at least 96% (upper threshold industry standard) at

the beginning of a week, the plant is run at capacity every hour of this week

irrespective of the price. This is done to prevent water being lost.

If the reservoir level is below 15% at the beginning of the week, the plant is notrun at all during that week.2

2 Thechoice of 15%as thelower thresholdis somewhatrandom, but close to a typicallevel.However,

this level varies according to the licenses given and the physical conditions present in the reservoir.



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In our simulations we have selected a value ofp such that the reservoir level at the

end of the eight-year simulation period is approximately equal to the reservoir level

at the beginning of this period. In practical use of this p strategy, it is not possible

to decide the value ofp in this way. However, the following are some guidelines for

selecting a suitable value ofp.

If there is no long-term trend in the spot price, let p D Q, where Q is the load

factor of the plant in percent. (IfA is the total production in GWh during a

given period, B is the capacity of the plant in GW and C is the total number of

hours during this period, the load factor (in percent) is Q D 100.A=.BC//.)

If there is a long-term increasing trend in the spot price, as shown in Figure 1

on page 26, let p be somewhat lower than Q, eg, 75% ofQ.

If there is a long-term decreasing trend in the spot price, let p be somewhat

higher than Q, eg, 110% ofQ.

Normally, this p strategy performs well if the reservoir level varies a lot over

years, but the upper threshold and the lower threshold are seldom or never hit.

If the reservoir level is often at the lower threshold, but very seldom at the upper

threshold, the production is too large on average, so one should select a lower

value ofp to reduce the average production. If the reservoir level is often at

the upper threshold, but very seldom at the lower threshold, the production is

too small on average, so one should select a higher value of p to increase the

average production. If the reservoir level is often at both thresholds, it means

that, in longer periods, the selected hours for generation are based on either

extremely high or extremely low reservoir levels (the threshold values of 96%and 15%, respectively, are activated) and not selected based on the spot prices,

as intended. In such cases, the p strategy is surely not optimal.

To illustrate the impact this strategy has on revenue, we have compared this

approach with three primitive approaches. One simple strategy is to fix the hours

in each week that the plant is run at full capacity. (IfA is the total production in GWh

during a given period, B is the capacity of the plant in GW and N is the total number

of weeks during this period, the plant has to be run A=.BN/ hours each week during

this period.) If we choose the hours of the week that, on average, have the highest

spot prices, we maximize the revenue given this fixed production level each week.

We call this a by day strategy as this implies that the plant is mostly running on

daytime MondayFriday. If we, on the contrary, choose the hours of the week that,

on average, have the lowest spot prices, we minimize the revenue given this fixed

production level each week. We call this a by night strategy as it implies that the

plant is mostly running at night. The difference in total revenue between the by day



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TABLE 1 Descriptive statistics for the virtual hydropower plants.

Average

yearly Reservoir LoadCapacity generation capacity Reservoir factorPlant (MW) (GWh) (GWh) quotient (%)

A 54.0 84.5 196 2.32 43.67B 6.8 16.2 48 2.96 28.0

Sum 30.8 100.7 244

and the by night strategy is the maximal increase in total revenue that is achievable

by moving production hours within the week. A third strategy is to combine daytime

production and avoid the summer months (MayAugust). (IfA is the total production

in GWh during a given period, B is the capacity of the plant in GW and N is the total

number of weeks during this period, the plant has to be run 3A=.2BN/ hours each

week outside the summer months during this period. As before, we choose the hours

in the week with the highest average spot prices.) We call this strategy not summer.

The difference in total revenue between the by day and the not summer strategies

measures what is gained by moving the production in the summer season to the other

seasons in this naive way.

3 MODEL APPLICATION

We apply the model to a small producer (price taker) controlling two hydropower

plants, A and B,3 located in the price area NO4 (Northern Norway). The studied

company controls parts of two larger hydropower plants, leaving them in control of

two virtual power plants. Hence, they can produce according to full capacity and

do not need to relate to the so-called best point of generation (where the efficiency

of the turbines is highest). Some descriptive statistics of the two plants are reported

in Table 1.

To conduct simulations we have used data collected from the producer and Nord

Pool Spot. This data includes:

data concerning the actual power plants, A and B;

data concerning the water reservoirs levels of plants A and B;

inflow data, on a weekly basis;

spot price data for area NO4 (hourly rates) for 20002009.

3 We have anonymized the plants in agreement with the controlling company.



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The simulations are conducted from January 7, 2002 through December 27, 2009,

ie, for 416 weeks. We then calculate the following when running the script.

The number of weeks in which reservoir levels were below the lower thresholdof the reservoir level, which is set to 15%. The power plants do not run during

these weeks.

The number of weeks in which reservoir levels were above the upper threshold

of 96% (industrystandard). In these weeks, plantsA and B produce, at all hours,

24 MW and 6.8 MW, respectively.

The number of weeks in which there was flooding.

Lost production, lost GWh due to flooding.

Total production indicates how many GWh in total are produced during the416 weeks.

Total revenue indicates the total income generated during the 416 weeks, when

using the spot price of NO4 for every hour of electricity generation.

The achieved average price is the quotient between total revenue and the sum

of total production and lost production. Thus, the achieved average price is a

measure of how well water resources are exploited in order to generate revenue.

The reservoir level at January 6, 2002 is set to 75% and 50% for plant A and

plant B, respectively. The level for plant A is taken according to the actual level

on this date. The level for plant B is set higher because the actual level, 32.7%,was unusually low.

The reservoir level on December 27, 2009 indicates the simulated water reser-

voir level in percent at midnight on that date.

When assessing revenue for the period, it is important to take into account the water

reservoir level at the end. Obviously, the water represents value. In order to be able to

ignore this aspect, we have tuned the strategies so that the simulated water reservoir

levels at the end are approximately the same as the start level. Hence, production for

the eight-year period is quite similar to total inflow and consequently the different

strategies are comparable.

The optimal value ofp is found when p D 34:5 and p D 21:3 for plant A and

plant B, respectively. These values are found on the basis of the deterministic end

value of the reservoir levels and are thus found retrospectively. Concerning the other

strategies, we have computed the mean of the spot price for each of the 168 hours in



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the week for the 416 weeks in the simulation period and picked the correct number

of hours with the highest/lowest mean of the spot price. As a result, the following

production hours are selected each week for the naive strategies. For plantA, we have

defined the by day strategy as production in hours 822 on Monday to Thursday

and in hours 820 on Friday. For plant B, we use production in hours 814 and 1719

on Monday, hours 819 on Tuesday, hours 813 and 1719 on Wednesday, hours

819 on Thursday and hours 912 on Friday. We have defined the by night strategy

as follows. For plant A, production in hours 16 and 24 on Monday to Thursday,

hours 16 and 2224 on Friday, hours 19, 1417 and 2124 on Saturday and hours

118 and 24 on Sunday. For plant B, production in hours 16 on Monday, hours 25

on Tuesday, hours 26 on Wednesday to Friday, hours 28 and 24 on Saturday and

hours 110 and 1417 on Sunday. The not summer strategy is defined for plant A as

production in hours 724 on Monday to Thursday, hours 723 on Friday, hours 1, 10

14 and 1723 on Saturday, and hours 1213 and 1823 on Sunday, but no production

in the months MayAugust. For plant B it is defined as production in hours 822 on

Monday to Thursday and in hours 815 and 1719 on Friday, except for during the

months MayAugust.

In order to say something about how well our model performs, we compute the

best possible theoretical outcome, best Q%. This is in retrospect, when all prices

are known. Q is the load factor in percent for the plant, ie, Q D 43:67 for plant A

and Q D 28:0 for plant B.4 This means that the simulation is performed on the upper

Q percentile of the NO4 hourly prices in 20029 in retrospect. Hence, the calculated

numbers do not represent any strategy. However, we have programmed the script

to ignore the upper and lower threshold, making the results definitely theoretical, as

shown in Figure 2 on the next page and Figure 3 on the next page concerning simulatedwater reservoir levels.Yet, this provides relevant information when assessing the other

presented strategies.

The results of the simulations concerning plant A and plant B are shown in Table 2

on page 33 and Table 3 on page 34, respectively. The simulated water reservoir levels

areshown in Figure 2 on the next page and Figure 3 on the next page. We have included

the strategy p D Q (ie, the new p strategy, but with p equal to the load factor Q

rather than the optimal value ofp) in the tables and figures to illustrate that this is

not an optimal choice ofp. We see that the total production is too high, such that the

reservoir level is low for a large part of the period. This means that the condition for

production should be stricter, ie, p should be lowered.

Thenumbers show that comparing the bynight strategy with the byday strategyreveals a difference of 29.9 million NOK and 6.9 million NOK for plant A and

4 The load factors are calculated on the basis of the inflow data 20029.



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FIGURE 2 Simulated reservoir level for plant A.

0

50

100

150

200

Reservoirlevel(%)

01/01/02 01/01/04 01/01/06 01/01/08 01/01/10

Solid black line:best 43.67%.Solid gray line:p D 34.5. Dashed black line:p D 43.67.Dotted black line: not summer.Dashed gray line: by day/by night.

FIGURE 3 Simulated reservoir level for plant B.

0

50

100

150

01/01/02 01/01/04 01/01/06 01/01/08 01/01/10

Reservoirlevel(%)

Solid black line: best 28%. Solid gray line: p D 28. Dotted black line: p D 21.3. Dashed black line: not summer.Dashed gray line: by day/by night.



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TABLE 2 Results of simulations for plant A.

Achieved Weeks WeeksTotal Total average Reservoir below above W

revenue production price level lower upper w(MNOK) (GWh) (NOK/MWh) (%) threshold threshold flo

Best 43.67% 283.4 731.2 387.5 75.6 p D 43.67 266.6 765.5 348.3 58.1 43 9 p D 34.5 266.0 732.8 363.0 74.8 0 11 By day 226.5 728.9 310.7 76.8 0 0 By night 196.6 728.9 269.7 76.8 0 0 Not summer 227.2 728.7 311.8 76.9 0 1

The reservoir level is given at December 27, 2009. The reservoir level at the beginning of the period (January 6, 2002) was 75%. MNOK den

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TABLE 3 Results of simulations for plant B.

Achieved Weeks WeeksTotal Total average Reservoir below above W

revenue production price level lower upper w(MNOK) (GWh) (NOK/MWh) (%) threshold threshold flo

Best 28.0% 57.7 132.7 434.7 50.6 p D 28 51.2 136.4 375.4 43.0 44 0 p D 21.3 53.7 132.8 404.7 50.3 5 3 By day 42 132.9 316.1 50.2 0 0 By night 35.1 133.1 263.4 50.2 0 0 Not summer 42.6 133.0 320.7 49.9 0 0

The reservoir level is given at December 27, 2009. The reservoir level at the beginning of the period (January 6, 2002) is set to 50.0%. MNO

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TABLE 4 The results of the pairwise formal tests of differences in strategies regardingplant A for the whole period 20029.

StandardPair of strategies Estimate error t-value Pr .>jtj/

Best 43.67%/p D 34.5 0.0002488 0.0000269 9.2641792 0.0007550

p D 34.5/by day 0.0005648 0.0000391 14.4485614 0.0001334

By day/by night 0.0004282 0.0000536 7.9831992 0.0013345

By day/not summer 0.0000105 0.0000293 0.3594597 0.7374245

Estimate is the estimate of the regression coefficient (the constant) and Pr .>jt j/ is the p-value in the Student tdistribution with four degrees of freedom.

TABLE 5 The results of the pairwise formal tests of differences in strategies regardingplant B for the whole period 20029.

StandardPair of strategies Estimate error t-value Pr .>jtj/

Best 28%/p D 21.3 0.000057 0.000008 7.416535 0.001764

p D 21.3/by day 0.000168 0.000011 15.506989 0.000101

By day/by night 0.000099 0.000012 8.518869 0.001042

By day/not summer 0.000009 0.000006 1.416152 0.229673

Estimate is the estimate of the regression coefficient (the constant) and Pr .>jt j/ is the p-value in the Student tdistribution with four degrees of freedom.

plant B, respectively. Moreover, the simulations show that at p D 34:5 for plant Aand p D 21:3 for plant B, the accumulated nominal earnings for the eight-year period

become much higher and quite close to the theoretical best possible outcome. The

optimal p strategy captures approximately 70% and 75% for plant A and plant B,

respectively, of the gap between the by day strategy and the best Q% approach

in retrospect. This indicates that the model is performing well.

We formally test whether or not the difference in revenue between two strategies

is statistically significant in the following way. We regress the differences in the

hourly revenues between the two strategies on a constant, using robust t-values with

the NeweyWest autocorrelation and heteroskedasticity consistent covariance matrix.

We use four degrees of freedom in these tests, as recommended in Lange et al (1989).

The information in Table 4 and Table 5 shows that, for each pair of strategies in the

table, the difference in revenue is significant at 0.2% significance level, except when

comparing the by day strategy with the not summer strategy. The results confirm

the well-known fact that the difference in revenue between the naive by day and by



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FIGURE 4 Cumulative revenue for plant A.

0

50

100

150

200

250

300

Quarter

Cumulativerevenue(millionNOK)

2002 Q1 2004 Q1 2006 Q1 2008 Q1 2009 Q4

Solid black line: p D 43.67. Dashed black line: p D 34.5. Solid gray line: not summer. Dotted black line: by day.Dashed gray line: by night. Dotted gray line: best 43.67%.

night strategies is highly significant. However, the difference between the optimal

p strategy (p D 34:5 for plant A and p D 21:3 for plant B) and the naive by day

strategy is even more significant, as the t-value has almost doubled (14.4 versus 8.0and 15.5 versus 8.5, respectively). We also see that the difference in revenue between

the best Q% approach and the optimal p strategy is approximately at the same

significance level as the difference in revenue between the by day strategy and the

by night strategy. However, we have to bear in mind that the best Q% approach

gives a theoretical upper bound for the revenue as the tests against the lower and

upper threshold of the reservoirs are removed. We see clearly from the plots of the

respective simulated reservoir levels for plant A and plant B, shown in Figure 2 on

page 32 and Figure 3 on page 32, that it is impossible to run the best Q% approach.

We also show the cumulative revenues for plant A and plant B in Figure 4 and

Figure 5 on the facing page, respectively. These figures confirm how well our model

performs, as the optimal p strategy clearly provides more revenue than the naive

strategies and is close to the theoretical best possible outcome for this eight-year

period. Details concerning production and revenue for each year are found in Table 6

on page 38.



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FIGURE 5 Cumulative revenue for plant B.

0

20

40

60

80

Quarter

Cumulativerevenue(millionNOK)

2002 Q1 2004 Q1 2006 Q1 2008 Q1 2009 Q4

Solid black line:p D 28. Dashed black line:p D 21.3. Solid gray line:not summer. Dotted black line:by day. Dashedgray line: by night. Dotted gray line: best 28%.

4 DISCUSSION

The numbers show a clear difference between the by day strategy and the by

night strategy. The difference in revenues represents the approximate gain achieved

by choosing the most favorable hours of the week. The increase in revenue is 15.9%

for both plants in total.

However, by using the optimal p strategy, one will more effectively capture all

the dynamics in the market, since one is then able to produce at favorable hours of

the day or days of the week, over seasons and over years. This strategy provides a

substantial additional income. In fact, the increase is larger from the by day strategy

to the optimal p strategy than from the by night strategy to the by day strategy.

If one relates the increases to the optimal p of 34.5 and 21.3 for plant A and plant B,

respectively, income is increased by 19.1% in total. However, on the other hand, this

provides a greater variation in income between years (see Table 6 on the next page).

This may be problematic for public owners needing a predictable income for their

budgets and for the planning of various public services.5

5 Around 8590%of Norwegian hydropower generation is publicly owned (by municipalities, coun-

ties and the state).



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TABLE 6 Simulated production and revenue for (a) plant A and (b) plant B each year in the period 20029 fothe best Q in retrospect. [Table continues on next page.]

(a) Plant A

2002 2003 2004 2005 2006 2007

GWh MNOK GWh MNOK GWh MNOK GWh MNOK GWh MNOK GWh MNOK G

Best 43.67% 30.9 13.95 93.8 33.67 10.6 3.07 12.9 4.12 195.4 79.19 51.2 17.94 18p D 43.67 105.8 28.36 191.6 57.57 44.6 12.13 74.5 20.2 163.5 67.41 41.5 15.07 13p D 34.5 103.5 27.77 173.9 53.66 22.9 6.48 57.3 15.86 187.8 76.78 27.1 10.41 14By day 90.1 19.14 91.5 28.47 91.8 23.43 91.1 22.87 91.1 37.98 91.5 23.51 9By night 89.7 16.81 91.3 24.63 91.5 21.24 91.5 20.12 91.6 34.18 91.3 19.52 9Not summer 90.4 22.05 91.5 29.83 91.9 22.55 91.2 22.23 90.9 36.94 91.1 24.78 9

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TABLE 6 Continued.

(b) Plant B

2002 2003 2004 2005 2006 2007

GWh MNOK GWh MNOK GWh MNOK GWh MNOK GWh MNOK GWh MNOK GW

Best 28% 7.2 3.48 11 4.86 0.1 0.04 0.8 0.32 42.5 18.49 8.8 3.34 45p D 28 19.5 6.29 33.1 10.95 1.2 0.37 12.5 3.53 35.4 13.28 4 1.63 29p D 21.3 15.5 5.55 26.8 9.51 0.3 0.09 11.4 3.16 47 19.38 1.2 0.55 29By day 16.4 3.55 16.7 5.27 16.7 4.31 16.6 4.25 16.6 7.01 16.7 4.38 16By night 16.4 3 16.7 4.41 16.7 3.83 16.7 3.59 16.7 6.16 1 6.7 3.46 16Not summer 16.3 4.07 16.8 5.59 16.9 4.22 16.6 4.16 16.5 6.86 16.6 4.66 16

The numbers show that the revenue would have varied considerably, particularly in 2004 where prices were low (a wet year), while 2006 an(dry years).The low figures for 2004 are partly because the cumulative prices in the database were dominated by the high prices in late 2naturally, lower for the naive strategies. MNOK denotes million NOK.

ResearchPaper

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FIGURE 6 Achieved average price for plant A.

0

100

200

300

400

500

600

Achievedaverageprice(NOK/MWh)

Best43.67% p=

43.67 p=

34.5 By day By night Not summer

Another source of information is the achieved average price, where we also include

the fact that some water is lost due to flooding (as for p D load factor). The simulated

average achieved price is given in Table 2 on page 33 and Table 3 on page 34 and

visualized in Figure 6 and Figure 7 on the facing page.

A key assumption for the model is that the empirical distribution of the latest

17 520 hourly spot prices is representative for future spot prices. If some kind of

long-lasting shock occurred, this could lead to a bad selection of generating hours,

because prices for the last two years were formed under different circumstances. Ifso, one could adjust the model by changing the p-value. However, one should not

lower the number 17 520, because one would not then capture the volatility between

seasons, nor between dry and wet years.

The simulated period has been characterized by a general increase in prices, as

shown in Figure 1 on page 26, due to a rising market over the past decade. This is the

main reason why the optimal p of the plants is lower than the load factor of the plants.

If the price trend had been the opposite, the optimal p would have been higher than the

load factor. However, the model would be applicable anyway. Even if a long-lasting

decreasing trend does not seem particularly probable, the model is robust. Anyway,

the choice ofp should be reassessed regularly.

5 CONCLUSIONS AND IMPLICATIONS

All the presented strategies represent simple models providing simple rules for

how a producer in the future can exploit his hydropower resources and adapt to the



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FIGURE 7 Achieved average price for plant B.

0

200

400

600

800

Achievedaverageprice(NOK/MWh)

Best 28% p=

28 p=

21.3 By day By night Not summer

dynamics of the Nordic electricity market. It is always easy to assess a strategy in

retrospect, but the simulations show how a small participant (price-taker) can adapt

to increase income in the future by applying our model.

As a conclusion of the analysis, we recommend that the producer implements the

optimal p of 34.5 for plant A and 21.3 for plant B. This will provide considerable

additional income. If the producer believes in a different future trend of electricity

prices,otherp-values can be considered according to previous comments in this paper.

Also, if reservoir levels become either very high or very low, adjustments should be

made.

Concerning implementation of the model, we do, however, see some counter-

arguments. This strategy provides a great deal of variation in income from the physical

production. The method implies that one can hold back for longer periods if the

prices are low. This is possible due to the high degree of flexibility in both reservoirs

and turbine capacity. The volatility can be reduced by using financial contracts, but

still the variation will remain significant.

The model assumes no large, long-lasting shocks. Short-term conditions are tackled

sufficiently, but the method needs to be modified in some way if it is to take account

of large and long-term changes in the market, possibly by adjusting the chosen value

ofp.

The model is designed for a small producer with relatively small resources and pos-

sibly a low level of expertise. Hence, even if the model is simple compared with other

strategies in the industry, implementation can, to a certain extent, prove demanding.

This can be overcome with the aid of consultants.



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We do not think that any of these counterarguments are particularly compelling.

There are therefore great advantages to be gained through implementing the model.

The approach stands up as robust with respect to fluctuations in days, weeks, seasons

and years. The method also allows one to generate during many of the hours with the

highest prices; the consequences in terms of extra revenue are significant. Over the

eight-year period, the simulations show that revenues would be more than NOK 50

million higher (19.1%) compared with the simpler by day strategy. Bear in mind

that the by day strategy is not that naive. The difference in income is considerable.

The model enables a producer that has a high degree of flexibility in their generation

to exploit most of the volatility of a hydropower-based electricity market such as the

Norwegian market.

REFERENCES

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Prez-Daz, J. I., Wilhelmi, J. R., and Arvalo, L. A. (2010a). Optimal short-term operationschedule of a hydropower plant in a competitive electricity market. Energy Conversionand Management 51, 29552966.

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