Energy Policy 38 (2010) 7299–7311

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Energy Policy

0301-42

doi:10.1

n Corr

E-m

Patricia

journal homepage: www.elsevier.com/locate/enpol

Managing a hydro-energy reservoir: A policy approach

Ann van Ackere a,n, Patricia Ochoa b

a HEC Lausanne, Internef, Universite de Lausanne, CH 1015 Lausanne, Dorigny, Switzerlandb London Business School, Regent’s Park, London NW1 4SA, UK

a r t i c l e i n f o

Article history:

Received 29 March 2010

Accepted 5 August 2010

Keywords:

Hydro-energy

Simulation

Policy

15/$ - see front matter & 2010 Elsevier Ltd. A

016/j.enpol.2010.08.005

esponding author. Tel.: +41 21 692 3454; fax

ail addresses: Ann.vanAckere@unil.ch (A. van

.Ochoa@edfenergy.com (P. Ochoa).

a b s t r a c t

Liberalisation and privatisation have increased the need to gain more understanding into the

management of hydro storage (HS) plants. We analyse what types of reservoir management policies

enable an owner or a public authority to achieve their respective objectives. By ‘‘policy’’ we understand

simple, easily applicable decision rules, which enable a decision maker to decide when and how much

to produce based on currently available information. We use a stylised deterministic simulation model

of a hydro-power producer (HP) who behaves strategically. We study a non-liberalised market, where

the authorities aim to minimise the total electricity cost for customers and a liberalised market where

the HP attempts to maximise his contribution. This enables us to evaluate the impact of the

liberalisation of HS production decisions on production volumes and electricity prices. We conclude

that imposing rigid policies with the aim of limiting the potential for strategic behaviour can create

incentives to produce only at very high prices throughout the year. This can lead to very high total costs,

especially when the producer has most flexibility (large reservoirs combined with large turbine

capacity). More surprisingly, we observe lower total production in a non-liberalised market.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

There has been a lot of effort devoted to attempting to assign avalue to the water in the reservoirs of hydro storage plants. This isa particularly tricky issue as the value of the water currently in areservoir depends not only on current prices (and thus on currentdemand and availability of alternative energy sources) but also onfuture prices and future inflows, both of which are unknown atthe time of decision making. Assigning a value to water becomeseven more complex if one takes into account the possibility ofusing inexpensive surplus energy at night for pumping purposes,to refill the reservoir.

Liberalisation and privatisation have transformed the decisionmaking process regarding how best to use the limited availablewater resources. Hammons et al. (2002) provide an interestingdiscussion of the consequences of deregulation in hydro-domi-nated markets, focussing on Latin America. They point out amongothers the often over-looked buffer-role of large reservoirs, whichcan hide the gap between demand and supply for a significantperiod of time, up to several years, thus distorting scarcity signals.

Many authors have analysed this problem using various formsof dynamic programming approaches. Early work in this area isreviewed in Lamond and Boukhtouta (1996). More recently,

ll rights reserved.

: +41 21 692 3305.

Ackere),

Lamond (2003) has developed more accurate and faster algo-rithms using a spline approach for a single reservoir, under theassumption that the price (reward) is a concave, piecewise linearfunction of the energy produced by the hydro-plant. Pritchardet al. (2005) also use dynamic programming but focus on a price-taking hydro-plant operating in a pool market, treating the priceas an exogenous random variable, i.e. independent of theproduction decisions of the hydro-plant. He moves the emphasisfrom optimal production to optimal bidding.

Costa Flach (2009) provide a detailed, critical review of morerecent dynamic programming work in this area. They proposea new approach, which models explicitly several hydro plantsand assumes stochastic inflows while taking into account thetime-coupling characteristic of hydro production and allowing thehydro-plant to be a price-setter rather than a price-taker.

Other authors have opted for an algorithm based approach.Examples include Afsar and Moeini (2008) and Bozorg Haddadet al. (2009). The former use an ant colony optimisationalgorithm, whereas the latter present a honey-bee matingoptimisation algorithm. Both consider a single reservoir system,but state that extensions to a multi-reservoir problem should befeasible once the method is thoroughly understood.

Our approach is different. Rather than aiming to devise analgorithm to determine the optimal production for each period,we aim to study what types of reservoir management policies arebest suited to achieve different objectives. In other words, we aimto create insight into why certain policies perform better thanothers for a given objective. For instance, a public authority in a

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–73117300

non-privatised market may have as main objective to keep thecost of electricity down for the final customer, or be interested inmaximising hydro production due to the increasing publicpressure for green energy, or pursue some combination of theseobjectives. A private company in a liberalised market will mostlikely be interested in maximising contribution.

By a ‘‘policy’’ we understand a fairly simple, easily applicable,decision rule which enables a decision maker to decide whetheror not to produce at a certain point in time, and how much, basedon currently available information: current reservoir level,forecasted inflow, availability of other generators, and priceexpectation for the period covered by the decision period(e.g. hourly decisions for the next 24 h).

Two examples of very simplistic policies are (i) producewhenever the forecasted reservoir level exceeds a threshold leveland (ii) produce only when the price exceeds a certain level. Notethat the first policy basically reduces the reservoir based facility tothe status of a ‘‘run of river’’ facility (production will closelymirror the inflows) and is thus not particularly interesting fromour point of view as it ignores price and cost considerations. Thesecond policy can have two objectives. On the one hand, if thereservoir is large, leading to significant flexibility, a high priceenables high profits. On the other hand, choosing a relatively lowprice can be interpreted as an attempt to stabilise prices: as longas there is sufficient water in the reservoir and sufficient turbinecapacity, the producer will generate the amount required to keepthe price at the specified level. Such a policy can backfire. On theone hand, attempting to stabilise prices at too low a level maycause the reservoir level to be low when demand is high, resultingin undesirable price spikes. On the other hand, while choosing ahigh price may maximise contribution in certain scenarios, it mayalso lead to significant overflows, higher marginal productioncosts, and thus a higher price for the customer.

There are two aspects to the decision concerning the timing ofproduction. The first one is quite straightforward: any water usedtoday cannot be used tomorrow. The second one is more intricate:producing today creates capacity in the reservoir to accommodatefuture inflows. This is why we consider more sophisticatedpolicies which define the threshold price level as a decreasingfunction of the forecasted reservoir level: the higher theforecasted reservoir level, the more inclined one should betowards producing now, so as to create space for future inflowsand thus avoid facing the dilemma: producing at a very low priceversus letting the reservoir run over.

This discussion also illustrates that there are two time-dimensions to this problem. On the one hand there is the shortterm ‘‘hourly’’ aspect: given that the generator wants to produce agiven amount over the next 24 h, at what hours of the day shouldthis production take place. On the other hand there is the longerterm ‘‘annual’’ aspect: at what time of the year should oneproduce to benefit as much as possible from high prices duringthe winter, while avoiding the reservoir flowing over, i.e. thetrade-off between keeping ‘‘as much water as possible’’ for thewinter and loosing production capacity due to reservoir overflowsin late summer.

We are particularly interested in evaluating how, for a givenobjective, the policy choice is affected by different factors. In thispaper we focus on changes in reservoir size and turbine capacity,keeping all the other aspects constant. Note that a change inturbine capacity affects both production capacity and theflexibility of the timing of production, while a modification ofthe reservoir size only influences the latter.

Following the argument by Bunn et al. (1997), we opt for anarrow scope (the strategic behaviour of HS firms) so as to be ableto limit the size of the model and the amount of detail necessaryto gain insight in this specific question we have chosen to address.

We develop a stylised model, calibrated for Switzerland, but themodel could easily be recalibrated for another country with asignificant hydro component.

In Section 2, we provide a brief literature review and motivatethe methodology. Section 3 presents the model, and in Section 4we discuss the simulation set-up and the choice of scenarios. Wediscuss our results in Section 5, before summarising the maininsights, and providing directions for further work in Section 6.

2. Literature review and methodology

The trend of liberalisation and privatisation of the past twodecades has significantly changed the environment. In the earlyyears, many authors in the field of energy economics havecontinued to focus on traditional economic models for optimizingwater allocation under assumptions of known demand andgeneration capacity, using one-period static games of profitmaximisation. Examples include Green and Newbery (1992),von der Fehr and Harbord (1993), and Borenstein and Bushnell(1999).

As liberalisation has become more wide-spread, authors haveincreasingly focussed on understanding the impact of thisevolution on optimal behaviour. For instance, Ambec and Doucet(2003) use a dynamic model to analyse differences in efficiencybetween two hydropower generation companies: a monopolistand a company in a competitive environment. Their model is ableto ‘‘capture either seasonal or shorter-term storage problems(daily, weekly), but not both simultaneously’’ (p. 590).

Pritchard and Zackeri (2003) develop a stochastic dynamicprogram to build explicit hydro-electricity offer curves in the NewZealand market. They focus on the short-term operation of aprice-taking hydro-storage generator. Inflows to the reservoirare assumed to be deterministic and known; thus, the onlyuncertainty in their model refers to the price.

More recently, Horsley and Wrobel (2007) restructure Koop-mans’ operation problem. In Koopmans’ problem (1957), theoperating costs of an electricity system are minimized byconstructing a water storage plan for the hydro operation thatminimizes the fuel cost of the thermal plants. Horsley et al.consider this approach inappropriate for modern decentralizedindustries and propose to restructure it as a competitive profitmaximisation problem and analyse how to operate a hydro-plantto maximise profit, how to value the plant’s capacity and its riverflow, and how to use these valuations in investment decisions,using a short-run profit maximisation model.

Other authors have focussed on the potential for strategicbehaviour in this new environment, especially in the presence of amix of thermal and hydro plants. For instance, Scott and Read(1996) use a dynamic programming model of the behaviour ofhydro reservoir managers in a mixed hydro thermal system, toanalyse the effects of contracts and company structure on theefficiency of a wholesale electricity market in New Zealand.Bushnell (2003) presents a Cournot oligopoly model with acompetitive fringe for analysing competition between multiplefirms having a mix of hydro and thermal generation capacities.

Crampes and Moreax (2001) analyse how the presence of ahydro-storage power station changes both the optimal and themarket equilibrium outputs of a thermal station. They develop adiscrete inter-temporal model of competition between a thermalstation and a hydro-storage station, and analyse the combinationof these two technologies in the case of a public monopoly, aprivate monopoly, and duopolistic competition where each firmoperates either a hydro-storage or a thermal power station. Theyconclude that, when competing with hydro, despite its static

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–7311 7301

characteristics, the optimized output from the thermal station isdetermined by inter-temporal specifications of cost and utility.

More recently, attention has also turned to the interactionbetween regulatory measures and strategic behaviour. Forinstance, Garcıa et al. (2001) analyse the effects of price caps,the efficiency of dispatch under strategic behaviour, and thelikelihood of collusion over the price formation process in aninfinite-horizon duopoly model where two hydro-storage gen-erators engage in dynamic Bertrand competition.

Our purpose is to analyse what reservoir management policiesenable an owner or a public authority to achieve their respectiveobjectives: profit maximisation or electricity cost minimisation.We use a stylised system dynamics model representing areservoir based hydro-energy producer, who behaves strategi-cally. River run plants are logically assumed to produce up tocapacity, and the behaviour of the other generators is assumed tobe captured by the offer-curve. We focus on two objectives: (i)keeping the total electricity cost down and (ii) maximising thecontribution of the HS producer (referred to as HSP). This enablesus to evaluate the impact of privatising the HS productiondecisions on the timing and quantity of production, and thus onelectricity prices. This type of model is also useful to study theimpact of exogenous changes. We illustrate this potential bysimulating a scenario representing an increase of air-conditioningdemand in summer due to a temperature increase.

System dynamics has been used extensively to analyseelectricity markets. Applications include large policy models foranalysing regulated markets (Nail, 1977, 1992; Ford and Geinzer,1990; Amlin and Backus, 1996), as well as more detailed modelsfor the analysis of specific problems after liberalisation (Lyneiset al., 1994; Bunn et al., 1997; Ford, 1999, 2001; Gary and Larsen,2000). The problem of determining policies for water allocation inhydro-storage plants, and more specifically how the objectives ofmarket participants impact the value that HS producers shouldassign to water in the reservoirs in the Swiss electricity market, isaddressed in Ochoa (2007).

3. Model description

We first state our main hypotheses, before providing anoverview of the model structure and its main elements. Next wedetail the decision policies, and conclude by discussing how themodel was calibrated and elaborating on the validation process.

3.1. Model assumptions

For the sake of simplicity we categorise hydro plants as eitherrun-of-river or hydro-storage, but one should be aware that inreality this is more like a continuum. Throughout this paper weuse the abbreviation RR to refer to run of river plants and HS forhydro-storage.

To be able to focus on the impact of HS policies, we assumethat the HS facility is the only strategic player in the market, i.e.we do not consider the interaction between several HS facilities,nor between HS, RR, and thermal plants. In particular, we assumethat RR plants always produce up to their capacity (whetherwater availability or turbine capacity), conditional on there beingsufficient demand. We also assume that the nuclear and thermalplants produce whenever the price exceeds their (exogenous)offer price. This behaviour will be captured in the model by anoffer-curve.

We justify these simplifications by arguing that RR planscannot gain from not producing as any unused water is lost andvariable costs are extremely low, while nuclear plants aretypically part of the base-load and have limited potential to vary

their production rate on an hourly basis. The situation of thermalplants is less clear-cut. There has been some discussion thatthermal plants may have behaved strategically during theCalifornian crisis but no evidence, as discussed by Sweeney(2002): ‘‘This large amount of generating capacity off-lineresulted from a combination of causes but the greatest fractionof generators was off-line reportedly for repairs or maintenance.However, whether the maintenance and repairs were forced uponthe generators, were part of a competitive cost minimisingsolution, or were designed to increase wholesale price has notbeen fully resolved. This empirical matter most probably cannotbe resolved without careful in depth assessment of facts thatcurrently are not publicly available.’’ (p. 158). Similarly, there issome evidence of strategic behaviour by National Power andPowerGen in the nineties in the UK (Amobi, 2007 and referencestherein), which has led the UK regulator to reform the system.Comparatively, HS plants are in a different situation: withholdingproduction when prices are low is a natural strategy for suchplants, given the scarcity of their key input which cannot bereplenished at will: water.

At this stage we do not consider pump-turbine facilities whichenable using inexpensive energy at night to pump water so as toproduce electricity at peak time. Including this aspect would add awhole new dimension to the issue of the daily management of thefacilities, in particular to the ‘‘hourly’’ aspect discussed above. It isworth noting that pump-turbine facilities are only meaningful inareas where there is inexpensive excess non-hydro-storageelectricity available during the low-price periods. This is the casein Switzerland, where pump-turbine facilities play an importantrole, but not for instance in Norway.

3.2. Model structure

The model consists of the following main elements: demand,precipitation which determines the inflow to the reservoirs of theHS plants and to the RR plants, production by RR plants andproduction decisions for the HS plants. We discuss each of thesein turn.

Hourly demand is generated as follows: given an averagehourly demand and the annual amplitude of daily demand wegenerate an annual demand pattern. We superimpose on this adaily demand pattern to obtain an hourly demand rate whichdepends both on the time of day and on the day of the year. Theannual demand is assumed to follow a sin wave, which capturesthe key seasonal characteristics of demand in Western Europe,while the daily pattern is based on the pattern of daily demand inSwitzerland.

Precipitation is modelled as an exogenous element, whosepattern is calibrated for Switzerland. This precipitation does notend up immediately into the reservoirs. Rather, in winter most ofthe precipitation accumulates in the mountains as snow, and willonly end up in the reservoirs after melting during spring andsummer, yielding (together with the rainfall), the potential inflowto the reservoirs.

While it is this potential inflow which is truly relevant for ourpurpose, the model includes an explicit representation of thesnow accumulation and melting process to enable us to use themodel in future work to accurately represent both the impact of achange in temperature on inflow for a given level of precipitationand the impact of a change in the level of precipitation.

The potential inflow reaches the reservoir, unless the reservoiris (close to) being full. This aspect is captured by the Loss fraction,which is a non-linear function of the reservoir status. Thereservoir status is the ratio between the current reservoir leveland the reservoir capacity. This structure is illustrated in Fig. 1.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–73117302

The RR plants’ potential production is determined by theirinflow and their maximum production rate (their turbinecapacity). The effective RR production is assumed to equal thepotential production, unless demand is lower. In this latter caseeffective production equals demand, and the remaining inflow islost as it cannot be accumulated.

Before discussing the HS production decision we need tointroduce a key concept of the model: the ‘‘Offer curve excludingHS and RR’’. This function captures the relationship between theproduction level and marginal production cost of the otherelectricity producers, in particular nuclear and thermal energy,and possibly, as is the case for Switzerland, long term importcontracts. It would seem natural to also include RR plants in thisoffer curve. We have chosen not to do so because, as discussedabove, the production logic of RR plants is different: given theirvery low marginal cost and their inability to store water, they willproduce up to their available capacity.

Fig. 2 illustrates the logic of this curve. Note that this functionis strictly increasing, reflecting the fact that production unitsoffering the lowest price will be called in first. If HSP wishes toobtain a price P, he should set the amount he is willing to produceat price P so that other producers are called upon to produce Q. Ifhe were to produce more, the other producers would produce less,and the price would be lower.

The logic of the HS production decision is illustrated in Fig. 3.The starting point is the price desired by HSP. We will considerboth the case where this price is a constant and the case wherethis price depends on the forecasted reservoir level (as indicatedby the dotted arrow). As explained above, combining this desiredprice with the offer curve of the non-hydro producers enables theHSP to determine the amount these producers should produce forthe price to reach this level. Recalling the assumption that RRalways produces to the maximum of its capacity, we compare this

Reservoir

HS Inflowrate

HS productionrate

LossFraction

Reservoircapacity

ReservoirstatusHS Potential

inflow

Fig. 1. HS reservoir.

Quantity offered by non-hydro producers

P

Q

Des

ired

Pric

e

Fig. 2. Logic of the ‘‘Offer-curve excluding hydro storage and run of river’’.

amount to the residual demand after the RR production has beenaccounted for to determine the desired HS production rate. Theactual amount produced depends on this desired production rate,the capacity of the plant (maximum HS production rate) andwhether there is sufficient water available in the reservoir. Thislatter aspect is elaborated upon in the discussion of theparameterisation of the model. HS production reduces the levelof the reservoir.

The model also includes the required structure to calculateselected output measures. We focus in particular on the annualelectricity cost to consumers, HSP’s annual contribution margin,and the total HS production.

3.3. Decision policies

This leaves the question: how does HSP determine this desiredprice? We assume that this decision is influenced by theforecasted reservoir level, assuming that no HS production takesplace. We consider a very simple forecasting model: a 2-monthforecasting horizon with perfect foresight. The underlyinghypothesis is that monthly inflows can be forecasted with areasonable level of accuracy for the next couple of months. Forinstance, in winter most of the precipitation is under the form ofsnow, so the inflow to the mountain reservoirs is very low. In thespring, inflows consist of rainfall and melting snow. Given areasonable estimate of the snowpack and the expected tempera-ture, the second component can be estimated with a reasonablelevel of accuracy. Our results are robust for forecasting horizonsranging from 1 to 3 months.

We consider two types of decision policies, i.e. relationshipsbetween forecasted reservoir level and desired price. These areillustrated in Figs. 4 and 5. For both types of policies there is alower reservoir limit (LL) such that if the forecasted reservoir levelis below this limit, the desired price is ‘‘very high’’, and thusproduction only takes place if prices reach this level, defined asthe highest value that can be achieved in the model (based on themarginal cost of combined cycle turbines (CCT)). There is also anupper reservoir limit (UL) above which the desired price equalsthe marginal HS generation cost, i.e. a very low value assumed tobe the lowest possible offer-price, and thus production willalways take place as long as the price is above this level.

For a given fixed price policy, there are three possible desiredprices: the marginal cost of HS, an intermediate price P (whichcharacterises this policy), and the marginal cost of CCT. If theforecasted reservoir level is below LL, or above UL, the desiredprice equals the marginal cost of, respectively, CCT and HS. Forintermediate forecasted reservoir levels, production will takeplace as long as the price is above the intermediate price P. Fig. 4shows a graphical representation of the relationship between theforecasted reservoir level and the desired price for fixed pricepolicies. In the scenarios we consider a range of intermediateprices between these two extremes (indicated by the dottedrectangle), yielding a total of 17 policies.

The piecewise linear policies are based on the same logic, butthe relationship between the forecasted reservoir level and thedesired price has a single inflection point (denoted (P, level) inFig. 5) between the two extreme values, rather than beingconstant. Each policy is thus characterised by a pair (P, level).We consider a grid of pairs (P, Level) in the dotted rectangleindicated in Fig. 5, which yields a total of 81 policies.

3.4. Parameter values and other key modelling assumptions

The model is calibrated against a reference value of an averagehourly demand equal to 1, which we refer to as 1 MWh/h. This

Reservoir

HS production rate

Maximum HSproduction rate

Reservoir forecast ifno HS production

Desired demandnet of HS and RR

Desired HSproduction rate

Offer curveExcluding HS and

RR

Desired price

Hourly demandafter RR

Impact of reservoirstatus on HS producton

Fig. 3. HS production decision process.

00

Forecasted Reservoir Level

Des

ired

Pri

ce

P

LL UL

Fig. 4. Fixed price policies.

00

Forecasted Reservoir Level

Des

ired

Pric

e

P

LevelLL UL

Fig. 5. Piecewise linear policies.

0.00

0.25

0.50

0.75

1.00

1.25

0Hour of day

Dem

and

mul

tiplie

r

4 8 12 16 20 24

Fig. 6. Daily pattern.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–7311 7303

amounts to an annual demand of 8640 MWh/year, assuming ayear of 360 days. All other parameters are calibrated relative tothis reference point, using Swiss statistics for 2006 to yieldrealistic values for the base case. Data sources include the RapportAnnuel (2006) of the ‘‘Association des enterprises electriquessuisses’’ for parameters relating to demand, production andcapacity, Filippini (2002) for parameters relating to the cost ofhydro-energy production and the Office Federal de l’energie(OFEN, 2001) for parameters relating to the cost of nuclear energy.

As stated above, actual hourly demand is derived by super-imposing both an annual pattern (to capture seasonality, i.e. longterm planning aspects) and a daily pattern (to capture within-daydemand, and thus price variations, i.e. a short term planningaspect). We have chosen not to include a weekly cycle, as thiswould complicate the model without providing any additionalinsights beyond those generated by the annual and daily patterns.

For the annual pattern we assume a sin wave with amplitude0.2. This implies that the maximum daily demand (typically inJanuary) equals 1.5 times the minimum daily demand (typicallymid-summer). Daily variations are captured using a multiplierwhich follows a stylised pattern of Swiss daily demand: a peakaround noon, a trough around 4 a.m. and a ratio of 1.8 between

the intra-day maximum and minimum values. This shape isillustrated in Fig. 6. These assumptions imply a maximum hourlydemand equal to 1*1.2*1.25¼1.5 (at noon in winter) compared toa minimum hourly demand of 1*0.8*0.7¼0.56 (at 4 a.m. insummer).

The annual pattern of precipitation is calibrated using monthlyaverage precipitation in Switzerland over the period 1961–1990,and approximated using a sin wave which peaks in July. Theaverage precipitation is set at 0.5 h�1, implying that the totalamount of precipitation is calibrated to represent 50% of the totalannual demand. The precipitation is assumed to be shared equallybetween RR and HS plants, again a rough approximation of theSwiss generation capacity.

A key aspect of the model is the assumption regarding the splitbetween snow and rain, as well as when the snow melts. Wecalibrated the model using data from the Nordic market(historically about 50% of annual inflow has been concentratedin the 3 months following week 18 (Kauppi and Liski, 2008)) andSwitzerland (80% of the total inflow occurs in the April–September period (Office federal de l’energie, 2007)), and theassumption that HS reservoirs are located higher up in themountains, implying more snow and later melting compared toRR plants.

In the base case we assume a reservoir capacity of 1200 MWh,equivalent to about 14% of annual demand, which correspondsapproximately to the total reservoir capacity of Switzerland’s HSplants. This will be considered a fairly large reservoir size in thescenarios, and we will explore the impact of having both a smallerand an even larger reservoir. Turbine capacity is assumed to be0.5 MWh/h in the base case. This assumption implies that, giventhe availability of water, the reservoir based hydro plants cansatisfy 50% of average demand, or equivalently, a third ofpeak demand. In the scenarios we consider values rangingfrom 0.25 to 1.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–73117304

We also model in a very crude way that for lower reservoirlevels, the maximum production rate decreases. Indeed, lowerreservoir levels imply lower pressure. But more importantly, wetake an aggregate view, i.e. we model the aggregate reservoir andthe aggregate turbine capacity of all HS plants. Consequently, alower aggregate reservoir level implies that some reservoirs mustbe close to their lower limit, and thus unable to use their fullturbine capacity. Specifically, we assume that when the overallreservoir level drops below 30% of its capacity, maximum HSproduction capacity decreases sharply, and drops to 0 when thereservoir level reaches 5% of its capacity.

Another technical assumption relates to the issue of overflowof the reservoir. Again, we model this in a fairly crude way byassuming that, when the reservoir level exceeds 90% of themaximum capacity, part of the potential inflow is lost (as somereservoirs have reached their maximum capacity), and thisoverflow fraction converges to 100% when the reservoir is full.

Note that both these technical assumptions (impact of verylow and very high reservoir levels) only play a role under extremeconditions or in extreme scenarios (e.g. the combination of a verylarge reservoir with very small turbines, or the other way round).In all the realistic scenarios, desirable policies insure that theseextreme situations are not reached.

The turbine capacity of RR plants is set at 0.5 MWh/h in thebase case, i.e. the same capacity as the HS plants in the base case.The available production capacity is determined by this para-meter and the inflow to the RR plants. The effective productionwill be determined by the demand: if demand is less that theavailable capacity, some of the potential RR capacity will bewasted.

The ‘‘Offer curve Excluding HS and RR’’ is a key modellingassumption. Its exact shape is shown in Fig. 7. We standardise themarginal cost of HS generation to be equal to 1, and call this unitc/MWh, where c can be any chosen currency. We assume themarginal cost of RR to be of the same order of magnitude, whilethe marginal cost of nuclear, gas turbines and combined cycleturbines are, respectively, assumed to be 2, 5, and 6 times higheron average. Additionally, Switzerland benefits currently from longterm import contracts at a preferential rate situated between themarginal cost of nuclear and gas turbine plants.

This curve assumes that nuclear capacity can cover approxi-mately 40% of average demand, and that exports cannot exceed25% of average demand. Thermal capacity currently representsless than 10% of average demand. We thus assume an offer curvestarting at a price of about 2 until demand reaches 0.4 (nuclear),increasing to 4 when demand reaches 0.65 (imports), andreaching 6 (thermal) for demands in excess of 0.75. We chooseto cap the offer curve as our objective is to focus on ‘‘normal’’conditions: we do not want our policy recommendations to beimpacted by occasional price spikes due to special events.

0

1

2

3

4

5

6

0Quantity (MWh/Hour)

Pric

e (c

/MW

h)

0.2 0.4 0.6 0.8 1

Fig. 7. Offer curve excluding HS and RR.

For the scenario regarding the impact of increased use of air-conditioning resulting from global warming, we need to makespecific assumptions about how this would impact demand. Forthis purpose we have combined two data sources: Frei et al.(2007) and Sailor and Pavlova (2003). One should of course beaware that these are very rough estimates, and our main objectiveis to illustrate how our model could be used to assess the impactof different scenarios. We need to make two assumptions: by howmuch will the daily electricity demand increases during thesummer, and how this increase will be distributed over the day.Regarding the increase in annual demand, the estimates men-tioned by Frei et al. (2007) for the service sector and thehousehold amount to an increase of about 1%. An alternativeapproach using the concept of cooling degree days combiningtemperature change estimates from Frei et al. (2007) and theimpact evaluated by Sailor and Pavlova (2003) yields a similarvalue. We assume that this increase will be concentrated in theperiod June–September, with the peak increase being 8%. Fig. 8illustrates our assumption regarding how this increase in demandis distributed over a day: the peak of the increase is assumed totake place during mid to late afternoon.

3.5. Validation

It is important to recall that, while the model is calibrated forSwitzerland, our objective is not to model a specific market, butrather to provide a stylised model of the decision process of HSPso as to be able to assess the qualitative impact of a change inobjective (low customer prices versus profit maximisation). Thestructure of the model has been chosen to be as simple aspossible, while capturing the key aspects of a production systemwith a significant share of HS and RR production capacity.

Recall that all parameters are expressed in relative terms, withaverage hourly demand and HS marginal cost both standardisedto equal 1. The choice of scenarios provides information about thesensitivity of results to key design parameters, in particularreservoir and turbine capacity.

The ‘‘offercurve excluding HS and RR’’ is also an essentialmodelling choice. This relates directly to the issue of modelboundary: as discussed in the introduction, our aim is to focus onthe behaviour of HSP, and we have thus focussed on modellingthis actor’s decision process. We have performed a large range ofextreme conditions tests to check the robustness of the model.

4. Simulation set-up, choice of scenarios, and method ofanalysis

The model was implemented using the Vensim& software.Results were collected over a 1-year simulation period which

00.20.40.60.8

11.21.41.6

0Hour of day

Dem

and

(MW

h/H

our)

Basewith AC

4 8 12 16 20 24

Fig. 8. Impact of increased use of air-conditioning on summer demand.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–7311 7305

followed a 1-year warm-up period to obtain appropriate initialvalues for the state variables. The time-unit is 1 h, with asimulation step of 1.

We consider five levels for the reservoir sizes (300, 600, 900,1200, and 1500) and four levels of turbine capacity (0.25, 0.50,0.75, and 1.00), which yields 20 combinations. Recall that the basecase has a reservoir capacity of 1200 and a turbine capacity of0.50. For each combination we consider the 98 policies describedin Section 3.2. For two demand scenarios: the base case and thecase with increased air-conditioning demand described above.This yields a total of 3920 simulation runs.

When analysing the results, we consider the point of view ofthe consumer who wishes to obtain electricity at the lowestpossible cost, and the point of view of HSP interested inmaximising profit. Where relevant, we also discuss the impactof different policies on total production because, HS being a‘‘green energy’’, more HS production implies less CO2, an objectiveof many governments.

5. Results and discussion

Given the large number of scenarios, it is not possible toanalyse all of these in detail. We first provide a general discussionof the results, focussing on aggregate results (annual cost for theconsumer and annual contribution for the producer) for thepreferred policies of both players. We analyse to what extendthese preferences are affected by reservoir and turbine size. Wealso discuss for which scenarios the choices of the twostakeholders converge, i.e. under what circumstances is there aconflict of interest. Next we will move on to a more detaileddiscussion of a few extreme cases, focussing on intra-year andintra-day dynamics.

We first detail the numbering used for the different polices.Type-1 policies are characterised by a single parameter: theminimum price at which HSP is willing to produce (referred to asthe desired price), which ranges from 1 to 5 in steps of 0.25. Thepolicies are referred to by this price. So policy 1.25 implies apolicy where the HSP is willing to produce for prices at or above1.25.

Type-2 policies are two-dimensional: they represent a piece-wise linear relationship between the desired price and thereservoir level, each policy being characterised by an inflectionpoint. The numbering method of these policies is showngraphically in Fig. 9. The horizontal axis expresses the reservoirlevel as a fraction of the reservoir size. The policies are grouped insets of 9 policies, numbered 01–09, 11–19,y,81–89 according totheir inflection point. All policies go through the points a–d, as

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0Reservoir level

Des

ired

pric

e

01

02

09

11

19 89

33

a b

dc

66

0.2 0.4 0.6 0.8 1.0

Fig. 9. Numbering of type-2 policies.

well as through the inflection point corresponding to theirnumber. The first digit of the inflection point refers to thereservoir level corresponding to the inflection point, and thesecond digit to the desired price: policies ending by 1 have theirinflection point for a desired price equal to 1, while policiesending by 9 have their inflection point for a desired price of 5.Policy 01 is an extreme policy where the desired price equals 1whenever the reservoir level reaches 25%. At the other extreme,for policy 89, the desired price stays at 5 unless the reservoir levelexceeds 92%. Note that these two policies are similar to type-1policies 1 and 5, respectively. Fig. 9 shows two intermediatepolicies: numbers 33 and 66.

5.1. General discussion

Table 1 provides an overview of the preferred policies of eachtype of both actors for the different reservoir size and turbinecombinations we considered. We have listed the top three type-1policies (out of 17) and the top five type-2 policies (out of 81).

We start with a discussion of the type-1 policies as these, beingone-dimensional, are easier to interpret. Three main conclusionsemerge. Firstly, for large turbine capacities and reservoir sizes, theHSP requires a higher price than the consumer to be willing toproduce. Secondly, when the reservoir size is small, HSP ‘‘always’’produces: his desired price equals 1, so he will produce as long asthere is water available, i.e. he behaves like an RR plant. This is alogical consequence of the lack of storage capacity. Thirdly, whenthere is limited turbine capacity, both produce most of the time:the desired price equals at most 2 except for the case where thereservoir level equals 600. Again this is logical: when turbinecapacity is small compared to the average inflow, it is notdesirable to store water, given that the turbine capacity limits theability to displace production in time.

Overall, the consumers’ desired price increases marginally inturbine capacity for a given reservoir size, and in reservoir size fora given turbine capacity. HSP’s behaviour is more complex. For agiven reservoir capacity, his desired price is non-decreasing inturbine capacity. For low to medium turbine capacity, the desiredprice is non-monotone in reservoir size: we observe first anincrease, and then a decrease. We can explain this intuitively asfollows. Consider a turbine capacity of 0.25. When the reservoir issmall, the producer operates the plant like an RR plant. For asomewhat larger reservoir, water is managed quite cautiously(policies 3.75–4.25), while for an even larger reservoir, water israrely a constraint given the turbine capacity, leading to a lowerdesired price. For high turbine capacity, he produces ‘‘always’’when the reservoir size is small, and very cautiously (desiredprice 5) when the reservoir is large.

If we compare the desired prices of HSP and the consumer, weobserve that these tend to converge in scenarios with a largereservoir and low turbine capacity, and show the most significantdivergence for the scenarios with large reservoirs and largecapacity. Intuitively, in the first case there is little scope forstrategic behaviour: water is plenty, it is best to produce up to theturbine capacity. In the latter case there is much more flexibilityin the timing of production.

Next, we move to the discussion of the type-2 policies. Thepreferred policies are summarised in Table 1 and illustratedgraphically in Fig. 10. We use the terminology ‘‘convex’’ and‘‘concave’’ policies to describe those which are, respectively,above and below the ‘‘diagonal’’. Convex policies are moreconservative, i.e. they are characterised by a high desired pricefor most forecasted reservoir levels, while for concave policies, thedesired price drops fairly fast as soon as the expected reservoirlevel increases above its lower limit. We use the term ‘‘corner’’

Table 1Overview of preferred policies.

Reservoir size 300 600 900 1200 1500

Turbine capacity 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00 0.25 0.50 0.75 1.00

Type 1

Consumer 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.25 2.25 2.25 2.00 2.25 2.50 2.50 2.00 2.25 2.50 2.50

2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.00 2.50 2.50 2.25 2.50 2.25 2.25 2.25 2.50 2.75 2.75

1.00 2.50 2.50 2.50 1.00 2.50 2.50 2.50 2.50 2.50 2.75 2.75 2.50 2.00 2.75 2.75 2.50 2.75 2.25 2.25

Producer 1.00 1.00 1.00 1.00 4.00 5.00 5.00 5.00 2.00 5.00 5.00 5.00 2.00 4.00 5.00 5.00 2.00 4.00 5.00 5.00

1.25 1.25 1.25 1.25 4.25 4.75 4.75 4.75 2.25 4.75 4.75 4.75 2.25 3.75 4.75 4.75 2.25 4.25 4.75 4.75

1.50 1.50 1.50 1.50 3.75 4.50 4.50 4.50 2.50 4.50 4.50 4.50 2.50 4.25 4.50 4.50 2.50 3.75 4.50 4.50

Type 2

Consumer 6 84 84 84 5 84 84 84 83 84 84 84 17 83 84 84 25 83 84 84

5 8 8 8 6 7 83 83 74 7 83 83 8 84 83 83 6 84 83 83

7 83 83 7 15 8 8 8 84 83 85 85 26 74 74 74 16 74 85 75

15 7 7 83 4 83 7 7 8 8 8 8 36 7 85 85 7 17 75 74

16 9 17 9 1 17 85 85 17 17 7 7 7 8 75 75 35 7 74 85

Producer 89 89 89 89 89 89 89 89 84 89 89 89 19 89 89 89 81 89 89 89

88 79 79 79 88 79 79 79 75 88 79 79 28 79 79 79 72 79 79 79

79 88 88 88 79 88 88 88 66 79 88 88 37 69 69 69 63 88 69 69

87 69 69 69 87 69 69 69 57 87 69 69 46 88 59 59 19 69 88 88

78 78 78 78 78 78 78 78 76 78 78 78 55 78 88 88 28 78 78 78

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.00Forecasted Reservoir fill rate

Des

ired

pric

e

Corner Concave Diagonal Convex

89

84

83

56

17

19

25

81

0.20 0.40 0.60 0.80 1.00

Fig. 10. Graphical representation of preferred type-2 policies.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–73117306

policies to describe extremely conservative policies (policy 89 andsimilar ones) where the desired price remains at the maximumlevel for most reservoir levels.

Using this terminology, we observe that HSP favours ‘‘corner’’policies (and to a lesser extend concave policies), unless he has alarge reservoir and comparatively small turbines, in which case hemoves towards ‘‘diagonal’’ policies. Note that these corner policiesare quite similar to the high-price type-1 policies favoured by HSPin scenarios with medium to high capacity and reservoir size.

The intuition is that when turbine size does not allowexploiting the full reservoir capacity during a short period ofhigh prices, it is preferable to produce also at lower prices. It isworth noting the very extreme and contrasting policies selectedby HSP in the case of a very small reservoir: among type-1 policieshe opts for a very low price, operating like a river-run plant, whileamong type-2 policies he selects corner policies, i.e. a very highprice unless the reservoir is nearly full. This is a consequence ofthe lack of flexibility of type-1 policies which do not allowreservation price to vary as a function of the reservoir level. In thiscase, a type-1 policy with a high reservation price would result invery low production. It is therefore preferable to jump to the otherextreme and operate like an RR plant.

The consumer generally favours concave polices, unlessturbine capacity is limited, in which case he prefers linear ofeven convex policies.

Comparing the choices of the consumer and HSP we canconclude that for a given turbine capacity, the customer has mostto loose from a profit-oriented strategy when the reservoir size islarge, and that for a given reservoir size, this loss increases asturbine capacity decreases. Divergence of interest is maximal for areservoir size of 300 and a capacity of 0.25: HSP favours cornerpolicies while the consumer favours convex policies. The highestdegree of convergence occurs for relatively large reservoirs andturbine capacity, where the producer still favours corner policies,but the consumer selects concave policies. This is quite differentfrom case of type-1 policies, where the maximal divergenceoccurred for a large reservoir and high capacity.

From this general discussion we can conclude that for eachscenario and each player the top choices for each policy type aresimilar. We can thus without loss of generality focus on the topchoice in each category. We next turn to the consequences ofthese different choices in terms of customer costs and producercontribution.

The producer always favours type-2 policies, i.e. his preferredtype-2 policy yields a higher contribution than his preferred type-1 policy for all the scenarios. The customer favours type-1policies, except in four cases: a turbine capacity of 0.25 combinedwith a reservoir size of 600 or 900, and a reservoir size of 1500combined with a turbine capacity of 0.75 and 1. Among these four,only in the case of a reservoir size of 600 and a turbine capacity of0.25 do his favoured type-1 and type-2 policies result insignificantly different total customer costs.

Table 2 provides an overview by averaging several keymeasures across the different scenarios, while Table 3 providesthe net loss for each scenario. Table 2 illustrates that the producerwould loose on average 30% of his total contribution if he wereforced to apply the consumers’ preferred policies, while theconsumer would face a cost increase of on average 10% if theproducer’s preferred policies were implemented. The next columnshows the net cost, calculated as total cost�total contribution:these numbers indicate that applying the producers policiesrather than the consumers’ policies results in a cost difference ofabout 5%, illustrating that the key difference between the two setsof policies is more a matter of how to share the profit/cost rather

Table 2Overview of comparison between preferred producer and consumer policies.

Total contribution Total cost Net cost HS production HS price

Producer policies 4818 31,681 26,863 2086 3.31

Consumer policies 3353 28,854 25,502 1706 2.96

Ratios

Producer/consumer 1.44 1.10 1.05 1.22 1.12

Consumer/producer 0.70 0.91 0.95 0.82 0.90

Table 3Net loss.

Turbine capacity Reservoir size

300 600 900 1200 1500

0.25 451 501 76 117 47

0.50 509 1168 1615 1912 1711

0.75 718 1123 1676 2308 3649

1.00 754 1165 1670 2364 3701

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

Turbine Capacity

Tota

l Cos

t And

Con

trib

utio

n

Prod Cost

Cons Cost

Prod Contr

Cons Contr

Reservoir Size

300 600 900 1,200 1,500

Fig. 11. Preferred consumer and producer policies: total cost and contribution.

0

500

1,000

1,500

2,000

2,500

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

Turbine Capacity

HS

Prod

uctio

n

Producer

Consumer

ReservoirSize

300 600 900 1,200 1,500

Fig. 12. Production of HS energy.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–7311 7307

than the total cost. It is worth noting that while, as expected, theweighted average price at which the HS energy is sold is lowerunder the consumer policies (about 10%), these policies result in alower total HS production (about 20%) and correspondinglyhigher overflow. We elaborate on this when discussing intra-yearand intra-day behaviour: allowing different policies for differentseasons would limit overflow.

Table 3 looks at the different scenarios from a social optimumperspective and shows the net loss, defined as total cost minuscontribution, when the producer’s preferred policies are chosenrather than the consumers’. For a given reservoir size, net lossincreases in turbine capacity. For a given turbine size, net lossincreases in reservoir size unless the turbine capacity iscomparatively small. Intuitively, once the turbine capacitybecomes the binding constraint rather than water availability, afurther increase in reservoir size has little impact. Similarly, for agiven reservoir size, as the turbine capacity increases, the net lossincreases significantly, until reservoir size becomes the bindingconstraint.

Fig. 11 provides a visual interpretation of these results. Wenotice that, when HSP’s preferred policy is implemented, reservoirsize and turbine capacity have only a limited impact on the totalcontribution and the customer cost. When the consumerspreferred policies are implemented, both contribution and costvary much more across scenarios.

The cost difference between HSPs’ and the consumers’preferred policies increases both in turbine capacity and inreservoir size, while the large difference in terms of contributionoccurs for intermediate reservoir sizes combined with largeturbines.

Fig. 12 illustrates the HS production resulting form thedifferent policies. The total annual production is systematicallyhigher when the preferred policy of the HSP is implemented,except in the four scenarios where the consumer chooses a type-2policy, in which case the production is the same. Given theproducers’ decision policies, HS production increases in reservoirsize when turbine capacity equals 0.25, and is constant for allother scenarios.

With the consumers’ policies production increases in turbinecapacity for a small or a large reservoir, but is slightly non-monotone for the intermediate cases. For a given turbine capacity,production increases in reservoir size, unless there is a switchfrom a type-2 to a type-1 policy (between turbine capacities 0.25and 0.5 for reservoir sizes 600 and 900).

The price obtained for the sale of HS energy is mostly higherunder the producer policy (Fig. 13). The only two exceptions arecases where the consumer favours a type-2 policy. Note thatalthough the weighted HS price is higher for the policies chosenby the consumer in these two cases, the weighted price for thecustomer is always lower (recall Fig. 11). In these scenarios (largereservoir and low turbine capacity) HSP produces when prices are

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–73117308

low and the reservoir is full at about 80% (a linear type-2) whilethe consumer’s rigid type-1 policy results in overflow.

Under the consumer policies, prices decrease monotonously inturbine capacity, and particularly sharply when turbine capacityincreases from 0.25 to 0.5. They initially decrease and thenincrease in reservoir level (for sizes 600 and up). The same patternis observed for the decisions of HSP if the reservoir is small. Forlarger reservoirs, the price peaks for a turbine size of 0.5. The priceis monotone in reservoir size, unless the turbine capacity equals0.25, in which case there is a peak for a reservoir size of 600.

Fig. 14 shows the contribution and cost resulting from HSP’spreferred type-1 and type-2 policies. While the difference incontribution is minimal (mostly less than 3%), there are largedifferences in cost (up to 20%), unless turbine capacity is verysmall. The difference in net cost (cost—contribution) is close to30% for certain scenarios. The average cost increase equals 6.5times the average contribution increase. This results from thesignificant increase in the average price at which hydro energy issold: 5.1 compared to 3.3. Consequently, although customers

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

Turbine Capacity

Uni

t Pric

e H

S

ProducerConsumer

Reservoir Size

300 600 900 1,200 1,500

Fig. 13. Unit sale price of HS energy.

05,000

10,00015,00020,00025,00030,00035,00040,00045,000

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

0.25

0.50

0.75

1.00

Turbine Capacity

Tota

l Con

trib

utio

n A

nd C

ost

Contribution P1Cost P1Contribution P2Cost P2

Reservoir Size

300 600 900 1,200 1,500

Fig. 14. Producer’s preferred policies: type-1 versus type-2 policies.

favour type-1 policies, requiring producers to apply such policieswithout regulating the price at which they are willing to producecould seriously backfire.

5.2. Intra-year and intra-day dynamics

Next we turn our attention to intra-year and intra-daydynamics for four scenarios. As expected, the previous discussionillustrates that as the flexibility of the HSP increases (through alarger reservoir and/or larger turbine capacity), the conflict ofinterest between the maximisation of contribution and theminimisation of cost increases. We therefore focus on fourextreme scenarios to analyse the intra-year and intra-dayconsequences of increased flexibility by considering two reservoirlevels (300 and 1500) and two turbine levels (0.25 and 1). Table 4provides a summary of the characteristics of these 4 scenarios forthe preferred policies of each type for both actors. The lines inbold indicate the preferred policies. In the discussion we identifythe P1 policies by their reservation price and the P2 policies bytheir number (recall Fig. 9).

With a small reservoir and small turbines, overflow isunavoidable. Surprisingly, the policy selected by the consumeryields by far the largest overflow (and thus the lowest HSproduction). This is caused by the reservation price of 2 for theconsumer’s P1 policy which drives HS production down at night,especially in summer and fall. HSP’s reservation price of 1 is neverconstraining, resulting in a production level equal to the turbinecapacity whenever sufficient water is available. It is interesting tonote that the consumer’s type-2 policy and HSP’s type-1 and type-2 policies result in the same total production, but distributeddifferently over the year, as illustrated in Fig. 15. The smallreservoir size does not allow for much intra-day accumulation,except in winter (very low inflow), where HSP’s type-2 policyinduces him to stop production for a few hours at night so as to beable to produce more during the day. Intraday price fluctuationsare limited, except in spring where we observe a price of 2.0 atnight, and peaking at 6.0 during the day.

Next let us consider a small reservoir with large turbines.Although the turbine size makes it possible to eliminate overflow,the consumer’s type-1 policy again results in overflow from latesummer to early winter, as the price at night falls below 2.0. Thelarger turbine size mainly affects intraday price fluctuations.Depending on the season and the objective, the fluctuations canincrease or decrease. Fig. 16 shows the production patterns andresulting prices for a typical fall day. While the consumer uses theincreased flexibility to level the price (bold line), HSP chooses toincrease the variation. It is worth noting that in both scenarios theaverage price at which HS energy is sold is well below the averageelectricity price: the lack of storage capacity results in a large partof the production taking place during the off-peak periods. Inother words: the HS facility operates during a significant part ofthe time as an RR plant.

Next, let us consider the case of a large reservoir. Note that inthis case, despite the 1-year warm-up period, the sum ofproduction and overflow is not constant, as the reservoir is notfull at the start of the simulation, so the final value can exceed theinitial value. If the turbines are small, the consumer and HSPbehave in a very similar way. Intra-day price fluctuations arenegligible in summer and fall, while prices vary from 2 to 6 on adaily basis in winter and spring. The combination of a largereservoir and low turbine capacity results in production beingfairly constant over the year: the ratio between maximum andminimum daily production equals 2, compared to more than 10with the small reservoir size.

Table 4Overview of extreme scenarios.

Reservoir

capacity

Turbine

size

Policy

type

Agent P1 (price), P2

(number)

Average weighted

price

Average weighted HS

price

Contribution Cost Production Overflow

300 0.25 P1 P 1.0 3.8 2.8 2812 33,007 1566 590

C 2.0 3.8 3.3 2643 32,647 1163 993P2 P 89 3.9 3.2 3440 33,895 1566 590

C 6 3.8 2.9 2952 32,890 1566 590

1.00 P1 P 1.0 3.8 2.4 3030 32,439 2156 0

C 2.0 3.5 2.6 2190 30,244 1410 746P2 P 89 3.8 2.7 3725 32,533 2156 0

C 84 3.6 2.6 3377 31,525 2156 0

1500 0.25 P1 P 2.0 3.6 3.6 4358 30,703 1651 201

C 2.0 3.6 3.6 4358 30,703 1651 201P2 P 81 3.6 3.3 4782 31,174 2043 113

C 25 3.6 3.3 4753 30,918 2055 101

1.00 P1 P 5.0 4.2 5.0 4760 36,709 1190 957

C 2.5 3.0 2.9 3247 25,883 1751 145

P2 P 89 3.5 3.5 5428 30,227 2156 0C 84 3.0 3.2 4752 25,850 2154 0

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0Days

HS

Prod

uctio

n

P1-300-0.25-P P1-300-0.25-C P2-300-0.25-P P2-300-0.25-C

50 100 150 200 250 300 350

Fig. 15. Scenario 1. Hydro storage production.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–7311 7309

Finally, let us consider the most interesting scenario, where thecombination of a large reservoir and large turbines gives the actorsthe most scope for strategic behaviour, which also implies a need forflexible policies: both HSP and the consumer favour a type-2 policy.This is illustrated in Fig. 17 which shows the production decisions andthe resulting prices. If HSP must choose a fixed price policy (type-1),he chooses the maximum price of 5.0, and limits his production to thepeak hours in winter and spring. Consequently, even in summer, theaverage price remains high. It is worth noting (see Table 4) that this isthe only scenario where the average weighted price received by HSPfor HS production significantly exceeds the overall average weightedprice (5 versus 4.2). The consumer favours a reservation price of 2.5,but this results in overproduction at the start of the winter, andrunning out of water around late February: production drops to a verylow level and prices soar (Fig. 17). Opting for a type-2 policy allowsboth players to achieve simultaneously lower costs and a highercontribution. This also results in less intraday price fluctuations,especially when HSP decides on production levels.

It is interesting to compare the two policies of the consumer:they yield about the same cost, but the contribution under thetype-2 policy is 50% higher. The latter also results in a smootherand more logical annual price pattern, with higher prices inwinter and lower prices in summer.

5.3. Exogenous change: air-conditioning

This type of model is also useful to study the impact ofexogenous changes. One example is global warming, which would

have multiple impacts. These include an increase in electricityconsumption through an increase in the use of air-conditioning insummer, and changes in the volume and the timing of precipita-tion which would affect electricity supply. This model allows us toanalyse these different effects separately and jointly. We brieflyillustrate this potential by simulating a scenario representing anincrease of air-conditioning demand in summer.

This scenario is most relevant when production capacity istight. We therefore focus on the case with a small reservoir andlimited turbine capacity. Although demand only changes insummer, the resulting change in preferred policy has knock-oneffects over the full year. Total cost and contribution increase forthe four preferred policies.

The only change in policy choice occurs for HSP’s type-1policy: his reservation price jumps from 1.00 to 4.25. This resultsin a significantly lower HS production (and correspondinglyhigher overflow) and thus a stiff increase in average price (from3.9 to 4.4). This change in policy also impacts the daily productionpattern: in spring, HSP will produce less at night, resulting in ahigher price at that time.

While the average price only increases marginally for the otherthree preferred policies, there is a significant impact on the pricepattern in summer. Consider for instance a typical summer day inlate July, as illustrated in Fig. 18. While the peak price equalledabout 2.3 in the base case, in this scenario the peak ranges from3.9 to 4.2 depending on the chosen policy. Note that three of thefour policies yield quasi-identical prices.

6. Conclusions and further work

Our objective was to illustrate how different contexts (a state-owned company versus a privatised producer) lead to differentobjectives (minimising the costs for the consumer versusmaximising the producers contribution) and can lead to differentproduction policies, which in turn will impact both annual andintraday production and price patterns, using a stylised simula-tion model.

We conclude that the impact of switching from a customerperspective to a profit maximising perspective will have thelargest impact in a situation where the producer has mostflexibility, i.e. the scenarios combining larger reservoirs with highturbine capacity. In this case, the increase in electricity costresulting from the change in policy far outweighs the producersincrease in contribution, resulting in a net welfare loss. In case ofsmall reservoirs and/or small turbines, the net loss is limited, but

02468

101214

0Days

HS

Prod

uctio

n

P1-1500-1-P P1-1500-1-C P2-1500-1-P P2-1500-1-C

0

1

2

3

4

5

6

0Days

Pric

e

P1-1500-1-P P1-1500-1-C P2-1500-1-P P2-1500-1-C

100 200 300 100 200 300

Fig. 17. Scenario 4. Annual HS production and resulting prices.

0

1

2

3

4

5

6

0Hour

Pric

e

P1-P P1-C P2-P P2-C Base case

5 10 15 20

Fig. 18. Air-conditioning: price patterns on a typical summer day.

0123456

0

Hour

Pric

e

P1-300-0.25-C P1-300-1-C

P2-300-0.25-P P2-300-1-P

0.0

0.1

0.2

0.3

0.4

0.5

0

Days

HS

Prod

uctio

n

P1-300-0.25-C P1-300-1-C

P2-300-0.25-P P2-300-1-P

5 10 15 20 5 10 15 20

Fig. 16. Scenarios 1 and 2. Intra-day price variations in fall.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–73117310

we do observe a reallocation: increased total cost and highercontribution.

A second conclusion is the importance of allowing for flexibleproduction policies. We illustrated this for the case where HSP isconstrained to the very rigid type-1 policy and this could result ina cost increase for the customer of more than 20% when theproducer has a lot of flexibility (large reservoirs and high turbinecapacity). A lack of flexibility can lead to a decision to let thereservoir flow over when prices are too low. We noted inparticular that the cost minimisation policies, which tend to beof the more rigid type-1, surprisingly lead to more overflow thanthe profit maximising type-2 policies, especially when thereservoir size is small.

This leads to the conclusion that not only should the allowedpolicy types be flexible, they should also vary by season, an optionwe did not allow here, and which is a natural direction for furtherwork.

As the comparison of scenarios with different reservoir size,turbine capacity and summer demand illustrates, our results aresensitive to the specific structural assumptions. In particular, wefocussed on an energy system where HS and RR plants represent50% of total generation capacity, and the annual inflow represents50% of annual demand. The selected offer-curve also impliesspecific assumptions on the alternative generation sources. Inparticular, we assumed a significant share of nuclear energy,which implies a low-cost alternative to hydro and thus limits thepotential for strategic behaviour.

The resulting policy choices are also influenced by the timingof inflows to the reservoirs. In case of an increase in the averagetemperature, or of a recalibration of the model for warmercountries, more of the inflow would be under the form ofrain rather than melting snow, leading to a more homogeneousinflow over the year. The smaller the reservoir comparedto the turbine capacity, the larger the impact on the resultingpolicy choices. In particular, HSP would less often be facedwith the trade-off between producing at low prices in spring (tocreate space in the reservoir) and taking the risk of wateroverflows.

Another direction for further work is the inclusion of theoption of overnight pumping. Such an extension would funda-mentally change the nature of the decision process, as the issue ofwater carry-over from one season to the next would disappear.Depending on the pumping capacity, the relevant time-horizonfor the analysis would vary from days to weeks, rather than thecurrent horizon of 1 year.

References

Afshar, M.H., Moeini, R., 2008. Partially and fully constrained ant algorithms for theoptimal solution of large scale reservoir operation problems. Water ResourceManagement 22 (12), 1835–1857.

A. van Ackere, P. Ochoa / Energy Policy 38 (2010) 7299–7311 7311

Ambec, S., Doucet, J., 2003. Decentralizing hydropower production. CanadianJournal of Economics 36 (3), 587–607.

Amlin, J., Backus, G., 1996. Utility Models for the New Competitive ElectricMarkets. Systems Solutions Inc., Fairborn, Ohio.

Amobi, M.C., 2007. Deregulating the electricity industry in Nigeria: lessons fromthe British reform. Socio-Economic Planning Sciences 41 (4), 291–304.

Association des entreprises electriques suisses, Rapport annuel, 2006. Availablefrom: /http://www.electricite.ch/uploads/media/Rapport_annuel_2006.pdfS.

Borenstein, S, Bushnell, J., 1999. An empirical analysis of the potential for marketpower in California’s electricity market. Journal of Industrial Economics 47 (3),285–323.

Bozorg Haddad, O., Afshar, A., Marino, M.A., 2009. Optimization of non-convexwater resource problems by honey-bee mating optimization (HBMO)algorithm. Engineering Computations 26 (3), 267–280.

Bunn, D.W., Dyner, I., Larsen, E.R., 1997. Modelling latent market power across gasand electricity markets. System Dynamics Review 13 (4), 271–288.

Bushnell, J., 2003. A mixed complementary model of hydro-thermal electricitycompetition in the Western US. Operations Research 51 (1), 81–93.

Crampes, C., Moreaux, M., 2001. Water resource and power generation. Interna-tional Journal of Industrial Organization 19 (6), 975–997.

da Costa Flach, B., Barroso, L.A., Pereira, M.V., 2009. Long term optimal allocation ofhydro generation for a price-maker company in a competitive market: latestdevelopments and a SDDP approach. Working Paper. Available from: /http://portal.psr-inc.com/portal/psr/iframe.html?altura=4000&url=/app/publicacoes.aspxS.

Filippini, M., Banfi, S., Luchsinger, C., 2002. Deregulation of the Swiss ElectricityIndustry: implication for the hydropower sector. Working Paper, No. 13,Centre for Energy Policy and Economics, Swiss Federal Institute of Technology.

Ford, A., 1999. Cycles in competitive electricity markets: a simulation study of theWestern United States. Energy Policy 27 (11), 637–658.

Ford, A., 2001. Waiting for the boom. Energy Policy 29 (11), 847–869.Ford, A., Geinzer, J., 1990. Adding uncertainty to least cost planning: a case study of

efficiency standards in the Northwest. Energy Policy 18 (4), 331–339.Frei, C., Calanca, P., Schar, C., Wanner, H., Schadler, B., Haberli, W., Appenzeller, C.,

Neu, U., Thalmann, E., Ritz, C., Hohmann, R., 2007. Les changementsclimatiques et la Suisse en 2050: Impacts attendus sur l’environnement, lasociete et l’economie. Available from: /http://www.occc.ch/products/ch2050/CH2050-rapport.htmlS (accessed 12.05.09).

Garcıa, A., Reitzes, J., Stacchetti, E., 2001. Strategic pricing when electricity isstorable. Journal of Regulatory Economics 20 (3), 223–247.

Gary, S., Larsen, E.R., 2000. Improving firm performance in out-of-equilibrium,deregulated markets using feedback simulation models. Energy Policy 28 (12),845–855.

Green, R., Newbery, D., 1992. Competition in the British electricity spot market.Journal of Political Economy 100, 929–953.

Hammons, T.J., Rudnick, H., Barroso, L.A., 2002. Latin America: deregulation in ahydro-dominated market. Hydro Review 10 (4), 20–27.

Horsley, A., Wrobel, A.J., 2007. Profit maximizing operation and valuation ofhydroelectricity plant: a new solution of Koopman’s problem. Journal ofEconomic Dynamics and Control 31 (3), 938–970.

Kauppi, O., Liski, M., 2008. Market power and storage. Evidence from hydro use inthe Nordic power market. Working Paper.

Koopmans, T.C., 1957. Water storage policy in a simplified hydroelectric system.In: Proceedings of the First International Conference on Operational Research,pp. 193–227.

Lamond, B.F., 2003. Stochastic optimization of a hydroelectric reservoir usingpiecewise polynomial approximations. Information Systems and OperationalResearch 41 (1), 51–69.

Lamond, B.F., Boukhtouta, A., 1996. Optimizing long-term hydro-power productionusing Markov decision processes. International Transactions in OperationalResearch 3 (3/4), 223–241.

Lyneis, J.M., Bespolka, C., Tucker, B., 1994. Planning for a competitiveenvironment—the prospects for America’s electricity utilities. In: Paper readat International System Dynamics Conference, Universtiy of Stirling, Scotland.

Nail, R., 1977. Managing the Energy Transition. Ballinger Publishing Company,Cambridge, MA.

Nail, R., 1992. A system dynamics model for national energy policy planning.System Dynamics Review 8 (1), 1–19.

Ochoa, P., 2007. The Dynamics of the Swiss electricity market: three essays. Ph.D.Dissertation, HEC—University of Lausanne.

Office Federal de l’energie (OFEN), 2001. Wirtschaftliche Auswirkungen derVolksinitiativen ‘‘Strom ohne Atom’’ und ‘‘Moratorium Plus’’ Analyse miteinem Gleichgewichtsmodell, Bern.

Office federal de l’energie (OFEN), 2007. Statistique Suisse de l’electricite 2006.Pritchard, G., Philpott, A.B., Neame, P.J., 2005. Mathematical Programming 103 (3),

445–461.Pritchard, G., Zakeri, G., 2003. Market offering strategies for hydroelectric

generators. Operations Research 51 (4), 602–612.Sailor, D.J., Pavlova, A.A, 2003. Air conditioning market saturation and long-term

response of residential cooling energy demand to climate change. Energy 28(9), 941–951.

Scott, T.J., Read, E.G., 1996. Modelling hydro reservoir operation in a deregulatedelectricity market. International Transactions in Operational Research 3 (3-4),243–253.

Sweeney, J.L., 2002. The California Electricity Crisis. Hoover Institution Press SIEPR,Stanford.

von der Fehr, N.H.M, Harbord, D., 1993. Spot market competition in the UKelectricity industry. Economic Journal 103, 531–546.