Investment In Generation Capacity

Restructured Models for a Restructured Industry ?

Yves Smeers

ENERDAYDresden Technological University

April 2006

Introduction

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An old and still relevant (Stoft, 2002) picture

GW

0

0

1

1

€

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The problem: before and today

Plant differing by

Ki investment cost (annual or /Mwh value)

ci operating cost (/Mwh)

A time varying (or stochastic) demand

A concern of security of supply

Loss of Load Probability (LOLP) or

Expected unserved Unergy

The determination of the cost of capital

The old days

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Before restructuring: the notion of capacity expansion planning

Assume

An horizon t = 1, …, T or the order of 20 years or more

A time varying demand for each t (e.g. decomposed in different times segments h = 1, …, H)

Demand is exogenously given (does not react to price)

Select a mix of generation capacity so as to satisfy demand at minimal discounted investment and operations cost, subject to some (possibly simplified) reliability criterion

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Before restructuring: an explosion of detailed capacity expansion planning models

Since the first models in EdF

Linear programming, nonlinear programming and control theory, mixed integer programming

With quite varying degrees of complexity for representing operations

And some attempts to use stochastic programming to deal with long term demand and fuel price uncertainty

Little concern about the cost of capital (pervasive CAPM)

A first shock

Engineers recede Financial consultants take the leadEconomists wait

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Uncertainty and option values

New question emerged in the late 80’s: The impact of uncertainty

Demand is uncertain and plants have different construction time

The higher the investment cost, the longer the construction time

With the result that deterministic models lead to an excess of capital intensive plants

The theory of option value preempted stochastic programming

Less capacity intensive technologies have an option value

They can be invested later, when more information is available

And hence allows one to better adapt to the demand and fuel price information

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The path breaking textbook (Dixit and Pindyck, 1994)

Most of (but not all) the book is devoted to the monopoly case

Questions about the use of the Net Present ValueSuppose a project whose payoff follows a stochastic process. It can be invested today or later at cost K

The main finding: NPV recedes; threshold for investment: wait till

MaxTε[V (T )−K)e−ρT ]

V≥V*> K

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Real options after restructuring (1)

A significant (but useful ?) impact

One no longer focuses on a mix of plants but on a single technology

One no longer focuses on an exogenously evolving load duration curve, but on an exogenously evolving price process

One stops talking about security of supply and reliability criteria

A grey area where one balances between CPAM and risk premia in traded securities

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Real options after restructuring (2)

A significant (but useful ?) impact

With a methodological shift towards

Analytic solution (of differential equations) when they exist that are seen as simpler and more intuitive than large mathematical programming models

Partial differential equation or dynamic programming otherwise (and a problem of dimensionality which is not always mentioned)

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A shift towards shorter term issues: individual plant valuation

Emphasis on the option to take advantage of high spot prices: value short term flexibility

First without unit commitment type constraints: option to start up and shut down

Then with unit commitment type constraints: as before but subject to plant constraints

Leading to a new interest in dynamic programming to asses the value of plants and gas contracts seen as exotic options

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And possibly a fatal flaw (1)

The price process, represented by the stochastic process, is exogenousHidden by technical (even though important) discussions

Gas and electricity price modelsEssentially mean reverting

Calibrated on relatively illiquid and short term markets

And a general feeling that these calibrations are not really satisfactory

Strange idea: assimilate a plant to a financial asset and use finance theory (can I sell short a coal plant ?)

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And possibly a fatal flaw (2)

A first question

Take some stochastic gas and electricity prices processes

Suppose one dispatches a generating system according to this process (a stochastic unit commitment per plant)

Suppose one trades the gas from long term contracts on spot markets in the same way (a stochastic unit commitment type model of a gas contract)

Are we sure that this will not modifyThe prices and henceThe spark and dark spreads ?

This is an equilibrium problem: the stochastic processes areendogenous

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And possibly a fatal flaw (3)

A second question

There is no obligation to servebut peak plants will be remunerated by high prices when there isscarcity of capacity

Are we sure we can model the high prices ?jumps are difficult to model and involve regime switching

Are we sure that regulators will not intervene to introduce price caps, that we cannot model ?

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And possibly a fatal flaw (4)

A third question

Are we sure that we can model boom and bust cycles and their impact on price processes ?

What about the risk premium associated to plants that may operate a few hours every two or three years ? Do we trust the CAPM sufficiently to find the capital cost of individual units separately from the cost of capital of a well diversified firm?

Maybe the plant by plant valuation does not really work because we remain so far from a perfectly competitive system where prices are indeed independent of each agent decision and all risks are traded on the market (market incompleteness)

The remedy ?

Here come the economists

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The next move: make the price process endogenous

Two approaches

Go back to the capacity expansion model and make demand price dependent

Expand real option and make the price process endogenous

This requires assumptions onMarket structure

Risk factors

Subject to the condition that the whole thing remains computable

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Market Structure

Three levels of conceptual and computational difficulty

Perfect competition

Open loop imperfect competition

Closed loop imperfect competition

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Risk factors (1)

Some can be taken as exogenous processese.g. coal or oil indexed gas prices

shocks on demand functions

Some are effectively endogenouse.g. electricity price

And some are complex rather unexplored derivativese.g. CO2 allowance price

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Risk factors (2)

Fuel pricesMix of mean reversions and Brownian motion system in continuous or discrete form for representing the underlying

Shocks on demand (Dixit and Pindyck, 1994)

where is an inverted demand function), x and y are industry wise and firm idiosyncratic risk factors

dx = αdt +σ dt, dx = αx dt +σx dzdx = η(x − x)dt +σ dz

P=D(Q)

P = x y D(Q)

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Risk factors (3)

Some risk factors raise a modeling issue on their own

E.g. - CO2 allowance prices are in fact derivativesThe result of an equilibrium on the allowance market some parts of which we know very little about

- Spot gas priceAnd the usual (solved ?) problem of equilibrium between long andshort term contracts

A relatively easy remedy

Conceptually easyData demandingComputationally demanding but doable

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Perfect competition and perfect foresight (1)

Expand the capacity expansion models

Make demand endogenous: Q becomes a variable related to price

Introduce consumer surplus in the objective function if demand is integrable

Or set up a more complex equilibrium model

Can imbed quite a lot of phenomena (if data is available)Impact of gas consumption on cif price (introduce supply functions of gas)

A CO2 allowance balance and hence an endogenous CO2price

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Perfect competition and perfect foresight (2)

What can this be used for ?

The difficulty

Ownership does not appear in perfect competition model (compare with a monopoly model)e.g. suppose the industry has room for 10 GW of a given type of plant with

utilisation from 6000 to 3000 hours. Will your plant run 6000 or 3000 hours ?

The usefulness

Scenarios with consistent endogenous prices:e.g. get consistent CO2 prices and study your own investment programe.g. value special access conditions to some sitesOr directly model your idiosyncratic positione.g. your plants are better so they will run 6000 hours, not 3000

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A possible illustration

The first and second compliance phase of EU-ETS

What is the impact of different allowance allocationssupply of credits from Certified Emission Reductions and

Emission Reduction Unitschange of interconnection capacities

A more difficult remedy

Conceptually relatively easyMore data demandingMuch more computationally demanding (doable today ?)

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Perfect competition and uncertainty (1)

Suppose uncertainty onFuel pricesDemand shocksPolicy (e.g. NAPs)Unknown parameters (demand elasticity, supply elasticity (gas))

Two approachesExpand the perfect competition models (general but heavy)

To focus on certain thingsResort to real option models (stylized but elegant)

To get insight

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Perfect competition and uncertainty (3)

The real option model (Dixit and Pindyck, 1994)

An industry with an homogenous goode.g. base load

And homogeneous firmse.g. companies only operating coal based unit

Uncertainty on demand with x industry wide risk and y firm idiosyncratic risk

Principle : Invest when the price reaches a certain level: find that level

P = x y D(Q)

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Perfect competition and uncertainty (4)

Insight :

Industry wide risk strengthens the investment criterion Payoff becomes concave because entry reduces profits from favourable industry wide events

Firms idiosyncratic risk introduces a value for waitingPayoff becomes convex because favourable events increase profits

In both cases the main result of the monopoly firm is preservedThe NPV criterion is replaced by a stronger criterionOne has to wait for a price higher than the one that set NPV at zeroDoes one find that behaviour in companies ? Yes add up on the cost of capitalDoes it have policy implications ? Yes

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Perfect competition and uncertainty (5)

Models to get more focused insight :

Expansion of the capacity expansion models to both equilibrium and uncertainty ?

E.g. the MARKAL team

How does this differ from the real optionThe techniques are completely different

differential equation vs. optimizationBut the underlying mathematical principle are the same

backward induction in optimization

⇒ Should thus give the same type of insight but more focused

A slippery road:Introducing imperfect competition

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Imperfect competition (1)

Competition can be imperfect for different reasonsMarket power: what everybody talks aboutE.g. Cournot model that we can master technically

but cannot validate empirically

Policy interventionE.g. price caps (one is well aware of it)

CO2 allocation (less known)

A major distinctionopen loop vs. closed loop

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Imperfect competition (2)

About the distinction: single stage vs. multistage models

Multistage model: investment/operationsInvest in period 0: Let X be the capacity vectorInvest in period 1: Let x be the operation vector

Suppose I have the old capacity expansion problem.Is this a single optimization problem ?

two optimization problems ?or two optimization problems that I can cast into one ?

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Imperfect competition (3)

Suppose I am in an equilibrium problemsame question: single, two, or two that I can cast in one equilibrium

problem

The question is much easier to answer in optimization than in equilibrium

The question also occurs in a multistage investment problem and is much more difficult to handle

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Imperfect competition (4)

Two viewsConsider the investment/operation model

Suppose I decide my investment and operation simultaneously The open loop problem

Suppose I decide my investment and operations sequentially

I will investing taking into account the equilibrium that will prevail inthe operations market)The closed loop system

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Imperfect competition (5)

The open loop system is quite manageable (in technical term: a complementarity problem)

The closed loop is quite unmanageable (in technical term: an equilibrium problem subject to equilibrium constraints)

Non convex problemPossible lack of pure strategy equilibrium with currently no way to detectPossible multiplicity of pure strategy equilibriumWe do not know how to compute mixed strategy equilibria

With a beautiful but dangerous resultClosed loop models are sometimes equivalent to open loop models (Kreps and Scheinkman, 1983)

A relative secure road: open loop models

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Imperfect competition and perfect foresight: open loop (1)

Expand the capacity expansion model

Recall the interpretationAgent i commit to a strategy (investment and operations/sales) for the whole

horizon, taking into account the strategy of the other agents

Technically often easy (but not always)e.g. non differentiable demand functions induced by price caps

Can imbed quite a lot of phenomenae.g. price taking behaviour on the gas market

price taking behaviour on a CO2 market

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Imperfect competition and perfect foresight: open loop (2)

The usefulnessFirms are individualizedas in the monopoly model one gets a hold on capacities of individual firms

The difficultiesThe Cournot assumption remains unvalidated in practicePrice elasticities of demand functions D(Q) are crucialAsymmetry of assumptions of market power with respect to other market (e.g. transmission)Some presentations have discredited the approach

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Imperfect competition and perfect foresight: open loop (3)

An untapped potential: assessing the impact of policy interventione.g. impact of granting CO2 allowances as a function of

- technology- past operation of plants

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Imperfect competition and uncertainty: open loop

Expand the capacity expansion model

Where each agent selects its investment/operation strategy on anevent tree

Can be done subject to the same pros and cons as in the certain case

Expand the real option model (e.g. Sawa and Roques (in progress))

Expand on Pindyck and Dixit model in a first partThe threshold level where one invest is increased for accounting for the

oligopoly of the market

The very slippery road:moving to closed loop models

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Imperfect competition : open loop vs. closed loop

Is investing under the open loop assumption the same as investing under the closed loop assumption ?

The law of unintended consequencesFutures contracts mitigate market powerRegulation (e.g. price cap) mitigates market power

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Is investing under the open loop assumption the same as investing under the closed loop assumption ? (1)

The (too) beautiful result of Kreps and Scheinkman

Suppose identical firms investing in stage 0 and practicing Bertrand competition in stage 1

Then the outcome is the same as a single stage Cournot competition

This is beautiful and of practical relevance: single stage Cournot models are easy to solve

But is it true in general ?

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Is investing under the open loop assumption the same as investing under the closed loop assumption ? (2)

One relies on Cournot assumption in electricity

Does a Kreps and Scheinkman’s like result hold for Cournot competition ?

Suppose a single demand block: e.g. base load and no uncertainty

Then: single stage: invest and sell everything forward= two stage : invest and sell on the spot market (naked merchant

plant)= three stage: invest, take futures position and sell on the spot market

(covered merchant plant)

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Is investing under the open loop assumption the same as investing under the closed loop assumption ? (3)

But this nice result does not hold when

demand is uncertain or variable

There already exists generation capacities

There are other markets (e.g. transmission)

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The law of unintended consequences (1)

Futures contracts mitigate power (the common wisdom)yes when capacities are fixed

But they may also hinder investments

In symmetric models (they will hinder investments, Grimm and Zoettl, 2005)

The effect is ambiguous in asymmetric models (Murphy andSmeers, 2006)

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The law of unintended consequences (2)(Grimm and Zoettl, 2005)

Regulation should be put in place to mitigate market power : suppose the following outcomes

Firms behave strategically in both stages XC

Firms behave competitively in both stages XFB

Investments are selected to maximize welfare subject to strategic investments in the spot markets XSB

Firms behave strategically at the investment stage but regulators manage to ensure competitive spot markets XORP

Then in term of welfareXORP < XC < XSB < XFB

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The law of unintended consequences (3)Zoettl (2005) (this meeting)

Price cap should be put in place to mitigate uncertainty becauseuncertainty is detrimental to investments. Suppose one introduces a price cap when

Firms behave competitively, thena binding price cap reduces investment (as one expects)

Firms behave strategically in both stagescertain price caps increase equilibrium investments (as one does not

expect)

The ultimate complexity

real option in strategic gamesonly irrelevant results today(this is an engineer’s point of view)

Conclusions

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Conclusions

We knew a lot about investment in the regulated days

We still know (or can know) a lot about investments in sufficiently competitive system

But we know very little when the market is imperfectly competitive and plagued by regulatory intervention.