The Value of Volatile Resources... Caltech, May 6 2010

IntroductionDAM/RTM Dynamic model

Multi-settlement Electricity MarketWho Commands the Wind?

Numerical ResultsConcluding Remarks

The Value of Volatile Resourcesin Electricity Markets

Sean P. Meyn

Joint work with: Matias Negrete-Pincetic, Gui Wang, Anupama Kowli, EhsanShafieeporfaard, and In-Koo Cho

Coordinated Science Laboratoryand the Department of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign, USA

May 5, 2010

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Outline

1 Introduction

2 DAM/RTM Dynamic model

3 Multi-settlement Electricity Market

4 Who Commands the Wind?

5 Numerical Results

6 Concluding Remarks

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Introduction

Increased deployment of renewable energy can lead tosignificant environmental benefits

However, the characteristics of renewable resources are verydifferent from those of conventional resources

It is imperative to understand their characteristics to fullyharness the benefits of renewable resources

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Introduction

6

Renewable Portfolio Standards

State renewable portfolio standard

State renewable portfolio goal

www.dsireusa.org / February 2010

Solar water heating eligible * † Extra credit for solar or customer-sited renewables

Includes non-renewable alternative resources

WA: 15% x 2020*

CA: 33% x 2020

NV: 25% x 2025*

AZ: 15% x 2025

NM: 20% x 2020 (IOUs) 10% x 2020 (co-ops)

HI: 40% x 2030

Minimum solar or customer-sited requirement

TX: 5,880 MW x 2015

UT: 20% by 2025*

CO: 20% by 2020 (IOUs) 10% by 2020 (co-ops & large munis)*

MT: 15% x 2015

ND: 10% x 2015

SD: 10% x 2015

IA: 105 MW

MN: 25% x 2025 (Xcel: 30% x 2020)

MO: 15% x 2021

WI: Varies by utility; laog 5102 x %01

MI: 10% + 1,100 MW x 2015*

OH: 25% x 2025†

ME: 30% x 2000 New RE: 10% x 2017

NH: 23.8% x 2025

MA: 15% x 2020 + 1% annual increase

(Class I RE)

RI: 16% x 2020

CT: 23% x 2020

NY: 29% x 2015

NJ: 22.5% x 2021

PA: 18% x 2020†

MD: 20% x 2022

DE: 20% x 2019*

DC: 20% x 2020

VA: 15% x 2025*

NC: 12.5% x 2021 (IOUs) 10% x 2018 (co-ops & munis)

VT: (1) RE meets any increase in retail sales x 2012;

(2) 20% RE & CHP x 2017

KS: 20% x 2020

OR: 25% x 2025 (large utilities)* 5% - 10% x 2025 (smaller utilities)

IL: 25% x 2025 WV: 25% x 2025*†

29 states + DC have an RPS

(6 states have goals)

DC 0

OW

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Wind power

Wind power is currently favored over all renewables

Its deployment presents major challenges in system operationsdue to its:

limited control capabilitiesforecasting uncertaintyuncertainty and intermittency

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Mon Tues Weds Thurs Fri SatSun0

1000

5000

6000

7000

Wind generation (MW)

Balancing Authority Load (MW) January 16-22, 2010

Figure: Example of load and wind generation data

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Different opinions...

“The Value of Wind - why more renewable energy means lower electricity bills,” AdamBruce, Chairman, British Wind Energy Association

“Wind is a free source of fuel. When the wind blows the UK’s electricity systemhas access to this free source and the power generated is automatically acceptedonto the system”

“Wind energy means lower bills; it’s as simple as that”

“Wind power’s dirty secret? Its carbon footprint”

“Wind power is touted as the cleanest and greenest renewable energy resource”

“You’ve got a non-carbon-emitting source of energy that’s free,” said DougJohnson of the Bonneville Power Administration

“However, Todd Wynn of the Cascade Policy Institute says it’s not as clean asadvocates claim. He says it’s simply because the wind is volatile and doesn’tblow all the time”

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Scope

Goal of this work

Understand how volatility impacts the value of wind generationFocus: Competitive market setting

Beyond mean energy...

We evaluate impacts of wind resources by focussing on twoparameters: penetration and volatility of wind generation.

Vehicle

Dynamic electricity market model,

Multi-settlement structure

Captures wind volatility

Ramping constraints

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Scope

Goal of this work

Understand how volatility impacts the value of wind generationFocus: Competitive market setting

Beyond mean energy...

We evaluate impacts of wind resources by focussing on twoparameters: penetration and volatility of wind generation.

Vehicle

Dynamic electricity market model,

Multi-settlement structure

Captures wind volatility

Ramping constraints8 / 50




Day-ahead market motivations

The day-ahead market (DAM) is cleared one day prior to theactual production and delivery of energy.

Economic world...

Forward markets for electricity which improve market efficiency andserve as a hedging mechanism

...Physical world

Facilitate the scheduling of generating units

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Real-time market (RTM)

At close of the DAM: The ISO generates a schedule of generatorsto supply specific levels of power for each hour over the next 24hour period.

RTM = Balancing Market

As supply and demand are not perfectly predictable, the RTMplays the role of fine-tuning this resource allocation process

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DAM/RTM

32000

30000

28000

26000

24000

22000

20000

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Meg

awat

ts

Hour Beginning

Actual Demand

Day Ahead Demand Forecast

Available Resources Forecast

Figure: March 4, 2010 CAISO forecast and real-time supply and demand

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DAM/RTM

Notation

Total demand at time t, Dttl(t) = dda(t) +D(t),

Total capacity at time t, Gttl(t) = gda(t) +G(t)Total reserve at time t,Rttl(t) = Gttl(t)−Dttl(t) = G(t)−D(t) + rda(t)

DAM Reserve policy

rda(t) ≡ rda0 is constant.

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RTM Model

RTM model of Cho & Meyn consists of the following components:

Volatility

Deviation in demand D is modeled as a driftless Brownian motionwith instantaneous variance σ2.

Friction

Generation cannot increase instantaneously: There existsζ ∈ (0,∞) such that,

G(t′)−G(t)t′ − t

≤ ζ , for all t ≥ 0, and t′ > t.

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RTM Model

Write dG(t) = ζdt− dI(t), with I non-decreasing, to model theupper bound on the rate of increase in generation.

Reserve process regarded as a controlled stochastic system,

Reserve process

dR(t) = ζdt− dI(t)− dD(t)

with control I.

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Market Analysis

Market analysis assumptions:

Cost

The production cost is a linear function of G(t),of the form cG(t) for some constant c > 0.

Value of power

Consumer obtains v units of utility per unit of power consumed:Utility to the consumer = vmin(D(t), G(t)).

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Market Analysis

Disutility from power loss

The consumer suffers utility loss if demand is not met:Disutility to the consumer = cbo|R(t)| whenever R(t) < 0.

Perfect competition

The price of power P (t) in the RTM is assumed to be exogenous(it does not depend on the decisions of the market agents).

“price-taking assumption”

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Market Analysis

The objectives of the consumer and the supplier are specified bythe respective welfare functions,

Welfare functions

WS(t) := P (t)G(t)− cG(t)

WD(t) := vmin(D(t), G(t))− cbo max(0,−R(t))− P (t)G(t)

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Market Analysis

The consumer and supplier each optimize the discountedmean-welfare

Discounted mean-welfare expressions

For given initial values of generation and demand g = G(0),d = D(0), the respective discounted rewards are denoted

KS(g, d) := E[∫

e−γtWS(t) dt],

KD(g, d) := E[∫

e−γtWD(t) dt],

γ > 0 is the discount rate.

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Market Analysis

The social planner’s problem is defined as the maximization of thetotal discounted mean welfare,

Social planner’s objective

K(g, d) = E[∫

e−γt(WS(t) +WD(t)

)dt].

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Market Analysis

The optimal reserve process is a reflected Brownian motion (RBM)on the half-line (−∞, r̄∗], with

Reserve threshold

r̄∗ =1θ+

log(cbo + v

c

).

where θ+ is the positive solution to the quadratic equation12σ

2θ2 − ζθ − γ = 0

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Market Analysis

The equilibrium price functional is a piecewise constant function ofthe equilibrium reserve process,

Equilibrium price functional

pe(re) = (v + cbo)I{re < 0}

The sum cbo + v is in fact the maximum price the consumer iswilling to pay, often called the choke-up price.

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A little bit of technical details...

On substituting the price into the respective welfare functions:

Expected welfare values

E[W∗S (t)] = (v + cbo)(E[D(t)I{Re(t) ≤ 0}]

+ E[Re(t)I{Re(t) ≤ 0}])− cE[Re(t)]

E[W∗D(t)] = −(v + cbo)E[D(t)I{Re(t) ≤ 0}]

where R = Re is the equilibrium reserve process.

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How does this look?...

v + cbo

0

r∗

PricesReserves

Normalized demand

Figure: Model price dynamics

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Familiar, right?

Purchase Price $/MWh

Previous week

Spinning reserve prices PX prices $/MWh

100

150

0

50

200

250

10

20

30

40

50

60

70

APX Power NL, April 23, 2007

California, July 2000Illinois, July 1998

Ontario, November 2005

0

1000

2000

3000

4000

5000

Mon Tues Weds Thurs Fri Mon Tues WedsWeds Thurs Fri Sat Sun

Tues Weds ThursTime3 6 9 12 15 18 213 6 9 12 15 18 213 6 9 12 15 18 21

Demand in MW Last Updated 11:00 AM Predispatch 1975.11 Dispatch 19683.5

Hourly Ontario Energy Price $/MWh Last Updated 11:00 AM Predispatch 72.79 Dispatch 90.822000

21000

18000

15000

1500

1000

500

0Fore

cast

Pri

ces

Fore

cast

Dem

and

Pric

e (E

uro/

MW

h)

Volu

me

(MW

h)

7000

6000

5000

4000

3000

2000

1000

0

400

300

200

100

0

Fri Sat Sun MonTues Wed Thus

Prev. Week Volume

Current Week Volume

Prev. Week Price

Current Week Price

Figure: Real-world price dynamics24 / 50




Coupling DAM/RTM

Multi-settlement market model: A coupling of the DAM and RTM.

Consumers’ welfare in the multi-settlement market

W ttlD (t) := vmin(Dttl(t), Gttl(t))− cbo max(0,−R(t))

− P e(t)G(t)− pda(t)gda(t)

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DAM/RTM Consumer’s welfare

Principle of optimality =⇒ Formulae for total discounted meanwelfare,

Consumers’ mean welfare in the multi-settlement market

KttlD = K∗D(r) + γ−1(r −G(0))(pe(r)− pda)

+∫ ∞

0(v − p(t))dda(t) e−γt dt .

in which K∗D(r) corresponds to the RTM welfare.

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Coupling DAM/RTM

Total supplier welfare: Through similar and simpler arguments,

Suppliers’ welfare in the multi-settlement market

W ttlS (t) =WS(t) +

(pda(t)− cda

)gda(t) (1)

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DAM/RTM Supplier’s Welfare

Principle of optimality =⇒ Formulae for total discounted meanwelfare,

Supplier’s mean welfare in the multi-settlement market

KttlS = K∗S (r) + γ−1(r −G(0))(pda − cda)

+∫ ∞

0

(p(t)− cda

)dda(t) e−γt dt .

in which K∗S (r) corresponds to the RTM welfare.

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Integrating Wind...

Figure: Who Commands the Wind?

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Extending the dynamic model

Goal

Extend the DA/RT market model to differentiate power generatedby wind and by conventional generation units

Assumption

All the wind power available is injected into the system

Key issue

Conventional generators serve residual demand.

Volatility of the residual demand will result in higher reserves inthe dynamic market equilibrium

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Emerging issues

Not only mean energy

The details depend on both volatility of wind and its proportion ofthe overall generation

What about now?

If the penetration of wind resources is low, then the increase inload volatility will be negligible, and hence there will be negligibleimpact on the market outcomes

What about in 2020?

Potential negative market outcomes are possible with acombination of high wind generation penetration and highvolatility of wind

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Who Commands the Wind?

Approach

To quantify the impact of volatility we obtain expressions for thetotal welfare in two market models, differentiated by whocommands the wind generating units

Main finding

Volatility can have tremendous impact on the market outcomes

Asymmetric and surprising result

The supplier can achieve significant gains,even when the consumer commands the wind

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Consumers command the wind

Wind generating units are commanded by the demand side:

Consumers’ and suppliers’ welfare expressions

W ttlD,W(t) = vmin(Dttl(t), Gttl(t) +Gttl

W(t))

− cbo max(0,−R(t))− P (t)G(t)− p(t)gda(t)

W ttlS,W(t) =

(P (t)− crt

)G(t) +

(p(t)− cda

)gda(t)

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Consumers command the wind

Welfare expressions: DAM/RTM decomposition

W ttlD,W(t) =W rt

D,W(t)

+{vdda(t)− p(t)(dda(t)− gda

W (t))}

+{

(P (t)− p(t))rda0 + vGW(t)

}W ttl

S,W(t) =W rtS,W(t) +

(p(t)− cda

)gda(t)

W rtD,W(t), W rt

S,W(t): Welfare obtained in the RTMwith residual demand Dnet(t).

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Suppliers command the wind

The other alternative is to consider wind as part of the supply side,

Consumers’ welfare

W ttlD,W(t) = vmin(Dttl(t), Gttl(t) +Gttl

W(t))

− cbo max(0,−R(t))− P (t)(G(t) +GW(t))− p(t)(gda(t) + gda

W (t))

=W rtD,W(t)

+{

(v − p(t))dda + (P (t)− p(t))rda0

}+ (v − P (t))GW(t)

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Suppliers command the wind

Suppliers’ welfare

W ttlS,W(t) =

(P (t)− crt

)G(t) + P (t)GW(t)

+(p(t)− cda

)gda(t) + p(t)gda

W (t)

=W rtS,W(t)

+(p(t)− cda

)gda(t) + P (t)GW(t) + p(t)gda

W (t)

The welfare gain p(t)gdaW (t) is now taken by the suppliers

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Numerical Results: Setting the stage I

Parameters used in all of our experiments:

Parameters [$/MWh]

Cost of blackout and value of consumption:

cbo = 200, 000 v = 50

Cost and prices of generation: crt = 30, and

cda = 0.75 ∗ crt, pda = 0.85 ∗ crt

Discount factor: γ = 1/12 (12 hour time horizon).

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Numerical Results: Setting the stage II

Parameters (physical)

Ramp limit: ζ = 200 MW/min

Mean demand: D̄ = 50, 000 MW

Standard deviation: σ = 500 MW.

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Numerical Results: Setting the stage III

Penetration and volatility

Coefficient of variation to capture the relative volatility of wind:

cv =σw

E[GttlW(t)]

Percentage of wind penetration:

k = 100 ∗ E[GttlW(t)]/D̄

.

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Numerical Results: Volatility Impacts

cv0 0.1 0.2 0.3 0.4

k = 0

k = 5

k = 10

k = 15

k = 20Optimal Reserve Level

0

20

40

60

80

100

120

140 x 103

Figure: Optimal reserves depend on penetration and coefficient ofvariation.

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Numerical Results: Volatility Impacts

x 106

0 1000200 400 600 80010

12

14

16

18

ζ = 200Total Welfare

σ

ζ =0.1

ζ = 500

Figure: Social planner’s welfare.

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Numerical Results: Consumers command the wind

0 0.1 0.2 0.3 0.40 0.1 0.2 0.3 0.4

x 106

Supplier Welfare

k = 0

k = 5

k = 10

k = 15

k = 20x 10

6

Consumer Welfare

10

0

5

15

k = 0

k = 5

k = 10

k = 15k = 20

3

4

5

cv

Figure: Consumer and supplier welfare when consumer owns wind fordifferent coefficient of variation cv and cda < pda < crt.

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Facing wind volatility

The results of this paper invite many questions:

C1

The impact of demand management and storage on the market

C2

The impact of supply management and storage on the market.e.g., modern wind turbines allow pitch angle control.

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Facing wind volatility

C3

Mechanisms to reduce consumers and suppliers exposure tosupply-side volatility.

C4

How to create policies to protect participants on both sides of themarket, while creating incentives for R&D on renewable energy?

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The main messages...

It is not so easy...

The main message of this paper is that consumer welfare may falldramatically as more and more wind generation is dispatched

A beautiful world...

This is true even under the most ideal circumstances:

consumers own all wind generation resources and

price manipulation is excluded

No “ENRON games” – no “market power”

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Concluding remarks

Volatility and mean energy are key parameters for new energysources. Our results show that resource volatility can havetremendous impacts on the market outcomes

Currently adopted wind integration schemes can be harmfulfor consumers with larger wind penetration

Suppliers can achieve significant gains even when theconsumer commands the wind

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Concluding remarks

Who faces the uncertainty and risk associated to volatileresources is a big challenge from an economic viewpoint

Under certain conditions consumers are better off notdispatching wind

Storage and demand management emerge as solutions for asmooth integration of wind power

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Concluding remarks

Market analysis requires dynamic rather than snapshotmodels

Greater wind penetration will require redesigns of bothpower system operations and electricity markets

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Thanks!

Figure: Celebrating with Dutch Babies after finishing part of this work

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Bibliography

S. Meyn, M. Negrete-Pincetic, G. Wang, A. Kowli, and E. Shafieepoorfard. Thevalue of volatile resources in electricity markets. In Proc. of the 49th Conf. onDec. and Control, pages 4921–4926, Atlanta, GA, 2010.

I.-K. Cho and S. P. Meyn. Efficiency and marginal cost pricing in dynamiccompetitive markets. To appear in J. Theo. Economics, 2006.

M. Chen, I.-K. Cho, and S. Meyn. Reliability by design in a distributed powertransmission network. Automatica, 42:1267–1281, August 2006.

I.-K. Cho and S. P. Meyn. A dynamic newsboy model for optimal reservemanagement in electricity markets. Submitted for publication, SIAM J. Controland Optimization., 2009.

D. J. C. MacKay. Sustainable energy : without the hot air. UIT, Cambridge,England, 2009.

L. M. Wein. Dynamic scheduling of a multiclass make-to-stock queue.Operations Res., 40:724–735, 1992.

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The Value of Volatile Resources... Caltech, May 6 2010

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