``Participation of Renewables in Electricity Markets''\Participation of Renewables in Electricity Markets" Pierre Pinson Technical University of Denmark. DTU Electrical Engineering

$Page 1: ``Participation of Renewables in Electricity Markets''\Participation of Renewables in Electricity Markets" Pierre Pinson Technical University of Denmark. DTU Electrical Engineering$
“Participation of Renewables in Electricity Markets”

Pierre Pinson

Technical University of Denmark.

DTU Electrical Engineering - Centre for Electric Power and Energymail: [email protected] - webpage: www.pierrepinson.com

5 March 2018

31761 - Renewables in Electricity Markets 1

[email protected]

www.pierrepinson.com

Learning objectives

Through this lecture and additional study material, it is aimed for the students to be ableto:

1 Explain how to design a market participation strategy

2 Caculate revenues from market participation (and compare them to optimalpotential revenues)

3 Formulate and solve a newsvendor problem


Outline

1 Starting with a practical example

setuptrading renewable energy generation for a given day in 2016various strategies and their performance

2 Decision-making under uncertainty

context: the newsvendor problem - revisitedformulating the problem, mathematically

3 Optimal offering for renewable energy producers

Specifics for renewables and electricity marketsformulating the problem, mathematicallysolving and applicationpotential extensions

4 Leading to some important conclusions


1 Starting with a practical example


The setup

Students of the course 31761 (“Renewables in Electricity Markets”) got convincedto join forces and start an energy trading company: Rogue Trading (RT R©)

And, the course responsiblesuggested you first invest inthat new-generation windfarm...

Nominal capacity: 350MW

Energy production soldthrough the Nord Pool(Western Denmark area)

Balance responsibility

From early 2016, you are to trade your energy generation through the Nord Pool


The setup

Students of the course 31761 (“Renewables in Electricity Markets”) got convincedto join forces and start an energy trading company: Rogue Trading (RT R©)

And, the course responsiblesuggested you first invest inthat new-generation windfarm...

Nominal capacity: 350MW

Energy production soldthrough the Nord Pool(Western Denmark area)

Balance responsibility

From early 2016, you are to trade your energy generation through the Nord Pool


How to proceed

What should we do before to get into the market?

1 Understand how the electricity market works!

It should be fine... if not, please go back to lectures 0-4

2 Get all necessary data/info to make informed decisions, for instance:

get a good grip of market prices (e.g., how they can be influenced by neighboringzones, or the local generation mix)

gain knowledge of price and volume dynamics through historical data analysis

find ways to know how much your wind farm is going to produce for every time unit

3 Design your offering strategy, which can consist of:

a totally improvised approach to market participation (you named your companyRogue Trading after all...)

a set of expert rules to decide on what to do when,

a well-thought optimization model


How to proceed













How to proceed













How to proceed













Sample trading day

27 March 2016 - 11am

Your forecast providergave you this windpower forecast fortomorrow: yi ,i = 1, . . . , 24

From power generationestimates, one readilydeduces 24 blocks ofenergy offered to themarket

However, how muchwill you actually offer?

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time of day [h]

pow

er [M

W]

1 6 12 18 24

050

100

150

200

250

300

350


Strategy 1

We call it “Let’s trust the forecast!”: directly take the forecasts and make themour offers (Ei , i = 1, . . . , 24) for the 28th of March

Ei = yi , i = 1, . . . , 24

hour 1 129 MWh hour 7 138 MWh hour 13 159 MWh hour 19 122 MWhhour 2 110 MWh hour 8 137 MWh hour 14 127 MWh hour 20 108 MWhhour 3 96 MWh hour 8 155 MWh hour 15 112 MWh hour 21 94 MWhhour 4 117 MWh hour 10 180 MWh hour 16 111 MWh hour 22 81 MWhhour 5 132 MWh hour 11 198 MWh hour 17 116 MWh hour 23 67 MWhhour 6 136 MWh hour 12 187 MWh hour 18 124 MWh hour 24 68 MWh

Now, we wait for market-clearing, to receive our cash...


Settlement after market clearing

28 March 2016 - prices after market clearing

time of day [h]

pric

e [E

uros

/MW

h]

1 6 12 18 24

2025

3035

4045

Revenue: RDA =∑24

i=1 λSi ∗ Ei

In the present case: RDA = 88.334, 49e... not a bad day!


Actual production from the wind farm

28 March 2016 - Comparing forecasts (yi , i = 1, . . . , 24) and power measurements(yi , i = 1, . . . , 24)

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time of day [h]

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1 6 12 18 24

050

100

150

200

250

300

350

● forecastsmeasurements

Is there a chance our revenue reduces due to balancing costs?31761 - Renewables in Electricity Markets 14

Balancing needs and prices

28 March 2016 - Nord Pool & Energinet data:

time of day [h]

pric

e [E

uros

/MW

h]

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1 6 12 18 24

1525

3545

spot priceup−regulation pricedown−regulation price

Need for downregulation on most of the hours of the day


Rules for settlement after balancing

Remember the basic rules of the two-price balancing system:

If producing more than expected (yi > yi ), each extra energy unit is sold atdown-regulation price

If producing less than expected (yi < yi ), each missing energy unit is bought atup-regulation price

When the system is in balance, one simply buys (if yi < yi ) or sell (if yi > yi ) at thespot price λS

Only those putting the system off-balance are to be penalized!

Resulting revenue from the balancing market:

RB =∑

j∈Ldown

λ↓j (yj − yj)−∑i∈Lup

λ↑i (yi − yi )

From the graph in slide 14:

Lup = {1, 2, . . . , 6, 17, 18, . . . , 24}Ldown = {7, 8, . . . , 16}


Balancing settlement

Based on:

rules described in the previous slidedifferences between hourly contracts and actual deliveryhourly balancing prices

we can calculate balancing revenues and costs for every market time unit.

hour 1 -837.93 e hour 7 684.11 e hour 13 558.90 e hour 19 -789.32 ehour 2 -934.85 e hour 8 1536.80 e hour 14 1020.60 e hour 20 -877.61 ehour 3 -787.80 e hour 8 1262.94 e hour 15 997.60 e hour 21 -613.58 ehour 4 -1171.28 e hour 10 318.80 e hour 16 321.86 e hour 22 -468.69 ehour 5 -931.60 e hour 11 132.50 e hour 17 -272.80 e hour 23 -188.58 ehour 6 -423.00 e hour 12 100.04 e hour 18 -769.44 e hour 24 -322.56 e

This gives an overall balancing cost RB = −2.454, 89e

And therefore a revenue for that day of RDA + RB = 85.879, 60e

Are you satisfied with your revenue?


Understanding and analysing revenues

The optimal revenue one could get from BOTH

day-ahead market, ANDbalancing market

is obtained if being able to offer your actual renewable energy generation to theday-ahead market...

R∗DA = RDA + RB = 86.627, 50e, (with RB = 0)

Let us then define a performance ratio for our trading strategies:

γ = (RDA + RB)/R∗DA, 0 < γ < 1 (then expressed in percentage)

The performance ratio for Strategy 1 (“Let’s trust the forecast!”) is γ1 = 99.1%(quite good already since forecast error is low...)

Having perfect foresight will never happen - Is there any other way to improveour revenue?

your proposal for a strategy no. 2 (hint: increase a bit your offer)your proposal for a strategy no. 3 (hint: let’s be bold)etc.


Strategy 2

We call it “Let’s tweak a bit the forecast!”: makes a small adjustment to theforecasts, to reflect your gut feeling about potential balancing needs and costs

Offers (Ei , i = 1, . . . , 24) for the 28th of March then become

Ei = τ yi , i = 1, . . . , 24

with τ close to 1.

For instance with τ = 1.05 (increase offers by 5%):

hour 1 135 MWh hour 7 145 MWh hour 13 167 MWh hour 19 128 MWhhour 2 117 MWh hour 8 144 MWh hour 14 133 MWh hour 20 113 MWhhour 3 101 MWh hour 8 163 MWh hour 15 118 MWh hour 21 99 MWhhour 4 123 MWh hour 10 189 MWh hour 16 117 MWh hour 22 85 MWhhour 5 139 MWh hour 11 208 MWh hour 17 122 MWh hour 23 70 MWhhour 6 143 MWh hour 12 197 MWh hour 18 130 MWh hour 24 71 MWh

The results from this trading strategy are:

RDA = 92.751, 21e RB = −6.680, 79e RDA + RB = 86.070, 42e

γ2 = 99.3%


Strategy 3

We call it “Let’s just be bold about it!”: fully trust your gut feeling and push it tothe bound...

Offers (Ei , i = 1, . . . , 24) for the 28th of March then become

Ei = 350MWh, i = 1, . . . , 24


RDA = 243.449, 50e RB = −156.822e RDA + RB = 86.627, 50e

γ3 = 100%

(Isn’t it a nice miracle?)

This most certainly deserves a little discussion and explanation...

[Extra reading: N.N. Taleb (2007). The Black Swan. Random House Publishing]


Key assumptions and issues

In this practical example, we only illustrated the potential (monetary) consequencesof our own decisions, all the rest being the same, i.e.,

prices (both day-ahead and balancing)energy volumesothers’ offering strategies

Is that realistic? ... this was discussed in a previous lecture (Lecture 7 - link)

Definition:

A market participant is a price taker if his decisions and resultingoffers (buying or selling) do not affect the market

You can then imagine what a price maker is...

Also, you will never know the balancing prices in advance!!!


http://pierrepinson.com/31761/Lectures/31761-lecture7.pdf

2 Decision-making under uncertainty


The newsvendor problem

The newsvendor problem is one ofthe most classical problem instochastic optimization (orstatistical decision theory)

It can be traced back to:

FY Edgeworth (1888). The mathematical theory of banking. Journal of the Royal Statistical

Society 51(1): 113–127

even though in this paper the problem is about how much a bank should keep in its reserves to

satisfy request for withdrawal (i.e., the bank-cash-flow problem)

It applies to varied problems as long as:

one shot possibility to decide on the quantity of interestoutcome is uncertainknown marginal profit and loss

the aim is to maximize expected profit!


Revisited: The “Roskilde ticket pusher” problem c©

Everybody seem to want to go and see Eminem,right? (could also be Brunos Mars or Gorillaz,for those who don’t like Eminem)

Maybe some could have the idea of making aprofit using this as an occasion...

[Note that this type of activity is not legal, as such purchased tickets cannot be

re-sold at a price higher than the official retail price] - Do not get any idea here!

1-day tickets for the day Eminem is playing

They are to be sold out fast, while you know that quite a lot of DTU students willnot be able to buy the tickets on time...

On 5 March 2018, you have an opportunity to make a good deal:

buy a batch tickets (up to 30) at an advantageous price!sell them out to your fellow DTU students


“Roskilde ticket pusher” problem c©: detailed setup

Sets of prices:

1-day tickets for Eminem: 1050 dkkretail price to DTU students: 1100 dkkunsold tickets can be given to your RUC pusher friend at 930 dkk

Why is it a newsvendor problem?

this is a one-shot opportunity - batch buy on 5 March 2018 (here and now!)actual DTU demand is uncertainthe marginal profit and loss are known - a profit of 50 dkk per ticket sold, and a loss of120 dkk per ticket unsold

the aim definitely is to maximize expected profit!!

If you were that “Roskilde ticket pusher”, how many ticket would you buy?

Socrative please... https://b.socrative.com/login/student/ - Room number 675366


https://b.socrative.com/login/student/

You need to know your probabilities

no. tickets

prob

abili

ty

0 10 20 30

0.0

0.2

0.4

0.6

0.8

1.0

Based on an expert assessment, here is thecumulative distribution function F for thenumber of tickets (X ) we may be able to sellto our DTU fellow students

It shows P[X ≤ n] as a function of n

Examples:

P[X ≤ 8] = 0: we are 100% sure to sell atleast 8 tickets

P[X ≤ 10] = 0.1: we are 90% sure to sellmore than 10 tickets

P[X ≤ 20] = 0.6: we are 40% sure to sellmore than 20 tickets

P[X ≤ 28] = 1: there is no way we sell morethan 28 tickets


In terms of marginal profit and loss

n P[X = n] Psell Pno-sell E[profit] E[loss] E[net]

≤8 0

9 0.05 1 0 50 0 50

10 0.05 0.95 0.05 47.5 6 41.5

11 0.05 0.9 0.1 45 12 33. . .

where

P[X = n]: probability that demand is EXACTLY n tickets

Psell: probability of selling the nth ticket

Pno-sell: probability of NOT selling the nth ticket

E[profit]: expected profit from selling the nth ticket

E[loss]: expected loss from NOT selling the nth ticket

E[net]: expected net profit related to the nth ticket


With the full table

n P[X = n] Psell Pno-sell E[profit] E[loss] E[net]

≤8 0

9 0.05 1 0 50 0 5010 0.05 0.95 0.05 47.5 6 41.511 0.05 0.9 0.1 45 12 3312 0.05 0.85 0.15 42.5 18 24.513 0.05 0.8 0.2 40 24 1614 0.05 0.75 0.25 37.5 30 7.515 0.05 0.7 0.3 35 36 -116 0.05 0.75 0.35 32.5 42 -9.5. . .28 0.05 0 1 0 120 -120

>28 0

So, how many tickets should our “Roskilde ticket pusher” buy?


Mathematical formulation

If we have

λP : purchase cost for a ticket (1050 dkk)

λR : re-sell price of a ticket (1100 dkk)

λT : transfer price for unsold tickets (930 dkk)

It then defines

π+: unit cost of buying less than needed

π+ = λR − λP (50 dkk)

π−: unit cost of buying more than needed

π− = λP − λT (120 dkk)

Then the optimal number n∗ of tickets to purchase is such that:

P[X ≤ n∗] =π+

π+ + π−(here, 0.294)

This defines the nominal level α∗ of our original cumulative distribution function F


The optimal quantile

no. tickets

prob

abili

ty

0 10 20 30

0.0

0.2

0.4

0.6

0.8

1.0

0.294

14

The optimal decision of the “Roskildeticket pusher” is to pick the quantilewith nominal level α∗ of his originalcumulative distribution function F

Graphically:

n∗ = F−1(α∗) = 14


3 Optimal offering for renewable energy producers


It is a newsvendor problem!

Let us focus on a market time unit i (say, the hour between 13:00 and 14:00)

Sets of prices:

day-ahead price: λSidownregulation price: λ↓iupregulation price: λ↑i

Why is it a newsvendor problem?

one decision to be made before gate closure (i.e., offer for various market time units)

actual renewable energy generation is uncertain

WE ASSUME THAT the marginal profit and loss are known...

π+i = λSi − λ↓i (for any generated MWh above day-ahead schedule)

π−i = λ↑i − λSi (for any lacking MWh w.r.t. day-ahead schedule)

the aim definitely is to maximize expected profit!!


Obtaining the optimal offer

As for the “Roskilde ticket pusher” example, the optimal generation offer of therenewable energy producer for the market time unit i is

E∗i = F−1i (α∗)

with

α∗ =π+

π+ + π−

The problem is... that we do not know F , π+ and π−

We definitely need some forecasts (!), so that

E∗i = F−1i (α∗)

with

Fi : a predicted distribution for renewable energy generation at time unit i

α∗i : a “predicted” optimal quantile based on forecasts for the marginal profit and loss

π+ and π−


We can get probabilistic renewable energy forecasts!

To be discussed more specifically in a future lecture...

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pred. intervals (cov. rates from 10 to 90%)point forecastsobservations

In short, one can get a description F of the cumulative distribution function ofrenewable energy generation for every market time unit


And expert assessments/forecasts on market penalties

The same forecast provider or your own market expert could give you a best guesson evolution of penalties for up- (π−) and down-regulation (π+)

This can be represented as ageneral loss function, herewith:

π+i = λS

i − λ↓iπ+i = 7, i = 1, . . . , 24

π−i = λ↑i − λSi

π−i = 2, i = 1, . . . , 24y − y

π

−1 0 1

01

23

45

67

The optimal quantile to trade is that for which: αi =7

7 + 2= 0.78, i = 1, . . . , 24


Results for the newsvendor strategy

The optimal quantileto trade can beextracted for eachmarket time unit,individually

Similar to otherstrategies, it tends tooffer more energythan what you expectto produce

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pred. intervals (cov. rates from 10 to 90%)point forecastsoptimal quantile (to trade)observations


RDA = 122.771, 40e RB = −36.030, 97e RDA + RB = 86.627, 50e

γnewsvendor = 100%


Be ready for a bumpy ride...!

The outcome of a “newvendor-type” offering strategy can highly fluctuate from onemarket time unit to the next, and from one day to the next

Since being the optimal strategy in expectation, it is only best in the long run, underA LOT of assumptions...

In practice, it wasobserved that thiscould lead to a bumpyride

Simple ways to controlthe “agressivity” oftrading strategies (oraccount forrisk-aversion) can bebeneficial


Final remarks

Participation in electricity markets with a portfolio of renewables requires

liquidity

being keen on going for a bumpy ride!

ANALYTICS (modelling, forecasting, and optimization...)

This is why the coming lectures will focus on renewable energy analytics


Further readings

For those who want to go into the more mathematical aspects:

P. Pinson, C. Chevallier, G. Kariniotakis (2007). Trading wind generation from short-term probabilisticforecasts of wind power. IEEE Trans. on Power Systems 22(3): 1148–1156 (pdf)

J.M. Morales et al. (2014). Integrating Renewables in Electricity Markets, Chapter 7: “Tradingstochastic production in electricity pools” (pdf)

N. Mazzi, P. Pinson (2017). Wind power in electricity markets and the value of forecasting. InRenewable Energy Forecasting: From Models to Applications (G. Kariniotakis, ed.): 259–278 (pdf)

A more general book chapter on the newsvendor problem:

E.L. Porteus (2008). The newsvendor problem. In Building Intuition: Insights From Basic OperationsManagement Models and Principles., Chapter 7 (pdf)


http://pierrepinson.com/31761/Literature/pinson2007.pdf

http://pierrepinson.com/31761/Literature/reninmarkets-chap7.pdf

http://pierrepinson.com/31761/Literature/MazziPinson2017.pdf

http://www.isye.umn.edu/courses/ie5551/additional%20materials/newsvendort.pdf

Thanks for your attention! - Contact: [email protected] - web: pierrepinson.com


Documents

``Participation of Renewables in Electricity Markets''\Participation of Renewables in Electricity Markets" Pierre Pinson Technical University of Denmark. DTU Electrical Engineering