Intraday imbalance optimization: incentives and impact of strategic intraday bidding behavior [original]

Vol.:(0123456789)

Energy Systems (2022) 13:409–435

https://doi.org/10.1007/s12667-021-00445-9

1 3

ORIGINAL PAPER

Intraday imbalance optimization: incentives andimpact

ofstrategic intraday bidding behavior

ChristopherKoch1

Received: 20 May 2020 / Accepted: 27 April 2021 / Published online: 10 May 2021

Abstract

Intraday markets are crucial to balance supply and demand in the very short-term,

up to delivery. They are often designed as continuous auctions with a pay-as-bid

pricing mechanism. While several studies assess trading strategies to balance dif-

ferent types of portfolios, they normally do not consider the incentives of the

imbalance prices for portfolio management. This paper analyzes a strategy of tak-

ing positions in the German intraday market based on expected imbalance prices

and examines its impact on system stability. Using a logistic regression model, it

is possible to accurately predict the direction of the overall system balance and to

apply a profitable trading strategy. For a period from 01/07/2017 to 30/06/2019,

the strategy outperforms a simple approach by EUR 47 000 per MW. However, this

behavior would predominantly not have been system supportive due to biased imbal-

ance price incentives. These are asymmetric price spreads and insufficiently low

imbalance prices compared to intraday prices. An efficient intraday price constraint

would partly solve the problem. The overall share of system supportive imbalance

positions would raise by ten percentage points. Insituations with high system wide

imbalances, up to three-quarters of the positions would stabilize the system. These

findings are important for regulation in Germany and other countries with a single

imbalance pricing as they provide an indication for crucial points of the imbalance

pricing rules to incite appropriate market behavior.

Keywords Electricity market design· Intraday market· Balancing mechanism·

Electricity portfolio management· Strategic behavior

Abbreviations

aFRR Automatic frequency restoration reserve

AIC Akaike information criterion

AM Additional measures

* Christopher Koch

christopher.k[email protected]

1 Department ofEnergy Systems, Technische Universität Berlin, Einsteinufer 25, 10587Berlin,

Germany

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BRP Balancing responsible party

Delta Deviation between a day-ahead forecast and the actual

Dev Deviation of a quarter-hourly value to the hourly mean

EM Emergency measures

ex Export

GC Gate closure

ID Intraday

IDP Intraday price

IGCC International grid control cooperation

im Import

IP Imbalance price

mFRR Manual frequency restoration reserve

neg Negative

q Volume of an aFRR bid

Q Total considered volume of aFRR to calculate expected imbalance

prices

Qd Quarter-hourly dummy

P Power

pIDH Volume weighted average intraday price of an hourly product

pIDQ,last15 Volume weighted average price of intraday trades within the last 15min

pos Positive

Pr Probability

SB System balance

tp Tendered period

TSO Transmission system operator

VolIDQ Trading volume of quarter-hourly intraday product

Wd Dummy for the working day

WP Working price of an aFRR bid

1 Introduction

Electricity trading in European countries is done in a sequence of interrelated mar-

kets serving different purposes to managers of generation and consumption portfo-

lios. Net suppliers and demanders use long-term contracts to hedge their price risks

by buying and selling standardized base and peak products on an exchange (futures)

or tailored bilateral contracts (forwards) [1]. The spot market is the main market for

physical delivery in hourly or quarter-hourly resolution. Most of the volume is traded

at the day-ahead market in a unique auction to aggregate liquidity [2]. The intraday

market gives portfolio managers the opportunity to trade until a couple of minutes

before delivery and thus react to latest information. This is crucial for portfolios

dominated by fluctuating renewable sources such as wind and solar, as the forecast

accuracy increases with less time to delivery [3, 4]. These forecast deviations have

a major impact on intraday prices as several studies show [5–10]. As intermittent

electricity generation becomes a more significant part of the electric power grid,

intraday markets are important for balancing supply and demand minute-to-minute.

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Intraday imbalance optimization: incentives andimpact of…

Consequently, examining efficient market design comes to the fore of scientific anal-

yses [11–15]. Next to the question of an appropriate market design, another research

focus is on the development and assessment of bidding strategies [16–22]. It has a

significant impact on the market value of both conventional and renewable power

plants [23].

So far, these two research topics have been analyzed separately as in the afore-

mentioned studies, but they are closely linked. On the one hand, market design

affects the profitability of trading strategies. On the other hand, market behavior

influences system stability and must be considered within the regulatory framework.

Therefore, this study goes beyond an individual consideration of these research top-

ics and combines them by examining a trading strategy and analyzing its impact on

the system balance. The question is whether it is possible to generate a return with

a speculation between current intraday and expected imbalance prices for Germany

and if the underlying positions would stabilize the system or not.

There are papers investigating partly the incentives of balancing mechanisms.

Just and Weber [24] discuss the opportunity of strategic optimization between spot

market and balancing energy. But they focus only on situations where the imbal-

ance price incentive is too low compared to the spot price. Based on empirical data,

they try to proof a misconduct of market participants in such situations and draw

conclusion on overall market data. The same holds for the study of Möller etal. [25]

who try to model the balancing energy demand considering arbitrage opportunities.

This analysis was done under a completely different market design as it is now. The

intraday market was illiquid and there was no marketplace with trading products in

quarter-hourly resolution. Therefore, their model includes only speculation on the

day-ahead market and an important factor is the quarter-hourly difference of load

compared to the hourly mean. Van der Veen etal. [26] analyze more generally the

impact of different imbalance pricing mechanisms on a balancing strategy for port-

folio managers. They focus on a day-ahead optimization looking for a general strat-

egy without predicting the actual balancing situation.

In contrast to these studies, the present paper provides a holistic assessment of

strategic intraday imbalance optimization. It is based on a unique data set of intraday

trade and order book data for Germany from 01/07/2017 to 30/06/2019. As intraday

trading is possible until a couple of minutes before delivery, it enables to estimate

the imbalance prices and to individually decide in each quarter-hour whether to

take a buy or sell position. So, the applied strategy simulates a decision with avail-

able information during active trading considering the current and not just average

market prices. It turns out that an advanced strategy based on a logistic regression

would have made a profit of EUR 42,000 per MW whereas a simple strategy based

on lagged system balances would cause a loss of EUR 5000 per MW.

In a second step, it is possible to examine the impact of this strategy on the overall

system. Even though the model was able to classify the system balance correctly in

68% of all quarter-hours, the strategy would not have been system supportive. More

than half of the positions would have increased the actual system balance, because

perverse price incentives would have caused some willful misconduct. The reasons

are asymmetric price spreads between positive and negative system balances and

insufficiently low imbalance prices compared to intraday prices. The implications of

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bad market behavior became apparent during some days in June 2019 when severe

situations with balancing reserve activations of up to 7.5GW have been aggravated

by prohibited conduct of some market players [27]. Such situations can be avoided

with a stricter intraday price constraint as part of the imbalance price calculation.

The TSOs provide a new proposal [28] which is also analyzed in this paper. The

willful misconduct would decrease by 12 percentage points and the positions based

on the trading strategy would be predominantly system supportive – especially

insituations with high system balances.

The paper is structured as follows: Sect. 2 provides background information

about the intraday market and balancing system and the price incentives for intraday

imbalance optimization. Section3 introduces the trading strategy and the underly-

ing methodological approach. Section 4 examines the success of the strategy and

its impact on system stability. It also analyzes the effect of a stricter intraday price

constraint with regard to profitability and the behavior related to the overall system.

Section5 concludes.

2 Background

This section provides some context to the analysis, first by introducing background

information on the German intraday market and the institutional setup of the balanc-

ing system. It also contains a detailed explanation of the imbalance price calculation

and its price incentives for strategic behavior on the intraday market.

2.1 The intraday market

The intraday market facilitates trading until a couple of minutes before delivery in

order to balance portfolios of generators and/or loads. For the German market area,

EPEX SPOT is the major exchange for short-term trading. The intraday trading

period officially starts with a quarter-hourly auction at 3pm the day before delivery.

It was introduced in December 2014 and enables to trade systematic deviations to

the hourly mean and thus scheduling in the required 15-min resolution. After this

auction, the intraday market is designed as continuous auctions for hourly and quar-

ter-hourly contracts. Market participants may submit their orders during the whole

trading session and a transaction is executed immediately as soon as two entered

orders match. The pricing mechanism is designed as a pay-as-bid scheme. Gate clo-

sure of continuous trading is at 30min before delivery with an extended period up

until five minutes before delivery for trading within the same control area [29].

Table1 summarizes key figures for the German intraday market. There are 270

exchange members registered for the continuous trading and 133 for the quarter-

hourly auction [30]. The average prices are around 40EUR/MWh for all three dif-

ferent product types showing that systematic arbitrage potential between the markets

is hard to find. However, trading volumes are much higher on the hourly than on the

quarter-hourly market. More than 5000MW are traded on average per hourly con-

tract, whereas it is 700MW for the continuous quarter-hourly trading and 750MW

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Intraday imbalance optimization: incentives andimpact of…

for the quarter-hourly auction. This shows that major deviations to the day ahead

forecast are compensated with hourly contracts due to the lower effort. The quarter-

hourly markets are predominantly used to compensate deviations from the quarter-

hourly to the hourly mean.

A large share of continuous intraday trading is done close to delivery to process

the best information about the portfolio balance. A common index is based on the

ID1 trading period which covers all trades executed within the last trading hour of

a contract up to 30min before delivery start [31]. This period contains 38% of the

hourly and even 48% of the quarter-hourly trading volume.

2.2 The balancing system

In AC electric grids, it is necessary to ensure the balance between demand and sup-

ply at every point of time to maintain a stable frequency and to ensure a reliable

electricity supply. A number of regulations, processes and markets have been devel-

oped to prevent large deviations. In Europe, the core of this system is the active port-

folio management of all market actors (generators, consumers, retail suppliers and

traders). They take the role of a balancing responsible party (BRP) and are obligated

to balance their portfolio through dispatch of physical assets or trading.

In Germany, there are more than one thousand BRPs [32–35]. Each of them must

send their schedules to the associated transmission system operator (TSO). The

remaining deviations between schedules and the actual physical positions are called

imbalances. Positive and negative imbalances offset each other and the TSOs com-

pensate only the net position by the activation of balancing reserves.

This compensation is done in high time resolution, but the imbalance settlement

period is 15min in Germany. The average net imbalance of all balancing groups

is called system balance (

). It includes all measures of balancing the remaining

deviations. These are the activation of automated and manual Frequency Restoration

Reserve (

aFRR

and

mFRR

) and additional measures (

) as well as emergency

measures for or from foreign TSOs (

).1 Furthermore, there is an International

Table 1 Key figures of German intraday markets from 01/07/2017 to 30/06/2019

Intraday continuous Quarter-hourly

intraday auc-

tion

Hourly Quarter-hourly

Number of market participants 270 133

Average price [EUR/MWh] 40.29 40.00 39.75

Average trading volume [MW] 5037 699 749

Average ID1 trading volume [MW] 1898 335

1 AFRR and mFRR mainly differ by the time of their activation which is 5 and 15min. Additional and

emergency measures are activated in special situations when the TSOs need emergency reserves from

foreign TSOs.

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Grid Control Cooperation (

IGCC

) to prevent unnecessary balancing reserve activa-

tions and a cooperation with Austria to exchange aFRR capacity whenever possible

[36]:

The system balance is defined from the perspective of the predominant direction

of activated measures. Thus, a negative system balance means an activation of nega-

tive balancing reserves and represents a power surplus in a grid. A positive system

balance corresponds to a shortage of supply in the system.

The system balance is also a key element for the calculation of the imbalance

price within the German imbalance settlement. The general idea is to distribute the

costs of all balancing reserve activations for every settlement period to the BRPs,

who caused the activations. The calculation reads:

This basic determination is supplemented by different constraints to limit or

increase the imbalance price. In case of a small quarter-hourly system balance, the

fraction can lead to high imbalance prices even though the system is not at risk. This

shall be avoided by a price cap to the highest working price of any activated asset

within the particular quarter-hour. There is also a linear function limiting the imbal-

ance price when the system balance is between −500MW and 500MW.

However, the imbalance price must always incite active intraday trading to bal-

ance predictable deviations. Currently, the comparison price is the volume weighted

average price of the corresponding hour. This constraint is under consultation

because it does not prevent that quarter-hourly intraday prices are higher than the

imbalance price and there is no focus on the market situation close to gate clo-

sure [37]. Section4.3 examines the potential impacts on the behavior of market

participants.

The last condition is a surcharge, if TSOs must activate 80% of the procured

aFRR and mFRR within one quarter-hour.2 It is the maximum of 100 EUR/MWh or

half of the imbalance price [39].

2.3 Price incentives forintraday imbalance optimization

The main purpose of the imbalance price is to incite active trading on the in an

appropriate manner. Van der Veen and Hakvoort [40] discuss some of the important

design variables that must be considered to develop suitable frameworks. European

countries follow two different ideas of imbalance pricing mechanisms: single and

(1)

(

PaFRR+−PaFRR−

)

(

PmFRR+−PmFRR−

)

(

PAM+−PAM−

)

(

PEM+−PEM−

(

PIGCC

im −PIGCC

(

PaFRR

im −PaFRR

(2)

Imbalance Price

∑

Costst−

∑

Revenuest

SBt

2 This is set to be changed in 2020. Then the surcharge is applied if the system balance exceeds 80% of

the procured balancing reserve. The surcharge mechanism itself will be changed in 2020 [38].

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Intraday imbalance optimization: incentives andimpact of…

dual pricing systems [41]. In dual pricing systems, BRPs with imbalances mitigating

the system balance only receive a lower imbalance price. It is typically based on the

day-ahead price [42]. A single imbalance pricing means, that BRPs, whose imbal-

ance position is opposed to the system balance, receive the same price as the BRPs

pay, who reinforce the system balance. This is the imbalance pricing mechanism

in Germany and it incites to take an intentional imbalance position [43, 44]. If the

expected imbalance price is lower than the current intraday market price, it might be

beneficial to take a sell position and pay the imbalance price (and vice versa).

Such a behavior is not allowed in Germany. According to Sect.4 (2) StromNZV

and the balancing group contract, BRPs are obliged to keep imbalances to a mini-

mum by taking reasonable measures [45]. Thus, it is not allowed to take intentional

imbalance positions. However, empirical analyses indicate that at least some mar-

ket participants react to imbalance price expectations [46]. It needs an appropriate

imbalance price so that this activity stabilizes the system. The imbalance price must

be higher than the intraday market price if the system balance is positive (shortage)

and lower than the intraday price if the system balance is negative (surplus). This is

especially important for trading close to intraday gate closure when market partici-

pants have the best indication for the own position and the overall system status of

the associated settlement period. Empirical data show that there have been situations

with inefficient imbalance prices. Between 01/07/2017 and 30/06/2019, the imbal-

ance price incentive was too low in 13% of the quarter-hours (Table2). Market par-

ticipants will contemplate this, if they react to imbalance price incentives. Thus, it is

important to consider it when modeling their behavior.

3 Methods andmaterials

This section presents the model approach to simulate the strategy of a market partici-

pant who takes intentional intraday positions at the EPEX SPOT market based on an

imbalance price estimation. The imbalance price prediction is compared with the prices

of the limit orders3 at the decision point. If the expected imbalance price is higher than

Table 2 Relation of system

balance and price deviation of

imbalance and intraday prices

from 01/07/2017 to 30/06/2019

The intraday price is the volume weighted average of all trades of

the last 15min of trading at EPEX SPOT. The numbers resemble a

count of quarter-hours

System balance > 0MW System bal-

ance ≤ 0MW

Imbalance price > intraday

price

34 692 2 827

Imbalance price ≤ intraday

price

6 480 25 626

3 Intraday trading at EPEX SPOT is organized as a continuous market. A trade is executed, if the sell

side accepts the buy limit order(s) with the highest price or if the buy side accepts the sell limit order(s)

with the lowest price.

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the best sell order, the market actor will take a buy position. If it is lower than the best

buy order, the he or she will take a sell position. The period of our analysis spans from

01/07/2017 to 30/06/2019.

Looking at the imbalance price formula presented in Eq. (2), the price estimation

should start with predicting the system balance. With this information, it is possible to

approximate the activation costs in the numerator by considering the potential working

price payments using the merit order of the different measures. With these informa-

tion, it would be possible to directly estimate the imbalance price (IP) depending on the

system balance (SB): E[IP|SB]. The problem of this approach is the high volatility of

the system balance. During the analyzed period, it has a standard deviation of 530MW

with an average absolute value of only 490MW. Hüttinger [47] developed different

models for a deterministic prediction. The root mean squared errors were not better

than 350MW proving the high uncertainty of such forecasts.

An alternative way is to use a binary classification model to estimate the probability

of a positive system balance which is the concept being applied in the present paper.

This approach is to calculate an expected profit for a sell and a buy position based on

actual intraday bids and the expected imbalance price for a positive and a negative sys-

tem balance. The advantage is that the trader is able to consider both the probability of

the potential system status and the associated price spreads. Figure1 shows an over-

view of the trading strategy which is explained in detail below.

The approach starts with a classification model to predict the probability of a posi-

tive system balance (

pos]

). It is not appropriate to use a linear probability model as

the fitted probabilities can be lower than zero or greater than one. This limitation can

Fig. 1 Overview of the trading strategy. It considers the best buy and sell limit orders (IDPBuy and

IDPSell) at the decision point (4min to gate closure). The trading volume for the strategy is set to 1MW

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Intraday imbalance optimization: incentives andimpact of…

be overcome by using a binary response model taking a function

with values strictly

between zero and one [48]:

We use

to denote the full set of explanatory variables and

𝜷

to indicate the set

of parameters.

In the present case, the chosen model is a logistic regression model, also called

logit model, with

where

is the function to link the probability of a positive system balance

Ppos

to the

explanatory variables. It is defined for every quarter-hourly time period

as:

The first group of regressors contains fundamental variables.

SBt−60

is the lat-

est published system balance and

ΔSBt−60

the gradient to the previous system bal-

ance. These parameters are included because of the strong autocorrelation of the

system balance [49]. Additionally, variables for load, wind and solar generation are

included as these portfolios are the main drivers of imbalances.

Devs

are the devia-

tion of the quarter-hourly day-ahead forecast from the mean of that hour. The

Deltas

for wind, solar and load are the deviations between the day-ahead forecast and the

actuals. Unfortunately, there are no public data for the latest intraday forecast, which

could be deployed to consider fundamental deviations of wind, solar and load. So,

taking the actuals is necessary for calculating an unbiased estimator of the deviation

between day-ahead and latest intraday forecast. Using these regressors should be

only a little additional information because the deviation between intraday forecast

and actuals should have the highest influence on the system balance. However, an

additional model is applied without these

Deltas

to calculate a floor of the potential

profit of the trading strategy. Power plant outages are not considered as these imbal-

ances must be compensated quickly after occurrence and shall not influence the sys-

tem balance [45].

The second class of regressors is based on intraday trading data.

VolIDQ

is the

trading volume of all trades for the corresponding quarter-hour being executed until

the time the model calculation starts.

VolIDQ,last15

is the same for the last 15min.

pIDQ,last15

is the volume weighted average price of intraday trades for the correspond-

ing quarter-hour carried out within the last 15min. It is also considered in relation

to the intraday price of the associated hourly product

pIDH

, as this is the price level

(3)

(Y=1

x)=G

(

𝛽

+x𝜷

)

(4)

(z)=

exp(z)

+ exp(z)

(5)

t=𝛽0+𝛽1SBt−60 +𝛽2ΔSBt−60 +𝛽3Delta

Wind

t+𝛽4Delta

Solar

+𝛽5DeltaLoad

t+𝛽6DevWind

t+𝛽7DevSolar

t+𝛽8DevLoad

+𝛽9VolIDQ

t+𝛽10VolIDQ,last15

t+𝛽11pIDQ,last15

+𝛽12

(

pIDQ,last15

t−pIDH

)

+𝛽13

(

Wdt

)

∑

q=1

𝛽i+13 ⋅Qdq,t+𝜀

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Table 3 Overview of data sources

Data Description Source

Intraday data Price and volume of intraday trades and orders Entelios GmbH

System balance The sum of imbalances from all German balancing groups Common platform of German TSOs:

https:// www. regel leist ung. net/ ext/ data/

Tender results for aFRR Working prices and volume of accepted aFRR bids Common platform of German TSOs:

https:// www. regel leist ung. net/ ext/ tender/

https:// www. regel leist ung. net/ apps/ datac enter/ tende rs/? produ ctTyp es= SRL,MRL

Wind and solar production Day-ahead forecast and actuals Transmission system operators: http:// www. 50Her tz. com, http:// www. ampri on. de,

http:// www. trans netbw. de, http:// www. tenne ttso. de

Electricity load Day-ahead forecast and actuals European Network of Transmission System Operators (ENTSOE): https:// trans

paren cy. entsoe. eu/

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Intraday imbalance optimization: incentives andimpact of…

for one of the imbalance price constraints (see Sect.2.1). The model also includes a

dummy for the day being a working day

and dummies for the quarter-hours of a

day

to cover other systematic influences.

𝜀

is the error term. Table3 provides an

overview of all variables and their data sources.

To address the problem of potential overfitting, a backward selection is applied

using the Akaike information criterion (AIC) [50]. It is a well-established estima-

tor for the quality of statistical models dealing with the trade-off between goodness

of fit and simplicity of the model. Comparing a set of different candidate models,

the preferred model has the minimum AIC value. A backward selection function in

programming language R calculates the AIC for the complete model specification

and every model excluding one of the regressors. It drops the variable for which the

associated model has the lowest AIC. This is done until there is no further improve-

ment by deleting a regressor. To reduce computing time and speed up the decision

process, highly insignificant quarter-hourly dummies are dropped upfront.

As the approach aims to simulate the actual behavior of a market participant, the

model is built as a rolling forecast. It is run only for one day and the training period

contains the data of a fixed amount of latest past days (in this case 30days). There-

fore, the model reduction with AIC and parameter estimation is done separately for

every day of the analyzed period.4

The second step is to estimate an imbalance price

for a positive and negative

system balance (see again Fig.1). It is not possible to calculate expected activation

costs without a deterministic forecast of the system balance. Thus, it needs a more

general approach. The price estimation is based on the working price bids of aFRR

as it is the mostly activated balancing reserve measure in Germany [51]. We calcu-

late for every tendered period

for both positive and negative balancing reserve the

average activation costs (sum of working price

times volume

of a bid) for a

fixed volume

. We consider the lowest working price bids

until

is reached.

(6)

E�

�

SBpos =1

�

∑I

i=0WP

pos

i,tp

⋅q

pos

i,tp

pos

Table 4 Average imbalance price and aFRR activation price for different activation volumes for positive

and negative system balances from 01/07/2017 to 30/06/2019

System balance Average imbalance price

[EUR/MWh]

Average aFRR activation price

250MW

[EUR/MWh]

400MW

[EUR/MWh]

700MW

[EUR/

MWh]

Positive 65.60 65.89 70.15 87.96

Negative 1.25 11.26 8.39 0.43

4 In reality, it would have been single runs for every quarter-hour to take the latest available system bal-

ances and intraday forecasts. The approach can be simplified because all data are already stored in a data

base.

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C.Koch

1 3

The considered volume

is kept constant for every tendered period. It shall lead

to price predictions that are on average equal to the mean imbalance price separately

for negative and positive system balances of the total analyzed period (July 2017 to

June 2019). Table4 shows the results for different levels of volume

. It follows to

take a volume of 250MW for positive aFRR and 700MW for negative aFRR.

Additionally, the intraday price constraint is respected as explained in Sect.2.1.

The final imbalance price forecast considers the volume weighted average intraday

price of the corresponding hour including all trades being executed until the deci-

sion point.

With the estimated classification probability and imbalance prices, it is possible

to calculate the expected profit of an intraday buy and sell position for every quarter-

hour (step three in Fig.1). We need to define therefor the time of trading simulation.

It depends on data availability and model calculation time. Gate closure of German-

wide intraday trading is 30min before delivery.5 The empirical study of Maskos

[49] shows that German TSOs regularly publish the past system balance 10.65min

after the quarter-hour. So, the latest information is available 4.35min before gate

closure. It takes about 20s to collect the latest data, calculate the model and take a

market position. Consequently, the strategy simulates intraday trading at four min-

utes to gate closure.

In addition to the estimated imbalance payment, the expected profit depends on

the available orders in the market. The strategy replicates a market participant exe-

cuting a market order. A buy market order stands for accepting the sell limit orders

with the best prices until the requested volume x is reached. The market participant

pays the volume weighted average price of the sell orders IDP

xMW

Sell

. If the trader initi-

ates a sell market order, he or she will pay the volume weighted average price of the

buy orders

IDPxMW

Buy

. The trading strategy is based on a one Megawatt trade. Accord-

ing to the law of iterated expectations, the expected profits for every quarter-hour

are:

(7)

E�

�

SBpos =0

�

∑I

i=0WP

neg

i,tp

⋅q

neg

i,tp

neg

(8)

ProfitBuy

]

t=E

[

Prpos

]

⋅E

[

SBpos =1

]

(

1−E

[

Prpos

]

)

⋅E

[

SBpos =0

]

t−IDP1MW

Sell

(9)

ProfitSell

]

t=IDP1MW

Buy −

(

[

Prpos

]

⋅E

[

SBpos =1

]

(

1−E

[

Prpos

]

)

⋅E

[

SBpos =0

]

)

5 There is also the “Same Delivery Area Trading” for trading within one of the four German TSO areas.

This is possible until five minutes before delivery. It is not considered here, since the liquidity is lower

than in German-wide trading [52].

421

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Intraday imbalance optimization: incentives andimpact of…

If the expected profit of a sell position is positive, the market actor will sell an

additional volume of 1MW at the market leading to a shorter portfolio. An expected

profit of a buy position causes a buy trade and a surplus of the portfolio. It is also

possible that both expected profits are negative because of the price spread between

the best sell and buy orders. The actual profit is calculated afterwards based on the

actual prices of the intraday market orders and the actual imbalance prices of the

analyzed period. Impacts on the imbalance prices can be neglected because of the

small volume of the simulated trading strategy.

So, the described approach simulates a trading decision based on available infor-

mation and evaluates its profitability with real market price data.

4 Results anddiscussion

This section presents the results of the trading strategy and the potential impact on

the system balance. It starts with a discussion of the model results including model

assumptions, the coefficients of the independent variables and the model accuracy.

It continues by analyzing the potential profit of the trading strategy to validate it

as a realistic approach for market participants. If it is possible to apply a beneficial

intraday imbalance optimization, it is appropriate to evaluate the effect on system

stability under the current imbalance pricing scheme and the potential adaptions to

improve the trading incentives.

4.1 Model results

Logistic regression models do not make many of the assumptions of linear regres-

sion models that are based on ordinary least squares algorithms. There is no need for

a linear relationship between dependent and independent variable and no assump-

tion for the distribution of the error terms. Homoscedasticity is also not required.

However, there are some assumptions that still apply. The dependent variable must

be binary which is obviously given here. The same goes for the independence of the

observations. Lastly, logistic regression assumes linearity between the independent

variables and the log odds. Otherwise the test underestimates the strength of the

relation. A solution would be to transform metric variables to an ordinary level. But

transforming variables before modeling might cause problems such as distortion of

confidence intervals or lack of fit. Instead, it is appropriate to examine the effective

sample size to allow complexity of the model [53]. The effective sample size is the

minimum number of observations for any class. According to Concato etal. [54] and

Peduzzi etal. [55], there must be at least 10 observations per independent variable.

(10)

ProfitBuyt

=IP

−IDP

1MW

Sell

(11)

Profit

Sellt=IDP

1MW

Buy

−IP

422

C.Koch

1 3

The minimum ratio is 11.61 for any model run. So, the sample size is always suf-

ficiently high.

As the assumptions for the logistic regressions are fulfilled, it is possible to ana-

lyze the estimated impact of different variables on the system balance direction.

Figure2 shows the share of selections for the fundamental and intraday variables

and the mostly selected dummies. All fitted models select the lagged system bal-

ance and the deviations between the day-ahead forecast and the actuals (abbrevia-

tion: delta) for wind and load. The gradient of the lagged system balance is chosen

in 90% of the model runs.

Delta PV seems to have a lower influence. A potential explanation is that TSOs

manage PV portfolios who are willing to close every open position. Therefore, it

could be that the system balance is less influenced by day ahead forecast errors.

The fitted models also select less often the deviations to the hourly mean for all

three fundamental factors. Intraday trading volumes seem to be less important as

well, whereas intraday prices are predicted to have a consistent impact. The model

chooses the volume weighted average price of the last 15min before in 95% of all

cases.

The dummy for the day being a working day is considered in three-quarter of all

model runs suggesting that there could be a difference in trading activity or forecast

accuracy between working and non-working days. Even though the model indicates

a regular pattern for some quarter-hours, most of the quarter-hourly dummies are

chosen less frequently compared to the other regressors. The share is lower than

30% for 74 dummies.

Figure3 completes the model description by showing the boxplots of the coef-

ficients for fundamental and intraday variables for all 730 model runs. The most

frequently chosen variables have the same sign whenever they are selected. That

Fig. 2 Share of selections for fundamental and intraday variables and mostly selected dummies. Deltas

are the deviations between the day-ahead forecast and the actuals. Devs are the deviation of the quarter-

hourly day-ahead forecast from the mean of that hour

423

1 3

Intraday imbalance optimization: incentives andimpact of…

means, the variables affect the log odds always in the same direction. The expected

influences are reasonable. For example, a higher system balance is expected to

increase the log odds of a positive system balance. The relation is less consistent for

some variables, that are rarely considered. The most noticeable examples are dev

load and the difference between the hourly and quarter-hourly intraday prices. These

are the only variables with a positive upper quartile and a negative lower quartile for

the estimated coefficients.

Fig. 3 Boxplots of coefficients for fundamental and intraday variables

Fig. 4 ROC curve of the logistic

regression model

424

C.Koch

1 3

The heterogeneous parameterization of the model confirms the approach of indi-

vidual model fitting for every day. But the premise of a successful intraday imbal-

ance optimization is a high accuracy of the classification model. Figure4 shows the

ROC curve for the logistic regression model (logit model) illustrating the true posi-

tive rate against the false positive rate for different thresholds for the classification.

It shows a clear deviation from the diagonal which represents an uninformative clas-

sification. At any threshold the model detects more true positive than false positive

observations. The area under the curve is 0.734.

To evaluate the accuracy of the logit model and later the profitability of the

underlying strategy (see Sect.4.2), it is compared to a reference strategy. A simple,

but efficient estimation can be based on the latest published system balance because

the system balance has a high autocorrelation [49]. So, the simple model is that the

sign remains the same for the traded quarter-hour.

The true classification rate is 68.6% for the logit model with a cut-off of 0.5 for

predicting a positive system balance. This is 2.4 percentage points better than a

prediction solely based on the latest published system balance (see Table5). So

even though the accuracy of the logit model is also slightly better at other thresh-

olds, there is only little additional information by including variables other than the

lagged system balance. The latter is the most important information for predicting

the direction of the system balance.

4.2 Trading strategy

The model accuracy indicates the potential of a profitable intraday imbalance opti-

mization. The simulation of the trading strategy applies the approach presented in

Table 5 True classification rate

of the logit model with different

thresholds compared to the

approach based on the lagged

system balance

Threshold True clas-

sification

rate

0.3 0.662

0.4 0.681

0.5 0.683

0.6 0.669

0.7 0.623

Lagged SB 0.662

Table 6 Potential profit of

trading strategy based on

logistic regression model and

lagged system balance from July

2017 to June 2019

Logistic regression Lagged

system bal-

ance

Percentage right decisions 68.6% 66.2%

Total profit [EUR] 42,069 −5093

Profit [EUR/MWh] 0.71 −0.07

425

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Intraday imbalance optimization: incentives andimpact of…

Sect.3. It uses the opportunity of predicting a probability for the system balance

direction and combines it with the expected price spread for a sell and buy posi-

tion. Therefore, it may be that the decision is to take a position in the same direc-

tion of the expected system balance, if the expected price spread differs significantly.

This strategy is compared with a simple one based on the lagged system balance. If

the lagged system balance is positive (system shortage), the trader will take a buy

position to be oversupplied for the traded period and vice versa for a negative sys-

tem balance. This approach does not need a complex model and the decision can be

done faster. Therefore, the results are calculated with market prices of five seconds

after the latest system balance publication (compared to 20s for the application of

the logit model, see Sect.3). Table6 presents the results for both strategies. They

vary widely even though the model accuracy is only 1.4 percentage points better

Fig. 5 Cumulated weekly profit of trading strategy based on logistic regression model and lagged system

balance

Fig. 6 Histogram of daily profit for the strategy based on the logistic regression model

426

C.Koch

1 3

for the logit model. Between 01/07/2017 and 30/06/2019, the strategy based on the

logit model would made a profit of EUR 42,000 whereas the simple strategy look-

ing at the lagged system balance would have made a loss of EUR 5000. It shows the

advantage of including the expected price spread in the trading decision.

Figure5 shows the development of profits and losses for both approaches over

the analyzed period. The strategy using the logistic regression model is profitable on

503 out of 730days (Fig.6) and in 90 out of 106weeks. So, its success is not caused

by some outliers, but by constant return and an application holds a reasonable risk

for portfolio managers.

As explained in Sect.3, the logit model uses the actuals for wind, solar and load

to calculate an unbiased estimator of the deviation between day-ahead and latest

intraday forecast. However, taking this information could lead to slightly better fore-

casts of the probability for the system balance. Therefore, an additional model is

applied without these Deltas to calculate a floor of the potential profit of the trading

strategy. The percentage of right decisions is at 67.7% and thus 0.9percent points

worse than the complete logit model. The profit is positive over the whole period at

EUR 18,700. So, the profit of a model including the deviation between day-ahead

and latest intraday forecast can be expected to be between EUR 18,700 and EUR

42,000.

4.3 Impact onsystem balance

Section4.2 shows the potential of an intraday imbalance optimization. The intro-

duced strategy is able to generate profits at reasonable risk. From a regulators per-

spective, it is therefore necessary to examine whether such a behavior would support

the system under the current imbalance price mechanism. We analyze therefore how

often the market player would have taken a position opposed to the actual system

balance. We compare again the results for both strategies to illustrate the differences.

They are presented in Table7.

A market player would have executed a trade in 86% of all quarter-hours by apply-

ing the logistic regression model. Less than half of these positions would have been

Table 7 Impact of intraday imbalance optimization on system stability

All quarter-hours Abs (system bal-

ance) > 1000MW

Logistic

regression

(%)

Lagged sys-

tem balance

(%)

Logistic

regression

(%)

Lagged sys-

tem balance

(%)

Position taken 86 100 88 100

Opposed to system balance 47 66 33 88

Willful misconduct 46 0 64 0

Willful misconduct, asymmetric price spread 35 0 26 0

Willful misconduct, insufficient intraday

constraint

11 0 38 0

427

1 3

Intraday imbalance optimization: incentives andimpact of…

opposed to the system balance (47%). As the model accuracy is 68%, there must be

a significant number of situations, where the expected imbalance price leads to a

position that is in the same direction as the model prediction for the system balance.

We dub these situations as willful misconduct. Such a behavior cannot happen by

applying the simple strategy looking at the latest published system balance without

considering the current market situation. In this case, the market player would trade

anytime, and every right prediction leads to a position that supports the system.

Additionally, it needs a detailed look on high absolute system balances as it is

even more important to take no positions in these quarter-hours that further destabi-

lize the system. The limit is set to an absolute value of 1000MW including around

6% of all quarter-hours. The price incentives were even worse in these situations.

The intraday position was opposed to the actual system balance in only one third of

the quarter-hours mainly because of increasing willful misconduct.

There are two potential reasons for a willful misconduct. The first one is, that

the price spreads are asymmetric for positive and negative system balances. This is

Fig. 7 Absolute imbalance price spread as a function of the absolute system balance (SB)

Fig. 8 Comparison of intraday and imbalance prices for positive (left) and negative (right) system bal-

ances. The red area highlights quarter-hours with insufficient imbalance price incentives. The intraday

price is calculated as the volume weighted average price of all trades within the last 4.35min of trading

428

C.Koch

1 3

already discussed in Koch and Hirth [51] whose empirical analysis shows a system-

atic shift towards a system shortage. If the system balance is short, the spreads tend

to be smaller (Fig.7). For the analyzed period, the average spread was 17.62EUR/

MWh for positive and 28.44 EUR/MWh for negative system balances. From a

BRP’s perspective, being undersupplied leads to a low penalty in case of a system

shortage, but to high profits when the system balance is oversupplied. So, if the esti-

mated probability for a positive system balance is slightly above 0.5, the strategy

would still be to take a sell position and be undersupplied as well. Such a bias (in

any direction) caused a willful misconduct in 35% of all quarter-hours.

The second reason is, that weak imbalance prices can lead to wrong incentives.

For example, if the expected imbalance price is higher than the current intraday

price even when the system is oversupplied, it is always beneficial to buy additional

volumes on the intraday market and be oversupplied as well. If the expected imbal-

ance price is in any case below the intraday market price, it is profitable to take a sell

position. Under the current imbalance price mechanism, this is possible due to the

weak intraday price constraint. The comparison price is the volume weighted aver-

age price of the corresponding hour. This does not prevent that quarter-hourly intra-

day prices are higher than the imbalance price as Fig.8 shows. With regard to the

trading strategy, it caused a misconduct in 11% of all quarter-hours and even 38%

insituations with a system balance above 1000MW or below −1000MW.

4.4 Stricter intraday constraint

The analyses of Sects. 4.2 and 4.3 allow two broad conclusions: it is possible for

market participants to apply a profitable intraday imbalance optimization and it

has the potential to stabilize the system (68.6% of correct classified system balance

directions). But biased balancing incentives influence the decisions of the underly-

ing strategy so that the final impact is negative (only 47% of supportive positions).

The problem of perverse imbalance price incentives became apparent during some

days in June 2019. There were four days with severe situations and balancing

reserve activations of up to 7.5GW in Germany [56]. Day-ahead forecast errors led

to a shortage of several portfolios. The intraday market reflected this situation with

high prices which were higher than the expected maximum of the imbalance price.

So, market parties with forecast errors got the incentive to pay the imbalance price

rather than correcting their schedule at the intraday market [57]. The German regu-

lator became aware of infringements and cautioned five different BRPs [27].

Avoiding such situations requires a reform of the imbalance price calculation. It

is not necessary to change the whole calculation approach, but it needs stricter con-

straints to give better price incentives to portfolio managers. This section focuses on

the imbalance price coupling to the intraday price. This restriction is currently under

discussion in Germany. The TSOs started a consultation emphasizing its importance

[37]— especially because the imbalance costs will potentially decrease with the

introduction of a separate auction of balancing energy which is scheduled for June

2020 [58].

429

1 3

Intraday imbalance optimization: incentives andimpact of…

The current proposal is based on the study of Consentec [59] and is described in

[28]. The approach is to consider the volume weighted average price of the quarter-

hourly trades with the shortest time lag to delivery and an aggregated volume of

500MW (

ID500

). If the total quarter-hourly trading volume is lower than 500MW,

the price index considers as much of the latest hourly trades to reach the 500MW.

The constraint is not applied if the combined trading volume of quarter-hourly and

hourly trading is below 500MW. Additionally, there is a price markup which is 25%

ID500

, but at least 10EUR/MWh. The price markup is reduced if the absolute

system balance is lower than 500MW. Thus, the definition of the imbalance price

including the new intraday constraint (

IPID

) is:

Positive system balance:

Negative system balance:

We rerun the analyses presented in Sects. 4.1 and 4.3 with this new price restric-

tion to evaluate the impact on the trading strategy and its effect on system stability.

The assessment includes also a calculation with a volume of 200MW instead of the

recommended 500MW. The reason is that the total quarter-hourly trading volume

is below 500MW in 32% of the quarter-hours and it also includes trades that are

executed way before the gate closure at potentially different price levels. Consid-

ering an accumulated volume of 200MW, there is still a moderate risk that mar-

ket participants try to influence the price constraint, as they would take a relatively

high position that shifts the own balancing group deviation in an unfavorable direc-

tion. The intraday price constraint considered at the decision point (4.35min to gate

(12)

t=max

(

IPt;ID500t+max

(

0.25 ⋅

ID500t

;10EUR∕MWh

)

⋅

SBt

500MW

)

(13)

IPID

t=min

(

IPt;ID500t−max

(

0.25 ⋅

ID500t

;10EUR∕MWh

)

⋅

SBt

500MW

)

Table 8 Impact of stricter intraday price constraint on the behavior of a market player applying the intra-

day imbalance optimization

All quarter-hours Abs(system bal-

ance) > 1000MW

TSO pro-

posal ID500

(%)

TSO pro-

posal ID200

(%)

TSO pro-

posal ID500

(%)

TSO pro-

posal ID200

(%)

Position taken 85 85 84 84

Opposed to system balance 54 57 65 74

Willful misconduct 34 31 31 21

Willful misconduct, asymmetric price spread 32 31 24 20

Willful misconduct, insufficient intraday

constraint

2.0 0.7 7.4 1.5

430

C.Koch

1 3

closure) is calculated with a reduced volume (100MW less) to reflect that a share of

the trades is executed afterwards. The constraint always includes the complete price

markup to provide a conservative estimation.

The evaluation starts by looking at the effect on the behavior in relation to the

overall system as it is the overarching goal of the constraint to provide better incen-

tives. An application of the constraint as it is proposed by the TSOs would have

significantly positive effects (see Table8). The share of quarter-hours with trad-

ing positions opposed to the actual system balance would increase from 47 to 54%

mainly because of the decrease of situations with willful misconduct (46% compared

to 34%). The impact on situations with high absolute system balances is even better.

Without the stricter intraday constraint, the predominant strategy was to take a posi-

tion in the same direction as the expected system balance. This reduced significantly

and now the positions would support the system in two third of all quarter-hours.

The willful misconduct caused by insufficient price incentives would decrease from

38 to 7.4%.

However, there is still a considerable number of quarter-hours were the constraint

is still inadequate. Literally, it applies on average to almost two quarter-hours per

day. Reducing the accumulated volume of the considered intraday trades to 200MW

would lead to better incentives. The willful misconduct reduces to a percentage of

31% and the predicted imbalance price is sufficiently high to 99.3%. The share of

supportive positions increases by 3 percentage points. There is even a higher impact

on situations with large system balances with 74% supportive positions. The share

of quarter-hours with insufficient imbalance price incentives drops by another 6%

points.

But what is the impact on the profitability of the strategy? Table9 presents the

profit again compared to a simple strategy only based on the lagged system balance.

It turns out that the new imbalance constraint would increase the potential return

of the strategy. It was EUR42,000 under the current regime and would grow to

EUR63,000 with the intraday constraint supposed by the TSOs and EUR76,000

with a considered volume of 200MW. There would be an even higher influence on

the strategy based on taking positions opposed to the lagged system balance. It was

unprofitable before but would make profits of EUR40,000 or rather EUR51,000. It

shows again that the advantage of combining predictions of system balance direc-

tion and expected price spreads was caused mainly by the biased price incentives

which partly vanish by applying a stricter intraday price constraint.

Table 9 Potential profit of

trading strategy based on

logistic regression model and

lagged system balance with the

new intraday price constraint

from July 2017 to June 2019

Logistic regression Lagged system

balance

ID500 ID200 ID500 ID200

Total profit [EUR] 63,021 76,133 40,357 51,279

Profit [EUR/MWh] 1.09 1.31 0.59 0.75

431

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Intraday imbalance optimization: incentives andimpact of…

5 Conclusion

This paper demonstrates that it is possible to apply a profitable trading strategy by

taking intraday positions considering imbalance price expectations. The basis is a

logistic regression model to predict the probability of the system balance to be posi-

tive or negative. This information is combined with an expected imbalance price for

positive and negative system balances to estimate the profits of an intraday buy and

sell position. From July 2017 to June 2019, this approach would have been profitable

on 503 out of 730days leading to a total return of EUR42,000. The results are bet-

ter than applying a simple strategy of taking positions that are opposed to the latest

published system balance.

From a system perspective, this behavior would not have been supportive. Less

than half of the decisions would have been opposed to the actual system balance

even though the model was able to classify it correctly in 68% of all quarter-hours.

The reason is that biased imbalance price incentives lead to a willful misconduct.

Firstly, the price spread between intraday and imbalance prices are systematically

higher for a surplus than for a shortage of the system. So, being undersupplied will

lead to a low penalty in case of a system shortage, but to high profits when the sys-

tem is oversupplied. If the estimated probability for a system shortage is slightly

above 0.5, the strategy would still be to take a sell position and be undersupplied as

well.

Secondly, there are multiple situations with imbalance prices providing insuf-

ficient trading incentives. This is the case if the intraday price is higher than the

imbalance price even though the system is undersupplied or if the intraday price is

lower when the system is oversupplied. In both cases, the beneficial strategy would

be to take a position in the same direction of the system. It caused a willful miscon-

duct in 11% of all quarter-hours and even 38% when the absolute system balance

was higher than 1000MW. The latter one is problematic as wrong market behavior

can destabilize the system when a large share of the procured balancing reserve is

already activated.

A part of the described problem could be addressed by a stricter intraday price

constraint. The TSOs provide a new proposal for coupling the imbalance price to

the intraday price. It covers quarter-hourly intraday trading and is more related to

trading close to gate closure by considering the last trades with an accumulated vol-

ume of 500MW. A rerun of the strategy shows that the profitability of the intra-

day imbalance optimization raises when considering for the proposed intraday price

constraint. The total profit would have been EUR63,000—an increase of 50%. But

it is important to mention that the adjustment yields to a more system supportive

behavior. The share of positions opposed to the system balance increases from 47 to

54% and the willful misconduct reduces from 46 to 34%. The price incentive would

be even better when reducing the considered volume to 200MW as the coupling

price would be closer to the market situation close to gate closure. This applies espe-

cially for the quarter-hours with high system balances. The adoption of the strategy

would reduce the system balance in 74% of all situations when using the strictest

intraday price coupling. This shows the importance of efficient regulation. A simple

432

C.Koch

1 3

improvement of the current imbalance price calculation enables system supportive

intraday imbalance optimization.

However, there would still be a considerable share of quarter-hours with bad

price incentives due to the asymmetric price spreads. This bias causes a systematic

shift towards a system shortage, if market participants consider it in their decision. It

needs further research to analyze the impact of this problem on system stability and

to find reasonable regulatory measures to improve the imbalance price incentive.

These findings are important for other regulators facing an increasing importance

of the intraday market in their countries. This holds especially for countries with a

single imbalance pricing mechanism such as UK, Belgium, Netherlands or Austria.

An application of the presented strategy will show whether their imbalance price

system also causes biased trading motives. Regardless of the pricing rule, it is neces-

sary in any case to establish an efficient intraday price constraint to provide appro-

priate balancing incentives for market participants.

Acknowledgements The author wants to thank Entelios GmbH for access to market data on successfully

settled intraday trades and order book status at EPEX SPOT. This research did not receive any specific

grant from funding agencies in the public, commercial, or not-for-profit sectors.

Funding Open Access funding enabled and organized by Projekt DEAL.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,

which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as

you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-

mons licence, and indicate if changes were made. The images or other third party material in this article

are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the

material. If material is not included in the article’s Creative Commons licence and your intended use is

not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission

directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen

ses/ by/4. 0/.

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