Industrial Demand Response in the Primary Reserve

IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2018 ,

Industrial Demand Response in the Primary Reserve

Markets

A case study on Holmen’s Pulp and Paper Mill FEDERICA TOMASINI

KTH ROYAL INSTITUTE OF TECHNOLOGY

Industrial Demand Response in the Primary Reserve Markets: A case study on Holmen’s Pulp and Paper Mill

FEDERICA TOMASINI

Master Thesis at School of Electrical Engineering & Computer Science EG230X Degree project in electric power systems

Academic supervisor: Kaveh Paridari Industrial supervisor: Filip Englund

Examiner: Lars Nordstr¨ om Date: December 2018

TRITA-EECS-EX-2018:692

Abstract

This thesis stems from the interest of Holmen group to investigate the opportunities available for large electricity consumers in the Swedish primary reserve markets.

The study performed focuses on one of Holmen’s paper mill and it aims at identifying a load inside the production process that is suitable for providing frequency containment services for the grid. The evaluation of the mill’s consumption profile and the technical requirements of the reserve market led to the identification of the electric boiler coupled with a steam accumulator as the most appropriate load.

Five case study simulating the participation of the mill to different energy and reserve markets have been evaluated. For each case a linear optimization problem has been formulated. The first simulation represents the current practice of the mill in relation to the energy purchased on the spot market (following it will be also referred as reference case). The second case study (II c.s.) integrates the use of the steam accumulator as a tool to perform thermal load shifting. In the third case study (III c.s.) the mill is modelled to bid on the spot and primary reserve market by offering some capacity of the electric boiler. The last two case studies (IV and V c.s.) recalls the first and last previously mentioned, but also include the possibility of having energy imbalance. This means that the imbalance settlement operated by eSett will produce an additional cost or profit for the mill.

The last three problem formulations fall under the definition of stochastic problems, since two random variable are present, namely: average hourly frequency value and imbalance settlement price. The uncertainty of the variables is represented through scenarios.

The outcome derived from the combination of the results for the winter and summer cases shows that each strategy brings an economic saving when compared to the reference case (I c.s.). The less interesting strategies are the ones that do not involve the reserve market, leading to about 0.03% (II c.s.) and 0.06% (IV c.s.) of saving on the overall yearly energy cost. Contrariwise, by offering FCR-N capacity, the cost of electricity can be cut by 5.15% (III c.s.) and 6.69% (V c.s.), respectively considering and not considering the imbalance settlement.

Keywords: industrial demand response, pulp and paper industry, primary frequency

control, stochastic optimization

Sammanfattning

Avhandlingen har sitt ursprung i skogsindustrikoncernen Holmens intresse att unders¨ oka m¨ ojligheten f¨ or stora elf¨ orbrukare att delta p˚ a den svenska prim¨ ar-reservmarknaden.

Studien som utf¨ orts fokuserar p˚ a ett av Holmens pappersbruk och syftar till att iden- tifiera en elektrisk process som, inom bruksgr¨ anserna, ¨ ar l¨ amplig f¨ or att tillhandah˚ alla frekvensregleringstj¨ anster till det nationella n¨ atet. En utv¨ ardering av brukets elf¨ orbrukning samt de tekniska krav som st¨ alls p˚ a reservmarknaden ledde till att en elektrisk panna med tillkopplad ˚ angackumulator identifierades som mest l¨ amplig.

Fem budstrategier som simulerar brukets deltagande till olika energi- och reserv- marknader har presenterats. F¨ or varje strategi ¨ ar ett linj¨ art optimeringsproblem for- mulerat. Den f¨ orsta strategin visar p˚ a nuvarande s¨ att bruket k¨ oper elektricitet p˚ a spot- marknaden. Den andra strategin integrerar anv¨ andning av ˚ angackumulatorn som ett verktyg f¨ or att utf¨ ora termisk lastskiftning. I den tredje modelleras deltagande ocks˚ a p˚ a prim¨ arreservmarknaden genom att erbjuda en viss kapacitet hos elpannan. De tv˚ a sista strategierna baseras p˚ a den f¨ orsta och tredje, men till˚ ater i till¨ agg obalanser vilket inneb¨ ar en extra kostnad eller m¨ ojlig intj¨ aning f¨ or bruket.

De tre sista problemformuleringarna faller under definitionen stokastiska problem, eftersom tv˚ a slumpm¨ assiga variabler ¨ ar n¨ arvarande, n¨ amligen: genomsnittligt timfrekvensv¨ arde och priset f¨ or obalans. Os¨ akerheten f¨ or variablerna representeras genom scenarier.

Resultatet visar att varje strategi ger en ekonomisk besparing j¨ amf¨ ort med refer- ensfallet (strategi ett). De mindre intressanta strategierna ¨ ar de som inte involverar reservmarknaden, vilka endast leder till ca 0,03% och 0,06% minskning av den totala

˚ arliga energikostnaden. D¨ aremot, genom att erbjuda FCR-N-kapacitet kan kostnaden f¨ or el minskas med 6,69% och 5,15% beroende p˚ a om obalanser till˚ ats eller ej.

Nyckelord: industriell efterfr˚ agesvar, massa och pappersindustrin, prim¨ arfrekvensstyrning,

stokastisk optimering

Acknowledgements

To begin with, I would like to thank Filip Englund, my industrial supervisor at Holmen, for believing in this project since the very beginning and giving me his time, teaching and support during this challenging, though enriching experience. I genuinely enjoyed working with him because of his stimulating and cheerful aptitude. I would also like to thank everyone from the Holmen team that helped me during these months either with technical or emotional support, especially I would like to mention Hannes Vomhoff, Magnus Rydstrand, Anna Ramberg and Emilia Larsson.

Naturally, great thanks goes to Kaveh Paridari, my academic supervisor, that en- couraged me with wise advice in all the most difficult moments. Many thanks also to Lars Herre, from KTH, for his generous, constant and priceless help.

Lastly, I want to express my gratitude to my family that is always supporting me

and that encouraged me to start these two years journey that made me part of an even

larger family. Thanks to the SELECT mates that taught me how to be enthusiastic and

open to every single opportunity that will come.

Contents

1 Introduction 8

1.1 Motivation . . . . 8

1.2 Research Question and Objectives . . . . 9

1.3 Methodology . . . . 9

1.4 Contribution . . . . 10

1.5 Thesis structure . . . . 10

2 Background 11 2.1 Swedish Power System . . . . 11

2.2 Relevant Energy and Power Markets . . . . 13

2.2.1 Energy market . . . . 14

2.2.2 Imbalance Settlement . . . . 14

2.2.3 Reserve Market . . . . 15

2.3 Literature review on consumers flexibility . . . . 18

3 Paper mill model 20 3.1 Pulp and paper production process in Hallsta . . . . 20

3.2 The flexible capacity identified in the mill . . . . 21

3.3 System modelling . . . . 21

3.4 Assumptions for the models . . . . 23

4 Case studies 24 4.1 Case study I - DA without the use of the accumulator . . . . 25

4.2 Case study II - DA with use of the accumulator . . . . 26

4.3 Case study III - DA & FCR-N trading . . . . 26

4.4 Case study IV - DA & speculation on IS . . . . 30

4.5 Case study V - DA, speculation on IS & FCR-N . . . . 31

5 Parameter Setting 33 5.1 Scenario selection . . . . 33

5.2 Values used for the simulation . . . . 34

5.3 Effects of Risk Adversity . . . . 37

6 Results and Conclusions 40

6.1 Results for winter case . . . . 40

6.2 Yearly results . . . . 45

6.3 Conclusions . . . . 47

6.4 Future Work . . . . 48

Appendices 50 A Complete problems formulations 51 A.1 Case study I . . . . 51

A.2 Case study II . . . . 52

A.3 Case study III . . . . 53

A.4 Case study IV . . . . 54

A.5 Case study V . . . . 55

List of Figures

2.1 Simplified scheme of the electricity exchange system [1] . . . . 12

2.2 Electricity and Balancing markets’ time line . . . . 13

2.3 Frequency restoration process [2] . . . . 16

3.1 Simplified plant scheme . . . . 22

3.2 Plant scheme including accumulator . . . . 22

4.1 Activation of a continuously controlled FCR-N capacity . . . . 29

4.2 Maximum and minimum energy (a) and power (b) consumption in EB . 29 5.1 Identification of the optimal number of price and frequency scenarios . . 34

5.2 DA, FCR-N and IS prices - winter case . . . . 35

5.3 Frequency scenarios for the winter case . . . . 36

5.4 DA, FCR-N and IS prices - summer case . . . . 37

5.5 CVaR vs cost in MSEK at increasing β (case study 5 - winter) . . . . . 38

5.6 PDF of the cost, Expected cost and CVaR (case study 5 - winter) . . . . 39

6.1 E

in case study 1 & 2 (left axis) against λ

(right axis) . . . . 41

6.2 Flexible capacity (left axis) against DA and FCR-N prices (right axis) . . 42

6.3 Q

(left axis) & frequency (right axis) in 5 scenarios for the first 6 hours . . . . 43

6.4 Day Ahead optimal bidding strategy - case study 4 . . . . 44

6.5 FCR-N optimal bidding strategy - case study 5 . . . . 45

6.6 FCR-N bids in a summer day - case studies 3 and 5 . . . . 46

6.7 Electricity price in the different study cases (yearly average) . . . . 47

List of Tables

2.1 Actions to take in case of frequency deviations . . . . 13 4.1 Number of times the hourly value of frequency stays in the ranges indi-

cated [3] . . . . 27

6.1 Results comparison for the summer case, values in [SEK/day] . . . . 46

Nomenclature

Acronyms

LW U Light Weight Uncoated

T SO Transmission System Operator DSO Distribution System Operator

Svk Svenska Kraftn¨ at

T M P Thermomechanical Pulp

DR Demand Response

V RE Variable Renewable Energy

DA Day Ahead

IS Imbalance Settlement

F CR − N Frequency Containment Reserve in Normal operation F CR − D Frequency Containment Reserve in Disturbed operation aF RR automatic Frequency Restoration Reserve

mF RR manual Frequency Restoration Reserve GAM S General Algebraic Modeling System ISDM Industrial Demand Side Management

f frequency

BRP Balance Responsible Party RP M Regulating Power Market

P AB Pay As Bid

P &P Pulp and Paper

Nomenclature used in the optimization problems

Sets

t ∈ τ Time index, hourly time step [h]

ω ∈ Ω Scenario index

Parameters

P R

Production Rate of pulp in the Refiners at hour t[ton/h]

P R

Production Rate of paper in the Paper Machine at hour t [ton/h]

E

Energy consumed in the refiners/paper machine at hour t [M W h

] Q

Steam produced in the refiners/consumed in the Paper Machine at

hour t [M W h

]

λ

Day Ahead market price at hour t (spot price) [

]

λ

Imbalance Settlement price for consumers at hour t, in scenario ω [

]

π

Probability of scenario ω [-]

f

Hourly average frequency value at hour t, in scenario ω [Hz]

λ

Price of FCR-N bid at hour t[

] Constants

SEC

Specific Energy Consumption in the refiners/paper machine [

pulp/paper

] SRF

Steam Recovery Factor in the refiners [

pulp

] StP Steam to paper ratio [

paper

]

h

Enthalpy of saturated steam at 2.4 bar [

] η Electric boiler efficiency [-]

F

Penalty fee for uninstructed energy imbalance [

e

]

α Confidence level

β Parameter used to weight the risk against the expected cost M Auxiliary large enough constant

F

Penalty fee for spilling steam [

th

]

Variables

E C

Expected cost in case study i [

] CV aR Conditional Value at Risk [

]

C

Daily cost for the energy bought on the day ahead market [

] C

Penalty cost for energy imbalance [

]

C

Cost or profit from Imbalance Settlement [

] C

Daily penalty cost associated to steam spilling [

]

C

Daily profit from the participation to the balancing market [

] E

Energy bought on the day ahead market for hour t [M W h

] E

Energy consumed in Real Time at hour t in scenario ω [M W h

]

∆E

Energy imbalance due to deviation from original plan at hour t in scenario ω [M W h

]

E

Energy consumed in the Electric Boiler at hour t in scenario ω[M W h

] Q

Steam produced by the Electric Boiler at hour t in scenario ω [M W h

] E

Energy contained in the steam accumulator at hour t in scenario ω

[M W h

]

Q

Steam flowing from the electric boiler to the paper machine at hour t in scenario ω[M W h

]

Q

Steam flowing from the electric boiler to the accumulator at hour t in scenario ω[M W h

]

Q

Steam flowing from the accumulator to the paper machine at hour t in scenario ω[M W h

]

u

Binary variables to determine if the accumulator is charging or dis- charging during hour t in scenario ω [-]

P

Flexible capacity offered to the FCR-N market at hour t [M W

] E

Instructed energy deviation for up (< 0) or down (> 0) regulation at

hour t in scenario ω [M W h

]

P

Power consumed in the Electric Boiler at hour t in scenario ω[M W

]

Chapter 1 Introduction

The following chapter aims at explaining to the reader the motivations from which the present study stems and the goals defined by the author, together with all the partners involved. A brief hint on the methodology used to approach the problem is also presented.

1.1 Motivation

In 2016 the four Nordic Transmission System Operators

(TSOs) Svenska kraftn¨ at (SvK), Statnett, Fingrid and Energinet have jointly published a report summarizing the upcoming challenges and opportunities for the Nordic power system [4].

Some of the elements identified as threats for the operation and planning of the power system are: an augmenting share of Variable Renewable Energy (VRE) in the electricity mix, the closure of thermal and nuclear power plant and the increased electrification of the industrial and residential sector. Alongside these factors, however, modern technolo- gies and current regulations are opening new opportunities to some of the traditional actors in the field. On the wave of these structural changes, Svenska Kraftn¨ at announced the opening of the primary reserve markets to consumers, enabling them to play a more active role [5].

It is in this framework that the Holmen group, which accounts for almost 3% of the whole Swedish electricity consumption [6], showed its interest in supporting a research evaluating this opportunity. The participation of end consumers to the market will even- tually benefit all the parties. On one side, it will facilitate the planning and operation of the power system meanwhile reducing the needs for grid investments [4]. On the other side, this will result in a decrease of the energy prices and a more reliable and stable power system for the consumers.

Holmen is a forestry industry group [7] having several business areas, such as paper- board, paper, timber and energy. The present project is developed under the supervision

1

A TSO is a national entity, having the responsibility for the security of supply, for the real-time coordination of supply and demand in the power system, and for the operation of the high-voltage grid.

The TSO also carrys the ultimate responsibility on the imbalance settlement according to the national

laws [1].

of the Holmen Energi team, but it is focusing on the largest electricity consuming activ- ity of the group, namely the paper production process. More specifically, the paper mill located in Hallstavik, north of Stockholm, is at the centre of this study. The scope of the work is mainly limited to the pulp and steam production process, while the paper section is considered untouchable due to business constraints. The market places taken into consideration in this work are: Day Ahead (DA), primary reserve and imbalance settlement, all of them in the Swedish context. Since this work is a preliminary study evaluating the profitability of the mentioned markets, the technical and legal require- ments for being a participant have been evaluated, but will not be expansively treated inside the report.

1.2 Research Question and Objectives

The research question that motivates the development of this thesis can be formulated as follow: What is the profitability of a pulp and paper mill when participating in the primary reserve market? Several steps have to be taken before eventually providing Holmen with a good estimation of the value contained in the primary reserve market.

The first objective is to understand, among the different reserve markets, which one is the most approachable and interesting for the paper mill in Hallstavik.

The second goal is to identify, within the facility, which is the object that can provide flexibility.

Finally, the last objective is to design a bidding strategy that minimizes the costs of energy and capacity traded on the day ahead and reserve markets.

1.3 Methodology

To achieve the three principal goals introduced above, a three stage methodology has been followed.

To begin with, it was fundamental to acquire a complete knowledge of the rules regulating the energy and reserve markets in Sweden, with a special attention to the new legislation coming into force in March 2019 regarding consumers’ flexibility. Desktop research, calls and meetings with people from SvK and consulting companies have been the tools used to become familiar with the concepts.

Once the background knowledge on the markets was built, the focus was moved on the paper production process and the loads used inside the mill. The aim was to identify those machines that can comply with the markets’ requirements, while still serving their purpose in the production chain. The suite WinMOPS from the software MOPSsys has been used to outline the material streams and load dependencies within the mill.

WinMOPS is an online live database, accessible via the intranet of the company, that

contains historical data on every measurement point of the mill. The use of this software

Finally, in order to identify an optimal bidding strategy, an optimization problem taking into account the mill and markets constraints was built. In order to do that, the two mathematical software Matlab and GAMS have been jointly used. Parameters for the models were constructed in Matlab and made readable for the second software in a .gdx (gams data exchange) file. The latter was imported in GAMS, where the set of equations describing the problems was computed. The solved algorithms were giving as an output another .gdx file that was sent back to Matlab, from which the analysis of the outcome is clearer. Good sources for the integration between the two software are [8], [9], [10].

1.4 Contribution

Given, on one side, the literature found on the topic of demand response in the paper industry and, on the other side, the work developed in this thesis; the contribution of the author can be summarized in three points:

A) A thorough description of the rules for the primary reserve market (especially FCR-N) in Sweden is presented;

B) The potential of using an electric boiler coupled with a steam accumulator as balancing object is assessed;

C) The inclusion of variable frequency deviations in the optimization problem is demonstrated to be relevant.

1.5 Thesis structure

Chapter 1 aims at giving the reader an understanding of the reasons from which the study was born and a glimpse on the methodology used to achieve the goals set.

Chapter 2 deals with the backgorund information needed to understand the rest of the work. It focuses on the Swedish power system and the regulations of its markets. A literature review on Industrial Demand Side Management (IDSM) closes the section.

Chapter 3 is dedicated to the description of the paper mill, its outline and the related hypothesis used in the models.

Chapter 4, being the core of the thesis, contains the description of the algorithms used to obtain the optimal bidding strategy in the several markets and system’s setting considered.

The methodology and values used for the simulations are cleared out in chapter 5.

Finally, results, conclusions and future work are presented in chapter 6.

Chapter 2 Background

In the following chapter the reader will be given the basic notions needed to understand the rest of the project. To begin with, a description of the Swedish power system structure is given. Following the energy and power markets that will be involved in the modelling are presented. To conclude, the outcomes of a literature review on the role of consumers offering balancing services are shown.

2.1 Swedish Power System

The current structure of the Swedish power system dates back to 1996, when the Swedish Competition Authority proposed to deregulate the electricity market [11]. Since then, the structure has not changed and the operations of energy transmission and manage- ment of the grid are entrusted to Svenska Kraftn¨ at (SvK), national TSO and state-owned authority. During the same period, Sweden started exchanging power with Norway, set- ting the basis for the currently existing Nordic market, that have been joined in the following years by Finland, Denmark, Estonia, Latvia and Lithuania. Nowadays, the Nordic system operators are collaborating with their central European counterparts for the harmonization of the legislation regulating the power system in order to create a sin- gle and unite power market able to ensure security of supply to all nations and efficient managing [1]. With the same purposes, from an energy market point of view, Sweden is divided into four price areas that are reflecting the limitations of the transmission system and the distribution of the resources and inhabitants of the nation. This division helps solving grid congestion problems with a market-oriented approach. Hallstavik, where the mill under study is situated, belongs to price area number 3 (SE3), the same of Stockholm.

In order to have an overview of the relations and roles of the different players active

on the Swedish power system, figure 2.1 is used.

Figure 2.1: Simplified scheme of the electricity exchange system [1]

On the bottom side of the picture the physical journey of electricity can be followed.

From the power plants, where it is produced, it is fed into the national grid, operated by SvK, and then distributed at regional and local level by the Distribution System Operators (DSOs) that eventually deliver it to the end users. Consumers can either be supplied by the local grid (at low voltage) or directly by the regional one (at medium voltage) - this is normally the case for energy intensive industries.

On the top part of the picture, the transactions associated with energy delivery are represented. The Nordic power exchange market is managed by Nord Pool and it includes the Scandinavian and Baltic states, Germany and UK. It is open to producers, consumers, traders and retailers that exchange energy and capacity depending on the auction they want to participate.

It is important, at this point of the report, to mention that principle of electrical systems that motivates this whole study. At the basis of a well-functioning network there is one major rule: balance between production and consumption of electricity must be kept at all times. When it comes to a national grid, the maintenance of the balance relies on a shared responsibility of different actors playing on the balancing markets (described in 2.2.3).

One indicator of the level of balance on the grid is the frequency value that, in

nominal conditions, should be stable at 50 Hz. A shortage of power on the net results in

a deviation of the frequency below 50 Hz, requiring up-regulating actions. On the other

side, a surplus of power is translated into an upward deviation of the frequency above 50

Hz and is solved with a down-regulating action. Consumers and producers participating to the balancing markets act in order to maintain the frequency at the nominal value, as summarized in table 2.1.

f < 50Hz f > 50Hz Cause Shortage of electricity Surplus of electricity

Direction of regulation Upward Downward

Consumers’ action ↓ consumption ↑ consumption Producers’ action ↑ production ↓ production

Table 2.1: Actions to take in case of frequency deviations

2.2 Relevant Energy and Power Markets

Electricity, from a purely economic point of view, is a commodity equals to many others.

It is traded on a liberalized market, where buyers and sellers meet, setting the spot price according to the typical demand & supply curve. There is, however, one peculiarity of this good that makes it slightly different from the others: it is yet not economically convenient to store it. This fact strongly affects the structure and rules of the markets where it is traded.

A recurrent term in the field of electricity trading is “day/hour of operation” and it refers to the moment during which electricity is physically delivered which does not correspond to the one when it is traded. In figure 2.2 all markets where energy and capacity are traded are rolled out on a time line, according to their temporal succession.

Figure 2.2: Electricity and Balancing markets’ time line

The future markets, bilateral contracts and intra-day market are out of the scope of

this thesis, therefore attention will be given only to the remaining ones.

2.2.1 Energy market

The energy market (also known as Day-Ahead (DA) or spot market) is the place where suppliers, retailers and consumers auction their bids and offers for the electricity being delivered and consumed the following day. It is based on short term forecasts of supply and demand and it is, therefore, the first place where balance between production and consumption is tempted to be achieved.

Bids must specify how much energy can be delivered (consumed) during a specified hour together with the maximum and minimum price that can be associated to the delivery (consumption) of it. This set of information has to be provided for every single hour of the day, before 12:00 CET of the day prior delivery (D-1), when the auction will be closed. Thereafter, Nord Pool calculates the aggregated curves showing the quantity and price (λ

) of energy to be exchanged on the next day. The intersection of the demand and supply lines sets the clearing price, which is valid for all players. This price setting scheme is called marginal pricing, since all the accepted bids (offers) receive (pay) the spot price, which coincides with the marginal cost of the most expensive produced power unit. In case large volumes have to be transmitted through network’s physical bottlenecks, the spot price will be different among different bidding areas.

2.2.2 Imbalance Settlement

The Imbalance Settlement (IS) is a financial settlement mechanism aiming at charging or paying Balance Responsible Parties

(BRPs) for their imbalances [12]. An imbalance happens when a BRP is unable to consume and/or produce in real time the exact same amount of energy that had contracted on the day ahead market. In Sweden imbalances are settled by eSett Oy, a company jointly owned by the three Scandinavian TSOs. In reality, the imbalance invoices are sent at the end of every week to each market player, however, in this thesis the transactions associated to the IS are assumed to be payed at the end of every day.

Imbalances are calculated as the difference between the real time energy consumption (production) and the day ahead contracted one: ∆E

= E

− E

, therefore it can be either positive or negative. Taking the perspective of BRP that has under its portfolio only consumers (i.e. it simply buys energy on DA market), an imbalance is positive when the energy consumed in real time is greater than the energy contracted on DA.

In this case, the BRP will have to ”buy” from eSett the extra energy at the Imbalance Settlement price. On the other hand, if less energy than contracted is consumed, the imbalance energy will have a negative sign. The BRP will have to ”sell” that energy to eSett at the Imbalance Settlement Price.

In Sweden there is a one pricing scheme for consumers in imbalance and a two pricing scheme for producers. The Imbalance Settlement price (λ

) for consumers is always

2

A company that has a valid Imbalance Settlement Agreement with eSett and a valid Balance

Agreement with a TSO and manages a Balance Obligation on its own behalf as a producer, consumer

or trader of electricity or on the behalf of other producers, consumers or traders of electricity [12]

equal to the Regulating Power Market (RPM) price. The RPM is the price of the most expensive tertiary reserve activated to give balancing services during the hour.

λ

is normally slightly higher than λ

during the hours when the system is in up-regulation (surplus of demand), while the opposite happens when the system is in down-regulation (shortage of demand).

In addition to get or pay the IS price, an actor being in imbalance has to pay a fixed fee for any MWh of energy deviation (being either positive or negative). This fee (indicated in the algorithms with the term F

) is, currently, 5 SEK/MWh.

From a consumer’s perspective the imbalance settlement can result either in a cost or in a saving depending on the difference between the DA and the IS price and the direction of regulation. The cases where the IS bring savings are:

• Positive imbalance during a down regulating hour: the consumer pays the extra energy at the IS price which is lower than the spot price

• Negative imbalance during an up regulating hour: the consumer gets, for the energy not consumed, the IS price which is higher than the price at which the energy was bought on the previous day

It becomes therefore clear that profit can be made on the imbalance settlement.

However, since the IS price is revealed only at the end of the operating hour, no one can predict with certainty the side on which it will be found. It is, therefore, normal practice to avoid energy imbalances in order to avoid risk. Additionally, it is stated in the BRP agreement that a BRP must strive to be balanced in real time [13].

2.2.3 Reserve Market

As introduced in the first section of this chapter (2.1), the balancing markets, also re-

ferred to as reserve markets, exist with the purpose of ensuring balance between demand

and supply on the grid. As the name suggests, the product traded on the reserve market

is not energy, but power (MW). The bidder, indeed, offers the availability of increasing

or decreasing the capacity of its load depending on the system’s need. According to the

kind of balancing service delivered, five different products exist in Sweden. It is made

use of figure 2.3 to illustrates the phases through which the system operator goes when

an under-frequency situation occurs and up-regulation is needed.

Figure 2.3: Frequency restoration process [2]

As frequency (red line on the bottom half of the graph) starts to decrease from the normal value of 50 Hz, Frequency Containment Reserves for Normal operations (FCR-N) are activated (upper half of the graph). Their power is used to hold back the deviation and is fully employed when frequency reaches 49.9 Hz. If, however, the measure is not effective enough, and the frequency continues decreasing, the Frequency Containment Reserves for Disturbances (FCR-D) are activated gradually. At the threshold of 49.5 Hz, all the available FCR-D capacities are fully employed. FCR-N and FCR-D belongs to the so called primary reserves. Within 15 minutes, the Containment Reserves must be fully restored in order to be ready for the next disturbance event. The Frequency Restoration Reserves (FRR) are, therefore, activated with the goal of bringing back the frequency to 50 Hz. FRR can be further divided into automatically (aFRR) and manually (mFRR) activated products.The first ones belongs to the secondary reserves and the second ones to the tertiary reserve.

The last balancing product existing in Sweden is the so called Peak Load Reserve, it is accounted into the national strategic reserves and it is procured only during the winter season, from 16 November to 15 March.

According to the System Operator Agreement [14], signed by the four Nordic TSOs, SvK needs to procure a total amount of around 750 MW FCR capacity for every hour of the day and has 1350 MW of FRR capacity installed.

The products mentioned above (FCR-N, FCR-D, aFRR, mFRR and Strategic Re- serve) differ one another on characteristics such as: endurance, speed of activation, minimum size and others. After a deep analysis of the requirements of the markets, and a comprehension of the possibilities inside the mill, it was agreed that the FCR-N market was to be the focus of this thesis. The regulations of the other balancing markets are, therefore, not treated in this report.

FCR-N: characteristics and procurement requirements

The Frequency Containment Reserves in Normal operations (FCR-N) belong to the

category of primary reserves and are by definition operating reserves with the purpose of

containing the frequency from deviating from the system’s nominal value. FCR products are activated in the time frame of seconds/minutes automatically, thanks to a local control unit able to detect a deviation of the frequency on the grid and adjust the power of the balance providing entity.

FCR-N is activated when the grid frequency is in the range of 49.9 and 50.1 Hz, which is considered normal operation. Due to the necessity of coping with higher and lower frequency value, FCR-N products have to be symmetrical, which means they need to be able to provide the same volume for up- and down-regulation. In order to fulfill the requirements of SvK, a FCR-N load must be activated up to 63% of its capacity within 60 seconds from the frequency drift and 100% within 3 minutes.

FCR-N products are traded on the primary reserve market, which is organized at a national level and takes into consideration the division of Sweden into the four balancing areas (corresponding to the four bidding areas). The rules of the market have been harmonized within all the Nordic TSOs [15] and are equal for both, production and consumption loads. Hereunder the most remarkable rules are listed [16] [17]:

• Bids must be submitted via electronic communication in Ediel QUOTES format

• Bids for the following 24 hours are submitted by the participants in the period from 12.00 CET of D-1 and D-2 until 18.00 of D-1 and 15.00 of D-2

• The minimum bid size is 0.1 MW and the maximum is 30 MW

• The minimum activation time (stamina) is 1 hour

• The maximum activation time is 6 hours for block bids (bids valid for more than one hour) offered in D-2 and 3 hours for block bids offered in D-1

• It is allowed to bid only on one of the two reserve type (among FCR-N and FCR-D)

• Cancelled bids cannot be retrieved by the BRP, but repurchases can be done on

the D-1 and after contact with SvK. Repurchases are made at marginal prices

The procurement is finalized by Svenska Kraftn¨ at by 21.00 on D-1 and by 16.00 on

D-2, but the prices are published on mimer.svk.se in the early morning of the day of

delivery. The participants are Paid As they Bid (PAB) for the procured capacity (MW),

while the remuneration for the potential energy activation (MWh) is calculated hourly

based on the frequency measurements. The price at which the energy activation is paid

is the Regulating Power Market price, in its dominant direction of activation. It is

interesting to notice that, since the yearly activation time of a resource can be relatively

small, the largest profit on the market is normally made on the capacity procurement

rather than on the activated energy remuneration.

2.3 Literature review on consumers flexibility

The Nordic TSOs recognize in Demand Response

(DR) one of the most promising solution to the challenges that the electrical grid is nowadays facing [4]. According to [19], Sweden can count on approximately 4,500 MW of flexible demand wherof 51% lies in the industrial sector.

Energy intensive industries are the ones that are expected to play a more determining role. Not only they are the ones that could contribute with the greatest capacity, but also they are the ones that would experience an higher economic benefit, being the most affected by electricity cost variations [20]. Within the Swedish energy intensive industries, the Pulp and Paper (P&P) firms are responsible for about 52% of the whole energy consumption, reason why, the Swedish Energy Agency affirms that changes in the sector’s use of electricity have a significant impact on the total industrial electricity use [21].

Most of the authors that analyzed the potential of DR in the P&P industry identified the widest source of flexibility in the pulp production process, particularly in the refiners’

load. According to Paulus and Borggrefe [22], the nominal capacity and the high utiliza- tion level of the machines rank them as the most promising ones for balancing services.

Additionally, the authors identify in the availability of large pulp storage a resource that can ensure peaks’ shaving also on the day ahead market. Aro [23], in his master thesis, proposes a methodology that aims at identifying those loads, within a paper mill, that can provide shifting and shedding services. The validation of the methodology on one of UPM’s mill shows that refiners are the most suitable motors for frequency restoration purposes. Helin [24], as well, develops an optimization algorithm simulating the partici- pation of some capacity from the refiners’ section to the regulating power market. This fact reconfirms that the highest potential is considered to be in the pulp production step.

However, it is of great importance to notice that none of these documents mention the degradation of the quality of pulp as a consequence of a slowdown of the process. This, instead, is the principal reason for rejecting the refiners from the analysis performed in the current thesis. A lower quality of the pulp results, inevitably, in a worse quality of the paper. Additionally, in these studies, the market considered is the tertiary reserve one, which allows for slower reaction times (15 minutes).

E. Candela and C. Petersson [25] also propose an optimal bidding strategy for an aggregator acting on the energy and regulating power market. Even though their work focuses on a freezer enterprise, it is of great help to understand the rules of the energy and reserve markets in Sweden. It is, in fact, one of the most clear paper describing the regulation of all the Swedish balancing markets available in English. The great majority of official documents from SvK are, indeed, in Swedish.

For what regards the formulation of the markets’ constraints in the optimization problem, the work of J. Dalton [26] has been of great inspiration. The author formulates a risk averse stochastic optimization problem, maximizing the profit of an aggregator

3

Demand Response is the ability of power consumers to adapt their demand to the network’s needs,

possibly shifting demand to other periods [18].

bidding on the energy and primary reserve markets. The structure of the objective function is recalled in this thesis for a large extent. Nevertheless, the physical problem modelled is totally different, dealing with electric vehicles smart charging.

The importance of including in the simulation the stochastic activation of the reserve

capacity was derived from the work developed by L. Nati [27]. The author simulates the

participation of a decentralized storage device in the energy and reserve market in the

Swiss context. The difference with the work developed in the current thesis stands in

the construction of the scenarios, that Nati generated synthetically, while here are the

results of a selection process from real data.

Chapter 3

Paper mill model

The chapter introduces the reader to the pulp and paper production process used in Hallsta paper mill and the energy consumption profile of the factory. Afterwards, the simplified mill’s scheme used in the mathematical model is presented.

3.1 Pulp and paper production process in Hallsta

Holmen manufactures paper products in two facilities, one located outside Norrk¨ oping and one in Hallstavik, a small village in the North of Stockholm. The focus of the thesis has been on the second paper mill, where Light Weight Uncoated (LWU) paper, and book paper are produced [28].

The production process begins with logs of spruce being debarked and chopped into chips. The material is accumulated in storage towers and transported to the pulp section when needed.

The pulp production process is thermomechanical pulping (TMP) and it is charac- terized by the following steps. A stream of wood chips enters into the refiners; the latter use their two counter-rotating grooved metal disks to canalise the chips towards the edges and extract the fibre contained in the wood. The process is responsible for around 70% of the whole energy consumption in the mill since substantial friction forces are in- volved. However, around 60% of the electricity consumed by the refiners is transformed into thermal energy in the form of low pressure steam. In fact, the water contained in- side the raw material evaporates due to the high temperatures reached in the machines.

This ”dirty” steam is used to produce clean steam that will be later sent to the paper machines.

Afterwards, the pulp passes through a series of cleaning and bleaching steps that improve its quality as required by the client.

When pulp is ready, it is pumped to the so called wet end of the paper machine.

Here, the de-watering step begins: a wide and flat nozzle continuously sprays the wet

pulp on a rotating fine net that transports the material to the pressing section. Here,

more water is lost and the thickness of the end product is adjusted. Following, the

sheet passes through the drying section, where the steam mentioned previously is used

to remove all the remaining water in the paper.

If, for any reasons (maintenance or fault), the refiners have not produced enough steam for the drying process, two large steam electric boilers are activated in order to make up for this lack.

The paper is now ready to be rolled up into reels that are finally cut to satisfy the client’s order.

3.2 The flexible capacity identified in the mill

As mentioned in section 3.1 the pulp production step is the most energy intensive one, accounting for nearly 70% of the whole electricity consumed in the mill. For this reason, when looking for loads able to provide flexibility, the first glance has been turned towards the refiners, being the largest capacity installed inside the plant. Additionally, other studies identified in the literature [22], [23], [24] were also considering these machines for providing reserve capacity. However, after many considerations and discussions with the company’s experts, it was chosen not to consider the refiners as appropriate for frequency containment purposes. The reason, as already mentioned, is the effect that a slow down of the machine has on the quality of the pulp produced. Since the company had stated from the very beginning that the final product shouldn’t be affected by the flexible load management, another load was to be identified.

As Aro [23] shows in his work, there are some characteristics that qualify a load to be a possible balancing reserve. For example, some are: large capacity installed, fast reaction time, ease of control and presence of buffer before and/or after the load.

Holding these features in consideration, the mill’s motors were screened again and the most appropriate load was considered to be the electric boiler. The main reason for this choice is the presence of a steam accumulator able to compensate, up to a certain extent, for the steam required from the electric boiler. Furthermore, the boiler is extremely fast to react in both directions (up and down) and the capacity installed in Hallsta makes it particularly interesting.

3.3 System modelling

As explained in 3.1, there are three main production sections in a paper mill: the pulp one, the paper one and the steam one. Their functionality has been largely simplified in the model developed in the thesis, which is presented here.

Given an hourly production rate of pulp (P R

, dashed brown arrow in figure 3.1), the refiners, core of the pulp section, are represented as machines consuming electricity and producing steam as a by product.

From there, the pulp and the steam are fed into the paper machine which, by consum- ing electricity and heat, delivers paper sheets with a certain production rate (P R

).

If the steam coming from the refiners is not sufficient to supply the paper process,

consuming electricity and producing steam with an efficiency of 99%. Figure 3.1 shows the energy and steam flows in the most basic system scheme.

Figure 3.1: Simplified plant scheme

In Hallsta paper mill, a steam accumulator is also present. In this thesis, this piece of equipment is simply modelled as a container being charged and discharged without suffering from any thermal losses. Currently, the accumulator is used as a backup system to avoid steam shortages in extreme cases where neither the refiners, nor the boiler can provide the required heat load to the paper machine. However, a more active use of this equipment could be done, serving as heat storage capacity to permit thermal load shifting between high and low electricity price hours. In this configuration, the plant scheme becomes a little more complex, as shown in figure 3.2.

Figure 3.2: Plant scheme including accumulator

In addition to allowing for thermal load shifting, the steam accumulator is also the

key enabler for using the electric boiler as frequency containment load. Whenever the

boiler is activated to deliver an up-regulating action, the accumulator will make up for

the missing steam. On the contrary, if the boiler is required to do down-regulation, the accumulator will accept the extra steam produced until its full capacity, the rest will be discharged in the atmosphere.

3.4 Assumptions for the models

As already said in section 1.2, the goal of this study is to propose an optimal economic strategy to bid on the energy and reserve markets. This denotes a decision making problem which is normally solved with an optimization algorithm. The latter can be either deterministic, when all the variables involved are thoroughly described, or stochas- tic, when some variables are characterized by uncertainty (taking the form of random variables) [29]. In this thesis, both types of problems have been formulated.

As outlined in section 2.2.3, the FCR-N market, as well as the spot market, is structured as a daily auction, taking place on the day prior delivery. This means that the planning of power and energy bids have to be done every single day for the following one. Ideally, the algorithms developed in this work will be used every morning by the mill’s energy manage to facilitate this decision. Given this premise, the assumptions made when building the optimization algorithms were:

• The planning horizon is made of 24 hours;

• the time step is 1 hour, therefore there is complete correspondence between energy (MWh) and power (MW)

• The production schedule for the next day is known and it will remain unchanged during the operational day (i.e. no slowdown or failure of production is included in the model): the production rate of pulp and paper are deterministic values;

• The spot price can be perfectly predicted: its daily profile is deterministic;

• The price that the mill sets for the FCR-N bids is always more competitive than the others’ actors price;

• All the bids (both on the energy and reserve market) are accepted at the price offered;

• The mill is a price taker actor;

• The fluctuating value of frequency is well represented by its hourly average;

• Automatic load control can be esaily performed without damages of the equipment involved;

• The investment costs for the participation to the FCR-N market (legal, installation

of measuring devices and implementation of a control system) are negligible;

Chapter 4 Case studies

In this work, five case studies, representing five different bidding strategies have been proposed. They are presented hereafter in increasing order of monetary saving:

1. DA without use of steam accumulator (Reference case): the electricity re- quired solely by the production process is bought on the DA market without using the steam accumulator as a thermal storage - i.e. there is no possibility of doing thermal load shifting

2. DA with use of steam accumulator : the electricity required solely by the production process is bought on the DA market and active use of the steam accu- mulator is made - i.e. it is possible to do thermal load shifting

3. DA & FCR-N trading : in addition to the electricity required by the production process, some more electricity is bought on the DA market so that some capacity of the electric boiler can be offered to the reserve market

4. DA & speculation on IS : electricity is bought on the DA market and energy imbalances are settled at the IS price (i.e. profit can be made by speculating on the IS price). The mill is modelled without considering the steam accumulator.

5. DA, speculation on IS & FCR-N : electricity is bought on the DA market, energy imbalances are settled at the IS price and capacity from the steam accu- mulator can be offered to the FCR-N market.

In the next coming sections, the mathematical formulation of the five bidding strate-

gies is reported in the same order as they have been presented above. The nomenclature

used in the problems’ formulation is reported at the beginning of the thesis. Note that

most of the parameters are deterministic in the first problems formulation and then be-

come stochastic in the following ones. In order to have the most complete denomination,

the variables have been presented as they are used in the last problem formulation.

4.1 Case study I - DA without the use of the accu- mulator

The presented deterministic linear optimization problem represents the reference case to which all the following ones will be compared. The system configuration considered, is the one depicted in figure 3.1. The explanation of the equations comes after their definition.

min C

 =

24

X

t=1

E

λ

(4.1)

s. t. E

≥ E

+ E

+ E

∀t (4.2)

E

≤ E

∀t (4.3)

E

= P R

SEC

∀t (4.4)

E

= P R

SEC

∀t (4.5)

E

η = Q

∀t (4.6)

E

≤ E

∀t (4.7)

Q

= P R

StP h

3600 ∀t (4.8)

Q

= E

SRF

∀t (4.9)

Q

= Q

+ Q

∀t (4.10)

The objective function 4.1 aims at minimizing the daily cost of energy bought on the day ahead market. This cost comes from the product between the DA energy bid (E

) and the DA price (λ

), given as parameter to the problem.

The bids put on the day ahead market have to ensure that all the energy required by the different steps of the production process has been purchased (4.2). An upper limit on the DA bids is set according to the contract that Holmen has with SvK (4.3).

Equations 4.4 and 4.5 define the energy consumed in the paper machine and refiners (E

, E

), given the hourly production rates of paper and pulp and the Specific Energy Consumption of the machines.

Equation 4.6 calculates the energy consumed in the electric boiler (E

) to produce the steam required from the electric boiler. The energy consumption of the boiler is limited from the top by the installed capacity of the electric boiler (4.7).

Relations 4.8 and 4.9 are representative of the steam consumed in the paper machine with regards to the paper production rate and other constant factors and the steam produced as by a product by the refiners.

Finally, equation 4.10 determines how much steam needs to be produced by the

Indeed, this is true. However, for the sake of consistency, the problem has been presented here since it constitutes the reference case to which all the others will be compared.

The equations regulating the energy and steam consumption in the pulp and paper sections will remain unvaried in all the models and will not be repeated in the next problem formulations.

4.2 Case study II - DA with use of the accumulator

The second case study shares with the previous one most of the equations. The differ- ence, however, stems in the inclusion of the steam accumulator as element allowing for thermal load shifting from high to low price hours. The system setting considered is the one in figure 3.2. The problem formulated is a deterministic mixed integer linear optimization one. The additional constraints are presented here.

Q

= Q

+ Q

∀t (4.11)

Q

= Q

+ Q

+ Q

∀t (4.12) E

≤ E

+ Q

− Q

∀t (4.13)

E

≤ E

≤ E

∀t (4.14)

Q

≤ u

M ∀t (4.15)

Q

≤ u

M ∀t (4.16)

u

+ u

≤ 1 ∀t (4.17)

In this formulation, the steam produced by the electric boiler can follow two paths, either going directly to the paper machine, or to the steam accumulator (4.11). The steam supplied to the paper machine is the combination of the streams coming from refiners, electric boiler and accumulator (4.12).

Equation 4.13 regulates the charging and discharging of the steam accumulator. Its flexible capacity is limited upwards and downwards by equation 4.14. Additionally, the steam accumulator is not allowed to be charged and discharged at the same time, therefore equations 4.15, 4.16 and 4.17 impose this behaviour. It is made use of two binary variables (u

and u

) and a large enough constant M that is used to make the problem linear.

4.3 Case study III - DA & FCR-N trading

In the third problem formulation, the reserve market is finally introduced. According

to this strategy, some amount of the electric boiler’s capacity can be offered to the

reserve market as frequency containment load. In fact, up to a certain extent, the steam

accumulator can compensate for a boiler’s slowdown or stop.

An analysis performed on historical hourly values of the frequency in the Nordic states demonstrated that, generally, grid operators tend to keep the frequency level above 50 Hz in order to avoid as much as possible power shortages. Therefore, from a consumer’s perspective, offering FCR-N capacity becomes even more interesting due to a lower risk of being activated to do up regulation (decrease the consumption). Table 4.1 shows the number of times in 2017 and part of 2018 where the hourly average of the frequency was above, under and equal to 50 Hz. The data about the frequency have been provided by one of Holmen’s collaborators [3].

f > 50Hz f < 50Hz f = 50Hz

Jan - Sept 2018 3056 2632 215

2017 4435 4038 287

Table 4.1: Number of times the hourly value of frequency stays in the ranges indicated [3]

Beside showing that the frequency is kept above, rather than under, 50 Hz, table 4.1 indicates also that the rated value of 50 Hz is rarely achieved. It would be, therefore, unrealistic to consider the frequency constant and the activation of the flexible capacity null. It is because of this reason that a variable value of frequency has to be consid- ered. Its stochastic nature, however, doesn’t allow to predict the daily profile with good accuracy, therefore it was chosen to simulate this imperfect data information with sce- narios. The explanation of how the scenarios have been selected can be found in section 5.1. Meanwhile it is enough to know that this problem is defined as two stage linear stochastic problem and index ω identifies the second stage decision variables.

This problem’s objective function (4.18) is composed by three terms. The first is the daily cost of energy bought on the day ahead market (4.19), to which a penalty cost related to steam spillage (4.20) is added and the profit from FCR-N market (4.21) is subtracted.

min C

 = C

+ C

− C

(4.18)

s. t. C

=

24

X

t=1

E

λ

∀t (4.19)

C

=

Nω

X

ω=1

π

24

X

t=1

Q

F

∀t, ω (4.20)

C

=

24

X

t=1

P

λ

∀t (4.21)

machine, or to the accumulator, or to the atmosphere. This last path will be followed whenever the boiler is required to increase its electricity consumption above the level required by the production process while the accumulator is already full. Spilling steam in the environment is not directly related to a monetary cost, but it was agreed with the mill’s operators that it should be limited to avoid attrition of the machine. Therefore, a penalty cost is included in the objective function with a fee that has an extremely low value compared to all other costs.

As explained in section 4.1, the terms E

, E

, Q

and Q

are parameters, therefore they are calculated in the same way as in the previous chapter. Additionally, the equations regulating the charging and discharging of the accumulator remain the same as 4.12, 4.13, 4.14, 4.15, 4.16, 4.17. The only difference is that most of the factors are now scenario dependent (i.e. Q

, Q

, Q

, E

, u

and u

).

The new equations, simulating the reserve market, are instead here presented.

Q

= Q

+ Q

+ Q

∀t, ω (4.22) Q

= E

+ E

η ∀t, ω (4.23)

E

= P

∆t ∀t, ω (4.24)

E

= 10P

(f

− 50)∆t ∀t, ω (4.25)

P

− P

≥ P

∀t, ω (4.26)

P

+ P

≤P

∀t, ω (4.27)

P

≤ P

∀t, ω (4.28)

E

≤ E

+ E

≤ E

∀t, ω (4.29) E

≥ E

+ E

+ E

∀t, ω (4.30) In this system’s setting the steam produced by the boiler does not depend only on the mill’s requirement, but it is also affected by the activation of the reserve capacity offered to the market, which depends on the frequency value. This is modelled in equation 4.23.

If relation 4.24 is clear, 4.25 comes from the following reasoning. Whenever a con-

sumer decides to offer a load to the FCR-N market, it will be required to provide the

TSO with a curve, showing how its load can react to a frequency deviation [30]. If the

load can be continuously controlled, the shape will likely be the one in figure 4.1.

Figure 4.1: Activation of a continuously controlled FCR-N capacity

According to how the problem has been written, an upward deviation of the frequency from its nominal value will result in an increased power consumption of the boiler and therefore an augmented steam production. In this situation, a positive energy activation (E

> 0) will be registered. The opposite will happen when the frequency goes below 50 Hz.

The amount of capacity that can be offered to the FCR-N market (defined as positive variable) can vary every hour and it is related to the amount of power expected to be consumed during the same hour in the electric boiler. The maximum up and down regulating capacity are defined respectively by equations 4.26 and 4.27. In order to comply with the hourly energy requirements of the mill, it is important to limit also the energy activation, as for equation 4.29. Figures 4.2 are used to figuratively show these last relations.

(a) (b)

Figure 4.2: Maximum and minimum energy (a) and power (b) consumption in EB

This means that the purchase is being made for the worst case scenario, i.e. when the capacity offered to the FCR-N market is completely shut down and the rest of the electric boiler’s capacity is fully activated.

4.4 Case study IV - DA & speculation on IS

The strategy modelled in this fourth problem formulation is the first one taking into consideration the imbalance settlement procedure. As explained in chapter 2.2.2, energy imbalances are settled at the imbalance settlement price (λ

) which is unknown to the market players until the end of the operating hour. This fact causes an inherent uncertainty in the definition of these prices.

According to the value of the difference between the DA and the IS prices and to the sign of the energy imbalance recorded, the settlement can result in a profit or a loss.

This concept has been more clearly explained in section 2.2.2.

The problem formulated hereafter simulates the uncertainty associated to the value of the IS price through scenarios resulting, therefore, in a two stage stochastic linear optimization algorithm.

Decisions made under uncertain conditions are characterized by a certain level of risk. The risk adversity of the company has, therefore, been considered in the problem by including the Conditional Value at Risk (CVaR) in the objective function. A deeper explanation of the meaning of the CVaR and its effects on the results is found in section 5.3.

The objective function (4.31)aims at minimizing the expected cost deriving from the purchase of energy on the day ahead market and the imbalance settlement, meanwhile minimizing the conditional value at risk. In this problem formulation, the presence of the steam accumulator is neglected and thermal load shifting is not allowed. The cost functions are shown hereafter.

min {(1 − β) E [C

] + β CV aR} (4.31)

s. t. E [C

] = C

+ C

+ C

(4.32)

C

=

T

X

t=1

E

λ

(4.33)

C

=

Nω

X

ω=1

π

T

X

t=1

∆E

λ

(4.34)

C

=

Nω

X

ω=1

π

T

X

t=1

| ∆E

| F

(4.35)

The expected cost derives from the sum of the costs associated to: energy purchased

on the day ahead market (C

), energy deviations from planned schedule (i.e. energy

imbalances) (C

) and penalty caused by energy imbalances (C

). The term C

can