Optimization of Virtual Power Plantin Nordic Electricity Market

STOCKHOLM SWEDEN 2019,

Optimization of Virtual Power Plant in Nordic Electricity Market

JWALITH DESU

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

KTH Royal Institute of Technology

Master Thesis

Optimization of Virtual Power Plant in the Nordic Electricity Market

Author:

Jwalith Desu

Supervisor:

Dr. Mohammad Reza Hesamzadeh

Examiner:

Dr. Mohammad Reza Hesamzadeh

A thesis submitted in fulfilment of the requirements for the degree of Master of Science

in the

Electricity Market Research Group (EMReG) School of Electrical Engineering

October 2019

I, Jwalith DESU, declare that this thesis titled, ’Optimization of Virtual Power Plant in the Nordic Electricity Market’ and the work presented in it are my own. I confirm that:



This work was done wholly or mainly while in candidature for a research degree at this University.



Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.



Where I have consulted the published work of others, this is always clearly at- tributed.



Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.



I have acknowledged all main sources of help.



Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

Signed:

Date:

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Abstract

With the world becoming more conscious about achieving 1.5-degree scenario as promised by the most powerful economies of the world, much needed push was received by the renewable energy technology providers. This has led to an increased a share of energy production from renewables and a decrease in the fossil-based energy production with the overall energy production. As a result, a large share of inertia of the system is lost and a big challenge in the name of flexibility is presented to the world of energy. Virtual Power Plant is quite a novel and new concept to address the new generation challenge of flexibility and can offer various other benefits like competitivity,reliability, accessibility etc. In this thesis, a commercial virtual power plant is studied by developing a mixed integer linear model to emulate the trading for short term markets with the risk mea- sures in a Nordic Electricity Framework. Further, the developed model is implemented in a quite a new mathematical programming language known as “Julia”. The model is implemented using a hypothetical portfolio consisting of a dispatchable unit, a battery system and a wind farm in the SE3 bidding zone of Sweden. An investigation on varia- tion of imbalance costs in three different modes also has been carried out, to demonstrate the advantage of such a virtual power plant concept in reducing the imbalance costs.

Keywords: Virtual Power Plant, mFRR market, spot market, CVaR, risk measures,

Stochastic Optimization, Nordic Electricity Market.

F¨ or att uppfylla 1,5-gradersm˚ alet som beslutats av v¨ arldens ledande ekonomier har olika typer av f¨ ornybar energiproduktion f˚ att ett stort uppsving. Detta har lett till ¨ okad en- ergiproduktion fr˚ an f¨ ornybara k¨ allor och minskad energiproduktion fr˚ an fossila k¨ allor.

F¨ or elsystemen inneb¨ ar en h¨ ogre andel f¨ ornybar produktion minskad sv¨ angmassa och

¨

okat behov av flexibilitet f¨ or att kompensera f¨ or variationen hos f¨ ornybara energik¨ allor.

Virtuella kraftverk ¨ ar ett nytt koncept f¨ or att tillgodose behovet av flexibilitet och kan

¨

aven ge andra f¨ ordelar som konkurrenskraft och tillf¨ orlitlighet. I denna uppsats stud- eras ett virtuellt kraftverk genom att utveckla en optimeringsmodell f¨ or att emulera handeln i elmarknader med riskm˚ att inom ett ramverk f¨ or den nordiska elmarknaden.

Modellen implementeras i det nya programmeringsspr˚ aket Julia. Modellen inneh˚ aller en hypotetisk blandning av resurser best˚ aende av ett planerbart kraftverk, ett batter- isystem och en vindpark i elomr˚ adet SE3 i Sverige. Balanseringskostnaderna i tre olika modeller unders¨ oks f¨ or att visa potentialen hos det virtuella kraftverket att minska dessa kostnader.

Nyckelord: Virtuellt kraftverk, mFRR marknad, spotmarknad, CVaR, riskm˚ att, stokastisk

optimering, nordiska elmarknaden

Acknowledgements

I take this opportunity to express my gratitude to everyone who have been associated with this thesis directly or indirectly.

I want to thank the team at GreenLytics AB for giving me an opportunity to associate with them on their amazing journey in decarbonizing the economy.Especially my Super- visor, Sebastian Haglund El Gaidi, and his team to answer all my questions patiently.

I would like to thank my parents, family and friends for their continuous support during the whole thesis.

Finally, I want to thank my supervisor and examiner at KTH, Dr. Mohammad Reza Hesamzadeh, for guiding and trusting me through the thesis.

ii

Declaration of Authorship i

Abstract i

Abstract i

Acknowledgements ii

Contents iii

List of Figures v

List of Tables vi

Abbreviations vii

Nomenclature ix

Nomenclature x

Nomenclature xi

1 Introduction 1

1.1 Background & Motivation . . . . 1

1.2 Existing Literature . . . . 4

1.3 Goal of the Study . . . . 6

1.4 Thesis Structure . . . . 7

2 Nordic Electricity Market 8 2.1 Introduction . . . . 8

2.2 Day Ahead Market- ELSPOT . . . . 9

2.3 Intraday Market- ELBAS . . . 10

2.4 Nordic Balancing Concept . . . 10

2.4.1 Manual Frequency Restoration Reserve (mFRR) - Tertiary Reserve 12 2.4.2 Automatic Frequency Restoration Reserve (aFRR) – Secondary Reserve . . . 13

2.4.3 Frequency Containment Reserve (FCR) – Primary Reserve . . . . 15

iii

Contents iv

2.4.3.1 Frequency Containment Reserve – Normal Operation . . 15

2.4.3.2 Frequency Containment Reserve – Disturbed Operation . 15 2.4.3.3 Pre-qualification, Reporting, Bidding & Procurement of FCR . . . 16

2.5 Imbalance Settlement and Pricing . . . 17

3 Methodology 20 3.1 Introduction . . . 20

3.2 Model Assumptions . . . 21

3.3 Model Description . . . 23

3.3.1 Modelling a Dispatchable unit . . . 24

3.3.2 Modelling of Flexible loads . . . 27

3.3.3 Modelling of Storage Unit . . . 28

3.3.4 Modelling of Stochastic Units . . . 29

3.3.5 Formulation of the Objective Equation of the VPP . . . 29

3.4 Energy Balance Constraints . . . 31

3.5 Other Constraints . . . 31

3.6 Selection of Scenarios . . . 34

3.7 Flow chart of the Stochastic Optimization Model . . . 36

3.8 Investigating the Imbalance Costs per MWh for different modes of VPP . 37 4 Case Study 39 4.1 Scope . . . 39

4.2 Input Data . . . 40

4.3 Implementation and Results . . . 46

4.4 Investigation of Imbalance Costs . . . 51

5 Closure 56 5.1 Summary . . . 56

5.2 Recommendations for Future Possibilities . . . 57

A Linearization of the Quadratic Fuel Cost Function 59

B Codes 61

Bibliography 76

1.1 VPP . . . . 3

2.1 MCP . . . . 9

2.2 FCR . . . 16

2.3 IB . . . 18

3.1 scenario generation . . . 35

3.2 Bidding Startegy . . . 37

4.1 day ahead price . . . 40

4.2 day ahead price scenarios . . . 41

4.3 Upregulation prices . . . 41

4.4 Upregulation prices Scenarios . . . 42

4.5 Downregulation price . . . 42

4.6 Downregulation price Scenarios . . . 43

4.7 mFRR prices . . . 43

4.8 mFRR prices scenarios . . . 44

4.9 Wind Power Forcast Scenarios . . . 45

4.10 hour1 . . . 47

4.11 hour2 . . . 47

4.12 hour23 . . . 48

4.13 hour24 . . . 48

4.14 scenario1 . . . 49

4.15 scenario2 . . . 50

4.16 scenario9 . . . 50

4.17 scenario10 . . . 51

4.18 imbalance costs month . . . 53

4.19 imbalance costs month . . . 53

4.20 imbalance costs . . . 54

4.21 cumulative profit . . . 55

A.1 fuel cost . . . 59

v

List of Tables

1.1 Comparison of all the existing literature . . . . 6 4.1 Calculation of imbalance costs in different modes of operation . . . 54

vi

API Application Programming Interface

ARIMA AutoRegressive Integrated Moving Average BM Balancing Market

BRP Balancing Responsible Party BSP Balancing Service Provider CHP Combined Heat and Power CVaR Conditional Value at Risk DER Distributed Energy Sources EMS Energy Management and System

ENTSO European Network of Transmission System Operators

EU European Union

EVPI Expected Value of Perfect Information FRR Frequency Restoration Reserve

GT Gas Turbine

ICT Information and Communication Technology JuMP Julia Mathematical Programming

MoNB Minutes outside the Normal frequency Band MILP Mixed Integer Linear Programming

NAG Nordic Analysis Group

NEMO Nominated Electricity Market Operator

PV Photo Voltaic

PX Power EXchange

RES Renewable Energy Sources

RM Reserve Market

RPM Regulating Power Market

vii

Abbreviations viii

SOA Standard Operating Agreement

TSO Transmission System Operator

VPP Virtual Power Plant

Indices

t Index of time periods in hourly resolutions from 1..T ω Index of scenarios from 1..N

G Dispatchable unit J Flexible Load

S Storage unit

W Stochastic unit i i

dispatchable unit j j

flexible unit k k

Storage unit q q

Stochastic unit

ix

Nomenclature

Parameters

T Total number of time slots

λ

Day Ahead Price at time t in scenario ω in Eur/MWh λ

Reserve Price (mFRR) at time t in scenario ω in Eur/MWh λ

Upregulation Price (mFRR) at time t in scenario ω in Eur/MWh λ

Downregulation Price (mFRR) at time t in scenario ω in Eur/MWh π

probability of occurrence in scenario ω

N

Total number of scenarios

S

Fixed cost derived from startup process in Euros S

Fixed Shutting down cost in Euros

∆

Ramp up or Ramp down rate of unit i η

Efficiency of the charging process η

Efficiency of the discharging process

x

Binary Variables

v

Functional state of generating unit i, 1 if active, else 0 at time t in scenario ω

y

Decision variable for the conventional unit to partici- pate in the reserve market, 1 if active, else 0 at time t in scenario ω

b

Decision variable used in linearization of fuel cost func- tion, 1 if the compiler in the interval n, else 0 at time t in scenario ω

Continuous Variables

P

Power exchanged with day ahead market in time pe- riod t in scenario ω , expressed in MW

P

Power exchanged with the reserve market at time pe- riod t in scenario ω , expressed in MW

ρ Monetary Profit

C

Total start-up cost of unit i in the same period in scenario ω

C

Total shutdown cost of unit i in the same period in scenario ω

P

Stochastic production from unit q at time t in scenario ω , expressed in MW

E

Generated electricity in MWh from the dispatchable unit i at time t in scenario ω

xi

Variables xii

P

Power output of dispatchable unit i at time tin sce- nario ω , expressed in MW

E

Amount of energy consumed by load j at time t in scenario ω in MWh

P

Power capacity of load j at time t in scenario ω , ex- pressed in MW

P

Discharging power of Storage unit k at time t in sce- nario ω , expressed in MW

P

Charging power of Storage unit k at time t in scenario ω , expressed in MW

E

Energy in Storage unit k at time t in scenario ω in MWh

P

Balancing Power in positive direction in scenario ω , expressed in MW

P

Balancing Power in negative direction in scenario ω ,

expressed in MW

Introduction

1.1 Background & Motivation

There is a rapid increase in the renewable energy resources contribution in the overall electricity mix of the Nordic economies. The new EU climate targets for 2030 are a) at least 40% cuts in greenhouse gas emissions (from 1990 levels), b) at least 32% share of renewable energy, c) at least 32.5% improvement in energy efficiency. Meeting these new targets will lead to proliferation of intermittent energy resources in the system. With the increasing concerns pertaining to the nuclear energy, especially after Fukushima nuclear accident in 2011, closure of many nuclear facilities has been inevitable. The Nordic energy mix is going to face many challenges due to this major change. Electricity being one of the biggest sectors to be affected by this radical change in the policy and strategy.

The long-term goal of creating a 100% renewable energy-based system will lead to many new market requirements, designs, concepts and products [1].

Traditionally, the power system and the market has been dominated by huge power producing facilities embedded in a centralised fashion and then the energy was deliv- ered to the end customer within the grid. Additionally, the act of balancing the system was principally provided by the supply side through the flexible generation. The idea of supply following demand has been a traditional way of the design of the power sys- tem, however with the increasing interest in protecting the environment, the concept of embracing sustainability in daily life with the faster adoption of renewable based controllable power generation and flexible load behaviours of consumers has led to a

1

Chapter 1. Introduction 2

radical change in the concept of revolutionising the design of the power system. The Nordics have been performing extremely well in combating the CO

emissions with an extensive and aggressive green revolution [2]. However, most of the Nordic and Baltic are still dominated by a traditional policy framework. As per the World Bank data, over the past decade (2005-2015), there is a rapid increase in the renewable sources from approximately 5% to 16% of the total electricity produced, except hydroelectric in Sweden. Government incentives to household users and businesses in Sweden receive a 30% subsidy for PV modules and 60% for batteries [3]. Furthermore, the rapid decrease in the cost of PV and Wind energy generating sources have led to a massive adoption of these technologies by small traders, households, industries etc. to meet their demands.

Small wind and solar farms depending on the size are also capable of producing enough energy to meet the consumption of a small village, county or a sector. With lot of small capacity asset owners capable of pumping power into the power system, the concept of prosumers and decentralised system is getting popular [4]. A gradual increase in electric cars and various controllable loads within the Nordics have opened ways to include de- mand response and introduction of various other services and products. However, due to their small capacities and the stochastic nature of these renewable sources makes it risky and very difficult to participate in the market and adhere by the requirements of the power system [5]. This increased intermittent source of energy injects a lot of instability and surges into the system which further increases the vulnerability of the system for imbalances. This rapid increase in the percentage share of the renewable sources adds a lot of uncertainty with their power production availability all the time.

This nature of intermittency requires new solutions and an improved decision-making strategy involving a better forecast to manage all the imbalances and other hidden costs [6]. Many challenges within power system and the economical setup of the system will rise and pose as major impediments in the smooth operation and to meet the desired climate targets. These can be only addressed with novel and innovative technologies in the energy sector.

During the years 2005-15, renewable consumption has shown an increasing trend from

40% to 54%, giving a clear indication of how the energy landscape would further transi-

tion to more an intermittent nature. In order to manage this new and pressing challenge

of maintaining the balance between production and consumption, a series of novel and

future ready solutions are to be devised for the electricity market. With digitalization

being adopted in every sector of economy, energy has been a sector behind in adopt- ing the next generation of ICT technologies in its operation and maintenance. Thus, a smart solution using ICT to battle these fluctuations induced due to the intermittent sources can be addressed. With the concept of aggregating a large number of intermit- tent sources, a smooth production profile can be achieved, and a lot of these disturbances can be dampened by the use of various other products of the electricity market. This concept of aggregation is sometimes referred as Virtual Power Plant (VPP). There are various services a VPP can offer like Flexibility to the grid operators as and when re- quired. Few industrial actors are currently acting as aggregators by combining small production units and some consumption units together.

The VPP concept, where production of individual renewable energy source is aggregated into a single operating profile, is supposed to be an efficient way toward the successful coupling of various products of electricity market [4]. VPPs can be an economically- attractive market participant that can easily contribute towards a greater reliability and resilience by adaptively using the pool of energy resources and spreading the generation across large geographical areas.

Figure 1.1: Concept of Virtual Power Plant. Source: Markettalknews

Chapter 1. Introduction 4

Characteristics of a VPP concept can be stated down as below [7]:

• Reliability: Having a portfolio with a large number of assets improves the capacity to face any outages in the system. One would rather have the loss of a small plant rather than a large one.

• Optimality: With the considerable variety and number of assets in the system, pos- sibility to locally optimize the dispatch can reduce overall losses and compensate for unplanned outages. Imbalances can also be handled by offering the flexibility of VPP to the TSO.

• Accessibility: A VPP can allow small capacity owners like residential owners, small workshop owners etc. to participate in the wholesale market by aggregating them all into one big virtual power producing entity.

• Competitivity: Since now there would be more number of participants in the system, trade volumes increase, competition would lead to better services and an improved overall social welfare.

• Profitability: Customers who are small owners and cannot participate in the mar- ket, with the concept of VPP now they can earn additional revenues by partici- pating in the market.

This capability of such a concept for a Nordic market landscape will be further discussed in this thesis.

1.2 Existing Literature

The concept of Virtual Power Plants (VPPs) have been perceived in many different ways by various actors/entities of the electricity market. VPPs are depicted/explained as micro grid [8, 9] Renewable energy resources [10], [11] and hydro-power system [12].

As per [13], a VPP is an “aggregation of the capacity of many diverse distributed

energy resources; it creates a single operating profile from a composite of the parameters

characterizing each DER and can incorporate the impact of the network on aggregated

DER output.” Similar definitions are also supported by some papers like [14], [15] and

[16] where a VPP consists of a combination of fossil based and intermittent sources

like CHP, Biomass and biogas, Small hydro power plants, Small capacity gas turbines, diesels etc., Wind, Solar, flexible loads (controllable/dispatch-able) etc. Ref [15, 17, 18]

also mentions that the heart of a VPP is an energy management system (EMS) which coordinates the power flows from generators, loads and storage units or small actors like industrial on-site generators, shopping centers etc.

Aspects of grid management is not considered in this thesis, as it’s extensively covered in the literature [19], [20]. A simple day ahead market scheduling strategy is modelled to maximize the VPP owners’ profit in [21], [22]. Ref [23] Further considers distribution network constraints while considering model decomposition for day ahead and real time markets. Ref [24] proposes a three-stage stochastic model for optimal dispatch of a VPP while considering the uncertainty in the rival’s offer for a day ahead market in the Greek electricity market. The studies from references [25] show that in a VPP consisting of micro-CHPs could benefit the owner in reducing imbalances caused due to renewable such as wind power. Reference [5] quotes from previous studies that scheduling of dispatch-able generators and deploying elastic demand can help reduce imbalance power caused by the intermittent renewable sources and decrease penalties, further increasing the overall profits. [26],[24] Propose a model consisting of price maker market actor model from a retailer’s perspective with flexible demands & rivals offer respectively, however this thesis assumes a price taker producer model who has no influence on the market prices.

There are various studies carried out on optimal economic VPP configuration for German market like in [27], which considers deterministic RES. [28] and [29] also propose a similar model considering the uncertainties in RES, demand but leave out uncertainties in price for Taiwanese and Australian electricity markets respectively. However, no specific studies have been carried out for a Nordic based electricity market framework, which is duly taken up with this thesis.

Papers [30, 31] propose a realistic VPP model considering a multi-market participation

while considering risk measures for two different markets namely New York and Iberian

respectively. [30] Has been carried out comprehensively over a period of three years and

have included all the three major markets i.e. Day ahead market, reserve market and

the real time balancing market, however it doesn’t include demand or the load into the

VPP portfolio. Whereas [31] is carried out in an Iberian market framework with the

Chapter 1. Introduction 6

similar portfolio of VPP as [30] while considering loads and its associated uncertainties.

Below table summarises the contributions of various papers while comparing it with the contributions of this thesis:

Table 1.1: Comparison of all the existing literature

Papers Reserve

Market (RM)

Real Time Imbalance settlement (BM)

Uncertainty

in the

prices (Day Ahead, RM, BM)

Risk Measure (CVaR)

Nordic Market Framework

15 x X x X x

16 X X X x x

17 x x x x x

21 x X x x x

22 x X X X x

39 x X Only BM x x

41 x X X x x

42 X X X X x

43 X X X X x

Proposed Model

X X X X X

This thesis deals with developing of Optimal bidding strategy for a virtual power plant trader similar to papers [30, 31]. However, there have been no similar models designed or developed specifically to address the Nordic market frameworks to the best of our knowledge. The MILP proposed will be used by traders as a decision tool to bid in the day ahead, reserve and the real time balancing markets.

1.3 Goal of the Study

The goal of the study is to develop a model for operating a VPP and to perform a

profit optimization for the whole portfolio. A tool based on Julia language has been

developed in order to determine on a daily basis in which product to bid on the Nordic

market. All the day ahead market, reserve market and the real time imbalance settlement

markets are taken into account to maximize the profit. Uncertainties pertaining to Day

ahead, Reserve market and real time imbalance settlement along with renewable power

generation are considered in the model to provide the expected energy activated using

stochastic optimization. The Renewable energy production forecast data are provided

by Greenlytics AB, for all the SE3 region of Sweden. As a consequence, the study gives

one possible realistic model of a VPP that can be marketed in the Nordic electricity market.

The results of this study will be of a great help to optimize the scheduling of the portfolio of the VPP among the different products over the time in order to maximize the profits and minimize the cost & penalties of use of the portfolio during the operation of the VPP.

1.4 Thesis Structure

The remaining of this thesis will follow the described structure:

Chapter 2 will provide an overview of the relevant energy markets for the Nordics, Chapter 3 describing the methodology of this study. The mathematical formulation of how the VPP is modelled with all technical and commercial operational constraints in the context of a Nordic Electricity market. Further lays foundation on how an indicative imbalance cost saving in 3 different modes of VPP is carried out.

Chapter 4 evaluates and discusses the implementation and performance of the model and presents the investigation of imbalance costs in different modes of operation of a VPP.

Chapter 5 concludes the thesis with the summary. Future opportunities are discussed

with related on to simplification of the model.

Chapter 2

Nordic Electricity Market

2.1 Introduction

After the liberalization of the electricity markets in Europe, there have been a major restructuring of the whole industry. The traditional system of the electricity markets was no longer beneficial for the producer/actors, a new but sustainable business models were required. Now the electricity actors were more empowered, which increased the trust of the actors to sustain and thrive in the system. The reform mainly separated the production and sale of the electricity from the transmission and distribution (network).

This exposed the production and traders to the competition – while the network oper- ators were monopolised [32]. Electricity is not only a commodity, but also a physical entity subjected to various physical laws. One of the major tasks being to maintain the balance between supply and consumption at all the time for a safe and secure operation of the system. At present due to the unavailability of the sufficiently efficient and cost- effective storage systems, it is not possible to implement these systems on a very large scale. Thus, it is important to always maintain the quality, i.e. constantly maintaining the frequency at 50Hz of the whole grid, if not large deviations could lead to failure of magnetic equipment and a chain effect mounting to a total blackout [33]. An upward deviation of the system from 50Hz implies an increase in demand which is more than the supply, whereas a downward deviation of the system from 50Hz implies an excess of supply when compared to the consumption/demand. It is therefore very important to forecast and foresee such deviations to avoid undesirable outcomes and make the system more resilient to such situations. Despite the balance between the supply and demand,

8

transmission system operators (TSO) often encounter imbalances in the system. Thus, there are technical and economical mechanisms in place to handle such imbalances and anomalies of the system. A new Nordic balancing concept is being under consultations to ascertain two new balancing market products [34], which will be discussed further in the report. The electricity market is a complex entity where financial trading is em- ployed in order to buy/sell electricity and is comprehensively covered in [35, 36]. A market operator in the Nordic region handles all these financial transactions in various markets such as day ahead and intraday markets, whereas Nasdaq handles the futures market and the respective TSO handle other reserve markets to maintain balance of the system.

2.2 Day Ahead Market- ELSPOT

The day-ahead market also in some cases referred as Spot markets, consists of all the electricity products scheduled to be offered/delivered a day after the closed auction. All the producers and consumers of the region submit their bids of production and their consumptions with the price they are willing to pay for consuming and the price they are willing to buy for producing the energy in order to maximize their profits. The bids are later sent to the Nominated Market operator before the decided gate closure time, after which the market operator matches the orders to maximize social welfare whilst taking network and other physical constraints provided by infrastructure operators into consideration to obtain the market clearing price for the energy per unit per hour.

Figure 2.1: Market Clearing price.Source:[7]

Chapter 2. Nordic Electricity Market 10

A digital platform ELSPOT, is used to carry out the whole process of submission of bids and offers and communicate the prices after the clearing process. Later that producers schedule their positions accordingly to meet their commitments. Figure 2.1 shows the intersection of the demand and selling bids sets the clearing price for the day ahead market. All the selling bids below this price have a profitable position and therefore get accepted. In a perfect market scenario, the price quoted by the producer needs to be as near as possible to the marginal cost of production in order to ensure the operations of the plant and to recover costs investments.

2.3 Intraday Market- ELBAS

This market supports trading of the energy closer to the hour of delivery, this is impor- tant for producers who have weather dependent sources of energy. It allows the producer to adjust their position according to the real time information and trade until 30 min prior to the delivery hour. The uncertainty associated with the renewable energy sources such as PV, wind etc. make the producer prone to large imbalances, thereby incurring considerable amount of monetary losses. Intraday Market products plays a vital role in reducing such undesirable situation leading to losses. Though, the low liquidity makes the intraday markets not so interesting for the traders to participate. Thus, various new initiatives to encourage the intraday trades have been taken up by the market operators and other associated stakeholders.

2.4 Nordic Balancing Concept

To maintain the quality of the power supply is of utmost importance to continue the operation of the system. A crucial mechanism of balancing is employed by the system operator, in this case the Transmission system operator (TSO) to ensure quality of the power supply. This section aims to give a better explanation to the Nordic balancing concept.

Electricity has become an important commodity for a proper functioning of business

and life. Thus, it should be prioritized to ensure secure, safe production, delivery and

maintain the quality of the electricity to the end consumers. Frequency of the system

at any given time period of operation is used as an indicator to identify the health and the quality of the system. Frequency deviations indicate imbalances in the system, which if not controlled can lead to complete black out of the system. TSO plays a crucial role in monitoring and maintaining the balance of the system for each and every time interval/period. The balance of the system is achieved by maintaining a perfect balance between the production and the consumption at every time period in every control area, thereby maintaining the frequency of the system to 50Hz. This balance could be disturbed by excess production leading to increased frequency, and a reduction in frequency if excess consumption is observed [37]. However, there may be numerous inevitable reasons for the imbalance in the system such as,

• Unplanned outages of generation units

• Unplanned outages of grid

• Deviations due to improper forecast of demand

• Deviations due to improper forecast of renewable units

The last point has over the time become more important as the recent nuclear aban- donment has picked up much momentum leading to a void in the mix, making the proliferation of renewable sources in the Nordics more rapid. The future power system will be dominated by these weather dependent energy sources, which are not 100% pre- dictable. Thus, the stochastic aspect of these weather dependent renewables can pose a big challenge in maintaining the balance. This thesis would try to model this stochastic aspect of the wind with the help of scenarios approach, which will used in the model.

There is an important distinction between BRPs and TSOs which needs to be distin-

guished clearly based on their responsibilities. BRPs must strictly balance their port-

folios for every time period (15min, 30min, 1hour), up to the operational time period,

through trading in various available markets such as day ahead, intraday market and

bilateral trades; which is also called as planning phase. After the gate closure of the

markets, balancing activity is taken up by the TSO through the operation of the bal-

ancing market mechanisms; aided with the final generation and demand schedules sent

by the BRPs 45 minutes prior to the operation period [38].

Chapter 2. Nordic Electricity Market 12

There are three types broadly used currently in the Nordics namely: tertiary, secondary and primary reserves depending on the purpose and features of the reserve in relation with the type of contingency encountered in the system. TSOs buy capacity of these mentioned reserves for any unforeseen eventualities leading to undesirable situations.

Depending on the nature of the imbalance a capacity bid can be invoked either to increase or decrease the power production. There are certain technical and economical requirements for each type of reserve that needs to be taken care of by any market participant if they want to trade their reserve product for the market. However, in the recent consultations report supported by ENTSOE, mentioned some new mechanisms being formulated to restructure the balancing market. The new concept of balancing in the Nordics would be based on a proactive and reactive approach, which are still open to discussions and debate [34].

The current Nordic balancing model lacks the prerequisites for taking advantage of the ongoing EU harmonisation in the balancing area. This could widen balancing markets to the Nordic Region, thereby enabling a cost-efficient use of resources within the region by increasing the trade of flexible resources with Continental Europe. The introduction of standard products and common platforms for exchange of balancing products as recommended by electricity balancing guideline will affect the balancing process and the products in the Nordic region.

2.4.1 Manual Frequency Restoration Reserve (mFRR) - Tertiary Re- serve

This type of reserve is manually ordered by the TSO in case of any contingency encoun- tered in the system. Commonly known as the Nordic Regulating Power Market (RPM), is requested for activation after 15 min of the contingency by the TSO.

This reserve can also be segregated into three types namely, balancing energy & capac- ity markets and Fast Disturbance Reserve. Bids in the balancing energy markets are activated in price order, taking into account all the associated technical requirements.

Separate bids for up and down regulation can be submitted or updated up to 45 minutes

prior to actual delivery by the market actors (BRPs, Traders, etc.). A minimum bid of

10MW throughout Sweden apart from SE4 (bidding/price zone 4) where the minimum

bid size is 5MW is to be submitted. The regulating prices displayed on NordPool web- site employs marginal pricing i.e. price is calculated by ordered energy and the most expensive bid used in each time period. Price levels can sometimes be better than Day ahead prices which can be hundreds or even to thousands of euros [39].

“Nordic TSOs have agreed that every country to have a must Fast disturbance reserve available the amount to adequate their own dimensioning fault in each part of the sys- tem” [39]. Depending on the dimensioning of this reserve, each country has liberty to choose the adequate amount of capacity for the same. The assets procured for fast dis- turbance reserve have to be strictly committed and cannot participate in other markets simultaneously. This service can also be traded among TSOs.

Balancing Capacity markets are generally availed by the TSO for securing unforeseen upregulation requirements using weekly bidding competitions [39]. Balancing service provider (BSPs) whose upregulation bid is accepted are obliged to deliver the energy to the balancing energy markets. Contrary to the balancing energy market, balancing service provider gets availability payment based on the balancing capacity bids.

2.4.2 Automatic Frequency Restoration Reserve (aFRR) – Secondary Reserve

As mentioned earlier, frequency imbalance can lead to disturbances of the whole syn- chronous area leading to a complete blackout. It is very important to maintain the frequency to its set point i.e. 50Hz. In 2013 aFRR was identified and agreed as one of the major measures to stop the weakening of the frequency quality [38]. The goal is to restrict the minutes outside the normal frequency band (MoNB) within 6000 minutes per year. The year 2016 saw approximately 13 862 MoNB which is way more than the limit decided earlier. A common Nordic aFRR market to handle and restrict MoNB was agreed upon and to start its operations by the first half of the year 2018 [40]. Moreover, a benefit of the aFRR can be based on the merit order and take congestions in the systems into account. This type of reserve is activated automatically on the signal given by the TSO. It is so designed that aFRR works in cognizance with FCR-N (primary reserves), which helps maintain the frequency and then aFRR restores the frequency to the original set point. In the whole process, aFRR shall be deemed as a “complement”

to mFRR due to its speed and ease of activation in just 30 seconds and fully activation

Chapter 2. Nordic Electricity Market 14

by 120 seconds. At Present, a total of 300MW of aFRR is being traded on the common Nordic aFRR market platform, 130MW of which is based in Sweden [41].

As per [42] the new process for procurement of aFRR will be handled in the following way:

• Daily auction with hourly products, gate closure D-2 at 8 pm in the evening.

• Minimum bid: 5MW and in multiples of 5MW

• Reservation of available transmission capacity for aFRR will be based on:

– Expected price difference between bidding zones in the day-ahead market.

– Prices of aFRR capacity bids.

– Rules to ensure a conservative reservation of capacity.

• Total volume & time period will be dependent on system needs

– Total demand is distributed over all eleven bidding areas forming local de- mand.

• No requirement for symmetrical bids (can be submitted in any direction)

• Pay as bid pricing methodology to be adopted

The common Nordic market for aFRR Balancing Services will consist of two separate mechanisms.

• A Nordic aFRR Capacity Market where aFRR Balancing Capacity is pro- cured before the Day-ahead market taking into account geographical distribution and network constraints. Reservation of Cross-zonal Capacity will be based on socioeconomic optimisation.

• A Nordic aFRR Energy Activation Market where aFRR Balancing Energy is activated based on a Common Merit Order List. Balancing Energy bids will be activated taking into account all the relevant network constraints in real time.

Balancing Energy in real time shall be provided by Balancing Service Providers

whose Balancing Services are procured in advance in the aFRR Capacity Market,

or by other Balancing Service Providers who can voluntarily offer Balancing Energy

based on their availability.

2.4.3 Frequency Containment Reserve (FCR) – Primary Reserve

Usually referred to as the primary reserve, is the first line of mechanism to automatically contain the frequency imbalance in the grid and maintain the frequency to the set point of 50Hz. This type of reserve can be further divided into two products for the Nordic context namely, FCR-N (Normal Operation) and FCR-D (Disturbed operation).

Currently the Nordic TSOs are rethinking and redesigning the Frequency Containment process within the Nordic Analysis Group (NAG) [43].

2.4.3.1 Frequency Containment Reserve – Normal Operation

For FCR-N, TSO does not send an automatic control signal as the frequency is measured on-site. As such, FCR-N is activated continuously all along the day within the ”normal operating band” of 50±0.1Hz with a delay of couple of minutes. FCR-N is symmetrical and changes with a linear relationship to the deviation of the frequency from 50Hz. In other words, as the frequency diverges further, up or down from 50Hz, the automatic activation of FCR-N proportionately increases or decreases, until it is fully activated at 50±0.1Hz. Within 60 seconds, 2/3rd of the reserve should be activated while the rest must be activated within 180 seconds if required. This market is organized in hourly and yearly based market products offering both capacity and energy payment methods. The prices for yearly product can be around 14Eur/MWh and few dozens of Eur/MWh for the hourly with a minimum bid of 0.1MW. The Standard Operating Agreement (SOA) between the TSOs requires capacity for FCR-N throughout the Nordics to be 600MW, of which Sweden must contribute 230MW [44]. The reserves must be capable of being maintained for 15 minutes continuously without any interruption [45].

2.4.3.2 Frequency Containment Reserve – Disturbed Operation

This type of reserve product is activated for large frequency deviations when there are

huge or sporadic changes in supply or demand suddenly. As soon as the frequency drops

beyond 49.90Hz, FCR-D is activated within 5-30 seconds to handle such an undesirable

situation [46]. Loads can have an option to participate with one step activation in 1-5

second activation time. Reference [39] mentions different options as shown below:

Chapter 2. Nordic Electricity Market 16

• 49,7 Hz 5 s

• 49,6 Hz 3 s

• 49,5 Hz 1 s

In case of Fingrid, it procures a maximum capacity of 100MW at each step while ac- tivating reserves [39]. These types of reserves are only used for up regulation and is available as an hourly and yearly product with a minimum bid of 1MW. The System Operating Agreement (SOA) requires FCR-D to be equipped to the N-1 criterion and hence has a volume of 1160MW for the Nordics. The requirements of each control area are established on the ratio of the energy produced in that control area compared to the energy produced in the entire synchronous area. Therefore, Sweden must contribute 400MW to the FCR-Disturbed operating reserve [44].

Figure 2.2: Chart depicting the boundaries of primary reserves in the Nordic Elec- tricity Market [39]

2.4.3.3 Pre-qualification, Reporting, Bidding & Procurement of FCR

For a market participant to participate in the FCR and FRR market needs to demon-

strate that the technical requirements for the reserve market are met, by completing a

prequalification with approved results [46]. After all the requirements and the service

tests are satisfied as stated above, the system operator in this case the TSO approves

entry and the provision of FCR will be included in the balance responsibility agreement.

Till now, the FCR pre-qualification specifications were designed keeping in mind for the hydro-power resources, however there are new renewable sources like wind are being considered by the TSOs.

As mentioned earlier a minimum bid for 0.1MW and 1 MW for FCR-N and FCR-D respectively are to be submitted for a minimum of one-hour blocks, D-1 or D-2, prior to the delivery day. As per [47] bidding opens at 12:00 noon and closes at 18:00 and 15:00 respectively for D-1 and D-2 with a maximum block bid size of three hours and six hours for D-1 and D-2 respectively.

Once the bids are drafted, the balance service providers are obligated to submit an FCR plan per constraint area to the TSO. All the information flows are carried out digitally using the “Ediel” platform – Nordic electronic information exchange. Bids for the FCR must be based on the marginal costs for regulation as outlined in the balance responsibility agreements. However, the current process of integration of Nordic market with continental Europe has led to some fundamental changes to the balancing concept, which can change the current designs and current perspective of the reserves.

2.5 Imbalance Settlement and Pricing

The purpose of imbalance settlement is to establish a financial balance in the electricity

market after the operation hour [48]. Every buyer and seller operating in the electricity

market needs to ensure his commitment towards delivering the products and services as

decided, which includes sometimes a forecast and pre planning of scheduling the energy

resources or loads. Due to errors in forecasting, the accurate delivery of commitment

is not possible at every moment. Thus, with the help of balancing services, a buyer or

seller can balance the difference between the acquisition and the committed delivery with

so called imbalance power [49]. A market entity using more electricity than estimated

pays extra for his electricity, and an entity using less is compensated. As a step towards

the integration of the Nordic to the Continental Europe, a Joint imbalance settlement

for the Nordic electricity markets has been launched in May 2017[49]. A Jointly owned

company by the Nordic TSOs solely for this purpose by the name “eSett Oy” is based

in Finland. A common platform was constituted in order to boost the operations of the

Chapter 2. Nordic Electricity Market 18

balance responsible parties, distribution network companies, electricity suppliers and service providers, as well as TSOs.

Companies which take up the balance responsibility for their constraint areas must register themselves with the joint Nordic platform “eSett Oy” in order to participate in the activity of imbalance settlement. Consumption and production imbalances are calculated for each BRP based on the production plans, PX market trades and bilateral trades at the same time with the realised consumption and production. Each BRP is financially liable for the imbalances under its responsibility, balanced by the balancing power procured from the balancing power market operated by the TSOs. The imbalance settlement is based on two types of imbalance volumes, namely production imbalance volume 2.1 and consumption imbalance volume 2.2.

P roductionImbalanceV olume = P rod. − P rod.P lan ± ImbalanceAdj. (2.1) ConsumptionImbalanceV olume = Cons.+P rod.P lan±T rade±ImbalanceAdj. (2.2)

If a BRP consumes more than what was planned for production as well as with the trades, then the deficit is to be settled with eSett by purchasing the imbalance energy.

Similarly, if a BRP produces less than what was planned, the deficit in the production imbalance volume is to be settled with eSett and the imbalance energy in this case too must be purchased from eSett.

Figure 2.3: Price Models for Imbalance Settlement [48]

Production imbalance is priced according to a two-price model, which means there are different prices for positive and negative production imbalances. This is so organised in such a way that the BRP never receives an advantageous price for production imbalances.

For example, in a situation of upregulation (high demand of energy in the system) the price for purchasing power is higher than the spot price for a BRP with negative production imbalance, while the price for positive production imbalance is the spot price.

Consumption imbalance price follows a single price mode, which means that positive

and negative consumption imbalances have the same price. The price always is the reg-

ulating price based on the net direction of the system for that price/bidding zone. In

the case of upregulation, the negative and positive consumption imbalances will have an

upregulation price, thus opening an opportunity for the BRPs with positive imbalances

to have a better price for what they are producing. A similar case would be for downreg-

ulating hours, the BRPs having a negative consumption imbalance or consuming more

can buy the imbalance energy at a lower price than the spot price, allowing the BRP to

have some extra profits [48].

Chapter 3

Methodology

3.1 Introduction

This chapter will dive into how the stochastic mixed integer linear model for a virtual power plant with multiple assets is developed for the Nordic Electricity Market. This model participates in two different markets namely as below and settles later for the imbalances:

• Day Ahead Market

• mFRR/Tertiary Reserve Market

The model is designed to maximize the profit of the VPP trader through developing a risk averse optimal bidding strategy when participating in the above markets. The output of the model are pairs of volumes to be offered and expected prices for the volumes. These pairs can be submitted further to the nominated market operator (NEMO) in this case is NordPool. Later an investigation is carried out with respect to the imbalance costs associated to three different modes of the VPP:

• Mode 1: Wind alone mode + real time imbalance settlement

• Mode 2: Wind farm + Battery Storage + real time imbalance settlement

• Mode 3: Wind farm + Inflexible Load + real time imbalance settlement

20

This investigation would give an indicative variation in the imbalance costs when oper- ated in different modes of operation with the help of Expected value of Perfect Informa- tion (EVPI) Concept.

Nature of the portfolio

Generally, a VPP can consist any number of different types of energy producers like dis- patchable, non-dispatchable assets and energy consuming assets like flexible or inflexible loads, charging a battery etc. The model designed in this thesis is developed based on considering assets as given below:

• A Dispatchable unit

• A Stochastic/Renewable source e.g. Wind, PV

• An energy storage system e.g. Battery, Pumped Hydro System etc.

• A Flexible Load

3.2 Model Assumptions

The thesis involves a mathematical model to emulate the operation of a VPP and cal- culate the optimal scheduling of the portfolio such that the overall profit is maximised.

However, utmost care is taken to emulate the real operation so that the outcome is indicative of the realistic results. There are 4 price/bidding zones in Sweden where the prices differ and inter zone allocation of capacity for trade is implicitly included by the market operator, In order to keep the model simple and avoid complexity, it has been assumed for the model to operate in one price zone, which means that all of the assets which are generating and the assets which are consuming lie in the same price/bidding zone.

It is always fair to have an environment of perfect market scenario to promote healthy

competition among the market entities which further ensures maximization of overall

welfare. This statement allows to assume the VPP trader to be a price taker rather

than price maker. However, the model can also be designed such that the rivals offer is

anticipated beforehand and is used to adjust their position as proposed in [26]. However,

to keep the market power in check, it is always recommended to be a price taker.

Chapter 3. Methodology 22

As it has been already highlighted in the research of existing literature, there have been many extensive studies carried out on design and development of a technical VPP considering all the grid operational constraints. This type of design of a VPP is like a DSO operating/managing asset keeping in mind about the bottlenecks of the system.

However, this thesis handles the assets from commercial VPP point of view, who has limited or no information of grid congestions and bottlenecks. Thus, it is very clear to restrict the model to a commercial VPP without considering grid management. This assumption would help the model improve the computationally tractability justifying the boundary of the thesis to restrict it to the Commercial VPP (CVPP) formulation.

Usually the intraday markets are used by traders of stochastic units to meet their com- mitments of delivering energy. The errors in the energy forecast can cause deviations with what is produced in real time, which can lead to larger penalties incurring losses to the traders. Intraday markets help largely renewable/stochastic power generators to adjust their positions 30 min prior to the actual delivery. However, with the concept of VPP, the uncertainty related to the renewable generation is handled well by other type of controllable assets in the system reducing the need of such a market to adjust their positions. This feature of VPP is known as a portfolio effect. With the recent report from NordPool suggesting a meagre liquidity in the intraday markets, indicating that this liquidity crunch may lead to fewer or no adequate indicators/signals available to anticipate the market prices for traders to take advantage of the market. Thus, it is assumed with comfort that excluding intraday markets would not affect the overall profit in a big manner.

Since the thesis is aimed at maximization of the overall profit of the VPP by optimally

scheduling the portfolio for day ahead and reserve (mFRR only upregulation) markets,

the initial investments related decision variables are not included in the model to keep it

simple. This way the model just focuses on operational point of view of the Commercial

VPP.Reserve mFRR market is modelled only for the dispatchable unit, as for any market

actor to participate in the mFRR market needs to qualify the minimum prerequisites

for operating the portfolio. As the thesis deals with helping the trader to take daily

decisions related to the optimal scheduling of his VPP portfolio, it is just restricted to

profit generated from the daily bidding in the market.

In the proposed optimization model, there are mainly two types of uncertainties consid- ered pertaining to prices and the weather dependent energy generation sources. These two types of uncertainties can affect the outcome of the model in different manners.

Generally, uncertainties are modelled using scenarios-based stochastic approach, where every situation is anticipated using various indicators like historical data, temporal data, temperature data, seasonal data etc and aggregated into a scenario matrix. Uncertainty associated due to stochastic energy producer units whose values would strongly affect the outcome of the optimal scheduling of the VPP. The other major uncertainty asso- ciated with the decision making is the electricity prices in different markets. Thus, this thesis handles both the types of uncertainties, but in different ways. Price uncertainties are handled using persistence models, which is explained in the following sections of this chapter. An API designed and developed by Greenlytics AB for forecasting the renew- able energy sources which are weather dependent are used as an input to the model which directly generates the scenario matrix for the optimization model.

There are two systems of settling imbalances of the system namely, a single price system and two price systems. Currently, two price system is being employed in the Nordic electricity market framework. A disadvantage with such a system is that it doesn’t allow the trader to benefit from his position relative to the market position. However, to increase the trust of the trader and increase the liquidity of the market, the new Nordic balancing concept has recommended a single pricing settlement model. This can allow the trader to benefit from his position relative to the overall market position. However, there was no clear indication on when such a system would go live, for that reason the thesis models two price system for calculating the optimal scheduling to maximise the profit of the VPP.

Lastly, the model doesn’t consider the futures contracts to keep the model simple. Thus, this model is restricted to just help the decision maker to schedule in short time markets like day ahead, hourly reserve markets and real time balancing markets.

3.3 Model Description

The VPP optimal bidding model uses the probabilistic price-based unit commitment

with the constraints for the inclusion of various assets of VPP. The objective equation

Chapter 3. Methodology 24

of the problem considered in this thesis is to maximise the expected value of the profit for the following day ahead horizon while considering the Conditional Value at Risk (CVaR).

The outputs of the optimization model for the bidding in the day ahead, reserve and the balance market can be summarized as below:

• Energy Bid to the day ahead market

• Energy Bid for the hourly reserve (mFRR) market

• Expected Imbalance settlements in the real time balance markets.

A simple representation of the objective Equation can be formulated as below:

ExpectedP rof it(ρ) = M aximize

T

X

t=1

(revenues − costs) (3.1)

where, Revenue = is the cash flow generated due to the participation of the portfolio in various markets like day ahead markets, reserve markets and the balance markets. In simple mathematical terms, it is the sum of the cash flows generated in all the markets.

Costs = is the cash flows assigned to the operational requirements like the Fuel cost, start-up and shutdown costs.

The revenues in this specific case of a VPP can also be represented as the cash generated by selling the energy from various assets like dispatchable sources, stochastic units, storage units and flexibility from controllable loads. The following sections will outline the modelling of each asset used in the VPP, and later will be realized as a mixed integer linear program model suitable for participating in the market.

3.3.1 Modelling a Dispatchable unit

There can be two different components which the dispatchable unit i in the VPP can

contribute towards the overall profit equation namely, a) revenue generated from par-

ticipating in the day ahead market and the reserve (mFRR- upregulation only) market,

b) costs associated with the operation mainly Fuel costs, start-up and the shut down

costs which characterised by a cost function, C(E

), which provides the cost C

(e.g. in

Euros) of the generating a certain amount of energy E

(e.g. in megawatt hour). This cost function is obtained by the multiplying the heat rate curve and the cost of the fuel.

The resulting curve is a quadratic function, which is approximated into a piece wise linear function (explained in the Appendix section A). The y-intercept of the equation represents the No-load cost, which takes place only during the time periods the unit is online. Thus, this term of the quadratic equation must be multiplied with a binary variable v

representing the on-off status of the unit, as shown in the equation 3.25.

P

is the power output of the dispatchable unit at a specific point in time t and scenario ω. The value of the power generated will be either 0, when the unit is idle or in the range [P

, P

]. Mathematically, the functional state of a dispatchable unit i can be easily modelled using a binary variable v

also called as unit commitment variable, which is equal to 0 when offline and 1 when online. The below formulation summarises the unit commitment of the dispatchable unit i of the VPP:

v

P

≤ P

+ P

≤ v

P

∀ω, t (3.2)

The variable P

in the above expression relates to the multimarket operation of the VPP which helps with optimal scheduling of the dispatchable unit i in the hourly

”upregulation” reserve market but only the tertiary reserve, as it has the maximum time of activation of 15 min so that there is enough buffer time to accommodate flexibility of the VPP.

However, the unit commitment variable is dependent on start-up and shutdown of the unit. Both transitions from idle to start-up and then to idle are associated with some costs which can be denoted by C

and C

respectively, which can be modelled as

C

≥ S

(v

− v

) ∀ω, t (3.3)

C

≥ 0 ∀ω, t (3.4)

And

Chapter 3. Methodology 26

C

≥ S

(v

− v

) ∀ω, t (3.5)

C

≥ 0 ∀ω, t (3.6)

Where S

and S

are the start-up and shutdown costs incurred while operating the dispatchable unit i of the VPP. In reality, when a VPP is to be operated in a cost efficient manner, the variables C

and C

will only take the actual values of the start-up and shutdown costs incurred by the power plant provided that these costs are to be minimized.

Besides, other technical constraints ramping constraints are also to be imposed on the model to restrict the undesired operation of the power plant while participating in the market. The formulations for such a constraint require a new parameter ∆

denoting the maximum ramp-up/ramp down rate of the dispatchable unit i which are shown below

P

− P

≤ ∆

∗ (1 − y

) ∗ τ ∀ω, t (3.7)

P

− P

≤ ∆

∗ (1 − y

) ∗ τ ∀ω, t (3.8)

The variable y

here in the above ramp up/down equations represent the binary variable attributed to the decision of participation of the dispatchable unit i in the reserve market.

The multiplier expression multiplied by the ramp rate restricts the operation of ramping when the dispatchable unit participates in the reserve market. It is designed in such a way that the simultaneous participation in the multiple markets is not allowed.

Lastly the equations 3.2, 3.7 and 3.8 are imposed on the power output P

of the

dispatchable unit i of the VPP. However, the C

(E

) term is a function in the terms

of the actual energy that is produced, E

. Thus, an additional expression that converts

power into energy would be necessary and is depicted as below:

E

= (P

+ P

)

2 τ ∀ω, t (3.9)

Where, τ is the time period for the market periods e.g. 1h, 15min etc.

3.3.2 Modelling of Flexible loads

Flexible demand has the ability to reduce, increase or decrease its requirement of elec- tricity consumption in line with the high market prices or market incentives. The math- ematical modelling of the flexible loads is mostly like the dispatchable unit of VPP.

Each flexible load j in the VPP is characterized by a concave quadratic utility function U

(E

), which provides the benefit (e.g. in dollars/euros) that the VPP obtains out of the amount of electricity, E

, it consumes. We can denote the power demanded by the flexible load j at a given point of time t and scenario ω by P

,

P

≤ P

≤ P

∀ω, t (3.10)

Similarly, to the dispatchable units ramping rate, it is the pickup/drop rate for a flexible rate j, ∆

( e.g. in megawatt per hour), that is

P

− P

≤ ∆

∗ τ ∀ω, t (3.11)

P

− P

≤ ∆

∗ τ ∀ω, t (3.12)

Both the equations represent the mathematical model for pickup and drop rate of the flexible loads between the time periods of length τ .

At the same time, considering the P

term to be piece-wise linear, we can mathe- matically compute the electricity consumed by the flexible load within the time periods t − 1 and t as,

E

= (P

+ P

)

2 τ ∀ω, t (3.13)