A MILP Approach for the Joint Simulation of Electric Control

Reserve and Wholesale Markets

Timo Breithaupt, Thomas Leveringhaus, Torsten Rendel and Lutz Hofmann

Institute of Electric Power Systems, Leibniz Universität Hannover, Welfengarten 1, 30161 Hanover, Germany

Keywords: Electric Power Market, Electric Control Reserve Market, Power Plant Dispatch, MILP.

Abstract: A mixed integer linear programming (MILP) approach for the joint simulation of electric control reserve

and electricity wholesale markets is described. This generation dispatch model extends an existing

integrated grid and electricity market model covering the Continental European electric power system. By

explicitly modelling the markets for primary and secondary control reserve, the model can reproduce the

decisions of generating unit operators on which markets to get involved. Besides, the introduction of

integrality conditions allows considering start-up costs and the calculus of generating units to pass through

economically unattractive periods with low or even negative prices in order to avoid another start-up.

Finally, the MILP approach allows to consider the fact that primary and secondary control reserves

provision usually requires operation of the respective generating unit and to fully include storages into the

optimization problem. In this paper, the generation dispatch model is described in detail, key assumptions

are presented and the implementation status is explained.

1 INTRODUCTION

The electric power system in Europe currently

experiences a strong transition. Political objectives

promote the, often decentralized, generation of

electrical energy from renewable energy sources

(RES), the liberalization of power markets and

cross-border trading and – in some countries – the

decrease of nuclear power generation. The resulting

system is characterized through high volatility in

generation (esp. by wind and photovoltaics),

increasing cross-border trading, an increasing

number of atypical market situations with very low

or even negative electricity prices (esp. in Germany

(Genoese et.al, 2010)) and in some cases high grid

expansion requirements in all voltage levels.

In order to analyze this transition scientifically,

e.g. in terms of generation dispatch, electricity

prices, load flows, and grid expansion demand, an

integrated grid and electricity market model (IGEM)

has been developed to simulate current and future

electric power supply scenarios. The model focusses

on the interconnected transmission grid of

Continental Europe, but can also be used to analyze

other regions, if respective data is provided and

possibly existing differences in market structures are

taken into account.

More and more, the liberalization finds its way

into the markets for primary control reserve (PCR)

and secondary control reserve (SCR). In the past, the

provision of PCR and SCR by large power plants

was instructed by the responsible transmission

system operator (TSO). Nowadays, local

liberalization leads to a market based allocation of

PCR and SCR in some European countries, while in

other countries the provision of PCR and SCR is still

instructed by the responsible TSO (ENTSO-E,

2015). Driven by the new ENTSO-E (European

Network of Transmission System Operators for

Electricity) Network Codes (ENTSO-E, 2017), the

provision of PCR and SCR will be liberalized

further and cross-border trading of PCR and SCR

shall be made possible (in fact it is already practiced

between some countries, e.g. between Germany and

several neighboring countries within the framework

of the International Grid Control Cooperation

(50Hertz Transmission et.al., 2014)).

In this paper, a method for the joint simulation of

electricity wholesale market and the markets for

PCR and SCR is developed and on this basis an

extension of the generation dispatch module of

IGEM is presented. While the existing module takes

into account only the electricity wholesale market

formulated as a linear programme, the new module

314

Breithaupt, T., Leveringhaus, T., Rendel, T. and Hofmann, L.

A MILP Approach for the Joint Simulation of Electric Control Reserve and Wholesale Markets.

DOI: 10.5220/0006441203140322

In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2017), pages 314-322

ISBN: 978-989-758-265-3

presented shall broaden the focus with respect to

 the calculus of generating units that their costs

can be covered by revenues not only from the

wholesale market but also by providing PCR

and SCR,

 the fact that for the provision of PCR and SCR

power plant operation normally is necessary,

 power plants passing through pricewise

unattractive periods to avoid start-up costs,

and

 a better representation of storages.

The existing model of IGEM described in

(Rendel, 2012) and (Rendel, 2015) is therefore

replaced by a mixed integer linear programming

(MILP) model including PCR and SCR dispatch.

Within this model, the generation dispatch is

calculated considering the interdependencies

between the different markets, cross-border trading

and storages for the whole period under

consideration.

The next chapter gives a brief overview about the

European power system, IGEM and key assumptions

for the generation dispatch module. In chapter 3, the

MILP approach for the generation dispatch module

is described in detail. Chapter 4 describes the

implementation status. The paper closes with a

conclusion and a description of further work

(chapter 5).

2 SIMULATION ENVIRONMENT

AND KEY ASSUMPTIONS

2.1 Simulation Environment

The area covered by IGEM nearly matches the

synchronous ENTSO-E grid area “Continental

Europe”, which reaches from Portugal in the West to

Romania in the East and from Denmark in the North

to Greece in the South and comprises 42 TSOs. To

facilitate changes and extensions, the whole model is

built modularly.

The basic model structure including the

generation dispatch module presented in this paper is

shown in Figure 1. The model is based on several

data bases comprising, among others, power plant

data, grid data, load data, feed-in time series of RES,

population data, market information, economic

indices and geographical data. Reference year for all

data presented in this paper is the year 2011. The

data is currently being updated to the reference year

2014, though.

Figure 1: Basic structure of IGEM.

The power plant data base contains about 1700

power plants and 500 storages with explicit position

data and about 3100 other entries with regionally

aggregated installed capacity of decentralized

generation. The level of regional aggregation is

determined by the data available. Depending on

availability, further information, such as energy

source, maximum capacity, year of construction and

efficiency (which is estimated using literature

values), is covered (Rendel, 2015). For generating

units with variable primary energy source, such as

wind, PV and hydro power plants, time series of

available energy for different geographical regions

are used (Rendel, 2015).

Load flow simulations are carried out using the

complete Newton Raphson load flow iteration and

are built on results of the generation dispatch.

Among others, modules to assign load, generation of

conventional power plants and generation of RES to

grid nodes are implemented. As different markets

are involved in the generation dispatch, the market

prices are no result of the dispatch module but have

to be calculated in a separate module.

Beyond that, for efficient usage IGEM has a

graphical user interface (GUI) and evaluation

functions such as to display generation dispatch,

electricity prices or power line utilization.

2.2 Key Assumptions

The model presented in this paper is based on the

following key assumptions:

 The actual generation dispatch in Europe is

economically optimal.

 Energy costs of PCR and SCR can be

considered indirectly.

 All non-linear relations can be linearized or

neglected.

A MILP Approach for the Joint Simulation of Electric Control Reserve and Wholesale Markets

315

 PCR and SCR can be allocated to generating

units on hourly basis.

Below, these assumptions are explained in more

detail and a brief description of the underlying

system is given.

In the countries covered by IGEM, the details of

the electricity wholesale markets (hereafter active

power market for a better differentiation to PCR and

SCR markets) differ, e.g. in terms of product

specifications, trading times and RES integration.

PCR and SCR provision is allocated partly market

based and partly determined by the relevant TSOs.

Additionally, not the generating units themselves but

their operators, who often operate several units and

have various contractual connections amongst each

other, are the market participants. However, these

structures are widely unknown. Assuming a market

driven cost optimal generation dispatch with respect

to active power production and PCR and SCR

provision enables abstraction from these details,

since a global optimization (cost minimization) with

an appropriate model time step (currently one hour)

produces the same results.

PCR and SCR are the main instruments of TSOs

to react on frequency deviations caused by

imbalances between load and generation by

counteracting these imbalances. While PCR is

designed for the first, very fast reaction within 30

seconds after the imbalance occurred; SCR is

designed to displace PCR within 15 minutes. There

are two types of costs related to PCR and SCR. The

provision of PCR and SCR results in capacity costs

caused by a more inefficient generation dispatch

compared to a dispatch only considering active

power production. The activation of PCR and SCR

results in energy costs for the additional infeed of

positive or negative power. These energy costs can

either be positive or negative. More information

about the approach to consider these costs in the

dispatch model is given in chapter 3. The provision

of tertiary control reserve (TCR), designed to

displace SCR currently is out of focus of IGEM, as

the requirements for TCR provision allow start-ups

for several types of power plants.

The electric power system is a complex techno-

economic system with various nonlinear

relationships. For instance, the efficiency of power

plants depends on the power output and can be

influenced by PCR provision, and start-up costs of

thermal power plants depend on the period of

idleness. Nevertheless, these relationships are

neglected or linearized in order to reduce model

complexity and to enable the deployment of highly

specialized MILP solvers.

Typically, PCR and SCR provision is allocated

for periods of several hours up to several days or

weeks. As already mentioned above, the relevant

market participants are generating unit operators

with various contractual relations amongst each

other and often operating several units. Therefore, it

is assumed that the operators allocate PCR and SCR

provision to the single generating units in an optimal

way for each model time step.

3 GENERATION DISPATCH

MODEL

Below, the generation dispatch model is described

according to the following convention: Vector

variables are lowercased and bold, matrices

uppercased and bold and scalars either uppercased or

lowercased, following given conventions, but not

bold. All variables are italicized. Variable indices

are italicized (e.g.

t

for different points in time),

notation indices are upright.

3.1 Objective Function

The optimization problem is formulated as

minimization of the total variable costs of electric

power production for the period under consideration

as shown in (1). Fixed costs are disregarded, as they

are not relevant for short-term operational planning.

T

min

f

x

(1)

The vector of optimization variables x consists

of three groups of variables representing all

generating devices except for storages (PP – power

plants), storages (STO) and power trade (T) for each

point in time.

TT T

PP S O

T

TT

[]xxxx

(2)

Power plants are described by their active

power (AP) production (

AP,PP

p

), a binary variable

indicating their operating status (

PP

op ), a binary

variable indicating whether they start-up at the

respective point in time (

PP

st

), and the symmetrical

(i.e. PCR can only be provided in positive and

negative direction) primary control reserve (

PCR,PP

p

),

positive secondary control (

SCRpos,PP

p

) and negative

secondary control (

SCRnegPP

p

) reserve provided:

SIMULTECH 2017 - 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

316

TTTTTT

PP AP,PP PP PP PCR,PP SCRpos,PP

T

SCRnegPP











xpopstpp

p

(3)

Contrary to power plants, storages have two

operating modes that have to be considered

separately, because they partially differ in key

factors, such as efficiency and maximum capacity.

Therefore, the variables used to describe power plant

operation exist for each mode – storage mode

(STOin) and generating mode (STOout). However,

some adaptions are necessary to account for the

specifics of storages:

While PCR as a symmetrical product is

represented by one variable in power plant

modelling, the total PCR of storages can be

composed of different variables for both operating

modes. For instance, a storage in generating mode

with little load can provide negative PCR not only

by reducing its generation but also by switching to

storage mode. Further differences are the neglect of

start-up costs and a variable representing the state of

charge:

TT T TT

STO AP,STOout AP,STOin STOout STOin

TTT

PCRpos,STOout PCRpos,STOin PCRneg,STOout

TT T

PCRneg,STOin SCRpos,STOout SCRpos,STOin

TTT

SCRneg,STOout SCRneg,STOin STO











xp popop

ppp

pp p

ppe

(4)

Power trading (T) is modelled separately for AP,

PCR, SCRpos and SCRneg. Active power trading is

defined between different bidding zones (market

area for AP, often identical to countries) and control

reserve trading between control zones (area for

which PCR and SCR has to be provided, often

identical to area controlled by a TSO). These zones

can be, but do not have to be identical:

TTTT T

T T,AP T,PCR T,SCRpos T,SCRneg







xppp p

(5)

The coefficients of the objective function are

grouped in the same way as the optimization

variables:

TT TT

PP STO T

[]

ffff

(6)

The PP coefficients are given in (7). The costs

essentially determining the power plant dispatch are

the marginal costs

mc and the start-up costs

st

.

Marginal costs are the derivation of the total cost

function and therefore contain only variable cost

elements, essentially fuel costs and carbon dioxide

emission costs. Start-up costs incur for the start-up

of thermal power plants. These power plants require

a certain time up to several hours to heat up and

begin effective operation.

It is assumed that PCR does not cause any costs

directly, because it can only be offered

symmetrically by power plants, and frequency

deviations occur in both directions. Though, the

need for PCR and SCR provision causes costs

indirectly, as it changes the power plant dispatch

towards a more cost intensive state. The coefficients

for SCRpos and SCRneg shall cover the fact that the

activation of positive SCR directly generates costs

and the provision of negative SCR saves costs. The

costs depend on the deployment probability, which

in turn depends on the composition of the pool

providing SCR which cannot be considered within

this linear model. Therefore, an ordinal scale (

os ) is

introduced. This scale, calculated as a share of the

marginal costs, enables the optimizer to choose the

power plants with the relatively lowest costs for

SCR provision without knowing the exact costs.

However, these SCR costs can theoretically bias the

whole generation dispatch and should therefore be

set as close as possible to the real costs.

TT TT T TT

PP

-











00fmcscosos

(7)

Storages have no direct costs in the objective

function. They provide flexibility between different

points in time to the optimizer and can be used to

reduce the total costs in the period under

consideration:

TTTTT

STO

TTTTTT

TTT











0000000000

000

f

(8)

Power trade is also not represented with direct

costs in the objective function. It provides flexibility

between different bidding zones (AP) respectively

control zones (PCR and SCR) and can be used to

reduce the costs within each point in time by a more

efficient dispatch. In case of additional direct costs

for the use of power lines connecting different

bidding zones or control areas, they can be

considered with these coefficients, though:

TTTTT

T











0000f

(9)

All vector elements of

PP

x and

PP

f

are

structured as shown in (10). Each power plant

n is

represented with an own optimization variable and

its coefficient for each point in time

t

. The total

number of power plants is

N

. The model considers

T

different points in time.

A MILP Approach for the Joint Simulation of Electric Control Reserve and Wholesale Markets

317

AP,PP,1,1

AP,PP,2,1

AP,PP,1,2

AP,PP

AP,PP, ,

nt

NT

P











p

(10)

All vector elements of

STO

x and

STO

f are

structured as shown in (11). Each storage

s

is

represented with an own optimization variable and

its coefficient for each point in time

t

. The total

number of storages is

S

.

AP,STOout,1,1

AP,STOout,2,1

AP,STOout,1,2

AP,STOout

AP,STOout, ,

s

t

ST

P











p

(11)

All vector elements of

T

x and

T

f

are structured

as shown in (12) depending on whether trade is

defined between bidding zones or control areas.

Each combination of exporting bidding zone

bze

(respectively exporting control area

cae ) and

importing bidding zone

bzi

(respectively importing

control area

cai

) is represented with an own

optimization variable and its coefficient for each

point in time

t

. The total number of bidding zones

is

BZ

(respectively

CA

for control areas).

T,AP,1,1,1 T,PCR,1,1,1

T,AP,2,1,1 T,PCR,2,1,1

T,AP,1,2,1 T,PCR,1,2,1

T,AP T,PCR

T,AP, , ,1 T,PCR, , ,1

T,AP, e, , T,PCR, e, ,

T,AP, , , T,PCR

;

BZ BZ CA CA

bz bzi t ca cai t

BZ BZ T

PP











pp

,,,CA CA T







(12)

3.2 Lower and Upper Bounds

The lower (

lb

) and upper bounds (

ub

) of the

optimization variables as defined in (13) are given in

(14). They are structured in the same way as the

optimization variables and therefore are time-

dependent. Most of the bounds represent technical

limits of the modelled system respectively its

components. Each power plant and storage is

designed for certain operating ranges which cannot

be violated. In three cases, the upper bound is

infinite (

Inf ), because it is defined in inequality

constraints. Power trading is limited by the cross-

border trading capacities. The binary optimization

variables defined in (15) are bound by zero and one.

The remaining variables are continuous.



lb x ub

(13)

3.3 Inequality Constraints

The total power generation of a power plant

n

must

not exceed its rated power

r,PP, ,nt

P . The possible

activation of positive PCR and SCR has to be

considered by adding the PCR and SCRpos

provision to the active power generation as given in

(16).

Equation (17) forces the binary variable

PP, ,nt

op

to take the value one whenever the power plant

generates active power or provides PCR, as PCR

provision is not possible without power plant

operation. The provision of positive SCR generally

is allowed in standstill given that the power plant is

able to start-up quickly enough. Whether operation

is necessary for SRCpos provision is considered by

the coefficient

SCR,PP, ,nt

on , taking the value 1 in case

operation is necessary and zero in case it is not.

SIMULTECH 2017 - 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

318

PCRmax,PP

SCRposmax,PP

SCRnegmax,PP

PCRmax,STOout

PCRmax,STOin

PCRmax,STOout

P

STOmin

;











Inf

p

Inf

p

lb ub

p

e

0

1

0

1

0

1

0

1

0

CRmax,STOin

SCRposmax,STOout

SCRposmax,STOin

SCRnegmax,STOout

SCRnegmax,STOin

STOmax

Tmax,AP

Tmax,PCR

TmaxSCRpos

Tmax,SCRneg







p

e

p

(14)

PP PP STOout STOin

,;,

NT ST

op st op op

(15)

AP,PP, , PCR,PP, , SCRpos,PP, , r,PP, ,

,

nt nt nt nt

PP P P 

1, 2,..., , 1, 2,...,nNtT

(16)

AP,PP, , r,PP, PP, , PCR,PP, ,

SCR,PP, , SCRpos,PP, ,

0,

nt n,t nt nt

nt nt

PPopP

on P





1, 2,..., , 1, 2,...,nNtT

(17)

Most power plants must not fall below a

minimum generation limit for technical reasons.

Therefore, (18) defines

min, PP, ,nt

P as lower bound for

active power generation in case the power plant is in

operation. As the minimum generation is also valid

during (negative) PCR or SCRneg activation, their

provision is added to

min, PP, ,nt

P .

AP,PP, , min,PP, , PP, , PCR,PP, ,

SCRneg,PP, ,

-

0, 1, 2,..., , 1,2,...,

nt nt nt nt

nt

PPopP

P

nNtT



 

(18)

Start-ups are recognized by means of (21).

Whenever the binary variable

PP, ,nt

op changes from

zero to one between two consecutive points in time,

the binary variable

PP, ,nt

st takes the value one for the

respective power plant and point in time. For the

first point in time the variable is set by (19) and (20),

depending on the starting condition

1,n

c .

PP, ,1 PP, ,1 1,

, 1,2,...,

nnn

op st c n N





(19)

PP, ,1

1,

PP, ,1

if 0, 1, 2,...

1

if 1, 1,2,...

0

n

s

tnN

s

tnN













c

(20)

PP, , 1 PP, , PP, ,

-0,

nt nt nt

op op st







1, 2,..., , 2,3,...,nNtT



(21)

Equations (22) and (23) correspond to (16) but

are formulated separately for each operating mode of

storages. As already mentioned above, PCR is

divided into PCRpos and PCRneg for storages,

because provision can include change in operating

mode.

AP,STOout, , PCRpos,STOout , , SCRpos,STOout, ,

r,STOout, ,

, 1, 2,..., , 1, 2,...,

s

tstst

st

PP P

Ps StT





(22)

AP,STOin, , PCRneg,STOin, , SCRneg,STOin, ,

r,STOin, ,

, 1, 2,..., , 1, 2,...,

s

tstst

st

PP P

Ps St T





(23)

Corresponding to (17), (24) and (25) set

STOout, ,

s

t

op respectively

STOin, ,

s

t

op to one, whenever

the storage generates (stores) active power or

provides PCR in generating (storage) mode.

Similarly to (17), SCR is only considered, if the

associated coefficient is one.

AP,STOout, , r,STOout, , STOout, ,

PCR,STO, , PCRpos,STOout, ,

SCRpos,STO, , SCRpos,STOout, ,

0,

s

tstst

st st

PPop

on P







1, 2,..., , 1, 2,...,

s

St T



(24)

AP,STOin, , r,STOin, , STOin, ,

PCR,STO, , PCRneg,STOin, ,

SCRneg,STO, , SCRneg,STOin, ,

0,

st st st

st st

PPop

on P







1, 2,..., , 1, 2,...,

s

St T



(25)

Equations (26) and (27) correspond to (18).

Whenever the storage generates or stores active

power, the minimum generation respectively storage

A MILP Approach for the Joint Simulation of Electric Control Reserve and Wholesale Markets

319

must be exceeded. Additional provision of PCR and

SCR is considered analogously to (18).

AP,STOout, , min,STOout, , STOout, ,

PCRneg,STOout, , SCRneg,STOout, ,

-

0,

s

tstst

st st

PPop

PP



 

1, 2,..., , 1, 2,...,

s

St T

(26)

AP,STOin, , min,STOin, , STOin, ,

PCRpos,STOin, , SCRpos,STOin, ,

-

0,

st st st

st st

PPop

PP



 

1, 2,..., , 1, 2,...,

s

St T

(27)

Depending on the storage technology and its

design, storages are able to operate in generating and

storage mode in parallel. Whether this is possible for

certain storages is indicated by the parameter

STO, ,

s

t

pop

in (28).

STOout,, STOin,, STO,,

1,

s

tst st

op op pop

1, 2,..., , 1, 2,...,

s

St T

(28)

3.4 Equality Constraints

The electric load in each bidding zone

L, ,bz t

P must be

covered for each point in time following (29). The

load is virtually increased by exports and storages in

storage mode. It can be covered by active power

generation of power plants and storages as well as

by imports. The power plants and storages are

assigned to the bidding zone (control zone) they are

located in by the respective element

,nbz

pbi (

,

s

bz

s

bi )

of a power-plant-bidding-zone (storage-bidding

zone) incidence matrix

P

BI

(

SBI

). The elements

of this

NBZ

- (

SBZ

-) matrix are one if the

power plant

n

(storage

s

) is located in bidding

zone

bz

, otherwise they are zero .

11

1

,AP,PP,, ,AP,STOout,,

,AP,STOin,, T,AP,,,

T,AP, , ,

1

L, ,

1

,

NS

ns

SBZ

sbzi

bze bz

B

nbz nt sbz st

s

bz s t bze bzi t

bze bzi

Z

bze

bz

t

ibz

bz t

pbi P sbi P

sbi P P

PP















1, 2,..., ; 1, 2,...,bz BZ t T

(29)

Equations (30) to (32) correspond to (29). They

ensure an even balance between PCR, SCRpos and

SCRneg provision and demand for each control area.

Consequently, elements of the power-plant-control-

area (

P

CI

) and the storage-control-area incidence

matrix

SCI

are used. They can be built analogously

to the matrices used in (29).

, PCR,PP, , , PCRpos,STOout, ,

, PCRpos,STOin, , T,PCR, , ,

T,PC

11

1

R, , , PCRref, ,

,

nca nt sca st

sca st caec

NS

ns

SCA

scai

cae ca

CA

cae

cai ca

ai t

cae cai t ca t

pci P sci P

sci P P

PP















1, 2,..., ; 1, 2,...,ca CA t T





(30)

11

1

, SCRpos,PP, , , SCRpos,STOout, ,

, SCRpos,STOin, , T,SCRpos, , ,

T,SCRpos, , , SC

1

Rposref, ,

,

nca nt sca st

s

ca s t cae cai t

cae cai t ca

NS

ns

SCA

scai

cae ca

CA

cae

cai ca

t

pci P sci P

sci P P

PP















1, 2,..., ; 1, 2,...,ca CA t T





(31)

11

1

, SCRneg,PP, , , SCRneg,STOout , ,

,SCRneg,STOin,, T,SCRneg,,,

T,SCRneg, , , SC

1

Rnegref, ,

,

nca nt sca st

s

ca s t cae cai t

cae cai t ca

NS

ns

SCA

scai

cae ca

CA

cae

cai ca

t

pci P sci P

sci P P

PP















1, 2,..., ; 1, 2,...,ca CA t T





(32)

As already mentioned above, PCR must be

provided symmetrically by each generating unit. The

equality between positive and negative PCR

provided by storages is ensured by (33).

PCRpos,STOout , , PCRpos,STOin, ,

PCRneg,STOout, , PCRneg,STOin, ,

0,

st st

PP







1, 2,..., , 1,2,...,

s

St T



(33)

Beside power plant start-ups and the

corresponding start-up costs, the state of charge of

storages links the different points in time which

could otherwise be considered independently. The

variation in the state of charge for each storage

(defined at the end of each point in time

t

) is

represented by (34) and (35). Specific values for

start and end point (

STO,start,

s

E and

STOend,

s

E ) are

SIMULTECH 2017 - 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

320

included by (34) and (36), while (36) is optional.

Active power generation reduces the state of charge

of the storage, active power storage increases it. For

both operating modes, the efficiency of the

respective mode (

STOout, ,



s

t

,

STOin, ,



s

t

) has to be

considered. Additionally, the state of charge is

reduced by SCRpos activation and increased by

SCRneg activation. As already mentioned above, the

individual deployment probability cannot be

modelled in this linear model. Therefore, the SCR

provision is multiplied by an activation coefficient (

SCRpos

ac

,

SCRneg

ac

) calculated as the historical mean

value of SCRpos respectively SCRneg activation

relative to the historical provision. Finally,

tributaries or outlets (water storages) or state-of-

charge-independent losses can be taken into account

by

STOtri, ,

s

t

E . The model time step

t

is used to

convert between power and energy.

AP,STOout, ,1

STOout, ,1

STOin, ,1 AP,STOin,s,1

SCRpos SCRpos,STOout, ,1

STOout, ,1

SCRpos STOin, ,1 SCRpos,STOin, ,1

SCRneg SCRneg,STOout, ,1

STOout, ,1

SCRneg STOin, ,1 SCRneg,STOin, ,

1

-

1









s

ss

s

ss

P

ac P

1

STO, , STOtri, ,1 STO,start,

-, 



s

ts s

EEE

ttt

(34)

4 IMPLEMENTATION STATUS

The generation dispatch model described in this

paper has been implemented using Gurobi Optimizer

and is currently being tested. Additionally, functions

reducing the optimization variables (e.g. by pooling

generation with identical or similar properties within

the same bidding zone and control area, mainly RES

generation) and to calculate valid start values for the

optimization have been implemented.

It is intended to simulate periods of one year

with IGEM, as this period corresponds to most of

the available statistical data. Beyond that, there are

typical cycles within the electric power system,

mainly influenced by the climate, that can only be

fully covered by considering whole years, for

instance the use of hydro storage power plants (not

pumped-storage power plants) filled in winter and

spring to generate power in summer and fall.

In the current implementation status the

simulation of a whole year formulated as a single

optimization problem is too computationally

expensive. Therefore, shorter, overlapping periods

are optimized and then combined. It is assumed that

the horizon for operational planning of generating

units apart from hydro storage plants is significantly

shorter than one year. This is currently being

investigated by comparison of results for periods of

different length. However, this approach requires a

separate strategy for hydro storage plants which is

currently being investigated.

AP,STOout, ,

STOout, ,

STOin, , AP,STOin,s,

SCRpos SCRpos,STOout, ,

STOout, ,

SCRpos STOin, , SCRpos,STOin, ,

SCRneg SCRneg,STOout, ,

STOout, ,

SCRneg STOin, , SCRneg,STOin, ,

1

-

1









st

st t

s

t

st

st st

s

t

st

st s

P

ac P

STO, , STO, , STOtri, ,

-,

 

t

s

tst st

EE E

tt t

1, 2,..., , 2,3,...,

s

St T



(35)

STO, , STOend,

,1,2,...,



sT s

EEs S

1, 2,..., , 2,3,...,

s

St T



(36)

5 CONCLUSIONS

A MILP approach for a generation dispatch module

for an integrated grid and electricity market model

covering the Continental European electric power

system has been presented. Beside the electricity

wholesale market, the model covers the markets for

PCR and SCR. By this, the model reproduces the

decisions of generating unit operators on which

markets to get involved. Besides, the introduction of

integrality conditions allows to consider start-up

costs and the calculus of generating units to pass

through pricewise unattractive periods in order to

avoid another start-up. Finally, the MILP approach

allows to consider the fact that PCR and SCR

provision usually requires power plant operation and

to fully include storages into the optimization

problem.

A MILP Approach for the Joint Simulation of Electric Control Reserve and Wholesale Markets

321

The fundamental assumption justifying the

chosen modelling approach is a perfect allocation at

the existing power markets. This implies that a

global optimization – namely a minimization of all

variable costs in the period of consideration –

reproduces the power market results in terms of

generation dispatch, disregarding different products

and trading periods. As the results combine

considerations about several markets, no market

price can be derived directly from them. The

different prices have to be calculated in another

module of IGEM.

The generation dispatch module has been fully

implemented into IGEM. First results are plausible.

Though, improvements are required to simulate one

full year formulated as single optimization problem.

In future work, decomposition strategies and

heuristics focusing on the coupling between bidding

zones and different points in time will be evaluated

with respect to a possible reduction of the

computational effort, a market price calculation

module will be implemented, and the simulation

results will be evaluated by comparison to real

market results.

REFERENCES

50Hertz Transmission GmbH, Amprion GmbH, Elia

System Operator NV, TenneT TSO B.V., TenneT

TSO GmbH, TransnetBW GmbH, 2014. Potential

cross-border balancing cooperation between the

Belgian, Dutch and German electricity Transmission

System Operators. Available at:

www.regelleistung.net.

European Commission (EC), 2017. Final Draft of

Commission Regulation (EU) on Establishing a

Guideline on Electricity Balancing. Available at:

www.entsoe.eu.

European Network of Transmission System Operators for

Electricity, 2015. Survey on Ancillary Services

Procurement, Balancing Market Design 2014.

Available at: www.entsoe.eu.

Genoese, F., Genoese, M., Wietschel, M., 2010.

Occurrence of negative prices on the German spot

market for electricity and their influence on balancing

power markets. 2010 7th International Conference on

the European Energy Market, Madrid, pp. 1-6.

Rendel, T., 2015. Erweiterung und Plausibilisierung eines

Modells für die integrierte Simulation des

europäischen Verbundnetzes und Strommarktes.

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Rendel, T., Rathke, C., Breithaupt, T., Hofmann, L., 2012.

Integrated grid and power market simulation. 2012

IEEE Power and Energy Society General Meeting,

San Diego, CA.

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