Using Flexibility Information for Energy Demand Optimization in the

Low Voltage Grid

Sandfordf Bessler

, Domagoj Drenjanac

, Eduard Hasenleithner

, Suhail Ahmed-Khan

and Nuno Silva

FTW Telecommunications Research Center, Donau-City 1, A-1220 Vienna, Austria

EFACEC Energia M

aquinas e Equipamentos El

ectricos, S.A, PO Box 3078, 4471-907 Moreira Maia, Portugal

Keywords:

Flexibility Models, Load Predictive Models, Optimization Models, Energy Scheduling, EV Charging, HVAC,

PV Generation, Aggregated Energy Controller, Day-Ahead Pricing, Setpoint Following.

Abstract:

Flexibility information that characterizes the energy consumption of certain loads with electric or thermal

storage has been recently proposed as a means for energy management in the electric grid. In this paper we

propose an energy management architecture that allows the grid operator to learn and use the consumption

ﬂexibility of its users. Starting on the home asset level, we describe ﬂexibility models for EV charging and

HVAC and their aggregation at the household and low voltage grid level. Here, the aggregated energy con-

troller determines power references (set points) for each household controller. Since voltage limits might be

violated by the energy balancing actions, we include a power ﬂow calculation in the optimization model to

keep the voltages and currents within the limits. In simulation experiments with a 42 bus radial grid, we are

able to support higher household loads by individual scheduling, without falling below voltage limits.

1 INTRODUCTION

The intensive deployment of photovoltaic based

power generation modules in private homes has

caused the most Distribution System Operators

(DSO) to come out with rules to limit installations that

would otherwise further increase the voltage and the

power injection into the grid during the sunny hours.

In the same time, a number of ﬂexible loads such has

HVAC for heating, air conditioning, combined heat

pumps, and electric vehicles multiplicate the actual

peak household consumption from 2kW to 7 kW, a

level which, if reached simultaneously by many con-

sumers, would create overload problems in the grid.

At the basis of this work, we use the concept of

power and energy ﬂexibility for consumption, gen-

eration or storage, as valuable information to be ex-

changed between the grid actors. In this way, the ﬂex-

ibility information reported by a distributed energy re-

source (DER) can be used for direct control by a DSO,

a utility or a third party aggregator. For alowing this

kind of remote intervention, the DER owner would

beneﬁt monetarily, however the contract and tariff as-

pects are beyond the scope of this paper.

The main objective of this work is to investigate

the feasibility of a (low voltage) grid environment,

in which ﬂexible assets report (future) ﬂexibility in-

formation to a grid level controller, which uses it to

schedule the power level of those assets optimally.

Flexibility information and actuation form a demand

response closed loop in which asset models are used

to predict the load, see (Palensky and Dietrich, 2011)

for a comparison of demand response schemes.

The major contributions of this work are:

• to deﬁne ﬂexibility models for EV charging, heat-

ing ventilation and air conditioning (HVAC) and

aggregate them to home or customer energy man-

agement system (CEMS) ﬂexibility,

• to formulate a CEMS optimization model that

uses the ﬂexibility to control its ﬂexible assets,

• to formulate the optimization model of an aggre-

gation controller,

• to build and evaluate a system of communicating

controllers that optimally schedule the consump-

tion/generation in a low voltage grid.

1.1 Previous Work on Flexibility

With the emergence of Distributed Energy Resources

(DER) in the last two decades, the decentralization of

324

Bessler S., Drenjanac D., Hasenleithner E., Ahmed-Khan S. and Silva N..

Using Flexibility Information for Energy Demand Optimization in the Low Voltage Grid.

DOI: 10.5220/0005448903240332

In Proceedings of the 4th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS-2015), pages 324-332

ISBN: 978-989-758-105-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

the energy network has started. Within their work to

integrate the DER into the energy network, the M490

Working Group (SG-CG/RA and SG-CG/SP) intro-

duced the concept of ﬂexibility, which combines the

consumption, production and storage into one ﬂexi-

bility entity. Within the ﬁve layer Reference Architec-

ture speciﬁed in the Smart Grids Architecture Model

(SGAM) (SGAM, 2012), the ﬂexibility interfaces are

situated in the Information layer (where the data mod-

els are situated) and the Communication layer (where

the protocols for interoperability are situated) (Orda

et al., 2013). The ﬂexibility interface conveys the

characteristics that a DER exposes to an aggregator

or virtual power plant. DERs are equipped with local

controllers that follow also local goals, (Biegel et al.,

2013). An aggregator manages multiple DERs.

Flexibility concepts have been used in the context

of electric vehicle charging (Lopes et al., 2011) and

ﬂexible home consumption. (Sundstr

om and Binding)

use the energy stored in the EV ﬂeet and the bounds

of this energy to optimize the charging schedules at

the ﬂeet (aggregator) level. In (Binding et al., 2013)

the authors present FlexLast, a solution for manage-

ment the consumption of power for cooling in super-

markets, based on the ﬂexibility reporting and con-

trol. Energy prices together with ﬂexibility informa-

tion have been used in a scheduling model in (Tu

sar et

al.,2011). The Danish project iPower, see (Harbo and

Biegel, 2013), goes a step further by deﬁning ﬂex-

ibility services contracted between players in which

the aggregator manages a portfolio with ﬂexible con-

sumers with low marginal ﬂexibility costs.

The rest of the paper is organized as follows: in

Section 2 we deﬁne the ﬂexibility of a charging EV,

an HVAC used for house heating and aggregate them

to household ﬂexibility. In Section 3 we describe

the system architecture and introduce the optimiza-

tion problem at the household level. In Section 4 we

introduce the LV aggregation controller and formulate

the scheduling problem at the LV grid level. In Sec-

tion 5 we report on numeric experiments in the simu-

lation environment and discuss the results. Finally we

conclude and present directions for further research.

2 FLEXIBLE ASSET MODELS

A DER exposes ﬂexibility information in order to al-

low a planning and scheduling algorithm to control by

means of setpoints the amount of energy in time that

ﬂows from or to that asset. The time is discretized to

N periods of duration T, where N = 0,1, . ..N-1 is the

set of periods deﬁning a forecast time horizon of du-

ration NT. In order to calculate the asset ﬂexibility,

a model of consumption and storage of energy will

be used. It is important to mention that the consid-

ered processes are relatively slow, they do not ”see”

transients, abrupt voltage or power changes, therefore

the mechanisms proposed are not suitable for voltage

control. If the period T is set to 15 minutes, the con-

sumed power of an asset during this period is the av-

erage power in this interval, etc.

In the next subsection we present simple asset

models: the electric vehicle and the HVAC used here

for heating a house. In the rest of the paper we will

use the following notation for the energy ﬂexibility

asset

and E

asset

, and for the power ﬂexibility P

asset

and P

asset

, where j is the time period index, and the

underline/overline notation means the minimum re-

spectively maximum ﬂexibility.

2.1 The Electric Vehicle (EV) Predictive

Load Model

In a simpliﬁed world, an EV i that is charged at a

charging point is a load which can be activated from

the plug-in time until the leave-time. In a residen-

tial scenario the plug-in and plug-out/leave time at

the charging point can be individually conﬁgured or

gained from history data, whereas in case of public

charging stations, reservations can provide in advance

information about the expected load. In this paper we

will restrict to the residential case in which the EV is

controlled by the Customer Energy Management Sys-

tem (CEMS).

The charging power varies from period to pe-

riod, p ∈ [0, P

max

], but is constant during a period.

At the end of the stay, the total charged energy

amount should be between a minimum demand and

a maximum demand value (full charged): E

∈

min

max

]. This provides additional freedom in the

charging process and expresses the fact that users do

not have to fully charge the battery.

The energy ﬂexibility is initially zero and repre-

sents the cummulative energy charged by the EV. The

convention used is that the power consumed during

period i corresponds to the cummulative energy at the

end of this period. Figure 1 illustrates the ﬂexibility

of a charging load with P

max

= 8 kW, D

min

= 4kWh

and D

max

=8kWh. In Figure 1 we depict the minimum

and maximum energy for the next eight periods, cal-

culated one period before EV arrival and 2 periods

later, where 2.5 kWh have been actually charged.

If we denote the already charged energy with D

the arrival period with a and the leave period with l,

then the maximum power and energy ﬂexibility are

UsingFlexibilityInformationforEnergyDemandOptimizationintheLowVoltageGrid

325

(

max

, if E

j−1

+ TP

max

< D

max

−D

0, otherwise.

(1)

= E

j−1

+ TP

, j = a,. ..,l (2)

The minimum ﬂexibility represents the latest time

to start charging in order to satisfy the remaining de-

mand D

min

−D

(

max

, if l −[(D

min

−D

)/T/P

max

] ≤ j < l.

0, otherwise.

(3)

= E

j−1

+ TP

, j = a,. ..,l (4)

Energy'[kWh]'

Time'periods'

Eﬂexmax"at"t" Eﬂexmin"at"t"

Eﬂexmax"at"t+2" Eﬂexmin"at"t+2"

Pﬂexmax'

Power&[kW]&

Time&periods&

Pﬂexmax' Pﬂexmin'

Figure 1: EV energy ﬂexibility at time t and t+2 (top) and

power ﬂexibility (bottom).

2.2 The HVAC Predictive Load Model

Heating, ventilation and air condition are good exam-

ples of thermal storage. Since a house is a complex

thermal system, a complete theoretical approach of

formulating the model is impractical. We use however

the ﬁrst law of thermodynamics to describe energy

consumption and storage capacity of a simple house

that consists of a two ﬂoors detached house placed

in Austria with a total size of 128 m

. Moreover, the

house is well isolated and the majority of windows are

facing south resulting in a total annual energy demand

of around 60 kWh/m

. The mathematical equation,

based on the ﬁrst law of thermodynamics, describing

the major thermal effects in the house is:

+ E

−E

trans

= mc∆Temp

(5)

where

• the heating energy at time i is E

= z

HVAC

where z

∈ {0,1} is the control signal in period

• E

is the energy (heat) generated by the presence

of people in the house, in our case 256 Wh,

• E

is the caloric energy generated by appliances

and lights; for 3W/m

, we obtain E

= 384Wh,

• E

is the energy received from sun (assuming

40% glass surface, south orientation), in our case

560Wh.

• E

is the energy lost via ventilation that depends

on the temperature difference between inside and

outside, E

= 45Wh,

• E

trans

= UP∆Temp

is the energy lost due to win-

dow and wall conductivity at time i. U[W/m

/K]

is a measure of the thermal resistance and P[m

]

is the surface of the speciﬁc material, ∆Temp

the temperature difference to outside.

Using the equation (5), the model estimates the in-

side temperature for the planning horizon, based on

a heating schedule. A temperature range of e.g 18 −

◦

C determines the point in which heating has to be

switched on, respectively has to be switched off.

In order to calculate the ﬂexibility, the HVAC uses

the current state: for the maximum ﬂexibility it can

heat continuously up to the maximum temperature,

then keep the upper limit. For the minimum, it can

remain off, until the lowest temperature is reached,

then it must heat for a minimum time. The energy

ﬂexibility is shown in Figure 2:

10"

12"

14"

16"

0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 11" 12" 13" 14" 15" 16" 17" 18" 19" 20" 21" 22" 23"

Energy'[kWh]'

Time'periods'

Eﬂexmin" Eﬂexmax"

Figure 2: 5kW HVAC energy ﬂexibility.

Given the ON-OFF operation of the HVAC heat-

ing in this example, the power ﬂexibility is straight-

forward: P

HVAC

= 0 and P

HVAC

= P

HVAC

, the heating

power.

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In the considered smart households, photovoltaic

power generation is also available. Although this en-

ergy cannot be stored, the generated active power

can be derated and/or curtailed. For a simple ac-

tive power control, the ideal photovoltaic output p is

ﬁrst limited by the inverter maximum power, P

rated

gen

= min(P

rated

,ηAI

solar

), where η is the efﬁciency

of the solar cells and A is their area in m

. To control

a certain range of this power output, we introduce the

generation factor gf ∈[gf

min

,1] with gf

min

< 1. For an

available power P

gen

, the PV generates therefore the

power p = gfP

gen

with gf

min

gen

≤ p ≤P

gen

≤P

rated

This model can be easily mapped to the industrial

modes of control using derated power and curtailing

(Pedersen et al.,2014).

Finally, in the household there is also the non-

ﬂexible consumption, which is characterized by an

individual proﬁle P

load

. In order to calculate the ag-

gregated energy ﬂexibility, we deﬁne the aggregated

power ﬂexibility of the household (here identiﬁed at

the level of the customer energy management system,

CEMS) at the time period i as follows:

CEMS

= max(−P

CEMS

load

+ P

HVAC

−P

gen

)

(6)

CEMS

= min(P

CEMS

load

+ P

HVAC

),i ∈ N

(7)

where P

CEMS

is the maximum alowed con-

sumed/generated power by the household, for

instance 6.9 kW.

For the energy ﬂexibility, the following recurence

is used

CEMS

= E

CEMS

i−1

+ P

CEMS

,i ∈ N −{0} (8)

CEMS

= E

CEMS

i−1

+ P

CEMS

,i ∈ N −{0} (9)

with initial E

CEMS

= P

CEMS

, and E

CEMS

= P

CEMS

3 ENERGY MANAGEMENT

ARCHITECTURE

We consider a radial low voltage grid supplying a res-

idential area, where each home is conﬁgured with the

assets described in the previous sections: an HVAC

used for heating, an EV charging point, PV generation

and non-ﬂexible loads. These assets are connected to

a local controller, the CEMS, via a bidirectional data

interface. The assets deliver ﬂexibility information to

the controller, and the controller calculates a control

signal, speciﬁc for each asset type, as will be pre-

sented in detail in the modeling section. In a further

aggregation step, the CEMS controllers communicate

Home

energy

controller

CEMS

Aggregated

energy

controller

asset

setpoint

proﬁle

asset

ﬂexibility,

load proﬁle

Home

energy

controller

CEMS

Charging

gen

HVAC

Model

load

events

ext.

temp.

irradiation

forecast

HH-load

proﬁle

CEMS setpoint

proﬁle, energy

prices

CEMS ﬂexibility,

load proﬁle

Figure 3: Energy Management Architecture.

with an aggregation controller, as depicted in Figure

The bidirectional interface between the LV energy

controller and the CEMS controller consists of fol-

lowing pieces of information:

• power ﬂexibility and energy ﬂexibility proﬁle

(from CEMS)

• prefered load trajectory (from CEMS)

• setpoint trajectory (to CEMS)

• market clearing energy prices (to CEMS)

3.1 CEMS Energy Optimization

As mentioned at the beginning, the basic idea of re-

porting ﬂexibility is to transfer the control of the

house energy management up to a certain extend to

the DSO or to an entity that participates in the energy

market, but in the same time to follow local manage-

ment goals.

The result is a multi-objective function with three

terms which can be weighted differently in order to

investigate the solution properties The ﬁrst term in

UsingFlexibilityInformationforEnergyDemandOptimizationintheLowVoltageGrid

327

(10) makes the CEMS to follow the setpoints imposed

at the LV grid level, and does so by minimizing the

deviation between the CEMS net consumption (or in-

jection in the grid) and the CEMS setpoint reference

ref

, similarly to the objective used in (Sundstr

and Binding),(Molderink et al., 2010). The second

term maximize the own generated power gf P

gen

over

the prediction time horizon, so that more energy is lo-

cally stored. Finally the third term uses the day-ahead

prices to minimize energy cost. The MCP (market

clearing prices) c

are published and available the day

before, for the whole grid. Even if the household does

not have an immediate monetary advantage for con-

suming more when the price is low, high prices cor-

relate to peak demand that we want to penalize in the

objective function. As the prices are positive, the min-

imization goal in (10) will cause the reduction of total

energy consumption, an effect that is not always de-

sired. For instance in the EV case, this would cause

that the charging will stop once the minimum demand

min

is reached. To solve this problem we have to bias

the price values around an average (the base value),

leading to positive and negative values of c

. The state

variables and control signals are deﬁned as follows:

Table 1: Notation summary.

Notation Description

charging power in kW during j

HVAC heating binary control in j

generation factor

EV charged energy until j

HVAC

energy (thermic) stored at time j

net power from or to the grid

in+

= P

if P

> 0 and zero else.

load

the non-ﬂexible load

trans

lost energy through walls see (5)

MCP energy prices every 15 minutes

The optimization program in Equations (10) - (18)

is quadratic and has integer (binary) variables. The

constraint (11) expresses the power ﬂows balance at

the house grid connecting point. The constraints (14)

and (15) express the accumulation of energy in the

battery, such that is has to be within the ﬂexibility

limits. Similarly, the HVAC in constraints (13) and

(17).

minimize

(

∑

j∈N

−P

ref

)

−K

∑

j∈N

gen

+ K

∑

j∈N

in+

(10)

subject to:

+gf

gen

−y

−P

load

−z

HVAC

= 0, j ∈N (11)

0 ≤ y

≤ P

max

, j ∈N (12)

∈ {0, 1}, j ∈ N (13)

= E

j−1

+ y

j−1

T, j ∈ N −{0} (14)

≤ E

, j ∈N (15)

HVAC

= E

HVAC

j−1

−E

trans

j−1

+ E

pasv

+ z

j−1

HVAC

T (16)

j ∈ N −{0}

HVAC

≤ E

HVAC

≤ E

HVAC

j ∈ N (17)

min

≤ gf

≤ 1, j ∈ N (18)

The results of the CEMS optimization are:

• a plan of the prefered net power consumption or

power injection in the grid P

, j ∈N.

• a plan for the control actions: a) z

, j ∈N towards

the HVAC, b) y

, j ∈ N towards the EV charging

point, c) gf

, j ∈N towards the PV inverter.

4 AGGREGATED ENERGY

MANAGEMENT IN THE LV

GRID

In this section we describe the model of the aggre-

gated energy controller, see Figure 3. Its main role

is to schedule the house loads, i.e. to decide which

of the houses require high consumption during each

time period. The problem is that, the knowledge of

the total load alone does not guarantee that the voltage

limits at the buses and the current limits in the feeders

and at the transformer are respected. This is the rea-

son for including information of the grid topology and

the optimal power ﬂow calculation in the optimization

model.

The key idea is to take the total power and to

distribute it in such a way that the resulting CEMS

setpoints correspond to allowed voltages and cur-

rents. The assumption that also the real loads on the

households lead to admissible voltages is of course

only true, if the setpoints are closely followed by the

household actual loads.

The proposed OPF (optimal power ﬂow) opti-

mization is repeated for each period j of the planning

time horizon. We assume for the sake of simplicity

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328

that a single household is attached to a bus in the ra-

dial LV grid. In practice, we assign to each bus several

households (or CEMS controllers) to be individually

controlled. Let B be the set of buses (households).

Based on the prefered load trajectory P

,i ∈ B re-

ceived from the CEMS, we deﬁne the variable β

, as

the additional power required to obtain the setpoint

for bus i, therefore P

ref

= P

+ β

As for the CEMS, the objective (19) of the

optimization problem has two terms: a) to minimize

the total squared error between offered loads on the

buses and the estimated setpoint values, and b) to

minimize the setpoint ﬂuctuation between subsequent

time periods. For the latter goal, we store the setpoint

calculated for j −1 and use it in period j as P

ref−

α is a parameter to tune the relative importance of

the goals. For each period j we solve therefore the

following problem:

minimize

∑

i∈B

+ (1−α)

∑

i∈B

+ β

−P

ref−

)

; (19)

subject to:

−(P

+ β

) −(

∑

(i, j)∈Y

i j

cos(φ

−φ

) + (20)

i j

sin(φ

−φ

))) = 0, i ∈B

−Q

−(

∑

(i, j)∈Y

i j

cos(φ

−φ

) + (21)

i j

sin(φ

−φ

))) = 0, i ∈B

min

≤V

max

,i ∈ B (22)

≤ E

CEMS

/T −

∑

k∈N|k≤j

,i ∈ B (23)

≥ E

CEMS

/T −

∑

k∈N|k≤j

,i ∈ B (24)

In the Kirchoff equations (17) and (21), the volt-

ages V

and the angles φ are variables, in addition to

. Y is the set of index pairs required for the admit-

tance matrix, of which G and B are the real respec-

tively imaginary parts. For the sake of simplicity in

the presentation, we omit the current limitation con-

straints and the apparent power limitation of the trans-

former (see (Andersson,2012) for a tutorial on power

ﬂow equations). P

is the power generated by the bus

i, besides households (where generation is included

in P

). Therefore P

= 0 except for the reference bus

which supplies power to the LV grid.

The ﬂexibility constraints (23) and (24) can be

better explained with the diagram in Figure 4. As-

sume β

> 0. For the selected period (e.g. j=2) the

setpoint P

+ β

should correspond to the point B,

and should be less than the ﬂexibility value E

CEMS

as expressed in Equation (23). Similarly, if β

< 0,

the setpoint value B’ should be larger than E

CEMS

expressed by Equation (24).

0" 1" 2"

B’"

Time%periods%

Cummulated%

consump2on%

 Q

load

 (

(i,j)2YBUS

cos(

 

)+B

sin(

 

))) = 0,i2 B (24)

min

 V

max

,i2 B (25)



 E

CEMS

/T 

k2N |kj

load

,i2 B (26)



 E

CEMS

/T 

k2N |kj

load

,i2 B (27)

For the sake of simplicity, we omit the current limitation constraints and the ap-

parent power limitation of the transformer (see XXX for a reference).

In the Kircho↵ equations () and (), P

is the power generated by the bus i,besides

the households which, in case P

load

< 0, would be considered generators. Therefore

= 0 except for the reference bus which supplies power to the LV grid.

The ﬂexibility constraints () and () can be better explained with the diagram in

Figure (). Assume 

> 0 For the selected period (e.g. j=2) the setpoint P

load

+ 

should correspond to the point B, and should be less than the ﬂexibility value E

CEMS

as expressen in Equation (26) Similarly, if 

< 0, the setpoint value B’ should be larger

than E

CEMS

, expressed by Equation (27).

Figure

5Simulationofrealisticusecase

5.1 Scenario

Within the FP7 project SmartC2Net we had access to data from a benchmark LV grid

with 42 buses and 130??? households. The background load data has been used to

create randomized samples for each household. The goal is to enhance the households

with heating HVACs, PV generation P

rated

= 4kW and for 10 households to add EV

charging points with various charging patterns (arrival, leave times, demand). The

HVACs’ starting inside temperature was randomly distributed between 18.1 and 21.9

degrees, the ouside temperature was 1 degree (January).

If we add to the setpoint following objective the Maximizing the gf (local generated

power), we obtain two e↵ects: ﬁrst, the average temperature in the houses is higher

and the total charged energy in the EVs is higher. This explains the second e↵ect: the

net supplied power by the grid to all houses is lower, because local generated power is

better used.

In order to evaluate the performance of the described system, we deﬁne s number

of key performance parameters (KPIs)

1. Avoidance of peaks and valleys of energy consumption in the grid. This can be

measured on several levels: total consumption proﬁle, load on each bus, etc.. Peak

reduction e.g 30% if users are willing to accept 1 degreed of temperature deviation.

[1]

2. renewable energy fed into the grid (less curtailing) while maintaining the power

quality

Q

(

(i, j)2YBUS

cos(f

f

)+ (19)

sin(f

f

))) = 0,i 2B

min

V

max

,i 2B (20)

 E

CEMS

/T 

k2N|kj

,i 2B (21)

 E

CEMS

/T 

k2N|kj

,i 2B (22)

In the Kirchoff equations (19) and (20), the volt-

ages V

and the angles f are variables, in addition to

. YBUS is the set of index pairs required for the

admittance matrix, of which G and B are the real re-

spectively imaginary parts. For the sake of simplic-

ity, we omit the current limitation constraints and the

apparent power limitation of the transformer (see [7]

for a tutorial on power ﬂow equations). P

is the

power generated by the bus i, besides the households

which, in case P

< 0, would be considered genera-

tors. Therefore P

= 0 except for the reference bus

which supplies power to the LV grid.

The ﬂexibility constraints (21) and (22) can be

better explained with the diagram in Figure 4. As-

sume b

> 0 For the selected period (e.g. j=2) the set-

point P

+ b

should correspond to the point B, and

should be less than the ﬂexibility value E

CEMS

, as ex-

pressed in Equation (21). Similarly, if b

< 0, the set-

point value B’ should be larger than E

CEMS

, expressed

by Equation (22).

0 1 2

B’

 Q

load

 (



(i,j)YBUS

cos(

 

)+B

sin(

 

))) = 0,i  B (24)

min

 V

max

,i B (25)



 E

CEMS



kN |kj

load

,i B (26)



 E

CEMS



kN |kj

load

,i B (27)

For the sake of simplicity, we omit the current limitation constraints and the ap-

parent power limitation of the transformer (see XXX for a reference).

In the Kirchoﬀ equations () and (), P

is the power generated by the bus i,besides

the households which, in case P

load

< 0, would be considered generators. Therefore

= 0 except for the reference bus which supplies power to the LV grid.

The ﬂexibility constraints () and () can be better explained with the diagram in

Figure (). Assume 

> 0 For the selected period (e.g. j=2) the setpoint P

load

+ 

should correspond to the point B, and should be less than the ﬂexibility value E

CEMS

as expressen in Equation (26) Similarly, if 

< 0, the setpoint value B’ should be larger

than E

CEMS

, expressed by Equation (27).

Figure

5Simulationofrealisticusecase

5.1 Scenario

Within the FP7 project SmartC2Net we had access to data from a benchmark LV grid

with 42 buses and 130??? households. The background load data has been used to

create randomized samples for each household. The goal is to enhance the households

with heating HVACs, PV generation P

rated

= 4kW and for 10 households to add EV

charging points with various charging patterns (arrival, leave times, demand). The

HVACs’ starting inside temperature was randomly distributed between 18.1 and 21.9

degrees, the ouside temperature was 1 degree (January).

If we add to the setpoint following objective the Maximizing the gf (local generated

power), we obtain two eﬀects: ﬁrst, the average temperature in the houses is higher

and the total charged energy in the EVs is higher. This explains the second eﬀect: the

net supplied power by the grid to all houses is lower, because local generated power is

better used.

In order to evaluate the performance of the described system, we deﬁne s number

of key performance parameters (KPIs)

1. Avoidance of peaks and valleys of energy consumption in the grid. This can be

measured on several levels: total consumption proﬁle, load on each bus, etc.. Peak

reduction e.g 30% if users are willing to accept 1 degreed of temperature deviation.

[1]

2. renewable energy fed into the grid (less curtailing) while maintaining the power

quality

Cummulative

Energy/T

 Q

load

 (



(i,j)YBUS

cos(

 

)+B

sin(

 

))) = 0,i B (24)

min

 V

max

,i B (25)



 E

CEMS

/T 



kN |kj

load

,i B (26)



 E

CEMS

/T 



kN |kj

load

,i B (27)

For the sake of simplicity, we omit the current limitation constraints and the ap-

parent power limitation of the transformer (see XXX for a reference).

In the Kirchoﬀ equations () and (), P

is the power generated by the bus i,besides

the households which, in case P

load

< 0, would be considered generators. Therefore

= 0 except for the reference bus which supplies power to the LV grid.

The ﬂexibility constraints () and () can be better explained with the diagram in

Figure (). Assume 

> 0 For the selected period (e.g. j=2) the setpoint P

load

+ 

should correspond to the point B, and should be less than the ﬂexibility value E

CEMS

as expressen in Equation (26) Similarly, if 

< 0, the setpoint value B’ should be larger

than E

CEMS

, expressed by Equation (27).

Figure

5Simulationofrealisticusecase

5.1 Scenario

Within the FP7 project SmartC2Net we had access to data from a benchmark LV grid

with 42 buses and 130??? households. The background load data has been used to

create randomized samples for each household. The goal is to enhance the households

with heating HVACs, PV generation P

rated

= 4kW and for 10 households to add EV

charging points with various charging patterns (arrival, leave times, demand). The

HVACs’ starting inside temperature was randomly distributed between 18.1 and 21.9

degrees, the ouside temperature was 1 degree (January).

If we add to the setpoint following objective the Maximizing the gf (local generated

power), we obtain two eﬀects: ﬁrst, the average temperature in the houses is higher

and the total charged energy in the EVs is higher. This explains the second eﬀect: the

net supplied power by the grid to all houses is lower, because local generated power is

better used.

In order to evaluate the performance of the described system, we deﬁne s number

of key performance parameters (KPIs)

1. Avoidance of peaks and valleys of energy consumption in the grid. This can be

measured on several levels: total consumption proﬁle, load on each bus, etc.. Peak

reduction e.g 30% if users are willing to accept 1 degreed of temperature deviation.

[1]

2. renewable energy fed into the grid (less curtailing) while maintaining the power

quality

 Q

load

 (



(i,j)YBUS

cos(

 

)+B

sin(

 

))) = 0,i  B (24)

min

 V

max

,i B (25)



 E

CEMS

/T 



kN |kj

load

,i B (26)



 E

CEMS

/T 



kN |kj

load

,i B (27)

For the sake of simplicity, we omit the current limitation constraints and the ap-

parent power limitation of the transformer (see XXX for a reference).

In the Kirchoﬀ equations () and (), P

is the power generated by the bus i,besides

the households which, in case P

load

< 0, would be considered generators. Therefore

= 0 except for the reference bus which supplies power to the LV grid.

The ﬂexibility constraints () and () can be better explained with the diagram in

Figure (). Assume 

> 0 For the selected period (e.g. j=2) the setpoint P

load

+ 

should correspond to the point B, and should be less than the ﬂexibility value E

CEMS

as expressen in Equation (26) Similarly, if 

< 0, the setpoint value B’ should be larger

than E

CEMS

, expressed by Equation (27).

Figure

5Simulationofrealisticusecase

5.1 Scenario

Within the FP7 project SmartC2Net we had access to data from a benchmark LV grid

with 42 buses and 130??? households. The background load data has been used to

create randomized samples for each household. The goal is to enhance the households

with heating HVACs, PV generation P

rated

= 4kW and for 10 households to add EV

charging points with various charging patterns (arrival, leave times, demand). The

HVACs’ starting inside temperature was randomly distributed between 18.1 and 21.9

degrees, the ouside temperature was 1 degree (January).

If we add to the setpoint following objective the Maximizing the gf (local generated

power), we obtain two eﬀects: ﬁrst, the average temperature in the houses is higher

and the total charged energy in the EVs is higher. This explains the second eﬀect: the

net supplied power by the grid to all houses is lower, because local generated power is

better used.

In order to evaluate the performance of the described system, we deﬁne s number

of key performance parameters (KPIs)

1. Avoidance of peaks and valleys of energy consumption in the grid. This can be

measured on several levels: total consumption proﬁle, load on each bus, etc.. Peak

reduction e.g 30% if users are willing to accept 1 degreed of temperature deviation.

[1]

2. renewable energy fed into the grid (less curtailing) while maintaining the power

quality

 Q

load

 (



(i,j)YBUS

cos(

 

)+B

sin(

 

))) = 0,i  B (24)

min

 V

max

,i B (25)



 E

CEMS

/T 



kN |kj

load

,i B (26)



 E

CEMS

/T 



kN |kj

load

,i B (27)

For the sake of simplicity, we omit the current limitation constraints and the ap-

parent power limitation of the transformer (see XXX for a reference).

In the Kirchoﬀ equations () and (), P

is the power generated by the bus i,besides

the households which, in case P

load

< 0, would be considered generators. Therefore

= 0 except for the reference bus which supplies power to the LV grid.

The ﬂexibility constraints () and () can be better explained with the diagram in

Figure (). Assume 

> 0 For the selected period (e.g. j=2) the setpoint P

load

+ 

should correspond to the point B, and should be less than the ﬂexibility value E

CEMS

as expressen in Equation (26) Similarly, if 

< 0, the setpoint value B’ should be larger

than E

CEMS

, expressed by Equation (27).

Figure

5Simulationofrealisticusecase

5.1 Scenario

Within the FP7 project SmartC2Net we had access to data from a benchmark LV grid

with 42 buses and 130??? households. The background load data has been used to

create randomized samples for each household. The goal is to enhance the households

with heating HVACs, PV generation P

rated

= 4kW and for 10 households to add EV

charging points with various charging patterns (arrival, leave times, demand). The

HVACs’ starting inside temperature was randomly distributed between 18.1 and 21.9

degrees, the ouside temperature was 1 degree (January).

If we add to the setpoint following objective the Maximizing the gf (local generated

power), we obtain two eﬀects: ﬁrst, the average temperature in the houses is higher

and the total charged energy in the EVs is higher. This explains the second eﬀect: the

net supplied power by the grid to all houses is lower, because local generated power is

better used.

In order to evaluate the performance of the described system, we deﬁne s number

of key performance parameters (KPIs)

1. Avoidance of peaks and valleys of energy consumption in the grid. This can be

measured on several levels: total consumption proﬁle, load on each bus, etc.. Peak

reduction e.g 30% if users are willing to accept 1 degreed of temperature deviation.

[1]

2. renewable energy fed into the grid (less curtailing) while maintaining the power

quality

Figure 4: Graphical interpretation of constraints (21) and

(22)

5 Simulation experiments

5.1 Scenario

Within the FP7 project XY (to be named in the ﬁ-

nal submission) we had access to data from a bench-

mark residential LV grid in a rural area in Denmark,

with 42 buses and 130 households. The background

load data has been used to create randomized samples

for each household. Already with the measured con-

sumption data, the grid was in winter evening hours

quite loaded, as the voltages at some buses reached

lows of 95%.

In the simulation, all the households have been en-

hanced with 5kW HVACs used for heating, and with

PV panels with P

rated

= 4kW. Ten houses have EV

charging points associated to various charging pat-

terns (plug-in, plug-out times, energy demands). The

HVACs’ starting inside temperature was randomly

distributed between 18.1 and 21.9 degrees, the ouside

temperature was 1 degree Celsius (January).

The ﬁrst set of simulation experiments concentrate

on time horizons less of one day in order to observe

microscopically the convergence of the energy control

loop, the rolling planning with a look ahead period of

six hours, the voltage changes, etc.

The system in Figure 3 has been impleented

in Java, using for the optimization tasks the MIP

solver Gurobi and for the nonlinear power ﬂows the

AMPL/minos environment. A six hours simulation

run on a MacBook Pro machine (2GHz Inter core i7)

lasted around 150 seconds.

5.2 Simulation results

The simulation of the controller operation should con-

ﬁrm that we can schedule higher loads than in the cur-

rent grid in such a way, that the grid infrastructure

needs not be enhanced.

For the simulation, we selected a reduced number

of 38 houses that have at 2pm an initial inside temper-

ature randomly distributed between 18.1 and 21.9 de-

grees Celsius, the limits being 18 respectively 22 de-

grees. The PVs are switched off for this experiment.

Because of the lower number of houses in the exper-

iment, the voltage limits have been tightened from

10% down to 5% around the nominal voltage. Four

of the 10 EVs charge during this time horizon with

a maximum charging power of 8 kW. The operating

point of the loads has been ﬁrst observed, then the LV

grid setpoint curve has been set to constant 50 KW,

and after 5 hours to 30kW.

We observe at each calculation step (T=15 min-

utes) the distribution of the loads on the buses: the

dark heating periods in Figure 5 are alternating among

the households. The light grey regions correspond to

loads between 1 and 4.9 kW and are mainly caused

by EV charging. The rest is background load.

Following the ﬁrst part of the objective (16), the

setpoint will be set as close as possible to the load,

max.%ﬂexibility%

min.%ﬂexibility%

Figure 4: Graphical interpretation of constraints (23) and

(24). The planned load curve is situated between the ﬂexi-

bility limiting curves.

5 SIMULATION EXPERIMENTS

5.1 Scenario

Within the FP7 project SmartC2net (SmartC2Net) we

used a scaled down version benchmark residential

LV grid in a rural area in Denmark with 53 buses,

to which a number of 38 households are connected.

The measured load has been used to derive the non-

ﬂexible load for each household. The original grid

was already in the winter evening hours quite loaded,

as the voltages at some buses reached a low of 95%.

In the simulation, all the households have been en-

hanced with 5kW HVACs used for heating, and with

PV panels with P

rated

= 4kW. Ten houses have been

conﬁgured with EV charging points associated to var-

ious parking periods and P

max

= 8kW. The HVACs’

starting inside temperature was randomly distributed

between 18.1 and 21.9 degrees, the outside tempera-

ture is 1

◦

C(January).

The simulation experiments have been performed

for a duration of 72 periods (18 hours) with a plan-

ning horizon of 6 hours. The system in Figure 3 has

been implemented in java, using for the optimization

tasks the MIP solver (Gurobi) and for the nonlinear

power ﬂows the AMPL/minos (AMPL) environment.

The 18 hours simulation was run on a MacBook Pro

machine (2GHz Inter core i7) and lasted around ﬁve

minutes.

UsingFlexibilityInformationforEnergyDemandOptimizationintheLowVoltageGrid

329

FP7-ICT-318023/ D4.1

Page 30 of 62

Figure 6. Topology of the low voltage residential grid. B denotes busses, L denotes cables and LD denotes

aggregated loads.

Table 2. Transformer station parameters.

Level

Ratings

Resistance [𝛀]

Reactance [𝛀]

Number of

taps

Voltage per tap [%

of nominal

voltage]

MV T1

50 MVA,

60/20 kV

(on-load)

1.25

MV T2

50 MVA,

60/20 kV

(on-load)

1.25

industry

1250 kVA,

20/0.4 kV

0.001

0.02

(off-load)

2.5

agriculture

200 kVA,

20/0.4 kV

0.002

0.05

(off-load)

2.5

commercial

400 kVA,

20/0.4 kV

0.004

0.04

(off-load)

2.5

residential

400 kVA,

20/0.4 kV

0.004

0.04

(on-load)

1.25

Figure 5: Low voltage benchmark grid.

5.2 Simulation Results

The simulation of the controller operation shows that

we can schedule higher loads than in the current grid

in such a way, that the grid infrastructure needs not be

enhanced.

We associated one house per bus, in total 38

houses and started the simulation at 6 AM during the

month of January. Because of the lower number of

houses in the experiment, the voltage limits have been

tightened from 10% down to 5% around the nominal

voltage.

In Figure 6 we illustrate the distribution of the

loads on the buses: the black colored heating periods

(more than 5kW) are alternating among the house-

holds represented on the columns of the diagram. The

light grey regions correspond to loads between 1 and

4.9 kW and are mainly caused by EV charging. The

uncolored rest is background load. Heating is more

frequent in the evening (towards the bottom of the ﬁg-

ure)

The overall system operation in energy closed

loop is illustrated in Figure 7, in which we plot the

sum of the bus loads and the sum of power setpoints

in the time from 6am to 12pm. We observe that loads

and setpoints follow each other. On the same axis are

shown the energy prices c

, relative to the base price

of 44,23 Euro/MW, and the effect of negative prices

on the consumption increase.

Considering a certain bus in detail, the load and

setpoint values converge as well. The load and set-

points of household LD2 are shown in Figure 8. EV

charging occurs from periods 12 to 28 and from 40 to

64). Heating takes place in period 28 and from 62 to

64. Note that the setpoint that is limited by the voltage

and current limits is only partially followed by actual

CEMS load.

Figure 6: Schedule of consumption load among the CEMS

during the simulation.

-40

-20

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71

Power [kW]

relative price [€/MW]

Time periods

total load relative energy price total ref. power

Figure 7: Total load and total reference power (setpoint)

during the simulation. Prices are relative to the base price.

-2

-1

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70

Power&[kW]&

Time&periods&

Load at ld2 Setpoint at LD2

Figure 8: Load and setpoint at LD2 during the simulation.

In correlation with the setpoint (and the load) we

depict in Figure 9 the voltage evolution at LD38,

which is situated at the end of a feeder. The voltage

constraint in (19) V

min

= .95 is often hit during lunch

time and in the evening.

In a further series of simulations, we examine the

performance of the EV charging. Several factors have

SMARTGREENS2015-4thInternationalConferenceonSmartCitiesandGreenICTSystems

330

!"#$%

!"#&%

!"#'%

!"#(%

!"#)%

!"#*%

!"#+%

!"##%

,"!,%

-./01

23%

Voltage

3.4%-10543%62&+%

7$%

,% &% (% *% #% ,,%,&%,(%,*%,#%$,%$&%$(%$*%$#%&,%&&%&(%&*%&#%',%'&%'(%'*%'#%(,%(&%((%(*%(#%),%)&%)(%)*%)#%*,%

Load%

Figure 9: Setpoint and voltage at the household LD38 dur-

ing the simulation.

18.00

18.20

18.40

18.60

18.80

19.00

19.20

19.40

19.60

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70

°Celsius

Time periods

PV#on# PV#oﬀ#

Figure 10: Comparison of average inside temperature dur-

ing the simulation with and without PV.

an impact, such as the local generated power from PV

and the energy price, both a function of the charging

time of day.

The local generation does not appear in the power

ﬂows in the grid, but has an impact on the inside house

temperature and on the energy stored in the batteries.

Figure 10 compares the inside temperature, aver-

aged over the houses: if PVs are on, the temperature

increases during the sunny hours. The same effect is

observed with the charged energy E

, in Table 2. In

general (during sunny hours) the PV generation adds

energy to the battery (not much because of the low PV

generation in winter).

Table 2: Comparison of EV charged energy in percent from

max

during the day hours, with and without PV, (** in

[kWh], * in % of D

max

BUS EV parking E

* E

* D

min

max

noPV PV * **

LD1 8am-12am 19 21.3 19 8.8

LD2 4pm-7pm 55 55 47 11.6

LD3 1pm-11pm 67 62 45 8.6

LD5 3pm-6pm 45.6 45.6 45.6 8.0

LD13 11am-4pm 37 43 37 6.8

LD30 9am-3pm 60.5 73 60.5 7.2

LD32 4pm-8pm 78 78 78 5.9

LD33 11am-4pm 45 47 45 8.4

LD34 6pm-9pm 22 22 22 6.8

5.3 Discussion

The described system is complex as it includes sev-

eral load models and a lot of constraints that stabilize

its operation, such as energy prices, limitation of cur-

rents and voltages, ﬂexibility limits, to consider only

a part. For the sake of a comparison, we assume that

prices have no inﬂuence and that the aggregation con-

troller provides each household with the energy it asks

for. Note that, even in this particular case, a six hours

load plan exists both at the aggregator and the CEMS

side, and that correct heating and charging function-

ality are not affected. One evaluation criterium is the

power quality, e.g. the frequency of the under-voltage

occurances, in our case voltages under 95% of the

nominal value. The simulation creates peak loads as

expected, such that 8.4% of the voltage measurements

are below the limit, compared to zero occurances, if

the aformentioned constraints were active, see Figure

11.

10"

20"

30"

40"

50"

60"

70"

80"

90"

100"

0.84" 0.85" 0.86" 0.87" 0.88" 0.89" 0.9" 0.91" 0.92" 0.93" 0.94" 0.95"

under&voltage-

occurances-

Voltage-[pU]-

Figure 11: Simulation without price information and with-

out voltage limit checks. Histogram of under-voltage occu-

rances.

6 CONCLUDING REMARKS AND

FURTHER RESEARCH

In this work we address the energy management of

distributed energy resources using power and energy

ﬂexibility information. In the selected residential sce-

nario, we deﬁne two interconnected controller enti-

ties, the CEMS controller and the aggregated energy

controller, and the appropriate energy optimization

models. The approach is based on forward planning

and optimized scheduling. Load predictive models

are crucial for the demand side management mech-

anism presented. Day ahead prices are used to penal-

ize or encourage demand at certain times of the day.

Eventual congestion is avoided by limiting the power

ﬂows (voltages and currents). If we relax the condi-

tions above, the power quality deteriorates drastically.

In an experiment with a moderately loaded grid we

UsingFlexibilityInformationforEnergyDemandOptimizationintheLowVoltageGrid

331

obtained 8.4% under voltage events from a total num-

ber of 3024 voltage measurements in the whole LV

grid.

The beneﬁt of using the ﬂexibility information to

control the assets is difﬁcult to quantify in normal

operation conditions: the EVs are charged to the re-

quired amount and the temperature is the houses re-

mains within limits. We think that the real beneﬁts

of this architecture will be better visible in real world

and failure cases, to be studied in the future:

• errors in the prediction of charging activities pa-

rameters such as plugin and leaving time, demand,

of heating requirements, of non-ﬂexible load, of

the solar irradiation, etc.

• failure through the temporary disconnection of the

communication network between the controllers,

or failure of the metering data collection. Normal

operation of loads and generators would continue

for longer time in our proposed system than in a

system without ﬂexibility information exchange.

Finally, in this work it has been assumed that the

aggregated energy management is done by the DSO,

with input from the market actors (prices, available

energy, etc.). However, if this functionality is imple-

mented by a third party as part of a demand response

system, then the grid topology information might not

be available at the third party. In such a case a future

system architecture should provide better interactions

between DSO and market actors, and in the same time

it should provide cooperative decisions vis-a-vis the

consumers, similarly to the joint optimization prob-

lem solved by the aggregator.

ACKNOWLEDGEMENTS

The research leading to these results has received

funding from the European Communitys Seventh

Framework Programme (FP7/2007-2013) under grant

agreement no 318023 for the SmartC2Net project.

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Biegel, B., Andersen, P., Stoustrup, J., Hansen, L. H.,

and Tackie, D. V. (2013, June). Information model-

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In American Control Conference (ACC), 2013 (pp.

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Sundstrom, O.; Binding, C., ”Flexible Charging Optimiza-

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Grid Constraints,” IEEE Transactions on Smart Grid,

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Lopes, J. A. P., Soares, F. J., and Almeida, P. M. R. (2011).

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Group, Smart Grid Reference Architecture.

http://ec.europa.eu/energy/gas electricity/ smart-

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Harbo, S., and Biegel, B. (2013, October). Contracting ﬂex-

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