integration of demand response with supply/demand … deliverables/d4_2.pdf · management variables...

This project has received funding from the European

Union’s Horizon 2020 research and innovation

programme under grant agreement No 768619

The RESPOND Consortium 2019

Integrated Demand REsponse

SOlution Towards Energy

POsitive NeighbourhooDs

WP4 ICT enabled cooperative demand

response model

T4.2 INTEGRATION OF DEMAND RESPONSE WITH

SUPPLY/DEMAND SIDE MANAGEMENT

D4.2 Demand response optimization

model

Ref. Ares(2019)6063634 - 30/09/2019

WP4 ICT ENABLED COOPERATIVE DEMAND RESPONSE MODEL

D4.2 DEMAND RESPONSE OPTIMIZATION MODEL

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PROJECT ACRONYM RESPOND

DOCUMENT D4.2 Demand response optimisation model

TYPE (DISTRIBUTION LEVEL) ☐ Public

☒ Confidential

☐ Restricted

DELIVERY DUE DATE 30.09.2019.

DATE OF DELIVERY 30.09.2019.

STATUS AND VERSION FINAL, 1.0

DELIVERABLE RESPONSIBLE IMP

CONTRIBUTORS DEXMA

AUTHOR (S) Marko Jelić, Nikola Tomašević (IMP)

OFFICIAL REVIEWER(S) Iker Esnaola (TEK)



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DOCUMENT HISTORY

Version ISSUE DATE CONTENT AND CHANGES

V0.1 15.8.2019. Draft version

V0.2 25.9.2019. Reviewer comments

V1.0 26.9.2019. Final version with reviewer comments integrated



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This deliverable describes a linear programming-based methodology for solving the optimization

problem with special regard to DR related optimizations. Namely, with the addition of load

management variables and constraints and formulated around the Energy Hub concept of

modelling energy distribution through transmission and conversion, the proposed system has the

capabilities of considering demand forecasts, renewable generation forecasts and grid supply

limitations and to facilitate either DR events implied by variable pricing profiles or by explicitly

defining instances of time in which any load deviation is to be penalized in addition to the cost

function that minimizes costs for end users.

The proposed methodology is instantiated for a single-household model for each pilot site, and

with one of them assumed as a reference, the methodology is tested using implied DR with slightly

modified pricing and synthetized load forecast and renewable generation forecast. This example

successfully demonstrated that both load and power import manipulations can be performed by

defining the aforementioned DR events.

EXECUTIVE SUMMARY



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TABLE OF CONTENTS

EXECUTIVE SUMMARY _____________________________________________________________ 4

TABLE OF CONTENTS ______________________________________________________________ 5

LIST OF FIGURES __________________________________________________________________ 6

LIST OF TABLES ___________________________________________________________________ 7

ABBREVIATIONS AND ACRONYMS __________________________________________________ 8

1. INTRODUCTION __________________________________________________________________ 9

2. ENERGY HUB MODELING________________________________________________________ 11

2.1 MODELING FUNDAMENTALS _____________________________________________________________ 11

2.2 FUNDAMENTAL (ENERGY MANAGEMENT) CONSTRAINTS _______________________________________ 13

2.3 SUPPLEMENTARY (LOAD MANIPULATION) CONSTRAINTS _______________________________________ 15

2.3.1 VARIANT 1 – INDIVIDUAL LOADS _________________________________________________________________ 16

2.3.2 VARIANT 2 – AGGREGATED LOADS________________________________________________________________ 18

2.4 BOUNDARY CONDITIONS ________________________________________________________________ 20

2.4.1 VARIANT 1 ___________________________________________________________________________________ 20

2.4.2 VARIANT 2 ___________________________________________________________________________________ 21

2.5 OBJECTIVE FUNCTION ___________________________________________________________________ 21

3. INDIVIDUAL USER PILOT MODELS _____________________________________________________ 23

3.1 AARHUS ______________________________________________________________________________ 23

3.2 MADRID ______________________________________________________________________________ 25

3.3 ARAN ISLANDS _________________________________________________________________________ 26

4. OPTIMIZATION USE CASES ___________________________________________________________ 29

4.1 IMPLICIT DR EVENT _____________________________________________________________________ 29

5. CONCLUSION ___________________________________________________________________ 33

6. REFERENCES___________________________________________________________________ 34



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LIST OF FIGURES

FIGURE 1 - RESPOND OPTIMIZATION LOOP .................................................................................................. 9

FIGURE 2 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 1) ................................. 14

FIGURE 3 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 2) ................................. 15

FIGURE 4 - EXAMPLE OF LOAD SHIFTING IN TIME FROM NOMINAL LOAD SCHEDULE (TOP) WITH SHIFTING

WINDOWS TO THE OPTIMIZED LOAD SCHEDULE (BOTTOM) ..................................................................... 17

FIGURE 5 - ILLUSTRATION OF A DR EVENT LOAD DEVIATION ..................................................................... 19

FIGURE 6 - AN EXAMPLE OF MODELING A SINGLE USER WITH A SINGLE ENERGY HUB............................. 23

FIGURE 7 - AARHUS PILOT SITE TOPOLOGY ................................................................................................. 23

FIGURE 8 - MADRID PILOT SITE TOPOLOGY................................................................................................. 25

FIGURE 9 - ARAN PILOT SITE TOPOLOGY (TYPE 1 TOP, TYPE 2 MIDDLE AND TYPE 3 BOTTOM) ................. 28

FIGURE 10 - PRICE PROFILES USED FOR DEFINING AN IMPLICIT DR EVENT................................................ 30

FIGURE 11 – PREDICTED AND OPTIMIZED LOAD PROFILES ......................................................................... 31

FIGURE 12 – NOMINAL AND OPTIMIZED INDIVIDUAL CARRIER IMPORT PROFILES ................................... 32



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LIST OF TABLES

TABLE 1 – VARIABLE DESCRIPTIONS FOR THE CORE ENERGY MANAGEMENT ENERGY HUB CONSTRAINTS

..................................................................................................................................................................... 11

TABLE 2 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 1)

CONSTRAINTS .............................................................................................................................................. 12

TABLE 3 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 2)

CONSTRAINTS .............................................................................................................................................. 12



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ABBREVIATIONS AND ACRONYMS

DR Demand response

LP Linear programming

MILP Mixed-integer linear programming

RES Renewable energy source

DHW Domestic hot water

STC Solar thermal collector

PV Photovoltaic



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1. INTRODUCTION

As residential Demand Response (DR) programmes are yet to be explored in depth, there are

not that many solutions for this problem in related literature. In this regard, the RESPOND project

proposes a novel solution through the use of optimization in a control loop presented in Figure 1.

It takes into consideration day-ahead energy prices, the forecasted renewable production and the

predicted loads from individual users aggregated into a neighborhood profile. Using the supposed

demand flexibility, the optimizer shifts the loads in intensity and in time to generate a profile that

is the most cost-effective for end users and most stable for the grid operator. However, given that

the RESPOND project is all about maintaining grid stability and making use of the untapped

potential of residential DR capacities, the DR events hold a special place in the optimization

process. The system allows for load shifting to occur both in cases where the convenience is

dictated by current pricing (low prices drive loads up, and soaring prices drive loads down) and

by direct requests from the utility company or DR aggregator by means of predefined DR events.

When the optimization engine has completed its run, an “optimal neighborhood profile” is available

for the next day. If this profile is upheld by the end users, lowest cost and maximum stability are

obtained. However, as the day progresses, the aggregated demand may slightly or more

significantly differ from what the optimizer has deemed best. That’s where the energy monitoring

service comes in. It looks at the optimized profile and the aggregated profile of an entire

neighborhood that is continuously being measured. Whenever a deviation is noticed, for example

when actual load levels are higher than optimal, this service looks at data from individual

households, scans for currently active appliances that are considered to be large energy

FIGURE 1 - RESPOND OPTIMIZATION LOOP



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consumers, and issues notifications trough the RESPOND dashboard and mobile app that

suggest to the end user that the activation of that appliance should be deferred to a later time. By

doing this, the user may obtain a monetary reward and maintain grid stability. Thus, the energy

management process is semi-automatized resulting in a minimal additional burden for the end

user, while maintaining full control since actions are not performed without explicit user

authorization.

This deliverable describes the core methodology behind the optimization process, the model that

was used to depict the topology of the system in all three pilot sites, and some variations of that

model that are introduced for individual and aggregate load management purposes. It also

describes a potential use case in which a DR event is induced using peak pricing in order to force

load decreases.



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2. ENERGY HUB MODELING

2.1 MODELING FUNDAMENTALS

A mixed-integer linear programming (MILP) model is most commonly defined as a problem where a vector of variables

𝑥 = [𝑥1 𝑥2 ⋯ 𝑥𝑚]𝑇 ∈ ℝ𝑚

is to be determined as an argument that optimizes (most commonly minimizes) a product with a predefined objective function 𝑓 as given by

𝑥opt = arg𝑥{min{𝑓𝑇𝑥}}.

At the same time, the optimal solution vector 𝑥opt must also adhere to a set of constraints. These constraints are split into five different categories being equality and inequality constraints, lower and upper bounds and integer constraints. Since a mixed-integer programming problem is being discussed, an

integer subvector 𝑥int of 𝑥 is defined as

𝑥𝑖𝑛𝑡 = [𝑥1int 𝑥2

int ⋯ 𝑥𝑚𝑖𝑛𝑡int ]

𝑇

and with a lower 𝑙b bound and upper 𝑢b bound vectors given as

𝑙b = [𝑙1 𝑙2 ⋯ 𝑙𝑚]𝑇

𝑢b = [𝑢1 𝑢2⋯ 𝑢𝑚]𝑇

the aforementioned constraints can be posed as

𝐴eq𝑥 = 𝑏eq

𝐴ineq𝑥 ≤ 𝑏ineq

(∀𝑖)(𝑙𝑖 ≤ 𝑥𝑖 ≤ 𝑢𝑖) (∀𝑖)(𝑥𝑖

int ∈ 𝑍, 𝑍 ⊂ ℤ).

The vector of variables 𝑥 is formed by arranging a set of all variables (input power, export power,

etc.) required for model simulation at each time step during the simulated horizon.

The variables used within the model are summarized in Table 1, Table 2 and Table 3.

TABLE 1 – VARIABLE DESCRIPTIONS FOR THE CORE ENERGY MANAGEMENT ENERGY HUB CONSTRAINTS

Label Variable name Variable type

𝑃in Imported power (from renewable sources, grid, etc.) Float

𝑃cin Power sent to the conversion stage Float

𝑃cout Power obtained from the conversion stage Float

𝑄in Power flow to or from the input stage storage Float

𝑄out Power flow to or from the output stage storage Float

𝐿 Load (demand) Float

𝑃out Power sent to the output stage Float

𝑃exp Exported power Float

𝑞in Converted power flow to or unconverted flow from input storage Float

𝐸in Input stage storage state of charge (available energy) Float

𝑞out Converted power flow to or unconverted flow from output storage Float



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𝐸out Output stage storage state of charge (available energy) Float

TABLE 2 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 1) CONSTRAINTS


𝑦 Device ON/OFF indicator Boolean (0/1)

𝑧 Device start indicator Boolean (0/1)

𝑑+ Positive load (power) deviation Float

𝑑− Negative load (power) deviation Float

𝐼(𝑑+) Indicator of positive load (power) deviation Boolean (0/1)

𝐼(𝑑−) Indicator of negative load (power) deviation Boolean (0/1)

TABLE 3 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 2) CONSTRAINTS


Δ𝐿+ Positive load (power) deviation Float

Δ𝐿− Positive load (power) deviation Float

𝐼(Δ𝐿+) Indicator of positive load (power) deviation Boolean (0/1)

𝐼(Δ𝐿−) Indicator of negative load (power) deviation Boolean (0/1)

To be operated programmatically, the variable values must be reordered into a flattened format.

Accordingly, what was, for example, natively considered as a 2D matrix like the imported power

that spans over time trough columns and over carriers over rows, written as

𝑃in = [

𝑃in(𝑖 = 1, 𝑘 = 1) 𝑃in(𝑖 = 1, 𝑘 = 2) ⋯ 𝑃in(𝑖 = 1, 𝑘 = 𝑛)

𝑃in(𝑖 = 2, 𝑘 = 1) 𝑃in(𝑖 = 2, 𝑘 = 2) ⋯ 𝑃in(𝑖 = 2, 𝑘 = 𝑛)⋮

𝑃in(𝑖 = 𝑛c, 𝑘 = 1)⋮

𝑃in(𝑖 = 𝑛c, 𝑘 = 2)⋱⋯

⋮𝑃in(𝑖 = 𝑛c, 𝑘 = 𝑛)

]

where 𝑖 represents the carrier counter, 𝑛c the total number of carriers, 𝑘 the time counter and 𝑛

the time horizon length (number of time steps during the simulation), is reordered into a vector of

format

𝑃in = [𝑃in(𝑖 = 1, 𝑘 = 1), 𝑃in(𝑖 = 2, 𝑘 = 1), ⋯ , 𝑃in(𝑖 = 𝑛c, 𝑘 = 1), 𝑃in(𝑖 = 2, 𝑘 = 1), ⋯ , 𝑃in(𝑖 = 𝑛c, 𝑘

= 𝑛)]𝑇 .

However, some of the variables represent individual appliances and not individual carriers. For

example, the device on/off status variable 𝑦 that might be natively considered as a 2D matrix like

𝑦 = [

𝑦(𝑖 = 1, 𝑘 = 1) 𝑦(𝑖 = 1, 𝑘 = 2) ⋯ 𝑦(𝑖 = 1, 𝑘 = 𝑛)

𝑦(𝑖 = 2, 𝑘 = 1) 𝑦(𝑖 = 2, 𝑘 = 2) ⋯ 𝑦(𝑖 = 2, 𝑘 = 𝑛)⋮

𝑦(𝑖 = 𝑛a, 𝑘 = 1)⋮

𝑦(𝑖 = 𝑛a, 𝑘 = 2)⋱⋯

⋮𝑦(𝑖 = 𝑛a, 𝑘 = 𝑛)

]

where 𝑖 represents the appliance number, 𝑛a the total number of appliances, 𝑘 the time counter

and 𝑛 the horizon length, is reordered into a new flattened-out form of

𝑦 = [𝑦(𝑖 = 1, 𝑘 = 1), 𝑦(𝑖 = 1, 𝑘 = 2), ⋯ , 𝑦(𝑖 = 1, 𝑘 = 𝑛), 𝑦(𝑖 = 2, 𝑘 = 1), ⋯ , 𝑦(𝑖 = 𝑛𝑎, 𝑘 = 𝑛)]𝑇 .

In further text, depending on the appropriate contexts, variables are used as both matrices and

vectors where such an application is deemed more suitable.



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2.2 FUNDAMENTAL (ENERGY MANAGEMENT) CONSTRAINTS

The fundamental constraints of the Energy Hub system depict energy flow and energy transformations through a set of stages:

• Input (raw) energy storage

• Input energy transformation

• Energy conversion

• Energy export

• Output energy transformation

• Output (user) energy storage

• Loads

Let 𝑃in(𝑘) be the imported power from a certain energy carrier (for example thermal (hot water) energy obtained by a solar thermal collector system as will be described in D4.4 or electric energy imported from the grid). The imported power can then be either stored within the input storage stage or sent further to the rest of the system using appropriate transformers and convertors. According to the law of conservation of power for the input stage, the balance

(∀𝑘)(𝑃in(𝑘) = 𝑆in𝑄in(𝑘) + 𝐹in𝑃cin(𝑘))

must hold. In this equation, 𝑄in depicts the instantaneous power that is being sent or obtained from the

input storage and 𝑃cin(𝑘) is the instantaneous power being dispatched to the conversion stage. Furthermore, the power dispatched to the storage system is converted into energy with a charge/discharge rate of 𝑞in through the expression

(∀𝑘) (𝑄in(𝑘) = 𝑆qin𝑞in(𝑘)).

The available energy (state of charge, SOC) of the storage system is given by an integral

expression that accumulates input and output energy

(∀𝑘 < 𝑁𝑇𝑠)(𝐸in(𝑘 + 1) = 𝐸in(𝑘) + 𝑞in(𝑘)𝑇𝑠)

with an initial condition given by

𝐸in(1) = 𝐸in1

defining the SOC in the first timestep which is most commonly set to zero unless the optimization

is being performed on consecutive time intervals where the final condition of one interval

influences the initial condition of the next one. The energy that is not being stored within the input

system is sent to the energy conversion stage as is given by

(∀𝑘)(𝑃cout(𝑘) = 𝐶𝑃cin(𝑘))

The output power 𝑃cout of the conversion stage can be exported back to the grid or sent to the

output stage. This routing is given by

(∀𝑘)(𝑃out(𝑘) = 𝑃cout(𝑘) − 𝑃exp(𝑘))

with the option of setting certain carrier’s export power to a predefined value (most commonly

used to block exporting power imported from the grid back to the grid) by

(∀𝑘)(𝐷exp𝑃exp(𝑘) = 𝑅exp)



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where 𝐷exp is a matrix that defines what carrier is to have a restricted export and 𝑅exp sets those

fixed values.

The power 𝑃out that is left over from the export process is sent to the output transformation stage

defined by a matrix 𝐹out that aggregates all the carriers into a given number of values depending

on the number of load types. This operation is obtained through the equation

(∀𝑘)(𝐿(𝑘) = 𝐹out𝑃out(𝑘) − 𝑆out𝑄out(𝑘))

where 𝐿 is the demand vector that needs to be fulfilled and 𝑄out is the power that can be stored

for later use within the output storage system. As was the case with the input, the output can also

feature a storage option. The charge/discharge rate 𝑞out is calculated using

(∀𝑘)(𝑄out(𝑘) = 𝑆qout𝑞out(𝑘)).

Analogous to the input stage, the output storage energy availability is calculated using an integral

expression

(∀𝑘 < 𝑁𝑇𝑠)(𝐸out(𝑘 + 1) = 𝐸out(𝑘) + 𝑞out(𝑘)𝑇𝑠)

and an initial condition is set with

𝐸out(1) = 𝐸out1

which concludes the set of equations governing the energy management aspect of the Energy

Hub system. However, additional equations must be added for load management mechanisms.

This document analyses two use cases for load management: one in which the loads are

FIGURE 2 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 1)



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managed individually on a per-appliance basis and one in which the loads are managed jointly,

as would be the case when viewing multiple users from a neighbourhood perspective or when

individual appliances for a single user are not accessible through sensors and actuators. Figure

2 illustrates the constraints that govern energy flow through the Energy Hub model with overlaid

formulas in accordance with the first load management variant. Here, the equality constraints are

denoted with a blue outline while the inequality constraints are denoted with an orange outline.

On the other hand, Figure 3 illustrates the second variant of energy management, with core

constraints being denoted with a blue outline and the load management constraints denoted with

a red outline.

2.3 SUPPLEMENTARY (LOAD MANIPULATION) CONSTRAINTS

The following subsections go into detail about how load manipulations are modelled. Generally,

there are to main types of approach in this regard. The first one (variant one) is where each

appliance’s activation are managed individually i.e. the appliance activations shifts in time and in

power value are traceable meaning that an optimal schedule can be obtained on a per appliance

basis. Such an approach is convenient when users are willing to provide detailed information

regarding the ways in which they use their appliances: the appliance’s nominal power draw, power

deviations if applicable, nominal activation timeframes and appropriate shifting windows in which

the appliances are to be moved around in time in order to optimize a given criterion function. The

second one (variant two) regards loads as an aggregate value, whether it be an aggregate of

multiple appliances within a single household (as will be discussed in this deliverable) or an

aggregate of multiple households that form a neighbourhood (as will be discussed in D4.3). Such

an approach is considered as more feasible because the variations and data uncertainty of the

baseline load are levelled out when the aggregation is performed

Since the data available for the RESPOND project does not assume any appliance specific

scheduling in this regard, the latter approach is selected as the method of choice for the

RESPOND services. However, for the sake of describing the potentials of the proposed

methodology, both methods will be briefly described.

FIGURE 3 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 2)



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2.3.1 VARIANT 1 – INDIVIDUAL LOADS

Load 𝐿 in this regard is considered as either 𝐿fix which cannot be shifted in time and cannot be

shifted in value or 𝐿flex which can theoretically be shifted in both time and value. What’s more, the

individual appliance activations for some appliances which are named dispersible can be split into

multiple time instances. The modelling of this process starts with the introduction of the activation

indicator, i.e. an on/off state variable 𝑦𝑖 defied for each appliance 𝑖 by

𝑦𝑖(𝑘) ≜ { 0, appliance 𝑖 is off at 𝑡 = 𝑘𝑇𝑠

1, appliance 𝑖 is on at 𝑡 = 𝑘𝑇𝑠.

If we let 𝑃𝑖 be the power draw of 𝑖-tha appliance, the flexible load at the 𝑘-th time sample can be

written as

𝐿flex(𝑘) = ∑ 𝑃𝑖(𝑘)𝑦𝑖(𝑘)

𝑖

with the total load being expressed as

𝐿(𝑘) = 𝐿flex(𝑘) + 𝐿fix(𝑘)

However, the product being summed in the equation that defines the flexible load would

represents a nonlinear operation between two variables and as such cannot be incorporated

within a mixed-integer model in its previously defined format. To mitigate this issue, 𝑃𝑖 is divided

into three sperate values: nominal power draw 𝑃𝑖nom, positive power deviation 𝑑𝑖

+ and negative

power deviation 𝑑𝑖− from the nominal value, or in other words

𝐿flex(𝑘) = 𝑃𝑖nom𝑦𝑖(𝑘) + 𝑑𝑖

+(𝑘)𝑦𝑖(𝑘) + 𝑑𝑖−(𝑘)𝑦𝑖(𝑘).

However, this equation still cannot be incorporated into the MILP model because it also

incorporates a product between two variables. nevertheless, if 𝑑𝑖+ and 𝑑𝑖

− are constrained to

having nonzero values only when the appliance is turned on, this last expression can be

shortened to

𝐿flex(𝑘) = 𝑃𝑖nom𝑦𝑖(𝑘) + 𝑑𝑖

+(𝑘) + 𝑑𝑖−(𝑘).

Now, total load can be expressed as

(∀𝑘) (𝐿(𝑘) = ∑(𝑃𝑖nom𝑦𝑖(𝑘))

𝑖

+ ∑(𝑑𝑖+(𝑘) + 𝑑𝑖

−(𝑘)) + 𝐿fix(𝑘)

𝑖

).

Having in mind that 𝑃𝑖nom is set before the model is optimized, it can be deduced that this

expression now represents a linear combination of subvectors of 𝑥 and can therefore be

implemented as a MILP constraint.

Related literature [1] provides a classification in which elastic loads are either classified as being

energy-based, meaning that they must consume a predefined amount of energy within a specified

time window, or comfort-based, researched previously in [2], meaning that they must control an

environmental variable within a desired range. However, comfort-based appliances are not

treated by the RESPOND services as the appliances’ operations that are supposed to be

optimized only allow on/off controls. Therefore, only energy-based elastic appliances are

considered for the aspect of demand side management with an option to elastically adjust their



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power within given power tolerances. Accordingly, a set of windows (activation cycles) is defined

for each appliance 𝑖 with one of them

𝑤𝑖(𝑛)

(𝑘) ≜ { 0, 𝑘 is not in the window 𝑛, 𝑘 is in the window

defining the 𝑛-th window of 𝑖-th appliance by having nonzero values equal to 𝑛 at time instances

that belong to that window. This type of implementation provides the possibility for windows to be

discontinuous i.e. they can be split into a given number of segments. Having in mind that these

windows are also defined prior to problem optimization just like the nominal power, they can be

used to form an energy constraint

(∀𝑖, ∀𝑛) ( ∑ 𝑃𝑖nom

𝑤𝑖(𝑛)

(𝑘)=𝑛

𝑇𝑠 ⋅ 𝑦𝑖(𝑘) = 𝑃𝑖nom𝛥𝑡𝑖

(𝑛))

that states how a specific appliance 𝑖 must only be active a given amount of time so that the

amount of energy it spends during that activation cycle 𝑛 is equal to the product between nominal

power 𝑃𝑖nom and the length 𝛥𝑡𝑖

(𝑛) of nominal activation belonging to that window. Nevertheless,

FIGURE 4 - EXAMPLE OF LOAD SHIFTING IN TIME FROM NOMINAL LOAD SCHEDULE (TOP) WITH

SHIFTING WINDOWS TO THE OPTIMIZED LOAD SCHEDULE (BOTTOM)



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deviations in power also affect the total energy consumed, and so it is also stated that the sum of

power deviations must be equal to zero during a given window, as given by

(∀𝑖, 𝑘, 𝑛) ( ∑ (𝑑𝑖+(𝑘) + 𝑑𝑖

−(𝑘))

𝑤𝑖(𝑛)

(𝑘)=𝑛

= 0)

thus, finalizing the set of equality constraints required for the model. Nonetheless, these relations

are not sufficient for the model and some additional conditions must be applied in form of bounds.

2.3.2 VARIANT 2 – AGGREGATED LOADS

When the load is considered as an aggregated value it is not separated into individual appliances

but rather viewed through its nominal value and the appropriate positive and negative deviations.

In this context, the deviation is defined as the difference between the realized load value 𝐿 and a

predefined load profile 𝐿required, as would be defined by

Δ𝐿 = 𝐿required − 𝐿.

The general idea here is that at certain instances of time, some segments of the criterion function

would force the load profile 𝐿 to resemble the required one 𝐿required. This can be performed by

penalizing the load deviation in these time instances. However, when the load deviation is

positive, such a penalty should be positive and if the when the load deviation is negative, such a

penalty should be negative. However, it is impossible to know in advance when the difference

between the optimized load profile and the required one will be positive and when it will be

negative. This poses an issue because the criterion function is defined before the model is

optimized, and so these instances of time have to be known beforehand. However, this issue can

be mitigated by splitting the load deviation into positive and negative (in a similar manner as the

individual appliance power draw values are modelled using positive and negative deviations in

variant one). The last equation is now rewritten as

Δ𝐿(𝑘) = Δ𝐿+(𝑘) + Δ𝐿−(𝑘) = 𝐿required(𝑘) − 𝐿(𝑘).

However, no constraints are implemented to force positive load deviations to actually be positive

and negative load deviations to actually be negative. Therefore, two binary variables are

introduced to illustrate when the positive load deviation is active and when the negative load

deviation is active. Since the load must be bounded on each side by an upper and lower bound,

these indicators are connected with the aforementioned bounds with the expressions

Δ𝐿+(𝑘) ≤ +𝐼(Δ𝐿+(𝑘)) ⋅ Δ𝐿max+ (𝑘)

Δ𝐿−(𝑘) ≤ −𝐼(Δ𝐿−(𝑘)) ⋅ Δ𝐿max− (𝑘).

Concretely, Δ𝐿max+ and Δ𝐿max

− define the largest possible (by absolute value) positive and negative

deviations between the total (aggregated) load and the required profile. However, implementing

these two relations by themselves allows for both positive and negative load deviations to exist

simultaneously. However, the binary nature of them can be exploited to restrict only one of them

to be allowed to assume a nonzero value at a given timestep. This is obtained by

𝐼(Δ𝐿+(𝑘)) + 𝐼(Δ𝐿−(𝑘)) ≤ 1.



19 | 34

Finally, if the mode described above where to be optimized using a price-based objective function,

the optimizer would drop all load levels to their lowest possible values. Therefore, an additional

integral window constraint must be enforced to maintain the integral level of load to a value related

to the predicted energy consumption. Such a constraint is defined as

∑ 𝐿(𝑘)

𝑘2

𝑘=𝑘1

= ∑ 𝐿predicted(𝑘)

𝑘2

𝑘=𝑘1

where 𝑘1 and 𝑘2 represent the beginning timestep and ending timestep of the window for which

the constraint is to be applied. This constraint can be applied for the full-time horizon but can also

be applied, if required, multiple times for day/night consumption use cases and/or peak hour

consumption use cases.

Figure 5 illustrates a case where an Energy Hub with three types of loads is employed to enforce

a requested load profile during a DR event. Here, the load deviations between the load variable

and the requested profile (which equals 80% of the predicted load during the DR event) are

separately penalized and so the optimized load follows the requested profile during the DR event

and remains otherwise unconstrained in this regard.

FIGURE 5 - ILLUSTRATION OF A DR EVENT LOAD DEVIATION



20 | 34

2.4 BOUNDARY CONDITIONS

To fully define the model, the equality and inequality constraints are supplemented with a set of boundary constraints that define upper and lower limits for the aforementioned variables. Since the imported power values cannot be negative, a limit is imposed in form of

(∀𝑘)(0 ≤ 𝑃cin(𝑘), 𝑃cout(𝑘), 𝑃out(𝑘), 𝑃exp(𝑘) ≤ ∞).

On the other hand, the portion of imported power 𝑃in that comes from renewable sources 𝑃renew

has to be exactly equal the amount of energy that is being generated, while the power imported

from the grid can be viewed as virtually unlimited (lower than the highest power that can be

delivered)

𝑃renew(𝑘)0

} ≤ 𝑃in(𝑘) ≤ {𝑃renew(𝑘), from renewables

∞, from the grid.

At both the input and output stages, storage levels must be between the lowest possible (zero)

and highest possible (battery capacity) SOC and so

(∀𝑘)(0 = 𝑆𝑂𝐶inmin ≤ 𝐸in(𝑘) ≤ 𝑆𝑂𝐶in

min),

and

(∀𝑘)(0 = 𝑆𝑂𝐶outmin ≤ 𝐸out(𝑘) ≤ 𝑆𝑂𝐶out

max),

with 𝑄in and 𝑄out being limited by

(∀𝑘)(−𝑄inmax ≤ 𝑄in(𝑘) ≤ 𝑄in

max )

and

(∀𝑘)(−𝑄outmax ≤ 𝑄out(𝑘) ≤ 𝑄out

max)

where 𝑄max is the highest achievable charge rate, and thus also bounding 𝑞in and 𝑞out.

2.4.1 VARIANT 1

In the case of managing load through individual appliance, the total load 𝐿 only has a defined

lower bound equal to the value of fixed load since the flexible load is non-negative and thus

(∀𝑘)(𝐿fix(𝑘) ≤ 𝐿(𝑘)).

As mentioned before, both positive and negative deviations 𝑑𝑖+(𝑘) and 𝑑𝑖

−(𝑘) also have bounds

that are equal to a predefined upper and lower deviation limit, respectively, applied during

specified windows as follows

(∀𝑘, 𝑖, 𝑛) (0 ≤ 𝑑𝑖+(𝑘) ≤ {

0, 𝑤𝑖(𝑛)

(𝑘) ≠ 𝑛

𝑃dev+𝑖

max , 𝑤𝑖(𝑛)

(𝑘) = 𝑛)

(∀𝑘, 𝑖, 𝑛) (0, 𝑤𝑖

(𝑛)(𝑘) ≠ 𝑛

𝑃dev−𝑖

max , 𝑤𝑖(𝑛)

(𝑘) = 𝑛} ≤ 𝑑𝑖

−(𝑘) ≤ 0).

As for the indicator variables, the device starts 𝑧𝑖 has a lower bound of zero and upper bound of

one for all time samples i.e.



21 | 34

(∀𝑘, 𝑖)(0 ≤ 𝑧𝑖(𝑘) ≤ 1)

while the on/off state 𝑦𝑖 has the same bound within windows and both bounds set to zero outside

(∀𝑖, 𝑘, 𝑛) (0 ≤ 𝑦𝑖(𝑘) ≤ {0, 𝑤𝑖

(𝑛)(𝑘) ≠ 𝑛

1, 𝑤𝑖(𝑛)

(𝑘) = 𝑛).

A similar logic is employed as to limit the deviation indicators

(∀𝑖, 𝑘, 𝑛) (0 ≤ 𝐼(𝑑𝑖+(𝑘)), 𝐼(𝑑𝑖

−(𝑘)) ≤ {0, 𝑤𝑖

(𝑛)(𝑘) ≠ 𝑛

1, 𝑤𝑖(𝑛)

(𝑘) = 𝑛).

Finally, since the indicator variables should only assume a value of either zero or one, thus

rendering this problem to be classified as MILP rather than LP, we specify

(∀𝑘)(𝑦𝑖(𝑘), 𝑧𝑖(𝑘), 𝐼(𝑑𝑖+(𝑘)), 𝐼(𝑑𝑖

+(𝑘)) ∈ {0,1}).

2.4.2 VARIANT 2

As for the case in which the load is managed through its aggregated profile, a load tolerance limits

are imposed in form of two margins (upper and lower margin) between which the loads can be

adjusted. This is obtained by enforcing a limiting constraint as

(∀𝑘) ((1 + tol−)𝐿predicted(𝑘) ≤ 𝐿(𝑘) ≤ (1 + tol+)𝐿predicted(𝑘)).

In this regard, the load tolerance is mentioned in literature [3] to be in the range of −tol− = tol+ =

20%, however as research related to this topic is relatively scarce, other load tolerance values

will be tested within the RESPOND platform as well. Having in mind that the load difference

between the optimized profile and the required one is modeled using positive and negative load

deviations, these variables must also be limited using

(∀𝑘)(Δ𝐿+(𝑘) ≥ 0) and (∀𝑘)(Δ𝐿−(𝑘) ≤ 0).

Finally, the indicator variables that depict the activity of the aforementioned load deviations must

be equal to either one or zero thus rendering this problem also to be classified as MILP rather

than LP, as set by

(∀𝑘)(𝐼(Δ𝐿+(𝑘)), 𝐼(Δ𝐿−(𝑘)) ∈ {0,1}).

After adequate transformations, the given expressions can be morphed into the 𝐴eq, and 𝐴ineq

matrices and 𝑏eq, 𝑏ineq, 𝑙b and 𝑢b vectors defining the constraints from the MILP problem

definition. What remains to be set in order to complete the model used for optimization is the

objective function 𝑓.

2.5 OBJECTIVE FUNCTION

The main objective that is being considered within the RESPOND optimization process is the minimization of costs that would ultimately fall on the end users. Therefore, the most beneficial factor to the cost function are the costs of individual energy types. These values are modelled by setting the objective function 𝑓’s

values to the corresponding energy import/export prices. Since the energy import (𝑃in) usually costs money if it is being imported from the grid, the corresponding values of those elements of 𝑓 are set to positive



22 | 34

values that depict electricity prices at the given time. Also, if the local legislative allows for renewable energy generation subsidies, the elements of 𝑓 that correspond to energy imports from renewable sources are set to negative values that are given by the acting generation tariff. Furthermore, the user can also receive monetary gains by exporting excess energy back to the grid (𝑃exp) and so the corresponding values

should also be set to negative values dictated by the acting feed-in tariff program. If 𝑖 and 𝑗 represent import and export power energy carriers, 𝛼 represents the costs of importing energy and 𝛽 represents the costs of exporting energy, the overall operational cost can be obtained as

𝐶 = ∑ ∑ 𝛼𝑖(𝑘)𝑃in(𝑖, 𝑘) +𝑘

∑ ∑ 𝛽𝑗(𝑘)𝑃exp(𝑖, 𝑘)𝑘𝑗

.𝑖

However, to enable simultaneous optimizations that include specific DR events in order to force the load to uphold the requested profile, the mentioned cost function is extended with the addition of load deviation penalization as is given by

𝐶′ = ∑ ∑ 𝛼𝑖(𝑘)𝑃in(𝑖, 𝑘) +𝑘

∑ ∑ 𝛽𝑗(𝑘)𝑃exp(𝑖, 𝑘)𝑘𝑗

+ ∑ (𝑤d+(𝑘)Δ𝐿+ + 𝑤d

−Δ𝐿−)𝑘

.𝑖

In this mixed criterion, the penalization factors 𝑤d+ and 𝑤d

− are supposed to have non-zero values only

when a specific DR event is active, with 𝑤d+ being strictly positive and 𝑤d

− being strictly negative in those

cases in order to force the deviations into their minimum optimal value. When defining these values, a balance should be made between the raw operational costs as given by 𝐶 and the additional factor

introduced in 𝐶′, i.e. the load penalization should not be significantly greater or smaller than the operational costs.

Besides the cost or running the system, other criteria are to be monitored as well. One of them is a renewable energy source (RES) share in the imported power and it can be calculated from

𝑅𝐸𝑆share =∑ 𝑃in(renewables, 𝑘)𝑘

∑ 𝑃in(all carriers, 𝑘)𝑘⋅ 100%.

Another interesting indicator of the ecological impacts of running the system are the effective CO2

emissions of running the system. This value can be estimated using the corresponding grid power fuel mix

and life cycle emissions provided by [4] through the expression

CO2 emiss = ∑ ∑ 𝑐𝑖𝑃𝑖𝑛(𝑖, 𝑘)

𝑖𝑘

where 𝑐𝑖 represents the carbon footprint value of the 𝑖-th energy carrier. These values can even be

included within the cost criterion in order to create a multi-criteria optimization function that would include

multiple factors.



23 | 34

3. INDIVIDUAL USER PILOT MODELS

The RESPOND project is to be deployed in three pilot sites: Aarhus (Denmark), Madrid (Spain)

and Aran Islands (Ireland). In the context of this deliverable, the process of modelling individual

users using the Energy Hub structure is described in detail. Figure 6 provides an illustration of

how a multi-carrier single-user energy system (household) is effectively replaced by the Energy

Hub structure that manages energy imports, conversions, exports and loads.

3.1 AARHUS

The Aarhus pilot site in Denmark is located in a public housing district that consists of around 30

residential buildings. RESPOND focuses on four of those buildings, with around 20 preselected

apartments that will be used as demonstrators of the RESPOND platform. There are three primary

energy carriers (from the aspect of the end consumers): electric energy that can be imported from

the grid, electric energy that is being generated by the shared photovoltaic (PV) panel array and

thermal energy contained within hot water that is being obtained from the district heating system.

The electricity imported from the grid passes through a transformer as is usually the case in

FIGURE 6 - AN EXAMPLE OF MODELING A SINGLE USER WITH A SINGLE ENERGY HUB

FIGURE 7 - AARHUS PILOT SITE TOPOLOGY



24 | 34

electricity distribution systems, while an inverter is used to adapt PV production to the AC

electricity that can be used by end users. Furthermore, the hot water from the district heating

system is directly dispatched to the heating system while, on the other hand, a heat exchanger is

employed to heat the secondary water loop and provide the domestic hot water supply. It is worth

mentioning that the excess of electricity generated by PV panels can be exported to the grid. The

model that correspond to this description, as depicted in Figure 7, is defined by

𝑆qin = [0 0 00 0 00 0 0

] , 𝑆in = [1 0 00 1 00 0 1

] , 𝐹in = [1 0 0 000

1 0 00 1 1

] , 𝐶 = [

0.98000

00.95

00

00

1.000

000

0.98

],

and

𝐷exp = [

1 0 0 00 0 0 000

00

1 00 1

] , 𝑅exp = [

0000

] , 𝐹out = [1 1 0 000

0 1 00 0 1

] , 𝑆qout = [0 0 00 0 00 0 0

] , 𝑆out = [1 0 00 1 00 0 1

]

with all storage capacities set to zero as no storage facilities are present within this pilot. The

aforementioned matrices are populated with multiple efficiency factors 𝜂transformer = 0.98,

𝜂inverter = 0.95 and 𝜂heatexch = 0.98, whose value ranges can be found in related literature [5],

[6], [7] and [8].

When modelling individual users, a rough estimate of how much electric energy coming from the

PV array can be distributed to each household can be obtained by dividing the total power

generation capacity of 622 kWp by the total number of households that, according to D1.1, equals

592 total apartments. Therefore, it can be assumed that each household has

622 kWp592

⁄ = 1.05 kWp

at its disposal. Since this value is used in this deliverable for the sole purpose of theoretical

demonstration, more precise figures regarding the aggregated PV availability for the considered

neighbourhood by the RESPOND project will be discussed in D4.3. D1.1 also states that the total

yearly electricity consumption of the entire public housing estate equals 1800 MWh while the total

heating demand is 6700 MWh. This allows for a rough estimate of

1800 MWh592⁄ = 3.04 MWh

total yearly electricity consumption per household and

6700 MWh592⁄ = 11.32 MWh

total yearly heating demand. When these values are distributed averagely for each day of the

year, the values of 8.3 kWh of daily electricity demand and 31.0 kWh of daily thermal demand are

obtained and can be used to generate an average demand profile. The daily DHW demand is

assumed to be equal to 23% of daily thermal demand in accordance with the analysis from [9]

with the leftover 77% corresponding to space heating demand.

As for the pricing scheme, the tariff is fixed at around 2.0 DKK/kWh = 0.27 EUR/kWh for electric

energy and 0.5 DKK/kWh = 0.067 EUR/kWh for thermal energy obtained from the district heating



25 | 34

system. Excess electricity produced by the PV array can be exported back to the grid for

0.6 DKK/kWh = 0.08 EUR/kWh

3.2 MADRID

Over on the Madrid pilot in Spain, the RESPOND project tackles shared areas and 24 preselected

dwellings among the total 69 individual households in three identical residential buildings. On the

roof of one of the buildings considered, a solar thermal collector (STC) system has been installed

with the capabilities of converting solar energy (irradiation) into thermal energy. In this way, the

water is heated and will be later used to fulfil the domestic hot water load. In addition, the tenants

have the ability of importing gas through the residential pipeline, which is then burnt in one of the

two gas boilers. The resulting hot water is either used to fulfil the heating demand or the DHW

demand (as a supplemental energy carrier to the energy obtained from the STC system). The

DHW loop is also equipped with two hot water tanks: the first one with the total capacity of

630 kWh that can be filled only by the hot water that is being heated within the STC, and another

with the total capacity of 420 kWh that can be filled by both the hot water from the STC and the

hot water that is being heated by the secondary gas boiler. This pilot does not have the ability of

exporting any types of energy back to the grid. The schema of the appropriate Energy Hub that

models one of the households is presented in Figure 8 with the model being instantiated using

the following structural matrices

𝑆qin = [0 0 00 0 00 0 1

] , 𝑆in = [1 0 00 1 00 0 0.98

] , 𝐹in = [100

00.97

0

00.97

0

001

] , 𝐶 = [

0.98000

00.98

00

00

0.980

000

0.98

],

and

𝐷exp = [

1 0 0 00 1 0 000

00

1 00 1

] , 𝑅exp = [

0000

] , 𝐹out = [1 0 0 000

1 0 00 1 1

] , 𝑆qout = [0 0 00 0 00 0 1

] , 𝑆out = [1 0 00 1 00 0 0.98

]

FIGURE 8 - MADRID PILOT SITE TOPOLOGY



26 | 34

with relevant DHW reservoir storage limits set to the appropriate capacities mentioned earlier.

The aforementioned matrices are populated with multiple efficiency factors 𝜂transformer = 0.98,

𝜂inverter = 0.95, 𝜂boiler = 97%, 𝜂heatexch = 0.98, whose value ranges can be found in related

literature [5], [6], [7], [8] and [10].

Pilot characterization from D1.1 suggests that all 69 dwellings consume 215 MWh of yearly

electricity for personal use and 1198 MWh yearly energy through gas consumption (disregarding

the 12 MWh for cooking purposes). Therefore, the yearly consumption per household would

equate to

215 MWh69⁄ = 3.16 MWh

of electric energy and

1198 MWh69⁄ = 17.36 MWh

of thermal energy. When downscaled to daily consumption per household, on an average day, a

single household would consume 8.54 kWh of electric energy and 47.57 kWh of thermal energy.

As the total value of thermal energy was measured before the STC system had been installed,

the daily DHW demand in this case is again assumed to be equal to 23% of daily thermal demand

in accordance with the analysis from [9] with the leftover 77% corresponding to space heating

demand.

As for the pricing scheme, grid electricity can be imported under a fixed tariff of 0.165 EUR/kWh

whilst gas can be imported at a fixed cost of 0.54 cEUR/kWh.

3.3 ARAN ISLANDS

The Aran Islands pilot in Ireland site consists of multiple distributed houses in the region of three

islands called Inis Mór, Inis Meáin and Inis Oírr with a total of 448 individual dwellings. However,

unlike the two other pilot sites, different households within the Aran Islands pilot have different

topologies. The houses that participate in the project at the moment of writing this deliverable can

be grouped into three types:

• Type 1: Electric energy is obtained either by importing from the grid or by utilizing the

distributed PV generation (with installed capacity of 4 kWp) and PV energy can be locally

stored in a battery with of 20 kWh capacity (house internally referred to as H2 is of this

type);

• Type 2: Electric energy is obtained either by importing from the grid or by utilizing the

distributed PV generation (with installed capacity of 2 kWp) (house internally referred to as

H1 is of this type)

• Type 3: Electric energy is only obtained by importing from the grid.

The corresponding Energy Hub structures of these three household types are presented in Figure

9. These hubs can be instantiated using

𝑆qin = [0 00 1

] , 𝑆in = [1 00 1

] , 𝐹in = [1 00 1

] , 𝐶 = [0.98 0

0 0.95],

and



27 | 34

𝐷exp = [1 00 0

] , 𝑅exp = [00

] , 𝐹out = [1 1], 𝑆qout = [0 00 0

] , 𝑆out = [1 00 1

]

and the storage limit set to the aforementioned value for type 1,

𝑆qin = [0 00 0

] , 𝑆in = [1 00 1

] , 𝐹in = [1 00 1

] , 𝐶 = [0.98 0

0 0.95],

and

𝐷exp = [1 00 0

] , 𝑅exp = [00

] , 𝐹out = [1 1], 𝑆qout = [0 00 0

] , 𝑆out = [1 00 1

]

for type 2 and finally

𝑆qin = [0], 𝑆in = [1], 𝐹in = [1], 𝐶 = [0.98],

and

𝐷exp = [1], 𝑅exp = [0], 𝐹out = [1], 𝑆qout = [0], 𝑆out = [1]



28 | 34

for type 3. The aforementioned matrices are populated with multiple efficiency factors

𝜂transformer = 0.98, 𝜂inverter = 0.95, whose value ranges can be found in related literature [5], [6]

and [7].

The total electricity consumption of all dwellings for a year, as given by D1.1, equates to

approximately 3.94 MWh. When scaled by the total number of households, each of them would

consume

3.94 MWh448⁄ = 8.79 kWh

with most of the consumption being attributed to space heating for which large amounts of fossil

fuels are imported to the islands and burnt.

Two types of electricity tariffs are at play: a fixed one with a price of 0.18 EUR/kWh and a time-of-

use day/night tariff with a high value of 0.203 EUR/kWh and a low value of 0.10 EUR/kWh.

FIGURE 9 - ARAN PILOT SITE TOPOLOGY (TYPE 1 TOP, TYPE 2 MIDDLE AND TYPE 3 BOTTOM)



29 | 34

4. OPTIMIZATION USE CASES

To demonstrate the methodology for a single-user (household/dwelling-level) hypothetical use

case, a topology is assumed in accordance with the model for the Aarhus pilot in Denmark that

was developed and previously described in Section 3.1. A single day is selected for the

optimization showcase, and a carrier availability and load profiles are synthetized whilst having in

mind the expected daily electric and thermal energy as well as the domestic hot water demand

requirement per household. All load types are modelled as functions that have two peak values:

one in morning hours and the other in the evening. These modelled demand levels are created

using Gaussian curves that have a mean value that correspond to the given peak time, and a

standard deviation that correspond to the dispersion intensity of that peak. The predicted electric

load is therefore defined as

𝐿elec(𝑘) = 8.3 (0.75 + 0.5𝑒

−(𝑘−7)2

2⋅12⁄+ 1.0𝑒

−(𝑘−18)2

2⋅32⁄

∑ (0.75 + 0.5𝑒−

(𝑖−7)2

2⋅12⁄+ 1.0𝑒

−(𝑖−18)2

2⋅32⁄)23

𝑖=0

) kW

while the predicted thermal load is defined as

𝐿thermal(𝑘) = 23.87 (0.50 + 0.5𝑒

−(𝑘−6)2

2⋅32⁄+ 0.5𝑒

−(𝑘−21)2

2⋅32⁄

∑ (0.50 + 0.5𝑒−

(𝑖−6)2

2⋅32⁄+ 0.5𝑒

−(𝑖−21)2

2⋅32⁄)23

𝑖=0

) kW

and the predicted DHW load as

𝐿DHW(𝑘) = 7.13 (0.25 + 0.5𝑒

−(𝑘−8)2

2⋅22⁄+ 0.5𝑒

−(𝑘−19)2

2⋅22⁄

∑ (0.25 + 0.5𝑒−

(𝑖−8)2

2⋅22⁄+ 0.5𝑒

−(𝑖−19)2

2⋅22⁄)23

𝑖=0

) kW.

The forecasted PV production is also synthetized using Gaussian curves as

𝑃in𝑃𝑉= 1.05 (

𝑒−

(𝑘−12)2

2⋅22⁄

∑ 𝑒−

(𝑖−12)2

2⋅22⁄23𝑖=0

) kW.

4.1 IMPLICIT DR EVENT

Namely, there are two main types of DR event enforcement methodologies: explicit and implicit.

Explicit DR events, on the one hand, are specified by directly arranging times and amounts of

energy that can be either increased or decreased over specific appliance activations over the

regular usage profile. On the other hand, implicit DR events can be induced by manipulating

carrier import and/or export prices to create time spans in which a certain carrier or carriers are

significantly more (or less) expensive than at other times, thus forcing the load to be reduced (or



30 | 34

increased) at those times. As a showcase, an implicit DR event is created by means of price

profile manipulations in this theoretical demonstration.

Concretely, electric energy imports are set to be 25% higher from 17:00 to 21:00 (including both

timesteps) than at other times and thermal energy is set to be 30% higher from 00:00 to 06:00

(including both timesteps) and from 15:00 to 23:00 (including both timesteps). However, the price

profiles are normalized in such a way that, for this demonstration, the average price per each

carrier remains the same as it was in the nominal (real) scenario and no load deviation

penalization was introduced. The obtained price profiles are depicted in Figure 10, where the real

prices are denoted with a dashed line and the manipulated prices are denoted with a full line.

Note: the dashed orange line lays underneath the full line.

The Energy Hub model of the considered pilot was optimized twice: once without a load shifting

margin (i.e. the optimized load had to be equal to the predicted value) and once with a predefined

non-zero load shifting margin (20% was selected for this demonstration). This was done in order

to obtain a realistic baseline profile of what the load levels and imported power levels would look

like without any price manipulations and to therefore be able to validate that the mentioned price

FIGURE 10 - PRICE PROFILES USED FOR DEFINING AN IMPLICIT DR EVENT



31 | 34

manipulations do have an effect of raising or lowering the load levels. The load profiles for the

predicted values (denoted in coloured dashed lines) optimized without any margin and those

optimized with a load margin (denoted in coloured full line), are presented in Figure 11. Here, one

can observe that the price manipulations did in fact have an effect on the final load profile in such

a way that the peak pricing drove all three load levels down at times where the system deems

that it is not cost-effective to consume energy because of high prices. At other times of day,

because of the integral energy constraints, the lowered load levels are shifted. This is most

noticeable during the mid-day period where the PV array is producing at its maximum capacity

and the district heating system’s hot water is the cheapest. It can also be noticed that the optimizer

did not completely reduce the thermal load in the evening peak period because the integral energy

constraint could not be met otherwise since the positive margin is used to its full extent during the

mid-day period.

FIGURE 11 – PREDICTED AND OPTIMIZED LOAD PROFILES



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Even though load manipulations were the primary objective of introducing DR, when viewed from

the grid standpoint, another important aspect of the DR programme is the manipulation of

individual carrier imports as that is what ultimately affects the stability of the system. The obtained

effects can be observed in the imported power profile in Figure 12, where it is abundantly clear

that the price increases in peak periods resulted in the reduction of the respective carrier

demands. This clearly indicates that the system, in its form defined in previous sections, has the

capabilities of performing both load and carrier import intensity manipulations. Note: the dashed

orange line once again lays underneath the full line.

Finally, it should be noted that the potential savings in both price and total energy imported,

although relatively minor in this discussed example, may be even greater depending on the

forecasted profiles, differences in price and load flexibility margins. These effects will be

discussed in more detail in D4.3

FIGURE 12 – NOMINAL AND OPTIMIZED INDIVIDUAL CARRIER IMPORT PROFILES



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5. CONCLUSION

This deliverable describes the development of a methodology that employs the Energy Hub

modelling concept specifically modified for load management applications. Two methodologies

were presented for load management applications: one in which individual appliance activations

are managed through the utilization of shifting windows and power tolerances, and another one

in which the loads are managed jointly as an aggregate value (a sum of either individual appliance

activations or multiple household’s aggregate load). Since RESPOND focuses on the

neighbourhood perspective, it makes use of the latter one.

The underlying model represents a mixed-integer linear programming problem that is solved

using IBM ILOG Optimization Studio’s CPLEX Python library. The output of the optimization

process are time series of model’s variables, being the most important ones the imported power

levels and the load levels. For each pilot site, appropriate Energy Hub models are defined for

individual households to credibly depict the ways in which different energy types are converted,

mixed and used to fulfil the required load.

Finally, in order to demonstrate the proposed methodology, the Hub for the Aarhus pilot is

instantiated with synthetized predicted load profiles and a slightly modified price profile to facilitate

an implicit DR event i.e. motivate load reduction by increasing prices in a peak period during the

afternoon for electric loads and night for thermal loads. Because of the differences in price, the

optimizer managed to lower the loads in the requested periods, but maintained the integral

demand for the entire simulated day.



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6. REFERENCES

Illustrations from freepik.com

[1] A. Barbato and A. Capone, “Optimization Models and Methods for Demand-Side Management of Residential Users: A Survey,” Energies, vol. 7, no. 9, pp. 5787–5824, Sep. 2014.

[2] M. Batić, N. Tomašević, G. Beccuti, T. Demiray, and S. Vraneš, “Combined energy hub optimisation and demand side management for buildings,” Energy and Buildings, vol. 127, pp. 229–241, Sep. 2016.

[3] “Achieving energy efficiency through behaviour change: what does it take?,” European Environment Agency. [Online]. Available: https://www.eea.europa.eu/publications/achieving-energy-efficiency-through-behaviour. [Accessed: 12-Aug-2019].

[4] Intergovernmental Panel on Climate Change, “Technology-specific Cost and Performance Parameters,” in Climate Change 2014: Mitigation of Climate Change: Working Group III Contribution to the IPCC Fifth Assessment Report, Cambridge University Press, 2015, pp. 1329–1356.

[5] T. Kubo, H. Sachs, and S. Nadel, “Opportunities For New Appliance and Equipment Efficiency Standards: Energy and Economic Savings Beyond Current Standards Programs,” p. 116.

[6] H. De Keulenaer, “The scope for energy saving in the EU through the use of energy-efficient electricity distribution transformers,” in 16th International Conference and Exhibition on Electricity Distribution (CIRED 2001), Amsterdam, Netherlands, 2001, vol. 2001, pp. v4-27-v4-27.

[7] “Inverter Efficiency - an overview | ScienceDirect Topics.” [Online]. Available: https://www.sciencedirect.com/topics/engineering/inverter-efficiency. [Accessed: 13-Aug-2019].

[8] “Elge Shell & Coil Heat Exchanger| WasteEnergy Recovery| AR MAC| GS Dunham.” [Online]. Available: http://www.gsdunham.com/heat.html. [Accessed: 13-Aug-2019].

[9] “Energy consumption in households - Statistics Explained.” [Online]. Available: https://ec.europa.eu/eurostat/statistics-explained/index.php/Energy_consumption_in_households. [Accessed: 13-Aug-2019].

[10] “Factsheet: Boiler Efficiency.” Departmant of the Environment and Energy, Australian Government.

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