DC Energy Flexibility Management Tool · AUTHOR(S) Marcel Antal, Tudor Cioara, Ionut Anghel,...

D4.3

DC Energy Flexibility Management

Tool

WORKPACKAGE

WP4

DOCUMENT

D4.3

VERSION

1.0

PUBLISH DATE

29/11/2019

DOCUMENT REFERENCE

CATALYST.D4.3.TUC.WP4.v1.0

PROGRAMME IDENTIFIER

H2020-EE-2016-2017

PROJECT NUMBER

768739

START DATE OF THE PROJECT

01/10/2017

DURATION

36 months

CATALYST.D4.3.TUC.WP4.v1.0 H2020-EE-2016-2017

DC Energy Flexibility Management Tool 768739

1

PROGRAMME NAME ENERGY EFFICIENCY CALL 2016-2017

PROGRAMME IDENTIFIER H2020-EE-2016-2017

TOPIC Bringing to market more energy efficient and integrated data centres

TOPIC IDENTIFIER EE-20-2017

TYPE OF ACTION IA Innovation action

PROJECT NUMBER 768739

PROJECT TITLE CATALYST

COORDINATOR ENGINEERING INGEGNERIA INFORMATICA S.p.A. (ENG)

PRINCIPAL CONTRACTORS SINGULARLOGIC ANONYMI ETAIREIA PLIROFORIAKON SYSTIMATON KAI

EFARMOGON PLIROFORIKIS (SiLO), ENEL.SI S.r.l (ENEL), ALLIANDER NV

(ALD), STICHTING GREEN IT CONSORTIUM REGIO AMSTERDAM (GIT),

SCHUBERG PHILIS BV (SBP), QARNOT COMPUTING (QRN), POWER

OPERATIONS LIMITED (POPs), INSTYTUT CHEMII BIOORGANICZNEJ

POLSKIEJ AKADEMII NAUK (PSNC), UNIVERSITATEA TEHNICA CLUJ-

NAPOCA (TUC)

DOCUMENT REFERENCE CATALYST.D4.3.TUC.WP4.v1.0

WORKPACKAGE: WP4

DELIVERABLE TYPE R/OTHER

AVAILABILITY PU

DELIVERABLE STATE Final

CONTRACTUAL DATE OF DELIVERY 30/11/2019

ACTUAL DATE OF DELIVERY 29/11/2019

DOCUMENT TITLE DC Energy Flexibility Management Tool

AUTHOR(S) Marcel Antal, Tudor Cioara, Ionut Anghel, Claudia Pop, Viorica Chifu,

Cristina Pop, Ioan Salomie (TUC)

REVIEWER(S) Laudicina Giuseppe (ENEL), Ariel Oleksiak (PSNC)

SUMMARY (See the Executive Summary)

HISTORY (See the Change History Table)

KEYWORDS Electrical and thermal flexibility management, flexibility shifting, multi-

criteria optimization, genetic algorithm heuristic, DC optimization engine



2

Change History

Version Date State Author (Partner) Description

0.1 16/10/2019 ToC TUC First version of ToC

0.2 25/10/2019 ToC TUC Final version of ToC

0.5 06/11/2019 Draft TUC First round of contributions

0.7 13/11/2019 Draft TUC Second round of contributions

0.9 14/11/2019 Complete Draft for

Peer Review

TUC Consolidated and finalized for peer

review

0.95 20/11/2019 Peer-Reviewed ENEL Review of the draft

0.95 20/11/2019 Peer-Reviewed PSNC Review of the draft

0.98 25/11/2019 Release Candidate TUC Deliverable version ready for quality

check

0.99 29/11/2019 Quality Checked ENG Quality check.

1.0 29/11/2019 Final ENG Final approval and submission to the EC



3

Table of Contents

Change History ....................................................................................................................................................... 2

Table of Contents ................................................................................................................................................... 3

List of Figures ......................................................................................................................................................... 4

List of Tables .......................................................................................................................................................... 5

List of Acronyms ..................................................................................................................................................... 6

Executive Summary ................................................................................................................................................ 7

1 Introduction .................................................................................................................................................. 8

1.1 Intended Audience .................................................................................................................................... 8

1.2 Relations to other activities ...................................................................................................................... 8

1.3 Document overview ................................................................................................................................... 9

2 DC Operation Optimization for Flexibility Management .......................................................................... 10

2.1 DC Multi-Criteria Optimization Problem ................................................................................................. 13

2.2 Genetic Algorithm based Heuristic ......................................................................................................... 19

3 CATALYST DC Optimization Engine ........................................................................................................... 24

3.1 Architecture and Implementation .......................................................................................................... 24

3.2 Installation Guidelines and User Manual............................................................................................... 27

4 Evaluation Results ..................................................................................................................................... 31

4.1 Electrical and Thermal Flexibility Management .................................................................................... 31

4.2 Genetic Heuristic Performance .............................................................................................................. 37

5 Conclusion .................................................................................................................................................. 40

6 References ................................................................................................................................................. 41



4

List of Figures

FIGURE 1. WP4 RELATION WITH OTHER WORK PACKAGES ............................................................................................... 8

FIGURE 2. OVERVIEW OF THE DC FLEXIBILITY SHIFTING OPTIMIZATION PROBLEM ............................................................ 10

FIGURE 3. DC SUB-SYSTEMS CONSIDERED IN THE OPTIMIZATION PROBLEM FORMULATION .............................................. 13

FIGURE 4. DC OPTIMIZATION PROBLEM FOR DELIVERY OF FLEXIBILITY SERVICES (BLUE – DC BASELINE ENERGY PROFILE, RED

– FLEXIBILITY ORDER FOR [𝑇1, 𝑇2] INTERVAL AND GREEN – ADAPTED DC ENERGY PROFILE AS RESULT OF FLEXIBILITY

SHIFTING ........................................................................................................................................................ 16

FIGURE 5. DC OPTIMIZATION PROBLEM FOR ENERGY TRADING (BLUE – DC BASELINE ENERGY PROFILE, BLACK –ENERGY PRICE

VARIATION IN THE ENERGY MARKETPLACE AND GREEN – ADAPTED DC ENERGY PROFILE AS RESULT OF FLEXIBILITY

SHIFTING) ....................................................................................................................................................... 16

FIGURE 6. DC OPTIMIZATION PROBLEM FOR HEAT SELLING (BLUE – DC BASELINE THERMAL PROFILE, BLACK –HEAT PRICE

VARIATION IN THE HEAT MARKETPLACE AND GREEN – ADAPTED DC HEAT PROFILE AS RESULT OF THERMAL ENERGY

FLEXIBILITY SHIFTING)....................................................................................................................................... 17

FIGURE 7. DC OPERATION OPTIMIZATION PROBLEM FOR FLEXIBILITY SHIFTING ............................................................... 19

FIGURE 8. GENETIC HEURISTIC FOR SOLVING DC MULTI-CRITERIA OPTIMIZATION PROBLEM ............................................. 23

FIGURE 9. CATALYST OPTIMIZATION ENGINE ARCHITECTURE ...................................................................................... 24

FIGURE 10. DC OPTIMIZATION PROCESS SEQUENCE DIAGRAM ...................................................................................... 25

FIGURE 11. DAY-AHEAD AND INTRA-DAY OPTIMIZATION ............................................................................................... 27

FIGURE 12. DEPLOYMENT DIAGRAM OF SOFTWARE COMPONENTS ................................................................................ 29

FIGURE 13. DC FLEXIBILITY MANAGEMENT AND OPTIMIZATION PAGE ............................................................................. 30

FIGURE 14. DC FLEXIBILITY MANAGEMENT OPTIMIZATION PLAN EXECUTION ................................................................... 30

FIGURE 15. PSNC DAY AHEAD FORECASTED: ELECTRICAL ENERGY DEMAND (LEFT); THERMAL ENERGY GENERATION (RIGHT)

...................................................................................................................................................................... 32

FIGURE 16. DC OPTIMIZED ENERGY PROFILE USING ELECTRICITY PRICE AS A SIGNAL ...................................................... 33

FIGURE 17. FLEXIBILITY ORDER AND DC INITIAL ENERGY PROFILE(LEFT); DC ADAPTED ENERGY PROFILE AS RESULT OF OPTIMAL

MANAGEMENT AND SHIFTING OF FLEXIBILITY USING FLEXIBILITY ORDER AS A SIGNAL ................................................ 33

FIGURE 18 DC ADAPTED ENERGY PROFILE AS RESULT OF OPTIMAL THERMAL ENERGY FLEXIBILITY SHIFTING (LEFT); WORKLOAD

SHIFTING TO PROVIDE THERMAL FLEXIBILITY (RIGHT) ............................................................................................ 34

FIGURE 19. WORKLOAD HOSTING AND RELOCATION FLEXIBILITY: DC ENERGY DEMAND PROFILE AND ENERGY PRICE (LEFT); DC

THERMAL ENERGY GENERATION PROFILE (RIGHT)................................................................................................. 34

FIGURE 20. DC WORKLOAD RELOCATION .................................................................................................................. 35

FIGURE 21. DC OPERATION MANAGEMENT TO DELIVER FLEXIBILITY ORDER (LEFT) ADDITIONAL WORKLOAD HOSTING FROM

OTHER DC (RIGHT) ........................................................................................................................................... 35

FIGURE 22. DC OPERATION MANAGEMENT TO DELIVER BOTH FLEXIBILITY ORDER AND HEAT ON DEMAND: OPTIMIZED ELECTRICAL

ENERGY PROFILE (LEFT) AND THERMAL ENERGY PROFILE (RIGHT) .......................................................................... 36

FIGURE 23. DC INTRA-DAY FLEXIBILITY OPTIMIZATION USES ESDS TO HANDLE UNFORESEEN WORKLOAD PEAK AND INCREASE

DEMAND: FLEXIBILITY REQUEST SIGNAL AND DC ENERGY DEMAND (LEFT); ESD FLEXIBILITY ACTIONS (RIGHT) ............ 36

FIGURE 24 DC INTRA-DAY FLEXIBILITY OPTIMIZATION USES ESDS TO LOWER THE DC ENERGY DEMAND: FLEXIBILITY REQUEST

SIGNAL AND DC ENERGY DEMAND (LEFT); ESD FLEXIBILITY ACTIONS (RIGHT) ......................................................... 37

FIGURE 25. FLEXIBILITY REQUEST MATCHING IN INTRA-DAY OPTIMIZATION: RMSE CONSIDERING PREDICTION ERROR (LEFT),

MAPE CONSIDERING PREDICTION ERROR (RIGHT) ............................................................................................... 37

FIGURE 26. FLEXIBILITY MANAGEMENT OPTIMIZATION SCALABILITY EVALUATION: THE RELATION BETWEEN DC SOS MODEL SIZE

AND WINDOW LENGTH (LEFT); COMPARISON BETWEEN LINGO AND GENETIC ALGORITHM HEURISTIC FOR OPTIMIZATION

WINDOW T = 24 (RIGHT) .................................................................................................................................. 39



5

List of Tables

TABLE 1. CONTROL VARIABLES AND ASSOCIATED FLEXIBILITY SHIFTING ACTIONS ............................................................. 13

TABLE 2. CONTROL VARIABLES AND ASSOCIATED FLEXIBILITY SHIFTING ACTIONS ............................................................. 14

TABLE 3. FLEXIBILITY SHIFTING OBJECTIVES AND ASSOCIATED SERVICES ........................................................................ 15

TABLE 4. GENES FOR CASE OF DC OPTIMIZATION FOR FLEXIBILITY SHIFTING ................................................................... 19

TABLE 5. CONTROL VARIABLE REDUCTION FOR OPTIMIZATION PROBLEM SOLVING ........................................................... 20

TABLE 6. CHROMOSOME AND GENES REPRESENTATION ............................................................................................... 20

TABLE 7. GENETIC ALGORITHM FITNESS FUNCTION CONSTRAINT SET ............................................................................. 21

TABLE 8. OPERATORS DEFINED AND USED IN THE GENETIC HEURITIC ............................................................................. 22

TABLE 9. CATALYST OPTIMIZATION PROCESS STEPS .................................................................................................. 25

TABLE 10. CHARACTERISTICS OF THE TEST BED DC CONSIDERED ................................................................................. 31

TABLE 11. OPTIMIZATION STRATEGIES EVALUATED AND OPTIMIZATION OBJECTIVE WEIGHTS USED ..................................... 32

TABLE 12. GENETIC ALGORITHM HEURISTICS PERFORMANCE FOR SOLVING FLEXIBILITY MANAGEMENT OPTIMIZATION PROBLEMS

...................................................................................................................................................................... 38

TABLE 13. GENETIC ALGORITHM HEURISTIC AND LINGO COMPARISON FOR SOLVING FLEXIBILITY MANAGEMENT OPTIMIZATION

PROBLEMS ...................................................................................................................................................... 38



6

List of Acronyms

API Application Programming Interface

COP Coefficient of Performance

DB Database

DC Data Centre

DR Demand Response

DSO Distribution System Operator

ESD Electrical storage device

HPC High Performance Computing

GPU Graphics processing unit

ICT Information and communication technology

IT Information technology

MAPE Mean absolute percentage error

NP-hard Non-deterministic polynomial-time hardness

REST Representational State Transfer

RES Renewable Energy Sources

RMSE Root-mean-square deviation

TES Thermal Energy Storage

SoS System of systems

UPS Uninterruptible Power Supply

WP Work Package



7

Executive Summary

This deliverable reports the work carried out for defining and implementing an ICT solution that allows the

DC to optimally manage its electrical and thermal energy flexibility. This solution supports DCs to achieve

better integration with the electrical and heat grids and contribute to the fulfilment of sustainability

objectives.

To formalize the problem of optimizing the DC operation to shift energy flexibility to meet different objectives

we have leveraged on the DC system of systems model presented in D4.1. On top, we have defined and

formalized the concepts of energy demand baseline, output flexibility, flexibility control variables, and

flexibility potential both at the individual subsystem level and at DC as a whole. They are used to define the

DC flexibility management as a multi-criteria optimization problem in which given a set of inputs and specific

flexibility target objectives we aim at determining a flexibility shifting action plan that minimizes the distance

to the goal while at the same time meets all the constraints for systems safe operation. As target objectives

we have considered (i) the electrical energy trading by shifting energy flexibility to allow it to sell energy when

the prices are high and buy energy when the prices are low in the electricity market, (ii) delivery of flexibility

services by shifting energy flexibility to match as close as possible a flexibility order provided by a flexibility

aggregator via the flexibility marketplace and (iii) heat trading by shifting energy flexibility increase as much

as possible the quality of recovered heat and sell it on the heat marketplace directly of via a Heat Broker.

Moreover, the DC operator is empowered to define its custom DC optimization strategy by defining weights

for each specific objective allowing the simultaneous delivery of more than one service at the same time.

The workload hosting and/or relocation to/from other DCs was considered as a potential source of additional

electrical and thermal flexibility thus the IT Servers and Server Room system model was extended to consider

it into the optimization problem.

The DC flexibility management optimization problem is classified as a Non-Linear optimization problem which

is NP-hard one because the unknowns are real, and the defined objective functions are nonlinear. To solve

it we have defined a genetic algorithm-based heuristic that is computing a flexibility optimization plan by

determining the values of systems flexibility control variables considering the predicted thermal and

electrical energy values determined by the Electrical and Thermal DR Prediction Modules presented in

deliverable D4.2. The optimization problem solution is encoded in a chromosome that is composed of a set

of genes correlated with the number of systems flexibility control variables and a discrete-time model

implemented for day-ahead and intra-day optimization. The number of variables unknowns are high and to

increase the time and space efficiency of solution computation several variables reduction methods have

been defined. The fitness function defined evaluates every chromosome within the population concerning

the objective of determining the optimal control variables for DC flexibility shifting such that the set objective

is met.

The flexibility optimization solution was implemented into the CATALYST Intra DC Optimization component

and was integrated into the DC optimization engine and flexibility management tool. To evaluate we have

conducted in lab experiments considering the hardware systems characteristics of a HPC DC and a medium

scale cloud DC. The obtained results are showing the potential of our solution in managing the energy

flexibility to allow DC to successfully provide specific services to the electrical and thermal energy grids and

with good scalability and low time overhead.



8

1 Introduction

In this deliverable, we describe the DCs energy flexibility management method which will allow them to

optimize their electrical and/or thermal energy profiles and deliver specific services in the electrical and/or

heat grids. The energy flexibility management is translated into a multi-criteria optimization problem defined

on top of the DC system of the system model. To solve this NP-hard constraint satisfaction problem with

good scalability and time-efficient manner we have defined a genetic algorithm-based heuristic featuring

flexibility constraints variables, variables reduction methods and fitness function aiming to identify control

variables values that are minimizing the distance to the goal. Also, we have implemented a DC flexibility

management tool that considers the monitored energy data and the predicted DC energy budget to

determine flexibility shifting action plans to meet different optimization objectives and achieve better

integration with electrical and thermal energy grids.

1.1 Intended Audience

The intended audience of this report is the CATALYST consortium and the European Commission (EC)

representatives tasked with reviewing the project and its progress towards meeting the specified milestones.

Also, stakeholders from the DC industry as well as people from the scientific and academic community

interested in the energy efficiency of DCs considering the thermal and electrical energy management and

associated flexibility exploitation.

1.2 Relations to other activities

Work Package 4 provides the technological means for allowing DCs to exploit their potential thermal and

electrical energy flexibility for optimal integration into smart energy grid scenarios (see Figure 1).

Figure 1. WP4 relation with other work packages

This deliverable reports the work and the results achieved concerning Task 4.4: DC Flexibility Management

and Optimization. The DC flexibility and optimization solution developed build upon the DC SoS model for



9

electrical and thermal energy systems integration defined in D4.1 [1] and considers as input in the

optimization decision process the DC electricity and thermal energy predictions as generated using the

techniques and tools delivered in D4.2 [2].

They are integrated into the CATALYST DC Energy Flexibility Management Tool that will be evaluated in the

CATALYST project pilot sites.

1.3 Document overview

The remainder of the report is organized as follows:

• Section 2 describes the DC thermal and electrical flexibility management for smart energy grids

integration as a multi-criteria optimization problem and defines a genetic algorithm-based heuristic

for its solving;

• Section 3 presents the DC optimization engine architecture, implementation and integration of

flexibility management into the overall process flow;

• Section 4 presents evaluation results using a HPC DC and a medium scale DC;

• Section 5 concludes the deliverable and presents future work.



10

2 DC Operation Optimization for Flexibility Management

The problem of optimizing the DC operation to shift energy flexibility to meet different objectives was

formulated on top of the system of system modelling approach (DC SoS Model) that was presented in detail

in deliverable 4.1. Figure 2 presents an overview of the optimization problem and the variables considered

by the optimization process implemented. Using a simulation of the DC SoS model each point representing

a system-level control variable in the Flexibility Control Space is translated into a flexibility value associated

in Flexibility Adaptation Space. The adaptability capability is represented by the green point from the control

space 𝐶𝐷𝐶 that is mapped by means of simulation to the green output point from the output space which

represents the adapted energy profile of the DC as result of flexibility shifting (𝐸𝐷𝐶𝑎𝑑𝑎𝑝𝑡𝑒𝑑

) which is closest to

the flexibility request (𝐸𝑓𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑟𝑒𝑞𝑢𝑒𝑠𝑡

) point coloured in blue.

Figure 2. Overview of the DC flexibility shifting optimization problem

Figure 2 shows the flexibility control and the adaptation space for a DC modelled as system featuring three

control variables which are varied by means of simulation to infer the associated energy flexibility. Thus, both

spaces are three dimensional ones 𝑅3 in which each of the axis corresponds to one of the values of the



11

controls (𝐶(1), 𝐶(2), 𝐶(3)), respectively energy flexibility outputs (𝑂(1), 𝑂(2), 𝑂(3)), for each time step form

the simulation interval.

The simulation of a DC operation using our complex system model over a time interval 𝑇 is defined as a

function that calculates for each moment of time and for a given set of input variables 𝐼𝐷𝐶 the energy

flexibility equivalent to the variation of the control variables used to determine the systems operation.

𝑆𝑖𝑚:𝑅𝑁𝐶×𝑇 → 𝑅𝑁𝑂× 𝑇 , 𝑂𝐷𝐶 = 𝐸𝐷𝐶𝐴𝑑𝑎𝑝𝑡𝑒𝑑

= {𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

(𝑡)|𝑡 ∈ [0. . 𝑇] 𝑎𝑛𝑑

𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

(𝑡) = 𝑆𝑖𝑚 (𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 , 𝑇, 𝐷𝑇𝐷𝐶 , 𝐼𝐷𝐶(𝑡), 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡(𝑡))} (1)

where

• 𝑁𝐶 and 𝑁𝑂 - represent the number of controls and flexibility dimensions,

• 𝑇 - is the simulation time window;

𝑇 = {24 ℎ𝑜𝑢𝑟𝑠 𝑓𝑜𝑟 𝑑𝑎𝑦 − 𝑎ℎ𝑒𝑎𝑑 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛, 4 ℎ𝑜𝑢𝑟𝑠 𝑓𝑜𝑟 𝑖𝑛𝑡𝑟𝑎 − 𝑑𝑎𝑦 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛} (2)

• 𝐷𝑇𝐷𝐶 - is the discrete time model considered in simulation:

𝐷𝑇𝐷𝐶 = {1 ℎ𝑜𝑢𝑟 𝑓𝑜𝑟 𝑑𝑎𝑦 − 𝑎ℎ𝑒𝑎𝑑 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛;1

2 ℎ𝑜𝑢𝑟 𝑓𝑜𝑟 𝑖𝑛𝑡𝑟𝑎 − 𝑑𝑎𝑦 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛} (3)

• 𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 - is the system of system model defined according to D4.1.

𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 = 𝐷𝑀𝐶𝑆 = {𝑉, 𝐸, DTDC} 𝑤ℎ𝑒𝑟𝑒

𝑉 = {𝐼𝑇 𝑆𝑒𝑟𝑣𝑒𝑟𝑠 & 𝑆𝑒𝑟𝑣𝑒𝑟 𝑅𝑜𝑜𝑚, 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 & 𝐻𝑒𝑎𝑡 𝑅𝑒𝑢𝑠𝑒 𝑆𝑦𝑠𝑡𝑒𝑚,𝑈𝑃𝑆} 𝑎𝑛𝑑

𝐸 = {𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑜𝑟 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝐿𝑖𝑛𝑘 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐷𝑀𝑆𝑆𝑖, 𝐷𝑀𝑆𝑆𝑗 ∈ 𝑉} (4)

• 𝐼𝐷𝐶 – predicted electrical and thermal energy profiles as outputted by the Electrical and Heat DR

Prediction components.

The baseline energy consumption of the DC over a time window 𝑇 for a set of given inputs is defined as the

set of energy flexibility outputs computed by a simulation that considers no action plan(𝑃𝐷𝐶𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒 = ∅), thus

setting default values for the control variables:

𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡) = 𝑆𝑖𝑚(𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙, 𝑇, 𝐷𝑇𝐷𝐶 , 𝐼𝐷𝐶(𝑡), ∅), ∀𝑡 ∈ 𝑇 (5)

In other words, the baseline represents the energy consumption of the DC if no energy flexibility action (no

demand response event) will be executed. We consider the baseline as the origin of the output flexibility

space 𝑅𝑁𝑜×𝑇 and the default control variable values as the origin of the control space 𝑅𝑁𝐶×𝑇.

We define the output flexibility of the DC as the set of all possible outputs that a simulation of the model can

reach, considering all valid flexibility shifting action plans for a given set of inputs 𝐼𝐷𝐶:

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡(𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 , 𝐼𝐷𝐶 , 𝑇) =



12

{𝑂𝐷𝐶|𝑂𝐷𝐶(𝑡𝑘) = 𝑆𝑖𝑚𝐷𝐶 (𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 , 𝑇, 𝐷𝑇𝐷𝐶 , 𝐼𝐷𝐶(𝑡𝑘), 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡(𝑡𝑘)) 𝑎𝑛𝑑 𝑃𝐷𝐶

𝑎𝑑𝑎𝑝𝑡 𝑖𝑠 𝑣𝑎𝑙𝑖𝑑}

(6)

The output flexibility is a subspace of the output space and contains only the multidimensional points the

output of 𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 can reach:

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡(𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 , 𝐼𝐷𝐶 , 𝑇) ⊆ 𝑅

𝑁𝑜𝑥𝑇𝑆 (7)

We can use the above terms to define the flexibility potential of a DC as the maximum output flexibility above

the baseline and the maximum output flexibility below the baseline

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 = {𝐹𝑙𝑒𝑥𝐷𝐶

𝑎𝑏𝑜𝑣𝑒; 𝐹𝑙𝑒𝑥𝐷𝐶𝑏𝑒𝑙𝑜𝑤} (8)

where

𝐹𝑙𝑒𝑥𝐷𝐶𝑎𝑏𝑜𝑣𝑒 = max

𝑡∈𝑇|𝑓𝑙𝑒𝑥𝑜𝑢𝑡𝑝𝑢𝑡(𝑡) − 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡)|, 𝑤ℎ𝑒𝑟𝑒 𝑓𝑙𝑒𝑥𝑜𝑢𝑡𝑝𝑢𝑡(𝑡) > 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡) (9)

𝐹𝑙𝑒𝑥𝐷𝐶𝑏𝑒𝑙𝑜𝑤 = max

𝑡∈𝑇|𝑓𝑙𝑒𝑥𝑜𝑢𝑡𝑝𝑢𝑡(𝑡) − 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡)|, 𝑤ℎ𝑒𝑟𝑒 𝑓𝑙𝑒𝑥𝑜𝑢𝑡𝑝𝑢𝑡(𝑡) < 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡) (10)

We define the flexibility control of the DC as the set of all possible values for the defined system level control

variables (𝐶𝐷𝐶) that can be converted to valid action plans 𝑃𝐷𝐶𝑣𝑎𝑙𝑖𝑑, thus leading to feasible simulations.

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝐷𝐶 (𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 , 𝐼𝐷𝐶 , 𝑇) = {𝐶𝐷𝐶|𝑃𝐷𝐶

𝑣𝑎𝑙𝑖𝑑 = 𝐴𝑑𝑎𝑝𝑡𝑎𝑡𝑖𝑜𝑛𝑃𝑙𝑎𝑛(𝐶𝐷𝐶) 𝑎𝑛𝑑

𝑃𝐷𝐶𝑣𝑎𝑙𝑖𝑑 𝑚𝑒𝑒𝑡𝑠 𝑎𝑙𝑙 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑎𝑛𝑡𝑠 𝑜𝑣𝑒𝑟 𝑇 } (11)

The flexibility control of the DC is a subset of the control space, containing only the points that correspond

to valid flexibility shifting action plans.

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝐷𝐶 (𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 , 𝐼𝐷𝐶 , 𝑇) ⊆ 𝑅

𝑁𝐶𝑥𝑇𝑆 (12)

We define the adaptability of the DC 𝐴𝑀𝐷𝐶 with respect to a given input set 𝐼𝐷𝐶, a valid flexibility shifting

action plan 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

and a flexibility request as the normalized distance between the flexibility request point

and the output flexibility generated as result of executing 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

:

𝐴𝑀𝐷𝐶 : 𝑅𝑁𝑜×𝑇𝑆 × 𝑅𝑁𝑜×𝑇𝑆 → 𝑅,

𝐴𝑀𝐷𝐶(𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑟𝑒𝑞𝑢𝑒𝑠𝑡) = (𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶

𝑜𝑢𝑡𝑝𝑢𝑡,𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑟𝑒𝑞𝑢𝑒𝑠𝑡)

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 ) (13)

The distance function is a metric that computes the distance between two points from the dimensional

space, such as the Euclidean distance or Manhattan distance.

The adaptability process of the DC with respect to a given input set 𝐼𝐷𝐶 and a flexibility request having the

distance from the baseline smaller than the flexibility potential 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 is defined as the

calculation of a valid action plan 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

in the flexibility control space 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝐷𝐶 that minimizes the

adaptability metric 𝐴𝑀𝐷𝐶 of DC SoS model with respect to 𝐼𝐷𝐶, 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑟𝑒𝑞𝑢𝑒𝑠𝑡 and 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

:



13

𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

= 𝑃𝑙𝑎𝑛𝐹𝑜𝑟(𝐶𝐷𝐶) 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑀𝑖𝑛 (𝐴𝑀𝐷𝐶(𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑟𝑒𝑞𝑢𝑒𝑠𝑡))

𝑤𝑖𝑡ℎ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶) ≤ 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 (14)

2.1 DC Multi-Criteria Optimization Problem

Figure 3 presents the main DC sub-systems considered in the optimization problem with the thermal and

electrical energy links that interconnect them.

Figure 3. DC sub-systems considered in the optimization problem formulation

For each DC sub-system, a set of control variables (i.e. coloured in purple) have been defined and are

associated with main actions that will shift the energy flexibility of that specific sub-system (see Table 1.):

𝐶𝐷𝐶 = {𝐶𝐼𝑇 𝑆𝑒𝑟𝑣𝑒𝑟𝑠 𝑎𝑛𝑑 𝑆𝑒𝑟𝑣𝑒𝑟 𝑅𝑜𝑜𝑚 ∪ 𝐶𝐶𝑜𝑜𝑙𝑖𝑛𝑔 𝑎𝑛𝑑 𝐻𝑒𝑎𝑡 𝑅𝑒𝑢𝑠𝑒 𝑆𝑦𝑠𝑡𝑒𝑚

∪ 𝐶𝑃𝑜𝑤𝑒𝑟 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑈𝑃𝑆 𝑆𝑦𝑠𝑡𝑒𝑚 } (15)

where

𝐶𝐼𝑇 𝑆𝑒𝑟𝑣𝑒𝑟𝑠 𝑎𝑛𝑑 𝑆𝑒𝑟𝑣𝑒𝑟 𝑅𝑜𝑜𝑚 = {𝐶𝑅 , 𝐶𝐻 , 𝐶𝐷}, 𝐶𝐶𝑜𝑜𝑙𝑖𝑛𝑔 𝑎𝑛𝑑 𝐻𝑒𝑎𝑡 𝑅𝑒𝑢𝑠𝑒 𝑆𝑦𝑠𝑡𝑒𝑚 = {𝐷𝑇𝐸𝑆, 𝑅𝑇𝐸𝑆}

𝐶𝑃𝑜𝑤𝑒𝑟 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑈𝑃𝑆 𝑆𝑦𝑠𝑡𝑒𝑚 = {𝐷𝐸𝑆𝐷, 𝑅𝐸𝑆𝐷}

Table 1. Control variables and associated flexibility shifting actions

DC Subsystem Control

Variables

Flexibility Actions Description

Electrical Energy Flexibility

IT Servers and

Server Room 𝐶𝐷 Shift Delay Tolerant

Workload The DC energy demand is reduced at timestamp 𝑡 with the

amount of energy needed to execute the delay-tolerant load



14

DC Subsystem Control

Variables

Flexibility Actions Description

that is shifted at timestamp 𝑡 + 𝑢, 𝑢 ∈ [1, 𝑇 − 𝑡] while the

DC energy demand at timestamp 𝑡 + 𝑢 is increased with the

amount of energy needed to execute the delay-tolerant load

shifted from timestamp 𝑡.

𝐶𝐻 , 𝐶𝑅 Host / Relocate

Workload The DC can host workload at time 𝑡 to increase the energy

demand at that time. The DC can relocate a percentage of

the delay tolerant workload at time 𝑡 to decrease the energy

demand.

Cooling and

Heat Reuse

System

𝐷𝑇𝐸𝑆 , 𝑅𝑇𝐸𝑆 Discharge / Charge

Thermal Storage

Devices

Dynamic usage of non-electrical cooling systems (i.e. TES) to

precool the DC and to compensate the electrical one. At

timestamp 𝑡 the TES is charged, its coolant (i.e. water based

thermal tanks) is overcooled by using the electrical cooling

at higher capacity resulting in an increased energy demand.

At timestamp 𝑡+ 𝑢, 𝑢 ∈ [1, 𝑇 − 𝑡] the TES is discharged, the

DC is cooled down using the precooled coolant and the

electrical cooling is used at low intensity resulting in a

decrease of DC energy demand.

Uninterruptible

Power Supply

Unit

𝐷𝐸𝑆𝐷 , 𝑅𝐸𝑆𝐷 Discharge / Charge

Batteries The DC energy demand is reduced at timestamp 𝑡 by the

amount of energy discharged from batteries and increased

at timestamp 𝑡+ 𝑢, 𝑢 ∈ [1, 𝑇 − 𝑡] by the amount of energy

charged in batteries.

Thermal Energy Flexibility

IT Servers and

Server Room 𝐶𝐷 Shift Delay Tolerant

Workload

Plan the delay tolerant workload execution as well as the

hosting of workload from other DCs to obtain a high servers

utilization ratio while increasing for limited time interval the

temperature set points in the server room while being

careful not to endanger the proper operation of IT

equipment.

𝐶𝐻 , 𝐶𝑅 Host / Relocate

Workload

Cooling and

Heat Reuse

System

𝐷𝑇𝐸𝑆 , 𝑅𝑇𝐸𝑆 Discharge / Charge

Thermal Storage

Devices

Increase the temperature set points in the server room for

limited period of time allowing the heat to accumulate while

at the same time increase the efficiency of the heat pump

operation for rising the temperature of waste heat leaving

the server room.

To be able to take into consideration the workload hosting and / or relocation to/from other DCs as potential

source of electrical and thermal energy flexibility the IT Servers and Server Room system model was extended

as presented in Table 2.

Table 2. Control variables and associated flexibility shifting actions

Formalism IT Servers and Server Room Sub-System Model

I (inputs set) Energy demand of workload with real time execution constraints: 𝐸𝑅 ∈ 𝑅

Energy demand of delay tolerant workload: 𝐸𝐷 ∈ 𝑅

O (output set) 𝐸𝑆, ℎ𝑒𝑎𝑡𝑇𝑜𝐵𝑒𝑅𝑒𝑚𝑜𝑣𝑒𝑑, 𝐸ℎ𝑜𝑠𝑡𝑒𝑑 , 𝐸𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒 ∈ 𝑅



15

C (control set) 𝐶𝐷 , 𝐶𝐻 , 𝐶𝑅 ∈ 𝑅𝑇

Actions 𝑆ℎ𝑖𝑓𝑡𝐷𝑒𝑙𝑎𝑦𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑡𝑊𝑜𝑟𝑘𝑙𝑜𝑎𝑑(𝑡𝑓𝑟𝑜𝑚, 𝑡𝑡𝑜, 𝑎𝑚𝑜𝑢𝑛𝑡)

𝐻𝑜𝑠𝑡𝑊𝑜𝑟𝑘𝑙𝑜𝑎𝑑(𝑡, 𝑎𝑚𝑜𝑢𝑛𝑡)

𝑅𝑒𝑙𝑜𝑐𝑎𝑡𝑒𝑊𝑜𝑟𝑘𝑙𝑜𝑎𝑑(𝑡, 𝑎𝑚𝑜𝑢𝑛𝑡)

S (internal state) 𝐸𝐷𝐸 ∈ 𝑅𝑇

f (transfer function) 𝐸𝑆(𝑡) = 𝐸𝑅(𝑡) + 𝐸𝐷(𝑡) ∗ (1 − 𝐶𝑅 + 𝐶𝐻) ∗ 𝐶𝐷(𝑡) + 𝐸𝐷𝐸(𝑡)

𝐸ℎ𝑜𝑠𝑡𝑒𝑑(𝑡) = 𝐶𝐻 ∗ 𝐸𝐷(𝑡)

𝐸𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒(𝑡) = 𝐶𝑅 ∗ 𝐸𝐷(𝑡)

ℎ𝑒𝑎𝑡𝑇𝑜𝐵𝑒𝑅𝑒𝑚𝑜𝑣𝑒𝑑(𝑡) ≅ 𝐸𝑆(𝑡)

g (state function) 𝐸𝐷𝐸(𝑡 + 1) = 𝐸𝐷𝐸(𝑡) + 𝐸𝐷 ∗ (1 − 𝐶𝑅 + 𝐶𝐻) ∗ 𝐶(𝑡)

Constraints C1: ∑ 𝐶(𝑡) = 1𝑇𝑡=1 , C2: 𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝐼𝑇

C3: 0 ≤ 𝐶𝑅 ≤ 1, C4: 0 ≤ 𝐶𝐻 ≤ 1, C5: 𝐶𝑅 ∗ 𝐶𝐻 = 0

The optimization problem defined in this case considers different criteria for DC operation adaptation that

are mapped onto associated objective functions. They are associated with the different types of services the

DC may provide in the respective market (see Table 3).

Table 3. Flexibility shifting objectives and associated services

Commodity Marketplace Service Type Flexibility shifting objective

Electrical

Energy

Electrical

Energy

Marketplace

Energy

trading

Sell energy when the prices are high and buy energy when the

prices are low. Energy flexibility is shifted away from the time

intervals when the energy prices are high, so the DC demand is

decreased.

Flexibility

Marketplace

Flexibility

Services

Provisioning

Adapt the DC energy demand by shifting energy flexibility to match

as close as possible a flexibility order provided by a flexibility

aggregator.

Thermal

Energy

Heat

Marketplace

Heat trading Sell waste heat on the Heat Marketplace directly of via a Heat

Broker. Shift energy flexibility to increase as much as possible to

quality of recovered heat and make it more marketable

In case of delivering flexibility services, the DC should address a potential flexibility order from a DSO /

aggregator in a specific time interval [𝑇1, 𝑇2] by adapting its next-day energy profile (𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

(𝑡))

having as starting point its baseline energy profile 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡), to match the request provided in a form

of a goal energy curve (𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑟𝑒𝑞𝑢𝑒𝑠𝑡(𝑡)). The moment in time when the energy needs to be shifted can

be before or after the [𝑇1, 𝑇2] of request (i.e. within the intervals [𝑇0, 𝑇1) or (𝑇2, 𝑇3]).

Figure 4 presents an example of such flexibility service the DC is empowered to provide in case of congestion

management which may imply either: (i) the reduction of DC energy demand profile during the service time

interval by managing its operation so that a specific amount of flexible energy is shifted later in time or (ii)

the increasing of DC energy profile during the service time interval by postponing the execution of some

tasks and altering its profile prior to the service time.



16

Figure 4. DC optimization problem for delivery of flexibility services (blue – DC baseline energy profile, red – flexibility

order for [𝑇1, 𝑇2] interval and green – adapted DC energy profile as result of flexibility shifting

The defined optimization objective aims to adapt the DC energy profile according to flexibility order signal

received by minimizing the distance between them and as results maximize the incentives received

(𝑆𝑒𝑟𝑣𝑖𝑐𝑒𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑡𝑖𝑣𝑒) by the DC for the energy flexibility service delivery.

𝑂𝑏𝑗𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑆𝑒𝑟𝑣𝑖𝑐𝑒 (𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝑆𝑒𝑟𝑣𝑖𝑐𝑒𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑡𝑖𝑣𝑒) =

𝑚𝑎𝑥∑𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶

𝑜𝑢𝑡𝑝𝑢𝑡(𝑡)

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑅𝑒𝑞𝑢𝑒𝑠𝑡(𝑡)∗ 𝑆𝑒𝑟𝑣𝑖𝑐𝑒𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑡𝑖𝑣𝑒(𝑡)

𝑡=𝑇𝑡=0 (16)

In the case of energy trading, the DC will adapt its energy profile (𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

(𝑡)) having as a starting

point its baseline energy profile 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝐷𝐶(𝑡) proportional with the energy price variation in the energy

market which is used as a driven signal.

Figure 5. DC optimization problem for energy trading (blue – DC baseline energy profile, black –energy price variation

in the energy marketplace and green – adapted DC energy profile as result of flexibility shifting)

Thus to buy electrical energy the DC will shift its energy flexibility from the time intervals when the prices are

high (i.e. [𝑇1, 𝑇2] ) decreasing its energy profile to the time intervals when the energy prices are low

(i.e. [𝑇2, 𝑇3]) and as result it will increase its overall energy profile (see Figure 5). To sell electrical energy the

a) b)



17

DC will decrease its energy profile by shifting the flexible energy outside the time interval in which the prices

are high allowing it to sell its surplus of energy generation.

The optimization objective aims to minimize the DC operational cost with energy by trading energy on the

Electrical Energy Marketplace. The goal is to adapt the DC energy demand 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

so that the DC

consumes less energy when the energy price 𝑃𝑟𝑖𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 is high on the marketplace by shifting flexible

energy to time intervals when the energy price is lower.

𝑂𝑏𝑗𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 (𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝑃𝑟𝑖𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦) =

𝑚𝑖𝑛∑ 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

(𝑡) ∗ 𝑃𝑟𝑖𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦𝑡=𝑇𝑡=0 (𝑡) (17)

where 𝑃𝑟𝑖𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 is the energy price in the energy market and 𝑇 is the length of the optimization interval.

In case of heat service offering, the DC will leverage on its internal thermal flexibility to increase the amount

and quality of the heat re-used from the server room allowing it to be valorised via heat pumps in local

neighbourhoods. As can be seen in Figure 6 the DC is able to adjust and optimize its thermal energy profile

by shifting its thermal flexibility in the time interval [𝑇0, 𝑇1] allowing it to take advantage of the high energy

prices for heat in the heat marketplace.

Figure 6. DC optimization problem for heat selling (blue – DC baseline thermal profile, black –heat price variation in

the heat marketplace and green – adapted DC heat profile as result of thermal energy flexibility shifting)

The optimization objective aims at maximizing DC profit by resulted from trading the otherwise wasted heat

on the heat market considering high reference prices 𝑃𝑟𝑖𝑐𝑒𝐻𝑒𝑎𝑡.

𝑂𝑏𝑗𝐻𝑒𝑎𝑡 (𝐻𝑒𝑎𝑡𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝑃𝑟𝑖𝑐𝑒𝐻𝑒𝑎𝑡) = 𝑚𝑖𝑛∑ 𝐻𝑒𝑎𝑡𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

(𝑡) ∗ 𝑃𝑟𝑖𝑐𝑒𝐻𝑒𝑎𝑡𝑡=𝑇𝑡=0 (𝑡) (18)

The DC can increase its revenue by participating simultaneously on all three energy marketplaces and

offering specific services. Thus, we have defined specific weights through which the DC operator can set its

optimization strategy by defining the importance of each of them into a composed optimization objective:

𝑊𝑒 +𝑊𝑡 +𝑊𝐹𝑆 = 1, ∀ 𝑊𝑒 ,𝑊𝑡 ,𝑊𝐹𝑆, ∈ [0,1] (19)

Where: 𝑊𝑒 is the weight associated with electrical energy trading, 𝑊𝑡 is the weight associated to heat trading

and 𝑊𝐹𝑆 is the weight associated flexibility services provision.



18

The DC optimization strategy is defined as a weighted sum of the previously defined optimization goals for

specific energy markets. The objective will be to maximize the overall DC operational revenue, by minimizing

the DC energy costs, maximizing the revenue due to thermal energy selling, maximizing the incentives

received for the delivery of flexibility services:

⟨𝑤𝑒 ∗ 𝑂𝑏𝑗𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦|𝑤𝑡 ∗ 𝑂𝑏𝑗𝑇ℎ𝑒𝑟𝑚𝑎𝑙|𝑤𝐹𝑆 ∗ 𝑂𝑏𝑗𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑆𝑒𝑟𝑣𝑖𝑐𝑒⟩𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐷𝐶𝑀𝑖𝑛𝐶𝑎𝑟𝑏𝑜𝑛𝐹𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡

𝑀𝐴𝑋𝑅𝑒𝑣𝑒𝑛𝑢𝑒 (20)

The optimization problem resulting from the electrical and thermal energy shifting to meet various criteria is

presented in Figure 7. The optimization problem is defining the thermal and electrical energy demand of

each DC’s sub-system modelled (and of the entire DC as a whole) at timestamp 𝑡 as a function of previous

demand states at timestamps 𝑡 − 𝑘 ∗ 𝐷𝑇𝐷𝐶. The optimization objective is to determine at each timestamp 𝑡

the optimal values of the control variables (𝐶𝐷𝐶) associated with each of the DC sub-systems together with

the amount of aggregated thermal or electrical energy flexibility to be shifted in time such that the DC

adapted energy profile matches the flexibility request. It is a constraint satisfaction problem in which the

unknowns can be reduced to the flexibility shifting actions associated to the control variables defined for

each DC sub-system, while considering the transfer functions and state functions of each DC sub-system

modelled and the equalities resulting from the links between sub-systems as well as the constrains and

variable bounds.

𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝐷𝐶 , 𝑣𝑎𝑙𝑢𝑒𝑠 𝑓𝑜𝑟 𝐶𝐷𝐶 = {𝐷𝐸𝑆𝐷 , 𝑅𝐸𝑆𝐷 , 𝐷𝑇𝐸𝑆 , 𝑅𝑇𝐸𝑆, 𝐶𝐷, 𝐶𝐻 , 𝐶𝑅}

𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 ⟨𝑤𝑒 ∗ 𝑂𝑏𝑗𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦|𝑤𝑡 ∗ 𝑂𝑏𝑗𝑇ℎ𝑒𝑟𝑚𝑎𝑙|𝑤𝐹𝑆 ∗ 𝑂𝑏𝑗𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑆𝑒𝑟𝑣𝑖𝑐𝑒⟩𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐷𝐶𝑀𝑖𝑛𝐶𝑎𝑟𝑏𝑜𝑛𝐹𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡

𝑀𝐴𝑋𝑅𝑒𝑣𝑒𝑛𝑢𝑒

𝐶𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝐷𝐶 𝑆𝑜𝑆 𝑚𝑜𝑑𝑒𝑙 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 𝐸1 − 𝐸11

𝑰𝑻 𝑺𝒆𝒓𝒗𝒆𝒓𝒔 𝒂𝒏𝒅 𝑺𝒆𝒓𝒗𝒆𝒓 𝑹𝒐𝒐𝒎 𝑺𝒚𝒔𝒕𝒆𝒎

𝐸1: 𝐸𝑆(𝑡) = 𝐸𝑅(𝑡) + (𝐸𝐷(𝑡) − 𝐸𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒(𝑡)) ∗ 𝐶𝐷 (𝑡) + 𝐸𝐷𝐸(𝑡) + 𝐸ℎ𝑜𝑠𝑡𝑒𝑑(𝑡)

𝐸2: 𝐸𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒(𝑡) = 𝐶𝑅(𝑡) ∗ 𝐸𝐷(𝑡)

𝐸3: 𝐸ℎ𝑜𝑠𝑡𝑒𝑑(𝑡) = 𝐶𝐻(𝑡) ∗ 𝐸𝐷(𝑡)

𝐸4: ℎ𝑒𝑎𝑡𝑇𝑜𝐵𝑒𝑅𝑒𝑚𝑜𝑣𝑒𝑑(𝑡) = 𝐸𝑆(𝑡)

𝐸5: 𝐸𝐷𝐸(𝑡 + 1) = 𝐸𝐷𝐸(𝑡) + 𝐸𝐷 ∗ 𝐶(𝑡)

𝑪𝒐𝒐𝒍𝒊𝒏𝒈 𝒂𝒏𝒅 𝑯𝒆𝒂𝒕 𝑹𝒆𝒖𝒔𝒆 𝑺𝒚𝒔𝒕𝒆𝒎

𝐸6: 𝐸𝐶(𝑡) =ℎ𝑒𝑎𝑡𝑇𝑜𝐵𝑒𝑅𝑒𝑚𝑜𝑣𝑒𝑑(𝑡)

𝐶𝑂𝑃𝐶+ 𝑅𝑇𝐸𝑆(𝑡) − 𝐷𝑇𝐸𝑆(𝑡)

𝐸7: 𝑇𝐸𝑆(𝑡 + 1) = 𝑇𝐸𝑆(𝑡) + 𝜌𝑅 ∗ 𝑅𝑇𝐸𝑆 − 𝜌𝐷 ∗ 𝐷𝑇𝐸𝑆

𝑷𝒐𝒘𝒆𝒓 𝑫𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒂𝒏𝒅 𝑼𝒏𝒊𝒏𝒕𝒆𝒓𝒓𝒖𝒑𝒕𝒂𝒃𝒍𝒆 𝑷𝒐𝒘𝒆𝒓 𝑺𝒖𝒑𝒑𝒍𝒚

𝐸8: 𝐸𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦(𝑡) = 𝐸𝑆𝑎𝑐𝑡𝑖𝑣𝑒(𝑡) + 𝐸𝐶

𝑎𝑐𝑡𝑖𝑣𝑒(𝑡) + 𝑅𝐸𝑆𝐷(𝑡) − 𝐷𝐸𝑆𝐷(𝑡)

𝐸9: 𝐸𝑆𝐷(𝑡 + 1) = 𝐸𝑆𝐷(𝑡) + 𝜌𝑅 ∗ 𝑅𝐸𝑆𝐷 − 𝜌𝐷 ∗ 𝐷𝐸𝑆𝐷

𝑻𝒓𝒂𝒏𝒔𝒇𝒆𝒓 𝑺𝒘𝒊𝒕𝒄𝒉 𝑺𝒚𝒔𝒕𝒆𝒎

𝐸10: 𝐸𝐷𝐶(𝑡) = 𝐸𝑓𝑎𝑐𝑖𝑙𝑖𝑡𝑦(𝑡) − 𝐸𝑅𝐸𝑁(𝑡)

𝑹𝒆𝒏𝒆𝒘𝒂𝒃𝒍𝒆 𝑬𝒏𝒆𝒓𝒈𝒚 𝑮𝒆𝒏𝒆𝒓𝒂𝒕𝒊𝒐𝒏

𝐸11: 𝐸𝑅𝐸𝑁(𝑡) = 𝑁𝑊𝐼𝑁𝐷 ∗1

2∗ 𝜌𝑎𝑖𝑟 ∗ 𝐴 ∗ 𝑊𝑖𝑛𝑑𝑆𝑝𝑒𝑒𝑑

3 (𝑡) ∗ 𝐶𝑃

𝑊ℎ𝑖𝑙𝑒 𝑚𝑒𝑒𝑡𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠 𝑓𝑜𝑟 𝐷𝐶 𝑠𝑢𝑏 𝑠𝑦𝑠𝑡𝑒𝑚𝑠 𝑠𝑎𝑓𝑒 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝐶1 − 𝐶14

𝐶1: ∑𝐶(𝑡) = 1

𝑇

𝑡=1



19

𝐶2: 𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝐼𝑇

𝐶3: 0 ≤ 𝑇𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝑇𝐸𝑆

𝐶4: 0 ≤ 𝑅𝑇𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝑅−𝑇𝐸𝑆

𝐶5: 0 ≤ 𝐷𝑇𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝐷−𝑇𝐸𝑆

𝐶6: 𝑅𝑇𝐸𝑆(𝑡) ∗ 𝐷𝑇𝐸𝑆(𝑡) = 0

𝐶7: 0 ≤ 𝐸𝐶 ≤ 𝑀𝐴𝑋𝐶𝑜𝑜𝑙𝑖𝑛𝑔

𝐶8: 𝐷𝑜𝐷 ∗ 𝑀𝐴𝑋𝐸𝑆𝐷 ≤ 𝐸𝑆𝐷(𝑡) ≤ 𝑀𝐴𝑋𝐸𝑆𝐷

𝐶9: 0 ≤ 𝑅𝐸𝑆𝐷(𝑡) ≤ 𝑀𝐴𝑋𝑅−𝐸𝑆𝐷

𝐶10: 0 ≤ 𝐷𝐸𝑆𝐷(𝑡) ≤ 𝑀𝐴𝑋𝐷−𝐸𝑆𝐷

𝐶11: 𝐷𝐸𝑆𝐷(𝑡) ∗ 𝑅𝐸𝑆𝐷(𝑡) = 0

𝐶12: 𝐸𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒 ∗ 𝐸ℎ𝑜𝑠𝑡𝑒𝑑 = 0

𝐶13: 0 ≤ 𝐸𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒 ≤ 𝑀𝐴𝑋𝑟𝑒𝑙𝑜𝑐𝑎𝑡𝑒

𝐶14: 0 ≤ 𝐸ℎ𝑜𝑠𝑡𝑒𝑑 ≤ 𝑀𝐴𝑋ℎ𝑜𝑠𝑡𝑒𝑑

Figure 7. DC operation optimization problem for flexibility shifting

The optimization problem as depicted in Figure 7 is classified as a Non-Linear optimization problem which

is NP-hard [3], because the unknowns are real, and the defined objective functions are nonlinear.

2.2 Genetic Algorithm based Heuristic

To solve the NP hard optimization problem described in the previous section we have defined a genetic

algorithm based heuristic that is computing an approximate solution while considering the predicted input

values determined by the Electrical and Thermal DR Prediction Modules presented in deliverable D4.2. We

have started by encoding the optimization problem solution in a chromosome as being composed of a set of

genes correlated with number of control variables and discrete time model implemented for day-ahead and

intra-day optimization (Table 4).

Table 4. Genes for case of DC optimization for flexibility shifting

Genes Composing Chromosome Day-Ahead Intra-Day

𝑪𝑫 24 values 4 values

𝑪𝑯 24 values 4 values

𝑪𝑹 24 values 4 values

𝑹𝑻𝑬𝑺 24 values 8 values

𝑫𝑻𝑬𝑺 24 values 8 values

𝑹𝑬𝑺𝑫 24 values 8 values

𝑫𝑬𝑺𝑫 24 values 8 values

Thus the genes contain the control variables for a given timestamp 𝑡: 𝐷𝐸𝑆𝐷(𝑡), 𝑅𝐸𝑆𝐷(𝑡), 𝐷𝑇𝐸𝑆(𝑡), 𝑅𝑇𝐸𝑆(𝑡),

𝐶𝐷(𝑡), 𝐶𝐻(𝑡), 𝐶𝑅(𝑡) while the chromosomes will contain arrays of such genes defining the control variables

over the entire optimization window 𝑇. The number of variable unknowns, in this case, becomes 6 ∗ 𝑇𝑆 + 𝑇𝑆2

where 𝑇𝑆 is the number of time steps according to the time model 𝐷𝑇𝐷𝐶 for the entire optimization window

𝑇.

To reduce this number, the notations from Table 5 are provided.



20

Table 5. Control variable reduction for optimization problem solving

Control Variable Constraint and Variable Reduction Explanation

𝐷𝐸𝑆𝐷 , 𝑅𝐸𝑆𝐷 𝐷𝐸𝑆𝐷 ∗ 𝑅𝐸𝑆𝐷 = 0, 𝐸𝑆𝐷𝑎𝑐𝑡𝑖𝑜𝑛 = {

𝐷𝐸𝑆𝐷 , 𝑖𝑓 𝑅𝐸𝑆𝐷 = 0 −𝑅𝐸𝑆𝐷 , 𝑖𝑓 𝐷𝐸𝑆𝐷 = 0

The number of unknowns is reduced

from 2 ∗ 𝑇𝑆 to 𝑇𝑆

𝑅𝑇𝐸𝑆, 𝐷𝑇𝐸𝑆 𝐷𝑇𝐸𝑆 ∗ 𝑅𝑇𝐸𝑆 = 0, 𝑇𝐸𝑆𝑎𝑐𝑡𝑖𝑜𝑛 = {

𝐷𝑇𝐸𝑆 , 𝑖𝑓 𝑅𝑇𝐸𝑆 = 0 𝑅𝑇𝐸𝑆, 𝑖𝑓 𝐷𝑇𝐸𝑆 = 0



𝐶𝐻, 𝐶𝑅 𝐶𝐻 ∗ 𝐶𝑅 = 0, 𝐶𝐿 = {

CH, 𝑖𝑓 CR = 0 −CR, 𝑖𝑓 𝐶H = 0



𝐶𝐷 A scheduling upper triangular matrix 𝑆 [𝑇 ∗ 𝑇] is

constructed line by line from the vectors 𝐶𝐷 using the

approach described in detail in [4].

The number of unknowns is reduced by

almost a factor of two, from 6 ∗ 𝑇𝑆 + 𝑇𝑆2

to 3 ∗ 𝑇𝑆 +𝑇𝑆2

2.

To ease the random generation, in case of the 𝐸𝑆𝐷𝑎𝑐𝑡𝑖𝑜𝑛 and 𝑇𝐸𝑆𝑎𝑐𝑡𝑖𝑜𝑛 that are strictly related to the state

variables 𝐸𝑆𝐷 and 𝑇𝐸𝑆 of the DC the latter are stored in the genes while the control variables will be

computed using the corresponding relations Figure 7.

Furthermore, in case of the 𝑇𝐸𝑆 the asociated restrictions defined by the flexibility optimization problem in

Figure 7 can be further refined as: the 𝑇𝐸𝑆 cannot be charged/discharged from the previous value with more

than MAXR−TES or MAXD−TES (maximum values for chardging / dischaging 𝑇𝐸𝑆):

𝑇𝐸𝑆[𝑡 + 1] ∈ [max{0, 𝑇𝐸𝑆[𝑡] − 𝑀𝐴𝑋𝐷−𝑇𝐸𝑆} ,min{𝑇𝐸𝑆[𝑡] +𝑀𝐴𝑋𝑅−𝑇𝐸𝑆,𝑀𝐴𝑋𝑇𝐸𝑆}] (21)

In case of 𝑇𝐸𝑆 discharge action, the discharge value cannot be higher than the actual cooling needs

(𝐸𝐶(𝑡) ≥ 0):

𝑇𝐸𝑆[𝑡 + 1] ∈ [ 𝑚𝑎𝑥 {0, 𝑇𝐸𝑆[𝑡] − 𝑚𝑖𝑛 {𝑀𝐴𝑋𝐷−𝑇𝐸𝑆,𝐸𝑐𝐶𝑂𝑃

}},

min{𝑇𝐸𝑆[𝑡] + 𝑀𝐴𝑋𝑅−𝑇𝐸𝑆,𝑀𝐴𝑋𝑇𝐸𝑆} ] (22)

Using a similar reasoning, the restrictions defined by the optimization problem from Figure 7, in case of the

𝐸𝑆𝐷 can be expressed as:

𝐸𝑆𝐷[𝑡 + 1] ∈ [ max{𝐷𝑜𝐷 ∗ 𝑀𝐴𝑋𝐸𝑆𝐷 , 𝐸𝑆𝐷[𝑡] − min{𝑀𝐴𝑋𝐷−𝐸𝑆𝐷 , 𝐸𝑆}},

min{𝐸𝑆𝐷[𝑡] + 𝑀𝐴𝑋𝑅−𝐸𝑆𝐷,𝑀𝐴𝑋𝐸𝑆𝐷}] (23)

Finally, the chromosomes and genes used by our heuristics specific for solving the DC energy flexibility

shifting problem is shown in Table 6.

Table 6. Chromosome and genes representation

Chromosome Description Gene Value Range Auxiliary

Variables

𝐸𝑆𝐷[𝑇] Array of length T containing the

battery charge level at each

timestamp during the interval T

𝐸𝑆𝐷(𝑡) [max{𝐷𝑜𝐷 ∗ 𝑀𝐴𝑋𝐸𝑆𝐷 , 𝐸𝑆𝐷[𝑡 − 1]− min{𝑀𝐴𝑋𝐷−𝐸𝑆𝐷 , 𝐸𝑆}},

min{𝐸𝑆𝐷[𝑡 − 1] + 𝑀𝐴𝑋𝑅−𝐸𝑆𝐷 , 𝑀𝐴𝑋𝐸𝑆𝐷}]

𝐸𝑆𝐷𝑎𝑐𝑡𝑖𝑜𝑛



21

Chromosome Description Gene Value Range Auxiliary

Variables

𝑇𝐸𝑆[𝑇] Array of length T containing the

TES charge level at each

timestamp during the interval

𝑇𝐸𝑆(𝑡) [max{0, 𝑇𝐸𝑆[𝑡 − 1] − 𝑀𝐴𝑋𝐷−𝑇𝐸𝑆},

min{𝑇𝐸𝑆[𝑡 − 1] + 𝑀𝐴𝑋𝑅−𝑇𝐸𝑆, 𝑀𝐴𝑋𝑇𝐸𝑆}]

𝑇𝐸𝑆𝑎𝑐𝑡𝑖𝑜𝑛

𝑆[𝑇 ∗ 𝑇] Scheduling matrix used to

schedule the delay-tolerant

workload

𝐶𝐷(𝑡) [0,1] CL

We have defined and used a fitness function to evaluate every chromosome within the population in relation

with the objective of determining the optimal control variables for DC flexibility shifting such that the revenue

is maximized (see relation 20).

However, even by constraining the domain of the variables and computing all the values using the already

described chromosome model, there can be some constraints that are not enforced. Consequently, a fitness

function constraint set is defined and used to validate the optimization problem solutions determined (see

Table 7).

Table 7. Genetic algorithm fitness function constraint Set

Fitness Function Constraint Motivation

FC 1: 𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝐼𝑇 By generating the scheduling matrix, the workload cannot exceed the

maximum allowed by the servers size.

FC 2: 0 ≤ 𝑅𝑇𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝑅−𝑇𝐸𝑆 By computing the TES level, the charge cannot exceed the maximum limit

FC 3: 0 ≤ 𝐷𝑇𝐸𝑆(𝑡) ≤ 𝑀𝐴𝑋𝐷−𝑇𝐸𝑆 By computing the TES level, the discharge cannot exceed the maximum limit

FC4: 0 ≤ 𝑅𝐸𝑆𝐷(𝑡) ≤ 𝑀𝐴𝑋𝑅−𝐸𝑆𝐷 Computing the ESD level, the charge cannot exceed the maximum limit

FC5: 0 ≤ 𝐷𝐸𝑆𝐷(𝑡) ≤ 𝑀𝐴𝑋𝐷−𝐸𝑆𝐷 Computing the ESD level, the charge cannot exceed the maximum limit

A constraint check function is defined to compute for every chromosome the number of genes that violate

the constraints from the FC constraint set:

𝑓𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡: 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 → 𝑅,

𝑓𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡(𝑐ℎ𝑟𝑜𝑚𝑜𝑠𝑜𝑚𝑒) = |{𝐹𝐶𝑖(𝑔𝑒𝑛𝑒𝑥𝑗) = 𝑓𝑎𝑙𝑠𝑒|𝐹𝐶𝑖 ∈ 𝐹𝐶 𝑎𝑛𝑑 𝑔𝑒𝑛𝑒𝑥

𝑗∈ 𝑐ℎ𝑟𝑜𝑚𝑜𝑠𝑜𝑚𝑒𝑥}| (24)

The operator |𝑋| represents the cardinality of the set 𝑋. Consequently, for each candidate chromosome,

besides evaluating the fitness function, the constraints mentioned above are checked for each gene. The

number of violated constraints is counted for every individual, the fitness function becoming:

𝑓𝑓𝑖𝑡𝑛𝑒𝑠𝑠: 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 → {𝑍, 𝑅},

𝑓𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑐ℎ𝑟𝑜𝑚𝑜𝑠𝑜𝑚𝑒) = {𝑓𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡(𝑐ℎ𝑟𝑜𝑚𝑜𝑠𝑜𝑚𝑒), 𝑓𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒(𝑐ℎ𝑟𝑜𝑚𝑜𝑠𝑜𝑚𝑒)} (25)

The genetic algorithm operators used are evaluation, selection, crossover and mutation. The crossover and

mutation operators are defined on each gene from the multi-gene. Thus, when two chromosomes are

combined, they exchange the corresponding genes from the chromosome, while the mutation randomly

changes a gene. Table 8 presents a general description of the operators used by the algorithm.



22

Table 8. Operators defined and used in the genetic heuritic

Operator Description

Evaluation Each individual within the population is evaluated by applying the fitness function defined above. The

best individual will be the one with the least violated constraints and the smallest value of the objective

function.

Selection The best half of the population was kept for further breeding, while the weakest half was newly

generated. The individuals were selected for combination two by two starting from the strongest one.

Crossover Two individuals are combined to get a new pair of individuals. A random split position is chosen, and

the two halves of the chromosomes after the split position are swapped, resulting a new pair of

chromosomes defining the new individuals.

Mutation Mutation is used to avoid blocking the algorithm in local minima. A random gene that violates the

constraints is changed to a random value.

The pseudocode for the genetic heuristic defined is presented in Figure 8. The algorithm starts by generating

a number of random possible valid action plans and associated control variables (line 1). The inputs of the

algorithm are the number of individuals P, the number of iterations, the predicted weather (wind speed) over

time window T and the predicted IT servers’ energy consumption over the time window T, split on the real-

time and delay-tolerant components. Then, it performs a number of iterations (lines 3-15), to evolve the

population. During each iteration, it evaluates each individual by performing a DC SoS model simulation with

the action plan extracted from the control variables encoded in the chromosome (line 5). Then, it computes

the fitness and saves the best individual. After this step, it applies the genetic operators on the population

(lines 11-14).

Inputs: Number of individuals 𝑃, Number of iterations 𝑛𝑜𝐼𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠

Predicted energy consumption of real-time workload: 𝐸𝑅 and delay-tolerant workload: 𝐸𝐷

Market reference prices: 𝑃𝑟𝑖𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 , 𝑃𝑟𝑖𝑐𝑒𝐻𝑒𝑎𝑡 , 𝑆𝑒𝑟𝑣𝑖𝑐𝑒𝑖𝑛𝑐𝑒𝑛𝑡𝑖𝑡𝑖𝑣𝑒𝑠 and flexibility order

𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑅𝑒𝑞𝑢𝑒𝑠𝑡

𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙

Outputs: individuals matching best the flexibility optimization problem goal containing the flexibility

shifting plan solution given by the control variables values

𝐷𝐸𝑆𝐷 , 𝑅𝐸𝑆𝐷 , 𝐷𝑇𝐸𝑆, 𝑅𝑇𝐸𝑆, 𝐶𝐻 , 𝐶𝑅, 𝐶𝐷

Begin

1. Generate initial population considering 𝐸𝑅 , 𝐸𝐷 , 𝑃

2. iteration = 0

3. while( iteration < noIterations) do

4. foreach 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 in population do

5. 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝐻𝑒𝑎𝑡𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

= simulate 𝐷𝐶𝑆𝑜𝑆−𝑀𝑜𝑑𝑒𝑙 with controls variables from

𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙

6. ComputeFitness (𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙, 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝐻𝑒𝑎𝑡𝐷𝐶𝑜𝑢𝑡𝑝𝑢𝑡

, 𝑃𝑟𝑖𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 , 𝑃𝑟𝑖𝑐𝑒𝐻𝑒𝑎𝑡 ,

7.

𝑆𝑒𝑟𝑣𝑖𝑐𝑒𝑖𝑛𝑐𝑒𝑛𝑡𝑖𝑡𝑖𝑣𝑒𝑠 , 𝐹𝑙𝑒𝑥𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝑅𝑒𝑞𝑢𝑒𝑠𝑡)

8. if(fitness (𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙) < fitness (𝑏𝑒𝑠𝑡𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙)

9. 𝑏𝑒𝑠𝑡𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 = 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙



23

10. end if

11. end foreach

12. population.selection();

13. population.crossover();

14. population.mutation();

15. iteration++

16. end while

17. return bestIndividual

End

Figure 8. Genetic heuristic for solving DC multi-criteria optimization problem



24

3 CATALYST DC Optimization Engine

3.1 Architecture and Implementation

Figure 9 shows the overall component-based architecture of the CATALYST DC optimization engine.

The Intra DC Energy Optimizer Component deals with DC management of energy flexibility by implementing

the DC operation optimization detailed in Section 2. It takes as input thermal and electrical energy

predictions determined by the Electricity and Heat DR Prediction Components (i.e. delivered in D4.2) as well

as the DC SoS model (delivered in D4.1) describing the operation of main DC sub-systems. Its main output

is the optimal flexibility shifting action plan (𝑃𝐷𝐶𝑎𝑑𝑎𝑝𝑡

) such the DC energy profile is adapted to provide various

services in the Electrical Energy Marketplace, Heat Marketplace and Energy Flexibility Marketplace. The

Energy Efficiency Metrics Calculator is responsible for computing indicators that are associated with the

optimization action plan that will reflect the efficiency of its implementation such as the potential carbon

savings, cost savings, amount of energy shifted, etc.

Figure 9. CATALYST Optimization Engine Architecture

The CATALYST Data Storage Component contains the DC energy monitored data, the DC sub-systems

configurations, the predicted energy data (determined by the Electricity and Heat DR Prediction Components)

and the optimization actions plans. It is designed according to the CATALYST Data Model as presented in

deliverable D2.3 [5] while the components interaction is facilitated by the DB API which implements the

REST API for getting and storing data also defined in D2.3.

The DC Operator Console displays the relevant information for facilitating the DC operator decision making

such as the electrical and thermal energy production/consumption/flexibility predictions on custom charts



25

for whole DC or major sub-systems on all time granularities and DC optimization actions plans to facilitate

their validation and simulation.

Figure 10 shows the main interactions between the developed components to implement the CATALYST DC

optimization process for flexibility management.

Figure 10. DC optimization process sequence diagram

The main steps of the optimization process showing the Intra DC Energy Optimizer component integration

are detailed in Table 9.

Table 9. CATALYST optimization process steps

Step No. Description

1. Electrical and thermal energy data are fed into the CATALYST data storage and are made available for

other components using the DB API

2a Electricity DR Prediction considers the latest data in the Data Storage and uses the trained energy

prediction models to forecast the day-ahead, intraday and near-real time energy consumption and

flexibility

3a The electrical energy prediction results are stored in CATALYST Data Storage

2b Heat DR Prediction considers the latest data in the Data Storage and uses the CFD simulations and

trained heat prediction models to forecast the day-ahead, intraday and near-real time heat generation

and associated heat flexibility



26

3b The thermal energy prediction results are stored in CATALYST Data Storage

4 The electrical and thermal DC energy predictions are displayed on the DC Operator Console.

5a The Intra DC Energy Optimizer considers the forecasted data, the technical capabilities of the DC energy

systems and the goal energy demand curve associated with the congestion management system and

instantiates the system of system flexibility model. On top of the instantiated models optimization, the

Intra DC Energy Optimizer runs the heuristics to solve the constraint satisfaction problem associated with

the service implementation

5b The calculated optimization actions plans are stored in the CATALYST Data Storage

6a The Energy Efficiency Metrics Calculator takes the optimization plan and estimates the values of

predefined metrics

6b The values of the metrics are stored in the CATALYST Data Storage

7a The optimization action plans and associated metrics are displayed on the DC Operator Console for

validation

7b Validation decision is stored in the CATALYST Data Storage. If the plan is validated its actions will be

executed.

The Intra DC Energy Optimizer component considers two time windows to compute the plans containing

flexibility management actions (Figure 11):

• The day-ahead optimization determines action plans at a 1-hour granularity for the next a 24-hour

period and computes the control variable values such that the optimization objectives defined

according to the optimization strategy weights are meet.

• The intra-day optimization refines, adjusts and improves periodically the optimization actions plan

determined for the day-ahead planner considering only the next 4 hours and the granularity of

½ ℎ𝑜𝑢𝑟 (𝐼𝑖𝑛𝑡𝑟𝑎−𝑑𝑎𝑦(𝑡) = [4 ∗ 𝑡, 4 ∗ (𝑡 + 1)]).

The Intra DC Energy Optimizer component uses the following steps:

1. The prediction components determine the DC energy forecast for the next day with a granularity of

one hour and time window length of 24 and the Intra Energy DC Optimizer component use them for

instantiating the DC SoS model.

2. The day-ahead optimization process implemented by the Intra Energy DC Optimizer component

determines the best flexibility management action plan (𝑃𝐷𝐶𝑑𝑎𝑦−𝑎ℎ𝑒𝑎𝑑

) for the day-ahead time window

to meet the optimization objectives set.

3. The 𝑃𝐷𝐶𝑑𝑎𝑦−𝑎ℎ𝑒𝑎𝑑

flexibility management action plan (and corresponding control variables) is saved in

the CATALYST Data Storage.

4. During the next day, the intra-day optimization process implemented by the Intra Energy DC Optimizer

component is called every 4 hours. The prediction components will determine a finer set of

predictions and more accurate for the next 4-hour time window and the Intra Energy DC Optimizer

component will use them creating a new instance of DC SoS Model.

5. Furthermore, because the aim of the intra-day optimizer is to improve the day-ahead flexibility

management plan, the set of actions from the day-ahead plan 𝑃𝐷𝐶𝑑𝑎𝑦−𝑎ℎ𝑒𝑎𝑑

scheduled for this intra-

day interval are extracted and simulated over the DC SoS model to update the model’s internal sub-

system states.



27

6. Using the predicted inputs and the states corresponding to the day-ahead action plan, the intra-day

optimization process implemented by the Intra Energy DC Optimizer component computes a new

plan that corrects the day-ahead plan considering the new and refined predictions.

7. The new updated flexibility management action plan is computed as the union of the old day-ahead

plan and the new intra-day plan 𝑃𝐷𝐶𝑑𝑎𝑦−𝑎ℎ𝑒𝑎𝑑

= 𝑃𝐷𝐶𝑑𝑎𝑦−𝑎ℎ𝑒𝑎𝑑

∪ 𝑃𝐷𝐶𝑖𝑛𝑡𝑟𝑎−𝑑𝑎𝑦

. The union operation

overwrites existing actions from the day-ahead plan with the new actions from the intraday plan,

while meeting the constraint that the state of the DC SoS model at the end of the simulation of the

newly added optimization plan is the same as the state of the DC SoS model at the end of the

simulation of the initial day-ahead plan, thus allowing undisturbed execution for further moments in

time.

8. Steps 4-7 are repeated 6 times (every 4 hours for 24 hours).

Figure 11. Day-ahead and intra-day optimization

3.2 Installation Guidelines and User Manual

The software prerequisites for the developed components are:

• 64 bit Linux / Windows OS;

• JRE (Java Runtime Environment) version 8 or above [6];

• Internet connection for package management;

• NVidia CUDA, Keras [7], TensorFlow / Python3;

• Apache Cassandra [8] and MySQL databases [9].

Hardware prerequisites for the developed components:



28

• Intel/AMD processor with at least 4 cores and 2.5GHz base frequency and 8 GB RAM;

• HDD/SSD with at least 100GB free space;

• Internet connection for package management;

• NVIDIA GeForce GTX 1050 (equivalent or above);

The deployment diagram of the developed components is presented in Figure 12. The Electricity DR

Prediction and Heat DR Prediction components use deep learning algorithms that require GPU to train them,

so NVIDIA CUDA should be installed on the platform. Furthermore, Python, TensorFlow and Keras need to be

installed directly on the OS of the hardware, to allow the use of the GPU when performing computations. All

the other modules of the CATALYST DC Optimization Engine, including the Intra DC Energy Optimizer, are

deployed in Docker containers, as follows:

• CATALYST Data Storage Component

o Cassandra DB: container that runs the Cassandra Server and the NoSQL database

containing the energy monitored data.

o MySQL DB: container that contains the MySQL server and the MySQL DB with the CATALYST

Data Model, generated optimization plans and DC energy predictions.

• CATALYST DB API

o Tomcat Server: container running a Tomcat Server in which the REST API (developed to

access the data stored in the CATALYST Data Storage) is deployed. Because the data is

accessible from other modules as well, the Tomcat container exposes the port 8080 for

external access.

• CATALYST Electricity DR Prediction and Heat DR Prediction components

o Tomcat Server: container running the applications corresponding to the two components.

• CATALYST Intra DC Energy Optimizer

o Tomcat Server: container running the DC optimization engine that uses services exposed by

the Electricity DR Prediction, Heat DR Prediction, and DB API.

• DC Operator Console

o Node JS Server: container running Node JS where the React JS components frontend is

deployed.



29

Figure 12. Deployment diagram of software components

Once deployed, the prototype can be run by accessing from the web browser the entry point to the

components front-end web interface: http://HOST_IP:/9094/catalyst-dc-operator-console.

One prototype instance is already configured and up and running and may be accessed through Internet at

the following public address: http:// 193.226.5.80:9094/catalyst-dc-operator-console.

To use the CATALYST optimization engine in the CATALYST DC Operator Console web page the DC operator

has to select the DC Flexibility Management and Optimization Tab. The operator can view the optimization

plan generated in relation with a specific request the effect on the energy profile of the DC as a whole, shown

in the left chart, or at sub-system level, illustrated in the right chart (see Figure 13). Furthermore, a list of

optimization actions with their details is shown in the lower part of the page. By pressing the validate button,

the plan is validated and made available for implementation.

Afterwards the user is redirected to the optimization action plan execution page, shown in Figure 14, which

allows to track in a step by step fashion the action plan implementation in a simulated manner using a step

granularity of 5 minutes. The DC operator can interact with the page using the simulation controls, starting

or pausing the simulation. The charts from the upper half of the page show the effect of the optimization

actions on the DC energy profile adaptation, while the lower charts of the page show the DC energy profile

without optimization. At the same time the energy impact of each flexibility shifting action is displayed as

well as the effect on the DC energy profile in relation to the baseline.

http://host_ip/9094/catalyst-dc-operator-console

http://193.226.5.80:9094/catalyst-dc-operator-console



30

Figure 13. DC flexibility management and optimization page

Figure 14. DC flexibility management optimization plan execution



31

4 Evaluation Results

We have conducted a set of in lab experiments to estimate the potential of our DC optimization engine to

manage the energy flexibility allowing DC to successfully provide specific services to different stakeholders

in the electrical and thermal energy grids (see Section 4.1). We have considered the hardware systems

characteristics of PSNC High Performance Computing DC (see Table 10) which are encoded in the DC SoS

Model implementation. At the same time, we have evaluated the performance of our genetic algorithm-based

heuristics in solving flexibility management and optimization problems in terms of time overhead and

solution scalability (see Section 4.2). For this evaluation, we have used characteristics of a medium scale

DC (see Table 10) which are encoded in the DC SoS Model implementation.

Table 10. Characteristics of the test bed DC considered

Sub- System Cloud DC HPC DC

Cooling and Heat Reuse System

Coefficient of Performance for cooling

𝐶𝑂𝑃𝐶 = 3.8

Coefficient of Performance for heating

𝐶𝑂𝑃𝐻 = 2.3

Maximum Cooling Capacity 𝑀𝐴𝑋𝐶𝑜𝑜𝑙𝑖𝑛𝑔 =

4000 𝑘𝑊

Maximum TES Capacity 𝑀𝐴𝑋𝑇𝐸𝑆 = 3000 𝑘𝑊

Coefficient of Performance for cooling 𝐶𝑂𝑃𝐶 = 3.3

Coefficient of Performance for heating 𝐶𝑂𝑃𝐻 = 2.3

Maximum Cooling Capacity 𝑀𝐴𝑋𝐶𝑜𝑜𝑙𝑖𝑛𝑔 = 400 𝑘𝑊

IT Servers and Server Room

9000 Servers HP 360 DL

Maximum Power Consumption 𝑀𝐴𝑋𝐼𝑇 =3000 𝑘𝑊

Delay Tolerant Workload Percentage =

20%

Heterogeneous servers

Maximum Power Consumption 𝑀𝐴𝑋𝐼𝑇 = 1000 𝑘𝑊

Delay Tolerant Workload Percentage = 20%

Uninterruptible Power Supply Unit

Maximum Charge Rate 𝑀𝐴𝑋𝑅−𝐸𝑆𝐷 =2000 𝑘𝑊

Maximum Discharge Rate 𝑀𝐴𝑋𝐷−𝐸𝑆𝐷 = 2000 𝑘𝑊,

Maximum Storage Capacity 𝑀𝐴𝑋𝑆−𝐸𝑆𝐷 =3000 𝑘𝑊

Maximum Charge Rate 𝑀𝐴𝑋𝑅−𝐸𝑆𝐷 = 450 𝑘𝑊

Maximum Discharge Rate 𝑀𝐴𝑋𝐷−𝐸𝑆𝐷 = 1500 𝑘𝑊

Maximum Storage Capacity 𝑀𝐴𝑋𝑆−𝐸𝑆𝐷 = 300 𝑘𝑊

4.1 Electrical and Thermal Flexibility Management

In this section, we evaluate the CATALYST DC optimization engine capabilities for managing and shift

flexibility to deliver electrical energy trading, flexibility services, heat selling services or combinations of

above. Table 11 shows the values of the weights used to configure the different DC optimization strategies

(i.e. according to relation 20) we have evaluated. The workload relocation and/or hosting to/from other DCs

has been considered as a potential source of extra energy flexibility which can be activated / deactivate on

demand (see 𝑅𝑒𝑙𝑜𝑐𝑊 variable in Table 11).



32

Table 11. Optimization strategies evaluated and optimization objective weights used

Scenario 𝑾𝒆 𝑾𝑭𝑺 𝑾𝒕 𝑹𝒆𝒍𝒐𝒄𝑾 Description

1 1 0 0 Disabled The Intra DC Energy Optimizer computes an action plan to minimize the

DC operational cost by shifting flexible energy to decrease energy profile

when energy price is high and to increase energy profile when energy price

is low.

2 0 1 0 Disabled The Intra DC Energy Optimizer computes an action plan to allow the DC to

follow a flexibility order curve and maximize gain of the service associated

incentives.

3 0 0 1 Disabled The Intra DC Energy Optimizer computes an action plan to maximize the

DC heat generation when the heat price is high by shifting flexible thermal

energy.

4 0.5 0 0.5 Enabled The Intra DC Energy Optimizer computes an action plan to allow the DC to

sell heat in the heat market when the prices are high and at the same

time buy electrical energy when the prices are low.

5 0 0.5 0 Enabled The Intra DC Energy Optimizer computes an action plan to allow the DC to

provide flexibility services by decreasing its demand using workload

relocation to other DC.

6 0 0.5 0.5 Enabled The Intra DC Energy Optimizer computes an action plan allowing DC to

provide flexibility services by increasing its demand hosting workload from

other DCs and at the same time sells waste heat taking advantage on high

heat prices on the market.

The initial situation for a regular day of operation for the PSNC HPC DC is shown in Figure 15. The left part

of the image shows the forecasted electrical energy demand split into main components, while the right side

of the image shows the forecasted thermal energy generation.

Figure 15. PSNC day ahead forecasted: electrical energy demand (left); thermal energy generation (right)

In scenario number 1 the flexibility optimization action plan allows the DC to modify its forecasted energy

demand to lower the operational costs by consuming less energy when the price on the electricity

marketplace is high by leveraging on the flexibility mechanisms for shifting energy to time intervals when the

energy price is low. Figure 16 shows the electrical energy profile of the DC after executing the optimization

action plan computed by shifting delay tolerant workload from time periods when the energy price was high

(hours 10-16) to time intervals when energy price is low (hours 17-21). By enforcing the optimization plan,

the DC operational cost with energy considering the energy price variation (i.e. the purple line in Figure 16)

for 24 hours, is reduced with approximately 1.24%.



33

Figure 16. DC optimized energy profile using electricity price as a signal

In scenario number 2 the flexibility optimization action plan allows the DC to modify its forecasted energy

demand to follow accurately a flexibility order signal curve. As Figure 17-left shows, the flexibility order signal

to which the DC should respond by increasing the energy demand in the interval between hours 16-21.

Executing the flexibility optimization plan the DC will deliver the expected flexibility by postponing some of

the delay tolerant workload in the response interval, as depicted in Figure 17-right. Prior to the flexibility

service interval, the DC is lowering its energy demand below the baseline (see intervals between hours 2 to

4) due to the shift of flexible energy.

Figure 17. Flexibility order and DC initial energy profile(left); DC adapted energy profile as result of optimal

management and shifting of flexibility using flexibility order as a signal

In scenario number 3 the flexibility optimization action plan allows the DC to adapt its thermal energy

generation dynamically to increase the amount and quality of heat delivered when the prices are high. As

Figure 15 and Figure 18-left show, the DC thermal energy generation is nearly constant, of roughly 300 kWh

during the 24 hours of the day (green line). The yellow line shows the energy price as having a peak in the

interval 8-15 hours due to increased demand in the nearby neighbourhood. Thus, the DC uses its flexibility

mechanisms to exploit the internal latent thermal flexibility by shifting delay tolerant workload to increase

the heat generation during the heat demand time interval and at the same time increases the temperature

setpoint. Thus, the DC heat generation is increased to match the heat demand by shifting delay tolerant

workload in the interval between hour 8 and hour 15, as shown in Figure 18-right.



34

Figure 18 DC adapted energy profile as result of optimal thermal energy flexibility shifting (left); Workload shifting to

provide thermal flexibility (right)

In scenario number 4 the flexibility optimization action plan allows the DC to leverage on workload relocation

and/or hosting to / from other DCs to further increase its thermal and electrical energy flexibility and as

result to increase the revenue streams from selling thermal energy while taking advantage of the low

electricity prices in the energy marketplace. The DC uses workload temporary shifting as flexibility

mechanism to decrease the energy demand during the time interval 1-7 when the energy price is high and

shifting the workload to the interval 8-17, when the energy price is low (see Figure 19-left). At the same time

due to a high heat demand in the same interval the DC is able to sale its excess heat generation and gain

additional profit (see Figure 19-right).

Figure 19. Workload hosting and relocation flexibility: DC energy demand profile and energy price (left); DC thermal

energy generation profile (right)

During the time internal 18-24, the workload is relocated to a partner DCs because locally energy price is

high, there is no need for extra heat demand (see Figure 20). Compared to the forecasted baseline energy

profile situation, depicted in Figure 15, the DC reduces its operational cost while delivering both trade

electrical energy and heat services.



35

Figure 20. DC Workload Relocation

In scenario number 5 the flexibility optimization action plan allows the DC to deliver energy flexibility services

by leveraging and the workload relocation to further increase its energy profile on demand. First, the

execution of a percentage of the delay tolerant workload is scheduled in the time interval between hours

16 and 21, to match the flexibility order signal (as shown in Figure 21-left). Because the DC energy demand

cannot be increased enough to satisfy the flexibility order additional workload is hosted and executed form

other DC as shown in Figure 21-right. Thus, as opposed to using only workload shifting to achieve energy

flexibility as in scenario 2 depicted in Figure 17, the DC enhances its flexibility leveraging on workload hosting

by managing to provide 300 kWh more as flexible energy to meet the flexibility demand.

Figure 21. DC operation management to deliver flexibility order (left) Additional workload hosting from other DC (right)

In scenario number 6 shows how the DC operation is optimized to provide energy flexibility services and at

the same time to sell heat in the heat market. The DC uses its internal flexibility mechanisms, such as delay

tolerant workload shifting, as well as workload hosting from other DC to increase its energy demand to match

the flexibility request signal (see Figure 22-left). Also, because the internal workload is not enough, the

optimizer computes an action plan involving workload hosting from partner DCs to increase the energy

demand by 100 kWh. Figure 22-right shows how the DC increases its thermal energy generation during the

interval between hours 16 and 21. About 500 kWh workload is hosted over that period to generate an excess

heat of around 150 kWh needed to satisfy the high thermal energy demand.



36

Figure 22. DC operation management to deliver both flexibility order and heat on demand: optimized electrical energy

profile (left) and thermal energy profile (right)

Finally having as reference starting point scenario number 2 (see Figure 17) we have evaluated the intra-

day optimization process capability of adjusting and improving the day-ahead optimization plans. We have

considered the situation for the first four hours (i.e. 0-4) presented in Figure 23-left in which there is a higher

DC energy demand during hour 2, miss predicted by the Electricity DR Prediction Component for the day-

ahead (the blue line from Figure 23-left). The intra-day optimization loop use as reference the intra-day

energy demand predictions which are more accurate and computes an optimization plan containing flexibility

actions of battery charge and discharge, as depicted in Figure 23-right, to compensate the high energy

demand of the workload and match the flexibility order signal (the red line from Figure 23-left). Thus, during

the peak energy demand of hour 2, batteries are discharged with about 100 kWh to compensate for the

extra load. During the next 2 hours of the intra-day period, the optimization plan computes battery charge

actions, to recharge the batteries and reach the initial steady-state condition.

Figure 23. DC intra-day flexibility optimization uses ESDs to handle unforeseen workload peak and increase demand:

flexibility request signal and DC energy demand (left); ESD flexibility actions (right)

The second intra-day period (hours 4-8) is presented in Figure 24, where the green line from the left chart

shows that the actual DC demand is lower than the expected one (as provided by the flexibility request signal)

during response hours 6-7. Thus, the intra-day optimization loop for hours 4-8 computes a flexibility

optimization plan using the ESD flexibility which is featuring a lower inertia (compared to other mechanisms)

to charge the batteries during the time intervals when the DC demand is lower than expected (see Figure

24-right). However, to have a battery steady state, they have to be partially discharged before the scheduled

charging (due to the fact that batteries are kept always charged at maximum), so three discharge battery

actions are used before the three charge battery actions.



37

Figure 24 DC intra-day flexibility optimization uses ESDs to lower the DC energy demand: flexibility request signal and

DC energy demand (left); ESD flexibility actions (right)

Finally, we aim to evaluate the intra-day optimization potential of masking day-ahead prediction errors and

improving the flexibility optimization plans. We consider again scenario number 2, where the DC has to

respond to a flexibility request signal and follow a given energy demand profile. As Figure 25 shows, we

consider day-ahead prediction errors from -15% up to +15%, meaning that the actual DC energy demand

during the intra-day period varies from 15% lower than predicted, up to 15% higher than predicted during

day-ahead.

Figure 25. Flexibility request matching in intra-day optimization: RMSE considering prediction error (left), MAPE

considering prediction error (right)

We compute the RMSE (Root-mean-square deviation) and MAPE (Mean absolute percentage error) errors

[10] of the intraday plan considering the given flexibility request curve. As shown in Figure 25, the errors are

compensated by the means of batteries (as shown in Figure 23 and Figure 24) until errors of about 5%

between day-ahead and intra-day predictions are achieved. From that point on, the intra-day plans relying

solely on batteries cannot compensate the prediction errors, thus the matching error between the DC energy

demand and the flexibility request increases linearly with the intra-day prediction error (Figure 25-right).

4.2 Genetic Heuristic Performance

This section evaluates the performance and accuracy of our genetic algorithm heuristic in reference with a

state of the art solver Lingo [11]. The DC multi-criteria optimization problem was implemented and solved

using both of them and a set of predefined flexibility management scenarios was run using a machine with



38

Intel® Core™ i3-540 Processor and 8GB DDR3 memory. The goal is to compute the optimal set of flexibility

optimization actions such that the operational profit of the testbed cloud DC described in Table 10 is

maximized considering a 24 hours’ time frame. To evaluate the solutions improvement percentage in

relation with the DC operation for a day for each flexibility management scenario run the following relation

has been used:

𝑝𝑟𝑜𝑓𝑖𝑡(𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛) = (1 −∑ 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙𝑝𝑟𝑜𝑓𝑖𝑡(𝑡)24𝑡=1

𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒𝑝𝑟𝑜𝑓𝑖𝑡) ∗ 100 (25)

Table 12 presents the results of the genetic algorithm on a set of flexibility management and optimization

scenarios run with different parameters of the algorithm. By increasing the number of iterations of the

algorithm, the fitness function is continuously improved leading to a better solution (evaluated using relation

25) while the population size which influences both the solution quality as well as the run time of the

algorithm. A trade-off between solution quality and run time was identified for population size 30.000 and

number of iterations 70, values that have been used for various flexibility optimization scenarios.

Table 12. Genetic algorithm heuristics performance for solving flexibility management optimization problems

Population Size Iterations Execution Time Improvement

10.000 40 8.5 s 3.23%

10.000 70 12.9 s 4.67%

10.000 100 17.3 s 4.73%

30.000 40 36 s 4.59%

30.000 70 55 s 6.38%

30.000 100 1 min 9 s 6.54%

70.000 40 1 min 39 s 4.71%

70.000 70 2 min 39 s 6.52%

70.000 100 3 min 33 s 6.68%

100.000 40 2 min 53 s 5.2%

100.000 70 4 min 47 s 7.76%

100.000 100 7 min 01 s 8.23%

Next, we have compared the genetic algorithm heuristics and Lingo evolution in the same set of flexibility

management optimization scenarios (similar with the ones analysed in depth in the previous section) setting

an optimization problem solving time limit of 5 minutes. For the genetic algorithm heuristic configuration we

was used 30.000 individuals and 70 iterations, having a solving time of 55 seconds (see Table 12).

Table 13. Genetic algorithm heuristic and Lingo comparison for solving flexibility management optimization problems

Scenario Lingo Improvement Lingo Run Time GA Improvement

1 3.64% 9s 3.88%

2 3.69% 5s 3.66%

3 3.17% 9s 2.98%

4 2.97% 3s 2.85%

5 2.4% 9s 2.4%

6 5.66% 2s 5.2%

7 6.08% 25s 5.73%

8 5.45% 31s 4.97%

9 - > 5 min 10.6%

10 - > 5 min 10.4%

The results from Table 13 show that our heuristics has better results than the Lingo solver in 3 of the

flexibility optimization scenarios used. Anyway, on average the cost improvement brought by Lingo is 3.3%,



39

while our solution solver manages a 5% saving, thus being more suited for the strict time limit optimization

use case. At the same time in 2 of the proposed scenarios the Lingo solver exceed the imposed time limit

due to the complexity of the input data making it unfeasible for complex systems and situations.

The result of evaluating the system scaling with respect to the number of sub-systems and optimization

interval length is shown in Figure 26. Figure 26- left a depicts on the horizontal axis the number of sub-

systems and the optimization interval length, while on the vertical axis shows the number of iterations

performed by the genetic algorithm to find an approximate solution using a population of 100.000

individuals. Due to the quadratic relation between the optimization window size and the number of

unknowns, the largest increase in the number of iterations is given by the optimization window interval.

Figure 26. Flexibility management optimization scalability evaluation: the relation between DC SoS Model size and

window length (left); comparison between Lingo and genetic algorithm heuristic for optimization window T = 24 (right)

The gradient of the iterations for the two solutions compared is shown in Figure 26-right, in case of an

optimization time window 𝑇 = 24. It can be noticed that for a smaller number of sub-systems, displayed on

the horizontal axis, the Lingo solver has a leaner slope than our proposed genetic algorithm heuristic.

However, when the number of systems increases, the Lingo solver shows an abrupt slope while the genetic

algorithm shows a near-linear behaviour scaling better with the increasing number of DC sub-systems and

associated control variables considered.



40

5 Conclusion

In this deliverable, we have reported the work done and main achievements of Task 4.4: DC Flexibility

Management and Optimization. A DC energy flexibility management solution is defined to allow the

optimization of DC energy profiles using flexibility shifting to deliver specific services in the electrical and/or

heat grids. The energy flexibility management is formalized as a multi-criteria optimization problem defined

on top of the DC system of system model which is an NP-hard problem. To solve it, a genetic algorithm-based

heuristic was defined featuring flexibility constraints variables, variables reduction methods and fitness

function aiming to identify control variables values that are minimizing the distance to the goal.

A DC optimization engine and flexibility management tool was designed and implemented to determine

flexibility shifting action plans to meet different optimization objectives considering the monitored energy

data and the predicted DC energy budget. Evaluation results are promising and are showing the potential of

our solution in managing the DC energy flexibility. They prove that our solution allows DC to successfully

provide specific services to the electrical and thermal energy grids and with a good scalability and low time

overhead.

For further work, the optimization engine and flexibility management tools defined in WP4 will be integrated

into the overall CATALYST software ecosystem and will be evaluated in the pilot DCs. Software

implementation refinement and corrective actions will be implemented, if needed, based on the evaluation

outcomes.



41

6 References

[1] C. Consotium, “D4.1 - Smart Energy Flexibility Modelling”.

[2] C. Consortium, “D4.2 - DC Energy DR Prediction”.

[3] C. K. S. L. J. L. J. L. a. A. M. P. Belotti, “Mixed-Integer Nonlinear Optimization,” Acta Numerica , vol. 22,

no. https://doi.org/10.1017/S0962492913000032, pp. 1-131, 2013.

[4] I. A. I. S. M. A. C. P. M. B. D. A. F. P. Tudor Cioara, “Exploiting data centres energy flexibility in smart

cities: Business scenarios,” Information Sciences, no. https://doi.org/10.1016/j.ins.2018.07.010,

2019.

[5] C. Consortium, “D2.3 - Final CATALYST Framework Architecture”.

[6] “Java Runtime Environment,” [Online]. Available:

https://www.oracle.com/technetwork/java/javase/downloads/jre9-downloads-3848532.html.

[7] “Keras vs TensorFlow vs scikit-learn: What are the differences?,” [Online]. Available:

https://stackshare.io/stackups/keras-vs-scikit-learn-vs-tensorflow.

[8] A. Foundation, “Manage massive amounts of data, fast, without losing sleep,” [Online]. Available:

http://cassandra.apache.org/.

[9] M. database. [Online]. Available: https://www.mysql.com/.

[10] A. Botchkarev, “Performance Metrics (Error Measures) in Machine Learning Regression, Forecasting

and Prognostics: Properties and Typology,” [Online]. Available:

https://arxiv.org/ftp/arxiv/papers/1809/1809.03006.pdf.

[11] Lingo, “LINGO 18.0 - Optimization Modeling Software for Linear, Nonlinear, and Integer Programming,”

[Online]. Available: https://www.lindo.com/index.php/products/lingo-and-optimization-modeling.

Date post:	27-Jun-2020
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

DC Energy Flexibility Management Tool · AUTHOR(S) Marcel Antal, Tudor Cioara, Ionut Anghel,...

Documents